Truth, Icons, and Reality in Peirce 311079358X, 9783110793581, 9783110793628, 9783110793673, 2022939308

Table of contents :
Preface
Contents
Introduction
I Propositions
Chapter 1 Signs Conveying Information On the Range of Peirce’s Notion of Propositions: Dicisigns
Chapter 2 Dicisigns and Habits Implicit Propositions and Habit-Taking in Peirce’s Pragmatism
Chapter 3 Peirce’s Theories of Assertion
Chapter 4 The Identity of Sweet Molly Malone Dicent Indexical Legisigns—A New Element in the Periodic Table of Semiotics?
Chapter 5 Co-localization as the Syntax of Multimodal Propositions An Amazing Peircean Idea and Some Implications for the Semiotics of Truth
Chapter 6 Sheets in the Wild A First Overview over Types of Propositional Surfaces
II Iconicity and Diagrams
Chapter 7 How Do Pictures Act? Two Semiotic Aspects of Picture Activity
Chapter 8 Dimensions of Peircean Diagrammaticality
Chapter 9 Iconicity of Logic—And the Roots of the “Iconicity” Concept
Chapter 10 Diagrammatic Problem Solving (with Svend Østergaard)
Chapter 11 Schematic Aspects of an Aesthetics of Diagrams
III Semiotics and Metaphysics
Chapter 12 Peirce as a Truthmaker Realist Propositional Realism as Backbone of Peircean Metaphysics
Chapter 13 Phenomenology and Logic in Peirce
Chapter 14 A Peirce for the 21 Century Theoretical Development as Key to Peirce’s Semiotics
Chapter 15 Blocking Evil Infinites A Note on a Note on a Peircean Strategy
Chapter 16 Peirce and Cassirer—The Kroisean Connection Vistas and Open Issues in John Krois’ Philosophical Semiotics
Chapter 17 The Riddle of Dependences How to Connect Entities across Pragmatism, Phenomenology, and Structuralism
Chapter 18 Conscious Self-Control as Criterion for Reasoning
Chapter 19 Limited Individuals and Unlimited Aims Peirce’s Philosophical Anthropology
Coda
Literature
Earlier Versions of Chapters of This Book
List of Illustrations
Notes
Name Index

Citation preview

Frederik Stjernfelt Sheets, Diagrams, and Realism in Peirce

Peirceana

Edited by Francesco Bellucci and Ahti-Veikko Pietarinen

Volume 6

Frederik Stjernfelt

Sheets, Diagrams, and Realism in Peirce

ISBN 978-3-11-079358-1 e-ISBN (PDF) 978-3-11-079362-8 e-ISBN (EPUB) 978-3-11-079367-3 ISSN 2698-7155 Library of Congress Control Number: 2022939308 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the internet at http://dnb.dnb.de. © 2022 Walter de Gruyter GmbH, Berlin/Boston Printing and binding: CPI books GmbH, Leck www.degruyter.com

Preface This volume collects a number of papers written over some years plus a final, newly written chapter. They would not have been possible without discussions, comments, help, and more from colleagues and friends. Thanks to Chiara Ambrosio, Myrdene Anderson, Francesco Bellucci, Priscila Borges, Patrick Blackburn, Per Aage Brandt †, Horst Bredekamp, Svend Brinkmann, Peer Bundgaard, Lorenzo Cigana, Marc Champagne, Andy Clark, Paul Cobley, Finn Collin, Jack Copeland, Marcel Danesi, Terrence Deacon, Anne Marie Dinesen, Charbel El-Hani, Claus Emmeche, Don Favareau, Hans Fink, Steve Fuller, Riccardo Fusaroli, Gabriele Gramelsberger, Frans Gregersen, Susan Haack, Vincent Hendricks, Jaakko Hintikka †, Aud Sissel Hoel, Michael Hoffmann, Jesper Hoffmeyer †, Nathan Houser, Tony Jappy, Hans Siggaard Jensen, Jørgen Dines Johansen †, Frank Kammerzell, Simo Køppe, John Michael Krois†, Kalevi Kull, Jobst Landgrebe, Robert Lane, Ulrik Langen, Aleksandra Lapčić, Kim Guldstrand Larsen, Jean Lassègue, Cathy Legg, Massimo Leone, Dario Martinelli, Michael May, Anders Michelsen, Irene Mittelberg, Matthew Moore, Winfried Nöth, Peter Øhrstrøm, Alin Olteanu, Svend Østergaard †, Markus Pantsar, Helmut Pape, David Budtz Pedersen, Esther Oluffa Pedersen, Stig Andur Pedersen †, Ahti Pietarinen, João Queiroz, Matthew Ritchie, Lucia Santaella, Karl Erik Schøllhammer, Sun-Joo Shin, Barry Smith, John Sowa, Leonard Talmy, André de Tienne, Ole Togeby, Kristian Tylén, Mikael Vetner, Tullio Viola, Cornelis de Waal, Donna West. I wish to dedicate this volume to my mother Mette Stjernfelt (born 1927) who faced the last phase of her life during my finishing the book. She has been strong, independent, and supportive all the way through her long life. Thanks to the University of Aalborg in Copenhagen for good working conditions. I also wish to thank Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, where I finished this book during a great stay as a visiting fellow at the KHK Kolleg “Cultures of Research” during 2021– 2022. Aachen, 2022 Frederik Stjernfelt

https://doi.org/10.1515/9783110793628-001

Contents Introduction

1

I Propositions Chapter 1 Signs Conveying Information On the Range of Peirce’s Notion of Propositions: Dicisigns Central Properties of Dicisigns 8 11 Varieties of Dicisigns Road Dicisigns as an Example 16 Biosemiotic Dicisigns 17 22 Adaptation to Dicisigns

7

Chapter 2 Dicisigns and Habits Implicit Propositions and Habit-Taking in Peirce’s Pragmatism 23 Aspects of Habits 24 Habits in the Pragmatic Maxim 24 26 Habit, Continuity, and Realism Acquired Habits, Innate Habits, Laws 29 Habit Straddling the Unconscious/Conscious Distinction 34 38 Self-Control and Consciousness The Status of the Final Action Habit—A Proposition or Not? 40 41 Habits and Dicisigns Revisited Chapter 3 Peirce’s Theories of Assertion 43 Assertion from Colloquial to Technical Term 43 Assertion as the Proposition Sign’s Self-Reference Assertion as Assumption of Responsibility 49 Assertion as Persuasion 52 The Role of Conscious Deliberation 54 Everyday and Scientific Assertions 57 58 The Scope of Assertive Responsibility Assertions in the Social Field 61

47

VIII

Contents

Chapter 4 The Identity of Sweet Molly Malone Dicent Indexical Legisigns—A New Element in the Periodic Table of Semiotics? 62 Predictions of the Sign Combination Strategy of the 1903 62 Syllabus The Riddle of Dicent Indexical Legisigns 64 Pragmatic Roles and Purposes of Dicent Indexical Legisigns Chapter 5 Co-localization as the Syntax of Multimodal Propositions An Amazing Peircean Idea and Some Implications for the Semiotics of Truth 70 71 The Syntax of Propositions What Kind of Sign is Co-localization Syntax? 77 Labels 80 83 Co-localization Syntax in Early Human Semiotics Co-localization in Comics and Diagrams 87 Framing—The Topological Character of Co-Localization 92 Co-localization and Linguistics 101 103 Co-localization in Biosemiotics The Ontology of Propositional Truth 107 Chapter 6 Sheets in the Wild A First Overview over Types of Propositional Surfaces Sheets of Assertion 110 A Few Examples of Sheets 111 Posters—Serious and Satirical 116 Types of Sheets of Assertions 119

II Iconicity and Diagrams Chapter 7 How Do Pictures Act? Two Semiotic Aspects of Picture Activity Silk Print of a Silk Weaver 125 Threatening Pictures 125 Implicit Information 128

123

110

68

IX

Contents

Chapter 8 131 Dimensions of Peircean Diagrammaticality From the 1885 “Algebra of Logic” to the 1903 Image-Diagram-Metaphor Trichotomy 131 Operational vs. Optimal Iconicity 136 138 Diagram Tokens vs. Diagram Types Diagrams as General Signs and as Conclusions of Arguments 139 144 Levels of Generality in Diagrams Diagram Experiments vs. Real Experiments 145 Generic and Degenerate Diagrams 146 147 Explicit vs. Implicit Diagrams Co-localization 148 Corollarial vs. Theorematic Diagram Reasoning—Explicit vs. Implicit 150 Meanings of Diagrams Logic Diagrams vs. Diagrams Facilitating Logical Inferences 152 Pure vs. Applied Diagrams 155 Continuous vs. Discontinuous Diagrams: Are Parts of a Diagram also 156 Diagrams? Linear vs. Multidimensional Diagrams 157 Diagrams in Non-Necessary Inferences 158 160 Diagrams in Peirce’s Mature Semiotics Chapter 9 Iconicity of Logic—And the Roots of the “Iconicity” Concept 162 Peircean Iconicity 163 Iconicity in Logic Formalizations 164 The Algebra of Logic 165 The Existential Graphs 167 Beta Graphs 170 Lines of Identity 171 Iconicity in Existential Graphs vs. Linear Notation 173 The Birth of Iconicity 177 Chapter 10 Diagrammatic Problem Solving (with Svend Østergaard) 179 180 Information Internal or External to the Problem Space Types of Insight Problems 182 Diagrammatic Re-description and Diagrammatic Re-encoding A Special Case: The Cog Wheel Experiment 187 Cog Wheel Lessons 188

186

X

Contents

Solution Strategies 191 Embodiment and Collaboration—Two Hypotheses Chapter 11 Schematic Aspects of an Aesthetics of Diagrams 196 Diagrammatic Perception Further Diagrammatization 197 197 Externalized Diagrams Diagram Inferences 200 Multimodal Diagrams 200 Potential Aesthetic Qualities of Diagrams

193

196

202

III Semiotics and Metaphysics Chapter 12 Peirce as a Truthmaker Realist Propositional Realism as Backbone of Peircean Metaphysics 211 The Basic Kantian Argument 211 Predicate Realism 213 214 Subject Realism Representation Realism 214 Realism of Indefinite Inquiry 216 Extrapolating from Propositions: Deducing Metaphysical Realism from 217 Semiotic Investigation Chapter 13 Phenomenology and Logic in Peirce 219 Phenomenology among the Sciences 219 The Road from Logic to Metaphysics 221 From Logic to Phenomenology 226 Methods and Findings of Phenomenology 229 Plurality of Paths to the Phaneron 233 Chapter 14 A Peirce for the 21 Century Theoretical Development as Key to Peirce’s Semiotics 235 The Mazes of the Development of Peirce’s Semiotics The Birth of Peirce’s Semiotics—The 1860s 238 From Semiotics to Pragmatism—The 1870s 240

235

Contents

The Johns Hopkins Years—The 1880s 241 243 How To Reason—Early 1990s Grammatica Speculativa—Late 1890s 245 The First Reform: Six Signs—1902 248 The Second Reform: Ten Signs—1903 250 The Third Reform: Twenty-Eight or Sixty-Six Signs—1904 – 254 1908 259 Semiotics in the World Chapter 15 Blocking Evil Infinites A Note on a Note on a Peircean Strategy Schlechte Unendlichkeit 261 262 Nota Notae

261

Chapter 16 Peirce and Cassirer—The Kroisean Connection Vistas and Open Issues in John Krois’ Philosophical Semiotics Sign Categorizations and Basic Phenomena 265 Pragmatism and Embodiment 265 266 Images and Symbolic Pregnance Semiotic Evolution 267 Embodiment as Extended Mind 269 270 The Krois Perspective Chapter 17 The Riddle of Dependences How to Connect Entities across Pragmatism, Phenomenology, and Structuralism 272 Husserlian Dependences 273 Peircean Distinctions 275 Hjelmslevian Dependences 278 Ingardenian Dependences 286 A Metalanguage of Dependences 289 Chapter 18 Conscious Self-Control as Criterion for Reasoning 291 Peirce’s Doctrine of Consciousness 292 Consciousness and Unconscious Mind 295 The Self of Self-Control 298

264

XI

XII

Contents

Self-Control and Reasoning 301 302 Ethics and Logical Self-Control Self-Control: Inhibitory or Creative? 304 The Self-Control Process 307 Levels of Self-Control and Hypostatic Abstraction 315 Machine and Animal Counterexamples The Role of Consciousness in Self-Control 321 324 Windows and Freedom

312

Chapter 19 Limited Individuals and Unlimited Aims Peirce’s Philosophical Anthropology 328 Man, a Sign 329 333 Limited Individuals with Unlimited ideals “Great Men” 337 1880s–1890s: Biological Instinct and Objective Idealism 340 345 From Anthropomorphism to the Celebration of Error Human Participation in Creation 350 Humans, Aliens, and Purposes of the Universe 355 Security, Uberty, and Humanity 357 358 The Human Predicament Coda

363

Literature

365

Earlier Versions of Chapters of This Book List of Illustrations Notes

385

Name Index

425

383

381

Introduction The present collection of Peircean papers stems from the 2010s up to 2022, the majority of them from the latter parts of the period. They are the result of a continuous interest in Charles Peirce’s logic, semiotics, and philosophy, earlier finding expression in books such as Diagrammatology (2007) and Natural Propositions (2014), insisting upon the investigation of the fecundity of Peirce’s notions of “diagram” and “dicisign”. Those central concepts have played an undervalued role in much Peirce scholarship and in the plethora of applied versions of Peirce’s semiotics. The papers in the present volume continue that quest. That task is double, for not only does it require detailed investigation and reconstruction of Peirce’s central arguments—but it also requires charting the possible present actuality and fertility of those results. This also finds expression in the importance of understanding not only the depth of Peirce’s investigations, but also the breadth of his conceptions: in which empirically appearing sign types and complexes do his ideal, theoretical conceptions find expression? Doing so continues a certain double strategy present in Peirce’s own mode of thinking—what could be called his a priori-a posteriori methodology. After, as a young man being extremely skeptical against a priori reasoning, e. g., in the 1877– 1878 definitions of pragmatism, the mature Peirce increasingly realizes that his own philosophical architectonic, his philosophy of logic, his semiotics, his philosophy of science, actually do constitute a priori theories. Still, Peirce now insists that such theoretical predictions should not be accepted immediately at face value, but should be constantly checked against reality, true to his insistence on the constant collaboration of ab-, de-, and induction in the research process. As to his semiotics in particular, it is crucial to scrutinize which kinds of actual sign token utterances realize which theoretically predefined sign types. Much too many interpreters remain content with citing and interpreting a selection of Peirce’s general, theoretical definitions without going into detail regarding which empirical phenomena they really cover. Thus, the proper understanding and development of Peirce’s ambitious logic-as-semiotics project requires the ongoing interplay between his ever-sharpening and proliferating conceptual definitions on the one hand, and the empirical semiotic phenomena they cover, on the other. In 1896, arguably the beginning year of Peirce’s large mature philosophical explosion peaking in 1903, Peirce explicitly stated this doctrine in his first review of his German disciple Ernst Schröder, when defining the triad of icon-index-symbol as so many different aspects of an assertion: “In such analyhttps://doi.org/10.1515/9783110793628-002

2

Introduction

sis of assertions there are two kinds of reasoning which we have to employ”, he emphasizes, one of the two is “rhetorical”, a term Peirce here takes from Schröder while remarking upon how the latter is a bit condescending about it because of its “undeniable formal imperfection” (“That Categorical and Hypothetical Propositions are one in Essence”, 1896, SWS, 58). It refers to inducting, generalizing, and abstracting “from below” the knowledge of the structure of assertions based on empirical observation of signs in the wild. Peirce defends this inductive stance: “Now to me this very imperfection marks the reasoning as being drawn direct from those observational sources from whence all true reasoning must be drawn; and I have often remarked in the history of philosophy, that the reasonings which were somewhat dark and formally imperfect, often went the deepest” (SWS, 58). Such inductive results, however, are not in themselves sufficient but must be organized by means of a theoretically developed conceptual apparatus: The other kind of reasoning which I employ in the analyses of assertion consists in deducing what the constituents of assertion must be from the theory, which I accept, that truth consists in the definitive compulsion of the investigating intelligence. This is systematical; but it is only half a method. For the deductions, or quasi-predictions, from theory having been made, it is requisite to turn to the rhetorical evidence and see whether or not they are verified by observation. If we find them to do so, not only does the analyses of assertion gain evidence of being completely rounded, but the theory of truth is rendered more probable (SWS, 59).

Here, Peirce goes on to deduce the classic triad of indices, icons, and symbols as aspects of assertions, in each step comparing, at length, his theoretically deduced findings with a host of very different empirical examples of such signs. Particularly, this effort strives to get as comprehensive a view as possible of the variety of signs in the wild actually incarnating the theoretical predictions. Thereby, Peirce goes against the logical tradition of erecting a linguistic standard norm for logical analysis of propositions built on Latin and other Indo-European grammars, as he underlines. Here, Peirce’s scope of examples goes to show that the too swift assumption of such canonical forms overlooks a large number of empirically found signs satisfying his theoretical predictions. Six years later, after having considerably developed his sign theory to the famous three-trichotomies-ten-signs calculus during his work on the 1903 Syllabus, he sums up the a priori–a posteriori method in the final version of that seminal paper, the “Nomenclature of Triadic Divisions”¹: The principles and analogies of Phenomenology enable us to describe, in a distant way, what the divisions of triadic relations must be. But until we have met with the different kinds a posteriori, and have in that way been led to recognize their importance, the a priori descriptions mean little; not nothing at all, but little. Even after we seem to identify the va-

Introduction

3

rieties called for a priori with varieties which the experience of reflexion leads us to think important, no slight labour is required to make sure that the divisions we have found a posteriori are precisely those that have been predicted a priori. In most cases, we find that they are not precisely identical, owing to the narrowness of our reflexional experience. It is only after much further arduous analysis that we are able finally to place in the system the conceptions to which experience has led us. In the case of triadic relations, no part of this work has, as yet, been satisfactorily performed, except in some measure for the most important class of triadic relations, those of signs, or representamens, to their objects and interpretants (1903, EP II, 289; CP 2.233).

This arduous task is the reason behind the interest of the present author to analyze examples from mathematics, logic, linguistics, biosemiotics, poetry, arts, and more.² Such examples transgress the limit of this volume, but I hope the constant interest of exemplifying is palpable also in the present selection of primarily theoretical papers. The different original contexts and datings of the papers of this book imply that the Peircean reflections are presented to different degrees of depth and explicitness. This also implies that the reader must be ready to accept certain redundancies or repetitions. Maybe this also holds an advantage. In any case, Peirce claimed that “A book that goes to the bottom of an abstruse and complicated subject in such a manner that it can with profit be currently read ought to contain repetitions” (Minute Logic, R 428, 1902, 115). The papers have been sorted in three compartments. The first contains papers continuing the interest in actualizing, developing, and applying Peirce’s theory of propositions which dominated my Natural Propositions of 2014. The very first paper gives a short intro to that theory, while the ensuing papers further develop aspects of it: the relation between habits and propositions; the speech act of asserting a proposition; the particular proposition category of “Dicent Indexical Legisigns”; the co-localization syntax of proposition sign tokens; and the use of Sheets of Assertions in the wild. The second block continues the interest in Peirce’s theories of icons and diagrams focused upon in the Diagrammatology of 2007: the seeming activity of images; the many dimensions and variabilities of Peircean diagrams; the roots of the concept of iconicity in the comparison of logic formalizations; an empirical investigation of different solution strategies in diagrammatic reasoning; the aesthetics of diagrams. The third block considers the roots of Dicisigns and Diagrams in more general semiotic and metaphysical issues. Peirce famously said: Find a scientific man who proposes to get along without any metaphysics (…) and you have found one whose doctrines are thoroughly vitiated by the crude and uncriticized metaphy-

4

Introduction

sics with which they are packed. (…) Every man of us has a metaphysics, and has to have one; and it will influence his life greatly. Far better, then, that that metaphysics should be criticized and not be allowed to run loose. (…). In short, there is no escape from the need of a critical examination of “first principles” (“Sketch of Some Proposed Chapters on the Sect of Philosophy Called Pragmatism”, c. 1905, CP 1.129).

No one could be more insistent than Peirce on the empirical investigation of facts to check one’s theoretical ideas, but he would never undersign any empiricist wholesale rejection of metaphysics. Quite on the contrary, his strong philosophical realism obliged him to consider seriously the metaphysical inventory of the world as well as which roads of inquiry are legitimate to investigate that inventory. This block addresses Peirce’s realism analyzed in its three components; his mature phenomenology and its relation to logic; his lifelong development of semiotics as charted by Francesco Bellucci; the rock bottom of structural “continuous predicates” as a sort of formal ontology; the connection between Peirce’s and Cassirer’s philosophies viewed through John Krois’ optics; the dependence theory inherent in his three-category phenomenology as compared with related fundamental ideas in Hjelmslev’s structuralist linguistics and Ingarden’s realist phenomenology; Peirce’s surprising insistence that reasoning proper demands scrutiny by conscious self-control; and finally, Peirce’s attempts at situating the logical-semiotic core of his thought in the wider perspective of the classical question of philosophical anthropology Was ist der Mensch—what is a human being? I hope the reader may glimpse the double prospect of theoretical richness and analytical fertility offered by Peirce’s logic, semiotics, and philosophy. In that case, Peirce’s beautiful Enlightenment belief in the further development of science and humanity across generations may find yet another small piece of verification.

I Propositions

Chapter 1 Signs Conveying Information On the Range of Peirce’s Notion of Propositions: Dicisigns This chapter introduces Peirce’s notion of proposition, “Dicisign”. It goes through its main characteristics and argues that its strengths have been overlooked. The concept does not fall prey to some of the problems in the received notion of propositions (their dependence upon language, upon compositionality, upon human intention). This implies the extension of Peircean Dicisigns is wider in at least two respects: they comprise 1) propositions not or only partially linguistic, using in addition gesture, picture, diagrams, etc.; 2) non-human propositions in biology studied by biosemiotics. Peirce’s notion of “Dicisigns” has led a strangely silent life in Peirce reception. It is, of course, Peirce’s notion for propositions, and the central place of that notion in the development of 20th century logic and analytic philosophy may have led many Peirce scholars to presume Peirce’s notion was merely a forerunner to that development, lacking any intrinsic interest. This is not true, and the aim of this chapter is to give an overview over Peirce’s notion of Dicisign as well as to highlight those aspects of it which differ from the received notion of propositions in logic and philosophy. Peirce’s notion of Dicisign includes logical propositions and is closely related to Peirce’s many discoveries in logic—but due to Peirce’s semiotic approach to logic, he is not only, like the logic mainstream, interested in the formalization of propositions and their structures, but also takes a crucial interest in which types of sign vehicles may express propositions.³ This is why Peirce’s Dicisign transgresses the narrowly logical notion of propositions in at least two respects. One is that a Peircean Dicisign needs not be expressed in language, ordinary or formal. A Dicisign may use gestures, pictures, diagrams only, or it may use such devices in combination with language or with each other. Thus, it is intrinsically multimodal, and the notion of Dicisigns covers a much larger range of human semiotic activity than ordinarily conceived of in the notion of propositions (it is true that most often, logic does not explicitly consider that range, focusing instead on formal properties of propositions and propositional content, however expressed)—it gives a much broader idea of which human activities serve to imply claiming something to be the case. The other extension in the notion of Dicisigns as compared to standard conceptions of propositions is that Dicisigns, not being confined to language, https://doi.org/10.1515/9783110793628-003

8

Chapter 1: Signs Conveying Information

also cover animal communication and lower biological sign use studied by biosemiotics. This should not come as a great surprise: communication of any sort couldn’t possibly reach any high degree of efficiency if it is not able to indicate things to be the case, which is the central property and purpose of Dicisigns. Many of the biological cases, however, do not imply that the signs used correspond to conscious, deliberate claims on the part of a communicating or signifying biological agent—which is probably why many scholars immediately refrain from considering the possibility of Dicisigns in biology.

Central Properties of Dicisigns Let’s begin by taking a look at the central properties of Peirce’s Dicisign doctrine.⁴ A basic way of describing Dicisigns is that they are signs which may be ascribed a truth value (Syllabus, 1903; partly reprinted in EP II). This is because Dicisigns claim something about something—and this claim may be true or false (or meaningless). The reason why Dicisigns are thus able to claim something is that they have a double structure: they 1) point out an object, and they 2) describe that object in some way. They possess, in some way, a Subject-Predicate structure. The formal part of this analysis of a proposition is largely shared by Frege and Peirce. Frege famously analyzed propositions to consist of two parts, functions and arguments (corresponding to Peircean Predicates and Subjects, respectively), functions indicating properties of the variables indicated by the arguments, and often indicated as F(a)—meaning a satisfies the function F; a takes the predicate F. Frege’s pathbreaking insight was that functions need not have one argument only—properties are not only properties of one object, many properties are relationally shared between objects. Peirce’s independent analysis of the Dicisign is quite parallel: a proposition consists of 1) a Predicate, in his terms an iconic rhema (corresponding to Frege’s function) and 2) one or more Subjects, in his terms indices referring to which objects are claimed to possess the property or relation described by the icon rhema (corresponding to Frege’s arguments). Peirce stuck to the established Aristotelian terminology, even if vastly generalizing the notions of Predicate and Subject. Frege and Peirce count as the founders of relational logic; both of them insist that one and the same rhema (function) may take several indices (arguments).⁵ Thus, the rhema “loves” may take two indices: “Peter loves Mary”; the rhema “gives” may take three, “Mary gives Peter a rejection”. Moreover, both Frege and Peirce invent quantification to give different recipes for the selection of the objects referred to by the indices of a Dicisign. Existential quantification: “Some berries are red”, universal quantification “All fruits are colored”—and possibly further quan-

Central Properties of Dicisigns

9

tifiers indicating other modes of selection of objects considered in the Dicisign. Frege and Peirce did not know about each other’s discoveries, and it is well known how Frege enjoys priority in these discoveries because he published them some years before Peirce. It is less well known that the current logical formalism, sometimes referred to as the Peano-Russell formalism, stems from Peirce (via the German philosopher Ernst Schröder) rather than from Frege. Peirce invented the basics of that formalism in his two “Algebra of Logic” papers (1880 – 1885), while Frege’s earlier diagrammatical formalism (in the Begriffsschrift of 1879) proved too cumbersome to be put to common usage.⁶ Thus, there is a large overlap between the basic Fregean and Peircean analyses of the structure of propositions. What differs lies rather in the more or less unspoken assumptions about where and how propositions occur. The Fregean tradition in logic and analytic philosophy (not necessarily Frege himself; the Begriffsschrift did indeed present a system for non-linguistic graphical logic representation) has, as a tendency, presumed two things: 1) that propositions must be linguistically expressed, in ordinary language or special, formalized languages, and 2) that propositions, in order to be expressed, require a speaking subject taking a “propositional attitude” or a “propositional stance”. These two assumptions focus, of course, on the ubiquitous example of propositions expressed by linguistically able human beings. The analytic tradition, having focused more upon the truth-preserving and formal properties of propositions, most often kept such assumptions in the background—but still these ideas form part of what Barry Smith (2005) ridicules as “Fantology”, the mistaken doctrine resulting from taking the structure of First Order Predicate Logic (FOPL) as the sole guideline for what should be taken to be the basic entities of ontology. Given the success of FOPL, the Kantian step of reading metaphysical structure directly off of logical structure may seem tempting—but then it is important to realize what does indeed belong to logical structure itself, and what is merely artifices of formalization. Smith nicknames the fallacy of disregarding this cautiousness “Fantology” after the F(a) structure charted by Frege—“F(a)ntology”— and he claims that FOPL formalism has led analytic metaphysics to assume that all generality, not only within the formalism, but also in the world, lies in the predicate and never in the subject. Thus, all existing objects are taken to be particulars, referred to by the a (or by the variables x’s, y’s, and z’s of more elaborated formulae), and they may, in turn, share different general properties, referred to by the Fs. This, according to Smith, gives rise to a minimalist and nominalist ontology, dispensing with all sorts of natural kinds otherwise central in science (electrons, earthquakes, animal species, revolutions, languages, etc.) —expressed, for instance, in Quine’s famous claim that to exist is to be a bound

10

Chapter 1: Signs Conveying Information

variable of a true proposition, the function or predicate part of the proposition hence having nothing at all to do with real existence. The ideas that propositions are necessarily 1) linguistic, 2) compositionally constructed from independent parts corresponding to function/argument, and 3) a prerequisite for human beings only, now form another piece of Fantology: we are led to assume these ideas from being accustomed to ordinary and formal languages. Here, Peirce’s more general notion of Dicisign, even if formally analogous to Frege’s, escapes all of these fantological dangers. Peircean Dicisigns are not confined to be expressed linguistically, they do possess the two aspects of Subject-Predicate but are not for that reason rendered compositional, and they do not require human beings nor indeed conscious intention to appear. These non-fantological properties of Peirce’s definition of the Dicisign appear in his basic semiotic description of it: “Every assertion is an assertion that two different signs have the same object” (“Short Logic”, c. 1893, CP 2.437).⁷ The Dicisign claims that two signs have the same object—and those two signs form parts or aspects of the Dicisign itself. The two signs are the indexical object reference and the iconical object description, respectively. As Hilpinen says, this notion corresponds to William of Ockham’s idea that a proposition is true if its subject and predicate “supposit for the same thing” (Hilpinen 1992, 475). One aspect of the Dicisign indicates its object, another aspect of it describes it, and the Dicisign now claims these two constituent signs have the same object. To be more precise, the iconic part of the Dicisign is not directly a description of the object; rather the iconic part of it is an icon of the very Dicisign itself, Peirce claims: “… every proposition contains a Subject and a Predicate, the former representing (or being) an Index of the Primary Object, or Correlate of the relation represented, the latter representing (or being) an Icon of the Dicisign in some respect” (Syllabus, 1903, EP II, 279). This, at first sight, surprising doctrine is developed at length in the Syllabus—the idea is that the predicate aspect of the Dicisign depicts not only the object, but also depicts the relation of the Dicisign itself to the object—which is an indexical-iconic relation. The reason for this doctrine is to avoid the merely compositional idea that any accidental combination of an index and an icon of the same object would constitute a Dicisign. The icon part is taken to represent not only the description, but also the description claim (indicated by the fact that the copula, on Peirce’s analysis, is included into the rheme). Thus “The Sky is Blue” really is a shorthand for the full Dicisign making the self-referential claim: “This sign is really connected to the Sky which is why it is authorized to claim about it the Predicate Blue”. This is consistent with Peirce’s idea that “The most perfectly thorough analyses throws the whole substance of the Dicisign into the Predicate” (Syllabus, 1903, EP II, 281), which, in turn, is motivated by his analysis that all Predicates

Varieties of Dicisigns

11

function as generalized verbs. In the Dicisign “The Sky is Blue”, thus, the Subject is “The Sky”, and the Predicate is not only the adjective “Blue”, but the verbal compound “_ is Blue” with an unsaturated slot which may be filled in by a Subject. Peirce vacillates as to whether these two aspects of the Dicisign must necessarily appear as two independent, explicitly distinguishable parts of the Dicisign: “That is to say, in order to understand the Dicisign, it must be regarded as composed of such two parts whether it be in itself so composed or not. It is difficult to see how this can be, unless it really have two such parts; but perhaps this may be possible” (Syllabus, 1903, EP II, 276). His subsequent analysis of photographical Dicisigns, however, seems to solve this puzzle: the P-role is here played by the shapes on the photographical plate while the S-role is played by the causal connection of these with the object, granted by the physical effects of focused light rays on the photosensitive surface, chemically or electronically—but without S and P here appearing as autonomous, separate parts of the sign. Consequently, a single photograph may act as a Dicisign, provided the observer is capable of connecting it to the Subject indicated, and of understanding its shapes as Predicates of that Subject. So, S and P in general could be characterized as aspects of the Dicisign rather than as independent parts—even if they may, in many cases, form such parts.

Varieties of Dicisigns On this basis, let us list some examples of Dicisigns—with their Subject and Predicate aspects indicated by S and P, respectively: ‒ Linguistic utterances in the indicative: “It (S) rains (P)”, “The Sky (S) is Blue (P)” or “He (S1) loves (P) her (S2)” or “Mary (S1) gives (P) Peter (S2) a present (S3)” ‒ The double gesture of pointing towards a person (S) and turning the finger pointing to one’s head to indicate that person is crazy (P) ‒ The gesture of pointing towards a person (S) and then pointing towards a caricature intended to portray him (P) ‒ A picture (P) with the object indicated (S)—specific examples include: ‒ A cartoon of a well-known figure (Donald Duck, S), acting and expressing graphically represented utterings (P) ‒ Road signs informing of (e. g.) danger of deer on the road (P), the location of the sign indicating the location of the presence of this danger (S) ‒ A portrait (P) with a title or label indicating the person portrayed (S)

12

‒

‒ ‒ ‒ ‒

Chapter 1: Signs Conveying Information

A photograph depicting its object by means of shapes and colors on a surface (P), indicating the object by the causal connection via focused light rays (S) A photograph (P) with the object made explicit by an accompanying linguistic byline (S) A diagram (P) used for describing the structure of an object indicated by accompanying indexical symbols (S)—specific examples include the following: A topographical map of stylized landscape shapes and types (P) equipped with names (S) of countries, cities, landscape features, etc. A mathematical graph in a Cartesian plane (P) equipped with specifications of the axis units and a legend indicating the physical phenomenon it describes (S)

A very important upshot of this open list of examples is that linguistically complete, grammatically well-formed Dicisigns do not in any way exhaust the category, rather, they form a special subcategory. Many mixed forms, involving gestures, pictures, objects, language in different combinations, may constitute Dicisigns. If you are at a friend’s door and he is not home, you may, lacking a pencil, indicate you have been there by leaving a small object you know he knows belongs to you—this object then acting as a minimal Dicisign saying “I (S1) was trying to visit (P) you (S2)”. As to the indexical aspect of the Dicisign, we find very different types of signs realizing it. In very simple cases, the very spatio-temporal context of the sign may indicate the (S)-aspect as in “It rains”, where the (P) part of raining is predicated onto the here-and-now of utterance. A bit further away, but still close to the object we find touching, gestural pointing or gaze directions (fundamental in human semiotics according to Michael Tomasello, 2008) denoting the object referred to, even further away are symbolic indices like proper names or pronouns, potentially used in the absence of the object. In any case, the Dicisign claims to stand in a direct, indexical connection with its object (if it is a true proposition, this claim will be true, referring to existing objects).⁸ A very important observation by Peirce is that, in order for a Dicisign to function, the receiver should possess “collateral” knowledge about the object indicated—the proposition should not be the only indexical source referring to the object. A photograph of unknown persons taken at an unknown time and place is thus no Dicisign in itself (apart from the very vague claim that something somewhere looked like this at some time)—but it might be used as part of a Dicisign by a person able to identify aspects of the objects caught in the photo: “This is Uncle Walter” or “This is how things were in Tübingen”. Given the existence of such collateral knowledge, however, an isolated photograph may function as a Dicisign, even without any additional text or other subject index. If you

Varieties of Dicisigns

13

happen to receive a letter containing recognizable photographs of yourself involved in embarrassing sexual activities, they immediately constitute Dicisigns claiming that you have indeed indulged in such activity (cf. Chapter 7).⁹ As to the Predicative or descriptive aspect of the Dicisign, it must contain or involve some kind of iconical representation of aspects of the object. This may be achieved by the direct means of pictures, gestures, diagrams describing aspects of the object’s properties, relations or behaviors, or it may be achieved less directly by means of symbolical icons, like conventional gestures, linguistic adjectives, common nouns, verbs etc. Finally, the relation between the S and P aspects of the Dicisign must be some sort of syntax: “Finally, our conclusions require that the proposition should have an actual Syntax, which is represented to be the Index of those elements of the fact represented that corresponds to the Subject and Predicate” (Syllabus, 1903, EP II, 282). This convoluted expression that the syntax is represented to be an index of the elements must be taken to mean that the Syntax depicts the fact involving the object and quality, in turn corresponding to the S and P parts of the Dicisign. It seems simpler and more appropriate to say that the S-P syntax of the Dicisign iconically depicts the combination of object and quality into a fact. This is also in accordance with Peirce’s claim elsewhere in the Syllabus that “Every informational sign thus involves a Fact, which is its Syntax” (CP 2.321). In Peirce’s 1903 system of trichotomies, Dicisigns form the second level of the triad Rheme-Dicisign-Argument (his version of the traditional logical TermProposition-Argument distinction, elsewhere named by him Sumisign-DicisignSuadisign, and a bit later generalized to cover all speech acts, Seme-Pheme-Delome). We already touched upon the Rheme generalization of the Predicate. Rhemes may form relational predicates with any number of subject slots to be saturated (even if Peirce famously claimed that any n-valence Rheme may be analyzed as a composition of a number of simpler, at most 3-valence Rhemes), and, as mentioned, they may be linguistic, gestural, pictorial, diagrammatical, etc.¹⁰ Arguments, on the other hand, are the rule-bound combination of Dicisigns so that one Dicisign, the conclusion, logically follows from another, the premise (which may be composite and combined from several Dicisigns). Diagrammatical reasoning, according to Peirce, is the general mode of thus inferring one Dicisign from another, again widening logical inference to embrace diagrammatical and pictorial representations alongside linguistic ones. As to the structure of Rheme-Dicisign-Argument as signs, Peirce gives this beautifully simple description (using the Sumi-Dici-Suadi terminology): “The second trichotomy of representamens is [divided] into: first, simple signs, substitutive signs, or Sumisigns; second, double signs, informational signs, quasi-propositions, or Dicisigns; third,

14

Chapter 1: Signs Conveying Information

triple signs, rationally persuasive signs, arguments, or Suadisigns” (Syllabus, 1903, EP II, 275). To the simple description of the Rheme, claiming nothing, the Dicisign fills in (some of) the empty slots of the Rheme by Indices, making the sign’s object relation double. The Argument adds the third claim that the object behaves in the lawful way indicated by the inference from one Dicisign to the next, hence the single-double-triple distinction based on the number of sign-object connections. As to which aspects of their object the three of them represent, Peirce gives the following list: “… we may say that a Rheme is a sign which is understood to represent its Object in its characters merely; that a Dicisign is a sign which is understood to represent its Object in respect to actual existence; and that an Argument is a sign which is understood to represent its Object in its character as sign” (Syllabus, 1903, EP II, 292). Finally, we may add the description in terms of degrees of explicitness of the signs: “A representamen is either a rhema, a proposition, or an argument. An argument is a representamen which separately shows what interpretant it is intended to determine. A proposition is a representamen which is not an argument, but which separately indicates what object it is intended to represent. A rhema is a simple representation without such separate parts” (“Lectures on Pragmatism”, EP II, 204; CP 5.139). So, Dicisigns and Arguments make their subjects and conclusions explicit as parts of the sign itself. The latter description generalizes the notion of rhema, to cover not only isolated predicates, but also isolated subject signs. As to the meaning of a proposition, Peirce defines it logically in terms of what may be inferred from it: “… what we call the meaning of a proposition embraces every obvious necessary deduction from it” (“Lectures on Pragmatism”, 1903, EP II, 214). The final interpretant of a proposition, according to Peirce’s later, triadic theory of interpretants, will embrace everything which may be deduced from it; the meaning here referred to is rather what he would call the immediate interpretant, the “obvious” implications of it, dependent upon the clarity of context as well as the intellectual capacities of the interpreter. This conception of the immediate meaning is thus pragmatic in the sense that it relies upon the information typically needed by the interpreter and easily extracted from the sign—most often for action possibilities. Even if many facts may be implied by the Dicisign, the immediate meaning is that fact which is immediately relevant to the Interpreter.¹¹ We already touched upon the relation between the Dicisign’s syntax and Peirce’s theory of facts. It is most often overlooked that Peirce developed an ontology of facts which is, to some extent, analogous to the contemporaneous doctrines in Austrian philosophy of Sachverhalt (Stumpf, Meinong, later Husserl, Wittgenstein). Like in them, the notion of fact as a part of reality is closely connected to that part’s representability in propositions, in Dicisigns:

Varieties of Dicisigns

15

A state of things is an abstract constituent part of reality, of such a nature that a proposition is needed to represent it. There is but one individual, or completely determinate, state of things, namely, the all of reality. A fact is so highly a prescissively abstract state of things, that it can be wholly represented in a simple proposition, and the term “simple,” here, has no absolute meaning, but is merely a comparative expression (“The Basis of Pragmaticism”, 1906, EP II, 378; CP 5.549).

Peirce’s theory of the Dicisign as representing a fact is thus a picture theory of semiotics, not unlike the early Wittgenstein’s Tractarian picture theory of logic. A very important caveat, however, makes Peirce distinguish between the object referred to by a Dicisign (given by the indexical aspect of that Dicisign) on the one hand, and the whole of the fact represented by the Dicisign, on the other. Here we see a strength of the analysis “throwing the whole of the Dicisign into the Predicate”: the object referred to is different from the fact claimed by the Dicisign. It might seem tempting simply to make the fact and the object of the Dicisign one and the same thing—but in that case, the existence of false Dicisigns would become a theoretical problem, if they involve a really existing object. False claims, of course, may refer correctly to existing objects—their falsity lies in the alleged facts in which they embed those objects: “Barack Obama is a Muslim”. This Dicisign successfully refers to a really existing object—Barack Obama—but the fact it represents, Obama being a Muslim, is non-existent which is why the Dicisign is false. The Russellian example of “The present king of France is bald”, on the contrary, does not refer to any existing object and hence cannot (as against Russell) be false, but rather without any truth value.¹² It is an important aspect of Peirce’s theory of Dicisigns, highlighted in his Existential Graph representation systems for logic, that Dicisigns are relative to some selected Universe of Discourse in relation to which their truth value should immediately be judged, rather than directly to reality as a whole (as presumed by Russell). The Universe of Discourse is the more or less implicit reference field, agreed upon by the interlocutors, of a given Dicisign. This emancipates Peirce’s doctrine from assuming the logic-as-a-universal-language idea with all the consequences in the shape of linguistic relativism, as argued by Jaakko Hintikka (1997)—to see logic instead as consisting of different calculi the plurality of which makes possible the notion of an independent reality to which all of them ultimately refer. There are many important issues related to Peirce’s doctrine of Dicisigns which merit a thorough discussion but which we may only mention briefly in the passing. One is the status of fictive propositions which refer to specific invented Universes of Discourse—and may be true within those Universes (“Donald Duck wears a sailor’s shirt”).¹³ Another is Peirce’s meticulous distinction, anticipating Speech Act Theory, of the proposition in itself and 1) the possible mental

16

Chapter 1: Signs Conveying Information

representation of it, 2) the possible assent to it by some agent, and 3) the possible assertive expression of it in a public sign (plus further uses, like in interrogatives and imperatives). Assertion is the public claim the Dicisign is true, whereby the utterer potentially subjects himself to public consequences (criticism, even court cases if the Dicisign contains threats, libel, etc.). You may publicly assert a Dicisign without yourself believing it (and so stating a lie), you may believe it without expressing it, you may think of it without either assenting to it nor asserting it, etc. The assertion “Osama bin Laden is dead”, uttered by a serious participant in a public debate, thus consists of the Dicisign expressed + 1) mental representation + 2) assent + 3) assertion. This embryonic Speech Act theory is very important in order to realize Peirce’s fundamentally anti-psychologistic notion of the Dicisign, making the notion of Dicisign or proposition much simpler than the notion of judgment, which involves psychological representation as well as assent and maybe even assertion (cf. Chapter 3). A corollary is that, to Peirce, one and the same Dicisign may form part of different types of speech acts such as assertions, questions, imperatives, wishes, etc.¹⁴

Road Dicisigns as an Example Before we proceed to discuss Dicisigns in biology, let us pause to consider a couple of examples of the arch-semiotic category of road signs. In them, the S aspect of the Dicisign is generally played by the very localization of the sign in time and space—not unlike the case in many biological Dicisigns. Consider, for instance, the following road sign (Fig. 1). The immediate interpretation, of course, of this Australian warning sign is that “Camels, emus, and kangaroos (P) may appear on the road in front of you for the next 150 kilometers (S)” On the internet, similar photos have been manipulated for satirical purposes, substituting a stylized missile, plane, and armed person, respectively, for the three animals, and “Baghdad 89 km” for “Next 150 km”. This ironic Iraqi warning sign correspondingly realizes the Dicisign that “Falling bombs, Fighter planes, and Insurgents (P) may appear before you on the road for the next 89 kilometers to Baghdad (S)” Such signs are, at the same time, descriptive and imperative. The speech act made on this propositional S-P basis describes a real possibility on the road ahead and warns the driver to prepare to avoid the general categories of objects depicted if they actualize on the road. The two signs refer to different universes of discourse; the former the real world, the latter a fictive world in which wartime eventualities are part of the system of road signs.

Biosemiotic Dicisigns

17

Fig. 1: Australian road sign.

Road signs thus have the peculiarity of being Dicisigns where the S-part is given by the co-localization of the sign interpreter with the sign and the sign’s object. The S-part of the sign indexically points out the location where the entities described by the P part may appear. The P part of the sign is the local circumstances described in general terms. Categorized by yellow color and the diamond shape as a warning sign, the speech act of the road sign addresses the behavior the driving recipient is advised or ordered to follow (this behavior, of course, will include other general subjects such as the categories of dangerous objects indicated by the Australian and Iraqi road signs).¹⁵ So while the subject of the propositional kernel of this Dicisign is the stretch of road ahead of the sign, the subject addressed by the imperative speech act made on this basis is the driver recipient. This structure of Dicisigns—that spatio-temporal whereabouts of the sign vehicle may play a central part for the determination of the S-part of the Dicisign—also occurs in many biosemiotic Dicisigns to which we now turn.

Biosemiotic Dicisigns Above, we made the case that human Dicisigns involve a large semiotic field with different combinations of language, gesture, pictures, drawings, diagrams, mov-

18

Chapter 1: Signs Conveying Information

ing pictures, etc. This forms one important extension of the Peircean Dicisign category. Another concerns biosemiotics—sign-use in biology. Peirce’s definition and description of Dicisigns is emphatically not dependent on human psychology (even if the range of Dicisigns which may be processed by the human brain, of course, vastly surpasses that accessible by simpler biological processes and agents). Peirce only rarely touches upon animal semiotics, but when he does, he leaves little doubt that he conceives of at least higher animals as being capable of processing Dicisigns.¹⁶ Thus, a strong argument can be made that not only do animal semiotics involve pre-linguistic concepts and meanings, but also proto-versions of propositions.¹⁷ Let us review some classic examples from different levels of biological evolution (with rough translations into human-language Dicisigns added in parentheses): ‒ E. Coli perceiving sugar and acting by swimming upstream in gradient (“There’s more sugar in this direction”) ‒ Fireflies signaling to possible mates with a species-specific flash (“Here is a Photinus female”) ‒ Von Frisch bee signaling (“Nectar can be found in this distance in that direction”) ‒ Vervet monkey signal calls (“An Eagle/ Leopard/ Snake is near!”) ‒ Higher animals trained by humans, able to utter acquired propositions. As an example, to the presentation of a hitherto unseen patch and the question “What matter?” Alex the Grey Parrot answers “Wool”. All of these examples of animal semiotics crucially involve Dicisigns—because all of them may be ascribed truth values, the fundamental Dicisign property. In a very basic sense, this ought not to be surprising: Dicisigns are the only signs which convey information—that is, simpler signs than Dicisigns, or sign aspects like pure Icons or pure Indices do not convey information and cannot, hence, function efficiently in biological cognition and communication. Still, most biosemioticians discussing biological signification using Peircean terminology (e. g., T. Deacon) prefer to restrict themselves to notions like Icon and Index. But pure Icons are nothing but mere possibilities, they potentially refer to any object which possess the required similarity—and cannot, then, be used in isolation to signify any precise, actually existing object; this requires an additional Index making of the whole a proposition. Pure Indices, on the other hand, are mere attention-directors—effects of or pointings to actual objects—without the descriptive part necessary to convey information about those objects. Of course, you can isolate Icons and Indices from their Dicisign contexts and investigate their structure, much like you can isolate single words outside of their sentence context. More complicated Indices, like the Dicisign subtypes Dicent Sinsigns or

Biosemiotic Dicisigns

19

Dicent Indexical Legisigns, may indeed convey such information and have truth values, but they do indeed include, being Dicisigns, Iconic information. The E. Coli example (resumed and discussed in Stjernfelt 2007, Chapter 9) pertains to the ability of Coli bacteria to perceive the presence of sugar in their surroundings and act accordingly. They have perceptors for certain selected chemicals (carbohydrates, certain toxins) enabling them to swim towards or away from such compounds. Normally, they swim in a Brownian-motion-like, so-called “random walk” trajectory where directed swimming is interrupted by brief “tumbling” phases changing their direction—not bad as a search strategy looking for nutrients. After the perception of carbohydrate, they change into “biased random walk” where the tumbling phases of their trajectory as a tendency orient their swimming along the carbohydrate gradient. The perception of sugar is made possible by a small, so-called “active site” on the perimeter of the macromolecule—which is why E. Coli, just like human beings, may be fooled by artificial sweeteners displaying the same active site on its molecule, despite being chemically quite different, the active site being literally a surface property only. Full-blown semiotics arguably begins with the possibility of “being fooled”, depending on the categorization, within one and the same semantic-behavioral category, of similar but different phenomena (carbohydrates and sweeteners, in this case). So, the (fallible) perception of carbohydrate displays the two basic aspects of a Dicisign: the “active site” provides the P aspect of “sugarlike”, while the direction indicated by the gradient provides the S aspect—in linguistic paraphrase: “There is sugar (P) in this direction (S)”. There is no communication at all present in this case, to be sure, the Dicisign has the same character as when human beings interpret the flag on a pole as indicating the wind coming from a certain direction. Moreover, we have no reason to assume there is any kind of conscious awareness present in the bacterium— the Dicisign structure is realized in the behavioral perception-action sequence of the single-cell organism. But if the Dicisign had not had its two crucial aspects, P (“sugar”) and S (“direction”), the sign would not have been able to convey information enabling the organism to act appropriately. An early and famous example of semiotic study of animal communication is von Frisch’s “bee dance” (1993). Having discovered a group of flowers with nectar, a bee, back in the hive, may communicate this knowledge to other bees by performing a specific, linear wriggling dance. The duration of the wriggling phase of the dance indicates the distance from the hive to the flowers, and the direction of the wriggling, relative to the angle of the direction to the sun, indicates the direction to the nectar-bearing flowers. Here, the wriggling behavior constitutes a Dicisign: “There is nectar (P) at this distance in that direction (S)”. The predicate part is communicated by the arbitrary symbol of wrig-

20

Chapter 1: Signs Conveying Information

gling (as opposed to normal, nonwriggling walking or flying), while the subject part is communicated by the direction and duration of the wriggling. Here, the most elaborate part of the Dicisign is concerned with indicating a location remote from the locus of communication. This code is genetically based and established in the long range of phylogenetic selection, but the actual sign use on the base of it takes place in the present now, informed by actual, local nectar data. A similarly complicated example is provided by firefly communication. Every firefly species has a specific flashing pattern, enabling males to locate females perched in the grass in order to mate. A whole arms race has taken place, enabling predator fireflies to fool other firefly species by imitating their specific flash patterns and thus lure lovesick males to approach, only to be eaten by the female (El-Hani, Queiroz, and Stjernfelt 2010). We shall not go into the intricacies of cross-species code imitating in this context—the basic point is that all the complexity of such mimetic warfare is based on the Dicisign structure of flash patterns in the first place. The temporal shape of the specific pattern forms the P part of the Dicisign while the S part is provided by the localization of the flashes—so the flashing behavior as a whole expresses the Dicisign “Here (S) is a Photinus female (P)”, giving rise to the appropriate mating behavior in the Photinus male. As opposed to the bee example, the complicated part of the Dicisign is the predicate part, specifying the species, while the subject part is given directly by the location of the flashes. In both the bee and the firefly cases, again, there is no reason to assume individual consciousness or ontogenetic learning to play any role (other than learning the actual location of nectar, of course). The character of these signs is the stable result of evolution, and they are automatized and not subject to individual change. The action interpretation of the signs, however, necessitates individual intelligence—the strategy of approaching the mate and the flowers indicated by the signs must be negotiated with individual perception and mapping of the surroundings. But even if the character of the signs is the result of the long duration of evolution, the use of them requires accommodation of the general sign to the particular situation and is played out in brief, individual, ontogenetic lifetime. A famous example of monkey communication is the alarm calls of vervet monkeys (Struhsaker 1967). The monkey has at its disposal three different calls which it may utter at the sight of an eagle, a leopard, and a snake, something like: [G-l-l-oi], [Arhw-Arhwhehehehe], [K-l-l-HRhr-hr], respectively. These calls cause conspecifics to perch to the ground, flee to a tree, or to search the ground around them, respectively. Such calls have s symbolic descriptive aspect (the specific, conventional sound pattern) playing the (P) role, while the time and place for the uttering of them plays, of course, the (S) role of the Dicisign, thus saying, in paraphrase “There is an eagle/leopard/snake (P) nearby (S)”. The ori-

Biosemiotic Dicisigns

21

gin of the sound patterns is disputed: it seems partially innate, and partially acquired so that young monkey alarm calls are corrected by their parents. Another issue of the dispute is the degree of intention in the monkey emitting the alarm call: does she intend to warn the others, or is she merely expressing an automatized sign which has been selected because it helps the group to survive? Reported cases of exploitative abuse of the sign to lure conspecifics away from fruits (without any actual presence of a predator) might be interpreted as indicating the presence of intention in uttering the calls, but this seems to be an open issue yet. The Dicisign structure, however, is independent of whether a conscious intention is present in the individual uttering the sign—the decisive issue is whether the sign does, in fact, function and lead to the appropriate actions in the receiver monkeys. Conscious awareness, if it is present, may facilitate more complicated behaviors, like the alleged fooling activity. Such activity is indeed found in human beings, and whether or not it is found in vervet monkeys, such more complicated behaviors depend on the simple Dicisign which does not need individual communication intention to be realized. A last example can be taken from the impressive feats performed by humantrained animals. Irene Pepperberg’s famous African Grey Parrot, Alex—now deceased—was able, after 20 years of training, to pronounce propositions and correctly answer simple questions pertaining to a series of qualities (number, shape, color, material) of previously unseen objects—like answering “Wool” to the question of “What matter?” or “Green” to the question of “What color?”. Alex had a vocabulary of around 150 words, among them the names of 50 objects, and was able to count up to seven.¹⁸ Thus, Alex was able to express Dicisigns in a way close to humans—characterizing present objects (S) by some of their qualities (P). Alex was rewarded for the answers, so the communicative goal was immediately food rather than any intentional wish to share information with the trainer—but, again, that does not take away the basic Dicisign characteristic of its utterances, the ability actually to convey information about an object. These biosemiotic example of Dicisigns vary as to cognition vs. communication, as to the emphasis on the S or P part of the Dicisign, as to the phylogenetic or acquired character of the sign, etc. They all share, however, the basic pragmatic feature that the communication is more or less closely connected to an action series which is either automatized or leads to an immediate reward in terms of survival or nourishment.¹⁹ Thus, the Dicisigns listed here seem to be simpler than the distinction between Indicatives and Imperatives in human languages; in some sense these biological Dicisigns are descriptive and imperative at one and the same time, leading directly to actions whose success, in most cases, serve as the grant that the sign has been appropriately interpreted.

22

Chapter 1: Signs Conveying Information

The appreciation of the widespread existence of Dicisigns in biology makes, I think, it a bit easier to imagine the crucial transition from animal to human semiotics.²⁰ The “propositional stance” is not a human, psychological privilege—rather, many biological systems adopt such a stance without necessitating conscious awareness or intention. The Peircean proposal for the specificity of human semiotics places the emphasis on the higher degree of self-control of human beings; cf. Chapter 18. Such levels of self-control enable humans to make explicit the sign which they use —which is what makes it possible, in turn, to analyze Dicisigns into their constituents, to compare several Dicisigns, to vary the inference from one Dicisign to another experimentally to see how far the inference holds, to invent signs about other signs (cf. Peirce’s notion of “hypostatic abstraction” for the creation of second-level thought-objects making reflection upon universals possible). It seems to me a good guess that the very development of consciousness in higher animals with central nervous systems serves to facilitate the growing explicit control, combination, and nesting of Dicisigns and their combination into Arguments.²¹

Adaptation to Dicisigns To conclude, Peirce’s theory of propositions, in the guise of “Dicisigns”, makes possible a renewed appreciation of the breadth of empirical phenomena displaying Dicisign structure and behavior—from human signs involving language, gesture, pictures, diagrams, etc. and many crossover forms intermixing them, and to very simple biosemiotic cognition and communication cases. It goes without saying that these Dicisigns vary considerably in terms of constituents, complexity, in degree of conscious access, in generality, and much more. But the unifying perspective of Peirce’s Dicisign doctrine seems to me to cast more light upon the appearance of semiotics through the process of evolution: natural selection has had to adapt to the structure of Dicisigns, rather than the other way around, because its basic S-P structure is necessary for efficiently conveying information. In that sense, it might be less precise to see Dicisigns as the result of evolution. We should rather see evolution as having increasingly adapted to the structures of Dicisigns.

Chapter 2 Dicisigns and Habits Implicit Propositions and Habit-Taking in Peirce’s Pragmatism “Dicisigns” is the concept developed by Peirce, in the context of his post-1900 generalized semiotics, in order to cover his vast generalization of standard conceptions of propositions. In his mature semiotic architectonic taking its beginnings from the Syllabus (1903), Peirce generalized the basic trichotomies of Term-Proposition-Argument and Icon-Index-Symbol to become, each of them, exhaustive, so that all signs will be either a term, a proposition, or an argument, as well as an icon, an index, or a symbol.²² During the composition of the Syllabus, yet another trichotomy, that of Qualisign-Sinsign-Legisign was added, as the first one of the three. This gave rise to the possibility of combining the three trichotomies to give the Syllabus table of ten combined sign types. The later extensions of Peirce’s semiotics, particularly in the Lady Welby letters, in terms of further trichotomies, up to a total of at least ten trichotomies, were established with the same claim for exhaustivity, in order to fit the same combinatorial pattern, famously giving a potential total of 66 combined signs. As to the conception of propositions in particular, the generalization indicated by the neologism “Dicisigns” (also “Dicent Sign”)²³ vastly extended its range from linguistically expressed truth claims to include propositions using diagrams, pictures, gestures, and more, as well as a vast swathe of “quasi-propositions” covering more or less natural indexical signs such as weathercocks, fossils, and the like. The rationale behind this generalization was the interconnected definitions of Dicisigns 1) by means of their ability to take a truth value and 2) by their functionally interpreted predicate-subject structure, according to which they function by means of simultaneously indicating an object by means of a subject and describing that same object by means of a predicate. In Natural Propositions (Stjernfelt 2014), I provided a reconstruction of Peirce’s elaborated theory of propositions as well an overview over actual interpretation possibilities of that theory. In this chapter, I investigate the relations between the Dicisign doctrine and the central conception of “habit” in Peirce’s logic, semiotics, and metaphysics. An immediate connection is indicated by the fact that most non-quasi propositions are symbols, and Peircean symbols are defined by their object connection relying on a habit: “A Symbol incorporates a habit, and is indispensable to the application of any intellectual habit, at least” (“Prolegomena to an Apology for https://doi.org/10.1515/9783110793628-004

24

Chapter 2: Dicisigns and Habits

Pragmaticism”, 1906, CP 4.531). Further investigation, however, reveals a series of complications to this simple scheme, taking us deep into fundamental structures and issues of pragmatism.

Aspects of Habits A major issue is that Peirce’s conception of habit, central as it is to pragmatism and semiotics alike, appears as somewhat less well-defined than most of the other central concepts of that edifice. Even if habit is central already in his early 1860s papers, Peirce’s conception of it changes considerably over the years. Let us run through some of the ambiguities or tensions involved. A first important complication is that symbols involve two set of habits; those of the sign itself, as a rule-bound legisign capable of identical repetition, and those of the purported behavior of the object referred to by the symbol “The word and its meaning are both general rules” (Syllabus, 1903, EP II, 274; CP 2.292 f; see also Nöth, 2010, 85; Pietarinen and Bellucci 2016). One thing is the habit governing the production of still new replicas of the symbol sign itself; another is the habit claimed to govern the behavior of the object referred to by that symbol. The former belongs to symbol expression in semiotics, the latter belong to the meaning expressed—and, if the symbol is true, to the (type of) objects referred to. Thus, the propositional symbol accounts for some of the habits of the object indicated: In contrast to the icon and the index, intellectual conceptions convey more about their object “… than any feeling, but more, too, than any existential fact, namely, the ‘would-acts’, ‘would-dos’ of habitual behavior; and no agglomeration of actual happenings can ever completely fill up the meaning of a ‘would-be.’” (“Pragmatism”, 1907, EP II, 402; CP 5.467).

Habits in the Pragmatic Maxim These, however, are results of Peirce’s mature semiotics. As early as in Peirce’s 1866 writings, habits appear as one of three basic elements of the mind, to be introduced as categories in “A New List” the year after.²⁴ He claims that there are “… three kinds of inference: 1st, Intellectual inference with its three varieties Hypothesis, Induction and Deduction; 2nd, Judgments of sensation, emotions, and instinctive motions which are hypotheses whose predicates are unanalyzed in comprehension; and 3rd, Habits, which are Inductions whose subjects are unanalyzed in extension. This division leads us to three elements of consciousness: 1st, Feelings or Elements of comprehension; 2nd, Efforts or Elements of extension;

Habits in the Pragmatic Maxim

25

and 3rd, Notions or Elements of information, which is the union of extension and comprehension” (Lowell Lecture XI, 1866, W 1, 491; CP 7.580). Here, the three categories are thus closely connected to the extension and intension—the reference and meaning—of propositions serving as conclusions to inferences. Already here, habits have propositional structure: a) they are inferred from vague inductions; b) their information is derived from that structure. Extension and intension being independent in propositions, the product of the two is taken to form the information they carry. That information, however, remains vague in habits because of their unanalyzed extension, that is, their lack of explicitly indicating for which contexts they hold. This is connected to the important fact that habit constitutes a structural element of mind which is not actually present at all times. For that reason, their type and degree of consciousness shall continue to form a matter of contention for years to come; see below. More generally, habit shall continue, during the development of Peirce’s thought, to appear as one of the major, regular means of characterization of the category of Thirdness, along with Continuity, Generality, Law, and so on, of which it is sometimes a synonym, other times a subtype. A particularly central role is played by habit in the articulation of the Pragmatic Maxim,²⁵ allegedly taking its beginnings in the early 1870s and appearing in its classic formulation in the 1878 papers. Inspired by Alexander Bain’s definition of Belief as “… that upon which a man is prepared to act”, introduced in the Metaphysical Club by Nicholas St. John Green and much discussed there, the pragmatic maxim forms an analysis of belief in terms of possible action habits.²⁶ Here, Belief is established as a particular subtype of habit in human thought: “And what, then, is belief? It is the demi-cadence which closes a musical phrase in the symphony of our intellectual life. We have seen that it has just three properties: First, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit” (“How to Make our Ideas Clear”, 1878, EP I, 129; CP 5.397). Here, beliefs are those habits of which we are aware and which mitigate doubt. Uncontroversially, Peirce assumes that familiarity with the use of a notion to form the first standard step of clearness, the ability to explicitly define the notion forming the second step. Deeming these two insufficient, he famously adds the third and final step of clearness to be that expressed in the pragmatic maxim: “It appears, then, that the rule for attaining the third grade of clearness of apprehension is as follows: Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object” (EP I, 132; CP 5.402). Here, habit is involved no fewer than on two occasions. The very con-

26

Chapter 2: Dicisigns and Habits

ception of possible effects of the object forms a habit of thought—thought taken to be a particular type of action: “the action of thinking” whose purpose is the removal of doubt. This habit of thought, in turn, establishes a further habit of action, relating to the effects of the object, in itself transcending thought: “The final upshot of thinking is the exercise of volition, and of this thought no longer forms a part; but belief is only a stadium of mental action, an effect upon our nature due to thought, which will influence future thinking” (EP I, 129; CP 5.397). This idea of the final meaning of a concept as consisting in a habit of nonmental action would continue to absorb Peirce in his attempts to construct a proof of pragmatism in the years after the turn of the century. But in 1878, the meaning of a proposition—a belief—is reducible to a claim about the conceivable effects of its object, while it is not addressed whether the resulting, final volitional action beyond thought but still governed by a general principle, also has, in itself, propositional structure. Habit being general, it possesses a schematic structure, as Rosenthal insists (1982, 231)—a diagram, as Peirce would say, incarnating the possibility of drawing particular action inferences from it.²⁷

Habit, Continuity, and Realism A constant theme in Peirce’s further development of the habit concept is its generality. A habit not only involves more than one occurrence of the relevant action, it also transcends any finite number of such instances (Letter to Lady Welby, Dec. 24, 1908, EP II, 487). Even if each single such occurrence constitutes an individual event, the structure permitting the indefinite extension of such occurrences is, in itself, general and thus forms a prime example of Peirce’s description of generality in terms of continuity. A habit transcends any number of actualizations, just like the continuum transcends any number of individual points, even infinite numbers.²⁸ For that reason, habits form a central example of general patterns referred to by Peirce’s realism of universals: habits are not themselves sums of individual existents or events, rather, they constitute patterns which possess the real power to make such existences incarnate them—even in the extreme case of never once becoming so actualized. Again, this structure, connecting some general rule with its possible instantiations in single cases mirrors that of propositions—consisting of general predicates, on the one hand, and of indices pointing out objects referred to, on the other hand. Another way of expressing said realism is that some of those general predicates describe real patterns—habits—of reality; and their presence in the mind can never exhaust them but must, by the same token, be one of a habitual

Habit, Continuity, and Realism

27

disposition, different from any here-and-now content of the mind. This also becomes evident the many times Peirce recognizes that the only way of presenting a habit is by predicatively describing the general behavior sequence common to each of its instantiations: To get back, then, to the die and its habit—its “would-be”—I really know no other way of defining a habit than by describing the kind of behavior in which the habit becomes actualized (Notes on “Doctrine of Chances”, 1910, CP 2.666).

Habits thus share the predicate/subject structure with propositions—general propositions due to the inherent generality of habits. The particular occasion that calls into action the general habit acts like the object of the proposition, the ensuing volitional act appearing as an inference from that proposition, as it is described in this long and pretty early quote locating this logical habit structure in neuropsychology with a frog as an example: The cognition of a rule is not necessarily conscious, but is of the nature of a habit, acquired or congenital. The cognition of a case is of the general nature of a sensation; that is to say, it is something which comes up into present consciousness. The cognition of a result is of the nature of a decision to act in a particular way on a given occasion. In point of fact, a syllogism in Barbara virtually takes place when we irritate the foot of a decapitated frog. The connection between the afferent and efferent nerve, whatever it may be, constitutes a nervous habit, a rule of action, which is the physiological analogue of the major premiss. The disturbance of the ganglionic equilibrium, owing to the irritation, is the physiological form of that which, psychologically considered, is a sensation; and, logically considered, is the occurrence of a case. The explosion through the efferent nerve is the physiological form of that which psychologically is a volition, and logically the inference of a result. When we pass from the lowest to the highest forms of inervation, the physiological equivalents escape our observation; but, psychologically, we still have, first, habit—which in its highest form is understanding, and which corresponds to the major premiss of Barbara; we have, second, feeling, or present consciousness, corresponding to the minor premiss of Barbara; and we have, third, volition, corresponding to the conclusion of the same mode of syllogism. Although these analogies, like all very broad generalizations, may seem very fanciful at first sight, yet the more the reader reflects upon them the more profoundly true I am confident they will appear. They give a significance to the ancient system of formal logic which no other can at all share (“A Theory of Probable Inference”, 1883, CP 2.711).

Here, logical habit leading from the general habit proposition (the major premise), occasioned by the appearance of the relevant particular information in a perceptual judgment proposition (the case, the minor premise) to the action conclusion, is instantiated in the neurophysiological system—propositional habit thereby extending also to cover inherited behavior structure: 1) Habit: “In case of A, do B”; 2) Occasion: A; 3) Action: B. The habit proposition—the major prem-

28

Chapter 2: Dicisigns and Habits

ise conditional—is later described as: “Real Habit—its subject would under certain conditions behave in a certain way, even if those conditions never actually do get fulfilled” (“A Sketch of Logical Critics”, 1909, EP II, 457)—the “certain conditions” given in the minor premise activate the habit conclusion. Habits in this very general sense, spanning from inherited biological instinct to acquired and learned customs and routines, thus form general, conditional propositions. So, not only explicit, consciously adapted beliefs, among habits, are propositional. Indeed, habit is propositional all the way down to biology. In short, habit in this sense is a general, conditional proposition urging a type of action, generally described, to occur on given conditions. Some of those habits, of course, may be intellectual, so that the resulting action is the thinking of a thought; in that case the relevant habits themselves are rules of inference. But if all habits have a propositional structure, forming the major premise of action arguments, beliefs are no longer those habits which are propositions. What then distinguishes beliefs as against habits in general? A mature version of the pragmatic maxim says: “A belief in a proposition is a controlled and contented habit of acting in ways that will be productive of desired results only if the proposition is true” (“Kaina stoicheia” (New Elements), 1901(?), EP II, 312).²⁹ The subtype of habits which are beliefs are now those subject to control (cf. Chapter 18). This is obviously a different criterion from that of the 1878 pragmatic maxim where the defining feature of beliefs as habits were awareness and assuaging of doubt. Importantly, these structures give rise to a couple of corollaries. One is the mirror definition of doubt as something which is only real if it actually breaks an already existing belief. Already from the Metaphysical Club period, Peirce refuses “parade” doubt,³⁰ which may be expressed explicitly but which is not evidenced by hesitation or changed behavior, that is, without real effects upon habit. The pragmatic maxim is therefore also a means to distinguish real doubt from parade doubt: “A true doubt is accordingly a doubt which really interferes with the smooth working of the belief-habit. Every natural or inbred belief manifests itself in natural or inbred ways of acting, which in fact constitute it a belief-habit. (I need not repeat that I do not say that it is the single deeds that constitute the habit. It is the single ‘ways,’ which are conditional propositions, each general)” (“Consequences of Critical Common-Sensism”, 1905, CP 5.510). We remark in passing that belief-habits may be inbred and are thus not subject to explicit control, unlike beliefs in the 1904 quote above. Another corollary is the realization that the existence of conscious habits necessitates that the mind has direct access to general objects, that is, not fully determined objects—not unlike Husserl’s notion of “categorical intuition”:

Acquired Habits, Innate Habits, Laws

29

We can understand one habit by likening it to another habit. But to understand what any habit is, there must be some habit of which we are directly conscious in its generality. That is to say, we must have a certain generality in our direct consciousness. Bishop Berkeley and a great many clear thinkers laugh at the idea of our being able to imagine a triangle that is neither equilateral, isosceles, nor scalene. They seem to think the object of imagination must be precisely determinate in every respect. But it seems certain that something general we must imagine. (…) At any rate, I can see no way of escaping the proposition that to attach any general significance to a sign and to know that we do attach a general significance to it, we must have a direct imagination of something not in all respects determinate (footnote added to “Fixation of Belief”, 1893, CP 5.371).³¹

Habit was introduced in order to understand structures of the mind which transcend immediate consciousness. But the fact that the mind is able to make conscious (some of) those habit structures has important consequences for the contents also of immediate consciousness. The fact that it is indeed possible to be aware of a habit is thus of central importance: this necessitates the controversial existence of not-fully determined, that is, general, representations. To sum up, habit is a conditional, general proposition, realist in the sense that it covers an indefinite series of possible instantiations, which, given the appearance of a particular occasion of a certain general description, leads to action, generally described. Explicit beliefs, as a subset of belief-habits, are also subject to awareness and to control.

Acquired Habits, Innate Habits, Laws Until now, we have implicitly assumed that habit is something generalized from the human mind to cover other types of biological cognition, such as in the frog example. But as so often with Peirce, generalization must be driven as far as possible. A controversial and pretty consistent implication of the Habit doctrine is that habit not only extends to animals but also spans across the received innate/acquired distinction, coming out of the principle of using … the word “habit,” without any implication as to the time or manner in which it took birth, so as to be equivalent to the corrected phrase “habit or disposition,” that is, as some general principle working in a man’s nature to determine how he will act, then an instinct, in the proper sense of the word, is an inherited habit, or in more accurate language, an inherited disposition. But since it is difficult to make sure whether a habit is inherited or is due to infantile training and tradition, I shall ask leave to employ the word “instinct” to cover both cases (Minute Logic, 1902, CP 2.170).

30

Chapter 2: Dicisigns and Habits

This, however, is not only a façon-de-parler, rather it is an ontological claim which insists that there is no principal difference between habits acquired during the phylogenetic course of evolution and habits acquired in the ontogenetic development of the individual: “The old writers call [them] dispositions, but I do not think there was any advantage in calling them by a separate name, but rather the reverse. Some call them ’hereditary habits’. If they are that, they are innate” (“Materials for Monist article”, 1905, R 288, 65 – 67). The basic idea that one of the essential elements of every possible mind is habit excludes the possibility that habits as such could comprise accidental developments during individual lifetime only: … every animal must have habits. Consequently, it must have innate habits. In so far as it has cognitive powers, it must have in posse innate cognitive habits, which is all that anybody but John Locke ever meant by innate ideas. To say that I hold this for true is implied in my confession of the doctrine of Common-Sense—not quite that of the old Scotch School, but a critical philosophy of common-sense. It is impossible rightly to apprehend the pragmaticist’s position without fully understanding that nowhere would he be less at home than in the ranks of individualists, whether metaphysical (and so denying scholastic realism), or epistemological (and so denying innate ideas) (“Consequences of critical CommonSensism”, 1905, CP 5.540).

Thus, Peircean habit does not comprise patterns of behavior acquired in the ontogenetic timescale of individual organisms only, but also patterns of behavior acquired in phylogenetic timescale of the lineages of species.³² Despite the fact that the “narrow” interpretation of habit to cover only the former is widespread, even to the degree that it forms a prejudice of our time, the biosemiotic idea that there is no deep ontological distinction between the two is supported by Peirce’s argument. Inherited habits, thus, form implicit conditional propositions ready to give inference-to-action when perceptual occasion adds the relevant minor premise needed. Given that Peircean habits thus pervade biology, the next issue called for by tentative generalization is whether they extend further into the pre-biological, purely physical universe as well. Immediately, there is a tendency to the exact opposite, to strongly contrast habits to physical laws. In Peirce’s first major outline of a cosmology, the “Guess at the Riddle” (1887), he describes habits in terms of neurophysiology, generalizing the frog example and anticipating Hebb’s law that connections used are connections strengthened: “Fourth, if the same cell which was once excited, and which by some chance had happened to discharge itself along a certain path or paths, comes to get excited a second time, it is more likely to discharge itself the second time along some or all of those paths along which it had previously discharged itself

Acquired Habits, Innate Habits, Laws

31

than it would have been had it not so discharged itself before. This is the central principle of habit; and the striking contrast of its modality to that of any mechanical law is most significant. The laws of physics know nothing of tendencies or probabilities; whatever they require at all they require absolutely and without fail, and they are never disobeyed. Were the tendency to take habits replaced by an absolute requirement that the cell should discharge itself always in the same way, or according to any rigidly fixed condition whatever, all possibility of habit developing into intelligence would be cut off at the outset; the virtue of Thirdness would be absent” (W 6, 191; CP 1.390). The “Law of Mind” cosmology of the first series of Monist papers around 1892 further sophisticates that point: The law of habit exhibits a striking contrast to all physical laws in the character of its commands. A physical law is absolute. What it requires is an exact relation. Thus, a physical force introduces into a motion a component motion to be combined with the rest by the parallelogram of forces; but the component motion must actually take place exactly as required by the law of force. On the other hand, no exact conformity is required by the mental law. Nay, exact conformity would be in downright conflict with the law; since it would instantly crystallize thought and prevent all further formation of habit. The law of mind only makes a given feeling more likely to arise. It thus resembles the “non-conservative” forces of physics, such as viscosity and the like, which are due to statistical uniformities in the chance encounters of trillions of molecules (“The Architecture of Theories”, 1891, CP 6.23).

Here, the bottom-line contrast, however, is more precisely that between conservative and non-conservative physical laws. The former are defined by dealing with those forces, like gravity, whose work on an object between two points is independent of the trajectory taken; the latter comprising, in particular, cases involving friction, thus the statistical laws of thermodynamics. This argument is allied to Peirce’s simultaneous idea of the objective existence of chance—the absence of “exact conformity” being responsible for merely statistical tendencies on the one hand as well as the possibility of development of novelty on the other. Thus, conservative laws are not habits while non-conservative laws are. But already in the same paper series, Peirce famously continues the generalization of the habit concept in the famous exclamation that “… what we call matter is not completely dead, but is merely mind hidebound with habits” (“The Law of Mind”, 1892, EP 1, 331; CP 6.158). But then physical laws, even pertaining to conservative forces, are also habits, only very strict or stiff habits. Similar ontological ideas stabilize after the 1897 adoption of the idea of the objective reality of “real possibilities” or “would-bes”, e. g., in the Minute Logic: “For every habit has, or is, a general law” (1902, CP 2.148). Thus, a mere physical probability, such

32

Chapter 2: Dicisigns and Habits

as that of a die, is now “quite analogous” to human habits, the difference being only one of degrees of simplicity: … the “would-be” of the die is presumably as much simpler and more definite than the man’s habit as the die’s homogeneous composition and cubical shape is simpler than the nature of the man’s nervous system and soul; and just as it would be necessary, in order to define a man’s habit, to describe how it would lead him to behave and upon what sort of occasion—albeit this statement would by no means imply that the habit consists in that action—so to define the die’s “would-be,” it is necessary to say how it would lead the die to behave on an occasion that would bring out the full consequence of the “would-be”; and this statement will not of itself imply that the “would-be” of the die consists in such behavior (Notes on “Doctrine of Chances”, 1910, CP 2.664).

The binary oppositions of habits vs. laws of the period around 1890 thus seems to give way to a more continuous conception according to which natural laws and human habits are but ends of one large, generalized continuum of “would-be’s”, only differing in complexity and plasticity. Thus, in the mature Peirce, we face a habit continuum along the lines of: conservative physical laws → non-conservative physical laws → innate biological patterns of behavior → acquired biological patterns of behavior → deliberately acquired human patterns of behavior → deliberately acquired human patterns of thought (beliefs) ³³

with increasing plasticity, and where the former influence the latter but do not fully determine them. Oftentimes, however, more “narrow” habit concepts in Peirce may still be used to single out selected later phases of this series. Still, a seminal difference seems to prevail between the physical and the biological phases of the continuum depicted. Biological habits serve a semiotic function because they implicitly describe certain possible environmental conditions, the actualization of which will trigger organism action with the local purpose of survival. Purely physical habits hardly could be said to serve such functions (if we do not subscribe to teleological theories of the whole of cosmos, as Peirce indeed sometimes did). Even if it is possible to render the gravitational pull between objects as a conditional proposition: “Object A is heavy, and if another heavy Object B appears, there will be a gravitational force between them proportional to the product of their masses”, this may be a quasi-proposition but hardly serves any clear function in itself, except when appearing in the Umwelt of some organism.³⁴ An important idea based on the plasticity increase along the habit continuum above is that of the variation of habits, becoming more and more crucial to Peirce. Within biology, this gives rise to the idea that human reason is more plastic than the reasoning of lower animals—making it more prone to error than rea-

Acquired Habits, Innate Habits, Laws

33

soning in simpler species, but at the same time functioning as a precondition of intellectual growth (cf. also Chapter 19): It is a truth well worthy of rumination that all the intellectual development of man rests upon the circumstance that all our action is subject to error. Errare est humanum is of all commonplaces the most familiar. Inanimate things do not err at all; and the lower animals very little. Instinct is all but unerring; but reason in all vitally important matters is a treacherous guide. This tendency to error, when you put it under the microscope of reflection, is seen to consist of fortuitous variations of our actions in time. But it is apt to escape our attention that on such fortuitous variation our intellect is nourished and grows. For without such fortuitous variation, habit-taking would be impossible; and intellect consists in a plasticity of habit (“Detached Ideas, Causation and Force”, 1898, CP 6.86).

Habit-taking thus considered along Darwinian lines as the combination of variation and selection places an increasing emphasis not only on the initial establishment of habits, but also on the subsequent development and changes of them. This is also connected to an important development in Peirce’s logic, namely the sophistication of the concept of deduction which would lead, ultimately, to the important corollarial/theorematic distinction after the turn of the century. A basic idea here is that deduction has been erroneously simplified, generalizing from syllogisms where there is but one deductive conclusion to be inferred—giving the received Kantian impression that there is nothing in the conclusion which was not already clearly there in the premises, and that deduction is thus algorithmically automatable, if not trivial.³⁵ But as Peirce realizes, in axiomatic systems, there is nothing like “the conclusion”: There is but one conclusion of any consequence to be drawn by ordinary syllogism from given premisses. Hence, it is that we fall into the habit of talking of the conclusion. But in the logic of relatives there are conclusions of different orders, depending upon how much iteration takes place. What is the conclusion deducible from the very simple first principles of number? It is ridiculous to speak of the conclusion. The conclusion is no less than the aggregate of all the theorems of higher arithmetic that have been discovered or that ever will be discovered (“Detached Ideas, The First Rule of Logic”, 1898, CP 5.579).

Consequently, even deductive inferences imply the need for the variation of inference habits—seeking by trial-and-error the comparison and selection between a variety of different possible proof trajectories. This also considerably complicates the pragmatic core idea that the meaning of a conception is the set of conceivable effects and correlated action habits—for the sum of those effects may, for a given conception, such as “the first principles of number” be far from simple and fully realized only in an idealized future.³⁶

34

Chapter 2: Dicisigns and Habits

Habit Straddling the Unconscious/Conscious Distinction The most complicated and open issue, however, in Peirce’s lifelong habit discussion, concerns the degree to which habits, in the narrower biological and human senses of the word, are subject to awareness, consciousness, deliberation, and self-control. We have already explored the idea that beliefs are not those habits that are propositions; they are, rather, habit propositions subjected to control. As to belief in particular, Peirce’s standard conception was that it is “something that we are aware of” as we saw in “How to Make our Ideas Clear” (1878). This, however, is subject to many qualifications and even contradictions. This seems to have to do with the Scotist roots of Peirce’s conception of habit. In his famous early articulation of his “scholastic realism”, Peirce wrote in 1871, addressing Scotus’ solution to the problem of universals: … it may be asked, first, is it necessary to its [the universal’s] existence that it should be in the mind; and, second, does it exist in re? There are two ways in which a thing may be in the mind,—habitualiter and actualiter. A notion is in the mind actualiter when it is actually conceived; it is in the mind habitualiter when it can directly produce a conception. It is by virtue of mental association (we moderns should say), that things are in the mind habitualiter. In the Aristotelian philosophy, the intellect is regarded as being to the soul what the eye is to the body. The mind perceives likenesses and other relations in the objects of sense, and thus just as sense affords sensible images of things, so the intellect affords intelligible images of them. It is as such a species intelligibilis that Scotus supposes that a conception exists which is in the mind habitualiter, not actualiter (Review of Fraser’s Works of Berkeley, 1871, EP I, 92; CP 8.18).

Thus, Peirce’s conception of how a habit inhabits the mind is derived from the Scotist theory of universals: the habit simply is the way that a universal is in the mind, for the universal—just like its regularity counterpart in reality—is not exhausted by any actual occurrence in the mind of conscious tokens of it.³⁷ So, it forms part of the mind’s structure, also when it is not present to the mind. But this implies the surprising consequence that this habitual existence does not depend upon consciousness: “This species is in the mind, in the sense of being the immediate object of knowledge, but its existence in the mind is independent of consciousness” (Review of Fraser’s Works of Berkeley, 1871, EP I, 92; CP 8.18). This holds important consequences for Peirce’s realism, but also for our actual interest in the mode of existence of habits in the mind: “… to say that an object is in the mind is only a metaphorical way of saying that it stands to the intellect in the relation of known to knower” (Review of Fraser’s Works of Berkeley, 1871, EP I, 92; CP 8.18). But as the existence of habits is independent of consciousness, this knowledge of habits must be unconscious or potential.

Habit Straddling the Unconscious/Conscious Distinction

35

Already in 1867, Peirce had insisted on the threefold character of Scotus’ distinction: “I adopt the admirable distinction of Scotus between actual, habitual, and virtual cognition” (W 1, 75, n.; CP 2.398, n.). Virtual cognition comprises the whole universe of possible forms that the mind may possibly address; an example lies in the fact discussed above that certain implications in the ultimate meaning of a conception may be logically possible but never reached, neither actually nor by the (use of the) existing habits concerning the meaning: … I do not think that the import of any word (except perhaps a pronoun) is limited to what is in the utterer’s mind actualiter, so that when I mention the Greek language my meaning should be limited to such Greek words as I happen to be thinking of at the moment. It is, on the contrary, according to me, what is in the mind, perhaps not even habitualiter, but only virtualiter, which constitutes the import. To say that I hold that the import, or adequate ultimate interpretation, of a concept is contained, not in any deed or deeds that will ever be done, but in a habit of conduct, or general moral determination of whatever procedure there may come to be, is no more than to say that I am a pragmaticist (“Consequences of critical Common-Sensism”, 1905, CP 5.504).

The triad of actual, habitual, and virtual may be resumed as follows: actualiter are the Greek words or sentences I may be processing at any given moment; habitualiter is my general knowledge of Greek, and virtualiter is the whole of the Greek language, including those parts I never learnt. So, the Scotist distinction between virtualiter, actualiter, and habitualiter cognition—to resume the three in the order of Peirce’s categories—may be explained using, again, the logical example of inference from habit: Habitualiter: an empirical thought habit may be: “If it lightnings, then it thunders”. Actualiter: any existing occurrence of lightening to the mind is an actual cognition. Virtualiter: the combination of the two may lead to the conclusion: “it thunders”. But even if the mind in question holds the habit mentioned and actually has the experience cited, there is no guarantee that the relevant conclusion will be drawn—it thus may remain virtual. In the pragmatic maxim meaning definition, we may surmise that many among the sum of the conceivable effects of a given conception will, at any point of time, remain virtual only. And to say that virtual cognitions, even if logically implied by a presently conscious cognition, are in any sense “in the mind”, may be to stretch the point beyond normal usage—which may be why Peirce sometimes mentions two out of the Scotist trichotomy only (on Peirce’s extravagant concept of “mind”; cf. Chapter 18). Actual cognitions are thus taken to be conscious, at least in general, while virtual cognitions are not. Habitual cognitions are more than their actual, conscious instantiations and thus have an unconscious basis; but they may, on the other hand, become conscious as objects of deliberate consideration. Thus, as to the def-

36

Chapter 2: Dicisigns and Habits

inition of belief as a thought-habit, Peirce is bewilderingly inconsequent as to its deliberate, conscious, self-controlled character—which had seemed so clear in the 1878 pragmatic maxim version. Suffice it to compare the following later quotes: A belief is a habit; but it is a habit of which we are conscious. The actual calling to mind of the substance of a belief, not as personal to ourselves, but as holding good, or true, is a judgment. An inference is a passage from one belief to another; but not every such passage is an inference (“How to Reason, Essence of Reasoning, Chapter 6”, 1893, CP 4.53). A belief need not be conscious. When it is recognized, the act of recognition is called by logicians a judgment, although this is properly a term of psychology. A man may become aware of any habit, and may describe to himself the general way in which it will act. For every habit has, or is, a general law. (…) What particularly distinguishes a general belief, or opinion, such as is an inferential conclusion, from other habits, is that it is active in the imagination (Minute Logic, 1902, CP 2.148). The purpose of reasoning is to proceed from the recognition of the truth we already know to the knowledge of novel truth. This we may do by instinct or by a habit of which we are hardly conscious. But the operation is not worthy to be called reasoning unless it be deliberate, critical, self-controlled. (“Logical Tracts no. 2”, 1903, CP 4.476). Belief is not a momentary mode of consciousness; it is a habit of mind essentially enduring for some time, and mostly (at least) unconscious; and like other habits, it is (until it meets with some surprise that begins its dissolution) perfectly self-satisfied. (…) a process of self-preparation will tend to impart to action (when the occasion for it shall arise), one fixed character, which is indicated and perhaps roughly measured by the absence (or slightness) of the feeling of self-reproach, which subsequent reflection will induce (“What Pragmatism Is”, 1905, EP II, 337; CP 5.417). … habit is by no means exclusively a mental fact. Empirically, we find that some plants take habits. The stream of water that wears a bed for itself is forming a habit. Every ditcher so thinks of it. Turning to the rational side of the question, the excellent current definition of habit, due, I suppose, to some physiologist (if I can remember my bye-reading for nearly half a century unglanced at, Brown-Sequard much insisted on it in his book on the spinal cord), says not one word about the mind. Why should it, when habits in themselves are entirely unconscious, though feelings may be symptoms of them, and when consciousness alone—i.e., feeling—is the only distinctive attribute of mind? (“Pragmatism”, 1907, EP II, 418; CP 5.492).

The chronological organization of these quotes may give the idea that the emphasis on the basically unconscious status of habits (including beliefs) is growing over Peirce’s mature period. There are, however, also counterexamples during that period (“[Readiness] to act in a certain way under given circumstances and when actuated by a given motive is a habit; and a deliberate, or self-controlled, habit is precisely a belief”, “Pragmatism”, 1907, CP 5.480), but the tendency does indeed go in the direction of the doctrine that habits as well as beliefs are basically unconscious, even if they may give rise to conscious feelings when instantiated. Habits themselves may, however, become the object of consciousness

Habit Straddling the Unconscious/Conscious Distinction

37

—as in the important case of the deliberate adoption of habits, in thought as in action. Adoption of habits may take place inductively, the habit being established by the repetition of similar acts, which are not necessarily deliberate and conscious —or it may take place by deliberate, conscious, imaginative experimentation in the mind, ensued by deliberate decision, akin to addressing an order to the future self which is, necessarily conscious (“Pragmatism”, 1907, EP II, 413; CP 5.487). Only the latter, the deliberate and conscious inference of one proposition from another, qualifies as reasoning, as Peirce repeatedly insists; cf. Chapter 18. The automatized drawing of inferences in a mechanical logic machine, however refined, will never be but quasi-inferences because they lack the quality of deliberate, conscious self-control. Thus, the very role of consciousness in mind is to make possible that increased level of self-control which characterizes real reasoning: “… I am far from holding consciousness to be an “epiphenomenon”, though the doctrine that it is so has aided the development of science. To my apprehension, the function of consciousness is to render self-control possible and efficient”, (“Pragmatism”, 1907, R 318, 74– 76). But human beings do lots of things which are not at all characterized by deliberate, conscious self-control. To repeat the nested series of processes from the above section: conservative physical laws → non-conservative physical laws → innate biological patterns of behavior → acquired biological patterns of behavior → deliberately acquired human patterns of behavior → deliberately acquired human patterns of thought (beliefs)

Human beings, of course, partake in all of them, and only a part of the latter small subset qualifies as reasonings. This would explain Peirce’s seeming vacillation as to the conscious status of habits and beliefs: the crucial subset of reasonings require conscious deliberation but human beings constantly acquire, follow, and change many habits and beliefs without this underpinning by explicit reasoning. Peirce’s criterion for reasoning as the subject of deliberate, conscious selfcontrol is only really developed from around 1902 (Minute Logic), figuring centrally in the 1903 Pragmatism lectures and the last Monist papers series. In 1905, Peirce dates, a bit hesitant, the appearance of the idea of ethical constraints on logic, based on the self-control criterion of reasoning, as late as to the 1903 Lowell Lectures (“Consequences of critical Common-Sensism”, 1905, CP 5.533), and it certainly takes center stage only from around 1902. The discussions around that criterion open a bundle of questions which we shall approach as a conclusion:

38

Chapter 2: Dicisigns and Habits

1)

What is the relation between consciousness and self-control? … the former as a special tool serving the latter. 2) How is self-control developed? … the hierarchy of levels of self-control. 3) What is the relation between self-control more generally and self-control of logical thought in particular? 4) What is the status of the final action habit claimed by the pragmatic maxim as the ultimate meaning of conceptions?

Self-Control and Consciousness We saw how Peirce’s mature theory of consciousness simply makes it a tool for efficient-self-control. Self-control thus is a wider phenomenon which has consciousness as one of its higher-level instruments. Connected to this is the realization that conscious control can only encompass certain highlighted steps of inference, not all of their preconditions all the way to the bottom. Consciousness, as a mark of deliberate reasoning, could never require full perspicuity as to all levels, preconditions, and implications of reasoning. This is indicated, of course, by the logica utens/logica docens distinction: only the scientific logician makes of logic an explicit doctrine; normal reasoners, including scientists and mathematicians, makes do with their logica utens that does not necessarily include access or appeal to the explicit formulation of logical rules and principles. So, deliberate, conscious self-criticism is taken to be possible with less than logica docens. Thus, reasoning normally makes do with a triple fundament of “perceptual judgments, original (being indubitable because uncriticized) beliefs of a general and recurrent kind, as well as indubitable acritical inferences” (“Issues of Pragmaticism”, 1905, EP II, 348; CP 5.442)—none of them subject to conscious self-control. The latter two are in the mind only habitualiter—that is, not necessarily in the conscious present, and the former, perceptual judgments, appear in the mind unconditionally, beyond criticism and must be taken at face value (of course, certain perceptual judgments may be criticized, but only on the basis of other such judgments which then lie beyond conscious control): … to say that an operation of the mind is controlled is to say that it is, in a special sense, a conscious operation; and this no doubt is the consciousness of reasoning. For this theory requires that in reasoning we should be conscious, not only of the conclusion, and of our deliberate approval of it, but also of its being the result of the premiss from which it does result, and furthermore that the inference is one of a possible class of inferences which conform to one guiding principle. Now in fact we find a well-marked class of mental operations, clearly of a different nature from any others which do possess just these properties. They alone deserve to be called reasonings; and if the reasoner is conscious, even vaguely,

Self-Control and Consciousness

39

of what his guiding principle is, his reasoning should be called a logical argumentation. There are, however, cases in which we are conscious that a belief has been determined by another given belief, but are not conscious that it proceeds on any general principle. Such is St. Augustine’s “cogito, ergo sum.” Such a process should be called, not a reasoning, but an acritical inference. Again, there are cases in which one belief is determined by another, without our being at all aware of it. These should be called associational suggestions of belief (Issues of Pragmaticism, 1905, EP II, 348; CP 5.441)

So, there are vast amounts of inference habits which are not subjected to conscious control (but may, of course, later be so subjected) and thus not proper logical reasoning, and even within such reasoning, the guiding principle may be the subject of vague acceptance only. Peirce obviously does not want normal scientists, those with little or no acquaintance with explicit formal logic, to be bereft of reasoning abilities, so he admits sufficient conscious control to remain just vague (for more on this, see Chapter 18). On the other hand, self-control is a far wider subject than pertaining to logical inference habits only; it potentially addresses all other types of habits, particularly moral habits of which logical norms are taken to be a special example only: “… while I hold all logical, or intellectual, interpretants to be habits, I by no means say that all habits are such interpretants. It is only self-controlled habits that are so, and not all of them, either” (“Pragmatism”, 1907; EP II, 431). Thus, logical reasoning is but a subtype of the last category of the continuum above: deliberately acquired human patterns of thought (beliefs) → logical reasonings

It comes as no surprise that the structure of deliberately establishing new habits by means of logical reasoning in the broad sense is co-extensive with scientific epistemology: In the process of inference, or the self-controlled formation of new belief on the basis of Knowledge already possessed, I remark three chief steps. They are, first, the putting together of facts which it had not occurred to us to consider in their bearings upon one another, second, experimentation, observation, and experimental analysis, which is substantially the same process whether it be performed with physical apparatus such as the chemist uses or with an apparatus of diagrams of our own creation, such as the mathematician employs, and third, the generalization of experimental results, that is, the recognition of the general conditions governing the experiment, and the formation of a habit of thought under the influence of it (“Three steps in inference”, no date but late, as Peirce speaks about having studied logic for 40 years; CP 7.276).³⁸

The deliberate, conscious formation of a habit of thought is the very fruit of scientific investigation.

40

Chapter 2: Dicisigns and Habits

The Status of the Final Action Habit—A Proposition or Not? Even if an explicit conclusion in the shape of a conscious, deliberately assented proposition is one type only among self-controlled habits, it takes a special position in Peirce’s works because it is the condition for science and thus is a central subject for logical and epistemological investigation. But here, a particular conundrum appears. The pragmatic maxim, in its different guises, identifies the final meaning of any conception with the bundle of action habits which the truth of that conception would ultimately give rise to. But is that set of action habits, in itself, a sign? Peirce tends to answer “no”. Being a fact, of course, such an action habit will still possess the structure of a proposition, but it will not, in itself, be a sign. The idea seems to be that ever so long chains, hierarchies, and diagrams of logical inferences serve, in the last resort, the arc taking us from perceptual judgment to action, two outer ends not in themselves logical: The real and living logical conclusion is that habit; the verbal formulation merely expresses it. I do not deny that a concept, proposition, or argument may be a logical interpretant. I only insist that it cannot be the final logical interpretant, for the reason that it is itself a sign of that very kind that has itself a logical interpretant. The habit alone, which though it may be a sign in some other way, is not a sign in that way in which that sign of which it is the logical interpretant is the sign. The habit conjoined with the motive and the conditions has the action for its energetic interpretant; but action cannot be a logical interpretant, because it lacks generality. The concept which is a logical interpretant is only imperfectly so. It somewhat partakes of the nature of a verbal definition, and is as inferior to the habit, and much in the same way, as a verbal definition is inferior to the real definition. The deliberately formed, self-analyzing habit—self-analyzing because formed by the aid of analysis of the exercises that nourished it—is the living definition, the veritable and final logical interpretant. Consequently, the most perfect account of a concept that words can convey will consist in a description of the habit which that concept is calculated to produce. But how otherwise can a habit be described than by a description of the kind of action to which it gives rise, with the specification of the conditions and of the motive? (“Pragmatism”, 1907, EP II, 418; CP 5.491)

But, as Hookway says (2009, 26 – 27): the very verbal description of the habit implied by the pragmatic maxim is, in itself, conceptual and thus a sort of further logical interpretant of it. In that sense, the action habit could not be the final logical interpretant. The same tension is present in the complicated Peirce quote just given: the central argument that “action cannot be a logic interpretant, because it lacks generality”. The conclusion of the habit inference, however, as discussed above, is no single action event. It is a general structure surpassing any number of such events. And that is exactly what the end of the quote addresses: a kind of action. Action is the dynamic interpretant, the conception of action is the logical

Habits and Dicisigns Revisited

41

interpretant. So it must be in another sense that the action habit is the final logical interpretant. The issue is not made simpler, obviously, by the fact that those ultimate action habits defining meaning also comprise cognitive action habits, that is, habits of thought. Pietarinen and Bellucci (2016, 278 – 279) rightly argue that in the special but central case of the leading principle of an inference, the explicit expression of that principle (taking it from logica utens to docens, so to speak) is, in a certain sense superfluous: “To regard a habit as a sign is analogous to regard the leading principle of reasoning as a premise of reasoning: by some sort of deduction theorem one can always express the leading principle (logical rule) as a conditional proposition (logical proposition), but as he had shown already in 1867, nothing is gained by so doing when the leading principle is logical, for the very same principle will be governing the new argument thereby obtained. In semeiotical terms, in reasoning no final logical interpretant can be considered as a sign without employing in this reasoning that very same logical interpretant”. This might give us the clue also to the final logical interpretant of thought signs in general.³⁹ The finality of the set of action habits should rather be seen from the perspective that they furnish the final arbiter of truth of the proposition of which they serve as interpretants. If any of those habits fail in some respect, it will be a sign there is something to be investigated about the relevant proposition.

Habits and Dicisigns Revisited This long development finally paves the way for our conclusion as to the relation between habits and propositions. Habits, in general, are articulated with the structure of conditional propositions—this includes even non-biological, conservative, physical laws. This does not make them propositions: consider Peirce’s definition of fact as a part of reality having the structure of a proposition (but not in itself being a proposition). As to the biological/human habit types of innate habits, acquired habits (specifications of more general innate habits), deliberately acquired habits, and so on, these will also be structured as conditional propositions. Animal and human behaviors, according to this analysis, have propositional structure, and a significant part of them, whether conscious or not, qualify as beliefs—the decisive criterion here being whether they articulate the double habit structure so that they themselves constitute rule-bound signs, in turn, referring to other rule-bound habits in their objects. This result probably, from the point of view of the parsimonious ontologist, gives us a vastly overpopulated universe. Why couldn’t we just do with a universe

42

Chapter 2: Dicisigns and Habits

of individual objects, while human minds take care of the analyses of those singular objects in terms of similarities, habits, laws, signs, propositions, inferences, etcetera? The basic reason is that such a universe is ineradicably dualist, and what is worse, strange. Throwing most of the complexity of the cosmos into the human mind, leaving only individual existents out there, gives us two radically different and incommensurable parts of that cosmos, that is, the human mind and the rest. It makes of the human mind a strange exception, constituting a small zoo of all sorts of objects otherwise denied existence in the “rest” universe: general objects, propositions, inferences, habits, etc. Such dualism not only invents a lot of epistemological puzzles hard if not impossible to solve; it also makes it difficult to envisage how the human mind with all its complexity could ever have evolved out of that naked universe. Thus, Peirce’s conception is deep down motivated by his naturalist monism. As to habits, it is monism that make him construct the habit chain of being, connecting regularities, spanning from conservative physical laws in one end of the chain and conscious human habit-taking in the other. As to propositions, it is monism that takes us from facts—structured like propositions—in one end of the chain, to fully-fledged, deliberately adopted, explicitly expressed proposition signs in the other. So, the basic motivation is naturalism. Thus, Peirce may serve as a possible inspiration for actual naturalism attempts, reminding us that naturalism may not necessarily give us a very simple ontology, rather the opposite. But why should it not? Chemistry progressed only when it realized that the number of elements exceeded four.

Chapter 3 Peirce’s Theories of Assertion A man first comes to the study of logic with an immense multitude of opinions upon a vast variety of topics; and they are held with a degree of confidence, upon which, after he has studied logic, he comes to look back with no little amusement. “The Regenerated Logic”, 1896, CP 3.432

It is fairly easy to give a brief account of the mature Peirce’s standard view of assertion, that is, after the many theoretical developments of the fertile 1902– 1904 period—the sixth and seventh phases of the development of Peirce’s semiotics, in Francesco Bellucci’s recent count (Bellucci 2017). In Reason’s Rules (1902), e. g., it goes like this: “… to assert a proposition is to make oneself responsible for its truth”.⁴⁰ It ties into the idea that propositions are general ideas and do not, in themselves, perform any action. They may, however, be put to use in concrete tokens in a number of different act types, utterances, questions, orders, wishes, beliefs, etc.—prominent about those being the act type of asserting a proposition. This, of course, amounts to the germ of a Peircean speech act theory in which the act of asserting a proposition in public differs, in particular, from the act of personally believing the same proposition to be true in private, an act also covered by concepts such as belief, judgment, and assent. Thus, it is possible to assert a proposition simultaneously with not assenting to it, that is, lying.⁴¹ This, however, also indicates that it would be a vain endeavor to try to define Peirce’s concept of assertion in isolation. Rather, it belongs to a considerable conceptual cluster charting the whole field of possibly truth-involving expressions and utterances, situated between logic, philosophy of logic, semiotics, pragmatics (or “speculative rhetorics” as Peirce would have it) and philosophy of science—a conceptual field involving terms like judgment, belief, assent, resolve, proposition, corollary, theorem, affirmation, claim, thought, thinking, fact, truth, reality, and several more. This chapter attempts to give an overview over Peirce’s development behind the mature standard view as well as to place that standard view in the context of the conceptual cluster mentioned—an overview which also gives occasion to noting certain tensions and even unresolved issues.

Assertion from Colloquial to Technical Term In much of Peirce’s early and middle period up to the mid-1890s, “assertion” is not singled out as a technical term but is rather used interchangeably with “proposihttps://doi.org/10.1515/9783110793628-005

44

Chapter 3: Peirce’s Theories of Assertion

tion” or even “judgment”, implying that, in this period, Peirce rarely considered the distinction between the structure and content of propositions on the one hand, and their utterance and force to claim truth on the other.⁴² Rather, he took for granted that it was part and parcel of a proposition itself to possess some sort of illocutionary force, often localized in the copula. As is well known, Peirce focused upon investigating and formalizing the relations and structure of propositions in his versions of propositional logic and first order logic in the two “Algebra of Logic” papers (1880 – 1885); among the other terms of the propositional concept cluster which Peirce develops in the early period, particularly that of belief stands out, to continue to play an important role also in his ensuing development (see Chapter 2). Famously, the definition of “belief” is crucial to the classic formulations of pragmatism in Peirce’s 1877– 1878 Popular Science Monthly paper series, developing further Alexander Bain’s quip “Belief is that upon which man is prepared to act”. That idea had been much discussed among Peirce, William James, Chauncey Wright, Oliver Wendell Holmes, and Nicholas St. John Green in their “Metaphysical Club” around 1870. In “How to Make our Ideas Clear”, Peirce found that belief “… has just three properties: First, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit” (EP I, 129; CP 5.397). The latter property, of course, constitutes pragmatism’s core idea that the meaning of a proposition lies in the conception of its effects having practical bearings, as stated in the “pragmatic maxim” (EP I, 132; CP 5.402). So, “the whole function of thought is to produce habits of action”, and “what a thing means is simply what habits it involves” (EP I, 131; CP 5.400). Real belief involves a readiness to act as if the involved proposition were true; ideas which do not entail such readiness may appear to be a sort of beliefs, they may even be believed to be beliefs, but they are not really beliefs. Thinking and mental habit-taking are thus one and the same thing, and the process of acquiring propositional insight by habit-taking should go on to form a relatively stable cornerstone in Peirce’s ongoing charting of the propositional field. It is important to note that in another of the 1878 pragmatism papers, Peirce already connects this action interpretation of belief propositions to his idea that the real, active proponent of science is the scientific community rather than the individual scholar: “… death makes the number of our risks, of our inferences, finite, and so makes their mean result uncertain. The very idea of probability and of reasoning rests on the assumption that this number is indefinitely great” (“The Doctrine of Chances”, 1878, EP I, 249; CP 2.654). This tension is resolved by merging the individual researcher into the continuum of existing and possible future scientists and by coupling our limited number of individual lifetime inferences into the in-

Assertion from Colloquial to Technical Term

45

definite series of future research. In that sense, “… our interests shall not be limited. They must not stop at our own fate, but must embrace the whole community. This community, again, must not be limited, but must extend to all races of beings with whom we can come into immediate or mediate intellectual relation. It must reach, however vaguely, beyond this geological epoch, beyond all bounds”. This beautiful Enlightenment idea about individual beliefs as finite building blocks of an infinite quest shall continue to inform the development of Peirce’s charting of the propositional field. Not much later, in his paper formalizing propositional logic, “On the Algebra of Logic” (1880), Peirce makes the following distinction: A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a belief. The representation to ourselves that we have a specified habit of this kind is called a judgment. A belief-habit in its development begins by being vague, special, and meagre; it becomes more precise, general, and full, without limit. The process of this development, so far as it takes place in the imagination, is called thought (W 4, 164; CP 3.160).

Here, an important vacillation is introduced, as to the degree of awareness which is required to entertain a belief. Habits are not necessarily conscious, rather most of them are not, but the special habit subtype of belief seems different. In 1878, a requirement for belief was that the believer was aware of it; now, more cautiously, judgment is defined as one’s representation to oneself that one has this or that belief—the implication being that the latter needs not, in itself, be the object of awareness or consciousness. This tension should occupy Peirce many times in the years to come; cf. Chapters 2 and 18. In the early and mid-1890s, working on the unfinished “Grand Logic” and “Short Logic”, Peirce returns to the propositional field and the idea, originally introduced in the “Algebra of Logic” papers, that the erasure of the subject indices of a proposition, be it expressed in a diagram or in a sentence, yields the result of a naked predicate structure with the small difference that “It differs from a relative term only in retaining the ‘copula,’ or signal of assertion” (“The Critic of Arguments”, 1892, CP 3.420). Here Peirce, in the passing, identifies the copula of a proposition as the sign of assertion, a widespread idea in the philosophy of logic at the time. At the same time, he expands on the idea: the copula in an assertion represents the experience which forces the specific combination of subject and predicate in a proposition: “The deliverer thus requires a kind of sign which shall signify a law that to objects of indices an icon appertains as sign of them in a given way. Such a sign has been called a symbol. It is the copula of the assertion” (“The Regenerated Logic”, 1896, CP 3.435).⁴³

46

Chapter 3: Peirce’s Theories of Assertion

Peirce would later toy with other possibilities for identifying what it is in a proposition that makes it not only taking a truth value, but makes it assert its truth. A couple of years later, however, things are already more complicated: “A proposition asserts something. That assertion is performed by the symbol which stands for the act of consciousness. That which accounts for assertion seeming so different from other sorts of signification is its volitional character. Every assertion is an assertion that two different signs have the same object. If we ask why it should have that dual character, the answer is that volition involves an action and reaction” (“Short Logic”, EP II, 20; CP 2.436 – 438). Here, two important new ideas appear. One is the idea that the assertion functions by addressing aspects or parts of the propositional sign itself: it claims that two partial signs of the proposition (the subject and the predicate) have one and the same object. A bit later, this idea is taken to make other mechanisms of assertion superfluous: “A proposition should be defined as that which professes to be true, or assigns a logical value to itself. The Truth is defined as that logical value which a proposition assigns to itself. Whether or not there really is such value, whether there is any truth is a question, not of definitions, but of fact” (“On the Logic of Quantity”, 1896, R 13,7). Here, this self-reference of the proposition is sufficient to make it assert its truth. The other new idea is that this claim is not really made by the proposition sign itself, but in an underlying act of will performed by a consciousness which is really here the source of assertion, while the expression of it in a symbol is a secondary representation of that volitional act. Oftentimes, it is surprising how psychologistic Peirce’s logic anno mid-1890s —Bellucci’s fourth phase—may appear, complete with an accompanying hesitation about the existence of truth and reality. But the two mentioned ideas are sufficiently important to play important roles also in the much more anti-psychologistic period beginning with the invention of the Existential Graphs in 1896 and the metaphysical introduction of “real possibilities” in 1897: the basis of the claim aspect of assertions lying in a specific type of self-reference of the proposition sign, and the actual realization of that claim by means of a further act, independent of that of shaping and understanding the proposition. The self-reference idea matures in the labyrinthic “Deduction of the Dicisign” of the Syllabus in 1903; the idea of a further assertion act on top of the proposition sign is fleshed out in further detail in the same period, beginning around the Minute Logic of 1902. Simultaneously, a competing idea shows up: in “That Categorical and Hypothetical Propositions are one in Essence, with some Connected Matters” (1895 – 1896 [c.], CP 2.334– 335), Peirce introduces the interpreter’s point of view as integral to assertion: “In every assertion we may distinguish a speaker and a listener. The latter, it is true, need have only a problematical existence, as when during

Assertion as the Proposition Sign’s Self-Reference

47

a shipwreck an account of the accident is sealed in a bottle and thrown upon the water. The problematical “listener” may be within the same person as the “speaker”; as when we mentally register a judgment, to be remembered later. If there be any act of judgment independent of any registry, and if it have any logical significance (which is disputable), we may say that in that case the listener becomes identical with the speaker”. This gives rise to the idea of assertions being involved in an argumentation which is essentially dialogical, even when it takes place in the mind of one individual. Peirce continues: “The assertion consists in the furnishing of evidence by the speaker to the listener that the speaker believes something, that is, finds a certain idea to be definitively compulsory on a certain occasion. There ought, therefore, to be three parts in every assertion, a sign of the occasion of the compulsion, a sign of the enforced idea, and a sign evidential of the compulsion affecting the speaker in so far as he identifies himself with the scientific intelligence”.⁴⁴ Here, the aim of the act of assertion becomes intersubjective: it is to provide evidence to an interpreter that the utterer has a certain belief. Again, this is couched in rather psychologistic terms, but it shall continue to develop into the idea that the assertive claim aspect of a proposition is there to persuade an interpreter that 1) the utterer believes in the proposition; 2) it is true. Some years later, the asserting role even passes to the subject term, the index, of the proposition: “It is remarkable that while neither a pure icon or a pure index can assert anything, an index which forces something to be an icon, as a weathercock does, or which forces us to regard it as an icon, as the legend under the portrait does, does make an assertion, and forms a proposition” (“Kaina Stoicheia”, 1901(?), EP II, 307).⁴⁵ Assertion here is undertaken by the index; not by its pointing out an object, however, but by its connection to an icon predicate which it forces to be read as a picture of that object. This, however, is seen from the point of view of the interpreter of the assertion, not of the utterer of the assertion. This idea should soon be overtaken by passing the role to the predicate itself, albeit in a new and daring interpretation of what it means to be a predicate.

Assertion as the Proposition Sign’s Self-Reference The issue of the assertion of the proposition—how it is possible for a composite sign to make a claim—is analyzed by the mature Peirce in a number of dimensions. One is the idea that a proposition not only combines a denoting index and a signifying icon, but it makes its claim by means of a specific self-reference involving these two parts, their interrelation, and the composite sign itself. We

48

Chapter 3: Peirce’s Theories of Assertion

already met the idea that an assertion asserts that the two parts of the assertion —the subject and the predicate—address one and the same object. In the “Deduction of the Dicisign” in the Syllabus, this self-reference is detailed in the following way. In order for a proposition to be able to “convey information” (“Sundry Logical Conceptions”, EP II, 277; CP 2.309)—one of the mature Peirce’s proposition definitions—it needs to refer to its own connectedness to its object in order to claim authority to report upon it.⁴⁶ Here, Peirce explicitly distinguishes this ability of the proposition from the issue of a person’s mental acceptance of it which he analyzes as a completely different, independent issue which cannot be used as an explanation of the assertion of the proposition nor of the proposition itself. In this analysis, the predicate of the proposition really becomes the part responsible for the assertion, and the predicate is analyzed as possessing a hidden structure of some complexity. To put it in a popular way, the predicate is really a shorthand for the proposition’s self-reference, so that saying “The sky is blue” really means what may be colloquially paraphrased as “This sign is really connected to the sky as a true index of it, which is why the sign is authorized to state that it can be described by the predicate blue”. Peirce’s argument goes as follows: “… a Dicisign must profess to refer or relate to something as having a real being independently of the representation of it as such, and further that this reference or relation must not be shown as rational but must appear as a blind Secondness. But the only kind of sign whose object is necessarily existent is the genuine Index. This Index might, indeed, be a part of a Symbol; but in that case the relation would appear as rational. Consequently, a Dicisign necessarily represents itself to be a genuine Index, and to be nothing more” (EP II, 276; CP 2.310). This complicated claim is what the predicate really states about the subject index of the composite proposition sign. The claim that the sign is really connected to its object introduces, at the same time, a first version of the much-discussed “immediate object” which is not any sort of preliminary description of the object and its qualities, but which has to do with the professed connection between the proposition and its primary object. It is a bit ambiguous whether this “secondary” object is simply part of the sign (as the claim must also be present in false propositions where the claimed connection does not exist, or in cases where the sign is made based on rumor in which case the connection may exist or not, no matter whether the sign is true), or whether it is an external connection between the sign and its primary object. But as we would not say the primary object is part of the sign in cases of propositions in which the object does not exist (“The present king of France”), we should probably also not say the secondary object is part of the sign in cases where it does not exist. The claim about the secondary object, of course, is a part of the proposition predicate; not the object itself.

Assertion as Assumption of Responsibility

49

This complicated way of making the predicate responsible for the proposition’s ability to convey information leads to an important array of corollaries in the Syllabus: the proposition sign’s double composition; this composition’s depiction of the sign-object relation by means of the predicate-subject relation; this depiction’s necessity of co-localizing in some topological sense the subject token and the predicate token of the proposition sign as an iconic illustration of the professed connection (on such co-localization, see Chapter 5). At the same time, these acts (of conveying, of professing) are ascribed to the proposition itself. But the mere ideal, repeatable structure of a proposition, even if self-referential, cannot perform any actions. It is only the actual utterance of a proposition, a fact which in the Syllabus deduction is inherent in the argument that the self-reference turns on the actual sign token, not its general type, that is, on the concrete, physical sign vehicles uttered and existing at a certain time and location. So, the intricate machinery of the self-referring predicate part of the proposition is only put into actual play in utterances, understood as any sort of “putting forward” a proposition. This dependence of assertions on actual acts of utterance comes to the fore in two other central analyses of assertions.

Assertion as Assumption of Responsibility In the vast semiotic thrust of 1902– 1903, a new definition of assertion appears: to assume responsibility for the truth of the proposition asserted, so that if it is shown not to be true, a certain penalty may be visited on the asserter in the shape of moral, social, or legal punishment. One of the first occurrences of that idea is “Reason’s Rules” from 1902: “An assertion is an act by which a person makes himself responsible for the truth of a proposition” (“Reason’s Rules”, 1902, CP 5.543). In another version of the same text, Peirce elaborates: Let us distinguish between the proposition and the assertion of that proposition. We will grant, if you please, that the proposition itself merely represents an image with a label or pointer attached to it. But to assert that proposition is to make oneself responsible for it, without any definite forfeit, it is true, but with a forfeit no smaller for being unnamed (“Reason’s Rules”, 1902, CP 5.543).

The elegant and brief definition of a proposition (“an image with a label or pointer”) makes clear that the naked proposition taken in itself is not sufficient to make an assertion: somebody must take responsibility for its truth. But what more lies in the responsibility definition of assertion? In order for the claimed responsibility to be effective, the assertion must be presented in some intersubjective or public forum—which is evident from the following precision: “An act of

50

Chapter 3: Peirce’s Theories of Assertion

assertion is a contract, the effect of which is that if what is asserted is not true, the assertor forfeits in a measure his reputation for veracity” (“Lectures on Logic, to be delivered at the Lowell Institute. Winter of 1903 – 1904. Lecture I”, R 454, 5). Contracts and reputations are social phenomena; the former characterizing explicit interpersonal deals involving mutual obligations, the second characterizing a person’s relation to some social group as a whole. So, the assertion is a contract proposal in which whoever interprets it may assume the role of the contractee, and in case the contract is not kept, the contractor risks his or her standing in a larger social group. Over the period of 1902– 1904, this aspect is described in increasingly acute terms and growing detail: Now it is a fairly easy problem to analyze the nature of assertion. To find an easily dissected example, we shall naturally take a case where the assertive element is magnified,—a very formal assertion, such as an affidavit. Here a man goes before a notary or magistrate and takes such action that if what he says is not true, evil consequences will be visited upon him, and this he does with a view to thus causing other men to be affected just as they would be if the proposition sworn to had presented itself to them as a perceptual fact. We thus see that the act of assertion is an act of a totally different nature from the act of apprehending the meaning of the proposition and we cannot expect that any analysis of what assertion is (or any analysis of what judgment or belief is, if that act is at all allied to assertion), should throw any light at all on the widely different question of what the apprehension of the meaning of a proposition is (Harvard Lectures on Pragmatism: Lecture I, 1903, EP II, 140; CP 5.29 – 31).

Here, Peirce completely distinguishes the act of understanding a proposition from the act of asserting it. Of course, in order to publicly reject a proposition, one must be equally capable of understanding it as in order to assert it. In the same period, assertion is repeatedly contrasted with another act type, with which it shares certain qualities, namely assent, the act of accepting the truth of a proposition. The two share the aspect that both of them aim at impressing the truth of the proposition upon somebody, in the former case another person or larger social group, in the latter case oneself: “What is the essence of a Judgment? A judgment is the mental act by which the judger seeks to impress upon himself the truth of a proposition. It is much the same as an act of asserting the proposition, or going before a notary and assuming formal responsibility for its truth, except that those acts are intended to affect others, while the judgment is only intended to affect oneself” (“Nomenclature”, 1903, EP II, 292; CP 2.252). In a certain sense, assertion and assent are subtypes of judgments, that is, acts of convincing somebody about the truth of a proposition—with the differentia specifica of the former being directed towards other persons or social entities, the latter towards oneself. While the former assumes responsibility towards others, the latter assumes responsibility for one’s own future action habits:

Assertion as Assumption of Responsibility

51

… an act of assertion supposes that, a proposition being formulated, a person performs an act which renders him liable to the penalties of the social law (or, at any rate, those of the moral law) in case it should not be true, unless he has a definite and sufficient excuse, and an act of assent is an act of the mind by which one endeavors to impress the meanings of the proposition upon his disposition, so that it shall govern his conduct, including thought under conduct, this habit being ready to be broken in case reasons should appear for breaking it. Now in performing either of these acts, the proposition is recognized as being a proposition whether the act be performed or not (“Sundry Logical Conceptions”, 1903; EP II, 278; CP 2.315).

Assertion and assent differ as to future consequences: the former act risks moral, social, or even legal punishment, the latter merely self-blame and personal habit action problems. Assertion and assent, on the other hand, agree in assuming future responsibility; the former in public, the latter in private. The emphasis on the public sphere becomes explicit in 1908: Unless truth be recognized as public,—as that of which any person would come to be convinced if he carried his inquiry, his sincere search for immovable belief, far enough,—then there will be nothing to prevent each one of us from adopting an utterly futile belief of his own which all the rest will disbelieve. Each one will set himself up as a little prophet; that is, a little “crank,” a half-witted victim of his own narrowness. But if Truth be something public, it must mean that to the acceptance of which as a basis of conduct any person you please would ultimately come if he pursued his inquiries far enough;—yes, every rational being, however prejudiced he might be at the outset (Letter to Lady Welby, 1908, SS 73).

Peirce virtually repeats Kant’s famous 1784 definition of enlightenment as taking place in public, from “Was ist Aufklärung?”—the argument here being that the connection of a proposition to the idea of truth-directed, indefinitely long future inquiry necessitates public expression; otherwise, as Peirce says, every individual might assume his or her own, crank and futile theories. The public aspect of assertion is what prevents us from that. It was probably Peirce’s work on the Existential Graphs begun in 1896 which gave him the idea that such public acts necessarily involve concrete tokens or replicas of the propositions involved, different from the same propositions considered as types, as general, repeatable signs. It was this insight which gave rise, during the elaboration of the Syllabus in 1903, to the adoption of a new sign trichotomy, that of Qualisign-Sinsign-Legisign (later: Tone-Token-Type) with its important distinction between concrete, individual, actual occurrences of a sign, tokens, and the same sign understood as a general rule for the articulation of such occurrences, a type.⁴⁷ An assertion, thus, can only be undertaken by the utterance of a particular token replica of the proposition made at a particular time

52

Chapter 3: Peirce’s Theories of Assertion

and place. In the context of Existential Graphs, this became evident in the principle that the very act of scribing the sign token on the sheet is equivalent to asserting it (hence the name of the sheet: “the sheet of assertion”): “The graphist may place replicas of graphs upon the sheet of assertion; but this act, called scribing a graph on the sheet of assertion, shall be understood to constitute the assertion of the truth of the graph scribed. (Since by 395 the conventions are only ’supposed to be’ agreed to, the assertions are mere pretense in studying logic. Still, they may be regarded as actual assertions concerning a fictitious universe.) ‘Assertion’ is not defined; but it is supposed to be permitted to scribe some graphs and not others” (Syllabus, 1903, CP 4.397). This is a specific convention of Peirce’s EG rule system, but it is chosen because it is informed by the general regularity that an assertion only assumes its contractual responsibility by actually being uttered in a concrete act of enunciation. In legal terms, it has been known since antiquity that a law becomes a law only when it is stated publicly (“Leges instituuntur cum promulgantur”—the Catholic Church’s rule for the validity of Canon Law: Laws are made valid by being announced, that is, publicly asserted). In conformity with Peirce’s generalization of propositions to potentially multimodal “dicisigns” in the same text (the Syllabus), such utterances need not use linguistic means of expression. Utterance here is taken in a more generalized sense: “By ‘Uttering’ I mean putting forth, whether audibly or visibly or otherwise any sort of sign. For instance, I should say that the master of a ship who should cause signal flags to be hoisted ‘Uttered’ that combination of flags” (“The Rationale of Reasoning”, Nov. 25, 1910, R 664, 7).

Assertion as Persuasion We already touched upon a third theory of assertion, defining it by its purpose (which, to Peirce is the proper way of defining, if possible, natural kinds, cf. Chapter 19): that of making evident what the speaker claims to believe to be true, with the intention of persuading an interpreter. Assertion in itself provides no logical ground for accepting the proposition (that would require an argument) which is the reason behind the close tie of assertion to the responsibility and reputation of the utterer. Having a strong reputation may help convincing the interpreter to actually believe that the asserted proposition stands in the claimed relation to its object as a guarantee for its truth. In the taxonomy of the propositional field which Peirce undertakes in the compact initiation of the 1902– 1903 developments in “Kaina Stoicheia” (1901(?)), assertion is now called “affirmation”:

Assertion as Persuasion

53

An affirmation is an act of an utterer of a proposition to an interpreter, and consists, in the first place, in the deliberate exercise, in uttering the proposition, of a force tending to determine a belief in it in the mind of the interpreter. Perhaps that is a sufficient definition of it; but it involves also a voluntary self-subjection to penalties in the event of the interpreter’s mind (and still more the general mind of society) subsequently becoming decidedly determined to the belief at once in the falsity of the proposition and in the additional proposition that the utterer believed the proposition to be false at the time he uttered it (EP II, 312– 313).

Here, persuasion (determining the belief of the interpreter) may even count as a sufficient definition, so that the whole complex of public responsibility is taken to follow from that definition: assuming responsibility for the truth of the assertion is a prerequisite for persuading anybody to believe in it. There are other means of persuasion, of course, both more implicit or non-logical by means of association, flattering, threats, etc. as well as more explicit and more logical means of full arguments making their conclusion explicit; assertion being itself explicit but still non-inferential requires that the asserter enjoys an untarnished reputation. That is why the persuasion definition may appear as the definition of assertion: “… a sign which belongs to a conventional system of possible signs, and which is intended and calculated to produce a belief in the mind to which it is addressed is an assertion” (“The Fourth Curiosity”, 1907, R 200, 91). Thus, three different theories of assertion can be found in the mature Peirce from around the turn of the century: assertion as a special self-reference of the proposition sign; assertion as a public utterance assuming responsibility for the truth of the proposition; and assertion as an utterance intended to convince an interpreter of the truth of the proposition. Oftentimes, only one of the three theories is addressed by Peirce when discussing assertions. It does not mean, however, that they form three competing or even mutually exclusive explanations. Rather, they are developed in detail in the very same fertile period of 1901– 1904, and they seem to form a series of presuppositions: persuasion as the final aim of assertion presupposes the assumption of responsibility by the utterer which, in turn, presupposes the proposition sign’s self-referential structure as potential indexical truth grant. Or, read in the opposite direction: the existence of self-referential proposition signs does not entail that anybody will actually take responsibility to assert them, and even if they are indeed so asserted, this is no guarantee that anybody will actually be persuaded.

54

Chapter 3: Peirce’s Theories of Assertion

The Role of Conscious Deliberation Belief is defined as an action habit in the field of thought. As such, it is connected to the concepts of judgment and assent as individual acts manifesting or changing belief. Assertion, by contrast, as an explicit, deliberate act of persuasion, is inherently social and public. As such, assertion forms the indispensable cornerstone in the spreading of belief, in social settings of everyday life as well as in the special case of more controlled belief-adoption of the scientific cross-generational community on its trajectory converging towards truth in the limit. In this connection between belief and assertion lie some interesting issues: assertion is a deliberate act, but to what degree is the belief which it communicates the object of deliberate, conscious decision? How do scientific beliefs and assertions differ from everyday beliefs and assertions? And what is exactly the scope of claims covered by the assertion’s assumption of responsibility? In the original, pragmatist definition of belief 1878, as we have discussed, belief was subject to awareness, manifested by a feeling of which content ideas—subject and predicate—it combines. In his subsequent evolution, however, Peirce again and again vacillates with respect to which degree of awareness or consciousness of beliefs is really possible.⁴⁸ This comes from the fact that belief is a subspecies of habit, which means that a belief is not an action hic et nunc, but a general law or tendency over a prolonged stretch of time during which it may give rise to any number of concrete acts. And there is no guarantee that the individual possesses conscious access to his or her own habits. This obviously clashes with another important standard: Peirce’s increasing insistence that the act of logical inference must be subject to conscious, deliberate self-control in order to count as real reasoning (cf. Chapter 18). Habits are overwhelmingly unconscious; reason must be conscious. In exactly the same period of Peirce’s mature theory of assertion, he develops the idea that human beings are characterized by five or six levels of self-control, the higher levels controlling the lower ones, and that the function of consciousness is to make higher levels of self-control efficient.⁴⁹ The type of self-control associated with consciousness, then, is deliberate control of reasoning. But if belief and change of belief are not so subject to self-control, the adoption of beliefs could not count as reasoning, and belief would be cut off from the possibility of attaining scientific status. Peirce never explicitly expresses this problem in such terms, but he does make attempts to solve it: “A belief in a proposition is a controlled and contented habit of acting in ways that will be productive of desired results only if the proposition is true. (…) A judgment is a mental act deliberately exercising a force tending to determine in the mind of the agent a belief in the proposition; to which should perhaps be added that the agent must be aware of his being liable to inconvenience

The Role of Conscious Deliberation

55

in the event of the proposition’s proving false in any practical aspect” (“Kaina Stoicheia”, 1901(?), EP II, 312– 313). Here, the responsibility part of assertion is included in what must be covered by awareness. More generally, the notion of judgment is taken to be the deliberate mental act of attempting to form a belief in a proposition. It follows that no act of deliberate will could unilaterally shape habit or belief. It may attempt or tend to do so, but that is all. Earlier, we saw an attempt to make judgment the becoming-aware or making explicit of a belief. But it remains contentious whether or to what extent human beings can really make explicit what they believe: “Belief does not principally consist in any particular act of thought, but in a habit of thought and a conduct. A man does not necessarily believe what he thinks he believes. He only believes what he deliberately adopts and is ready to make a habit of conduct” (“Sketch of Dichotomic Mathematics”, 1904, NEM IV, 297– 298). Persons do not necessarily believe what they themselves think they believe. This pessimistic claim stands in a strange tension with the next claim: that they only believe what they deliberately decide as a habit of conduct. The former claims there is a distance between believed belief and real belief; the latter that this distance may be, nonetheless, overcome by deliberate action. This may sound like a sort of almost desperate decisionism, far from logical self-control. In this light, the actions of assertion and assent are indeed deliberate, but not necessarily subject to meticulous self-control. The problem is related to Peirce’s pessimist suspicion that the amount of logical reasoning in everyday life is really pretty small: Of excessively simple reasonings a great deal is done which is unexceptionable. But leaving them out of account, the amount of logical reasoning that men perform is small, much smaller than is commonly supposed. It is really instinct that procures the bulk of our knowledge; and those excessively simple reasonings which conform to the requirements of logic are, as a matter of fact, mostly performed instinctively or irreflectively. Reasoning, properly speaking, cannot be unconsciously performed. A mental operation may be precisely like reasoning in every other respect except that it is performed unconsciously. But that one circumstance will deprive it of the title of reasoning. For reasoning is deliberate, voluntary, critical, controlled, all of which it can only be if it is done consciously (Minute Logic, 1902, CP 2.181– 182).

Here, the vast majority of knowledge is instinctive and beyond the reach of conscious, logical self-control. The same must hold for the vast majority of assertions giving public voice to such knowledge. Here, the optimism inherent in Peirce’s enlightenment vision of the scientific community approaching truth in the limit comes close to vanishing. It seems to be in order to prevent such a consequence that Peirce considerably downgrades or delimits what it takes to be conscious of a piece of reasoning:

56

Chapter 3: Peirce’s Theories of Assertion

This does not imply that we must be aware of the whole process of the mind in reasoning or, indeed, of any portion of it. It is very desirable to have a clear apprehension of this distinction. We are, so to speak, responsible for the correctness of our reasonings. That is to say, unless we deliberately approve of them as rational, they cannot properly be called reasonings. But for this purpose, all that is necessary is that we should, in each case, compare premisses and conclusion, and observe that the relation between the facts expressed in the premisses involves the relation between facts implied in our confidence in the conclusion. What we call a reasoning is something upon which we place a stamp of rational approval. In order to do that, we must know what the reasoning is. In that sense, it must be a conscious act, just as a man is not bound by a contract if it can be proved that he signed it in his sleep. It must be his conscious act and deed. But for that purpose he only needs to know the character of the relation between the premisses and the conclusion. He need not know precisely what operations the mind went through in passing from the one to the other. That is a matter of detail which is not essential to his responsibility. The mind is like the conveyancer who has drawn up a deed. What books he looked into in choosing his verbiage is no concern of the person who signs, provided he knows what the paper binds him to doing (Minute Logic, 1902, CP 2.183).

Peirce compares reasoning to a contract—cf. his description of the responsibility inherent in an assertion as a contract. In order to understand a contract, one must understand its logical structure: what it compels one to do, if the other party fulfils its requirements. One does not have to remember the exact wording of this logical structure (cf. also Chapter 18). That is, one has to know the logical relation between premises and conclusion but one has no need to have conscious awareness of the detail of psychological processes resulting in that knowledge. This forms a sort of subtle compromise between the unconscious character of most beliefs on the one hand and the subset of logically controlled reasonings on the other. This compromise also entails that one may logically develop the conscious parts of a belief by elaborating on further consequences in the imagination: Beliefs—more so than other habits—permit of exercising such future acts in fantasy, finetuning eventual, potential action if it once should occur in a situation. Such working on imaginary diagrams of possible future activity permits the extension of awareness of the logical structures of belief, sometimes changing those structures in new habit-taking—even with no guarantee of ever articulating and criticizing the whole of belief which remains instinctual. But then what about the decisionist influence on those acts which are the ultimate ends of beliefs? “By a categorical resolution I mean a representation to oneself that one will behave in a certain general way in a certain expected contingency, this representation being received with satisfaction, being rehearsed with pleasure, and perhaps exciting a special effort to learn it as a lesson. The purpose toward the accomplishment of which the action tends is taken for granted” (“Pragmatism”, 1905, CP 5.517, n.). A “categorical resolution”—some-

Everyday and Scientific Assertions

57

times also called a “resolve”—is the firm decision to adopt a particular action habit in the future. Here, there is no control with the logicality of the relevant belief. This, of course, does involve the possibility for the ongoing logical control of them. In the quote, Peirce describes a successful case of “categorical resolve” but it goes without saying that far from all such resolves necessarily succeed— think of the fate of most “New Year’s Resolutions”, be they ever so firm. The activity through which one attempts to force oneself to adopt the assent or resolve of a belief is described by Peirce as the person uttering an assertion in the internal dialogue with him- or herself: I says to myself: “Do we not all perceive that judgment is something closely allied to assertion? That is the view that ordinary speech entertains. A man or woman will be heard to use the phrase, ‘I says to myself’. That is, judgment is held to be either no more than an assertion to oneself or at any rate something very like that” (Harvard Lectures on Pragmatism: Lecture I, 1903, EP II, 140; CP 5.29 – 31). So, assertion is the vehicle for the person’s attempt to persuade not only other persons to adopt a particular habit, but also to persuade him- or herself to the same. Thus, the result of this tension between instinctual belief and self-controlled reason is a role of assertion far away from a naïve, immediate theory of assertion as the expression of belief. It is rather the opposite: assertion as a means to attempt to induce or even change belief, in others as in oneself.

Everyday and Scientific Assertions This tension between belief and reason is also behind a surprising distinction between colloquial and scientific assertions: Hence, I hold that what is properly and usually called belief, that is, the adoption of a proposition as a {ktéma es aei} [that is, a precious or invaluable piece of property, fs] to use the energetic phrase of Doctor Carus, has no place in science at all. We believe the proposition we are ready to act upon. Full belief is willingness to act upon the proposition in vital crises, opinion is willingness to act upon it in relatively insignificant affairs. But pure science has nothing at all to do with action. The propositions it accepts, it merely writes in the list of premisses it proposes to use. Nothing is vital for science; nothing can be. Its accepted propositions, therefore, are but opinions at most; and the whole list is provisional. The scientific man is not in the least wedded to his conclusions (“Philosophy and the Conduct of Life”, 1898, EP II, 33; CP 1.635).

In the pragmatism papers of 1878, it was implicitly understood that the analysis of the third degree of conceptual clarity held for all beliefs, scientific or not—and that the adoption of the principle might aid the clarification of concepts particularly in

58

Chapter 3: Peirce’s Theories of Assertion

the scientific field. That principle is completely given up here: the pragmatic maxim is all but deemed irrelevant to science because the purpose of science is tentative understanding, not action. But would that imply that the scientist does not make judgments and does not assent to his or her conclusions, that the scientist’s presentation of results makes no use of assertions? It is a very weak portrayal of science Peirce gives here, even given the constraints of fallibilism: science is but a bundle of preliminary opinions without belief. The quote is from the 1890s, arguably a period in which Peirce comes closer than ever to psychologism and skepticism, but which he would resolutely leave in the next years: But in science instinct can play but a secondary rôle. The reason of this is that our instincts are adapted to the continuance of the race and thus to individual life. But science has an indefinite future before it; and what it aims at is to gain the greatest possible advance in knowledge in five centuries or ten. Instinct not being adapted to this purpose, the methods of science must be artificial. As Professor Trowbridge hints, pure science has nothing to do with belief. What I believe is what I am prepared to go on today. Imagine a general besieging a city. He sits in his tent at night preparing the details of his plan of action for the morrow. He finds that what his orders ought to be and perhaps the whole fate of his army depend upon a certain question of topography concerning which he is in need of information. He sends for his best engineer officer,—a highly scientific man,—and asks how he is to ascertain the fact in question. The officer replies, “There is only one possible way of ascertaining that. So and so must be done.” “How long will that take?” “Two or three months.” The general dismisses the man of science,—as Napoleon dismissed Laplace,—and sends for another officer, not half so scientific, but good at guessing. What this officer shall say, the general will go by. He will adopt it as his belief (“Telepathy”, 1903, CP 7.606).

Here, the tension between ordinary, individual belief on the one hand and collective science is maintained, but the analysis of the difference differs. Science is systematically critical against belief and instinct because their purpose differs: theirs is that of the survival of the individual, that of science is the advance of collective knowledge in the limit. The sneaking skepticism of the former quote has vanished: now the difference is due to different purposes, to different future action of the assertions in everyday belief and in those of science.

The Scope of Assertive Responsibility The vast difference of the temporal horizons of instinctive belief and of the scientific endeavor is related to an unaddressed issue in the responsibility definition of assertions: how wide is the scope of the responsibility one undertakes when uttering an assertion? Is it the literal truth of the claim of the asserted, or does it also comprise some or even all of its implications? If I claim that Bru-

The Scope of Assertive Responsibility

59

tus killed Caesar, it would seem strange if I refused thereby to have also assumed responsibility of the claim that Caesar was killed by Brutus. But if I claim the elementary axioms of arithmetic, do I thereby also assume responsibility for all theorems which may now, and in an indefinite future, be derived from them? Peirce actually picks that Hilbertian example: There is but one conclusion of any consequence to be drawn by ordinary syllogism from given premisses. Hence, it is that we fall into the habit of talking of the conclusion. But in the logic of relatives there are conclusions of different orders, depending upon how much iteration takes place. What is the conclusion deducible from the very simple first principles of number? It is ridiculous to speak of the conclusion. The conclusion is no less than the aggregate of all the theorems of higher arithmetic that have been discovered or that ever will be discovered (“Detached Ideas, The First Rule of Logic”, 1898, EP II, 45; CP 5.579).

The upshot of both the logic of relations and the axiomatic method in mathematics is that there is no such thing as the conclusion of most propositions. Most often, there are several, even many, even an indefinite number of possible inferences to be drawn from an assertion. Which among these are covered by the utterer’s responsibility? The issue is connected to the classic conundrum of “logical omniscience”: why is it that a person knowing something, and knowing the rules of elementary logic, can be (and most often is) unaware about the consequences of his or her own knowledge? This question receives an answer from one of the main developments of Peirce’s eighth and final period in Bellucci’s enumeration of the phases of his semiotics, namely the distinction between types of “interpretant”, that is, of meaning of a sign. That distinction originates from Peirce’s correspondence with Lady Welby: A little book by Lady Victoria Welby has lately appeared, entitled “What is Meaning.” The book has sundry merits, among them that of showing that there are three modes of meaning. But the best feature of it is that it presses home the question “What is Meaning.” A word has meaning for us in so far as we are able to make use of it in communicating our knowledge to others and in getting at the knowledge that these others seek to communicate to us. That is the lowest grade of meaning. The meaning of a word is more fully the sum total of all the conditional predictions which the person who uses it intends to make himself responsible for or intends to deny. That conscious or quasi-conscious intention in using the word is the second grade of meaning. But besides the consequences to which the person who accepts a word knowingly commits himself to, there is a vast ocean of unforeseen consequences which the acceptance of the word is destined to bring about, not merely consequences of knowing but perhaps revolutions of society. One cannot tell what power there may be in a word or a phrase to change the face of the world; and the sum of

60

Chapter 3: Peirce’s Theories of Assertion

these consequences makes up the third grade of meaning (“What Makes a Reasoning Sound?” 1903, EP II, 256; CP 8.176)

Welby’s triad of meanings becomes, in Peirce’s interpretation, one of the first versions of what later became the distinction between the immediate, the dynamic, and the final interpretant. Here, the first grade of meaning of an expression is its ability to communicate a piece of knowledge. The second grade is those implications of the assertion which the person intends to be held responsible for. And the third is the total sum of the maybe infinite number of consequences the assertion would have in the limit. Here, a possible solution to the scope of responsibility is outlined: the utterer of an assertion is responsible for all predictions of it, which are intended by that person: “A Proposition is nearly the same as an ‘Assertion.’ The distinction which I use the two words to mark is that an Assertion includes no more than it is the intention of the Utterer to declare, while the Proposition includes all that he does declare, which is inevitably considerably more than he intends” (“The Rationale of Reasoning”, Nov. 25, 1910, R 664, 8). Here, Lady Welby’s second and third levels are used to distinguish the contents of an assertion and the corresponding proposition, a bit like Gricean speaker’s meaning vs. sentence meaning. The former, as an utterance hic et nunc, is tied to the intention of the utterer, while the latter, as a general claim beyond particular situations, is not tied to any single utterance of it and potentially involves more than intended by the utterer. Such a solution may immediately sound tempting, until we realize that in the vast majority of cases, assertions do not at all make explicit what that intention is. It remains a psychological escape which an asserter in distress may cynically use by simply restricting his or her claim about which entailments were originally intended by the assertion. It is true that you may indeed often find such restriction attempts in the public sphere when an utterer is attacked for an assertion uttered, and the distinction is pertinent to the extent that it is correct there is a possible tension between implications realized by an utterer and the sum total of possible implications; cf. the riddle of logical omniscience. The distinction, however, gives us no clear picture of what the responsibility of any particular assertion covers. Rather, the distinction opens the scope for unending quarrels between asserters and their interpreters where the latter may ascribe the former more encompassing intentions than the former are willing to admit. “I did not mean to imply that …” This becomes evident if we compare Welby’s second meaning with Peirce’s later second interpretant, the “dynamic interpretant”, which is the sign’s effect in an actual situation, the meaning as actually understood by a particular interpreter. Understood as a dynamic interpretant, the second Welby meaning would not

Assertions in the Social Field

61

amount simply to the utterer’s intention, but rather to something like: the intention of the utterer as understood by the interpreter. This would make explicit the point that in contentious cases, the intention of how much assertive responsibility covers is exactly what utterer and interpreter may disagree about. It makes evident that the intention is not only for the utterer him- or herself to decide but is, in itself, a central part of potentially ensuing dialogical negotiations between parties, both in friendly and in more inimical cases.

Assertions in the Social Field Peirce’s Theories of Assertion—combining the self-reference of proposition signs, the assumption of responsibility on part of the utterer, and the purpose of spreading belief in the proposition (to others or to him- or herself), forms an important link between Peirce’s philosophy of logic and his theory of science. It is intimately connected to his realism in both senses of the word: the independent existence of the objects of science, and the basis in reality of many general predicates (cf. Chapter 12). It is an important corollary, however, that one does not have to accept these metaphysical commitments in order to see that the theory may be put to pragmatic use in an important sense. The responsibility part of the theory claimed that asserting something is to assume responsibility for the claim’s truth, implying willingness to accept penalties in case the assertion proves false. By this definition, we can scrutinize the social field for where such penalties are actually practiced.⁵⁰ When a journalist is sacked for not checking sources and publishing unwarranted claims, when an academic is relegated for having provided falsified evidence, when a draughtsman is threatened for claimed implications of a cartoon, and in many more cases, we see Peircean responsibility-for-assertion at work. The theory does not give us tools to settle such cases because they depend upon the actual facts referred to and the negotiations around the intended responsibility of the utterers, but it shows us why struggles over the truth of assertions are omnipresent in the public sphere of modern societies. In a period of infights over “fake news”, Peirce’s theories of assertions may give us a semiotic grasp of what is going on which differs radically from the more or less explicit truth agnosticism or even nihilism of more conventionalist or constructivist currents of semiotics. It is hard to remain a relativist, however, if one does not want to dismiss the totality of such struggles over assertions as mere wars of raw power.

Chapter 4 The Identity of Sweet Molly Malone Dicent Indexical Legisigns—A New Element in the Periodic Table of Semiotics? Peirce’s sign type of “Dicent Indexical Legisigns” has received relatively little scholarly attention, and it is sometimes confused with the “Dicent Symbol” category. This stems from an inconsistency between Peirce’s general explanation and his exemplifications of the category. Taking the lead from the latter, this chapter argues that while the role of “Dicent Symbols” is descriptive, the task of “Dicent Indexical Legisigns” is not to describe but rather to establish identity of reference by connecting some proper name to an object or to another identifying sign of that object. Thus, it appears as an overlooked sign type playing an important role both in everyday agreement upon reference and in scientific negotiations over identity, terminology, existence, etc.

Predictions of the Sign Combination Strategy of the 1903 Syllabus “Dicent Indexical Legisigns” appear as a result of the combinatory strategy of the 3x3 elementary sign aspects defined by the three basic sign trichotomies of Qualisign-Sinsign-Legisign, Icon-Index-Symbol and Rheme-Dicisign-Argument, a new strategy developed by Peirce in the 1903 Syllabus. It is well known how such aspects do not combine freely, hence not resulting in 3x3x3 = 27 sign types, but only in 10 sign types, due to the application of the rule aptly summarized by Bellucci as “a certain combination is possible if it satisfies the following partial ordering: [first element ≥ second element ≥ third element]”—referring to the category numbers of the first, second, and third elements, respectively.⁵¹ The resulting ten-sign inventory, see next Chapter, Fig. 3. The Dicent Indexical Legisign (again, no. 7 in the list of the ten types) is the middle of three different Dicisign types in the ten-types classification, the other two being the Dicent Sinsign (4) and the Dicent Symbol (9). There are thus three subtypes of propositions—“Dicisign” or “Dicent” having been chosen by Peirce as the notion for the new, generalized concept of proposition resulting from the adopted combination strategy. Combination of course required that each trichotomy involved have the same scope, namely, all signs. A consequence of this principle was that propositions were now generalized from symbolic, prihttps://doi.org/10.1515/9783110793628-006

Predictions of the Sign Combination Strategy of the 1903 Syllabus

63

marily linguistic truth claims to cover all signs to which a truth value may be attributed, including natural signs as well as human signs not or only partially involving language. This new taxonomy thus adds two simpler sign types to the crucial category of “Dicent Symbols” that had constituted the center, under different notions, of Peirce’s logic and semiotic interest in propositions ever since the 1860s. One of these, Dicent Sinsigns, had been considered at least since the 1890s, and their existence may have been one of the anomalies which prompted Peirce to construct the new ten-sign schem. Two of the three, then, Dicent Symbols and Dicent Sinsigns, thus constitute sign types with a long ancestry in Peirce: the former are simply ordinary propositions (even if they are now, as mentioned, considerably extended such as to include partially or wholly nonlinguistic versions of propositions), and the latter are Indices capable of expressing propositions, like the standard Peircean example of weathercocks, considered as signs at least since the 1890s. Dicent Sinsigns, however, in addition to such natural Dicent Indices, now also comprise the special sub-subset of Replicas, that is, individual, concrete token expressions of three higher, general categories: Dicent Indexical Legisigns, Dicent Symbols, and Arguments (EP II, 297; CP 2.265). This covers, e. g., all sorts of particular utterances or representations of standard propositions, such as this very sentence you are now reading on page or screen. So, the combinatory definitions of Dicent Symbols (Legisign+Symbol+Dicisign) and Dicent Sinsigns (Sinsign+Index+Dicisign) are pretty easily interpreted or derived from standard sign types that Peirce had already studied in the development of his semiotics. But what about Dicent Indexical Legisigns? Their “newness” arises from the introduction of the Qualisign-Sinsign-Legisign trichotomy elaborated during Peirce’s work on the Syllabus and that appeared in the final “Nomenclature and Divisions of Triadic Relations” version of the Syllabus. ⁵² When the Legisign (defined by the generality of the sign itself) is now distinguished from the classic generality of Symbols (pertaining to the generality of the meaning of the sign), the possibility arises for a type of proposition that is general in the former sense but not in the latter: general in itself, but without any general meaning. Such a sign is the Dicent Indexical Legisign. The ten-sign classification of the Syllabus forms the first (and only) finished result of the mature Peirce’s strategy, originating in the 1902 Minute Logic,⁵³ of seeing the received Peircean trichotomy definitions not as referring simply to triads of sign types but to triads of sign aspects, which, for that reason, must be combined in order to give full, finished sign types. That procedure forms a specific a priori-a posteriori strategy charted in Peirce’s 1896 Schröder review (Bellucci 2017, 236). The definition and, later, combination of the trichotomies constitute an a priori deduction of signs; subsequently, however, the single results of

64

Chapter 4: The Identity of Sweet Molly Malone

that procedure are tested a posteriori by being connected to empirically established sign categories in the wild, in order to validate and understand the results of the a priori combination. A model and its interpretation, as it were. In a certain sense, that procedure realizes a deductive, modeling phase and an inductive, testing phase known from Peirce’s abduction-deduction-induction epistemology, inductively testing the results of the deductive diagram experiment of aspect combination. In the Dicent Indexical Legisign case, however, unlike in the other two Dicisign cases in the 1903 taxonomy, the resulting sign combination does not immediately fit any already empirically established sign category. This does not, of course, indicate that it is superfluous. Rather, we should expect of such a combinatorial system, if executed successfully, that it will permit the prediction of new, hitherto undetected sign types, a bit like Mendeleyev’s Periodic Table permitted the prediction of new, undiscovered chemical elements.⁵⁴ Peirce the chemist actually compares Mendeleyev’s periodic table with his own ten-sign classification in R 292’s draft of “Prolegomena to an Apology for Pragmaticism” (excerpted in CP 1.288 ff.). The Dicent Indexical Legisign seems to appear as such a new element in the periodic table of semiotics constructed in 1903. The famous 1901(?) summing up of Peirce’s sign theory simply bears the title “Kaina Stoikheia”—New Elements (EP II, 300 – 324).

The Riddle of Dicent Indexical Legisigns In their description of that new element, many scholars remain content with repeating or rephrasing Peirce’s brief description from his exegesis of the ten types —but unlike many of the other ten combined-sign type descriptions in the Syllabus, there is nothing obvious in Peirce’s description of it that indicates which empirical signs are covered by the category. Peirce’s characterization goes as follows: Seventh: A Dicent Indexical Legisign [e. g., a street cry] is any general type or law, however established, which requires each instance of it to be really affected by its Object in such a manner as to furnish definite information concerning that Object. It must involve an Iconic Legisign to signify the information and a Rhematic Indexical Legisign to denote the subject of that information. Each Replica of it will be a Dicent Sinsign of a peculiar kind. (CP 2.260; also, without bracketed insertion, in EP II, 294– 295)

In this passage, the seemingly helpful exemplification by way of a street cry appears in brackets; it was inserted by the CP’s editors Hartshorne and Weiss, who took it from Peirce’s elucidation of Dicent Indexical Legisigns in the context of

The Riddle of Dicent Indexical Legisigns

65

his description of one of the other ten signs, namely the Fourth, the Dicent Sinsign: Thus, the ordinary Dicent Sinsign is exemplified by a weathercock and its veering and by a photograph. The fact that the latter is known to be the effect of the radiations from the object renders it an Index and highly informative. A second variety is a Replica of a Dicent Indexical Legisign. Thus any given street-cry, since its tone and theme identifies the individual, is not a Symbol, but an Indexical Legisign; and any individual instance of it is a Replica of it which is a Dicent Sinsign. (EP II, 297; CP 2.265)

As with any Legisign, the Dicent Indexical Legisign achieves concrete existence and effect only in Replicas, that is, in material Sinsigns, individual token occurrences of the relevant general type of sign. Those Replicas, then, are Dicent Sinsigns of a special type. Here, the example of the street cry is briefly elaborated: it “identifies the individual”, that is, the person uttering it. He or she is supposedly recognizable from the tone and theme of the utterance of the sign. We must imagine that if you hear the tender cry of “Cockles and mussels, alive, alive, oh!” in the street below you are permitted to infer that it is indeed Sweet Molly Malone with her wheelbarrow who is the vendor shouting.⁵⁵ You infer that conclusion from the “tone and theme” of her singing the phrase—the former supposedly being the special melody or timbre of voice on which we often recognize individual persons, the latter being the particular way of phrasing the theme uttered which we—from Peircean collateral observation—have earlier observed this particular saleswoman to use for marketing. We know Molly’s particular voice, and we know her special way of announcing her sales offers, both of them from previous (“collateral”) experience, which is why we are able to identify the presence of her individual person from her street cry emerging from below. It is the individuality of this meaning and reference which distinguishes the Dicent Indexical Legisign from an ordinary proposition, the general Dicent Symbol. The differentia specifica between the two is the individuality vs. the generality of the sign’s meaning, respectively. And the meaning of the street cry is not general, but individual, because the observer uses it to identify the individual shouting. But that is not the way central commentators interpret the Dicent Indexical Legisign. In two important if brief interpretations, in Thomas L. Short’s “Life among the Legisigns” (1982) and Francesco Bellucci’s magisterial Peirce’s Speculative Grammar (2017),⁵⁶ the Dicent Indexical Legisign version of the street cry is interpreted by referring to the products marketed by the salesman shouting. Short says that they “serve not only to call attention to their utterer but to inform one of what it is he is selling” (1982, 303). So the indexical aspect of the Dicent Indexical Legisign should come from the attention to the utterer, and the dicent aspect should come from its asserting the character of the goods sold. But these

66

Chapter 4: The Identity of Sweet Molly Malone

are two completely different objects, and it is not easy to see how they should come together in one simple proposition. To Peirce, there is only talk about one object: the individual indicated by the yelling. Bellucci, similarly, describes the street cry as “the short melodic phrases called out by sellers to advertise their ware in streets and markets” (2017, 273) and thus also draws the emphasis in the direction of the reference to and description of the products marketed. But that is not at all addressed in Peirce’s brief description, and such a sign would, as argued, qualify as a perfectly normal Dicent Symbol, not as a Dicent Indexical Legisign. For Peirce, the dicent aspect of the sign lies not in its claim about the ware but in the assertion that it involves about the identity of the uttering person. Any claim about the quality or price of the goods, of course, would constitute a completely normal proposition, a Dicent Symbol in the ten-sign classification, because it would refer to some general characterization of the goods— as, e. g., “Cockles and Mussels”—and potentially adding further general description of some of their qualities, for instance their being “Alive, Alive, Oh”, thus combining, as does Molly, that reference and description into a full, standard symbolic proposition claiming that this seafood in my wheelbarrow is fresh. That it is so, is easily seen by its use of a general predicate “Alive”—symbols being defined as general signs with general meaning. If we were interested in going shopping for dinner, the shout “Cockles and Mussels, alive, alive, oh!” would be interpreted as a proposition with general description of the stock of goods drawn through the streets—of the type of seafood available from Molly’s wheelbarrow—and hence form a normal proposition claiming that live seafood is for sale. So, the confusion comes from the fact that the very same street cry performs two different functions at the same time: with reference to the ware marketed, it is a normal, Dicent Symbol, and with reference to the vendor shouting, it is a Dicent Indexical Legisign. The Dicent Indexical Legisign, however, is indeed a general sign (a Legisign), but it is not a Symbol, that is, it does not have a general, descriptive meaning. Its meaning, rather, is to claim the existence, presence, or identity of an individual (or a set of individuals)—doing this by means of a general sign, such as a proper name, the known timbre of the voice, a recurrent piece of idiolect in the discourse—but not describing that reference in general terms. That interpretation is also supported by the brief additional example that Peirce gave in his discussion of Dicent Sinsigns as Replicas of various higher sign types: Besides the normal variety of the Dicent Indexical Legisign, of which a street-cry is an example, there is a second variety which is that sort of proposition which has the name of a well-known individual as its predicate; as if one is asked “Whose statue is this?” the answer

The Riddle of Dicent Indexical Legisigns

67

may be, “It is Farragut.” The meaning of this answer is a Dicent Indexical Legisign (EP II, 297; CP 2.265).⁵⁷

The Farragut example is an assertion that identifies the reference of a statue by means of the proper name of the individual referred to—supposedly an individual already known to the asking interlocutor. Again, it is the assertion about an individual without general description that makes the sign differ from a normal, general proposition, a Dicent Symbol. The difference, on the other hand, from Dicent Sinsigns, is the fact that the Dicent Indexical Legisign uses a repeatable, general sign to assert the identification of the individual: in this case, the proper name of the famous admiral of the American Civil War. So, the purpose of the Dicent Indexical Legisign is to assert the identity or the existence of individual objects—not to generally describe them in any way, which would be the task of a Dicent Symbol. The tendency to turn the attention to the products announced by the street cry—and thus conflate the Dicent Indexical Legisign with a standard proposition —may be connected to Peirce’s theoretical a priori description of the sign type that stands in a strange contrast to his examples centered on the identification of individuals. “It must involve an Iconic Legisign to signify the information and a Rhematic Indexical Legisign to denote the subject of that information”, Peirce said in the definition of this category of Dicisigns quoted above, and the latter signs, Rhematic Indexical Legisigns, are identified simply with proper names, while the former, Iconic Legisigns, can be exemplified in diagram types, apart from their individual appearance in concrete diagram tokens (which are Iconic Sinsigns). But in the examples given, the proper name does not appear as the subject but in the predicate slot of the proposition: “It is Farragut”, “It is [the street vendor with a characteristic voice]”—say, Molly Malone. So, the general feature of Dicent Indexical Legisigns seems to be that Rhematic Indexical Legisigns (that is, proper names of different types) occur as their predicate (rather than, e. g., Iconic Legisigns or Symbolic Rhemes which would be typical predicates). What would a sign look like that actually fit the elaboration of Peirce’s a priori definition? It would have a proper noun (or pronoun) as a subject and a diagram type as the predicate. It might be, e. g., a map with a legend, such as a map of Rome (the diagram predicate part) with the name “Rome” and other geographical names indicated in the map (the proper name subject part). But why would such a sign not simply be a Dicent Symbol? Every map is, to some degree, general and provides information not only about the geographical layout of an area at a particular point of time like a photo snapshot would do. The examples that Peirce himself gives are thus quite different from what he actually says in

68

Chapter 4: The Identity of Sweet Molly Malone

the definition of the sign type. They pertain to information about the referent of object names and Indices—that is, identification statements (the street cry identifying the person yelling it; “It is Farragut” identifying the individual depicted). These examples give the idea that the category of Dicent Indexical Legisigns should rather be categorized as Dicisigns in which names or indices occupy the predicate slot. So Peirce’s definition—“It must involve an Iconic Legisign to signify the information and a Rhematic Indexical Legisign to denote the subject of that information”—seems to confuse the two sides of the Dicent Indexical Legisign and should rather, as we can infer from his own examples, be something along the lines of: “It must involve an Iconic Legisign (or other collateral information) to denote the subject of the information and a Rhematic Indexical Legisign to give the name or reference of that information”. The Rhematic Indexical Legisign would be “Farragut” or the recurrent “tone or theme” of the vendor,⁵⁸ and the collateral experience would be the appearance of the statue or the former acts of shouting by the salesman, making possible the identification of them. In the Map of Rome case, it would correspond to the situation when we already had sufficient knowledge of the map of the area to identify it as a city map, but had, for some reason, no idea that the name of that area was “Rome”, as in this dialogue stub: “What is that a map of?”, “It is Rome”.

Pragmatic Roles and Purposes of Dicent Indexical Legisigns In this analysis, the Dicent Indexical Legisign rather identifies two Indices as referring to the same object, somewhat like “The Morning Star and the Evening Star are one and the same thing”. Maybe that category would also involve various types of naming speech acts, definitions, baptisms, introduction of terminology, cross-identification between reference frames, localizations of objects in space and time (“This is known as a Z”, “I refer to this as an X”, “I baptize thou Y” , “This is the girl I told you so much about”, “Let me present you to Mr. and Mrs. W” , “That bird in the sky is called a ‘Grus grus’”, “I used to call this a ‘Token’, but now I define it as a ‘Symbol’”, “The plant I referred to is that just to the left of the bridge”, etc.). The common feature of such propositions is the establishment or control of reference of names and other Subject Indices. In Dicent Symbols, names will be used as subjects to refer to objects; in Dicent Indexical Legisigns, the object reference of names will be claimed, discussed, and established.⁵⁹ If we take that actually to be the case, the otherwise hazy and strangely marginal category of Dicent Indexical Legisigns would occupy an important role pertaining to all sorts of identification, naming, and terminology activities, both in

Pragmatic Roles and Purposes of Dicent Indexical Legisigns

69

everyday and scientific contexts. As is evident from the examples already given, the names involved may refer to individuals, but they may also refer to classes or kinds because it is not their general meaning, but the identification of the reference, that is at stake in this type of proposition. Thus, it would involve signs that not only name, locate, or identify individual objects, but also classes or continua of such objects (“I define a line as that which has length and no breadth”, “Cutlery can be found in the second drawer”, “To reach the village, turn left and then right”, “Element no. 92 is Uranium”), that is, ostensive definitions, giving of directions in space and time, claims about relations between class-names, etc.⁶⁰ One reason for confusion here might be that the very same constituents may be combined in a Dicent Indexical Legisign and in a Dicent Symbol—like in the map-of-Rome example above. Take a stuffed specimen of a bird with a label saying “Grus grus”. The co-localization of these two signs may be read as constituting a Dicisign in two syntactically quite different ways. One is that of a Dicent Symbol, in which “Grus grus” is the subject and the animal, taken as representative of its species, is the predicate. In that version, the combination says something like: “A Grus grus looks like this, is almost 2 meters tall, has a long beak, etc.”. But the same information may be turned the other way, with the animal occupying the Subject slot and the name the Predicate slot, to give a Dicent Indexical Legisign, saying something like “A bird of this kind and with these properties is called ‘Grus grus’”, establishing reference. In that case, the descriptive characters of the bird are not predicated of it but are taken as collateral-experience identifiers permitting the viewer to identify the creature subsequently given that name. Compare “The ostrich is the tallest bird in the world” and “The tallest bird in the world is called an ostrich”. To sum up: in this analysis, the differentia specifica between Dicent Symbols and Dicent Indexical Legisigns is that the former offer some kind of general description of some object pointed out, while the latter offer some kind of identification of which individuals a name or other general index refers to.

Chapter 5 Co-localization as the Syntax of Multimodal Propositions An Amazing Peircean Idea and Some Implications for the Semiotics of Truth It is, on the contrary, extremely difficult to bring our attention to elements of experience which are continually present. “The Idea of a Law of Nature”, 1901, CP 1.134

This chapter develops an idea advanced by Peirce during the construction of his mature theory of propositions in the years after 1900. It is the idea that, in a generalized notion of propositions (including multimodal propositions not linguistic or only partially linguistic), the unity of Subject and Predicate is signaled by the co-localization of those two constituents in a spatio-temporal neighborhood of some sort. The core idea is briefly indicated by Peirce in passing and never developed in detail. I believe, however, that there are some fundamental, important, and fertile possibilities in the idea which ought to be developed further.⁶¹ A first such development is what I attempt in this chapter. The co-localization idea is evident in a recurrent example of a proposition suggested by Peirce: a painting with a title. Unlike most analytic philosophers, preferring staple examples of propositions like “The sky is blue” or “The cat is on the mat”, Peirce, without further ado, often selects examples of propositions which are only partially linguistic: “A proposition is, in short, a Dicisign that is a Symbol. But an Index, likewise, may be a Dicisign. A man’s portrait with a man’s name written under it is strictly a proposition, although its syntax is not that of speech, and although the portrait itself not only represents, but is a Hypoicon.” (Syllabus, EP II, 282; CP 2.320, 1903).⁶² The ‘syntax is not that of speech’, Peirce says. A purely negative definition, but elsewhere, Peirce elaborates on what would more positively characterize such a non-linguistic syntax—namely that the Subject and Predicate are somehow subjected to some ‘form of conjunction’⁶³ which, in itself, functions as a symbol of their unity. More precisely, ‘juxtaposition’,⁶⁴ that is, some spatio-temporal conjunction is what unites Subject and Predicate to form a proposition. I think Peirce has found here a very important, elementary, and ubiquitous structure of the expression of truth-claiming signs— which is, at one and the same time, deep and banal, the latter to such a degree that the phenomenon most often escapes notice: the fact that it is possible to make a truth claim about something by spatially connecting a sign referring to https://doi.org/10.1515/9783110793628-007

The Syntax of Propositions

71

the Object with another sign describing that Object. I find it is an elementary sign function with deep roots in biosemiotics and with a plethora of different application in human semiotics. This chapter is intended to present Peirce’s basic idea, based on his theory of the syntax of propositions in general, and to elaborate Peirce’s sketch-like ideas in much more detail, elucidating it through the analyses of examples from a wide array of different semiotic contexts.⁶⁵ As you will find, many of the examples analyzed in the following will border on the banal or trivial. Still, I believe the fertility of Peirce’s idea lies in three things: drawing attention to a widespread complex of basic semiotic issues often escaping notice; synthesizing all of these seemingly insignificant trivia within an overarching theoretical framework expressing deep principles of logic and semiotics —and, very relevant in an age of ‘fake news’, giving far greater prominence to the wide variety of sign complexes able to state truth claims, a function which is, on this account, much more ubiquitous than often assumed.

The Syntax of Propositions In Peirce’s mature semiotics, from around 1902– 1903, a number of basic presuppositions changed. In the Minute Logic of 1902, a new principle was introduced. Until then, Peirce’s main terminological toolbox in semiotics was the triadic distinction of signs after their Object reference, Icon-Index-Symbol, while the other important distinction, the classical logical triad of Term-Proposition-Argument of old, was most often seen as a further subdivision of the sign type of symbols, something like the following (Fig. 2):

Fig. 2: Peirce’s pre-1902 sign taxonomy.

Now, Peirce realized that such distinctions did not simply refer to kinds of signs, but rather to kinds of sign aspects, and that, in order to reach a taxonomy of kinds of signs, the different triads of sign aspects had to be combined to form sign types. During the elaboration of the 1903 Syllabus, arguably the most-quoted source of Peirce sign definitions, he went from the combination of the two triads mentioned to three triads, now adding the new triad of Qualisign-Sinsign-

72

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

Legisign pertaining to the sign vehicle itself, to the two trichotomies mentioned. Now, there were trichotomies referring to each of the sign’s three constituents, the sign vehicle itself, the sign object, and the sign interpretant. It is also well known how the three trichotomies of sign aspects do not combine freely (which would have given 3 x 3 x 3 = 27 sign types). A more restricted principle of combination⁶⁶ gave rise to a total of ten sign types, famously presented as a main conclusion of the Syllabus (Fig. 3):

Fig. 3: Peirce’s combinatorial 10-sign taxonomy of the 1903 Syllabus.

An elementary prerequisite to this combination strategy was that all the three trichotomies involved had to be generalized so as to cover, each of them, all signs, in order to grant that the combination of them cover the same field, namely, all signs. The Aristotelian logical trichotomy of term-proposition-argument thus ceased to be a subdivision of symbols, and it was now generalized to cover all signs. This had the implication, among other things, of a generalization of the concept of proposition from covering linguistically expressed, symbolic, general statements only, now to cover, instead, all signs able to take a truth value, no matter whether symbolic or linguistic or not.⁶⁷ Consequently, the new, more general concept of proposition required a new notion, for which Peirce chose “Dicent” or “Dicisign” (a sign saying something

The Syntax of Propositions

73

about something). Peirce realized that such signs no longer had to be restricted to the medium of language. Immediately, working out the new combinatory of sign aspects in the Syllabus, he furthermore saw that as propositions were no longer linguistic only, the issue of their internal composition could no longer be understood by a more or less implicit reference to linguistic syntax. As mentioned above, this lies behind his long, rather complicated argument pertaining to the “deduction of the Dicisign” in the Syllabus, highlighting the issue of what unites the parts of a Dicisign. Here, I shall restrict myself to a brief summary of the argument.⁶⁸ The issue is: what connects the Predicate and the Subject(s) of a proposition? On a basic level, Peirce’s idea is that propositions mirror the fact which is or would be their “truthmaker” (whether such a fact actually holds or not)—a picture theory of propositions in some respects not unlike the early Wittgenstein’s; cf. Chapter 12 below. Thus, he was able to state that “Every informational sign thus involves a fact, which is its Syntax” (Syllabus, EP II, 282; CP 2.320), “informational signs” being another term for propositions. Consequently, the combination, in reality, of a property or relation with some Object(s), constituting a fact, is the very same combination structure which furnishes the syntax uniting Predicate and Subject(s) in the proposition sign.⁶⁹ This simple mirroring idea, however, has some underlying complications, for even if it does account for the possible truth of a proposition (the particular combination of Subjects and Predicate is true, if the corresponding combination of Objects and Property occurs in a real fact), it does not account for the proposition’s character of claiming that truth (or its potential for being used to do so; cf. Chapter 3). The truthclaim involves a hidden self-reference in a proposition. Peirce claims that what, on the surface, is a sign claiming “The sky is blue”, is in reality a sign speaking about itself in the following way: “This sign is really connected to its Object, the sky, which is why this sign is able to make the claim that that Object can be described by the predicate ‘blue’.” Thus, the truth claim is analyzed as a self-referring claim that the sign has a real, indexical connection to the Object pointed out by the Subject of the sign. As this claimed connection is referred to by the sign, it follows, furthermore, that that very connection must, in itself, form part of the reference Object, about which the sign speaks. This implies that the Object of a proposition is double: the denoted referent Object (whether it exists or not), plus the claimed reference relation between sign and Object (this is a first version of the distinction developed as Dynamic vs. Immediate Object). But now, this claimed indexical connection of the sign with its Object must also be described by the sign, that is, pictured iconically by the sign—which it what the sign achieves by presenting its Subject tokens as directly connected to the Predicate token, that is, by co-localizing them spatio-temporally to form a proposition sign, a Dicisign.

74

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

In the linguistic version: the Subject “Sky” must be placed so as to occupy the empty slot of the Predicate: “_is blue”, in a juxtaposition of Subject and Predicate, in order for the proposition to be realized. As Peirce says: “… it is the juxtaposition which connects words. Otherwise they might be left in their places in the dictionary” (“Kaina Stoicheia”, 1901(?), EP II, 310). But the important implication of Peirce’s Deduction of the Dicisign is that some such sort of juxtaposition must hold for all truth-claiming signs, for it is that juxtaposition which serves to describe the sign’s own claimed indexical relation to its Object—and so makes possible the expression of that truth claim. Thus, the very co-localization of Subject and Predicate is an iconic sign that the resulting proposition is connected to its Object. Peirce does not himself use the notion of ‘co-localization’, but I think it constitutes a technical term offering a fair summary of the various examples that he gives (using shifting notions like “syntax”, “connection”, “conjunction”, “juxtaposition” etc., but never deciding upon a fixed terminological choice). Let us take a look at these examples. One is a photograph, which, Peirce realizes, rather to his own surprise it seems, may function, in itself, as a proposition. The reason is that the physical process connecting the photograph with the Objects emanating or reflecting the light rays caught by the photo-sensitive plate, implies that the resulting traces on the plate, as a cross-section of the rays, may function as Subjects referring to those Objects, and the shapes of those traces, correlatively, are iconic Predicate signs describing those Objects. Thus, the photograph simultaneously realizes the referential Subject–Object connection and the Predicate description of the same Object—as he says, “It will be remarked that this connection of the print, which is the quasi-Predicate of the photograph, with the section of the rays, which is the quasi-Subject, is the Syntax of the Dicisign …” (Syllabus, 1903, EP II, 282; CP 2.320). Here, the connection establishing the syntax is due to the physical process of photographic recording, as in another classic Peirce example, that of a weathercock where the physical connection between the wind and the direction of the pointer constitutes its syntax. In other cases, however, the connection may be purposive rather than causal (corresponding to Peirce’s distinction between two kinds of Indices, Reagents and Designators, causal and purposive, respectively). In the following quotation, Peirce elaborates upon his painting-witha-legend example: So, if a symbol is to signify anything, and not be mere verbiage, or an empty logical form, it must ultimately appeal to icons to monstrate the elementary characters, both of sense and of conception. One of the simplest examples of a symbol that can readily be found is, say, the portrait of a man having printed under it: ANDREAS ACHENBACH. This form of conjunction of an icon and an index is a symbol telling me that the celebrated artist looked like that. It has that signification, because of the rule that names so prominently printed

The Syntax of Propositions

75

Fig. 4: A print of Andreas Achenbach, 1884. under portraits are those of the Subjects of the portraits. Were the same name to be found written small upon the portrait in one of the lower corners, something altogether different, and not so simple, would be conveyed (The largest of several drafts of the article “Exact Logic” for the Baldwin Dictionary, c. 1900, R 1147, 12).

76

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

Fig. 5: Dauthage’s 1883 portrait of Andreas Achenbach, Wikimedia Commons.

A 1884 print of the German landscape painter Andreas Achenbach (1815 – 1910) fits Peirce’s description and could have been the very portrait to which Peirce referred (Fig. 4). The basic idea, of course, is that “… the rule that names so prominently printed under portraits are those of the Subjects of the portraits”, a convention common in Western painting (extending also to journalism and other branches where text under a picture is often taken to provide the reference of that picture).⁷⁰ That it is indeed a convention is seen from Peirce’s counterexample: “Were the same name to be found written small upon the portrait in one of

What Kind of Sign is Co-localization Syntax?

77

the lower corners, something altogether different, and not so simple, would be conveyed”. The alternative rule which Peirce refers to, of course, says that a name in one of those corners refers to the painter or photographer (or, in some cases, the printer) of the picture, in any case a person (partially) responsible for originating the painting. These conventions, it is possible to imagine, could have been different; the Object could have been indicated by the corner name and the painter by the large name below. What could not have been different, however (and is thus not subject to convention), is that both names, each in their way, must form a “conjunction” by means of “juxtaposition” with the painted surface by means of co-localization. Taken together, the three would form one synthetic proposition, saying something like “This painting portrays Andreas Achenbach and was made by (say) Dauthage”—as is in fact the case with another Achenbach print by Adolf Dauthage from 1883 (Fig. 5). Indeed, the artist’s signature appears in the lower left of the print motif itself, with the year of execution added. Here, however, still further propositions are realized by the co-localization of further names, this time with the function of those names related to the print explicitly indicated: in the lower left corner, the publisher is indicated as one Adolf Eckstein, while in the lower right corner the printer is given as L. Schilling. In this way, effectively, this complex as a whole is equivalent to the joint proposition involving the print: “This print portrays A. Achenbach, was drawn by Dauthage, published by Adolf Eckstein, and printed by L. Schilling”. The explicit addition of the functions of Eckstein and Schilling indicates that there is no stable convention to place the publisher in the lower left and the printer in the lower right corner on the margins of the print. The co-localization of all four Subject tokens in each their position in the vicinity around the graphic Predicate, however, remains a pre-conventional syntactic fact. Such Subject clusters in painting-with-legend examples realize the parsing of Subjects to assume different syntactic roles as in case grammar, and give you the idea that linguistic grammar, with all its subtleties and combinations possibilities, is but a special, sophisticated version of co-localization where grammatical roles have been conventionalized by means of sequential syntax, conjugation, morphemes, lexical items, governance, and other features from the linguistic toolbox—but that all of them are but refinements of that elementary syntax that functions by placing Subjects and Predicate side by side.

What Kind of Sign is Co-localization Syntax? Peirce vacillates considerably in his description of the conjunct sign of the type of the Achenbach print: is it an index (as when he takes the painting-with-a-leg-

78

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

end as an example of the Dicent Sinsign category), is it an icon, as he claimed about co-localization in the Syllabus deduction of the Dicisign, or is it a symbol, as in the quotation given above? The confusion may stem from the fact that the meaning of co-localizing the two constituent signs is indeed general—it is the same from one sign to the next, namely that the Subject refers to the same Object which the Predicate describes—while the use of that general meaning is to confer a much more particular meaning (here, the profile and shape of this individualized portrait) to an individual Object (here, the German painter indicated). In a certain sense, this needs not confuse us much, for the fact is that Predicates come in a vast range of generalities. Thus, picture-with-legend propositions may be found where the iconic Predicate can be much more general, e. g., using the technique of composite photographs in which Peirce took an interest (the superposition of many related photographs in order to obtain a general photo of e. g., “woman of the year”).⁷¹ Such a photo proposition will qualify as a Dicent Symbol, for its meaning is no individual thing or event, but a general structure shared by many women. Diagrams of all sorts may serve as predicates on many different levels of generality. This leaves, however, the interesting and, I think, deep question of whether syntax (logical, linguistic, or other) is in general iconic, indexical, or symbolic. In his 1885 “Algebra of Logic”, Peirce strongly argues for logical syntax to be iconic, because syntax shows the relations between the logical items it connects, and no other sign but icons, neither indexical nor symbolic signs, can show anything. This is why algebras are here taken as a central example of the icon type of diagrams, facilitating reasoning exactly because they directly display relations. Later, in the 1890s, he equally strongly emphasizes that syntax is symbolic, for the reason that its meaning is general; it relates its relata in the same, significant way across many indefinite individual utterance occasions (here also because of the fact that he still held syntax responsible for the proposition’s character of assertion, an idea he gave up with his later idea that the same syntactical proposition may form the basis for different speech acts, of which assertion is but one; cf. Chapter 3). In his 1901(?) “Kaina Stoicheia”, he insisted that syntax is indexical, because it brings together, in the actual here and now, two physical objects, namely the individual token replicas of the signs Predicate and Subject.⁷² There may be a deeper reason for this seeming confusion. When constructing his final 2D logic formalism of Existential Graphs in the years around 1900,⁷³ Peirce’s central syntactical tool in the Beta part addressing Predicate logic is the “Line of Identity” taking care, at one and the same time, of identity, predication, subsumption and quantification (without knowing it, thus countering the Frege-Russell criticism of the ambiguity of the “is” copula, effectively claiming that these four functions can be adequately depicted by the same sign and so actually do

What Kind of Sign is Co-localization Syntax?

79

possess one and the same root). In the two Beta Graphs below (Fig. 6), the Line of Identity is the line that connects the two Predicates “_is good” and “_is ugly” to form the two propositions “Something exists which is good and ugly” and “Nothing exists which is good and not ugly” (or “All that is good is ugly”, the closed curve signifying negation).

Fig. 6: Two Beta graphs.

Here, Peirce proudly insists that this conventional syntactical sign, the Line of Identity, has an almost perfect balance of icon, index, and symbol, respectively. We quote at length to give justice to this important argument: The value of an icon consists in its exhibiting the features of a state of things regarded as if it were purely imaginary. The value of an index is that it assures us of positive fact. The value of a symbol is that it serves to make thought and conduct rational and enables us to predict the future. It is frequently desirable that a representamen should exercise one of those three functions to the exclusion of the other two, or two of them to the exclusion of the third; but the most perfect of signs are those in which the iconic, indicative, and symbolic characters are blended as equally as possible. Of this sort of signs the line of identity is an interesting example. As a conventional sign, it is a symbol; and the symbolic character, when present in a sign, is of its nature predominant over the others. The line of identity is not, however, arbitrarily conventional nor purely conventional. Consider any portion of it taken arbitrarily (with certain possible exceptions shortly to be considered) and it is an ordinary graph for which Fig. 81 might perfectly well be substituted. But when we consider the —is identical with— Fig. 16 connexion of this portion with a next adjacent portion, although the two together make up the same graph, yet the identification of the something, to which the hook of the one refers, with the something, to which the hook of the other refers, is beyond the power of any graph to effect, since a graph, as a symbol, is of the nature of a law, and is therefore general, while here there must be an identification of individuals. This identification is effected not by the pure symbol, but by its replica which is a thing. The termination of one portion and the beginning of the next portion denote the same individual by virtue of a factual connexion, and that the closest possible; for both are points, and they are one and the same point. In this respect, therefore, the line of identity is of the nature of an index. To be sure, this does not affect the ordinary parts of a line of identity, but so soon as it is even conceived, [it is conceived] as composed of two portions, and it is only the factual junction of the replicas

80

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

of these portions that makes them refer to the same individual. The line of identity is, moreover, in the highest degree iconic. For it appears as nothing but a continuum of dots, and the fact of the identity of a thing, seen under two aspects, consists merely in the continuity of being in passing from one apparition to another. Thus uniting, as the line of identity does, the natures of symbol, index, and icon, it is fitted for playing an extraordinary part in this system of representation. (“Logical Tracts”, No. 2, 1903, LoF II, 151– 152; CP 4.448).

My contention is that Peirce’s characterization of this specially selected conventional syntactical sign of the EG system, as simultaneously iconic, indexical, and symbolic, may hold, with some provisos, for syntax in general as well. Syntax is iconic, for it directly shows the structure of relations; it is indexical, for it makes actual connections between sign tokens, and it is symbolic, for it has a general, repeatable meaning from one use to the next. This is not to say that all grammars and all syntactic means of co-localizing signs share the same perfect balance between the three, which Peirce claims for his particular invention of the Identity Line sign in his Existential Graph system. Rather, our hypothesis would be the more general one that all syntax must make use of all three sign aspects, maybe in different ratios and weightings. We shall return below to some corollaries of this idea.

Labels An enlightening example as to the function of co-localization syntax is the following: Every proposition has three elements. 1st an indication of the universe to which it relates, 2nd its general terms, 3rd connection of the terms … Every proposition relates to something which can only be pointed out or designated but cannot be specified in general terms. ‘No admittance, except on business’ over a door is a general proposition, but it relates to that door which may have no qualities different from these of some other door in some other planet or in some other tri-dimensional space of which there may be any number scattered through a quinqui-dimensional continuum without anywhere touching one another. But the hanging of the sign over this door indicates that this is the one referred to. The indescribable but designable Object to which a proposition refers always has connected with it a variety of possibilities, often an endless variety. In the example we have taken, these possibilities are all the actions that can have a relation to that door. The proposition declares that among all these actions there is not to be found any permitted passage through the door except on business. ([Elements of a Proposition], no date, R 789).

Again, Peirce does not illustrate his example which might have looked something like the sign below (Fig. 7):

Labels

81

Fig. 7: “No Admittance” sign.

The important issue here is Peirce’s insistence that every proposition points out its Object in a way which cannot be ultimately translated into any combination of general meanings.⁷⁴ In a sense, it is the Peircean version of Kant’s famous insistence that existence is not a predicate. No amount of general predicate description suffices to identify an individual—it must be aided by some version of direct acquaintance (or a reference to such acquaintance or a description of how to achieve it). In this case—unlike the painting-with-legend type examples—the Predicate is co-localized not with a Subject index but with the very Object of the sign itself (in this case, that door to which the sign refers). This particularly simple type of co-localization, where the Predicate is directly attached to the Object or forms part of the Object itself, could be termed labelling and is found in an immense number of social and biological cases, from consumer goods labels, naming and describing the ware inside the package, over name tags on conference attendants or sports players, species names attached to stuffed animals, to book titles on the front cover, or signs on buildings yielding information about the persons, companies, or activities inside them. In biology, labels in this sense are found in the characteristic looks of a species used to connect to or scare conspecifics or members of other species—or in the scent marks used to delimit a territory: “this territory right here belongs to an agency smelling like this”, where the scent mark thus has two objects, one present (the territory), the other absent (the author of the mark). Labels thus attached directly onto the Objects to which they refer form a particularly primitive subset of propositions.⁷⁵ The fact that such labels, taken

82

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

together with the Objects to which they are attached, constitute truth claims can be seen from the fact that the falsification of them is ripe with consequences for the falsifier if detected, ranging from criticism over sacking to judicial cases against the falsifier or even violent attack (cf. Chapter 3). To give but one example: the food producer misidentifying the chemical additives of his or her product on its label is liable to prosecution and punishment. Documents with the function of identifying the bearer (such as passports), similarly function as labels in this sense, and serious trouble may follow from posing as another person by using his or her passport when trying to cross borders. An important sub-subset to the subset of labels is traffic signs, an old staple of semiotic analysis (cf. Chapter 1). Traffic signs are typical propositions, some of them assertions, some of them realizing other speech acts such as warnings, imperatives, prohibitions, conditional imperatives, etc. The important issue in the label context, however, is that traffic signs signify by the implicit reference to the location where they sit or stand. Parking is prohibited, “not on some other planet”, as Peirce would say, but here, under the sign or in its proximate vicinity. If a more specific subset of the surroundings of the sign is intended, the sign is typically supplemented by means of an auxiliary indexical sign indicating that parking is prohibited fifty meters in a certain direction during certain hours of the day, etc., referring to the very location of the sign as the origo of such further spatio-temporal restrictions. Again, failing to recognize the elementary labelling Predicate-Subject co-localization axis of such a sign may bring the road user into problems with the local authorities. Labels in this propositional sense of the word are so widespread and their precise localization so important that everyday behavior is, to varying degrees, aided, guided, determined, or forced by them. In all public spaces like lecture halls, cinemas, hotels, airports, bus stations, etc., for instance, some doors are co-localized with the sign ‘EXIT’ to indicate an escape-way in case of fire, flood, attack, or other such force majeure emergency events. This simple sign and its placement, taken together by means of co-localization syntax, means: in case of urgency, take this door to reach an escape-way from the room you are presently in. This is a propositional content, and if placed erroneously, indicating escape where there is none, such signs will constitute false propositions and make the owner of the building liable to legal prosecution because sign readers may face grave problems unsuccessfully trying to escape. A most peculiar feature of such simple propositions is that they require little learning in order to be understood. The word ‘EXIT’ in itself, to be sure, requires learning parts of the English language, but once known, the very combination of that sign with the door over which it hangs require little explicit teaching. There is a semantic fit, to be sure, between the EXIT meaning “way out” and the actual

Co-localization Syntax in Early Human Semiotics

83

door as a well-known technology taking you to from one room to the next, which makes a semantically good pair out of the two, all of which involves learning. But in a hall with many doors, it is the simple syntactical structure of co-localization sign–door which is the important feature telling you which of the doors to select in case of emergency. Co-localization is hardly a convention learned; it is rather the other way around: co-localization is a prerequisite to learning. Labels seem to come in at least two basic classes: natural and imposed. Putting a sign over a door restricting access is evidently an imposed label, just as are given names, brands on the wrapping of goods, and much more. A natural label would be a property of the thing itself serving to identify or classify it by some observer. As with all Peircean distinctions, we should be open to a continuum of intermediary cases; there are imposed labels which stick to the degree that they are hardly removable or changeable (tattoos); just as there are natural labels which may vanish by themselves over time (freckles) or which may be surgically or otherwise removed (birthmarks or moles). Biological labels evolve over time to adapt to surroundings—like a walking stick assuming the appearance of a branch for mimicry reasons. In a certain sense, then, such a natural label is imposed by selection pressure over many generations, so the natural/imposed distinction is far from exclusive but rather involves a continuum where natural signs may be imposed over long evolutionary timescales. This is a basic reason that the category of symbols in Peirce do not refer, as often assumed, to human, conventional signs exclusively, but also comprises natural symbols, the decisive criterion for a symbol being the generality of its meaning. An orthogonal continuum, independent of the natural/imposed distinction, concerns the relative distance of the label to its object: body odor as an identifying label may be perceived nearby or at a distance, road signs may identify a city at its entry, but may also appear at any number of kilometers’ distance from the city, with a pointer and distance indication added. Such continua should not confuse us, but rather give an elementary idea of the variability space of labels.

Co-localization Syntax in Early Human Semiotics Once you have grasped the principle, co-localization propositions appear as ubiquitous in human semiotics, even across cultures. Cultures on many levels, of course, will add particular, different conventions specific to local traditions, but as further icing on the base of the co-localization principle which remains indispensable. Pictures with accompanying text, video clips or news footage with voiceover speech, brand names on consumer goods, gesture combined with language

84

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

or images … such propositions come in a vast array of types and appearances. A hypothesis that such multimodal propositions should be a particular, late product of our visual age with print, TV and internet technologies may sound tempting but is most certainly wrong. Rather, multimodal co-localization seems to be found along with some of the earliest occurrences of writing. Take the intriguing example of multimodal Egyptian propositions from around 2900 BC below (Fig. 8):

Fig. 8: King Den ivory tablet, Abydos.

This is a small ivory tablet or label⁷⁶ (5.4 x 4.5 cm, London British Museum EA 55586), seemingly originally attached to a pair of sandals or a jar of wine— an ambiguous sign on its flip side may mean either. It is one among twenty such tablets from the tomb of King Den (or T’an) in Abydos, mid-first Dynasty (c. 2900 BC) excavated by the British archaeologist Flinders Petrie in the late nineteenth century. The main face of the label shows a pharaoh to the left, easily recognizable by the Uraeus snake symbol on his headdress, lifting his weapon against a kneeling enemy. The pair of fighters are surrounded by no fewer than four co-localized groups of hieroglyphs. The translations in the illustration (Fig. 9) are due to the German Egyptologists Kammerzell and Peust.⁷⁷ The uppermost of the four hieroglyph groups here rendered in red reads “Horus T’an”, that is King Den, the pharaoh’s traditional “Horus name” identified by the royal Horus falcon on top of a rectangle whose contents further indicate the name of the particular pharaoh. It simply functions as a name label for

Co-localization Syntax in Early Human Semiotics

85

Fig. 9: Decipherment of the King Den tablet.

the human figure under it, effectively forming the joint proposition “This figure is King Den”. The rightmost hieroglyph group reads “The first time of defeating the East” and may be taken as a sort of headline of the whole scene depicted, supported by the fact that the (tendential) reading convention goes from right to left so it will be the first linguistic message the reader meets when interpreting the label.⁷⁸ Thus, that message, co-localized with the whole scenery of the label, makes a statement which identifies it as a war scene from the first Egyptian victory over their Eastern enemies. The hieroglyph group to the left presents the proper name “Jakurjan”; it seems uncertain whether it refers to the artist behind the drawing of the scenery or maybe the owner of the label (and, indexically, of the Object to which the label may have been attached). This leaves the last, small, central hieroglyph group reading “They shall be finished!”. This text item, situated in the space intermediary between the two fighting opponents, probably indicates an oral utterance on the part of the pharaoh about his slain or soon-to-be-slain enemy, reassuringly addressing the reader (and maybe his own army) and referring to the enemy in the third person: “They shall be finished”. Pharaoh and enemy fighter, of course, are metonymies of

86

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

their respective armies, which did the actual fighting. Kammerzell and Peust state: “The document shown in [this figure] is not only the first case of a recorded speech report in Ancient Egypt—and probably in human history as well—but also marks the onset of a long tradition in Egypt of associating written texts rendering the contents of a speech with depictions representing the respective speaker. Its typological similarity to modern comic strips is astonishing” (2002, 294). We return to co-localization in comics below. Thus, the fourth hieroglyph group of this label might be the first historic appearance of what we now call a speech bubble—in the sense of recorded speech cited within the confines of a picture by placing the cited utterance close to the person supposed to pronounce it. It expresses, co-localized with the Den figure, a joint proposition which may be paraphrased as “King Den says: ‘They shall be finished!’”, one proposition nested within another. The drawn bubble itself is a much later pictographic invention, of course,⁷⁹ but the fact that early Egyptians dealt in quotes of recorded speech is supported by the appearance, a couple of centuries later, of various types of quotation marks the hieroglyphic use of which is traceable all the way down to the fourth century CE (Kammerzell and Peust 2002, 295 – 296). The Den label is doubly remarkable. One thing is the early appearance of multimodal propositions, combining drawn figures with text in order to make assertions. It is obvious that the four propositions are presented, implicitly, as conjunct, so that if each of them is true, their conjunction will be true: “This label (owned or drawn by Jakurjan) depicts the first victory over the East, in which King Den beat the enemy, exclaiming ‘They shall be finished!’” Another notable feature is the four different functions of co-localization within one and the same sign, effectively constituting four elementary propositions. If the analysis given is correct, there is an overall proposition taking the whole depicted scenery as its Predicate, identified by the Subject headline claiming that this depiction refers to the first victorious battle against the Eastern enemies. On a lower level, then, is the identification of the main character inside the picture—standard painting-with-a-legend—and on an even lower level of enunciation, then, there follows the utterance by the pharaoh so identified. More uncertain is the role of the last, leftmost proper name, as we do not know who the individual Jakurjan might have been, but it seems certain it does not co-localize with any particular part of the depicted content, so the most obvious conclusion is that it refers to some person’s relation to the material sign vehicle of the label as a whole, maybe identifying its creator. There does not seem to be a fixed set of conventions for the placement of the texts in relation to the pictures—with the possible exception of the “headline” to the right. The two text items “in” the picture seem to function immediately by means of their relative proximity to the royal figure. It

Co-localization in Comics and Diagrams

87

might be objected that the spoken sentence is no closer to the king than to his enemy; indeed, it is closer to the mouth of the latter than of the former. Still, naming one figure but not the other seems to act as a sort of scope sign indicating that what is said is produced by the named figure, the main character of the picture. These analyses suggest two ideas: (1) co-localization may be used to attach a number of Subject tokens to a Predicate picture, each with different grammatical roles; (2) co-localization may display structured levels of enunciation so that some co-localized messages occur within the scope defined by higher-order such messages—here: (a) headline of whole picture → (b) figure named → (c) figure speaking. If the proper name is indeed the artist, he may be added at the uppermost level of enunciation, as the author of the whole quoted three-level structure, effectively giving four distinct levels of enunciation.

Co-localization in Comics and Diagrams Kammerzell and Peust point to the structural similarity between the Den label and modern comics. In present-day comics, cartoons, caricatures, etc., we actually do find different types and levels of co-localization propositions. Fig. 10 displays the initial frames of a Donald Duck classic, Carl Barks’ “Only a Poor Old Man” from 1952. The opening splash panel’s picture with Donald witnessing Uncle Scrooge money-diving in the fortunes of his money bin comes with a handful of co-localized text items. Just as Scrooge is foregrounded in the picture, his name is foregrounded in the title complex to the upper left, effectively tying the two of them together in one proposition, simultaneously naming and describing the main character of the frame (and of the story to follow). Just as in the Den label case, the named central figure produces an utterance: “I dive around in it like a porpoise!”—the first of Scrooge’s classic triad of mottos about money gymnastics, the other two lines following in the next two frames. As in the Den case, the other animate figure—here, Donald Duck—remains silent. And here, too, there is a higher-level statement forming a proposition addressing the whole scenery: the voice-over narrator in the upper middle box speaking directly to the reader: “If you had a fortune of umpteen-centrifugillion dollars, what would you do with it? Well, rich old Scrooge McDuck has that much money, and this is what he does with it!”—effectively forming the parallel to the right-side headline in the Den label case. Finally, as in the Den label, a proper name is also added at the margins of the whole scenery—that of Walt Disney. In this case, a genitive s indicates that Uncle Scrooge as a figure belongs to him,

88

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

Fig. 10: Introductory Donald Duck image sequence (© Disney).

in some sense. He certainly did, as Disney held the copyright to the Scrooge figure, but we should not mistake this for him creating the character. While Disney did create Donald, it was his employee Carl Barks who created Scrooge (and wrote and drew all the classic stories about him), although he was never credited as an author in his own creations and only gradually became known among comics readers after his retirement in the sixties. If Jakurjan refers to the owner of the label (and its attached object), rather than to the draughtsman, we may have a similar structure there, with the artist remaining anonymous in the drawing. The text complex at the upper left adds another function, one

Co-localization in Comics and Diagrams

89

not present in the Den label, for obvious reasons—a reference not to the present frame exclusively but to the whole ensuing narrative which has no equivalent in the Den label: the Hollywood convention of “starring” in a movie is mimicked in the circle giving the overall title of the whole story “Only a poor old man”. But parallels to all of the four co-localization propositions of the Den label are actually found in this Duck comics frame. In the next frame, yet another function is introduced, that of sounds emanating from events and actions within the picture: the “Blubbidy Blub” of Scrooge’s “under-money” breathing. While a modified speech bubble here indicates the animate source of the sound, more generally event sounds are depicted as emanating directly from their acoustic source in the picture—the relevant event often highlighted by motion lines—so the “CRASH!” is presented close to two colliding objects, effectively constituting the proposition that the event drawn sounds like indicated. Kammerzell and Peust were indeed right when they pointed to the structural similarity between the Den label and modern comics, with respect to the amount and types of co-localized propositions. Again, in both the Egyptian and the American case, we find a case grammar structure in the co-localization of a central picture predicate with a number of linguistic subjects playing different grammatical roles. But picture-with-legend types of Dicisigns are not restricted to pictorial representations in any narrow sense. The vast realm of different types of diagrams also makes use of the syntax of co-localization. Take geometrical diagrams, for example (Fig. 11). Here, lower-case a, b and c refer to the three sides of the triangle respectively, effectively saying ‘this side is called a’, etc., while the capital letters A, B, and C, in turn, refer to the three angles in so many similar propositions. In this case, the propositions act as stipulative definitions—their meaning is that in the proof to follow, the line segments and angles will be referred to after the naming convention given by the six such propositions of the diagram.⁸⁰ Look at the letter ‘B’—it is a little closer to the two

Fig. 11: Diagram of a geometrical triangle.

90

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

adjacent sides than it actually is to the angle summit. But this does not make the observer doubt that it refers to the angle, partly because the two sides are already named, but also because of the fact that the angle summit, as a singularity, holds a special diagrammatical prominence.⁸¹ Very often, in diagrams, singularities are pointed out for some reason by means of arrows, line crossings, small point-like line segments, etc., and equipped with some name or description so as to form label propositions. Take the Cartesian plane, for example (Fig. 12). The integers, of course, refer to the singularities marked on the axes by means of small, perpendicular line segments marked with smaller line breadths—and not to points infinitesimally close to those singular points, even if they are no farther from the number tokens. The “1” refers to the singular point indicated, not to the value 1 micrometer to the right of that point. “0” refers to the intersection point of the origo, and thus doubly refers to both axes, while “x” and “y”, neither of them close to any marked singular point, are easily taken as higher-level references to the variables of each of the two axes as a whole. All of these signs constitute propositions when taken together with their co-localized points. Such contents, of course, are processed so quickly, easily and below the threshold of consciousness as usually to escape attention. What really interests a diagram reader, of course, is the shape of the curve and what it communicates about the relation between the x and y variables—but in the finer details of the machinery of meaning making such interpretation possible, co-localization plays its indispensable role at many places in the diagram.

Fig. 12: The Cartesian Plane.

The diagram type of maps is equally impossible without co-localization. Below a segment of a topographical map of southern Germany (Fig. 13). Cities are not

Co-localization in Comics and Diagrams

91

Fig. 13: Segment of a topographical map of southern Germany.

points, but they are comparatively small enough that they or their city centers are depicted by tiny circles, and their names are communicated by putting one end of the token of their name close to the localization of the city symbol token on the map, like, in this case, “Straubing” and “Regensburg”, the latter with a larger symbol and the name in a larger typeface to indicate it belongs to a class of larger cities. River names are written in parallel to the streams they refer to (and, using iconicity, in the same blue color). Over the whole of the section, the landscape or region name ‘Falkensteiner Vorwald’ is spatialized so as to indicate that this forest name does not refer to any particular quasi-singularity on the map, but rather (unlike the city name case) to the whole extended area covered by the name. All of these names, co-localized in different ways with partial area depictions on the map, constitute so many propositions: “Here sits Regensburg”, “Here flows Donau”, “Here spreads the Falkensteiner Vorwald”. Thus, it should come as no surprise that maps, in general, make truth claims. They may be erroneous (like early maps of North America taking California to be an island), they may be outdated (old maps failing to represent recent motorways), they may be deliberately deceptive (like falsified military maps leaked to the enemy), they may be too coarse to be truthful for certain purposes (the Germany map appears as if no villages existed), etc.—different types of falsities which go

92

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

to show that in general, maps are intended to be truthful and so possess a truth value. Of course, they may be true in some respects, false in others, just as the case with a linguistically articulated text. They assert that a named area has the structure depicted, and that particular points, lines and, subareas of the map refer to significant substructures of the landscape of the same reference names in reality. As is evident from these trivial examples, such propositions are extremely elementary, to the point that most comics readers, diagram interpreters, map users, etc., automatically process such propositions unproblematically, most often without being aware of it. I am slightly embarrassed to annoy the reader with examples this simple. It is, however, to prove my point: if there is anything strange here, it is the unrecognized ubiquity of this co-localization propositional sign function and the considerable ease with which such propositions are uttered, read, interpreted, and acted upon. And, of course, the strange thing that such signs have generally not been categorized as propositional, this having most often been taken as the privilege of a much more restricted set of explicit, linguistically expressed truth claims only.

Framing—The Topological Character of Co-Localization As already indicated above, co-localization of Subject and Predicate in a proposition could not simply be the issue of a short metric distance between them. A Subject sign on one side of a newspaper page may be micrometers from a Predicate sign on the flip side, but this short distance does not unite the two into a proposition. Co-localization is rather topological in a sense to be further explored. The space in which the two parts or functions of a proposition are co-localized is a connected neighborhood or field—connexity being the elementary property of topological spaces, and the presence of such a field must be communicated and recognized in some sense by the sign interpreter, explicitly or implicitly. If co-localized inside such a connected field, the two sign tokens of Predicate and Subject may fuse into a proposition while another sign token, even if metrically located very closely nearby, does not so fuse if not included in the particular, connected field. In the graphical 2D formalism for logic representation called Existential Graphs (EGs) which Peirce developed from 1896 onwards, the sheet on which the representations for logical structure are drawn is called the “Sheet of Assertion” or the “Phemic Sheet”, representing in an implicit, “undeveloped” sense all the true propositions of the given Universe of Discourse. Writing particular propositions, predicates, logical relation symbols on the Sheet corresponds to

Framing—The Topological Character of Co-Localization

93

photographically developing some of the propositions implicitly given and making them explicit. In Peirce’s conventions for the EGs, the presentation of two propositions side by side signifies their conjunction (he first experimented with the alternative “Entitative Graphs” where the same co-localization would signifiy their disjunction, but he gave up that version because he considered it more iconic if co-localization of propositions meant “and” rather than “or”).⁸² Furthermore, we could add, choosing the first option selects the convention which is operative in most actually occurring co-localized propositions “in the wild” where propositions placed within the same frame are most often taken to be conjunct (at least, if relations such as negation or disjunction are intended, they seem to require further spatial conventions or the addition of special signs); cf. the following chapter. This issue of the co-localization of several propositions and the higher-level meaning of such juxtapositions is a different issue, of course, from the more elementary co-localization constituting those propositions in the first place (which is addressed, as we saw, in the Beta predicate logic part of EGs where “Lines of Identity” take care of connecting Predicates and Subjects to form propositions). Thus, both the elementary constitution of propositions from Predicates and Subjects and the simple logical operation of conjunction of several propositions are performed by two differently marked versions of co-localization (with and without an additional special sign, respectively). In a certain sense, then, our notion of a “connected propositional field” is a generalization of Peirce’s concept of Sheet of Assertion (or, vice versa, Peirce’s concept forms a special, abstracted, technically more precisely defined, version of such fields in the wild). In comparison to the linguistic case, simple versions of the connected field here correspond to the sentence or period of linguistically expressed propositions, although in larger-scale cases, such as the topographical map, the comprehension of it may make a comparison to the whole text page, text section, or document more pertinent. Unlike the linguistic case with a relatively clear limit between sentence grammar and transphrastic issues, there is no general limit between simple and complex propositional fields. Both levels of colocalization expressed in Peirce’s EGs may appear “in the wild”: the elementary co-localization of Subject and Predicate to constitute propositions, and the co-localization of propositions to constitute conjunctions—see Chapter 6 below. An important issue here is if and how other logical relations than conjunction are presented in co-localized propositions “in the wild” (in ordinary or formal languages, of course, special constructions in the shape of word classes or explicitly designed signs take care of such possibilities). Disjunction may sometimes be expressed by a list, like a drop-down menu of options, or a side-by-side presentation of parallel possibilities, e. g., “first goal scorer” in a particular soc-

94

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

cer match where odds for the different, mutually exclusive outcomes are presented in a list of individual players with their respective odds for scoring the first goal. A standard pictorial way of expressing negation is, of course, the crossing-out of the negated content or proposition—or the addition of the negation symbols like “no”, “non”, “never”, or the minus sign, etc., to a diagram or picture. Spatial sequential presentation may be used to express implication (such as in the “before-after” images in certain types of marketing). Initially the sequence may appear to be temporal only, but it is really conditional (if you use our product then the “before” conditions will disappear to the benefit of the “after” conditions, as in photographs of the same man with a bald head and with more hair, in that sequence). Subsumption may be indicated by Porphyrian trees, explicitly or more implicitly—or by means of a superordinate level expressed by an upper proposition in large font, and a subordinate level with smaller font: OXFORD UNIVERSITY Bodleian Library Fig. 14: Library sign.

—expressing the Rylean fact that the Bodleian Library constitutes a part of Oxford University (Fig. 14). Thus, it is certainly not the case that other logical functions than conjunction cannot be more or less spontaneously expressed in a connected propositional field in the wild by different means—the bottom line is that they seem to require special contexts or further conventions to deviate from the standard conjunction which prevails between several expressed propositions as a default value. An even more elementary question is: by which means can the presence of a connected propositional field be recognized? An explicit marker to delimit and define such a topologically connected field is that of the frame, often explicitly expressed by means of a printed or drawn line or a material limit, in other cases implicitly present only. Take the examples of the Egyptian label and the cartoon above. In both cases, there is an immediate and easily palpable limit of the connected space allowing for the expression of propositions. In the King Den label, it is simply the edge of the small ivory tablet itself which constitutes, simultaneously, the limit of propositional space. Its flip side contains a space of its own with another expression, the double sign there assumedly meaning “sandals” or “wine”, which constitutes a proposition of itself, in contradistinction to the propositional complex on the front side dealing with the king’s military achievements. In many cases, such a material border immediately constitutes the topological space within which a proposition is synthesized—the tomb-

Framing—The Topological Character of Co-Localization

95

stone’s physical limits, the edge of a book cover, the rim of a metal traffic sign, the limit of the poster or billboard, the edge of the blackboard, or of the program window or the whole of the computer screen. The early development from papyri scrolls to parchment codices takes us from a simple case where the limits of propositional space is the edge of the long sheet of papyrus to the convention that a number of similar-shaped parchment or paper bits bound together constitute one coherent, sequential propositional space addressable by what is characteristically called “scrolling” through the book. Take the book cover as example. It most often contains at least three co-localized text items—the title of the book, its author, and its publisher, effectively coming together in the proposition: “This book is Harry Potter and the Philosopher’s Stone, written by J.K. Rowling, published by Bloomsbury”, as in the Fig. 15 example.⁸³ Very often, there is a difference in font size indicating a hierarchy of co-localized information. Here, author and title share the same typeface, but the main character part of the title appears in large font with the author next and the subtitle third, all sharing the same column so that line length determines font size. The publisher, in a slightly different font, is at a distance from the author and title, and does not share the column, indicating information on a different level. Very often, the proposition is supplemented by further illustration (here, a photo of a red mineral supposedly the stone of the title) adding further information about the book’s contents to the final, synthetized proposition complex of the front cover. You may ask: but is all of this not merely an issue of ‘association by contiguity’, the standard psychological notion for the process of connecting ideas perceived in close spatio-temporal juxtaposition? In a certain sense, yes, but the reason why such an analysis is correct, but not sufficient, is that the propositional complex is not just a symmetric association between a number of ideas—it is asymmetric and has a truth value: it actually claims that this book is about Harry Potter, written by Rowling, etc. If, by some publishing house error, the author of that book was given as Daniel Defoe on the cover, Bloomsbury would have to withdraw the book from the market in order to correct the error and the cover designer or other actor responsible might expect to be sued or at least face a salary reduction for committing it. As in the book cover case, various pragmatic contexts have developed subgenres where we expect a certain set of propositional information given. In a tombstone, the name and lifespan of the deceased is the standard label attached in close proximity to the place beneath which the coffin or urn containing the remains of the person concerned is supposedly buried (Fig. 16).⁸⁴ Sometimes, additional information can be attached, maybe his or her occupation, maybe an additional expression of the emotions of the relatives left behind, maybe a quote, maybe a small pictorial symbol, a cross, an angel, a bird, rarely much more than

96

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

Fig. 15: The cover of Harry Potter and the Philosopher’s Stone.

that. In other cases, like that of posters and homepages, less fixed-genre structures are present. Very often though, the feature of a ‘headline’ is used, making a high-level proposition referring to all that follows, indicating that the main theme is that announced by the uppermost text bit in large graphic font. The cartoon example shows a different strategy than material framing: a line separates a subspace from a larger connected field, and within this graphical frame, Predicates and Subjects may come together to synthesize into proposi-

Framing—The Topological Character of Co-Localization

97

Fig. 16: The Peirces’ tombstone, Milford PA (author’s collection).

tions. In cartoons, the standard technical term for the drawn rectangle (more rarely, circle, triangle, or other closed curve) segregating the proposition field is indeed “frame”, and what we are addressing here is framing in an elementary, topological sense of the word (not in the widespread, more metaphorical version of the term where it refers to contextualizing a message in different significant ways). Here, it involves cutting out a topological field of propositionality, within which the different signs presented are presumed to be fused in the characteristic way giving rise to propositional truth claims. The cartoon frame is a convention, claiming that what is depicted inside it is a scene actually happening, tak-

98

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

ing place over a relatively short period of time, ranging from the snapshot instant to maybe around ten seconds of time (exceptional cases may extend this time limit by various tools, but here we address the typical cartoon frame). An immediate idea might be that cartoon frames are rather like drawn snapshots of an event, but that is really only rarely the case. The presence of speech bubbles in many if not most cartoon frames ensures that the frame depicts a moment lasting at least as long as it takes to utter the sentences represented. Often, the turn-taking of a dialogue segment is presented in one frame with a number of speech bubbles representing so many lines spoken, effectively claiming that this conversation takes place in the sequence as recorded by the speech bubbles, often with an implicit time vector in the reading direction (first lines represented in the top of the frame to the left, later replies represented lower and more to the right). Another means of “stretching” the moment is movement lines of different sorts, indicating a temporal sequence of an object’s displacement within the frame. We shall not go deeply into comic frame conventions here (see Østergaard and Stjernfelt 2013); these remarks serve simply to give the idea that the proposition complex which the frame frames does not relate to an instant without extension, but rather to the extended moment of the events of a brief scene which the comic frame proposition claims to happen. Another sort of framing is that from which the general concept borrows its expression: that of physically crafted frames added to and enclosing the selected topological space, well-known from the different painting frames of art history. Such frames emphasize the margin of the propositional field and makes it conspicuous that what is inside really differs from non-propositional space around it. As an extended object, the frame may develop into a subspace of its own, adding further content to the space inside it. The decoration of the frame, e. g., with ornament, gilding, expensive material, etc., may glorify or ennoble the propositions expressed by the canvas or by the canvas-plus-frame complex in various ways, just as the frame gives an extra space which may be used for propositional purposes—like the addition of the name of the person portrayed, or, in other cases, the location of a landscape painting or, more generally, the title of the painting. Such a frame, of course, may be copied in the sense that it may be drawn, printed, or otherwise reproduced on a piece of paper, a computer screen or elsewhere. The ornamentation of the frame adding some kind of elevation, celebration, or even sacralization of the proposition inside it has its special prehistory in the cartouche, having an early root in the Egyptian tradition of presenting the names of gods or rulers in an oval enclosure to make them stand out among other, not so enclosed hieroglyphs.⁸⁵ In many Middle Eastern and Western traditions, this developed into the funeral cartouche ennobling the name of the deceased inside it; later a branch of the cartouche tradition identi-

Framing—The Topological Character of Co-Localization

99

fied it with a stylized military shield, giving rise to the heraldic tradition of armories for noble houses (with all of the special, narrow conventions of their representation of ancestry, titles, and territories) as well as to the tradition of military insignia characterizing a weapon, building, or warrior labelled by them— and expressing the proposition that they belong to this or that regiment or other military unit. Such ornamented frames thus add more or less explicit further claims to the basic proposition expressed within their confines. The presentation of the topological field permitting the fusion of Predicate and Subject may use still other means. In the geometric examples above, there was no frame indicated (apart from the implicit one of the text column or book page on which they appear). They manage instead to present the topological space by means of the synthetic unity of the figure itself. The triangle is a closed, finished Object floating in an indefinite, empty space, and the letter names of its parts are given with the same typeface, adding to the unity of the figure. Quite different is the Cartesian plane, which is, in principle, open in all four directions indicated by the arrowed axes, even if, very often, only the upper right quadrant corresponding to positive x, y-coordinates is made explicit. Still, the figure of the Cartesian plane is so widespread and entrenched that it has become a stable sign, so to speak able to stand its ground and synthesize its parts, all in order, of course, to serve the understanding of the points or curves represented in it (in a certain sense, the Cartesian plane is, in itself, a particular kind of frame giving meaning to those points and curves expressed in the metrical field given by the axes). Thus, certain propositional picture-text complexes may be so traditionalized as to be in no need of further framing around them in order to be understood as synthetic proposition-bearing topological fields. The curve itself is a proposition complex claiming a specific relation between x and y; in empirical cases, many statistical apparatuses have been developed in order to grant the most well-supported curve connection between data points given, effectively forming a general assertion uniting the particular assertions stated by each data point. Another way of establishing the topological field for co-localization is stylistic. Using the same typeface, for instance, for the different messages assembled in a poster, an advertisement, or a homepage, is a way of indicating that all these messages address the same state of things in the same Universe of Discourse (as Peirce would say), so that the area over which they spread, an area often also containing non-linguistic sign material, is a topologically connected propositional space. Such stylistic unity may be achieved by a multitude of means: typeface, shape, color, common historical, geographical, ethnic reference (e. g., period typefaces for period films). In the Bloomsbury title reproduced above, such stylistic unity is ensured by picking a related typeface for the three text bits.

100

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

The explicit, adorned frame and the stylistic unity as markers of propositional topological space are examples of cases where the sign explicitly communicates that it is indeed a sign. This gives some substance to Peirce’s potentially surprising claim from the Syllabus Deduction of the Dicisign: namely, that the proposition not only makes a claim about some fact or state of things, but it also makes a claim about the sign itself, a claim that it is a sign which stands in a certain, indexical connection to its Object, in turn granting its truth. This might occur as a strange, over-complicated claim about simple linguistic or painting-with-alabel propositions. But the very delineation of a topological field of propositional expression in the middle of the ordinary perceptual field forms exactly such a self-reference. Stylistic unity basically communicates this—all of the content stylistically synthesized is indicated as belonging to one and the same topological field and should be interpreted together as a propositional complex referring to the same complex of facts in the same universe of discourse. Take again the trivial example of traffic signs. Before any particular message of theirs is expressed, the road user has first of all to acknowledge that here is a sign. Such a message is conveyed by means of the structurally similar design of all traffic signs. They are composed from a strict selection of few focal colors (typically red, white, black for the most important ones, going into blue and yellow for the less important ones, while green and brown are used to a lesser degree and orange and purple almost never), printed with strongly reflecting paint on metal so that they light up in the dark when hit by car lights. Their design is stylized, often with simple shapes (round, rectangular, or triangular) and a broad frame or rim enclosing their message. All of these features of the traffic sign serve to communicate, before any particular propositional content of the single sign type, that this is a propositional sign, as a first message intended to make the road user take a closer look and try to understand the sign’s further message. Therefore, Peirce’s insistence, in his deduction of the Dicisign, that propositions involve a self-reference is supported by this observation that, in actually occurring signs, the very establishment of the topological field of co-localization in the eyes of the interpreter is dependent upon the sign first communicating that it is indeed a sign. That it is indeed a sign, furthermore, which claims to be a truthful index of its Object, as Peirce says, is often underpinned by institutional means. In traffic signs, their expensive, standardized, and stylized character points to public traffic regulation and the authority and government-funded policy behind them (a bit like the peacock’s famous tail as a sign of its health, strength, and good genes) as a guarantee that their signaling is generally truthful and can indeed be taken as a reliable index of road conditions as well as of the enforcement of traffic regulations (there is an obstacle on the road ahead, and authorities may attempt to punish you if you do not slow down, etc.)

Co-localization and Linguistics

101

Co-localization and Linguistics The general issue of connecting Predicate and Subject is an issue of syntax, Peirce said, but different from linguistic syntax. That is certainly correct, but the question is whether this difference is categorical and refers to two completely different modes of conjunction, or whether it is rather a difference of degree. I tend to opt for the latter. Some of the label examples we have discussed (the book front cover, the tombstone) may make use of linguistic items only, and many multimodal propositions unproblematically include linguistic parts. On top of that comes the fact that linguistic syntax proper only holds within the confines of the sentence, the elementary linguistic field of co-localization. As soon as we pass into transphrastic linguistics—the combination of sentences into periods, periods into sections, sections into genre-structured texts, texts into dialogue or strife with other texts, etc.—we are dealing with the co-localization of linguistic items within that especially restrained field of co-localization which is the one-dimensional string of lexemes. But the isolation of that string is, in itself, to some degree an artifice of text linguistics. Take books, for example. The book consisting of text only, in one one-dimensional “tube” from (but not including) the title page to the final page, is, in the larger perspective, an exception rather than a rule. Illustrated texts, books, magazines, newspapers, internet pages, texts including paintings, photos, drawings, prints, diagrams in the shapes of maps, graphs, tables, matrices are, in the larger perspective, the multimodal semiotic rule rather than the exception. On top of that, such illustrations most often are also accompanied by paratext fusing with them to constitute propositions of their own, so that illustrations are not the secondary, auxiliary means added besides the main text as they are sometimes understood to be—indeed, in many scientific papers, diagrams form the center of attention, and the accompanying text rather serves to make understandable that central fusion of data, hypotheses, and theory which is presented in a synthetical diagram. Linguists may accept such claims but add the counterargument that such issues are really the concern of pragmatics, an additional, tertiary discipline pertaining to language use, after the more crucial ones of syntax and semantics, forming the center of the study of signification. The great irony here is that this very taxonomy—syntax-semantics-pragmatics—actually arose from Charles Morris’ reinterpretation of Peirce’s logico-semiotic triad of speculative grammar, critical logic, and methodeutic or rhetoric. But to Peirce the pragmatist, pragmatics would never come last in any sense of being secondary or least important. To him, syntax and semantics (or semiotics and logic, as he would rather call them), are motivated through and through by their pragmatic purposes so that the isolation of them may indeed be a practical

102

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

tool for focusing investigation on certain questions but not an ontological claim for their radical autonomy or priority. In this light, we should rather conceive of linguistic syntax as a very special case of more general propositional co-localization, often restricted to a one-dimensional space and with the sophisticated development of a large number of special linguistic tools to articulate propositions more unanimously, process them quicker, make possible a recursive hierarchy of propositions talking about other propositions, cross-identify items across levels, etc. A linguistic tradition which may point in this direction is that indicated by the so-called localist hypothesis discussed in linguistics for some centuries and which recently has enjoyed a renaissance within cognitive linguistics (cf. Leonard Talmy, Ronald Langacker, etc.).⁸⁶ A basic idea in this context is that central syntactico-semantic issues like case structure and prepositions should be understood in spatial terms; perhaps there is even a spatial element or dimension in most or all of semantics. In our multimodal examples (like the Egyptian tablet and the comics frame), the roles of the linguistically represented Subject terms, filling in slots around a central pictorial Predicate, may easily be paraphrased by prepositional or case grammar means: The label theme is about the first victory over the East, Den is the name of the king, the exclamation of victory is uttered by the king, and the label is owned or drawn by Jakurjan. This being the case, what would, linguistically, be expressed and linearized by means of prepositions or grammatical cases, is multimodally expressed (albeit in a less precise or less explicit manner) by different types of co-localization. A corollary of Peirce’s hypothesis is that propositions are no privilege of language—propositions of many sorts abound outside of language, and they existed long before human language—cf. the discussion of biosemiotics below. In such an overall conception, human language appears instead to be a late, hyperspecialized, detailed, leveled, strongly controlled and restricted version of a co-localization field, giving rise to new levels of precision, processing, speed, and recursion. But what is indeed the basis of the ubiquity of propositions originating in co‐localization? My contention is that this very basic status of the co-localization syntax of propositions can be described in two registers: an ontological or metaphysical register and, empirically, in a phylogenetic, biological register. Let us take the empirical case first.

Co-localization in Biosemiotics

103

Co-localization in Biosemiotics In biosemiotics,⁸⁷ my hypothesis is that Peircean signs will be found from the most primitive beginnings of semiotics among bacteria. Therefore, I reject the idea that simple signs or even proto-signs occurred early which only much later combined into more complicated signs such as propositions. Rather, the opposite picture: that primitive versions of all Peircean signs are there from the beginning. Primitive propositions enable organisms to be informed about relevant aspects of their environment, and primitive arguments permit them to draw pragmatic action inferences based upon inherited habits, in an Uexkü ll perception-action cycle, important for their survival. I do not claim consciousness need be involved, as many signs already in human semiotics are produced and interpreted without the intervention of consciousness; on top of this, we have no stable criteria yet to establish the presence of consciousness in other creatures, especially not in species very different from our own. Isolated icons or indices—often-mentioned candidates for more simple or “proto” signs— could not serve an organism in any way if no proposition were there to interconnect such signs to provide information, or if no argument permitted the inference from that information to subsequent relevant action.⁸⁸ Sign evolution rather takes place by adding further layers of control, e. g., by means of the evolution of consciousness; adding further articulation, subdivision and hence control of primitive propositions and arguments; adding further dimensions of freedom in the individual ontogenetic learning of signs. Many people frown at this generalization of “proposition” and “argument” which they prefer to keep as linguistic and human privileges. They might claim it is “anthropocentrism” to generalize such concepts—you could rather call it anthropocentrism to claim a human privilege for those concepts, often leading to construe biological semiosis as much too close to simple mechanical causal chains, ultimately making Cartesian automata out of animals and other organisms. I shall not go further into that discussion in this context.⁸⁹ In what follows, I apologize for giving a general, speculative draft only, as well as for revisiting central biosemiotic examples already often covered: the nutrition hunt by the E. coli, the mating signals of fireflies, the aposematic scare signs of wasps, honey bee communication, etc.⁹⁰ As is well known, E. coli bacteria have the ability to detect the presence of carbohydrates and orient their swimming in the direction of the carbohydrate gradient.⁹¹ That ability relies on simple sensory organs able to identify carbohydrates from a specific “active site” on the periphery of the macromolecule. That lies behind their possibility of committing error, based on the fact that non-carbohydrates with the same active sites exist—like artificial sweeteners—which give rise to the same oriented

104

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

swimming behavior in the bacteria. In this case, the Subject will be the actual molecular interaction establishing the contact between the sensor and the molecule, the Predicate will be the active site shape classification of “sugar” (as opposed to the classification of certain toxins which is also within E. coli capacity). In our context, the important feature is that the Predicate, given by the character of the active site, is attached to the Object, indeed is a peripheral part of it. In this way it constitutes a very primitive case of “labeling”—rather like a sack with the word “sugar” upon it, apart from the fact that no one is here communicating with the bacterium. There is no distance between sign and Object, and the former is a specific part of the latter. I suggest that there is reason to believe that in the majority of most primitive cases, proto-propositions are labels in the sense discussed here. In such cases, there is not yet any marked field of colocalization because co-localization is here taken care of by the elementary mereological structure granting that the sign, as a part of the object, is automatically co-localized with it. Firefly mating signals are, by contrast, communicative—they are also labels in the sense that the Subject (the flashing light against a dark background) and the Predicate (the species-specific flash pattern identifying the kind of insect flashing) are both emitted in the here-and-now window of communication from the body of the communicator about which they also inform.⁹² Still, some distance is introduced: there is no immediate chemical contact between the two parties which comes only later, after initial communication. But Subject and Object are co-localized as aspects of one and the same signal whose extension forms an emerging if brief, spatiotemporal field of co-localization. In the wasp aposematic example, the yellow-and-black striping is recognized as a signal of danger across species, scaring predators from attacking the poisonous wasp. As in the firefly example, the sign-claiming-it-is-a-sign has made the appearance: the sign has evolved so as to stand apart from its non-semiotic surroundings—there are generally few natural flashes in the dark, and the yellowblack combination stands out against green foliage, other more discretely colored insect species, and the grey-beige-brown-black color range of the ground. In this way the striping communicates that it is a sign, and the proposition it claims is something like “This is a dangerous creature”. Here, too, the strategy is an example of labeling, the pattern being part of the communicating animal itself. Again, the possibility of deception illustrates the striping is a truth-value claiming sign: other, less dangerous species without a sting like hoverflies and wasp beetles use the same sign to scare away predators.⁹³ In the case of an animal leaving scent marks to delimit a territory, the proposition presented to competing conspecifics can be paraphrased along the lines of “This territory belongs to the originator of this particular scent”. In relation to

Co-localization in Biosemiotics

105

the territory, this proposition is a label, but not so in relation to the animal which may be far away at the time of its rival interpreting the sign. Both, however, form aspects of one and the same sign which approach a minimal field of co-localization. The same goes for the predator tracing its prey from involuntarily left-behind traces like footprints, scent marks, broken twigs, etc.,—here it goes without saying that the prey has left behind propositional signs interpreted by the predator, signs which preserve an earlier here-and-now index serving as the Subject of the proposition combining with a Predicate, the species-revealing composition of the smell or shape of the prints, to give something like “a hare was here”— and, in combination with several such signs: “it left in that direction”. Therefore, I propose that biological evolution began with very simple, noncommunicative label propositions in which co-localization is automatic and not yet subject to compositionality, only to evolve into full, communicative propositions with possible absence of the Object, with the development of long-distance perception possibilities like smelling, hearing, vision and their subsequent integration into environmental maps which E. coli could not at all be said to possess. This anecdotal summary of some biosemiotic cases should not, of course, count as evidence, rather as giving an overall scheme for the possible evolution of propositional signs emerging from simple labels where propositional interpretation is closely tied to simple sensation in direct Object contact, in a certain sense, an extreme co-localization bordering to identity. An important constraint, however, seems to prevail, all the way up to human semiotics—namely the small spatio-temporal window in which the synthesizing cognition of co-localized Subject and Predicate is possible. Here, I owe much to my Estonian colleague Kalevi Kull, who has insisted upon bringing Ernst Pöppel’s concept of the present now into biosemiotics. A large amount of biosemiotic sign exchange takes place based on habits and instinctive behaviors acquired on an evolutionary timescale of at least many thousands, more often millions of years. Yet, the actual sign exchange on that basis takes place typically in the matter of seconds. The male firefly flies around in the dark, emitting flashes, while the females sit, perched in the grass, responding. This dialogue sequence takes place in the present now and may lead to the male diving in order to meet the female, at least in a sufficient number of cases to continue the species. This exchange, in which the Subject-Predicate couplings are performed by each of the two genders, take place in a very brief time window. Already some insects may artificially extend this window by some short-term memory, as when the honey-bee is able to inform her conspecifics in the cube, by means of “waggle dancing”, about nectar she has found several hundred meters away, several minutes or maybe even hours ago. This communication has a very detailed propositional content—paraphrasable as “Nectar can be found 150 me-

106

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

ters away in the direction of 25 degrees from the present position of the sun”. The bee is even able to correct for the sun’s movement since the initial time of observation. This obviously requires a pretty impressive amount of short-term memory, considerably enlarging what can be communicated about. But again, the very sign exchange spreading the crucial information to her colleagues and combining Subject and Predicate in the waggle dance, is performed by the bee in the present now shared with the fellow bees watching. Here, the waggle movement—which is used during communication only—communicates that the sign is indeed a sign, and the relatively small spatio-temporal extension of that movement forms an early example of a field of co-localization where the two object-identifying subject indices, direction (relative to the sun) and the distance (the length of the dance) are expressed simultaneously (the Predicate “nectar” remaining implicit as a presupposition). Direction and distance effectively come together in the dance as a diagram of location relative to the cube. This relatively small extension of the communicative time window, probably rarely much more than a matter of seconds, appears as the temporal equivalent to the delimited extension of the spatial, topological field permitting the unity of Subject and Predicate. As Kull says, referring to the development of the concepts of “moment” and “specious present” in Karl Ernst von Baer and William James: “… the existence of the specious present is coextensive with semiosis’ (Kull 2018, 137). Human spoken language parsed in periods exploits a similar time window, losing cohesion and meaning if more than a number of seconds elapse between the uttering of each word.⁹⁴ With the evolution of central nervous systems, of cross-modal integration of perceptions (so that different sense modalities may be perceived as referring to one and the same object), of hard-wired propositional parsing of perceptions,⁹⁵ of short-term memory, of ontogenetic learning adding to inherited habits, of semantic memory, of episodic memory, of explicit syntheses in consciousness—with a long series of evolutionary scaffolding achievements, the abilities of detailed understanding and acting in this brief time window are multiplied immensely. The experiential, perceptive-active core at the center of semiotic activity, however, seems to remain tied to this rather small time window of perceptual processing, the spatial correlate of which seems to be the delimited topological field of co-localization to be scrutinized in one or a few glances. In a certain sense, then, co-localization is essentially spatio-temporal and given by the perceptual experience window, the more exact size of which depends upon the species discussed. This is not to deny that higher animals may have both short term, long term, and semantic memory and maybe even to some degree episodic memory, all of which support coherent or even planned activity in time and space, stretching far beyond that small spatiotemporal window—but still these abilities seem to merge, fuse, or synthesize experiential moments with, in each case, far more re-

The Ontology of Propositional Truth

107

stricted spatiotemporal extension. But in that delimited spatio-temporal extension window, the central synthesis of Subject and Predicate of general propositions takes place.

The Ontology of Propositional Truth It is well known that the notion of “truth” has been the subject of centuries of philosophical debate, attempts at redefinition, relativization, and even at eradication seeking to replace it with ontologically less demanding notions (based on coherence, consensus, regularity, utility, and more). The notion of truth inherent in Peirce’s general concept of proposition may merit a consideration in the context of the ontology of propositions. It also is well known that Peirce was a realist in no fewer than two senses: (1) a basic scientific sense, in which reality is that which is independent of any particular representation of it; (2) a more ambitious, “scholastic” sense, claiming the reality of certain universals, particularly those investigated scientifically—the competing notion being nominalism claiming that all universals are but human-invented, imposed labels with no fundamentum in re—see Chapter 12 below.⁹⁶ These realisms provide the backdrop of Peirce’s theory of facts—which are, in present-day parlance, the truthmakers of propositions:⁹⁷ (1) The truth of a proposition is independent of who thinks or utters it; (2) True propositions exist which involve general terms—which is Peirce’s basic reason for accepting that some of these general terms must possess reality. This can be called truthmaker realism: If a certain fact holds, the correspondent proposition claiming that fact, is true. Indeed, the whole of Peirce’s edifice is based on the Kantian idea of beginning with assuming the existence of true propositions and defining ontological commitments from the principle that the real is that which is presupposed to exist by true propositions. Facts are correlatively defined as so much of reality as is represented by a true proposition. This Peircean conception contrasts with the more general notion of “occurrence”, referring to some spatio-temporal section of reality. A fact, by contrast, is a part of reality which is structured like a proposition.⁹⁸ Two important caveats should be added here, an ontological and a sociological one. Peirce does not, by this theory, subscribe to any doctrine about “elementary facts”, “logical atoms”, or anything which in this way would assume some fixed ontological bottom level. Facts may occur at all levels of reality, from mathematics through logic and metaphysics to all of the special sciences, physics, biology, psychology, history, and so forth. This is directly connected to his logical theory, whose doctrine of reference is inherited from de Morgan and Boole’s notion of “Universe of Discourse”. Any proposition is related, more or less explicitly, to a Universe of Dis-

108

Chapter 5: Co-localization as the Syntax of Multimodal Propositions

course which is some selected subset of reality or imagination (but imagination is but a special, dependent part of reality). Universes of Discourse may range from containing all possibilities, over all reality past and future to the here and now, over the various realms investigated by each special science and to very select and local subsets such as the room in which I am now, the confines of this chapter you are now reading, the fictive world of Uncle Scrooge—and the truth of propositions is thus always relative to some such Universe of Discourse. In the Duckburg universe it is simply false to claim that Donald is the world’s richest duck. This in contradistinction to Russell’s and Wittgenstein’s rigid and simplistic idea that the Object of logical propositions is invariably the whole of reality and that their ultimate truth grant must lie in ‘logical atoms’ or anything like it. To the special and typical speech act function of asserting a proposition Peirce gives, as we saw, a pragmatic, sociological definition: by asserting something, one makes oneself liable to sanction from relevant authorities if the assertion proves false.⁹⁹ If I claim that Donald is the world’s richest duck, I shall earn stern rebuke from comic lovers and Carl Barks scholars alike. If, as an academic, I knowingly publish falsified data or ‘fake news’, I may be subject to severe retribution, including the termination of my position. If I falsify signatures in documents, I may face prosecution under criminal legislation. And so on. This criterion seems to corroborate the widespread appearance of multimodal propositions across human society in so far as a vast number of cases can be found in which such propositions are being taken seriously as truth claims found to contain error meriting sanction.¹⁰⁰ In biology, the failure of an organism (or species) to process propositional information and act appropriately may lead to individual death and collective extinction. In a certain sense, the doctrine of co-localization propositions comes with fairly strong ontological claims, in the sense that it accepts both of Peirce’s conceptions of realism. In another sense, the co-localization hypothesis does not come with any strong particular claims to ontology, leaving it to the special sciences to determine which universals in multimodal propositions correspond, in fact, to real kinds, patterns, tendencies, forces, or causes. Even ontological sceptics may embrace important and central parts of the theory, however, restricting themselves to accepting Peirce’s sociological doctrine of assertion. There is hardly any doubt possible that social sanction of many different kinds is indeed put to effect against a vast array of falsities expressed by means of co-localized propositions in Peirce’s generalized sense, from white lies and rather innocent deviations from truth to severe cases of intentional and systematic deceit, fraud, cheating, and misinformation. In order to understand such systems of sanctions, no matter whether one finds them just or condemnable, Peirce’s general doctrine of propositions will be helpful.

The Ontology of Propositional Truth

109

But an important general corollary of a Peircean doctrine of co-localization as the general syntax of multimodal propositions will be: many more empirical sign complexes than usually assumed do actually carry truth claims and should be investigated as such in our analyses of semiotic exchanges of nature and culture alike.

Chapter 6 Sheets in the Wild A First Overview over Types of Propositional Surfaces This Chapter investigates how Peirce’s formal idea of a “Sheet of Assertion” (SA) from his Existential Graphs may be generalized to cover certain simple classes of signs in the wild, that is, in the semiotic world outside of logic formalizations. In the EGs, a graph is asserted if scribed on a “Sheet of Assertion”, and several such graphs side by side express the assertion of the logical conjunction of the represented propositions. In the wild, we find a lot of different cases where “Sheets”, that is, delimited areas of attention within the field of perception, have the same function: signs placed on such a Sheet are cognized as fused together into one asserted proposition. We already saw a couple of examples in the previous chapter. Such “sheets in the wild” fulfil an overlooked function in many media from paintings, posters, billboards, movies to the internet—to fuse signs into propositions, to combine propositions into conjunctions, facilitating the quick, often quasi-automatic cognitive processing of truth claims. This paper gives a first overview over types of sheets in the wild.

Sheets of Assertion When Peirce, in the mid-1890s, began drafting his Existential Graphs formalism of logic, he picked as its base the empty page endowed with a special interpretation: “We must appropriate a sheet to the purpose, and the diagram drawn or written on the sheet is to express an assertion. We can, then, approximately call this sheet our sheet of assertion”.¹⁰¹ The “Sheet of Assertion” (SA) on which logic graphs were to be written, was defined with a number of elementary properties. One was that the sheet was taken to involve, implicitly, all truths about the relevant Universe of Discourse agreed upon by those using it for representing propositions and attempting to conduct proofs. Another was that the very scribing of a proposition on the sheet amounted to asserting the truth of that proposition, so that such assertion was equal to photographically developing and making explicit the relevant, implicit part of the Universe of Discourse. Finally, writing two or more propositions placed in the same part of the Sheet of Assertion was equivalent to asserting the logical conjunction of those propositions. This was the simplest way of expressing the conjunction of two propositions, by just representing https://doi.org/10.1515/9783110793628-008

A Few Examples of Sheets

111

them side by side. Peirce argued this representation was the most iconic way of representing conjunction.¹⁰² That simple convention, forming the basis of Peirce’s Alpha Graphs for propositional logic, went on to form the base also for Peirce’s Beta system for first order predicate logic and his bundle of various further developments of the Gamma Graphs: “p q” meaning “p ∧ q” or “p & q”. The proposal of this chapter is that Peirce’s “Sheet of Assertion” is a formalization of a way of representing simple parts of propositional and first order logic which is already present “in the wild”, in book covers, posters, homepages, and in a long series of other, widespread semiotic phenomena. A parallel argument pertains to the additional convention which Peirce adopted for his Beta Graph representation of first order predicate logic. Here, Peirce invented the notion of an oriented “identity line” connecting a predicate sign with one or more subject P” meaning signs in order to represent the composition of a proposition: “S “S is P”. The line furnishes an alternative way of connecting signs; while the simple co-localization meant conjunction, another graphic representation, that of a connecting line, represented the co-localization of subject and predicate indicating their fusion into a proposition. Similar connecting lines are also often found “in the wild”, indicating propositional syntax. In Chapter 5, I developed further the Peircean idea of a graphical co-localization syntax. Here I shall focus upon the detail of which types of “Sheets in the Wild” can be found. In the wild, Peircean assertion is defined by some user taking responsibility for the truth of a proposition, thereby admitting social sanctions against that user in case of falsity; cf. Chapter 3. Oftentimes, such assertion is purely linguistic, but in a surprising number of cases, assertion uses multimodal or mixed-media Sheets of Assertion to express propositions. Let us consider a couple of examples.

A Few Examples of Sheets A simple case is Peirce’s standard example of a proposition—a painting with a legend.¹⁰³ The combination of two such signs constitute a proposition: the legend (or title, or label) functions as a subject index, informing the observer about what is the object of the sign; the painting functions as a predicate, furnishing some description of the same object. Signs need to have these two sides in order for them to take a truth value: if the description fits the object pointed out, the composite sign is true, if not it is false. The important issue here is the syntax which fuse the two constituent signs into one.¹⁰⁴ As only the legend part of the sign is linguistic, it cannot be due to linguistic syntax only. Rather, its syntax is the co-localization of the two signs on some surface. Oftentimes, the legend is presented on the frame of the painting, in other cases on the flip side, in still others in a special, separate sign adjacent on the

112

Chapter 6: Sheets in the Wild

same wall, etc. In all cases, however, the two should be presented in proximity so as to be processed as one complex sign, that is, occupying nearby parts of the same topological sheet. Such co-localization is facilitated by taking place within the confines of a special 2-dimensional surface delimited by an ex- or implicit border constituting a connected, topological space—a propositional field. Here an example from 1772 showing the execution of the German prime minister in Denmark and his assistant (Fig. 17).¹⁰⁵ He had recently introduced Press Freedom and offended the local nobility. The legend says: “Depiction of the Execution of the Twain Counts STRUENSEE and BRANDT”, followed by a mocking verse advising the reader to stay true to God and King, in order to avoid a similar fate. The simple fact I am talking about here, however, is how the image and legend parts of this proposition, establishing the identity of some of the depicted persons, come together as two sections of one and the same Sheet of Assertion, delimited by a common outer frame. In such cases, Subject and Predicate—here, text and image—are fused without a connecting identity line, merely by being colocalized as two parts of the same sheet.

Fig. 17: Woodcut sheet reporting on the execution of Danish prime minister Struensee and his alleged accomplice count Brandt, Copenhagen 1772.

A Few Examples of Sheets

113

In other cases, several such picture-with-legend signs may form part of one and the same sheet, as e. g., in many anatomical charts:

Fig. 18: Anatomical chart of the thorax with selected parts.

Here, simple identity lines are used to fuse Predicate and Subject into propositions (Fig. 18).¹⁰⁶ In the example, nine such legend-picture propositions indicate the relative position of parts of the upper thorax around the heart by means of arrows, functioning simultaneously as identity lines constituting propositions (“This is the Trachea” … etc.).¹⁰⁷ Just as in Peirce’s SA, their placement on one and the same sheet indicate the claim that the conjunction of all nine of them is true. Something similar takes place in topographical maps where names of cities, countries, areas, landmarks, etc. are most often given by simply placing the relevant name in proximity to the sign of the object it refers to, that is, without any explicit arrow or connecting line, cf. above. Also here, the map as a whole constitutes one complex proposition taken to be true if all constituent propositions are true.¹⁰⁸ Of course, they need not be, as the example of early maps of Antarctica covering most of the Southern Hemisphere testify. In legend+picture propositions, the 2D space of the picture sign is taken to depict a projection of some of the spatial features of the object. That is not the case in Peirce’s purely logical SA definitions. But we also find such abstract Sheets in the wild. Take, for instance, a book cover (Fig. 19):

114

Chapter 6: Sheets in the Wild

Fig. 19: Title page of Spinoza’s Tractatus Theologico-Politicus, anonymous publication, Amsterdam 1670.

It constitutes an abstract sheet which does not depict its object—which is the book itself and its contents. Rather, the different signs on its surface make claims about the book. Most often, the title is highlighted by the largest font type, as here in Spinoza’s “Tractatus Theologico-Politicus” from 1670.¹⁰⁹ That sign claims the proposition: “This book is a copy of the Tractatus …” Other signs, linguistically unconnected to the title, float in the same 2D space of the sheet, so, for instance, the printer’s name “Künrath” and the city of publication, Hamburg. They make propositional claims that “This book was printed by Künrath in Hamburg”. Both of those claims, by the way, are false. Spinoza wrote in a period when there was immediate danger connected with expressing “Libertas philosophandi”, freedom to think, as the subtitle has it, and not only did he prefer not to put

A Few Examples of Sheets

115

his name on the title page, but also to place those false propositions there. We now know the book was printed by a certain Israel de Paul in Amsterdam, but Spinoza or de Paul himself considered it wise to disguise his identity behind a false name.¹¹⁰ By being placed on the same Sheet of Assertion, those three independent propositions all claim to be true about the book on which they sit, even if two of them are deliberately erroneous. Simultaneously, the book cover is an example of the proposition type which could be called a “label” because its predicate forms part of or sits directly upon one of the objects referred to by the proposition—namely, the book.¹¹¹ That is why such propositions do not have to mention that object by means of an explicit subject index. They do not have to explicitly say “This book is a copy of the ‘Tractatus …’”, etc.; it is sufficient to give the title on the label which is the book’s title page. The title page’s character of a sheet of assertion whose Uuniverse of Discourse is the book (with its context) to which it is attached, may be underlined by the fact that oftentime users may add further propositions on the sheet. Users of some copies of the Tractatus have added the absent name of the anonymous author on the title page, owners may add their name, librarians add a catalogue code, constituting so many further propositions. Once a sheet of assertion is opened, it offers itself for the possible addition of further proposition signs. This example does not, however, imply that abstract Sheets of Assertion are only found in Label signs. Those two properties of Sheets in the Wild are independent, as can be seen from a sign like this:

Fig. 20: Department of Semiotics sign, Estonia.

If this Abstract Sheet is placed on the entrance door of the semiotics department at 2, Jakobi Street in central Tartu, Estonia, it will indeed be a label. But if serving as a letterhead it is no longer a label but only claims the proposition that the relevant letter or email stems from that institutional destination, of which the three nested names are claimed to hold. Conversely, non-abstract sheets depicting spatial aspects of their objects may also be labels—as when you find, for instance, a sign with a map on a pole in a nature reserve, firmly tying the map to the very area of which it informs the sign interpreter, typically with a red point in

116

Chapter 6: Sheets in the Wild

the map indicating the location of the map itself on the map. Or the packaging of some product endowed with an image of that product. The Tartu sign also shows another syntactical possibility of Sheets in the Wild: the indication of part-whole relations by means of vertical subordination: the Department is a part of the Institute of Philosophy and Semiotics which forms, in turn, part of the Tartu University as a whole.

Posters—Serious and Satirical Complicated sheets may combine several of such strategies in a complex web of propositions. The movie poster is such a case. In the classic 1939 “Gone with the Wind” poster (Fig. 21), the overall sheet is non-abstract, presenting the likenesses of the two main actors in a landscape setting, dressed as their role parts Rhett Butler and Scarlett O’Hara, and identified by the next largest subject indices as the actors Clark Gable and Vivian Leigh. These are classic picture-with-legend propositions. The title of the movie, however, figures on a separate, roughly book-shaped, abstract sheet, inserted into the picture predicate. Actually, this secluded abstract sheet is what catches attention first, due to its largest typeface which is typically reserved for the claim about the film’s title, establishing the film, with its contents, production, and display, as the overall frame for the Universe of Discourse of the whole poster. The verb “starring” here serves to connect the two different sheets, the superordinate abstract and the subordinate (but larger) non-abstract sheet. The addition of two further such autonomous, abstract sheets towards the bottom fulfil other purposes: one informing about playing time and prices, another about the film company and director behind the movie. The main, non-abstract sheet, however, may contain further propositions, namely about the fact that David Selznick is the producer of this version of Margaret Mitchell’s book Story of the Old South. This only indirectly forms a legend+picture proposition, in so far as Mitchell’s title is epitomized by the background scene location showing a typical Southern mansion, just like the fashion of the actors’ attire signal pre-civil-war times of the Old South.¹¹² All this is deeply trivial, and I do not claim, in any way, to provide an original analysis of this classic movie poster. My aim is rather to convince the reader that Sheets in the Wild are ubiquitous and may serve the presentation of nested structures of propositions, in this case serving to cross-identifying fictive and real persons and presenting a fictive universe and its two main protagonists nested within a realist environment of authors, directors, producers, actors, playing-

Posters—Serious and Satirical

117

Fig. 21: “Gone with the Wind” poster, 1939.

times and prices—about all of which truth-claiming propositions are presented in the combined sheets. In sheets in the wild, this connectedness of the Universe of Discourse pertaining to the sheet typically becomes central. It is not a priori precluded that wide or vague universes of discourse could be addressed in a sheet—conjugating, e.g., widely different propositions like “2+2=4”, “Biden is US President”, and “Donald Duck wears a sailor’s cap”—but the typical case is one in which it goes without

118

Chapter 6: Sheets in the Wild

saying that one and the same sheet addresses one Universe of Discourse which is in some sense focused, in the sense of comprising a connected set of states-ofthings, like the movie, its contents, and its context in the poster sheet. The truth-claiming character of propositions presented on such sheets is such a matter of course that it may be, without further notice, be taken as the syntactical basis of complicated parodies as in this recent example which in a certain sense abuses these conventions of the poster sheet:

Fig. 22: Political satire poster, US 2020.

Types of Sheets of Assertions

119

The Russian and former American presidents normally do not appear together as a pop duo under the stage name of “Putin and the Pussygrabbers”. Real-life Putin rarely displays an electric guitar, just like Trump does not often don his Elvis suit. The parodic rhetoric of this anti-Trump poster of the US election year 2020 rests on the fact that the Sheet of Assertion of your standard concert poster normally presents truth-claiming propositions about the displayed artists and their performances. This is evidently not the case here, making the interpreter curious, hopefully to discover another truth claimed on a more metaphorical level. “Acting in Concert”, of course, has a double meaning: playing music together or coordinating actions. The two presidents are indirectly accused of collusion leading to election fraud on Nov. 3, 2020, and, consequently, to the loss of freedom in the USA; cf. “Farewell Freedom Tour” as the name of the concert series. This complicated piece of parodic propaganda, however, is possible only on the base that the reader tacitly understands the normal practice of co-localizing proposition constituents into propositions, and, on a higher level, co-localizing propositions in conjunction in a Sheet of Assertion claiming the truth of those propositions.

Types of Sheets of Assertions Sheets in the wild seem to use primarily a few of the features and rules of Peirce’s formal SAs: the very idea of a propositional field; co-localization indicating conjunction of propositions, and co-localization or simple identity lines as signs of Subject-Predicate syntax. Sheets in the wild do not express full propositional logic nor full first order predicate logic; rather they are pragmatic semiotic vehicles using primarily the few simple functions mentioned. This does not preclude, however, that they may sometimes experiment with more complicated logical functions like disjunction, negation, implication, even if they require more conventional representations than the strangely “free” conventions of co-localization and simple identity lines. This does not, however, prevent us from systematizing, from our hasty analytical examples a first distinction of some types of sheets in the wild, as expressed in a handful of elementary, independent distinctions. 1) Sheets parts of whose 2D space directly depict spatial features of the object vs. sheets whose space forms an abstract space of assertion only. 2) Sheets in which conjunction of propositions is the main logical function vs. sheets in which co-localization syntax of subject and predicate fuses those constituent signs into propositions, with or without identity lines. Both functions, however, may be present in one and the same sheet, just as is the case,

120

Chapter 6: Sheets in the Wild

more formally, in Peirce’s Beta Graphs. In that case, they are typically nested so that propositions united by S-P proximity may be, in turn, be put in conjunction with other such S-P complexes. 3) Sheets referring, by means of subject indices, to more or less remote (if existing) objects, vs. sheets (labels) directly forming part of or glued or otherwise fixed immediately to their referent objects, thereby dispensing from the need of representing the sign object via a subject index. 4) Sheets being simply co-extensive with the surface of the physical sign vehicles supporting them vs. sheets brought to attention by the addition of explicit delimitations emphasizing some area or field of attention by means of physical borders, limits, frames, lines, etc.¹¹³ 5) Sheets in the Wild use, as mentioned, wild forms of EG conjunction and identity lines. They only rarely, however, utilize anything like Peirce’s use of a cut-out or specially colored sheet part to mean negation or a double cut to mean implication. Special sheet conventions, less widespread in the wild, may be found, however, adding further improvised syntactical machinery like negation, part-whole or subset-set relation, disjunction, implication, etc.¹¹⁴ Semiotics has, for much of its history, hesitated to take much interest in truthclaiming signs—maybe because semiotics institutionally grew strong in art and literature departments studying more or less fictitious artefacts not centrally concerned with truth-claiming. That might be the reason that semiotics has too long neglected the central and ubiquitous function played by Sheets in the Wild, making possible truth claims in semiotic vehicles like posters, billboards, book covers and title pages, homepages, tombstones, print and internet ads, paintings, newsreel with voiceover speech, press photos with legends, documents, scientific diagrams of many sorts, topographic maps, charts, lists, traffic signs, product packagings, and much, much more.¹¹⁵ In an age of fake news,¹¹⁶ however, it is about time that semiotics rises to its responsibility to investigate how signs claim truths—in the technical confines of logic and philosophy, to be sure, but certainly also where truth really matters: in the wild.

II Iconicity and Diagrams

Chapter 7 How Do Pictures Act? Two Semiotic Aspects of Picture Activity Recently, leading scholars have focused upon the strange phenomenon that some pictures may seem to possess an intention of their own and thus act upon the observer in ways not unlike other intentional subjects. W. J. T. Mitchell famously asked What Do Pictures Want?,¹¹⁷ and most recently Horst Bredekamp has presented his argument for a “theory of picture action” in Theorie des Bildakts,¹¹⁸ arguing from example and discussing a selection of artifacts, pictures, and artworks, of which he claims that they display this strange action potential. These arguments are based upon a basic phenomenological experience—namely of pictures in some sense gazing back upon the observer and taking action. Bredekamp, of course, takes care not to presuppose any vitalist assumptions in his description of picture acts, just as he retains a minimum of human involvement as a requirement in his general definition of pictures, of Bilder. Natural images may appear, but they only qualify as pictures, according to his definition, by a minimal degree of human involvement: the addition of aesthetic arrangement or framing creating an “iconical difference” (Bredekamp 2010, 27)—“… that you can speak about pictures when natural objects display a minimum of traces of human elaboration”.¹¹⁹ It seems this minimum of human interference in the picture is connected to the picture act notion—it is human intervention and intention which is delegated, maybe in a transformed and remote manner, which reappears to emerge as a strange action potential so strikingly experienced in many pictures. My argument here is that another aspect of this action potential of pictures has roots in the structure of pictures themselves, irrespective of the degree of human participation in their origin. Bredekamp refers to Peirce for his emphasis on the spontaneous activity of matter—thereby placing himself in the hylozoist tradition reaching back through Radical Enlightenment to Lucretius and Epictetus.¹²⁰ Here, I shall refer to a couple of other important aspects of Peirce’s concept of iconicity—namely the ability of icons to enter into propositions and to function as vehicles for reasoning. Both of them add to the experienced “liveliness” or “intentionality” of pictures. As to the former—picture propositions— Peirce’s notion of “Dicisign” is important. It is, of course, his version of the logical notion of “proposition”, and Peirce was among the early formalizers of propositional logic, constructing, inter alia, his “Alpha Graphs” as a graphical notation system for propositional logic. But an important aspect of Peirce’s conhttps://doi.org/10.1515/9783110793628-009

124

Chapter 7: How Do Pictures Act?

Fig. 23: Michel-Marie Carquillat: Portrait of Joseph-Marie Jacquard, 1839, woven silk, 60.3 x 50.8 cm.

ception of logic as semiotics is the fact that his notion of which signs may serve as vehicles for propositions is much broader than that of most other logicians. Thus, a portrait with a legend is as good a representative of propositions as any purely linguistic expression, be it in everyday or formalized languages. This is because the painting with its title displays the basic subject-predicate double structure of propositions—the painted surface providing the descriptive predicate while the legend provides the subject reference.

Threatening Pictures

125

Silk Print of a Silk Weaver The portrait of the silk weaver Joseph-Marie Jacquard (1839) is basically a proposition, the legend “A la mémoire de J.M. Jacquard” playing the Subject role and the silk print portrait of a seated person playing the Predicate role (Fig. 23). The resulting proposition combining these two parts simply claims that the picture predicate presented depicts J.M. Jacquard. On top of this proposition comes the explicit speech act admonishing the observer to remember the weaver and inventor. More implicitly, the very technique of the portrait also adds to what should be remembered: The picture was woven on one of the special silk looms which Jacquard had invented; it required no less than 24,000 punched cards to create. Charles Babbage owned one of the few copies of the picture and it is assumed to have played a central role in early computing theory, the punched cards implicitly containing the information encoding the woven picture. Hence, an additional picture act more implicitly presented here can be rephrased as follows: “Remember Jacquard, for it was he who made possible the technique of this very picture.” This example is half pictorial, half linguistic, and my contention is that most (not all) pictures in everyday life do not appear in isolation but as part of propositional wholes involving text, gesture, or other semiotic machinery. But pictorial propositions without any linguistic part at all are also possible.

Threatening Pictures I may show you a photograph of a person who is present and, at the same time, point to that person in order to indicate it is he who is portrayed in the photograph. This picture act is as good as any linguistic proposition, claiming the identity of the person in flesh with the person in the photograph. But this S-P double structure may be even more subtle. Take a well-known example from the political scene: a male politician receives by mail a copy of a photograph of himself showing him in company of professional prostitutes—one need only think of the videos from the Turkish sex scandal connected to the Ergenekon case, allegedly showing leaders of the Turkish opposition party “The Nationalist Action Party” engaging with prostitutes (Fig. 24). Such photographs have been known at least since the time of Otto von Bismarck’s famous “Greenhouse” brothel in Berlin, which was equipped with hidden cameras in order to be able to intimidate politicians frequenting the place. Such a letter is obviously a picture act, even in the complete absence of any accompanying written legend or message. It is, of course, a threat—fully equivalent to the linguistic speech act

126

Chapter 7: How Do Pictures Act?

Fig. 24: Screenshot from the newscast of the Ergenekon case at www.thedailybeast.com, May 27, 2011.

of threatening. It tells you that somebody out there knows you have been engaged with a prostitute and participated in a humiliating kind of sexual intercourse —and it immediately implies the threat of sharing that information with a broader public. For preventing this, you must, of course, be ready to accept to bow to a certain pressure which may be made more specific in subsequent correspondence. The decisive criterion for such photographs is of course the identifiability of the blackmail victim in the picture. If this is indeed the case, the bare photograph itself performs both the S and the P function of the Dicisign at once—it identifies the Subject and it describes an action he has been involved in. In such a case, no linguistic legend is needed. This is what Peirce calls “collateral

Threatening Pictures

127

knowledge” of the Subject of the proposition. If no such knowledge is possessed by the addressee of the proposition, some procedure for locating the subject must be given (by a proper name, a pronoun, a pointing gesture, a logical quantifier, etc.) in the S part of the proposition. But the important insight for our argument here is that, in the presence of such collateral knowledge, the picture in itself may constitute a full-fledged proposition, even a speech act. In the case of political blackmail, of course, the shooting of the photo and the ensuing mailing are human actions governed by human intentions which aim to set up the picture as a proposition smearing the person in question. But the fact that the picture itself may constitute such a proposition loosens it from any intention promoting that proposition. The picture may present a proposition without any intentions on behalf of the manufacturer, provided that “collateral knowledge” is present in the observer. An adolescent photograph of a political candidate showing him smoking marijuana may cause grave effects to his career—even if the photograph was originally taken with the best of intentions, only as a part of cozy teenage social life. But still the photo may serve as a threatening proposition, given that collateral knowledge sufficient to identify the candidate is present. This implies that pictorial signs may function as propositions without any deliberate “propositional attitude” being put forward by the photographer or any other promoter of the picture. It may be shipped to the receiver by someone without any responsibility in creating it—yea, the politician may accidentally find the picture on his own hard disk and realize its very existence constitutes a threat, in case a hacker should penetrate his firewall. In this sense, the picture is able to act—in a broader sense of the word, it is able to assume a “propositional attitude” and perform a picture act on the beholder. Of course, as is the case in all Speech Acts, such an action can only be completed in the presence of a beholder—providing the collateral knowledge and the cognitive skills necessary to understand the depicted scene. But the picture is not a mere extension or delegation of the interpreting propositional attitude of the receiver. Quite to the contrary, the proposition involved in the picture act may present a highly unwelcome, surprising, disgusting information for the recipient, just as the potential consequences might not at all be of a kind he intended or wished for. So, a basic ingredient in the quality of Bildakte, of picture acts, is the ability of pictures to be involved in propositions without any intending sender being present. But there is more involved.

128

Chapter 7: How Do Pictures Act?

Fig. 25: Map of Manhattan, Kitcher and Varzi 2000.

Implicit Information Propositions, of course, make up the basic ingredients of reasoning, arguments generally taking us from one proposition to another in a truth-preserving manner. This is highlighted in Peirce’s notion of “diagrammatical reasoning”, which takes deductive reasoning to result from the manipulation of or experimentation with a diagram.¹²¹ The icon subtype of the diagram thus makes it possible for the user to reveal information implicit in a diagram and to render it explicit. Peirce’s notion of the diagram is famously broad, covering prototypical examples such as geometrical figurae or graphs, but also algebraic equations and linguistic or formal grammars on the one hand, and picture and image structures on the other. The central

Implicit Information

129

criterion is whether the icon in question can be used experimentally to disclose implicit information about its object—for instance when conducting a proof with a geometrical figure, solving an algebraic equation, reasoning on the basis of grammatically presented information—or with regard to images, manipulating a picture, in one’s imagination or on paper, screen, slate, or canvas. The old saying that a picture is worth a thousand words really presents a vast understatement, as Philip Kitcher and Achille Varzi argue in a short paper.¹²² A simple map, e. g., of Manhattan (Fig. 25), may serve as support for an infinite number of linguistically expressed propositions pertaining to distances between any two salient points on the map, contour curvatures, area, etc. Even if the map, as a whole, may be considered as one proposition—the S part being played by the proper name “Manhattan” next to the other indexical references given in the map, the P part being played by the iconic outline of geographical and other structures—such sentences are only implicitly present in the map sign. But they may be read off of the map and be made explicit by a recipient familiar with the rules of map reading. Such extraction of explicit information from a picture may come in various degrees of difficulty. To trace a route on a map or a GPS and follow it in reality is an everyday experiment with diagrams—involving many different cognitive capacities, all the while being so ingrained in many users as to appear almost effortless. However, some of the implicit aspects of pictures may take much more effort to discover. The similarity between the shapes of the east coast of South America and the west coast of Africa may be striking even to a child’s eye, but it took the gaze of an ingenious scientist—Alfred Wegener—to draw groundbreaking conclusions for geographical and geological ontology from this observation. The potential difficulty inherent in diagram experiments with pictures may derive from many different sources: One is the inherent difficulty of the problem—cf. the classic Traveling Salesman problem of finding the shortest route between a number of cities on the map, or Peirce’s distinction between corollarial and theorematic reasoning;¹²³ another is that the relevant clue in the picture may be minimal—cf. the written messages allegedly recently discovered in the irises of the Mona Lisa. Furthermore, it may require the discovery of new, yet undiscovered manipulation rules—for instance the discovery of non-Euclidean geometries; or it may be due to the simple fact that nobody had paid sufficient attention to this particular aspect of the picture before—think of the photographer discovering a murder in his innocent photographs from a London park in Michelangelo Antonioni’s Blow Up. But the important lesson with regard to picture acts is that all pictures possess a large amount of implicit information most of which was never explicitly “put there” by the painter, photographer or constructor of the picture, and thus is not the result of any intention.¹²⁴ Such information constitutes the secret

130

Chapter 7: How Do Pictures Act?

of the picture, to put it dramatically. Of course, the same holds true for the world itself: it is ripe with relations not yet mapped or made explicit. However, in contrast to the ever-changing structures and the indefinite extension of reality, pictures are stiffened, localized, repeatable, as if brooding over their treasure of implicit information, virtually ready to be revealed. Just like the potential involvement of pictures in non-intended propositions, this is a quality not necessarily foreseen by their producers or promoters. They possess this information themselves, and they may outlive us as information repositories. This is a further reason why they may often appear to us so lively, subject-like, and curiously pregnant with activity. This quality of picture acts thus does not require the ascription of any vitalist mysteries to pictures, nor the intervention of human intention, but lies in their very semiotic structure.

Chapter 8 Dimensions of Peircean Diagrammaticality Diagrams play the center role in Peirce’s epistemology, both for mathematics, logic, and, radiating from there, for all of the special sciences.¹²⁵ They are central in his whole final thrust beginning in 1902, adding lots of new developments of dimensions to his pragmatism and his semiotics. In this development, a number of different properties, distinctions, and variabilities of diagrams are addressed, many of which, I believe, remain relevant to this day when diagrams are again investigated for their role in scientific and everyday thought. Taking its point of departure in the origin of the notions of “diagram” and “iconicity” in Peirce’s philosophy of logic, this chapter reviews and discusses a series of different dimensions along which such diagrams may be compared, measured, and subdivided: diagrams vs. images and metaphors; operational vs. optimal iconicity in diagrams; diagram tokens vs. diagram types; diagrams as general signs; generic vs. degenerate diagrams; corollarial vs. theorematic diagram reasoning; pure vs. applied diagrams; logic diagrams vs. diagrams facilitating logical inferences; continuous vs. discontinuous diagrams; one-dimensional vs. multidimensional diagrams; diagrams in non-deductive reasoning. Some of these distinctions are explictly elaborated by Peirce, others are more implicit. Even if most of these developments occur in the mature Peirce after the turn of the century and thus form an important part of his mature semiotics, they do not relate in any simple or straight-forward manner to his attempts at enlarging his combinatorial semiotics from its bases in the three-trichotomy theory of the 1903 Syllabus over the six-trichotomy theory of 1904– 1906 to the sketchlike ten-trichotomy versions of 1908. In addition to charting a number of important properties and variabilities of diagrams, a leading question of this chapter is: in all of Peirce’s mature sign taxonomies, diagrams rarely figure in the terminologies of the many sign-types discussed—why?

From the 1885 “Algebra of Logic” to the 1903 Image-Diagram-Metaphor Trichotomy The very notions of diagram and iconicity grow out of Peirce’s life-long strive for the analysis and formalization of logic and reasoning, only to reach center stage in his mature logic and semiotics after the turn of the century. The first thorough reflection upon diagram reasoning thus occurs in the context of a “philosophy of notation” in connection with his linear formalization of first-order predicate logic https://doi.org/10.1515/9783110793628-010

132

Chapter 8: Dimensions of Peircean Diagrammaticality

in the second “Algebra of Logic” paper in 1885. In that paper, he constructs the first version of modern formal logic with quantifiers, what is now called the prefix-matrix distinction and the norm of prenex normal form of expressions (isolating the quantifiers in the left side of the formula and the relational proposition in its right, “Boolean” side). Via Schröder, Peano, Russell, etc., that formalism, with minor changes in single signs but essentially no changes in syntax and meaning, developed into modern “symbolic” logic. Peirce, however, in the principal semiotic introduction to the paper, strongly emphasized that such a formalism could not be exclusively symbolic but was forced to make use of both iconic, indexical, and symbolic signs. The single conventional signs with a general meaning were symbolic; quantifiers pointing out how to determine the objects referred to were indexical; while icons appeared at two important levels: 1) that of predicates which, though symbols, must imply some sort of iconic description of objects, on the one hand, and 2) that of the overall arrangement of symbols and indices in a spatial algebraic syntax which cannot be generally described nor indicated but must be shown, in order for the reader to observe the relations between signs and become able to reason by permuting those signs. As to the latter issue, the iconicity of the syntactic relations between symbols and indices in assertions, Peirce wrote: With these two kinds of signs alone [indices and symbols, fs] any proposition can be expressed; but it cannot be reasoned upon, for reasoning consists in the observation that where certain relations subsist certain others are found, and it accordingly requires the exhibition of the relations reasoned within an icon (W 5, 164; CP, 3.363).

The overall structure of logic formalisms, then, must be iconic. Peirce develops the notion of how to reason with such formalisms as follows: … all deductive reasoning, even simple syllogism, involves an element of observation; namely, deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of the parts of the object of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts (W 5, 164; CP, 3.363).

This is probably his first close connection of diagram experiments with deduction. It is only, however, in connection with Peirce’s development of his mature semiotics after the turn of the century that this germ of a theory of diagrammatical reasoning unfolds, partially in connection to Peirce’s development of the alternative logic formalism of Existential Graphs (EGs) from around 1896 where the selection of each single convention is delicately tested for its degree of iconicity (cf. next chapter)—and partially as a generalization from the experience with the

From the 1885 “Algebra of Logic” to the 1903 Image-Diagram-Metaphor Trichotomy

133

EGs to a general doctrine of diagrammatical reasoning, covering mathematics and deduction as such. In the same period, Peirce undertook the final development of his theory of signs, beginning in the Minute Logic (1902) and the various drafts of the Syllabus and the Pragmatism and Lowell Lectures (1903). It seemed natural to embed the flowering notion of diagrams in that endeavor, and a much-quoted attempt of that theoretical fusion occurred with the image-diagram-metaphor trichotomy (as a small section of the attempt of integration of logic and semiotics addressed in Pietarinen 2019). The central quote regarding this trichotomy stems from the early versions of the Syllabus manuscript on which Peirce worked in 1903 and which furnishes the first drafts of his mature sign theory and its principle of defining signs in a combinatory of sign aspects: “Hypoicons may be roughly divided according to the mode of Firstness of which they partake. Those which partake of simple qualities, or First Firstnesses, are images; those which represent the relations, mainly dyadic, or so regarded, of the parts of one thing by analogous relations in their own parts, are diagrams; those which represent the representative character of a representamen by representing a parallelism in something else, are metaphors” (EP II, 274; CP 2.277). This brief quote is the sole argued presentation of the Image-Diagram-Metaphor trichotomy, and numerous interpreters have attempted to further develop that promising distinction. The notion of Diagram is the only one among the three terms of the trichotomy to receive thorough discussion in Peirce’s work— so the determination of “Image” and “Metaphor” as technical terms in his classification of signs has not much more than this brief quote to build upon. The strange thing is that two conflicting criteria seem to compete in the short quote. Images and Diagrams seem to be classified as First and Second among icons after the adicity of the relations they depict: images use “simple qualities, or First Firstnesses”, that is, monadic relations such as “_is red”, “_is round”, an idea which fits nicely with the brief contrast description of diagrams as representing by means of “relations, mainly dyadic”. This principle would obviously lead one to expect, then, that the third term of the trichotomy, Metaphors, should be characterized by representing triadic (or maybe polyadic) relations. This is not the case, however, and it would indeed be a strange analysis of Metaphors. They, by contrast, are described by means of the existence of an intermediary object, involving a parallelism, between the sign and its object. This parallelism supposedly pertains to the relational structure which is mapped from object to sign via the intermediary object, thus resulting in a triad in the representational structure sign-object which is normally conceived of as dyadic. But that is a completely different issue than triadic relations within the object and its depiction. So, the first criterion seems to point to the adicity of relations involved, that is, concern-

134

Chapter 8: Dimensions of Peircean Diagrammaticality

ing which aspects of the object are depicted in the icon, while the second criterion rather concerns the degree of complexity of the sign-object relation, and it is difficult to see how it could be generalized to cover the definition of “Image” and “Diagram” which, both of them, accord to the standard dyadic sign-object relation. The problem indeed seems to be that none of these two competing criteria is really generalizable to all three cases which is probably why they change along the triad. As mentioned, it would seem strange if icons depicting triadic relations should form a special category, and it also does not seem really correct to assume that diagrams depict “relations, mainly dyadic, or so regarded” only, as indicated in the famous quote. Rather, triadic relations seem firmly within the scope of diagrammatic depiction—in another part of the Syllabus, Peirce explicitly defines a graphical representation of triadic relations by the diagrammatic means of three lines meeting in a point: “… a point upon which three lines of identity abut is a graph expressing the relation of teridentity” (CP 4.406). The triadic structure of the Metaphor, of course, would have a nice dyadic sign-object counterpart in the diagram and its analogous mirroring of relational structure between the part-whole structure of the sign and that of its object—but here images would suffer, for they could not work with one entity only, they must also display the basically dual sign-object structure; if not, they would cease to be signs at all.¹²⁶ You might say that the sign-object duality is more pronounced in diagrams while the sharing of simple qualities in images may tend to make a confusion or even a merging or indistinguishability between the sign and its object, which share basic qualities, more probable; cf. Peirce’s early claim that “Icons are so completely substituted for their objects as hardly to be distinguished from them” (“On the Algebra of Logic”, 1885, EP I, 226; CP 3.362—but here, his example of such hard-to-distinguish icons are not Images and their supposed simplicity, but the “diagrams of geometry”). Thus, a clear 1– 2– 3 structure in terms of complexity of the sign relation between icon and object also does not really seem a possibility. The fact that metaphorical mappings may take all adicities of relation as their basis of the structure mapped also argues against any idea of the metaphor as defined by adicity of the relation depicted (cf. examples like the croissant pastry metaphorically named after its shape in common with the crescent moon (adicity 1); the father-children metaphor for the relation between king and people (adicity 2); the nuptial gift from groom to bride as a metaphor for love (adicity 3), etc.). Not only is the proposed tripartition not developed any further in the semiotically fertile years after the Syllabus, it also comes in variant versions in discarded drafts of the Syllabus: “Icons may be distinguished, though only roughly, into three which represent are icons in respect to the qualities of sense, being

From the 1885 “Algebra of Logic” to the 1903 Image-Diagram-Metaphor Trichotomy

135

images, and those which are icons in respect to the dyadic relations of their parts to one another, being diagrams, or dyadic analogues, and these which are icons in respect to their intellectual characters, being examples” (R 478, alt. version 44, ISP 174). Here, the third member of the trichotomy is no longer metaphors, but “examples”. No further explanation of the category is given, but the idea seems to be that general conceptions are thirds, and icons functioning as examples of such conceptions are then general pictures (maybe like the typicalized mushroom drawing illustrating the general description of a mushroom species in a field guidebook for mycologists or collectors of fungi—such a drawing must take care to include all of the typical general feature of the species in question and is, in that sense, a general depiction). Again, such an explanation will lack the expected triadic relations in the third category after the monadic qualities and dyadic relations defining its first two members—maybe that was why metaphors were substituted for examples in the final version. So, something fishy remains about the attempts of constructing a tripartition of the hypoicon, and it is probably no coincidence that this attempt at a taxonomic determination of the diagram never turns up again in Peirce’s manifold discussions of definition and description of the essentials of diagrams and diagrammatical reasoning in the ensuing years. Rather, it seems like no less than three different issues are confused in the Image-Diagram-Metaphor triad. One is the degree of skeletal part-whole analysis of the object in the icon sign—which does indeed come in a range of very different shades from images to diagrams. Quite another is the iconic depiction of relations of different adicities, from simple, monadic properties to dyadic and triadic relations. And a third is the issue of direct versus indirect, mediated signobject reference. So, the conclusion seems to be that Peirce saw three important issues relating to icons and tried—in a quick but unsuccessful attempt, in his hasty, intensive work on the Syllabus in the fall of 1903—to synthesize them. A related issue here is that the trichotomy of image-diagram-metaphor is not presented as a subdivision of icons as such, but rather of “Hypoicons”, that is, actual, mixed signs which are primarily, but not exclusively, iconic by nature. This implies two things: that they are actual, concrete functioning signs, that which only a bit later in Peirce’s elaboration of his combinatorial semiotics in the Syllabus is covered by the new “Sinsign” or “Token” category of the Qualisign-Sinsign-Legisign trichotomy, developed only in the course of his work on the Syllabus. The other thing is that Hypoicons are mixed signs, with both indexical and symbolical aspects in addition to their central, iconic aspect. The former issue may be dealt with by regarding “Hypoicon” as a preliminary term for what, in the 10-sign taxonomy of the later Syllabus, would appear as “Rhematic Iconic Sinsigns”. That is the road taken by Farias and Queiroz (2006) who go on

136

Chapter 8: Dimensions of Peircean Diagrammaticality

to try and trace the different subtypes of that category in Peirce’s more developed (but also much more tentative and unfinished) 66-sign taxonomies of 1906 – 1908. The lack of any definitive definition nor sequence of the 10 trichotomies whose combination would yield the 66 sign types, however, gives rather different combination results depending upon which definitions and sequence are chosen. Even if this road may sometime prove fruitful, once the character and sequence of the 10 triads are finally determined, it still does not address the second issue, the fact that Hypoicons seem to cover not only Iconic Sinsigns—a pretty narrow category—but also mixed signs with an emphatic aspect of iconicity in general. The diagram type of the topographic map, to take an example, is indeed predominantly iconic but at the same time, it typically is claimed to be true of a particular landscape indicated in the map by means of the indices of proper names added to the naked diagram structure; moreover, the single, token map on paper or screen can only be understood as a token of the related diagram type, and this type, again, has a general object, namely the general features of the landscape which are depicted in the sign, and thus functions as a symbol. Other examples include arguments completed by means of diagram transformation where iconicity plays a prominent role—but where the sign use involved vastly transgresses the confines of Iconic Sinsigns only. Diagrams—like indeed most signs—are Replica Tokens of general Types, and it is this generality which makes them fit for supporting reasoning. Such connections are developed in detail in Peirce’s mature doctrine of diagrams, but they seem to fall under the table if we simply stay content with taking Diagrams to form a subset under Iconic Sinsigns only. So, my conclusion here is that the famous and much-quoted introduction of the concept of “hypoicon” and its associated trichotomy “image-diagram-metaphor” in the early sketches of the Syllabus not only forms a hapax in Peirce’s work, but also that they form a first, swift attempt at solving issues most of which are better and more convincingly dealt with later—some of them already in the later versions of the Syllabus from the same year, where the first trichotomy, Quali-Sin-Legisign (or Tone-Token-Type), is introduced.

Operational vs. Optimal Iconicity The trichotomy of Icon-Index-Symbol is not only one of the most well-known features of Peirce’s sign classifications; it is also early and constant already from the 1860s (even if the exact definitions and terminological notions used may vary). As to the hypostatic abstraction of the term “iconicity” as a property, which signs may possess to different degrees, it appears only around 1900—in

Operational vs. Optimal Iconicity

137

the same period where Peirce undertakes what Bellucci (2017) calls the “first reform” of the basic principles of Speculative Grammar, of semiotics, which is to pass from the classification of signs to the classification of semiotic parameters which, in turn, may combine to give types of signs.¹²⁷ That reform finally reached clarity in the Minute Logic of 1902, and “iconicity” and its antonym “aniconicity” appear in Peirce papers beginning in 1897—all in the context of discussing the degree of iconicity of different logic representations (cf. next chapter). In that respect, Peirce certainly took the 1896 EGs to be superior to his earlier Algebra of Logic—even if he himself from now on continued to use both systems, each of them seeming preferable over the other in certain contexts and for certain purposes. Simultaneously, however, Peirce developed a definition of iconicity based on operations using an icon. Thus, the “Algebra of Logic” of 1885 and the Beta system of EGs were equivalent because the same set of theorems could be proved by operating with them.¹²⁸ In that sense, they were iconically equivalent. In another sense, however, EGs were taken to be the iconically superior system—an example being that in the EGs, one and the same variable is referred to by means of one continuous “Line of Identity” (however branched it may be), while that same reference would necessitate several different occurrences of the same sign in the Algebra of Logic. Take the proposition “Everybody loves someone”, which, expressed in the 1885 Algebra of Logic, would be (Fig. 26): ΠxΣy(l)x,y Fig. 26: Algebra of Logic expression of “Everybody loves someone”.

Here, Π is the universal quantifier, Σ the existential quantifier, l the two-place predicate “_loves_” and x and y the two variables lover and loved. It consists of an indexical and an iconical part—the “Hopkinsian” part of the quantifiers provides an index of which objects are spoken about,¹²⁹ while the “Boolean” part of the predicate with variables provides a symbolic icon of the two-place relation of loving. Finally, the very syntax uniting the two parts by putting them together on the line is, as quoted in the beginning of this chapter, iconic. At the same time, all of the single signs of the expression are conventional symbols. In the EGs, the same proposition would be represented as follows (Fig. 27):

138

Chapter 8: Dimensions of Peircean Diagrammaticality

Fig. 27: Beta graph of “Everybody loves someone”.

The cut enclosures formalize negation, two nested cuts formalize implication, the two variables are represented by the two Identity Lines at each end of the predicate, and so the graph expresses that it is not the case that there exists someone who does not love someone, or, if someone exists, he or she loves someone else. This, now, is more iconic, so Peirce, because each variable is here represented once, each by its Ligature (the two horizontal lines), while in the algebraic expression, x and y occur twice each. So, the representation one variable—one occurrence is more iconic than several occurrences of the same variable. Even if operationally equivalent, then, the latter of the two representations is judged more iconic than the former. This optimality principle may be expressed as follows: “A diagram ought to be as iconic as possible; that is, it should represent relations by visible relations analogous to them” (“Logical Tracts. No. 2. On Existential Graphs, Euler’s Diagrams, and Logical Algebra”, 1903, R 492). Thus, I argued (Stjernfelt 2011a, 2014) that two different notions of iconicity are, implicitly, at stake in the mature Peirce—1) operational iconicity which focuses upon which implicit propositions may be made explicit by the manipulations of a certain diagram; which theorems may be proved from it—and 2) optimal iconicity, distinguishing even between formalisms which are otherwise operationally equivalent. Both iconicity concepts are important, each for their purpose, so it is perfectly reasonable that Peirce develops and applies both of them. I argue, however, that it is preferable to provide them with explicit terminology so as to be able to make clear which of them you appeal to in a particular case or argument.

Diagram Tokens vs. Diagram Types A very elementary distinction is that between the individual physical diagram token on a piece of paper, on the screen, on the blackboard, etc.—and the general Type of diagram which is instantiated in those different replicas. This, of course, is based on the Type-Token or Legisign-Sinsign distinction of Peirce’s first trichotomy, introduced during the work on the Syllabus in 1903, which

Diagrams as General Signs and as Conclusions of Arguments

139

holds for all signs which are identically repeatable. As no two physical objects are exactly identical, the Type comes in Tokens, which necessarily have a lot of individual, different, superfluous properties that have to be bracketed by the observer in order to grasp the underlying general Type. Given a particular spoken word, e. g., dialect, prosody, voice pitch, speed of pronunciation etc. may have to be bracketed in order to grasp the word Type instantiated. The same goes for diagrams: color, thickness of lines, lacking rectilinearity of lines, imprecision of drawing, and much more may have to be bracketed as accidental token qualities (Peirce: “prescinded”) in order for the simpler, general, ideal type of diagram to be reached. In many cases, the information of which properties are essential to the Type and which ones are accidental and thus only belong to certain Tokens of that Type, comes quasi-automatically, from tradition, context, learning, etc.—in other cases it requires specification by means of explicit symbolic legends, axioms, rules, etc. accompanying the diagram: “Accordingly, every diagram must be supplemented by certain general understandings or explicit rules, which shall warrant the substitution for one diagram of any other conforming to certain rules. These will be rules of permissible substitution, partly limited to the special proposition, partly extending to an entire class of diagrams to which this one belongs” (“An Appraisal of the Faculty of Reasoning”, c. 1906, R 616). Very often, such rules, implicit or explicit, will be co-motivated by the general type of object which is depicted by the diagram. The diagram as Type or Legisign, namely, furnishes the precondition for diagrams to function symbolically, that is, being not only general signs in themselves, but also possessing a general meaning, as when we take the Type of a parabola as the general (hence, symbolic) Diagram for the trajectory of all falling bodies in a field of gravity without friction.

Diagrams as General Signs and as Conclusions of Arguments A diagram is a Type that is instantiated in Tokens—but how does it come about that the diagram Type is, in turn, capable of referring to a general object? The reference to general objects is the very definition of the Peircean sign type of symbols¹³⁰—does this mean that the diagram has to be accompanied by explicitly added symbols in order to accomplish the reference to general objects, or may the diagram perform, in itself, the symbolic task of general object reference? Sometimes, Peirce expresses himself as if the former were the case, as if diagrams invariably need the assistance of explicit symbols in order for them to perform general reference. Take for instance the following:

140

Chapter 8: Dimensions of Peircean Diagrammaticality

A diagram appeals to the eye like a picture, while it differs from a picture in that it obtrusively involves conventional signs. A conventional sign has, since Aristotle and earlier, received the name of symbol; but besides conventional symbols there are signs of the same nature except that instead of being based on express conventions they depend on natural dispositions. They are natural symbols. All thought takes place by means of natural symbols and of conventional symbols that have become naturalized (Lowell Lecture II A, 1903, R 450, 6).

The detailed exposition of the general reasoning process, which Peirce puts forward in the 1906 Ms. known as “PAP”, may also be interpreted in that direction: Meantime, the Diagram remains in the field of perception or imagination; and so the Iconic Diagram and its Initial Symbolic Interpretant taken together constitute what we shall not too much wrench Kant’s term in calling a Schema, which is on the one side an object capable of being observed while on the other side it is General (“PAP”, 1906, NEM IV, 318).

This idea makes of the diagram a descendant to Kant’s famous notion of the Schema, uniting the generality of understanding with the particular exposition of intuition, by coupling the Diagram with its Symbolic Interpretant, the two furnishing the observable and the general aspect of the Schema, respectively. Similarly, in the other end of the reasoning process, Peirce concludes: The transformate Diagram is the Eventual, or Rational, Interpretant of the transformand Diagram, at the same time being a new Diagram of which the Initial Interpretant, or signification, is the Symbolic statement, or statement in general terms, of the Conclusion. By this labyrinthine path, and by no other, is it possible to attain to Evidence; and Evidence belongs to every Necessary Conclusion (“PAP”, 1906, NEM IV, 318).

After having been transformed, the final diagram presents a new symbolic interpretant which is the conclusion and its statement expressed in general terms. Thus, we may get the idea that there are symbols in the beginning and end of the diagram transformation process, while the intermediary manipulation phases dispense with generality, such as Peirce noted 20 years earlier in his first presentation of diagram reasoning in connection to the Algebra of Logic: A diagram, indeed, so far as it has a general signification, is not a pure icon; but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing. So in contemplating a painting, there is a moment when we lose the consciousness that it is not the thing, the distinction of the real and the copy disappears, and it is for the moment a pure dream,—not any particular existence, and yet not general. At that moment we are contemplating an icon (“On the Algebra of Logic”, 1885, 180 – 181)

Diagrams as General Signs and as Conclusions of Arguments

141

During the reasoning phase, we bracket the abstractness and treats the diagram icon as if it were the object itself. Still, I think the important analogy with Kant’s Schema may lead us astray in presupposing that in order to make a statement— that is, assert a proposition—the diagram necessarily must involve the support of an additional symbol. In the two PAP quotes, symbolicity was not something which was added by means of a further sign to the diagram, rather, both in the initial and final phase, symbolicity lay in the initial interpretant of the diagram sign, that is, in the immediate, obvious meaning of the sign. But the meaning of a sign is not an additional entity, but part and parcel of the sign itself.¹³¹ This has to do with the fact that diagrams are, themselves, “Iconic Legisigns”, they are types which may appear in many different, individual, material tokens. As signs, they are general, and this combined with the insight that icons are often difficult to distinguish clearly from their object, and even in certain phases of reasoning are identified with their object, makes it easy to see that they may transfer that generality to their object and hence function symbolically (cf. symbols as sign with general objects). So, let us instead investigate the possibility that the symbolic generality is something in or about the diagram sign itself. It is interesting that in several of his definition of symbolicity, Peirce explicit mentions images or diagrams which may function as symbols, e. g., when he once more defines the IconIndex-Symbol trichotomy and comes to the symbol: … it may, as a “Symbol,” be related to its object only because it will be represented in its interpretant as so related, as is the case with any word or other conventional sign, or any general type of image regarded as a schema of a concept … (1904?, R 914, 8).¹³²

Sometimes, Peirce even identifies a general idea as such with a diagram able to be applied to a manifold of objects: It is from that experience that we draw our conception of existence,—if it can be called a conception. Properly it is not a conception; because a conception is general idea,—a sort of picture or diagram which we think of as variously applicable (Lowell Lecture III(b), 1903, R 462).

Various applicability—generality of meaning—is the central definitory property of symbols. Peirce also entertains the idea that the diagram and its conclusion may be so complicated that ordinary language is unable to express it, which implies that we should not expect that the symbolicity of the conclusion of a diagram transformation necessarily lies in its translation from diagram back to language:

142

Chapter 8: Dimensions of Peircean Diagrammaticality

It will also be seen that the reasoning must in all cases be at bottom schematic, or diagrammatic, or else it will not be reasoning at all, but the mere practice of the rule of thumb; and furthermore, the diagram must be made very prominent by alterations being made in it, in the course of the demonstration, or else no vigorous advance in knowledge will be made. As a general rule the diagram will be so complicated that ordinary language is put to a severe strain to express it at all, even though facile perspicuity be not attempted; and naturally the clear mental representation of the problem, and then the invention of the proper alteration of the diagram, call for the closest of thought. (Minute Logic, 1902, R 430, 431a).

Regarding Peirce’s obsession with the development of formalisms representing elementary logic, we must ask: how is the conclusion of an argument expressed in those formalisms? Is it sufficient to present the transformate diagram which states the theorem reached in the system of the formalism—like the two formalizations of the proposition “Everybody loves someone” above taken as conclusions to preceding arguments? That is indeed not sufficient, but not because the conclusion is in need of further symbolic elaboration. It is rather because the conclusion, taken in nuce, does not represent which previous reasoning process lead to accept that conclusion as a result. Here, again Peirce speaks of the Beta version of the EGs formalizing first order predicate logic: I will now only say that, which this system does present Semes, yet it would not be incorrect to say that everything scribed according to this system, down to its smallest parts, is a Pheme; and is not only a Pheme, but is a Proposition. Delomes (dee’loamz) also are brought to view. Yet no Delome (dee’loam) is ever on the diagram. A Graph in this system is a type which expresses a single proposition. Without just not troubling you with an adequate description of the Delome (dee’loam), I may point out that it represents no statical determination of thought, but a process of change from one state of belief to another. So, let us agree that this new system of diagrammatizing the course of thought, which you and I, Reader, are to build up again from the foundation together, as a new thing to you, and to me a critical review and reading of what I have done before by myself,—let us, I say, make it our very first germ of the plan of this system that the diagram, in any one state of it, shall represent a state of belief, usually a pretended state merely, upon some point or points of some subject. A Delome (dee’loam) shall be represented by a series of such diagrams imagined to be phenakistoscopically combined (“Prolegomena to an Apology for Pragmaticism”, 1906, R 295).¹³³

In his newly adopted Seme-Pheme-Delome terminology for the further generalization of the Rheme-Dicisign-Argument trichotomy (see Bellucci 2019) which already lay in the observation that Dicisigns may use proposition structure in many different speech acts, Peirce sees that a single sheet of graphs cannot present anything but propositions. Inferences are made by series of manipulations with the figures on the sheet so as to constitute Delomes—Arguments. But that implies that the Argument may be presented as a cartoon of a series of diagrams.

Diagrams as General Signs and as Conclusions of Arguments

143

A single icon or diagram cannot represent an Argument, that will require a sequence of such signs.¹³⁴ The “moving picture of thought” may be represented, in the absence of actually performing the manipulation with a Token diagram, by a series of snapshots of the changing conformation of diagram structure during the phases of reasoning, maybe brought to life by the technical representation of it as a movement. Had Peirce known Disney or computer graphics, the depiction of the actual diagram movements and changes—with a replay button for control—might have constituted an alternative. But only when you have access to the whole of the transformation history—like the steps of a mathematical proof—you are able to synthetically grasp the conclusion as a conclusion, the theorem as a theorem. It also presupposes, of course, that the general meaning of the diagrams used is kept in mind (even if maybe bracketed during phases of diagram manipulation). But it does not necessarily require additional symbolic signs to make the conclusion evident, even if they may, in many cases, support such evidence. This is obviously an issue of actually mastering the formalism. Early phases of learning will include instruction and thus the use of symbols in the shape of linguistic symbols. In case you have practiced with the formalism and have become a skilled user, you are able to appreciate the conclusion directly from the diagrammatic formalism without necessitating a previous translation-back into ordinary language or other additional symbols. The very cartoon sequence of diagram phase snapshots may be, in that case, sufficient. But all symbols, being based on “rules of thumb” as they are, are habits that require learning, ontoor phylogenetically, so there is nothing strange if learning by practicing the rules of a diagram system provides the condition for the direct understanding of the general meaning of a transformate diagram. Skilled map readers—scientific diagrammers, military campaign commanders, or orienteering athletes— similarly may turn directly to action in the field after consulting their detailed map diagram, without any necessity of translating their conclusion into supplementary, non-diagrammatical signs before understanding it. Of course, such translation may be very useful, even indispensable, for communication purposes: “Follow the small ditch in NNE direction until you reach a water mill, everybody!” But it is not necessary in order to grasp the general conclusion from the map manipulation undertaken. Cf. how Peirce presents the appreciation of “evident consequences” of his two types of diagram reasoning without any appeal to accompanying signs (more about those two types below): Here I will tell you a secret about necessary consequences. It is a very useful thing to know, although most logicians are entirely ignorant of it. It is that not even the simplest necessary consequence can be drawn except by the aid of Observation, namely, the observation of

144

Chapter 8: Dimensions of Peircean Diagrammaticality

some feature of something of the nature of a diagram, whether on paper or in the imagination. I draw a distinction between Corollarial consequences and Theorematic consequences. A corollarial consequence is one the truth of which will become evident simply upon attentive observation of a diagram constructed so as to represent the conditions stated in the conclusion. A theorematic consequence is one which only becomes evident after some experiment has been performed upon the diagram, such as the addition to it of parts not necessarily referred to in the statement of the conclusion (Lowell Lecture II, 1903, NEM, III/I, 419).

We shall return to the corollarial-theorematic distinction below. Here, the important thing is that evidence is provided directly by diagram observation in each of those two cases. So, our conclusion is that the skilled diagram user may be able directly to appreciate the meaning of the final, transformate diagram in a general, that is, symbolic conclusion—without the aid or support from further symbolic signs. In that sense, diagrams function as symbols— by having a general meaning and object.

Levels of Generality in Diagrams An important issue here is that the Type reading of the diagram gives a special sort of observational access to general features of the sign, so that any sterile dualism between perception and conception is avoided and those general features are subject to acts of perception involving a special, generalizing attitude. And the generality of the diagram sign itself is what makes it possible for diagrams also to perform the symbolic act of referring to general objects. Maps, e. g., may refer to general features of the landscape; algebraical expressions, e. g., may refer to general regularities of arithmetic, that is, general objects empirical as well as a priori. Such generality, however, comes in many different degrees. A topographic map is general because, unlike an aerial photograph of the same area, it does not depict a particular moment’s snapshot information of the object territory, but an information covering an indefinite timespan, typically in the range of years (until, that is, landscape changes affecting the features mapped necessitate a redrawing of the map). And, depending upon the scale of the map, different maps of the same territory may depict it on different levels of granularity, different levels of generality. Such generality, of course, has a much narrower span than, say, diagrams of the structure of the solar system which may be valid for millennia or more, not to speak about the eternal diagrams of geometry, supposedly valid at any time. The generality of diagrams, thus, comes in many different degrees and may refer to empirical regularities of different timescales as well as to atemporal a priori structures.

Diagram Experiments vs. Real Experiments

145

Diagram Experiments vs. Real Experiments Logical inferences in diagrams are reached by a process which Peirce very often describes as experimentation with the diagram. The idea is that something must be done—the very action of collecting and synthetizing the premises into one overarching diagram sometimes directly gives the conclusion; in other cases that synthetic diagram must be further processed by manipulation, moving, deleting, or substituting parts of it, adding further parts to it, etc. These procedures are undertaken as an open trial-and-error process, attempting to reach the intended conclusion, which is why the analogy with the open-endedness of empirical lab experiments suggested itself to Peirce: Indeed, just there […] lies the advantage of diagrams in general. Namely, […] one can make exact experiments upon uniform diagrams; and when one does so, one must keep a bright lookout for unintended and unexpected changes thereby brought about in the relations of different significant parts of the diagram to one another. Such operations upon diagrams, whether external or imaginary, take the place of the experiments upon real things that one performs in chemical and physical research. Chemists have ere now, I need not say, described experimentation as the putting of questions to Nature. Just so, experiments upon diagrams are questions put to the Nature of the relations concerned (“Prolegomena to an Apology for Pragmaticism”, 1906, CP 4.530).

The analogy between empirical lab experiments and experiments with diagrams thus turns on two things: 1) their openness in the sense that it is not beforehand given what will be the result of the experiment, whether it will show up to support the hypothesis tested or not; 2) a wide conception of “Nature” which may mean both Nature in the sense of the empirical world studied by the special sciences and the structures, patterns, and laws that it involves, one the one hand, and Nature in the sense of the structure of hypothetical, ideal relations studied by mathematics, supposedly a priori and subject to deduction, on the other. It is this which makes it possible for Peirce to include mathematics and philosophy under the classic empiricist requirement that all knowledge is by observation. This idea is not, however, connected to empiricist reduction attempts of general or abstract knowledge to results from secondary mental processings of empirical data. Rather, the idea is that observation may take several kinds of objects, both empirical, concrete, particular objects in lab experiments (such objects are typically subjected to experiments as Token examples of some Type of object to which the knowledge collected pertains)—and general, ideal objects addressable due to their representation in diagrams.

146

Chapter 8: Dimensions of Peircean Diagrammaticality

Generic and Degenerate Diagrams Diagrams of the same object or state of affairs may preserve more or less of diagrammatic structure. Take, for instance, Harry Beck’s famous topological diagram of the London subway, presenting spatially the totality of connection relations between subway lines (Fig. 28):

Fig. 28: The central section of a London Underground map, developed from Harry Beck’s 1931 original.

A simpler representation of parts of the underground system (and its diagram) selects one single subway line for diagramming (Fig. 29), with connections no longer depicted by lines intersecting but, instead, indicated by symbolic indices at each station where change to another line is possible:

Fig. 29: Map of Bakerloo line, London Underground 2020.

Explicit vs. Implicit Diagrams

147

Such diagrams, of course, are useful for focusing upon the sequence of possibilities when traveling with one particular line. If you took a sequence of all of such linear diagrams of each of the single 11 lines constituting the London Underground, the information of Beck’s total diagram would be preserved, even if the synthetic spatial structure of the whole would now be lacking and, correspondingly, it would be more difficult to compute a complicated trajectory involving several line changes. In such linearization, there is a conversion of parts of predicative, diagrammatic structure to indices affixed to the linear sequences. We might say, then, that the series of linear diagrams are degenerate, in a special sense of the word, in comparison to the generic diagram explicitly representing spatial structure. The decisive difference is the substitution of symbolic indices for direct, diagrammatic-iconic representation; cf. the example of “selectives” in the next chapter as an alternative to iconic representation by “identity lines” in Peirce’s Beta Graphs for predicate logic. Also here, symbolic indices may be substituted for (parts of) complex Identity line structures for simplification or perspicuity of particular contents.¹³⁵ The Bakerloo Line diagram, then, will be degenerate in comparison to the representation of the same line in the the total diagram. Degeneracy, in this sense of simplifying diagram structure by means of substituting symbolic indices for spatial iconicity, is not an absolute characteristic of a diagram, but rather a relational, comparative property: one diagram may be degenerate in relation to another, more generic diagram. Thus, there is no value judgment intended in the terminology.¹³⁶ A degenerate diagram of certain states-of-things may be more useful for certain purposes, while other purposes may call for a more generic diagram of the same content.

Explicit vs. Implicit Diagrams Diagrams most often appear in externalized, physical media, like paper, blackboards, computer screens, etc. as a strong vehicle for Extended Mind activity. Simple diagrams, of course, may be imagined by the user without external support. But an even more indirect case is that where the diagram itself is only implicitly present, be it ex- or internally. Peirce, in R 1214 (mid-1890s) describes the process of synthesizing two propositions into one, made possible by the fact that they share subjects. He takes the two propositions of “A loves B” and “B hates A” as an example and concludes that it is the very co-localization of the two, which furnishes the relevant diagram:

148

Chapter 8: Dimensions of Peircean Diagrammaticality

The student will ask: where is that diagram we have heard so much about? The reply is that in this case the diagram is so elementary, and the observation of it is so easy, that it escapes notice. Yet it is there. It consists of the two lines of writing A loves B B hates A We observe the sentence. We see that the B that ends the first begins the second. In imagination, we fit the second upon the end of the first, and look upon the loving of a hater of oneself as a character of A. The peculiarity of these conjunctive signs is not so much that they join two things as that they actually display a relation the like of what they signify. It is they that are entitled to be called demonstrative signs; although the word is by the usage of grammarians applied to signs that are merely indicative or finger-pointing (R 1214, 97– 98, ISP 18 – 19).

Thus, here it is the very action of co-localizing¹³⁷ the two propositions on one and the same sheet, which suffices to make it clear that their subjects are the same and that they may be taken as one, complex proposition in which A is the lover of his own enemy. Thus, simple diagrammatic representations and manipulations may be so ingrained and obvious that their diagrammatical character may pass unnoticed by the users. This possibility may be closely connected to the proficiency of the user in practical diagram use where the logica utens interest lies in reaching and considering the conclusion as quickly and easily as possible, rather than dwell on the single steps taken to reach it. In many applied diagrams where the interest of the reasoner lies firmly with the subject matter considered and with the ease of reaching a conclusion, we may expect that the diagrammatical means used, its structure and possibilities, may be, to some degree, only implicitly present.

Co-localization The realization that the simple co-localization of two propositions in order to connect them into one, complex proposition, forms a simple and widespread form of diagram reasoning was used by Peirce in one of his basic conventions in the Existential Graph system—namely, that the scribing of two proposition symbols on the same area of the sheet represents the logical conjunction of the two. But this explicit convention of the EG system is a formalization of a practice used implicitly in a wide variety of diagrams in the wild; cf. Chapter 6 above on Sheets in the Wild. This goes for the conjunction of several propositional signs (as in a road sign combining the sign meaning “parking prohibited” with the sign “roadworks

Co-localization

149

ahead”), but it also appears in the coupling of subject and predicate to constitute a proposition. This is addressed by Peirce in Every proposition relates to something which can only be pointed out or designated but cannot be specified in general. “No admittance, except on business.” over a door is a general proposition, but it relates to that door which may have no qualities different from these of some other door in some other planet (…) But the hanging of the sign over this door indicates that this is the one referred to (R 789, no date).

The subject of the general proposition is indicated by placing the predicate rheme close to the relevant door. This elementary spatial syntax is widespread in diagrams. When, in a topographical map, the name of a city is given near the sign indicating that city on the map, this co-localization is what provides the partial proposition of that map that this city bears the name indicated. When, in a geometrical diagram, the letter b is positioned close to the vertex of an angle, it is a sign that this angle will, in the proof attempt to follow, be referred to by the proper name of “b”. When, in a matrix structure like a timetable, the slot indicated by the intersection of the column of Tuesday with the row of 8 – 9 AM may be filled in by the determination “Math”, then the localization of that noun in that structural location gives the partial proposition that math will be taught during that Tuesday morning hour. We are so used to reading diagrams like the ones mentioned, that the peculiar properties of such co-localization very easily escape us. In a certain sense, co-localization forms a primitive, diagrammatic ur-syntax—implying that the indexical closeness in space-time of two semiotic devices is iconically interpreted as indicating some form of connection between them. This is not to say that such co-localization may not be the subject of further conventionalization—in Western painting since the Renaissance, for instance, the convention has become widespread that if a name is added in the corner of the painted surface, it refers to the painter, while a name added on the frame refers to the person portrayed in the painting; cf. Chapter 5. Both of these, of course, are cases of co-localization, with a simple syntactical convention added, a convention which might have been different. But co-localization seems to form the very basis of such conventions, not vice versa, and the combination could arguably not be subject to convention only, without regard to co-localization. We might imagine a convention informing us that the name of the man portrayed was not given on the picture frame, but rather in some specified region of Saturn. Such a convention, however, would have to be described symbolically, and that description, in turn, would have to be indexically connected both to the painting and the Saturnian location, e. g., by means of a telescope. So, the user of that dispersed set of semiotic devices would have to stand in contact with both locations of the parts, in order to be able to undertake the co-lo-

150

Chapter 8: Dimensions of Peircean Diagrammaticality

calization required. Rather, all sorts of syntactic conventionalizations would be understandable as secondary, analytical elaborations and sophistications, for different purposes, of the basic, spatio-temporal, diagrammatical co-localization of sign parts. Linguistic syntax, e. g., in its many variants, will form elaborated conventions of how to co-localize signs in the close diagram structure of one single sentence or period. Simple, pre-grammatical co-localization abundantly appear in diagrams as the self-evident means of piecing diagram parts, e. g., diagram structure and names of diagram parts, together. Co-localization pertains not simply to the metric distance between the sign parts involved, rather, it rests upon a basic notion of topological connectedness (which may, of course, in many cases be realized metrically). But the basic status of co-localization in propositions seems to indicate that semiotic space is intrinsically diagrammatic: connecting things spatially may immediately imply their semiotic connectedness. Peirce formalized such an idea in his Existential Graphs in the notion of the blank sheet as the “Sheet of Assertion”, containing in potentia all true propositions of the universe of discourse referred to—but this step seems to formalize a widespread use of local wild such sheets in ordinary sign use where the co-localization of terms is immediately interpreted as meaningful (cf. Chapter 6). This elementary and often-overlooked phenomenon of diagrammatic co-localization seems to be in need of further study: which possible types of co-localization are there, which types of conventionalizations of them?

Corollarial vs. Theorematic Diagram Reasoning—Explicit vs. Implicit Meanings of Diagrams Sometimes, like in the action of drawing close the two sign tokens of “A loves B” and “B hates A”, the very co-localizing of the representation of two premises is sufficient not only to form a synthetical proposition, but also for the conclusion to be directly read off of that proposition. In other cases, of course, like in Euclid’s major theorems, an ingenious manipulation with the diagram must be undertaken in order to reach that conclusion. This observation lies behind Peirce’s distinction, after 1900, of two different forms of diagram deduction, named “corollarial” and “theorematic”, respectively, after two inference types in Euclid, the easy “corollaries” and the more difficult “theorems”.¹³⁸ They now form two basic varieties of deduction in Peirce’s system, and they correspond to what is explicitly, viz., implicitly represented by a proposition: “The “meaning” of a proposition is what it is intended to convey. But when a mathematician lays down the premisses of the Theory of Numbers, it cannot be said that he then in-

Corollarial vs. Theorematic Diagram Reasoning

151

tends to convey all the propositions of that theory of which the great majority will occasion him much surprise when he comes to learn them. If to avoid this objection a distinction be drawn between what is explicitly intended and what is implicitly intended, I submit that this manifestly makes a vicious circle; for what can it be implicitly to intend anything, except to intend whatever may be a necessary consequence of what it explicitly intended?” (“Logical Tracts. No. 2. On Existential Graphs, Euler’s Diagrams, and Logical Algebra”, 1903, R 492).

He may also say that the immediate interpretant of a proposition is all the obvious inferences from it, while the final interpretant is the sum of all possible inferences from it—which we might never be able to grasp in its totality. Peirce was very proud of the Corollarial-Theorematic distinction. In the Carnegie Application from 1902, he famously called it “my first real discovery”, and this is how he presented it to James some years later: There are two kinds of Deduction; and it is truly significant that it should have been left for me to discover this. I first found, and subsequently proved, that every Deduction involves the observation of a Diagram (whether Optical, Tactical or Acoustic) and having drawn the diagram (for I myself always work with Optical Diagrams) one finds the conclusion to be represented by it. Of course, a diagram is required to comprehend any assertion. My two genera of Deductions are, first, those in which any Diagram of a state of things in which the premisses are true represents the conclusion to be true and such reasoning I call Corollarial because all the corollaries that different editors have added to Euclid’s Elements are of this nature. Second kind. To the Diagram of the truth of the Premisses something else has to be added, which is usually a mere May-be and then the conclusion appears. I call this Theorematic reasoning because all the most important theorems are of this nature (Letter to William James, Dec. 28, 1909, EP II, 502).

Much can be said about the nature and varieties of Theorematic Deduction, suffice it here to point out that the notion of theorematic experiment with diagrams constitutes an important de-trivialization of deduction. Famously, Kant claimed, based on the simple example of the unmarried bachelor, that all information in the conclusion of a deduction was already given in the premises—from which it follows that deduction is little more than a banal repeating of what is already known, an idea which was taking further in logicism and its triumphant claim that mathematics was but a sum of logical tautologies. Theorematic reasoning, rather, points to the fact the process of deductively proving something may involve the work of making information explicit which was only, maybe in remote and convoluted ways, implicitly given in the premises. Furthermore, it entails that there is not necessarily any given algorithm of how to disentangle that information. In many cases, auxiliary lines or other additional material must be added to the diagram. Such addition, of course, is subjected to the rules governing that specific type of diagram—but that is not the same as to know how those rules

152

Chapter 8: Dimensions of Peircean Diagrammaticality

should be specifically applied. So, an important trial-and-error phase here may concern which series of diagram experiments to undertake in order to reach the desired theorem proof.¹³⁹ Famously, in mathematics, such processes may take centuries and involve many vain attempts and the effort of many generations of scholars. Only when the proof is actually reached, the clear chain of deductions may be isolated, in retrospection, to stand out. Thus, Peirce’s notion of theorematic diagram experiment importantly implies that the deductive experimentation with the idealized structures of diagrams may be hugely non-trivial and involve abductive guesses and inductive inspiration from other branches of mathematics until the final chain of deductive steps is established.

Logic Diagrams vs. Diagrams Facilitating Logical Inferences Discussing diagrams in general is something which Peirce predominantly does in the context of introducing and discussing formalizations of logic—the Algebra of Logic from the 1880s and the alternative formalization of his Existential Graphs around 1900. Those formal representation systems, of course, have their aim in formalizing logical structure and relations like those normally associated with logical connectives (“second-intention icons” like and, or, implies, not, etc.), as in propositional logic and Alpha Graphs, the addition of quantifiers and predicate structure in predicate logic and Beta Graphs and further notational machinery in the different extensions of Gamma Graphs. Peirce’s general doctrine of diagrams, however, is not restricted to the diagrammatization of logical relations which rather appears as a special concern of logicians in the study of logical structure. Here, an important distinction is that between diagram icons used for explicitly representing logical relations (icons of second intention) holding between symbols, indices, and icons of first intention, one the one hand, vs. diagram icons appearing as predicates in propositions (icons of first intention) on the other.¹⁴⁰ The special icons of second intention are those concerned with the connectives and syntax of logical representation systems—the linear syntax of standard formal logic and the 2D syntax of the Existential Graphs. Such icons serve to present logical structure in a way so that it is, simultaneously, observable and intelligible. In formal logic, the first-order icons are typically underdeveloped; predicate logic famously does not say much about the content of predicates except for their relational structure (whether it is a 1, 2, 3, 4, … place predicate). Most often, the content of the predicate is represented by some natural language expression of it or its abbreviation (like “Red(x)” or “R(x)” meaning “x is red”).¹⁴¹ This in contradistinction to the vast amounts of diagrams in mathematics, the

Logic Diagrams vs. Diagrams Facilitating Logical Inferences

153

special sciences, media, communication etc. where it is various structural aspects of the subject matter discussed which are predicated to play center stage and where the content of the relevant predicates used to describe that subject matter is diagrammatically depicted. Peirce often referred to such diagrams even if he rarely went far into analyzing them: For there is no way of representing complicated facts that begins to be so expressive as the way a diagram represents it. Compare for example all one could possibly carry away from a half-hour’s oral description of a tract of country with the idea one could gain of it from three minutes study of a good map,—supposing of course, that one is habituated to the use of maps. The latter idea would far surpass the former; and yet it would not nearly so much surpass the description as the knowledge one would gain from a halfhour’s study of the map would surpass that which could be gained from a five hours’ oral account;— to say nothing of the relative fatigue (“Diversions of Definition”, R 650, 1910, 8).

Here, the topographical map of an area is given as example. The focus in this quote lies upon the synthesizing and information-condensing effect of landscape information in the map. But that should not give us the idea that diagrams of non-logical matter do not offer inference possibilities, quite on the contrary. One of the chief virtues of topographical maps is that they, just like logic diagrams, make inferences possible that makes explicit relations which were only implicitly given in the diagram. So even if maps do not represent logical connectives (they obviously represent spatial relations present in their object, in this case the landscape), they offer rich possibilities for making explicit relations which are not given as such in the diagram (e. g., the number of possible routes between two locations on the map, the relative sizes of woodland, agriculture and lake areas in a given district, the density of roads in an area, the elevation profiles of the landscape, and much more). So, here, inferences may be made directly in the material of the predicate. In a map, the spatial structure given by coastlines, contours, roads, categorization of landscape parts etc. forms the predicate aspect of the map diagram, while the proper names connecting that predicate to an existing object landscape form the index subjects of the diagram. The two co-constitute the whole of the map as one huge proposition—so in this case, the logical inference-drawing takes place by the manipulation of parts of the predicate (tagged, of course, with subject indices) describing landscape structure. In the vast majority of diagrams which are non-logical in this sense, it is still the possibility offered of drawing inferences by manipulating diagram parts that gives them their epistemological strength.¹⁴² So, the conclusion is that the diagrams of logic formalizations constitute a special, select subset of diagrams—characterized by picking out logical relations and structure as the particular object to be depicted—while the more general genus of diagrams may

154

Chapter 8: Dimensions of Peircean Diagrammaticality

take any structured field, a priori or empirical or combinations of both, as its object of depiction. Peirce even made the argument that such manipulation of diagrams invariably contains a mathematical core (just like topographical maps involve the mathematical issue of 3D→2D projections mentioned). This lies in his mature identification of mathematics with ideal reasoning, which is possible only by making deductions which, again, are possible only in diagram manipulation. So, all diagrams are mathematical, and all of mathematics is diagrammatical. This entails that all applied diagrams in different subject fields will contain mathematical structure—even if, in simple cases, they may be so easily readable so as to escape notice. Here, logic diagrams form that special case which uses mathematical structure to chart logic regularities (apparent in the name of algebra of logic for Peirce’s 1885 system). The distinction between logic diagrams and diagrams facilitating reasoning is connected to Peirce’s distinction between “logica docens” and “logica utens”. The latter is characterized by logic in use, while the former is characterized by taking logic as its object of study. Logic diagrams form a central tool of the latter, and, as Peirce says, the best diagrammatic representation in this respect is that which provides as differentiated and detailed picture of the single steps of the logical reasoning process as possible. That is not the purpose, however, for other users of diagrams, e. g., by mathematicians, who must be expert reasoners in the sense that they know how to make and manipulate diagrammatical formalizations of the mathematical structure they investigate—but who need not at all be expert reasoners in the sense that they are able to make explicit the logical principles put to use in their reasoning. They practice “logica utens”—like all other non-logicians using diagrams—while leaving it to the logicians to investigate logical structure by means of making explicit detailed logical structure and process in “logica docens”. So, the distinction between logic diagrams vs. diagrams facilitating inferences correspond to the docens-utens dichotomy, and the diagrams used correspondingly differ: from the docens requirement of diagrams best fit to make explicit the minutest detail of reasoning vs. the utens requirement of diagrams best fit to reliably and perspicuously presenting organized data and provide quick and easy inference-drawing in the relevant universe of discourse and subject field. This does not imply, of course, that diagrams of utens may not require highly skilled expertise for their construction, ongoing perfection and use; cf. the centuries-old process of perfection of mapmaking, involving the nontrivial issue of the geometry of different projections from a 3D sphere to a 2D plane map, the determination of the “geoid”, the precise shape of the earth in geodesy (a business to which Peirce was himself contributing during a large part of his life as a gravitation measurer for the American Coast Survey), the triangulation of landscape survey measurements from selected stations in

Pure vs. Applied Diagrams

155

the area, the rule-bound stylization of aerial photography, and much more, an expertise involving both mathematical, physical, and practical abilities. So, non-logical diagrams in this sense of diagrams not depicting logical structure but facilitating the drawing of inferences directly in the predicative structure of the sign form a vast field of signs in the wild, from the complexity and variety of diagrams in the special sciences to elementary diagrams widespread in media and everyday communication.

Pure vs. Applied Diagrams A closely related, but not identical distinction is that between pure and applied diagrams. It concerns whether a diagram is used in application to addressing and formalizing a given empirical subject matter. Take again the example of a topographical map of a given area. If we bracket the reference of that diagram by deleting all proper names and place names from it, we can treat the resulting diagram as an unsaturated diagram rheme which no longer refers to any particular empirical area, but only to some possible, imaginary territory. In that sense, it is now a pure diagram icon as it, like all pure icons, only refers to possible areas and no longer functions with any accompanying indices making truth claims pertaining to an empirical object. It now depicts but a fantasy territory, so to speak. That is one level of purification where we isolate the diagram predicate from the propositional function of map. But we may go further and delete also the legend of the map (its scale, and all the standard explanations of how to connect map features with particular natural kinds of the ontology of geography (blue for lakes, green for woodland, contour lines for height, parallel lines for roads, etc.). In short, the diagram is torn out of the regional ontology of geography. Now, the map predicate does not even refer to any possible geographical object preferentially—rather, more generally, it refers to any spatial object that happens somehow to share the shape of the naked line structure remaining in the map predicate. This structure, of course, may still be the object of geometrical and topological study in order to determine peculiarities about its metrics, shape, topology, connectedness, etc. It will still be a geometrical diagram, a pure diagram which, given the addition of general, geographical ontology on the one hand and particular subject references to some concrete landscape on the other, may come to function as the core of an applied diagram of topography. But it is a corollary of Peirce’s doctrine of diagrammatical reasoning, deduction and mathematics being co-extensive, that such a pure, mathematical object, simple or complex, explicit or implicit, must constitute the core of every diagram. So, under the regional ontological and referential cloak of any applied diagram,

156

Chapter 8: Dimensions of Peircean Diagrammaticality

there will lie the pure, relational-skeletal part-whole core structure which makes the application possible.

Continuous vs. Discontinuous Diagrams: Are Parts of a Diagram also Diagrams? The rational subdivision of diagram types forms one of the great challenges of diagram research, and Peirce only vaguely gestures at a taxonomic proposal, that of maps, algebras, and graphs, in that sequence. He describes them as composed from lines, from arrays of signs, or from both, respectively—without further giving many reasons for that proposal.¹⁴³ So, the following interpretation attempt at that trichotomy is my responsibility. In Peirce’s life-long obsession with the continuum, in metaphysics as well as mathematics, he reaches the idea that a continuum is a whole whose parts are homogeneous with the whole, are of the same kind as the whole. This is, of course, a recursive determination, holding also for the parts of parts, etc. Based on this definition, we may be able to distinguish continuous from discontinuous diagrams, depending on whether parts of a given diagram, of the same dimensionality as the whole, are themselves diagrams. It is obvious that a part of a map is also a map, albeit of a smaller territory, as is a part of a part of a map, and so on (up to granularity, of course). It is equally obvious that an algebraic diagram does not in general have parts which are also algebraic diagrams: partial algebraic sign complexes may easily cease to satisfy grammatical norms, be deemed ungrammatical and refer to nothing, in the absence of the whole of the equation or expression of which they form a part. So, maps and algebras seem to be clearly distinguished by being continuous and discontinuous representations in this sense, respectively. It even fits well with their positions as firsts and seconds of Peirce’s proposed triad. What then about graphs, the supposed third member of the trichotomy? “Graphs” were also chosen by Peirce to be the technical term for the Existential Graph systems of his mature years, so we should expect that they exemplify the third category of the trichotomy. It is well-known that Peirce’s trichotomies are not equal distinctions between independent phenomena—rather, the higher levels of the trichotomies typically involve specimens of the lower ones: algebras, albeit discontinuous, involve continua as represented in variables, etc.¹⁴⁴ Graphs, being mixed signs involving both lines and arrays of signs, then, might more generally mean diagrams involving both continuous and discontinuous representations of their content. The EGs actually do that: they are basically a continuous topological formalism adding a strongly discontinuous interpreta-

Linear vs. Multidimensional Diagrams

157

tion convention: systems of closed, nonintersecting curves subdivide the plane into “even” and “uneven” regions, interpreted as regions of positive vs. negative propositions. In that sense, they would be a candidate for a Graph mixing continuous and discontinuous diagram features. Candidates for the Graphs category may also, literally, be continuous diagrams supported by algebraic expressions—the most well-known example of course being the Cartesian plane where all arithmetic equations may find expression in curves, and all curves may be seen as the expression of equations algebraically expressible. In that case, by contradistinction, maps would be continuous diagrams where the shapes are not analyzed while graphs would be continuous diagrams whose shapes are, to some degree, analyzed or conventionalized by algebraic means. Graphs would then differ from maps by explicitly furnishing analyses of spatial structure—while maps are simpler icons which may be recorded by some feature-preserving procedure but without the addition of any explicit formal analysis of their content. The process from an aerial photo of a territory to a topographical map via a series of stylizations and categorizations would, in that case, count as a move from a simple map in the direction of a graph in this sense.

Linear vs. Multidimensional Diagrams Oftentimes, maps are 2-dimensional while algebras are 1-dimensional in the sense that the former find expression in diagrams covering proper parts of a geometrical or topological plane, while the latter consist of a linear array of signs. This fact should not, however, simply make us identify maps and algebras with multi- and unidimensional diagrams. Maps of one dimension exist, cf. the map of the isolated Bakerloo line above; algebraic expressions requiring more than one dimension exist, cf. diagrams like the following:

Fig. 30: Commutation diagram used in the proof of the “Five Lemma”.

158

Chapter 8: Dimensions of Peircean Diagrammaticality

So, the distinction between uni- and multidimensional diagrams is independent of that between maps, algebras, and graphs. In all cases, however, the dimensionality of any diagram may be locally increased by the addition of signs, iconic, indexical, or symbolic, which do not form part of the given dimensional representation. In algebras, superscripts and subscripts of many kinds add further dimensionality to the sequential array of symbols; in topographical maps, a similar role may be played by the addition of signs like that of a small square for “capital” or a small icon of a building, none of which are proper parts of the isomorphic 2-D landscape diagram but add additional information, in a certain sense orthogonal or independent, about locations in that diagram. Such local additions could be said to increase dimensionality; not, however in the sense of adding a full, new dimension of the same kind as the existing diagram (which would result, e. g., in a 3-D map), rather in the sense of adding a dimension of meaning independent of that expressed in the founding diagram. In 2-D maps, information about some restricted range of a literal third dimension, height, may be added by the use of a discretizised dimension of color shades (typically from deep to light green, yellow, lighter and darker brown for increasing elevation), or by a discontinuous dimension indicated by isohypses. A third dimension, of course, may also be introduced in 2-D diagrams by different versions of perspective; even a fourth dimension may be hinted at by 2-D diagrams describing the relations between the parts of a 4-D cube, etc. So, additional signs of several different kinds may be added to the basic dimensionality of a diagram, both in order to add further dimensions of signification, and in order to indicate some aspects of higher spatial dimensions.

Diagrams in Non-Necessary Inferences As we have seen, in Peirce’s mature semiotics, diagrammatic reasoning forms the defining feature of deduction, which, in turn, is identified with mathematics. But as the non-necessary inferences abduction and induction are defined as inversions of deduction, they are also involved with diagrams, although in different manners: “All necessary reasoning is diagrammatic; and the assurance furnished by all other reasoning must be based upon necessary reasoning. In this sense, all reasoning depends directly or indirectly upon diagrams” (“PAP”, 1906, NEM IV, 314). It is a major issue in the development of Peirce’s mature semiotics that he vacillates in the ordering of abduction, deduction, and induction after the three categories. After proposing the abduction-induction-deduction ordering in the 1860s where the three follows a sequence of increasing inferential strength

Diagrams in Non-Necessary Inferences

159

from possible over probable to necessary, and their definition is based on whether their inference is based on likeness, indexicality, or symbolicity, respectively, the standard view of the mature Peirce inverts the places of induction and deduction to the abduction-deduction-induction sequence. This is elaborated after the turn of the century where the combinatorial schema now demands there must be two subtypes of deduction and three of induction—giving rise to the corollarial/ theorematic deduction and crude/quantitative/qualitative induction distinctions, respectively. This ordering also has the benefit that it follows the standard sequence of reasoning so that abduction, based on a surprising information, proposes an explanatory diagram as a hypothesis; this hypothetical diagram is then investigated in deduction, and various implications of it are laid bare; these hypothetical implications are then tested in induction where collections of samples of empirical material after different techniques check the validity of the deductive proposals. While the explanatory hypothesis in abduction is general and of a diagrammatic nature, the inductive testing seems to follow a principle where the ideal diagram results of deduction are measured on a sort of inductive diagrams emerging from the empirical material: It is true that a distinctively mathematical reasoning is one that is so intricate that we need some kind of a diagram to follow it out. But something of the nature of a diagram, be it only an imaginary skeleton proposition, or even a mere noun with the ideas of its application and signification is needed in all necessary reasoning. Indeed one may say that something of this kind is needed in all reasoning whatsoever, although in induction it is the real experiences that serve as diagrams (Lowell Lecture V(a): Multitude, 1903, R 459, R 459(s)).

Even if strangely matching, however, there seems to be no theoretical principle dictating that the phase sequence of inferences in inquiry should follow the order of their categorial structure—there are no other among the many Peircean trichotomies where their 1– 2– 3 structure is taken as the basis or syntax for a corresponding 1– 2– 3 temporal process unfolding. The strange thing is that after having developed this abduction-deduction-induction ordering in some detail over the intensely creative years after the turn of the century, Peirce again gives it up in 1905 to return to the original abduction-induction-deduction categorial ordering. As says Bellucci: “In Peirce’s classification of signs of the years 1905 to 1908 (…), induction is connected with the category of secondness, while deduction is connected with the category of thirdness. Peirce thus finally reverted to the 1867 scheme, as announced in the draft of the Harvard lecture quoted above. As I noticed, the 1867 scheme does not fit with the principle of categorial subdivisibility and with the three-stages conception of scientific inquiry. Yet, it is a fact that Peirce reverted to his original position and maintained it in his subsequent classifications of signs …” (Bellucci 2017, 211) There are several

160

Chapter 8: Dimensions of Peircean Diagrammaticality

quotes indicating that the mature, post-1900 Peirce vacillated with respect to this issue which is ironic given the fact that it was the very issue of analyzing and classifying the three inference types which originally prompted his investigation of semiotics as a means to this classification in the 1860s in the first place. This classificatory enigma does not seem, however, to shake the relation of the three types to diagrams: the role of abduction is to propose an explanatory diagram which has the event or fact to be explained as its necessary implication; the role of deduction is to scrutinize and perform experiments on the diagram in order to trace and make explicit hitherto unseen implications of it; the role of induction is to make and analyze a sample from the field in question, structuring the data in a diagram comparable to the ideal diagram results of deduction.

Diagrams in Peirce’s Mature Semiotics Diagrams and diagrammatical reasoning loom large in the mature Peirce’s sign theory. His interest in these issues is constantly fueled by his development of the Existential Graphs, and thus logic graphs naturally form the ongoing particular examples occupying him the most. But simultaneously, important developments holding for diagrams in general take place again and again—some of which I have addressed in this chapter, attempting to provide an overview over distinctions relevant for a Peircean diagrammatology. It may appear strange that diagrams, on the surface, may seem to take a peripheral role in Peirce’s simultaneous attempts at further developing his three-trichotomy combinatorial semiotics into six- and later ten-trichotomy versions. The only taxonomical attempt at defining diagrams is the 1903 image-diagram-metaphor distinction which was given up and must be considered a failure. The reason for this seeming lack of connection between two of the important semiotic developments in the mature Peirce, however, is probably pretty simple. The reason is that, increasingly, diagrams came to be the central species of icons, becoming responsible for most if not all that is analyzed as iconicity in the Existential Graphs—and responsible for the ambitious, overarching identification of mathematics and deduction more generally. So, the diagram concept has grown so as to swallow most of the iconicity concept—thus when the classic icon-index-symbol triad is involved in the various combinatorial attempts of 1904 – 1908, diagrams generally come as a sort of contraband under the “icon” headline. Another important place where diagrams increasingly play center stage is, as we just saw, the ongoing issues with categorizing Peirce’s three inference types, which sparked the whole development of his semiotics in the 1860s in the first place—abduction, deduction, and induction. With the identification of deduction with diagram experiment

Diagrams in Peirce’s Mature Semiotics

161

(and the less developed insistence that even the other two inference types are dependent upon diagrams), this trichotomy of arguments places diagrams centrally in the various generalizations of the term-proposition-argument trichotomies. If we take a look at Peirce’s classic articulation of his mature semiotics—in the three-trichotomies, ten-signs combinatorial taxonomy developed in the 1903 Syllabus, it is true that diagrams appear nowhere as species name under the sign genus (nor under the icon genus). But that is probably because diagrams are involved, again and again, at so many places that they could not possibly serve as single sign category. Thus, the Second sign category of “Iconic Sinsigns” gives as examples diagram Tokens, that is, individual, concrete diagram signs, which form Replicas of the diagram Types mentioned as the typical example of the Fourth sign category of “Iconic Legisigns”—general iconic signs. Simple diagrams may appear already in the Fifth category of “Dicent Sinsigns”, because such signs function by means of an index involving an icon—thus the simple diagram of a pointing arrow provides the icon giving the weathercock its predicative meaning. Again, diagrams may appear as predicates in propositions which is why they are there in the Eight category of Symbolic Rhemes—general, unsaturated predicates—as well as when those predicates may be saturated by the addition of index subjects to form the ninth category of full-blown Dicent Symbols, ordinary propositions which are now generalized to embrace non-linguistic (or only partially linguistic) examples of propositions such as those appearing in the diagrammatic EG formalizations. Finally, the crowning tenth category of Arguments are based on the stepwise experimental modification of Diagrams from premises to conclusion. The articulation of the syntax of propositions is, in itself, diagrammatical, as is the level-higher structure of inference-drawing. In a certain sense, there are diagrams all over the place in the 1903 sign taxonomy, which goes on to form, of course, the core of the more tentative six- and ten-trichotomies experiments of the following years. My contention, in any case, is that there is a rich vein of important insights to be found in the mature Peirce’s doctrine of diagrams—and that they lie at the core of also of the shifting Immediate Object trichotomies (and their attempt at grasping the interface between the diagrammatic predicate of propositions and their dynamical objects), as well as at the core the many extension attempts in the direction of speech acts (where the triads addressing illocutionary acts and perlocutionary effects generalize the diagrammatical propositions and arguments from the 1903 doctrine). So, the reason that diagrams are not visible on the surface of the many different taxonomical proposals of the 1904 – 1908 period is rather that it is them, their structure, use, activities, purposes, and results which those taxonomies aim to explain.

Chapter 9 Iconicity of Logic—And the Roots of the “Iconicity” Concept “… iconicity, or the palpability of being represented in a diagram” (R 229, c. 1897; NEM II, 595).

It seems to be a standard assumption that Charles Morris originated the concept of “iconicity” on the basis of Peirce’s icon-index-symbol discussions. This chapter rather locates the origin in Peirce himself, in the context of judging the merits of different mathematical and logic representations—the more iconic such representations generally being preferable to less iconic ones. This chapter provides the context of logic representations in order to show how Peirce’s articulation of the concept of “iconicity” comes out of the attempt to find as iconic a way as possible to depict logical relations. Moreover, this indicates a use of “iconicity”, from the very beginning, which addresses not only similarities between different visual representations—but also representations of formal, abstract contents. Thus, the very notion of iconicity comes out of deep issues in the discussion of formal logic and different ways of representing it. If something exists which can be called logical structure, distinct from the different incarnations, representations, or formalizations of that structure, then those different formalizations may be measured by the degree to which they adequately depict logical structure. That is, by their degree of iconicity. This is not, however, a case of iconicity between two sensory presentations, e. g., visual phenomena—rather, it addresses the issue of visual representations of logical structure, which is not in itself visual. This, again, raises important issues about the basic status of iconicity itself. Actually, the very term of iconicity emerges out of the discussion of different logic representations. There seems to be a widespread urban legend that the concept of iconicity originates in Charles Morris’ interpretation of Peirce’s iconindex-symbol triad, e. g., in his Signs, Language and Behavior (1946).¹⁴⁵ This, however, is not correct. The concept is already found in Peirce’s doctrine of signs. And here, it is articulated exactly in the context of different logic representations. So, the very origin of “iconicity” lies in the interface between semiotics and logic, which I think might be a useful piece of knowledge, not least for the iconicity research community.¹⁴⁶ In Peirce’s Collected Papers, “iconicity” occurs only once, in a discussion of different possibilities for representing bound variables in his “Existential Graphs” notation of predicate logic: https://doi.org/10.1515/9783110793628-011

Peircean Iconicity

163

But of what variety of Linear Continuity is the heavy line more especially the Icon in the System of Existential Graphs? In order to ascertain this, let us contrast the Iconicity of the line with that of the surface of the Phemic Sheet (“The Bedrock beneath Pragmaticism”, 1905, R 300, 4.561, n.).¹⁴⁷

The quote addresses the use of so-called Identity Lines to refer to individuals— more about this below. There is not yet any occurrence of “iconicity” in the ongoing chronological publication of Peirce’s Writings, which may not be strange as the published volumes are only reaching the year 1892. One mathematical use of the word from around 1897 is found in the New Elements of Mathematics selection of Peirce Mss.¹⁴⁸ Further “iconicity” occurrences in the vast amount of unpublished Peirce manuscripts can, of course, not be precluded. The converse, negative concept of “aniconicity” may also be found in the discussion of logic representations: “One system seems to be about as good as the other, except that unnaturalness and aniconicity haunt every part of the system of entitative graphs, which is a curious example of how late a development simplicity is” (“Logical Tracts no. 2”, 1903, CP 4.434). Here, the discussion addresses Peirce’s choice between two different graphical representations of Logic, his “Entitative” and “Existential Graphs” (cf. below). Also, verbalization (“iconize”) and adjectivizations (“iconic” and “iconical”) of the term “icon” are widely used by Peirce, especially in the context of discussing logic representations.¹⁴⁹ In this chapter, I shall investigate which ideas of logical iconicity are at stake in Peirce’s logic representations.

Peircean Iconicity As is well known, Peircean iconicity is not restricted to visual nor perceptual similarity, nor to easily recognizable resemblance. Quite on the contrary, Peircean iconicity began with logic. At least two basic issues are addressed at length here: a) which parts or aspects of logic necessitate the use of iconic signs (cf. predicates rather than subjects)?—and b) the higher-level issue of which aspects of logic structure itself may be iconically expressed (cf. the choice between different representation systems)? Thus, the Peircean notion of iconicity goes far beyond perception, as is evident from what I have earlier called his “non-trivial iconicity definition”:¹⁵⁰ “For a great distinguishing property of the icon is that by the direct observation of it other truths concerning its object can be discovered than those which suffice to determine its construction” (“That Categorical and Hypothetical Propositions are one in Essence”, 1895, SWS, 63; CP 2.279).

164

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

This surplus of information is accessed via manipulation of or experimentation with the icon—actions realizing deductive inferences. This implies that Peircean iconicity has a far wider extension than accepted by many later iconicity scholars. The criterion of being an icon is simply whether such “other truths” may be inferred from it. Thus, the extension of iconicity not only comprises the ordinary series of pictures, images, and photographs, but also examples like: ‒ 2D continuous charts → manipulation of icon ex.: Finding routes on topographical maps, extrapolating graphs, etc. ‒ Algebraically expressed equations → manipulation of icon ex.: solution of equations: x +2 = 4 → x =2 ‒ Aspects of linguistic syntax → manipulation of icon ex.: “John beats Peter” → “Peter was beaten by John” ‒ And many more. Thus, Peircean iconicity addresses, from the outset, a logical issue: which information may be inferred from a sign?

Iconicity in Logic Formalizations In order to understand the notion of logical iconicity, we must address the issue of how to express logical relations. Often, the logic tradition has favoured linguistic representations, like the syllogism “All men are mortal. Socrates is a man. Hence, Socrates is mortal”. In the 19th century, however, increasing interest was given to graphical representations of logic, such as Euler Circles or Venn Diagrams. In the 1870s, Friedrich Albert Lange, in his Logische Studien (1877) argued that logic as such relies on spatiality and, hence, is best represented graphically—an argument which deeply impressed Peirce.¹⁵¹ Famously, Frege in his 1879 Begriffsschrift was the first to introduce quantifiers and relational logic, simultaneously proposing a graphical formalization of propositional logic and first order predicate logic. Not knowing Frege’s achievements, Peirce proposed alternative, algebraic representations of the two, in 1880 and 1883 – 1885, respectively. Twenty years later, he constructed yet an alternative graphical representation system, the “Existential Graphs”.¹⁵² Thus, Peirce constructed no less than two different sets of elaborated logic representations: 1) The “Algebra of Logic”, formalizing propositional logic (1880) and first-order predicate logic (1885) in a linear language—which was the first version of the formal logic which, via Schröder, Peano, and Russell, became modern standard usage 2) The “Existential Graphs” (1896 onwards), formalizing propositional logic (Alpha), first-order predicate logic (Beta), and an unfinished series of further

The Algebra of Logic

165

logics (Gamma—second-order Predicate Logic; modal logic; three-value logic; temporal logic; speech act logic, etc.)¹⁵³

The Algebra of Logic Peirce’s two 1880s logic representations appear in two homonymous papers: 1) “On the Algebra of Logic” (1880), concerning the formalization of Propositional Logic (“Logic of Non-relative Terms”) 2) “On the Algebra of Logic” (1885)—the introduction of quantifiers; the formalization of First Order Predicate Logic (“Relative Logic”) Let us first take a look at his proposals for the connectives of propositional logic (1880)—the very first version of modern formal logic.

Fig. 31: Peirce notation and modern notation of elementary signs of propositional logic.

As is evident, all of Peirce’s proposals are syntactically equivalent to present-day use—the only difference lies in the shape of the individual sign of the connective. In some cases, there is even close relations among the sign’s actual character in Peirce and modern notation, respectively—the asymmetric, directed character of the implication sign, the prefix negation sign, the “and” signs taken from arithmetic multiplication. The next step, the system for relational logic, what is now called First Order Predicate Logic, followed in 1885 introducing quantifiers and polyadic relational predicates, just like Frege had done it graphically six years earlier, but now in a linear, algebraic notation. Here, Peirce’s proposal addressed which different aspects of relational logical expressions should be expressed iconically, indexically, and symbolically, respectively. If we take the sentence “Somebody loves something”, it will be expressed as follows: ΣiΣj(l)ij—meaning “There exists an i and there exists a j so that i loves j”. This expression now has three parts:

166

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

1)

an index part—quantification—ΣiΣj—pointing out the objects to which the proposition refers 2) an iconic part—the Boolean part—describing the relations claimed to hold—(l)ij —“love” being a two-part relation iconically depicted by a bivalent predicate 3) a “token” (symbolic) part—presented by symbolic signs, each of which is conventional and general: i; j; >; Σ; 0; l … This apparatus allows the expression of existentially and universally quantified propositions (Fig. 32): ΣiΣj(l)ij > 0 – meaning: something is a lover of something ΠiΣj(l)ij >  – meaning: everything is a lover of something Fig. 32: Examples of existential and universal quantification in Peirce’s Algebra of Logic.

Peirce’s notation is algebraically motivated. Πi means “For all i …” while Σj means “There exists a j …”. Here, the Πi notation has been chosen with reference to “Product” and Σj with reference to “Sum”—the Boolean idea being that the truth of a claim can be expressed by the value 1 and falsity by the value 0. Then, Πi is the product of all the truth values of the single i’s. If the claim is false about just one i but true about all the others, then that single 0 suffices to make the whole product zero—meaning that it only holds for all i’s if the product is larger than zero. Conversely, Σj is the sum of all the truth values of the single j’s. If the claim is now false for all j’s except for one j, then this single 1 is sufficient to make the sum larger than zero—meaning there exists one j making the claim true (Fig. 33). Peirce quickly realized that the “> 0” part might be skipped as being superfluous, as it would appear in all propositions and thus be pragmatically empty. Universal quantifier: ΠxPxx “Π” for Product—originally meaning the product of Px cases >  – i.e., no single Px case may be zero for the product to be true Existential quantifier: ΣxPx “Σ” for Sum—originally meaning the sum of Px cases >  – I.e., at least one single Px case must be one for the sum to be true Fig. 33: Universal and existential quantifier signs in the Algebra of Logic.

Let us compare this representation system to Frege’s 1879 notation and modern notation—all of the three here expressing the proposition that “There exists a red ball” (Fig. 33):

The Existential Graphs

167

Fig. 34: Frege, Peirce, and modern notation of existentially quantified expressions.

We shall not here go deeply into the details of Frege’s more cumbersome notation, suffice it to point out the close relatedness between Peirce’s notation and modern notation developed on the basis of it. Peano took it over from Schröder, substituting the inverted Es and As (from “exist” and “all”) for Peirce’s algebraic notions, but the overall syntax remained unaltered. Similarly: “All balls are red” (Fig. 35):

Fig. 35: Frege, Peirce, and modern notation for universally quantified expressions.

The Existential Graphs A chief occupation of the mature Peirce around the turn of the century was the construction of a quite different logic formalism, which he baptized as “Existential Graphs”.¹⁵⁴ An important question here immediately jumps to mind: Why “Existential Graphs”? Peirce’s 1880 – 1885 notation was the origin of modern formal logic via Schröder, Peano, and Russell (Frege’s Begriffsschrift notation never came in use) and had already received some degree of recognition. So why did

168

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

Peirce develop an alternative notation 20 years later (from approximately 1896 onwards)? He had every reason to remain satisfied with his 1880 – 1885 achievements, which were even spreading and gaining recognition in Europe via the work of Schröder. Peirce could not know that his role in the origin of modern formal logic would soon be forgotten along the Schröder–Peano–Russell line with the result that most later logicians have little or no knowledge of his role and, in many cases, even erroneously think that Frege was responsible rather than Peirce. This dispute about priority hence did not occupy him and has only become an issue addressed by (much) later intellectual historians (cf. Putnam, Anellis, etc.). So why did Peirce set out to begin from scratch, constructing a wholly new graphical representation system for Propositional and First Order Logic? For reasons of iconicity! As Peirce quite explicitly states: The purpose of “Existential Graphs” is “… to afford a method (1) as simple as possible (that is to say, with as small a number of arbitrary conventions as possible), for representing propositions (2) as iconically, or diagrammatically and (3) as analytically as possible” (“The Bed-Rock Beneath Pragmaticism”, 1905, R 300; CP 4.561, n.). What, then, is the iconicity claimed for these graphs? Let us take a look at the simplest “Existential Graphs”, the Alpha system formalizing, again, Propositional Logic (Fig. 36):

Fig. 36: Alpha Graphs for propositional logic.

The Existential Graphs

169

Alpha Graphs are much simpler than the 1880 Algebra of Logic. They have two primitives only:¹⁵⁵ ‒ Co-localization: “And”—the location of two propositions at the same part of the page means the conjunction of the two ‒ Inclusion: “Negation”—the inclusion of a proposition in a “cut”, separating it from the rest of the page means the negation of that proposition ¹⁵⁶ Behind these two conventions lies the interpretation of the blank page. It is called the “Sheet of Assertion” or the “Phemic Sheet” and is taken to iconically depict the Universe of Discourse which is what the whole set of possible propositions at stake refers to. Thus, the continuous, empty page refers, implicitly, to all relevant truths. Peirce’s idea is now that this is a more iconic way of representing logical relations: to represent two propositions side by side, embraced in the same, true part of the universe, is a more iconic representation for “and” than representing them with an additional sign like “×” or “∧”. And to represent negation by cutting away the proposition from the sheet of truths is considered more iconic than attaching a purely conventional negation sign like “~” or “¬” to that proposition. Among the advantages Peirce saw in Existential Graphs was their multiple interpretability:

Fig. 37: Alpha Graph for disjunction.

The non-linear Existential Graphs are multiply interpretable and may be read as realizing a series of logical propositions which, in the ordinary notation, would require proofs to establish as equivalent. Thus, the graph of Fig. 37, in ordinary language reading “It is not the case that not-R and not-S” is immediately equivalent to the following compound propositions in modern notation: ‒ ¬ (¬R ∧ ¬S) ‒ ¬S ⇒ R ‒ ¬R ⇒ S ‒ R∨S ‒ Etc. …

170

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

This range of different depictions, in linear logic (including Peirce’s own earlier Algebra of Logic), of the very same structure is taken to be an anti-iconic property which should be avoided.

Beta Graphs The next logical step was to substitute Beta Graphs for the Algebra of Logic notation of First Order Predicate Logic.¹⁵⁷ It builds on Alpha graphs, and adds to Alpha Conventions further ideas: ‒ Dots refer to individual objects or variables ‒ Lines of Identity connecting two dots identify those individuals—thus, each Line of Identity refers to one individual or variable ‒ Lines of Identity may be composed into Ligatures, structures of Lines each referring to the same constant or variable—Ligatures may thus identify several variables, just as they may cross negation cuts ‒ Lines of Identity may connect to hooks of Predicates written directly on the Sheet so that S—blue means that the individual S has the property blue ‒ Polyadic predicates have as many hooks as their valency indicates, and they may be connected to a Line of Identity at each hook, thus A—loves—B means “A loves B” and —loves— means “Somebody loves something”. Each Identity Line segment represents a variable. Thus, a basic iconicity holds between the number of relata of a relation and the number of hooks of the corresponding predicate. ‒ The Line of Identity also expresses quantification; the outermost end of an Identity Line signifies quantification. If the line ends directly on the sheet or is enclosed by an even number of negations, this means existential quantification, “There exists an individual …”; if the line is oddly enclosed by negations, this means negative universal quantification, “It is not the case that there exists an individual …”—that is, “No x …”. Standard universal quantification, then, is expressed by implication using two cuts (below). Thus, the Line of Identity takes care of identity, existence, predication, as well as subsumption—the four different functions of the copula which, in the Frege-Russell tradition, were analyzed as ambiguous for that very reason. Let us take a couple of examples of Beta Graphs to see the expression of quantification and variables by means of Lines of Identity (Fig. 38):

Lines of Identity

171

Fig. 38: Beta Graphs with linguistic and modern interpretations.

The first graph has both ends on the sheet and is thus quantified existentially, meaning: “there exists an x”. This line is connected to the hooks of two oneslot predicates, “is good” and “is ugly”, respectively. The whole graph hence means “Something exists which is good and ugly”. The standard formalization is given for comparison. In the second graph, the Identity Line has its outermost end in a negative area. Thus, existence is denied: “It is not the case an x exists which is good and not ugly”. This, of course, is equivalent with the sentence: “If anything is good, it is ugly”—or, again, “For all x’s, if x is good, it is ugly”, or colloquially, “All which is good is ugly”. Thus, the nested graph of two cuts, one within the other, just like in Alpha Graphs, expresses material implication, if-then. Peirce took this as a particularly successful iconic representation, showing how the consequence is contained in the premises.

Lines of Identity In case of polyadic predicates, several Lines of Identity may be attached to different slots in the predicate (Fig. 39):

172

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

Fig. 39: Beta Graph with trivalent predicate.

“If there exists anyone, this person blames somebody to somebody else”—or, “Everybody blames someone to somebody”. It is easy to see that the number of individuals referred to by such a proposition is equivalent to the number of Lines of Identity Ligatures—in this case, three. According to Peirce, Lines of Identity and their composition into Ligatures are, for this reason, more iconic, because of this simple rule: there is one Ligature for one variable—contrary to the linear notation where the same variable is repeated several times through the formula. Compare again these two representations of the same proposition (Fig. 40): ∀ (x): G(x) ⇒ U(x)

Fig. 40: Linear and Beta Graph versions of “All that is good is ugly”.

In the linear notation, the variable x appears thrice—in the EG notation, the same variable appears only as one Ligature. This is deemed more iconic, as there is only one variable referred to, not three. Peirce first experimented, in the mid-1890s, with a dual system called “Entitative Graphs”, where the end point of an Identity Line on the Sheet meant Universal instead of Existential Quantification and where the fundamental connective, represented by co-localization, was OR instead of AND. Giving up “Entitative Graphs”, he argued that it was more iconic for a simple end point of a line to mean “There exists an x …” than to mean “For all x’s …”— and it was more iconic that “PQ” would mean “P and Q” rather than “P or Q”. The reason behind these iconicity claims is that one point iconically presents the idea in Existential Quantification that (at least) one x exists. The quote referred to on

Iconicity in Existential Graphs vs. Linear Notation

173

“aniconicity” above rejects “Entitative Graphs” exactly because of their lack of iconicity.

Iconicity in Existential Graphs vs. Linear Notation Let us now sum up the arguments for Existential Graphs being more iconic than the linear notations of the Algebras of Logic: 1) The blank sheet, as mentioned, is an iconic sign for the Universe of Discourse because it involves all possible points—that is, all possible true existential propositions 2) Co-localization as a sign for “and” is more iconic than “p∧q” or “p•q” because it immediately gives the idea that the two propositions joined form parts of the same Universe of Discourse 3) The cut (or “sep”) as a sign for negation is more iconic than ~p, or non-p, or ¬p because it literally separates the negated content from the universe of discourse 4) The Line of Identity as a sign for existence, identity, subsumption, predication, all at once, is more iconic than the various means used in the Algebra of Logic. As to quantification, it is more iconic than the algebraic Product/ Sum quantifier symbols and their repeated x’s because of its unity and its continuity. As to identity, it is more iconic than conventional signs like “=” because of its continuity, directly connecting the two points identified. As to predication, it is more iconic than P(x,y), again because of its continuity, directly connecting the variable with the relevant slot in the predicate. As noted above, Peirce compared Ligatures combining Identity Lines with another possible device called “Selectives”. What lead him to this consideration was that in cases with many Identity Lines and Ligatures, some of them crossing one another, such lines may form a maze which is not immediately perspicuous to the observer. In such cases, a Line of Identity may be cut into pieces, and each piece then identified by an attached letter instructing the observer that the line pieces with the same letter should be read as referring to the same individual or variable. Take the below graph, meaning “There exists a woman and if she has a child, she loves it” (Fig. 40). The first version involves crossing Lines of Identity, necessitating the convention of a small “bridge” preventing the two from merging (which would indicate reference to the same individual). The second version shows how Selectives reintroduce the array of X’s and Y’s from the linear notation:

174

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

Fig. 41: Equivalent Beta Graphs with Identity Lines vs. Selectives.

So, two different purposes of logic representations clash: the iconicity of the logical analysis of the diagram (Ligatures)—and immediate perspicuity and readability (Selectives). Here, Peirce definitely preferred Ligatures—and the very quote in which he introduces the notion of “iconicity” in the logic discussion occurs in an argument addressing exactly this: that Ligatures are more iconic than Selectives because of their continuity. He goes on to compare the explicit reference of 1D Ligatures involving individual variables to the 2D continuity of the whole sheet which then refers to the whole Universe of Discourse to which no particular attention is paid but which has the objects highlighted by the Ligature as parts. Selectives may be compared to the discussion of degenerate diagrams above (Chapter 8). 5) The end point of line as the sign for Existential Quantification is more iconic than “Σx” or “∃x” because it selects one point from the Universe of Discourse 6) The negated Existential Quantification is an iconic sign for Universal Quantifier, because Universal claims are inherently negative—to claim that All X’s are Y’s is to say there are No X’s that are not Y’s—so to actually find such an X would provide a counterexample 7) Predicates are represented with hooks (empty slots) whose number iconically corresponds to the valency of the predicate 8) The nested structure of negations gives, at the same time, the scope of quantifications 9) In implications, the implied is in an inner cut of the outer cut—im-plication.¹⁵⁸ Now we are in a position to appreciate the early appearance of the notion of iconicity in the middle of an argument pertaining to Existential Graphs. This addresses the lack of iconicity in Selectives mentioned in bullet 5), arguing for the superiority of the Identity Line notation instead. In this decisive quote, Peirce takes the deficits of Selectives one by one—first, they are not as simple; second,

Iconicity in Existential Graphs vs. Linear Notation

175

they are not as iconic, and third, they are not as analytical (the “two S’s” here correspond to the X’s in the Figure D example above): The first respect in which Selectives are not as analytical as they might be, and therefore ought to be, is in representing identity. The identity of the two S’s above is only symbolically expressed (…) Iconically, they appear to be merely coexistent; but by the special convention they are interpreted as identical, though identity is not a matter of interpretation— that is of logical depth—but is an assertion of unity of Object, that is, is an assertion regarding logical breadth. The two S’s are instances of one symbol, and that of so peculiar a kind that they are interpreted as signifying, and not merely denoting, one individual. There is no analysis of identity. The suggestion, at least, is, quite decidedly, that identity is a simple relation. But the line of identity which may be substituted for the selectives very explicitly represents Identity to belong to the genus Continuity and to the species Linear Continuity. But what variety of Linear Continuity is the heavy line, more especially, the Icon in the System of Existential Graphs? In order to ascertain this, let us contrast the Iconicity of the line with that of the surface of the Phemic Sheet. The continuity of this surface being two dimensional, and so polyadic, should represent an external continuity, and especially, a continuity of experiential appearance. Moreover, the Phemic Sheet iconizes the Universe of Discourse, since it more immediately represents a field of Thought, or Mental Experience, which is itself directed to the Universe of Discourse, and considered as a sign, denotes that Universe. Moreover, it [is because it must be understood] as being directed to that Universe, that it is iconized by the Phemic Sheet. So, on the principle that logicians call “the Nota notae” that the sign of anything, X, is itself a sign of the very same X, the Phemic Sheet, in representing the field of attention, represents the general object of that attention, the Universe of Discourse. This being the case, the continuity of the Phemic Sheet in those places, where, nothing being scribed, no particular attention is paid, is the most appropriate Icon possible of the continuity of the Universe of Discourse—where it only receives general attention as that Universe—that is to say of the continuity in experiential appearance of the Universe, relatively to any objects represented as belonging to it. / (…) Now for the continuity of the line of identity. This being one-dimensional, or dyadic, (i. e., running two ways only,) should represent an internal, or mental, continuity; and being definitely marked, should iconize a continuity of attention. But the heavy line is generated by the continuity of the different places of a heavy dot, which is the appropriate icon of an individual object in a Universe of continuous co-being; and, therefore, the continuity of the line is, best, the Icon of the continuity in attentive observation of an individual object (“The Bedrock beneath Pragmaticism”, 1905; R 300, LoF III, 327; partially in 4.561, n.).

The notion of “iconicity” occurs in the comparison of the continuity of the Line of Identity with that of the whole Sheet of Assertion on which the Line is drawn. The Sheet is two-dimensional and objective in the sense that it represents the entire world or Universe of Discourse, which the actual piece of reasoning addresses. The Line is one-dimensional only and makes explicit a small part of the former. It is “mental” not in the sense of psychological but in the sense of representing the continuous existence of the object it refers to, which is granted by an act of continuous attention to that object. In that sense, it is what Peirce

176

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

elsewhere calls “the immediate object” of a sign—which is the indexical connection claimed to exist between the sign and the object, granted (when it actually does exist) by the simultaneous existence of that object and attention to that object. Thus, this was what this first—as far as we know—first occurrence of the term “iconicity” was intended to explain.¹⁵⁹ The demand for as high a degree of iconicity as possible, however, does not imply the suppression of indexicality or symbolicity. Peirce, proud of his invention of the Line of Identity, rather claims that the advantage of this particular notation lies in its satisfying an ideal of equilibrium between these three sign functions: The value of an icon consists in its exhibiting the features of a state of things regarded as if it were purely imaginary. The value of an index is that it assures us of positive fact. The value of a symbol is that it serves to make thought and conduct rational and enables us to predict the future. It is frequently desirable that a representamen should exercise one of those three functions to the exclusion of the other two, or two of them to the exclusion of the third; but the most perfect of signs are those in which the iconic, indicative, and symbolic characters are blended as equally as possible. Of this sort of signs the line of identity is an interesting example. As a conventional sign, it is a symbol; and the symbolic character, when present in a sign, is of its nature predominant over the others. The line of identity is not, however, arbitrarily conventional nor purely conventional. Consider any portion of it taken arbitrarily (with certain possible exceptions shortly to be considered) and it is an ordinary graph for which Fig. 16 might perfectly well be substituted. But when we consider the —is identical with— Fig. 16 connexion of this portion with a next adjacent portion, although the two together make up the same graph, yet the identification of the something, to which the hook of the one refers, with the something, to which the hook of the other refers, is beyond the power of any graph to effect, since a graph, as a symbol, is of the nature of a law, and is therefore general, while here there must be an identification of individuals. This identification is effected not by the pure symbol, but by its replica which is a thing. The termination of one portion and the beginning of the next portion denote the same individual by virtue of a factual connexion, and that the closest possible; for both are points, and they are one and the same point. In this respect, therefore, the line of identity is of the nature of an index. To be sure, this does not affect the ordinary parts of a line of identity, but so soon as it is even conceived, [it is conceived] as composed of two portions, and it is only the factual junction of the replicas of these portions that makes them refer to the same individual. The line of identity is, moreover, in the highest degree iconic. For it appears as nothing but a continuum of dots, and the fact of the identity of a thing, seen under two aspects, consists merely in the continuity of being in passing from one apparition to another. Thus uniting, as the line of identity does, the natures of symbol, index, and icon, it is fitted for playing an

The Birth of Iconicity

177

extraordinary part in this system of representation (“Logical Tracts, No. 2”, 1903, LoF II, 151– 152; CP 4.448).

Peirce’s celebration of the harmonious concert of symbol-index-icon begins “from above”, as it were. The Line of Identity is a symbol, because it rests on a convention, the convention discussed above giving the rules according to which it may express identity, existence, predication and subsumption, all at the same time. But these conventions make rules for a sign which is already fit to serve these purposes. Its indexicality here is argued by observing that, as all general signs, it may only exert its general, symbolic function in the shape of an actual sign token existing here-and-now—a line drawn on a sheet, in this case. And this line factually connects its extremities—unlike other candidates for the same general meaning. This factual connection, again, is supported on the most basic level, by iconicity—by the continuity of the Line of Identity depicting the continuity of existence of the constant or variable referred to.

The Birth of Iconicity The birth of “iconicity” takes place in the middle of an investigation aiming to settle which logic representation most iconically represents logical structure. Let us sum up the arguments schematically (Fig. 42):

Fig. 42: Linear logic representation and Beta Graphs compared.

178

Chapter 9: Iconicity of Logic—And the Roots of the “Iconicity” Concept

The EGs were taken by Peirce as a means of analyzing logical structures as unambiguously and detailed as possible—not as an easy calculus aiming at computing swift inference results.¹⁶⁰ It is for this reason he is so adamant in his pursuit of iconicity. A calculus—with an eye to quick reasoning—may, quite on the contrary, benefit from being less iconical—having more logical primitives, more ways to express the same thing, more rules of thumb for shortcuts. But Peirce’s obstinate demand for iconicity in logic also has relevance for iconicity in general. It argues the more general case that different spatial representations of abstract structures—in this case, topological representations of logic—may be subject to iconicity criteria. It argues that iconicity plays a basic role in the selection among competing scientific formalizations—also in abstract and formal sciences. And it argues that there may be a trade-off between optimal iconicity and heuristic utility, which may strike different compromises in different cases, depending on pragmatic purposes. Abstract structures also inhere in more immediately accessible iconic signs like paintings, photos, movies, diagrams, poetry etc. Thus, we should expect to find the different degrees and modes of logical iconicity playing a role in such representations as well.

Chapter 10 Diagrammatic Problem Solving (with Svend Østergaard) In this chapter, we shall look at types of problems and their interplay with diagrammatic representation. The general notion of diagram goes back to Peirce; cf. the previous chapter.¹⁶¹ Here, we shall focus upon prototypical diagrams—a two dimensional, stylized topological (geometric) representation of some subject matter. In some cases, this representation is analogical as for instance in a map of a country, but in other cases it is a geometric representation of quantitative relations as for instance in a pie chart diagram. The difference is whether we map an already existing geometric relation onto the diagram or whether it is quantitative or other relations which are geometrized. If we add time as a dimension to the traditional spatial dimensions, we can also interpret temporal relations as geometric so for instance a flowchart diagram of information currents in a company will qualify as a diagram of geometric relations. However, there are other relations than spatial/temporal and quantitative; for instance, interpersonal relations: a crime investigator might set up a diagram of possible interpersonal relations between the different suspects and associates in order to get an overview of the problem. In short: a prototypical diagram is a two-dimensional geometric representation of something we may qualify as “relations” which might then be spatial/temporal relations, quantitative relations, interpersonal or other relations. When we have a diagram, it is possible to explore it. This exploration can take two forms 1) the exploration does not add anything to the diagram but consists in an examination of possible true statements that may be deduced directly from the diagram. This is the case of most information in both the pie chart diagram and the map of the country. From the map we can read the distance between A and B (given the map scale), find the shortest route between A and B, etc. without adding anything further to the map.¹⁶² 2) In the second type of explorations there is a manipulation of the diagram. In the example with the crime investigation the detective might add some connections in the diagram just to check if these connections are true what can then be deduced. In Peirce’s theory these two types of diagrams are called theorematic (when there is manipulation or the addition of further elements) and corollarial when the information can be read off the diagram directly.¹⁶³ This terminology is well known from mathematics where the theorems that the mathematician proves are the hard stuff requiring information that is imported from outside the problem space, https://doi.org/10.1515/9783110793628-012

180

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

often introduced as lemmas, and the corollary is a true statement that can be read off directly from the theorems without further manipulation. It is clear from Peirce’s definition and examples of theorematic reasoning that by “,manipulation” he does not just refer to external manipulations of the diagram but also to any mental manipulation so that if the problem solver confronted with the diagram imagines some kind of operation on the diagram it qualifies as theorematic reasoning; for instance, in the mundane case of a map one can imagine things like “if I go this way I get to B”, etc. For this reason, theorematic reasoning constitutes a heterogeneous set ranging from simple to complex cases, which may be explored further for internal differences and subtypes.¹⁶⁴ Solving a problem is, to a large degree, a question of focusing on the right information, and a diagram is a representation of information relevant in the situation. In the following we shall briefly present a typology of types of problems and the corresponding diagrams. The diagram is per definition a geometric/topological structure so if the source is not itself geometric the diagram is the result of a mapping from another source domain to a geometric domain and this mapping is performed by humans, so the diagram is not just the visual representation but is in fact indicative of ways of how the human mind may work. In other words, thinking is already diagrammatic. This connects to Peirce’s radical claim that solving any mathematical problem necessarily involves diagrammatic manipulation; this is because it is through diagrammatic representation and diagrammatic manipulation that the mind accesses the information necessary to solve any given problem.

Information Internal or External to the Problem Space A major distinction concerning problem solving is whether all information is present in the diagram or whether one has to add information from outside the problem space. The first is the prototypical case and includes all types of dynamic operations on a given diagrammatic representation. They may be mental, or they may involve addition of elements as long as they belong to the problem space. A case of a rule-governed manipulation we find in chess. The position on the board can be considered as a diagram which you can only manipulate following certain rules; the chess player reasons by imagining moving a piece and estimating the possible opponent moves and in this way, he or she might find the optimal solution of the position. The classical example mentioned by Peirce is Euclid’s proof that the sum of the angles in a triangle is 180°, a version of which is given above (Fig. 43). Given the triangle ABC, you extend the line BC to D, and from C you draw a new line CE

Information Internal or External to the Problem Space

181

Fig. 43: Triangle diagram with auxiliary lines in a proof of the angle sum.

parallel with AB. The angle between this new line CE and AC is identical to the angle A and the angle between the new line and the extended line CD is identical to the angle B. So, the three angles meeting in C are the same as the three angles of the triangle, and as BD is a straight line, the three add up to 180°. So, the sum of the angles is 180°. Although two new elements are added, making it a piece of theorematical reasoning, they do not come from outside the problem space, on the contrary they, as well as the triangle, are part of two-dimensional space, and they are drawn according to the general axioms of Euclidean geometry—analogous to the chess player who imagines moves in accordance with the general rules of chess. In both cases, however, what is additionally required for the problem solver is some strategic information. It is not sufficient to know Euclid’s axioms and chess rules—in both cases, some sort of strategy must be pursued: the relevant auxiliary lines to add must be chosen over an infinity of others possible, and strategically clever moves sequences must be chosen among the finite but large set of possible moves. A subclass of problems in the general category of information extraction from the diagram space is what we could call a perspective shift. This might include all cases where there is a reorganization of the elements in a diagram based on abductive reasoning, i. e., a manipulation that is not rule-governed. For instance, the crime investigator might reorganize the relations shown in his diagram of the possible connections between the criminal elements, this might involve a perspective shift where instead of A, B now is considered the main culprit. An example from science could be Copernicus’ reorganization of the Ptolemaic model of planetary movements. Instead of taking the Earth as the center of the movements Copernicus took a sun-centered viewpoint, not based on any rules but because he sensed that this could explain the empirical observations better. In Stjernfelt 2014, 278 f., another Peircean example from

182

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

mathematics is discussed—a proof of Desargues’ theorem—where the reorganization consists of embedding the elements in a three-dimensional space instead of two dimensions. The type of problems described above contrasts the cases where the information needed is not present in the problem space. For instance, the diagram of the criminal investigator typically contains question marks: Empty slots in the diagram that the investigator tries to fill out by looking for clues he does not yet know about. The typical examples of this group of problems are mathematical problems, though. Mathematical problems will in many cases need helping theorems, so-called lemmas. A lemma is itself a theorem of a simpler kind and often not directly connected to the problem in question; for instance, to know if one can find the solutions to an equation of nth degree one has to know something about the possibilities of permuting a row of n letters, which obviously belongs to another domain than solving an equation.

Types of Insight Problems In the gestalt approach to problem solving, the focus is on another distinction, namely whether the solution requires insight or not (Köhler 1925, Duncker 1945, Ohlsson 1992)—which may be seen as a correlate to the theorematic/corollarial distinction. Insight can be defined by whether a specific target element has to be accessed in order to solve the problem or not. Consider for instance the following problem: Describe how to put 27 animals in 4 pens in such a way that there is an odd number of animals in each pen. This problem can only be solved by putting all the animals in one pen and place the other pens in concentric circles around it. The target element is in this case the diagram of concentric circles; without accessing that diagram, the problem cannot be solved. If you do not consider the possibility that one pen may contain another, you cannot solve the problem. We may schematically represent the idea of a target element in the following way (Fig. 44):

Information Internal or External to the Problem Space

183

Fig. 44: Target elements in insight problems.

To the left, we have the different positions that the problem solver will move between without getting the solution, but he or she might accidentally cross the boundary and hit the target element on the right, in which case the solution becomes trivial. Insight problems are opposed, of course, to problems that do not require insight. The borderline between the two classes is slippery, though, and also depends upon solution strategies; take, for instance, a chess problem. One can make a program that can solve any problem instantly and this is not done by insight but by systematically going through all possibilities until it hits upon the solution, but for humans, the cognitive process that leads to the solution will proceed along strategic schemata and have the characteristics of insight. So, insight and non-insight strategries may exist pertaining to the same problem. Insight is possibly measurable in the problem-solving human individual as an increase of entropy in behavior just before discovering the target move. For instance, in Metcalfe and Weibe 1987, people’s feeling of warmth are recorded while they solve insight and non-insight problems. There was a progressive increase in warmth during non-insight problems. But with insight problems the warmth ratings remained at the same low level until suddenly increasing dramatically shortly before the solution was reached. Similarly, in Stephen et al. 2009, it is shown that when people solve a gear problem (see below) there is an increase in entropy just before they see the optimal strategy of counting the gears. Here, the entropy is measured through eye tracking, i. e., the gaze pattern is stable for a long time, but just before reaching the solution it becomes instable. So, it seems that in terms of behavioral dynamics the insight problems are determined by a catastrophic point, namely reaching the target element

184

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

whereas solving non-insight problems is determined by a continuous process reflecting that these problems are routine tasks and tasks where information is used incrementally, as e. g., in the Tower of Hanoi problem (Ohlsson 1992). We can now classify problems and their relation to diagrams according to whether it is an insight problem or not. If it is not an insight problem, then the diagram is a representation of some subject matter and from this representation it is possible to extract information by making mental operations without fundamentally changing the diagram, as mentioned above. For instance, a prototypical diagram is a flow chart diagram, which is a representation of the temporal dynamics of some domain: water flow in a heating system, information flow in an institution, etc. Given such a diagram, one can read off possible routes in the diagram; similarly in the pie chart diagram one can get direct information about relative size of expenditures in a single domain. However, in these examples, as is often the case, the diagram is a representation of a source domain so one can make experiments on the diagram in order to find alternative organizations of the source: if the heating system doesn’t work properly one can look at the diagrammatic representation to solve the problem. Whether the manipulation is relying on insight or not is determined by the underlying process as mentioned above, so if we manipulate a map incrementally to get to the solution it will not count as insight, but if we have to use some hitherto unknown or unused property of the diagram it may be insight. Insight problems we propose to divide into three types. Firstly, we have the insight that relies in information that is present in the problem space and which, although not easy to find, does not violate entrenched schematic representation of the field. Solving the problem of finding the sum of the angles in a triangle is an example of this. Remember: insight problems hinges on a target element that gives access to the solution. In the case of the sum of the angles, the target element is the line parallel with AB; cf. the figure above. When this line is added to the diagram the problem becomes corollarial because this line provides direct access to the solution. Although not easy to find, the parallel line does not violate any schematic knowledge about geometry; cf. above. Secondly, we have the problems where the solution requires new elements that are not directly accessible. This includes the cases mentioned above: the criminal investigation where one clue might give the insight to the solution and of course the mathematical problems where some external element might be the clue. Thirdly, we have an interesting class of problems where the target element might or might not be part of the problem space but where it will, in any case, constitute a violation of entrenched knowledge or entrenched schematic representations of the world. Entrenched knowledge may give rise to fixation ac-

Information Internal or External to the Problem Space

185

cording to the gestalt theorists (Duncker 1945). While the corollarial-theorematic distinction is related to the structure of the problem itself, fixation rather points to how the capabilities of the diagram manipulator may be blocked. The mind is fixed in a specific representation, blocking access to the solution. The problem of the pens mentioned above is an example of fixedness of representation, since we tend to think of animal pens as disjoint. Manipulating the pens rather than the animals in order to solve the problem is a diagrammatic manipulation. In this work, one can only solve the problem if one stumbles upon the target element, which in this case is the concentric arrangement of the pens. In Stjernfelt 2014, Chapter 10, we find an example of the same type of problem, namely the German geographer and explorer Alfred Wegener’s discovery of the plate-tectonics of current geology. Wegener was doing simple diagrammatic manipulation using the information you have on a map of the world and noticing that the West coast of Africa fit with the East coast of South America. This is more than just using the information present in the diagram because it requires the breaking up of the entrenched assumption that the continents were fixed on the surface of the globe. Geometrically, of course, the manipulation is simple, but geologically, the manipulation broke with entrenched ontological assumptions about the structure of the Earth crust. One can also mention the Copernican revolution as an instance of this, breaking with the entrenched and theologically motivated assumption that the Earth be the center of the universe—or the discovery of nonEuclidean geometry breaking with the assumption that if we have a point outside a line, we can draw exactly one other line through the point that is parallel with the given one. Or the definition of imaginary numbers: When Cardano tried to find a solution of an equation of the third degree, he introduced the square root of a negative number in the formulas for the solution. In order to solve a problem concerning real numbers, he had to invent a wholly new type of number outside of the domain of real numbers. So, this is a case where the diagrammatic manipulation of the equation reaches an obstacle which give rise to a redefinition of our very concept of numbers.¹⁶⁵ This is, in many cases, a central purpose of diagrammatic reasoning, namely, to find the problematic spots in the reasoning process. To summarize: we have problems that imply simple diagrammatic manipulations and problems that can only be solved by accessing one (or more) target elements, for instance in finding the sum of the triangle there might be several different elements that could provide the solution. In the last case the target element might, in some cases, constitute a break with our entrenched knowledge about the world, and finally the target element might be part of the problem space as is the case with the four pens and the sum of the triangle or it has to

186

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

be imported from outside the problem space as is often the case for mathematical problems.

Diagrammatic Re-description and Diagrammatic Re-encoding One of the characteristics of human cognition is the ability to represent a subject matter in an external format; for instance, represent the landscape in a map or the country’s finances in a pie chart diagram. This is a re-description of a subject matter in a representational format, i. e., a representational re-description. We find this notion in Karmiloff-Smith 1992, where the ability to redescribe a subject matter in another symbolic representation is seen as a basic aspect of the cognitive development of children. As the examples suggest, a diagram is a representational re-description, so the basis for this cognitive ability and thereby the ability to make abstractions is the diagrammatic thinking. The diagrammatic redescription is the key to improve already existing representations. Take as a simple example the decimal number 5,5. In this number, there are two fives, but they don’t mean the same thing. The meaning is determined by the spatial position and for that reason it is an example of a diagram that would replace a more cumbersome representation using fractions. We find another prime example of diagrammatic re-description in algebraic geometry. The basic idea is that curves can be represented in a different format by equations. For example, x 2 + y 2 = 5 represents a circle of radius 5. One geometrical diagram, a drawn circle, is represented by another algebraic diagram, an equation. It is possible to make (algebraic) manipulations with the latter diagram and thereby prove any number of properties of curves easier than by the purely geometric methods of the classical Greeks. The notion of diagrammatic redescription is closely related to the gestalt notion of re-encoding (Ohlsson, 1992). In the gestalt tradition re-encoding means that some aspect of the problem representation is reinterpreted. In a diagrammatic representation, this means that elements in the diagram are given a new interpretation; for instance, in Wegener’s discovery the continents are re-encoded as being slowly floating instead of being stationary. As the example suggests, re-encoding is mostly a case of insight. The situation is coded according to some entrenched assumptions which block access to the solution. In other words, access to what we have called the target element sometimes requires a re-encoding. In terms of diagrammatic representation, this is of course relevant for the problems whose solution relies on perspective shift and the examples mentioned above would be typical for a recoding procedure: recode the problem as embedded in 3D and recode the sun as the center for the planetary movements.

A Special Case: The Cog Wheel Experiment

187

A Special Case: The Cog Wheel Experiment In an experimental setup that is described in more detail below, participants organized in pairs look at a board with a string of connected cog wheels; they then have to determine what way to turn the first cog wheel in order for the last one to turn left or right. This example shows a dual aspect of diagrammatic thinking: on the one hand the problem is presented in the form of a diagram, so the board with the represented cog wheels is no different from a map of a country, a pie chart diagram, etc. It is now possible to perform bodily and/or mental operations, i. e., experiments on the diagram. However, in this case the representation the participants make in solving the problem are themselves diagrams; for instance, one pair might make gestures of circles at the diagram, another might follow the contour of the cog wheels in a continuous curve, etc. We consider all these gestures as diagrammatic representations of a procedure leading towards a possible solution. The transformations of these gestures during repeated trials correspond to the manipulations of a diagram whereby the diagram may change considerably. For instance, a participant may start by making circles, alternating between circles turning clockwise and circles turning anti-clockwise from wheel to wheel, this may degenerate into a simple wriggling and then finally just a pointing. This corresponds to a process where superfluous information is discarded, “prescinded” in Peirce’s terminology, and the implied diagram changes appropriately. For instance, the process full circle → wriggling → pointing gestures corresponds to discarding first information about the size and turning of the wheels, leading to a simple wriggling indicating changing direction, then discarding information about the direction of turning, leading to a simple pointing, often accompanied with speak indicating symbolized directions. This corresponds to a process of prescissive abstraction, which is a way to make a representation of the subject matter discarding unnecessary information. Is this case of diagrammatic problem solving an instance of insight or not? The answer is that it may be both. If the solver sticks to the mechanics of the system of wheels, then it is easy to solve the problem in a pedestrian way by keeping track of how each individual wheel turns. This is mechanical and does not require any insight; it is like finding one road in a map. The insight requires a perspective shift as in the cases mentioned above, namely from a system that consists of n wheels to a system that contains two wheels only. Every second wheel is categorized as the same so every time we count an odd number of wheels it is the same as the starting wheel, and every time we count an even number it is the same as the second wheel. The final insight is then to see that also the exact number of wheels is unnecessary information. The only necessary information is whether there is an odd or even number of wheels (so the

188

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

counting may also proceed as “odd-even, odd-even, …” or “A-B, A-B, …”). The purpose of the experiment is to see if the participants are able to get to this insight, and if so, how. And, if they do, to what extent can this be predicted from the gestures (diagrams) and comments they produce from the very beginning.

Cog Wheel Lessons In the following, we shall present some results from the cog wheel experiment realized at the Center for Semiotics in Aarhus in 2012– 2014.¹⁶⁶ The overall idea is to present cog wheel problems as described above to two persons, in order to investigate their collaboration activity during solution. The problem was presented to each pair of participants on a 60” screen on the wall with an empty space before it so that the pair was able to go close to the screen, gesturing and touching it if they so wished. The activity of each pair was then video-filmed and recorded, just like their gestural activity was recorded by measurement devices mounted on their wrists. A simple example of the task is the following:

Fig. 45: Example of a Cog Wheel problem. Which lever to pull in order to save the rabbit?

Cog Wheel Lessons

189

The task is to determine whether to pull the left or right lever in order to give the rabbit access to the carrots rather than to give the lion access to the rabbit (Fig. 45). The cog wheel diagram requires an interpretation in which the single wheels are able to move around their center and thus pass energy and resulting movement to connected wheels. This interpretation of the diagram, in itself static, as a dynamical physical system is so obvious that participants immediately adopt it, requiring no explicit instruction in diagram rules in order to begin solving the problem. In the experimental setup, each of 25 pairs of participants solved a series of such cog wheel tasks. Each pair was subjected to 18 trials with different gear systems, advancing from around 5 – 6 connected wheels to 13 gears. In a final trial, they were presented with a problem containing 28 gears, in which their solution time was measured. The initial idea behind the experiment was that two different solution strategies are at hand (Stephen et al. 2009)—one continuous and one discrete. The continuous strategy follows the imagined wheel movements from one wheel to the next—while the discrete strategy indicates, in stepwise sequence, the movement of each wheel as the opposite direction of the former. Earlier experiments (Stephen et al. 2009) seem to show that the former strategy is the most immediate while access to the latter, more efficient strategy takes the shape of a phase transition in the conceptualization of the problem. By presenting the problem to collaborative pairs of participants rather than to single participants, the idea was to investigate whether the phase transition in solution behavior was primed or accompanied by significant changes in communicative behavior, gestural or linguistic, between the two. Findings proved more complicated, however, indicating that there are indeed several possible phase transitions in solution strategies, combining verbal and gestural behavior in characteristic ways. The simplest and to some participants most immediate strategy traces the movement of the initial wheel with a circling finger and then goes on, continuously, to successive wheels. This can be called the “continuous motor strategy”, and in the respondents, this strategy is never accompanied by verbal differentiation of direction (like “this way”/“that way”, “left”/“right”, “up”/“down”, etc.). Group 13 is an example of this strategy (Fig. 46). Its final trial solution time is a bit above average. Another strategy could be called the “wriggling hand” strategy. Instead of continuously tracing movement from one wheel to the next, the movement of wheels is indicated by alternate hand movements, typically with the hand a bit further removed from the screen. The “wriggling hand” differentiates directions and often leads to effective (abstract) strategies, such as the accompanying of wriggling with verbal differentiation of direction or pointing accompanied by counting.

190

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

Fig. 46: Reaction time development over successive trials, Group 13.

Fig. 47: Reaction time development over successive trials, Group 24.

Group 24 forms an example of the wriggling strategy (Fig. 47). A peak in reaction time around trials 13 – 14 might indicate problems in solution strategy which are subsequently solved, forming a phase transition to a better strategy—with a resulting last trial significantly below average time.

Solution Strategies

191

Solution Strategies Looking at the whole population, the types of behavior are found to show considerably more possibilities than the simple continuous/discrete phase transition originally assumed. Focusing upon gesture, we find no less than 5 qualitatively different hand/ arm movement patterns: 1) Drawing a full circle for each wheel, typically with just one finger on the screen 2) Drawing the half arc of a circle before continuing to the next wheel, typically with one finger. 3) Wriggling the open hand left or right over each wheel 4) Drawing one continuous curve following the outlines of the gears 5) Pointing sequentially to wheel after wheel, typically with one finger As to verbal behaviors (apart from coordination talk, meta-talk, and jokes, etc. among participants), we observe 4 qualitatively different types: 1) Causal reasoning: “if we pull this one, then this one goes up”, abbreviated to “if this way, then this way” or just “this way, this way” 2) Describing the alternating directions of movement of the wheels: “left, right” or “clockwise, anti-clockwise” 3) Silence (while gesturing) 4) Counting: 1, 2, 3, etc. These different gestural and verbal behaviors are found to combine in the following sets of stable patterns (Fig. 48): Gesture

Language

Chaotic use of gestures Circle/half-circle Circle/half-circle Wriggle Wriggle Continuous curve Pointing Pointing

Causal Gesture Direction Causal Direction Silence Direction Counting

Fig. 48: Gesture-language combinations.

These behaviors combine sequentially in a series of typical developments which may be indicated in the following flow chart diagram over the landscape of dif-

192

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

ferent phase transitions between stable solution strategies (each arrow indicating a shift in strategy):

Fig. 49: Flow chart over typical developments across groups.

No very simple pattern of phase transition between two states is found, as suggested by Stephen et al. 2009. Rather, a more complicated landscape of phase transitions appears, with two attractors: the continuous curve-following and the discrete marking of the two directions, terminating in counting (Fig. 48). Gestures accompanied by causal reasoning is generally instable as a strategy and will develop into either of the two stable states, the Continuous-silence and the Pointing-counting positions. Obviously, not all pairs of respondents reach one of these end point attractors, but it seems as if those settling upon the less than optimal Continuous-silence strategy will typically remain there. All the different strategies characterized by a verbal indication of direction, however, may develop further to Pointing-direction or, ultimately, to the Pointing-counting strategy. There are some indications that early behavior during the trials may indicate later strategy choices. Early alternation between left-right movements might be indicative of later discretization in terms of Wriggle-direction of Pointing-counting, while, on the other hand, reliance upon causal arguments following wheel contours may be indicative of settling for the Continuity-silence strategy. It is interesting to compare the strategies by reaction time at the last trial (Fig. 50):

Embodiment and Collaboration—Two Hypotheses

193

Fig. 50: Average reaction times for different solution strategies.

Causal reasoning is obviously the slowest strategy, followed by the more efficient continuous strategy. After this comes, in order of increasing efficiency, the three strategies involving verbal indication of wheel directions—the Circle, Pointing, and Wriggling strategies with direction indications, respectively. It is remarkable that the Wriggle-direction strategy is almost as efficient as the Pointing-counting strategy, making it understandable that strategy developments may stop at the Wriggle-direction strategy.

Embodiment and Collaboration—Two Hypotheses These results hold some important lessons as to the role of embodiment in diagram reasoning. It has often been pointed to the fact that diagrams facilitate reasoning by means of their spatial presentation of problems, making it possible to solve them by means of real or imagined bodily manipulation with parts of the diagram. Additionally, externalized diagrams on paper, board, screen, or elsewhere facilitate the simultaneous or consecutive collaboration on the diagram by several persons. Both of these aspects, of course, are involved in the Cog Wheel experiment. As to the embodiment issue, an important result seems to be that “more” embodiment does not equal better solution strategy. The strategies which closely mimic the causal chain or the movement pattern of the

194

Chapter 10: Diagrammatic Problem Solving (with Svend Østergaard)

wheels, touching the screen, are the least effective. The more effective strategies are the more abstract ones of Pointing-counting and Wriggle-direction which are by no means completely disembodied but which use gesture (pointing, wriggling) to address the discrete structure of the problem rather than its concrete, continuous materiality. We may consider the different gestures as diagrammatic representations of possible solution strategies. Here, the causal arguments contain, in a sense, too much information. This is also the case with the continuous curve which is more efficient than simple causal reasoning but remains a suboptimal solution. Getting to the optimal solution requires an instance of insight. This step of abstraction seems to involve moving focus from local information about how two wheels influence each other to a more abstract, global regularity about every second wheel moving in the same direction. To get to the optimal solution, then, it seems necessary to get away from a closely embodied interaction with the target. Indeed, certain solvers successfully used the wriggling-direction strategy at a distance of several meters from the screen. This may give rise to the following hypothesis. Not all reasoning is based on immediate embodied experience—but rather on abstraction from immediate, concrete and local embodied experience. It should be added, however, that such abstraction is by no means completely disembodied but accompanied with specific embodied strategies supporting abstraction—in this case the wriggling and pointing gestures. As to the collaboration issue, the provisional results of the Cog Wheel experiment seem to indicate that mixed-media strategies involving both language and gesture are the more efficient. Using existing linguistic abstract concepts

Fig. 51: Final reaction time for individuals and pairs; pairs = 31 (n=62); individuals = 23.

Embodiment and Collaboration—Two Hypotheses

195

(left-right, numbers, etc.) support the abstraction and simplification of gestures, effectively constituting a gestural-linguistic two-sided schema. Moreover, comparisons with individuals solving the same task seem to show that pairs are more efficient than individuals (Fig. 51).¹⁶⁷ Why do pairs perform better? A hypothesis may be that several reasons combine. One explanation is that the task affords abstraction—and as pairs speak, language may form a route to finding the more abstract solution strategies. Another explanation is that individuals may tend to get stuck with their first solution, while pairs may bring different perspectives and strategies motivating the intuition that there might be more than one solution strategy to be tried out. A further explanation may be feedback between the two parties, in the shape of one participant watching the other’s gesture and drawing further conclusions; more generally in the shape of collaboration or competition or both (the two should not be seen as mutually exclusive, rather as two feedback aspects which may even enhance each other).

Chapter 11 Schematic Aspects of an Aesthetics of Diagrams What could diagrams possibly have to do with aesthetics or the arts? The prototypical diagram is a stylized graphical model facilitating interrelated information about some subject—hence, as a tendency, pragmatic, no-nonsense, fact-oriented, obvious. Facilitating the retrieval of information—scientific, political, practical, or otherwise—diagrams seem to emphasize direct accessibility over aesthetic depth and elaboration of representation detail. This initial consideration, however, covers certain complications.

Diagrammatic Perception A first thing to note is that ordinary perception has certain diagrammatic qualities. Contrary to a widespread common-sense (and sometimes phenomenological) conception, perception does not simply consist of 100 % determinate, particular sense data—so that all sort of general content or schematic structure should be something derivative, pertaining to secondary, higher order cognitive processing. Rather, the structuring of perceptive contents is part and parcel of the perception process and, in the central example of vision, begins already in the retina. Thus, central features like contour enhancement begins pre-cortically with the interaction between retinal cells, and the basic distinction of where and what in the visual field is provided by the basic structural separation of the dorsal (where) stream and the ventral (what or how) stream of visual processing in the brain. The former continuously updates structural information about immediate environmental space in terms of attention, object borders, accessibility etc.—the latter continuously categorizes objects and events within that space.¹⁶⁸ Each of these have diagrammatical qualities. The former structures space into connected subspaces and thus lays the foundation of the ability to articulate and rationally connect a spatial whole into parts which is so central to the understanding of diagrams. The latter involves the schematic representations of the semantics of categories—the basic visual structure of chairs, tables, birds, clouds, and all the mesoscopic inventory of our surroundings which we categorize most often automatically without explicitly intending it. These processes—and many more—yield the highly structured character of the resulting visual perception experience. It contains many diagrammatic aspects, even if we may not realize it at every glance—accustomed as we are to its quasi-immediate appearance. But those diagrammatic aspects of experience are what allows us to draw immediate https://doi.org/10.1515/9783110793628-013

Externalized Diagrams

197

inferences from it and act in a matter of moments—as well as to draw more complicated, longer-lasting inferences from certain perceptions which merit our more detailed attention. But it is not as if we could “switch off” these ongoing structurings and fall back on the unstructured, fleeting experience of the simple flow of incoming light or sense data.

Further Diagrammatization When making pictures, including diagrams, we may choose to further emphasize such features of perceptual content as have already been highlighted in the perceptual process. This gives pictures and images of all sorts a potential degree of further diagrammatization. Contour enhancement may be further strengthened, e. g., by means of the addition of contour lines. Stylization may simplify and typify the representation of categorized objects so as to make them easier to recognize—or more general in their reference. Discretization may simplify the amount of colors and shapes used to conform to a smaller repertoire of selected such features. Selecting the right moment of an action, from which an optimum of information about the near past and future of the process may be inferred (the Lessing Principle, as it were).¹⁶⁹ Compactifying several different moments within one picture may represent a diagrammatical timeline, facilitating the reconstruction of a longer process beyond the immediate snapshot quality of moment representation. Thus, the amounts of diagrammatic qualities in ordinary perception are typically (not always) only increased in pictural representation. Of course, artistic strategies may take as their aim rather to minimize diagrammatic representation by all sorts of blurring, ambiguization, abstraction (in the painterly rather than the logical sense).

Externalized Diagrams Thus, we arrive at diagrammatic representations proper—typically explicitly articulated graphical structures on screen, blackboard, paper,—realizing that in a certain sense, they form the explicit tip of the iceberg only. Diagrammaticality there is already in perception, it typically increases in pictures and images only to reach full, explicit and often intended expression in charts, maps, matrices, tables, block or pie charts, curves, graphs, and so on. Diagrams in this sense are known since antiquity and reach an early apogee in Euclid. Diagrams in this sense express wholes composed from rationally related parts, where the rational relations are represented by spatial position, sequence, connection, con-

198

Chapter 11: Schematic Aspects of an Aesthetics of Diagrams

Figs. 52 – 53: The first version of the present chapter was originally written for the New York artist Matthew Ritchie’s project “The Temptation of the Diagram” (2017), centered around a 27-foot sheet of the same name of which the present illustration is a part (at the exhibition “Noema” at the El Segundo Museum of Art, California). So, the essay appeared along with prints of the sheet as part of numbered and boxed versions of that particular artwork. Below is a photo of the exhibition space (both illustrations © Matthew Ritchie).

Externalized Diagrams

199

tinuity etc. Diagrams presuppose abstractions in the sense that they represent a few selected properties only of the object they depict—those properties are idealized and made the focus of the diagram. Topographical maps constitute an exemplary case: they depict selected landscape features such as buildings, roads, forests, lakes, elevation, coastlines while other landscape features and variation are abstracted away. Special maps may highlight other features: biodiversity, geology, demography, economy, political status and much more. Such generalization inherent in diagrams implies that most often, a diagram holds for an indefinite number of individual cases: the topographical map, unlike the aerial photograph, does not refer to landscape conditions in one single moment only, but holds for a more extended period, that is, an indefinite number of moments, until landscape changes make it invalid. The object of the diagram is thus more or less general—but generality also characterizes the diagram sign itself. It may be reproduced in a number of replicas without ceasing to be the same diagram. This may be expressed, also in the opposite direction, so to speak: the individual diagram token as printed on a page or emitting light from your computer screen, occurring in the present now, constitutes a window to the more general diagram type which it represents. Diagrams thus make possible the direct contemplation of general subject matters. This quality is a basic reason for their pragmatic ubiquity: they facilitate the easy grasp of a complicated matter of fact in one or a few gazes. But their generality has several sources: one is the graphical formalism in itself—idealized, stylized, simplified as it is. Another is the accompanying (or implicit) symbolic information which indicates the type of diagram and type of object referred to. Take again Harry Beck’s famous 1931 London Underground Map, in its continuously updated versions in use to this day, and arguably one of the world’s most famous diagrams (Chapter 9). For a first user, the text “London Underground” gives the double information that this spaghetti of colored lines should be read as referring to the structure of subterranean city train lines. This indicates how the diagram should be read, in general. Thus, diagrams generalize Kant’s famous definition of a schema: they unite spatiotemporal representation with symbolic understanding of the entity represented. The spatiotemporal layout of the diagram plus the indication of what type of object it represents unite to perform that function. A yet unsolved question with regard to diagrams, as mentioned, pertains to their subtypes: is there a rational taxonomy of diagram types? Charles Peirce proposed, as we heard, a first hypothesis, that they comprise maps, algebras, and graphs. The appearance of algebras in this list may surprise as they are not typically regarded as diagrams in our ordinary parlance. The reason for this lies in his important observation that diagrams may facilitate reasonings.

200

Chapter 11: Schematic Aspects of an Aesthetics of Diagrams

Diagram Inferences To Peirce, diagrams comprise all structures that are fit to facilitate deductive inferences. In the topographical map, e. g., you may trace possible routes from one location to another—thus inferring a piece of information which was only implicitly present in the diagram. The routes thus found are truly there as real possibilities in the landscape, given that the map as a premise is, in itself, a true representation of the landscape (if the map is false, of course, you cannot be sure to draw true conclusions from it). Thus, Peirce’s argument is that diagrams form the proper generalization of the various formalisms of deductive logic. And this is why algebras come under the headline of diagrams: algebraically expressed states-of-affairs may be used to infer other truths—e. g., an arithmetic equation, algebraically expressed, may be solved. Diagrams are ideal models with deductive possibilities. This implies that diagrams, as signs, importantly differ from the pneumaticdispatch model of communication: the idea that the sender has an intended claim, codes it in a message which is, in turn, decoded by the receiver. In diagrams, the manipulation or experimentation with the diagram icon makes possible the retrieval of information from the diagram which was never explicitly put there by the sender. There is no reason to believe that the producers of maps have already calculated e. g., the distance between any two points of interest on the map—or any other particular information which may be deduced from the map. Diagrams, of course, differ enormously as to the extent of implicit knowledge derivable from them. Some, like topographical maps, seem to have an indefinite amount of information which may be inferred from them—others, such as algebraic equations may, in some cases, be yet unsolved so that important knowledge possibly derivable from them has not yet been established. In any case, the fact that diagrams hold implicit information, simple or complex, easy or difficult to derive, is probably what gives them their immediate appearance of depth—something is, to some degree, concealed here, and it may require work or even genius to derive it and make it appear.

Multimodal Diagrams Are all diagrams graphic? Indeed, graphically expressed, 2D visual diagrams form the core of our everyday diagram conception, but for a closer gaze it is not obvious that the rational category of diagrams is thus delimited. If diagrams are all formalisms from which implicit information may be derived, there is no reason why diagrams may not exist in other sense modalities. Particularly spo-

Multimodal Diagrams

201

ken language may represent a large number of 1D diagrams in an auditory, temporal medium which overlap with the 1D visual, spatial medium of linear writing. Tactile diagrams are used by blind people. So, one set of subtypes of diagrams is that of their different sensory representations. Here should also be counted imagined diagrams—whole diagrams up to some threshold of complexity (which is probably highly individually variable) may be imagined and manipulated before the mind’s eye, without the support of externalized diagram tokens. And in many cases, the use of externalized diagrams on paper or screen requires the use of imagination—quick inferences may be drawn from maps by means of imagined manipulations of them rather than real, physical manipulation with hand, ruler, pencil, etc. A basic distinction mentioned is that between pure and applied diagrams. The London Underground map can be seen as a purely topological network structure if we bracket both the general interpretation of it as depicting train lines and its indexical reference to the particular city of London. In that case, it is a purely topological object whose general properties may be investigated. What is found on that pure, general level will be inherited by the virtual applied uses of the structure, for instance, to refer to those subway trains running under London. Thus, all applied diagrams possess a formal spatial structure whose possible transformations may be studied in and of itself, regardless of application. Another important distinction is probably that between continuous and discontinuous diagrams. Topographical maps are continuous in the sense that any full-dimension part of them is also, in itself, a map —which is not the case with algebraical expressions or other diagrams using symbol sequences on a line or in a matrix. A further distinction is dimensionality. Human language, spoken or written, interpreted as diagrams, are in a certain sense 1D, just like many logic or algebraic languages. The most typical diagrams are probably 2D—maps, charts, Cartesian planes, etc.—but there seems to be no a priori reason why diagrams could not have any dimensionality. Particularly, idealized 3D models inherit the easy accessibility with whole-part structure, the derivability of information by (imagined) manipulation and so on, and computer simulations may approach such diagrams by making 2D representations of a 3D object variable with time so as to view that object from different angles. What has been said until now is a set of basic prerequisites to be reflected upon before, by means of hypotheses, some aesthetic possibilities pertaining to diagrams may be discussed.

202

Chapter 11: Schematic Aspects of an Aesthetics of Diagrams

Potential Aesthetic Qualities of Diagrams Initially—depending, of course, on use, materials, context, reference, style, and other expressive variants—a number of potential aesthetic qualities of diagrams, exploitable for artistic purposes, may be listed. Unavoidably, some of the qualities here indicated will have overlaps. Abstractness. Diagrams are abstract in at least two ways. First, they abstract away certain variant or irrelevant aspects or properties of the object they depict. Second, the properties and relations selected are, themselves, subjected to an idealization which may, sometimes, also be called abstraction. “Abstraction” in 20C high modernism often approach diagrammatic qualities. Analyticity. Diagrams not only select certain properties; they also analyze them and their mutual relations. Diagrams do not display object parts, properties, and relations isolated from each other like in a list, rather, they portray them in (some of) their interrelations; that is, the diagram as a whole synthesizes, in turn, the parts first analyzed. Arrows. Far from all diagrams use arrows; however, many do. Arrows may mean rather different things. They may signify some oriented relation between two parts connected by them, be it a temporal, spatial, or semantic relation. They may, e. g., signify a cause-effect relation, they may signify an oriented flow of material or energy, they may signify a possible transport, they may signify an intention, a logical dependence, or an inference. Constructivity. Diagrams are constructs of the intellect. That does not make them constructivist, rather the opposite; diagrams are typically realist with respect to the aspects of some reality which they isolate and highlight. But their construction, simultaneously, hints at the intellect able to isolate those aspects and connect them in the proper manner. Depending upon the degree of simplicity or complexity of the diagram in question, this implicit intellect may be a simple mind or a genius; most often diagrams intimate a mind with some analytic interests and powers. Dots. Again, far from all diagrams use dots, but in those who do, dots typically indicate some entity which is a localized part of a larger structure, be it a person, a place, an institution … In maps, dots may be cities, mountain tops, depth of valleys, stations, location of the treasure buried, in short, any place or part of particular interest—it may be named, it may be categorized by means of a legend giving dots with particular shapes or colors particular meanings, or it may be described directly. Economy. Diagrams are basically economical structures—in the sense that they leave out of consideration an immense amount of information in order to focus on the essential, thus serving economy of thought, or “economy of re-

Potential Aesthetic Qualities of Diagrams

203

search”, as Peirce often said. In many cases, it is easier to make use of a diagram than of a full-detailed description of the same object, because in the diagram, irrelevant structures have already been filtered away, and the important and relevant information immediately leaps to the eye. Essentialism. This word has had, for unknown reasons, a bad press recently, but there is really nothing wrong with searching for the essence of an object which is just equivalent to those properties without which that object would cease to be that kind of object. The economy and abstraction of the diagram often serves this purpose. Of course, like all signs, diagrams may be fallacious or even mendacious, in which case the purported essence is not real. Evil. External diagrams are prototypical examples of Extended Mind. For that reason, they may appear as having their own mentality, intention, potentially at odds with wishes or intentions of their human creators or users. Containing implicit information, they may appear as inscrutable, magic, alien, even evil to interpreters unable to make the relevant experiments to unlock that secret information. Filling-In. The idea is from the philosopher Ingarden: that in many cases, when confronted with ideal, indeterminate signs such as diagrams, the observer is called to fill-in the Unbestimtkeitsstellen—the spots of indeterminacy—with more or less concrete, imagined realizations. This filling-in is undertaken by the observer’s own fantasy, sometimes supported by indications in or accompanying the diagram. Fragility. The structural, skeletonized character of the diagram may, in many cases, give it a fragile expression—a frail composition of thin lines which may seem to be about to fall, collapse, or disintegrate, if we (erroneously) interpret it as a real object. Ideality. Diagrams not only abstract away properties deemed irrelevant, they also (unlike sketches) subject the remaining properties to idealization. This gives the diagram a sort of Platonic, outerworldly quality—as the deep reality behind many related appearances. Imagination. Diagram use requires imagination—the individual diagram sign is not in itself ideal, consisting of physical lines and figures. So, in order to arrive at ideality, imagination must strip away irrelevant features of the diagram sign— for instance, often the color of lines may be insignificant and the user must imagine a line with no particular color. Then, imagination may go on to experiment with the resulting diagram. Indeterminacy. The very same quality as idealization, viewed from another angle, gives the diagram a certain openness. The fact that many properties of the object referred to are left indeterminate makes the diagram fit many possible concrete, particular cases and thus, in itself, gives it a quality of partial empti-

204

Chapter 11: Schematic Aspects of an Aesthetics of Diagrams

ness. Such emptiness may be taken in different directions such as desolation on the one hand or space of possibilities on the other. Intersubjectivity. The diagram as an outer representation can be addressed, developed, and used by a multiplicity of persons at one and the same time, as well as sequentially over hours, days, centuries. This takes it far away from the idea of representations being only in the head, and gives it an optimistic air of collaboration, dialogue, and even possible progress. Simultaneously, when seeing a diagram, unlike natural objects, you know somebody has seen it before you do, and unlike many other cultural objects, you know it is indeterminate, unfinished and that somebody, maybe you, could improve upon it. Line. Probably the most widespread semantic tool of diagrams is that of lines. The signification of lines is really an issue of polysemy. Lines may signify all sorts of connection between their end points, they may signify contours of objects, they may signify opposition between the areas on each side of them, they may be barriers preventing movement across them, they may delimit an area of interest from one of irrelevance, and much more. Manipulability. To Peirce, real or imagined manipulation is the key to retrieving implicit information from diagrams. The experimental manipulation with the diagram following certain rules, explicit or not, gives the user the possibility of inferring new claims from it which will be true, given that the information put into the diagram is true. This gives the diagram the character of an ideal machine. Its possession of implicit information also may give it a quasi-mystical quality of the looming presence of something not explicitly there. Mereology. The diagram is a whole of connected parts—claiming to mirror the structure of a real or possible object. So, any diagram involves a double, or multiply layered, gaze, one, distant, giving the outline of the whole, the other, closer, giving the internal organization connecting parts of that whole, sometimes on several different, nested levels. Objectivity. In most cases, diagrams are used to claim something about the structure of some object, event, or plan. That gives the diagram a cool, detached, objective, no-nonsense quality. Overview. The mereological structure of the diagram implies that it may give the observer the overview of something otherwise difficult to synthesize. The object may be seen from impossible viewpoints, it may be dissected, analyzed, cut open, or laid out in counterintuitive ways in order to give that overview. Oftentimes, the overview may synthesize different temporal phases into one, ideal glimpse of a whole sequential structure otherwise bound to stepwise experience. Possibility. A well-executed diagram represents a possibility. Many impossible objects which it is easy to address in linguistic representations cannot be represented in a diagram: “the round square”. This is not to say that craftily con-

Potential Aesthetic Qualities of Diagrams

205

structed diagrams may not take advantage of the peculiarities of human perception to represent impossible objects; cf. Escher’s stairs. But they remain tied to such ingenious peculiarities and cannot, like compositional language, represent any impossible object you might wish. Planning. Diagrams are often used as planning or construction tools due to their overview capabilities. That gives them, in many cases, a prospective quality of possibilities not yet realized, manipulation, or realization possibilities to come. Its use in planning, of course, may also carry less positive associations of compulsion, constraint, even exploitation or totalitarian politics. Rationality. The analytical and inferential quality of diagrams, of course, give them an acute air of rationality. To Peirce, diagrams are simply tools with which to make deductions—the core of logic. Regularity. The ideal quality of diagrams makes them, in a sense, rules for many individual realizations. Simultaneously, the manipulation of them relies upon rules explicitly or implicitly given. This gives them a strong quality of regularity which, importantly, does not conflict with their openness. This is due to the fact that their regularity is not that of an algorithm to be followed blindly, rather it is like the rules of a game, facilitating an indefinite number of games played. Remoteness. The overview quality of diagrams also gives them, conversely, a certain remote quality. They conceive of their object as if from afar, placing the observer (falsely?) at safe distance. Schematicity. This is almost another word for diagrammaticity—however, with a stronger emphasis on their selective, skeleton-like character. Scientificity. Diagrams have, of course, been used by most sciences, and often a scientific paper is built around one or a few central diagrams able to synthesize all of the conceptual preconditions and empirical findings into one irreducible whole the understanding of which often amounts to the understanding of the conclusion of the paper as a whole. Diagrams thus very often come with a strong association of science, discovery, experiment—but also, then, the possible dullness and repetitive quality of secondary run-of-the-mill science. Secrecy. The implicit information of the diagram may give it the character of a chest, black box containing some hidden treasure only accessible to one who knows the key to unlock it—or some of it, as the totality of its information derivable may be indefinite. Sages or witches are often depicted brooding over magic diagrams. Sheet. The plain white piece of paper or blank screen on which the diagram appears require special attention. Peirce, in his “Existential Graphs” formalizing elementary logic, makes of the Sheet a Universe of Discourse, so to speak an undeveloped photograph of all the implicit knowledge that the users of the dia-

206

Chapter 11: Schematic Aspects of an Aesthetics of Diagrams

gram tacitly agree upon. Sometimes the sheet directly depicts the object—thus the surface of the Earth in topographical diagrams. Sometimes it displays an ordered field of possibilities, like in an ordinary Cartesian plane. The empty page, in short, may mean rather different things; in any case its blank quality gives the diagram a certain emptiness or, conversely, richness of possibilities. Sketchiness. Sketches often have spontaneous diagrammatical qualities, so to speak on the way to full diagrams. Conversely, diagrams are typically sketched before they reach ideal completion, and in any case, the individual diagram token sign invariably keeps certain irrelevant qualities giving it a sketchy quality. Slenderness. Oftentimes, the skeleton-like quality of the diagram gives it elegance, simplicity, delicacy—or emaciation. Technicity. The affinity to planning and science points the diagram in the direction of technology. It is, in itself a technology of knowledge, thought economy, of remembering, of analyzing, synthesizing, inferring, but it may also associate to other technologies of which it may serve as blueprint or construction device. Unfinishedness. Openness and sketchiness may take the diagram in the direction of unfinishedness. More properties and relations of the object than actually selected could have been there—maybe, in some cases, they are lacking. Complicated diagrams may be works in progress over very long periods—like for many centuries the geographical task of mapping the Earth. Virtuality. The indefinite amount of implicit information in the diagram gives it a virtual, hypothetical quality, just like its ideality makes it an object different from ordinary, non-ideal, and fully determinate objects. In a certain sense, all of these qualities are not isolated but different aspects of the same diagram essence. Different designers, scientists, and artists may select or emphasize some of those aspects over others. These qualities, then, may go into many different aesthetic strategies. Diagrams may be used as objets trouvées, exploiting their well-known or strange qualities as they appear. Diagrams may be cut up, suspending parts of full-blown diagrams to investigate effects of dysfunctionalized diagrams. Diagrams may be challenged by reconnecting diagrammatic structure with that substance from which they were abstracted in the first place—or by combining incompatible diagrams on the sheet. More generally, diagrams may be subject to all of the enormous toolbox of subversive artistic strategies developed over 150 years of modernism. Such strategies, however, will exploit or distort some of the possibilities sketched in this overview.

Potential Aesthetic Qualities of Diagrams

207

Fig. 54: From Matthew Ritchie’s 2018 interactive installation “The Demon in the Diagram” (Moody Center for the Arts at Rice University, Houston, Texas), © Matthew Ritchie.

III Semiotics and Metaphysics

Chapter 12 Peirce as a Truthmaker Realist Propositional Realism as Backbone of Peircean Metaphysics This chapter argues that there is a narrow connection between the different aspects of Peirce’s philosophical realism and his doctrine of propositions, forming a strong, early version of what is now called “truthmaker” realism. Distinguishing predicate realism, subject realism, and representation realism, it is argued that these three realisms connect to each their aspect of true propositions. Finally, the argument is made that Peirce’s metaphysics, over his career, grows by means of still new metaphysical deductions from results reached in semiotics and logic, so that propositional realism, simultaneously, develops from defining the real as that which makes true propositions true to all that which is involved in making true propositions true. Much has been written about Peirce’s realism, most lately Robert Lane’s strong volume Peirce on Realism and Idealism (2018).¹⁷⁰ It is well-known that Peirce was a realist in at least two different senses of the word—1) realism understood as the doctrine that the real is that which is independent of what any particular person or group may think about it and 2) realism in the “medieval” sense that universals or general predicates may refer to general properties, structures, patterns and laws of reality. Independence realism and universals realism, as it were. Most of what has been written, however, fails to go into detail with the narrow interdependence between Peirce’s realism and his philosophy of propositions—which is the subject of this brief chapter. Peirce was an early and strong proponent of what is nowadays discussed under the headline of “truthmaker realism”¹⁷¹—real is that which makes a true proposition true. I am not certain much new is really said here—the attempt is rather to present some well-known aspects of Peirce’s realism in a new, synthesizing optics.

The Basic Kantian Argument It is well known that Peirce as a teenager in the 1850s was intoxicated with Kant and that the development of his early philosophy from around 1860 was hugely inspired by the Kritik der reinen Vernunft. Kant based his critical philosophy on the existence of science which was taken as the explanandum to be rendered understandable by investigating its Möglichkeitsbedingungen, its conditions of poshttps://doi.org/10.1515/9783110793628-014

212

Chapter 12: Peirce as a Truthmaker Realist

sibility. An important step in this endeavor was Kant’s establishment of a transcendental argument for the validity of the twelve categories which Kant took to be the basics of all understanding—a step involving the famous “metaphysical deduction” of those categories based on the critical principle that metaphysical categories can be derived from logical concepts only. While the transcendental argument should grant the validity of the categories by showing they were a priori conditions of possibility of experience, the metaphysical deduction should, in the first place, establish their existence as metaphysical conceptions derived from logic. Peirce took over that idea to form a veritable backbone of argumentation during the whole of his career. Almost 40 years later, in the 1902 Minute Logic, he sums up: As to Metaphysics, if the theory of logic which is to be developed in this book has any truth, the position of the two greatest of all metaphysicians, Aristotle and Kant, will herein be supported by satisfactory proof, that that science can only rest directly upon the theory of logic. Indeed, it may be said that there has hardly been a metaphysician of the first rank who has not made logic his stepping-stone to metaphysics (Minute Logic, CP 2.121).¹⁷²

Logic and semiotic results were, for that reason, immediately charged with the possibility of developing new metaphysical conceptions. Famous is Peirce’s early development of his three categories in the 1867 “New List” paper, which developed from an attempt to cleanse Kant’s category table from unclarities. The nature of this derivation has been the subject of some discussion (see Bellucci 2017, Chapter 1), and much points to the fact that Peirce’s method differs from Kant who took as his point of departure an unproblematized logical tradition. Peirce, admirer of Kant the philosopher but detractor of Kant the logician, admitted no such thing but instead took his point of departure in what he assumed to be the central synthesis of knowledge: the unity of experience in an argument built from true propositions. A proposition is the form which brings unity to the mass of unordered impressions—and it does so in three ways, a unified representation which charts a relation with some quality. That was the “New List” version of the three categories. Much later, after 1900, those categories were elevated to form the center of Peircean phenomenology (cf. the following chapter). In Kant’s point of departure, the existence of objective science, Peirce zoomed in on the undoubtable existence of true propositions. Here, he paralleled the neoKantian movement developing in Germany at the same time, which had an early culmination in Hermann Cohen’s dictum: “It still seems so needed today, that content of the transcendental method: experience is the given; and it is to discover the conditions on which its possibility is founded”.¹⁷³ Experience as a fact is the given, whose conditions of possibility philosophy must uncover in order to account for how objective knowledge of reality is possible. Later,

Predicate Realism

213

Cohen famously summed up this idea as beginning from “the fact of science”.¹⁷⁴ To Peirce the neo-Kantian, this fact consisted in the undoubted existence of true propositions:”.… a realist is simply one who knows no more recondite reality than that which is represented in a true representation” (“Some Consequences of Four Incapacities”, 1868, EP I, 53; CP 5.312).¹⁷⁵

Predicate Realism The “New List” gave Peirce’s category table of three: Quality, Relation, Representation. Each of the three gives rise to an aspect of Peirce’s realism. Probably the most controversial of these is the medieval or “Scotist” realism, with reference to John Duns Scotus whom Peirce read intensively in the 1860s.¹⁷⁶ Peirce’s just quoted 1868 argument for reality as represented in a true representation emphasizes this realism: … it follows that since no cognition of ours is absolutely determinate, generals must have a real existence. Now this scholastic realism is usually set down as a belief in metaphysical fictions. (…) Since, therefore, the word “man” is true of something, that which “man” means is real. The nominalist must admit that man is truly applicable to something; but he believes that there is beneath this a thing in itself, an incognizable reality. His is the metaphysical figment (“Some Consequences of Four Incapacities”, 1868, EP I, 53; CP 5.312).

Peirce’s argument claims that the existence of true propositions involving general predicates implies that those predicates refer to structures of reality. Contrary to widespread assumptions, it is not the realist who invents unnecessary and superfluous metaphysical entities, but it is his opponent the nominalist. The nominalist opposition—Peirce goes on to refer to Scotus’ later opponent William of Ockham—is really the position, which is forced to invent metaphysical fantasies, namely a recondite reality which can never be reached by representations. Peirce would admit no such thing. By this argument, Peirce simultaneously attacks Kant’s supposition of the existence of an unreachable Ding an sich. Peirce should go on to articulate his Scotist realism in his well-known 1871 review of Fraser’s publication of Berkeley (EP I, 83 – 105; CP 8.7– 38), and to sharpen it, e. g., with his introduction of “real possibilities” in 1897 which made him a modal realist as to generals. The propositional roots of his realism as to universals, however, are already clear in the 1860s.

214

Chapter 12: Peirce as a Truthmaker Realist

Subject Realism Peirce never left the age-old Aristotelian doctrine that propositions consist of two parts, predicates and subjects, although he radically further developed and generalized those notions. With his introduction of the logic of relatives around 1870 and his formalization of first order predicate logic in 1883 – 1885, he considerably expanded the notions of predicate and subject to include relational predicates able to attach to any number of subjects. The role of those subjects is not to contribute anything to the description of the object of the proposition, but merely to indicate or identify those objects as assumedly existent entities separate from the proposition. Here, Peirce stuck to another Kantian idea, that existence is no predicate. The role of the subjects of a proposition is to claim existence, the role of predicates to describe that claimed existence, and propositions may even be defined as signs which separately indicate their objects and so claim their existence. The development of the concept of the index as the type of sign responsible for reference to independently existent objects really got underway in the 1880s after the 1885 “Algebra of Logic” formalized propositions in two parts: a predicative part involving a predicate satiated with bound variables and an initial subject part quantifying those variables. But already in the 1867 “New List”, this existence-claiming role of subject indices was developed within the frame of a likeness-sign-symbol distinction (later, icon-index-symbol), in which the second category comprise those signs “.… whose relation to their objects consists in a correspondence in fact, and these may be termed indices or signs” (EP I, 7; CP 1.558).¹⁷⁷ Thus, subjects and predicate of the proposition take care, as it were, each of their aspect of realism. Subject signs claim to refer to objects independent of their representation in propositions and in case of true propositions, they actually do so refer. Predicate signs claim to describe those same objects, and in true propositions, they actually do so describe. Conversely, when both parts of the proposition successfully satisfy these functions, the proposition is true. Thus, subject signs incarnate independence realism, predicate signs incarnate realism as to universals.¹⁷⁸

Representation Realism The realisms of the two parts of the proposition come together in what could be termed Peirce’s realism of facts or of states of things. Peirce very often refers to “states of things” in some Universe of Discourse as that which the representation of a proposition, as a whole, claims to represent. In his mature period after the turn of the century, this relation is made the object of explicit scrutiny: “A state

Representation Realism

215

of things is an abstract constituent part of reality, of such a nature that a proposition is needed to represent it” (“The Basis of Pragmaticism”, 1906, EP II, 378; CP 5.549). The whole of a propositional representation has, as its correlate in reality, a state of things, also sometimes called a fact. This takes place simultaneously, of course, with the Austrian development of the notion of “Sachverhalte”, state-of-affairs, initially coined by Hermann Lotze and Carl Stumpf, later famously popularized by Husserl and Wittgenstein.¹⁷⁹ In Peirce, the two realisms of predicate and subject come together and fuse in a realism of states-ofthings: they are independent of any particular representation, and they incarnate general properties which are real. Many of Peirce’s formulations of independence realism simultaneously refer to representation realism. But states-of-things in themselves also enjoy a certain independence. The relative independence of states-of-things in reality can be seen from the fact that their depiction in propositions forms independent “medads”, that is, 0-valent expressions. In Peirce’s well-known doctrine of valency of expressions, 1-, 2-, and 3-valent predicates, monadic, dyadic, and triadic, are irreducible and may combine to form higherorder predicates with any number of slots to be potentially satiated by subject signs. But when such a predicate is fully satiated by subject signs in all slots, the resulting proposition forms a medad with zero valency, and Peirce sometimes speak of propositions as “complete” signs. This allows for a transcendental deduction of conditions of possibility with an important lesson on the elementary structure of reality: Reality must be structured in such a way so that it is possible for true propositions to slice it into the appropriate, corresponding statesof-things which may, in many cases, be considered in isolation in order to judge the truth value of the relevant propositions. This loose connectedness of reality is made possible by its composition from three types of being, different both from a holist world with stronger connectedness and a world of independent elements with no connectedness. Notably, states-of-things differ from simple parts or subsets of reality. Relations of cause and effect hold between states-of-things or facts, not simply between things. In a certain sense, propositions are what correspond to Wittgenstein’s famous “logical atoms” in Peirce’s theory. But unlike Wittgenstein who supposed the existence of logical atoms but was unable to point out one single example, in Peirce examples abound, for they comprise all true propositions: “A fact is so highly a prescissively abstract state of things, that it can be wholly represented in a simple proposition, and the term “simple”, here, has no absolute meaning, but is merely a comparative expression” (“The Basis of Pragmaticism”, 1906, EP II, 378; CP 5.549). In Wittgenstein, logical atoms were supposed to be simple in an absolute, elementary, and compositional sense of the word which was why they were difficult to identify. That is explicitly not the case in Peirce where “simple” is merely comparative, that is, in com-

216

Chapter 12: Peirce as a Truthmaker Realist

parison to complexes of facts which require several propositions and arguments for their description. Peircean facts, moreover, are ontologically neutral: they can be abstracted by true propositions on all levels of reality from mathematics to the special sciences, and they are so to speak fractal: any state-of-things charted by one proposition may be potentially analyzed into further parts and aspects not yet acknowledged by the given proposition, in order to be investigated in further propositions.¹⁸⁰ An open issue, however, remains whether all states-of-things of reality may be charted by true propositions or whether there may be inaccessible lacunae of reality, of facts.

Realism of Indefinite Inquiry Large parts of reality are not yet covered by science. This simple fact becomes a problem for Peirce’s definition of reality as the truthmaker of true propositions. It would be a strange consequence to claim that yet uncharted parts of what is are not real because there are not yet any true propositions to represent them. This gives rise to Peirce’s well-known definition, in the 1878 pragmatism papers, of the real as that which is the object of the total set of true propositions to which science will converge in the limit—and his corresponding idea of science as a collective, indefinite endeavor by investigators across generations. There is no guarantee, however, that all parts of what is will, in fact, eventually yield to scientific investigation. Robert Lane (2018, Chapter 7) charts how Peirce vacillates between different ways of solving this conundrum—by changing the realism of final investigation from the indicative to the subjunctive so that the real is not what will, but what would be the result of investigation carried sufficiently far—by claiming propositions addressing e. g., past events whose traces have been lost are meaningless—by claiming that the lack of true propositions in a given field implies there must be corresponding lacunae in reality itself (Lane: “deficit indeterminacy”)—by developing a three-value logic with a borderline limit truth value category L between true and false so that undetermined propositions “in between” refer to undistinguishable, merely possible parts of reality with a sort of degenerate mode of being. Be that as it may, Peirce’s struggle with this problem testifies to his unwavering insistence that the real is that what is, will, would, or could be represented by true propositions.

Extrapolating from Propositions

217

Extrapolating from Propositions: Deducing Metaphysical Realism from Semiotic Investigation While this challenge that such “hidden secrets” pose for propositional realism remained unsolved, that did not prevent Peirce from vastly extrapolating propositional realism. In 1907, Peirce returned to judge his early efforts of the “New List”: The first question, and it was a question of supreme importance requiring not only utter abandonment of all bias, but also a most cautious yet vigorously active research, was whether or not the fundamental categories of thought really have that sort of dependence upon formal logic that Kant asserted. I became thoroughly convinced that such a relation really did and must exist. After a series of inquiries, I came to see that Kant ought not to have confined himself to divisions of propositions, or “judgments”, as the Germans confuse the subject by calling them, but ought to have taken account of all elementary and significant differences of form among signs of all sorts, and that, above all, he ought not to have left out of account fundamental forms of reasonings (Notes on “The New List”, 1907, CP 1.561).

The implication of the last period of the quote generalizes propositional realism from its core in logic proper to cover also the semiotics of the “grammatica speculativa” as prerequisites to logic proper on the one hand, and to the investigation structures of the “speculative rhetoric” or “methodeutics” on the other hand. That is, logic in its broad sense, comprising semiotics, logic proper, and scientific methodology, every part of it may now be taken as point of departure for the metaphysical deduction from logical categories to metaphysical categories. We already saw how the famous triplet icon-index-symbol was connected to the metaphysical deduction of the “New List”, so that the existence of such sign types was connected to the existence of objective resemblance relations, of objective reactions in the here-and-now, and of general, lawlike behavior, respectively. But even more ambitious are the possible metaphysical results to be harvested from extrapolating propositional realism to the broader field of investigation. The ineradicability of measurement uncertainty in empirical research, which Peirce knew well from his gravimetric work as a practicing physicist, could give rise to the metaphysical idea of the real existence of “objective chance” or “tychism” around 1890. Similarly, the existence of a continuity of possible occasions for using a general term in true propositions gave rise to the idea that such continuity exists as part of reality itself (“synechism”). The structure of the chain of arguments in investigation could yield metaphysical results in the claim that biological evolution in its move from one species to the next constitutes a sort of inference, reaching a conclusion based on the premises of earlier

218

Chapter 12: Peirce as a Truthmaker Realist

species and environments. During that process, it may even appear that nature itself performs processes of abduction, deduction, and induction. Yes, the whole evolution of the universe may be seen as one large argument (Harvard Lectures on Pragmatism, 1903, EP II, 193; CP 5.119). Correspondingly, it seems to be the character of indefinite development from less to more knowledge in the neverending process of investigation which forms the logical mould of the metaphysical idea of the evolution of the universe from chaos and chance to more and more well-ordered, lawlike and varied behavior in Peirce’s cosmology from the 1880s “Design and Chance” and “Guess at the Riddle” to the 1890s Monist papers and beyond.¹⁸¹ The “Guess at the Riddle” is simply structured over the supposed inheritance of the metaphysical structure of three over the descending chain of philosophy and special sciences, from the Kantian fountainhead of reasoning to metaphysics, and psychology, over physiology, biology, physics, to sociology and theology—going metaphysically far further than any orthodox Kantian, to be sure. Some of such deductions surely have a more experimental, abductive ring to them, and not all results of them were kept in the course of Peirce’s development. But they all share the character that Peirce so to speak takes the step from defining the real as that which makes true propositions true to the broader claim that real is all that which is involved in making true propositions true. In short, through this expansion of logic to cover all aspects, details, and procedures of the process of investigation, Peircean metaphysics would, in turn, reach many of its most adventurous claims of cosmology (cf. Chapter 19). This is not the place to investigate the validity of such claims, merely to resume a handful of them in order to point to the growing breadth of the results of this constant motor in Peirce’s development. Every new result in semiotics, logic, and epistemology, expanding from the 1860s core of propositional realism, immediately would raise the possibility of new metaphysical deductions expanding the ontological commitments of Peircean metaphysics. Doing so, he went farther than most other “truthmaker” realists.

Chapter 13 Phenomenology and Logic in Peirce Phenomenology among the Sciences It is a central idea in the phenomenological tradition that logic is not primitive but must be founded upon phenomenology. In Husserl, this idea is already present in the Logische Unterschungen (1900 – 1901; “Logical Investigations”),¹⁸² and later, he famously consecrated a whole volume to investigating this dependence —Erfahrung und Urteil (1939; “Experience and Judgment”). The mature Peirce, in the years after 1900, also held the idea that logic is dependent upon phenomenology. This comes out explicitly in his classification of the sciences of that period —e. g., in the Carnegie application 1902—where the top part of the classification appears as follows (Fig. 55): 1) Mathematics ) Philosophy a) Phenomenology b) Normative Sciences i) Aesthetics ii) Ethics iii) Logic I) Speculative Grammar or Semiotics II) Critic or Logic Proper III) Speculative Rhetoric or Methodeutic c) Metaphysics Fig. 55: The top tiers of Peirce’s classification of the sciences c. 1902.

After these disciplines follow all of the special sciences, divided into physical and psychical sciences.¹⁸³ The general principles of classification are taken from Comte: higher sciences provide principles for the lower ones while lower ones depend upon the higher ones. Thus, Phenomenology is taken to provide principles for Logic, in all its three subfields, Semiotics, Critic (or Logic in the narrow sense), and Methodeutic (roughly, Scientific Method). So far, the mature Peirce is on a par with nascent European phenomenology in taking logic to be dependent upon the charting of elementary structures of phenomena. This immediate agreement, however, covers some important differences with their roots in the development of Peirce’s doctrine which is the subject of this chapter. First, Peircean phenomenology differs considerably from https://doi.org/10.1515/9783110793628-015

220

Chapter 13: Phenomenology and Logic in Peirce

Husserlian phenomenology. It seems probable that Peirce was inspired to the terminological choice of “phenomenology” from Husserl. When speaking about phenomenology, Peirce several times explicitly refers to Hegel’s Phenomenology of the Spirit for the reference, probably because of his “ethics of terminology” advising the giving of priority to whom made the earliest use of a given term; his doctrine of what may appear to any mind regardless of reality, may have some similarity to Hegel’s idea of the emergence of the spirit through history, but certainly much more to Husserl’s notion. Furthermore, Peirce’s use of the term appears only after 1900, and we know that Peirce quickly got hold of a copy of the 1900 – 1901 Logical Investigations. A bit later, c. 1904 – 1905, however, he substituted the notion of “phaneroscopy” (or “phenoscopy”, or even “phanerochemy”) for “phenomenology”.¹⁸⁴ The methodology indicated by Peirce for his phenomenology is not unrelated to his European counterparts, invoking a parallel to Husserl’s famous epokhé principle of bracketing any supposition of existence of the phenomena investigated: It will be plain from what has been said that phaneroscopy has nothing at all to do with the question of how far the phanerons it studies correspond to any realities. It religiously abstains from all speculation as to any relations between its categories and physiological facts, cerebral or other. It does not undertake, but sedulously avoids, hypothetical explanations of any sort. It simply scrutinizes the direct appearances, and endeavors to combine minute accuracy with the broadest possible generalization (“Phaneroscopy”, 1905, CP 1.287).

The aim of this study, then, is to chart the distinct, general forms of all possible experiences—as Peirce says when introducing the idea of Phenomenology in 1902: … Phenomenology, or the Doctrine of Categories, whose business it is to unravel the tangled skein [of] all that in any sense appears and wind it into distinct forms; or in other words, to make the ultimate analysis of all experiences the first task to which philosophy has to apply itself. It is a most difficult, perhaps the most difficult, of its tasks, demanding very peculiar powers of thought, the ability to seize clouds, vast and intangible, to set them in orderly array, to put them through their exercises (Minute Logic, 1902, CP 1.280).

The standard method often presented by Peirce is that of the meticulous scrutinizing of what is common to all direct appearances—the idea being that what seems cannot be subject to doubt.¹⁸⁵ Simultaneously, given the classification of the sciences, the only external aid expected is that of mathematics, with which it shares the lack of postulating any positive reality at all: “… phenomenology (…) must, if it is to be properly grounded, be made to depend upon the

The Road from Logic to Metaphysics

221

Conditional or Hypothetical Science of Pure Mathematics …” (Harvard Lectures on Pragmatism, 1903, EP II, 144; CP 5.40). This standard position, however, is challenged by certain irregularities, so to speak. It is well known what Peirce then found as the result of these investigations— indicated here by the identification of phenomenology with the “Doctrine of Categories”. It is indeed the three categories, Firstness, Secondness, and Thirdness, which make up the bulk, if not the totality, of his Phenomenology. And it is equally well known that they were, originally, the result of his youthful efforts already almost forty years earlier, culminating in “On a New List of Categories” (1867). So, this double status of the three categories poses a riddle: the results of Peirce’s Phenomenology were there long before the discipline of Phenomenology itself. Or, rather, did Peirce for many years, up until the turn of the century, pursue Phenomenology without realizing it? To some degree indeed he did—and this comes out of the struggle with another German inspiration —that of Kant; cf. the previous chapter.

The Road from Logic to Metaphysics What Peirce found in the compact “New List” paper took its point of departure in a central Kantian idea from the first Critique—namely that the function of concepts is to synthesize perceptions. The very first statement of the paper claims, speaking Kantese, “… that the function of conceptions is to reduce the manifold of sensuous impressions to unity and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it” (EP I, 1; CP 1.545). Peirce’s analysis then investigates the steps of this reduction process. It takes its beginning in the yet uncharted material of the world indicated by attention—and works towards its end in the synthetic claim made by a true proposition. In short, a trajectory from blind Substance to articulated Being, as it were. Through this process, Substance is predicated, and Being, signified by the final proposition involving both Subject and Predicate, is expressed in the propositional claim connecting the two. Thus, Substance in itself, as the starting point, allows for no predicates but remains a mere undifferentiated IT, while Being, as the end point, has no substance but is a mere signification. From matter to form, as it were. Here, Peirce’s later philosophy of the proposition—or “Dicisign”—takes its beginnings: propositions unite subjects—the indexical pointing out of objects—with predicates—the iconical description of the relational properties of those objects. This distinction of Substance and Being is a version of a Kantian claim always kept in high regard by Peirce: existence is no predicate, no amount of description may ever exhaust

222

Chapter 13: Phenomenology and Logic in Peirce

or determine any existing individual. What is descriptively found in the object is taken out of it by means of ensuing abstraction, and the result is the “metaphysical parts” of the object highlighted by the predication of the resulting proposition: “Before any comparison or discrimination can be made between what is present, what is present must have been recognized as such, as it, and subsequently the metaphysical parts which are recognized by abstraction are attributed to this it, but the it cannot itself be made a predicate” (EP I, 2; CP 1.547). These metaphysical parts, now, are abstracted in three steps (EP I, 6; CP 1.555) where the higher may be abstracted from the lower, but not vice versa (Fig. 56): Being Quality (reference to a ground) Relation (reference to a correlate) Representation (reference to an interpretant) Substance Fig. 56: Metaphysical parts of the object, “New List”, 1867.

Peirce works his way backwards from Being, eventually expressed in a proposition, towards its preconditions, giving him, in turn, the three possible types of accidents which the proposition may ascribe to the substance—and finding on his way the early version of the three categories. Peirce’s table of categories thus originally had five categories all in all—it is well-known how the three accidents were soon all that was left, Substance and Being being but everchanging beginning and end limit points of the ongoing predication process of knowing. Almost forty years later, now, these three categories were taken to form the core of Phenomenology. But in their origin, they were taken to be the metaphysically indispensable aspects of a true proposition describing some aspect of Being. Here, a bundle of important ideas come together which forms a central axis through Peirce’s development: the analysis of propositions; realism; the distinction between indicative existence and predicative description; the relation between logic and metaphysics. One central upshot is that our ontological commitments—to use Quine’s term—are given by the preconditions for a true proposition to be true. What is real is what we need to presuppose to exist in order to account for the possible truth of propositions. This is made explicit already the next year, in connection with fallibilism, in “Some Consequences of Four Incapacities” (1868, EP I, 52; CP 5.311– 312; cf. Chapter 12):

The Road from Logic to Metaphysics

223

Now, a proposition whose falsity can never be discovered, and the error of which therefore is absolutely incognizable, contains, upon our principle, absolutely no error. Consequently, that which is thought in these cognitions is the real, as it really is. There is nothing, then, to prevent our knowing outward things as they really are, and it is most likely that we do thus know them in numberless cases, although we can never be absolutely certain of doing so in any special case. But it follows that since no cognition of ours is absolutely determinate, generals must have a real existence. Now this scholastic realism is usually set down as a belief in metaphysical fictions. But, in fact, a realist is simply one who knows no more recondite reality than that which is represented in a true representation.

And that which is represented in a true proposition implies the reality of all three universal classes of accidents—qualities, relations, representations—representable in predicates with valencies 1, 2 and 3, respectively, in Peirce’s logic of relatives of 1870, finally articulated in the “Algebra of Logic” of 1883 – 1885. Introspection counts as one of the paper’s four incapacities—barring us from arguing from intuitions based on our own psychological experiences. Instead, the logical structure of intersubjectively accepted truth claims is taken as the non-introspective starting point. That which any true proposition asserts is real, in the sense of being as it is regardless of what you or I may think about it. Let this proposition be a general conditional proposition as to the future, and it is a real general such as is calculated really to influence human conduct; and such the pragmaticist holds to be the rational purport of every concept (“What pragmatism is”, 1905, EP II, 343; CP 5.432).

Forty years later, thus, this doctrine prevails: true propositions as reality guidelines not only form the access to basic categories of reality, but also to the core of pragmatism: true general conditionals are what form our habits, more or less accessible to consciousness, because their condition of possibility is the existence of stable tendencies in reality (cf. Chapter 2; 18). Thus, metaphysically very ambitious conclusions are taken to follow from the study of logic—as Peirce never ceases to emphasize: “The list of categories (…) is a table of conceptions drawn from the logical analysis of thought and regarded as applicable to being” (“The List of Categories: A Second Essay”, 1894, CP 1.300). Again, in 1898, commenting upon the “New List” of 1867, he recalls how he had been running wild trying to extend or revise Kant’s category table from a lot of different sources: “I finally concluded the only way was to attack it as Kant had done from the side of formal logic” (“Comments on ’On a New List of Categories’”, 1898, CP 1.563). Even long after Phenomenology has assumed its dignified place in Peirce’s hierarchy of the sciences, this fundamental principle connecting logic and metaphysics is celebrated:

224

Chapter 13: Phenomenology and Logic in Peirce

In my studies of Kant’s great Critic, which I almost knew by heart, I was very much struck by the fact that, although, according to his own account of the matter, his whole philosophy rests upon his “functions of judgment,” or logical divisions of propositions, and upon the relation of his “categories” to them, yet his examination of them is most hasty, superficial, trivial, and even trifling […] I was thus stimulated to independent inquiry into the logical support of the fundamental concepts called categories (“Pragmatism”, 1907, EP II, 424; CP 1.560).

The basis for the derivation, not only of the categories, but more generally, of any investigation of metaphysics, thus comes from a vast generalization of the Kantian principle that metaphysics is possible only on the basis of logical structure: Of what use does this new logical doctrine promise to be? […] In the next place, if Kant has shown that metaphysical conceptions spring from formal logic, this great generalisation upon formal logic must lead to a new apprehension of the metaphysical conceptions which shall render them more adequate to the needs of science. In short, “exact” logic will prove a stepping-stone to “exact” metaphysics. In the next place, it must immensely widen our logical notions (“The Logic of Relatives”, 1897, CP 3.454).

Before we return to Peircean phenomenology, let us take an overview over Peircean results reached by means of this central Kantian trajectory from formal logic to metaphysics. Again, looking back from the vantage point of his mature system, Peirce gives the following survey: The first question, and it was a question of supreme importance requiring not only utter abandonment of all bias, but also a most cautious yet vigorously active research, was whether or not the fundamental categories of thought really have that sort of dependence upon formal logic that Kant asserted. I became thoroughly convinced that such a relation really did and must exist. After a series of inquiries, I came to see that Kant ought not to have confined himself to divisions of propositions, or “judgments,” as the Germans confuse the subject by calling them, but ought to have taken account of all elementary and significant differences of form among signs of all sorts, and that, above all, he ought not to have left out of account fundamental forms of reasonings. At last, after the hardest two years’ mental work that I have ever done in my life, I found myself with but a single assured result of any positive importance. This was that there are but three elementary forms of predication or signification, which as I originally named them (but with bracketed additions now made to render the terms more intelligible) were qualities (of feeling), (dyadic) relations, and (predications of) representations (“Pragmatism”, 1907, EP II, 424; CP 1.561).

Here, the central results of the “New List” are recapitulated along with some implications only briefly outlined back then but developed in far more detail after the turn of the century. Logic, from its core of propositions, is extended ’downwards’, to “all elementary and significant differences of form”, as well as ’upwards’, to “fundamental forms of reasonings”, in short, to the entirety of Peirce’s

The Road from Logic to Metaphysics

225

updated version of the mediaeval grammar-logic-rhetoric triad. The central part of logic devoted to arguments and truth preservation, is here called “critic”; but in addition to this comes a semiotic doctrine of the elements of logic which is scholastically called “speculative grammar”—and to the other side the doctrine of proposing, developing, and testing the truth of propositions, “methodeutics” or “speculative rhetoric”, which we would nowadays call pragmatics, the scientific parts of which would be heuristics or philosophy of science. “Speculative grammar” gives rise to Peirce’s theory of signs with all its triadic distinctions, developed in detail after 1902; “Speculative rhetoric” gives rise to his many proposals regarding inference types, pragmatism, persuasion, strategies of scientific investigation, etc. The role and efficacy of the Kantian logic-metaphysics correlation axis in Peirce can be found in the central metaphysical assumptions springing from his results in logic, in this doubly extended sense. The more logic is extended —to cover semiotics, epistemology, and pragmatics—the more metaphysical results may be harvested as fruits from this Kantian logic-metaphysics highway connection. Probably this even added fuel to Peirce’s burning interest in logic: new logical results now come with an immediate double effect—in logic proper, as well as in metaphysics. To remind of a couple of the more ontologically heavy Peircean claims: The fact that general propositions may be true gives rise to his metaphysical doctrine of continuity. The fact that pragmatic investigations follow the abduction-deduction-induction cycle of methodeutics gives the metaphysical correlate that already processes in nature, like biological evolution, may realize that same structure, the appearance of new species forming a sort of natural conclusions to evolutionary arguments. The diagrammatical character of all deduction gives the metaphysical correlate that all applied mathematical structures found in the special sciences are diagrammatical, deductive, and observable. So, the royal road leading from results in formal logic to claims in metaphysics not only gives rise to the three basic categories, but also to some of the most ambitious, contested, if not outlandish claims of Peircean metaphysics. Before the appearance of Peircean Phenomenology in early 20th century, however, such results seem squarely to belong to metaphysics—to Peirce the science which describes reality on the most general level (and, as such, sometimes given the place as the first positive science in the classification of the sciences). What happens with the emergence of Phenomenology around 1902, then, is an ambitious reshaping of his overall philosophical architectonics, so that what was earlier relegated to metaphysics is now divided into two parts—one addressing reality in categorical propositions, preserving the title of metaphysics, on the one hand, and, on the other, a much more general discipline, addressing any possible conception, real or not, now acquiring the new title of Phenomenology, bracketing all reality assumptions. So,

226

Chapter 13: Phenomenology and Logic in Peirce

now the three categories, originally developed from propositions claimed true about this world, are taken to be valid categories for any possible world and any possible experience of it. It is really not evident which additional results, on top of the three categories already established, Peirce would now like to include in Phenomenology rather than in metaphysics—a question which certainly merits some scrutiny. But it is certainly the case that the main results craved for Phenomenology—the three categories—were originally the basic and indeed founding Peircean result of the Kantian logic-metaphysics axis.

From Logic to Phenomenology And that simple fact seems to imply that Phenomenology did learn from Logic, via Metaphysics, both of them inferior disciplines in the classification of sciences. Would this, now, run counter to Peirce’s Comtean claim for the higher place of Phenomenology as compared to Logic in the mature classifications of the sciences and the dependence of the latter on the former? The higher sciences—so the idea—should provide principles for the lower ones thus dependent upon them. This would indicate a one-way, top-down, flow of influence. But Phenomenology seems to have received even its core principles—the three categories —from a lower discipline, namely Metaphysics, and ultimately Logic. An immediate conclusion from this may seem to be that the ontological dependence hierarchy of sciences does not imply any privileged trajectory of discovery. It is also not the case that applied mathematics, widespread in the special sciences, would inherit mathematical structure via the explicit intermediary of, e. g., Phenomenology and the series of other intervening sciences in the hierarchy. This points to the fact that the traffic between disciplines in that hierarchy is not only the top-down movement between adjacent levels, giving principles from higher sciences to immediately lower ones ontologically depending upon them. Rather, a bottom-up traffic provides material from the lower sciences to the higher ones, appearing there by abstraction, not necessarily appearing there step-by-step along the ladder. Thus, a further, even primary type of interaction between the sciences in Peirce’s classification seems to be that of abstracted material from the lower to the higher ones—Phenomenology thus receiving its basic inventory by the Kantian road from Logic via Metaphysics. But this also holds important teachings as to the kind of relation holding between Phenomenology and Logic in Peirce. We should not assume Phenomenology to be completable before Logic, so to speak. Particularly, it is not the case that the ontological priority of Phenomenology over Logic should imply any sort of temporal or procedural priority of it in the process of gaining knowledge.

From Logic to Phenomenology

227

This is already evident in the compact argument of the “New List”: even if a process of thought is taken to go from unanalyzed Substance and to analyzed Being, the philosophical unraveling of it proceeds in the opposite direction. The possession of a true proposition is taken to be the starting point—similar to the Kantian “fact of science”—and the argument of the paper uncovers successive levels of presupposition to the articulation of that proposition. The idea is not that the mind genetically begins with simpler experiences, and then builds up true propositions step by step. The mind is always-already in a chain of articulating, inferring, and judging propositions—continually attracting new input from unityforming processes. This forms a contrast to the increasing evolution from static to so-called “genetic” phenomenology in Husserl, where perceptual experience is taken, in Experience and Judgment, to be the non-logical starting point from which logical articulations comes only at a later, higher, and supposedly more abstract level. In Peirce, perception is rather always-already shaped and experienced as propositional. And in the philosophical discovery process, both Metaphysics and Phenomenology depend upon Logic—because charting the preconditions of true propositions forms the central procedural axis. But then we have no reason to expect that ontological dependence relations —from which the hierarchy of sciences is constructed—should shape, simultaneously, the trajectory of cognition nor that of research, even if Peirce sometimes seems to support such an idea.¹⁸⁶ In that case, the whole of mathematics would have to be completed before trustworthy results could be reached in phenomenology, the whole of phenomenology to be completed before any results could be found in the normative sciences including logic, the whole of these to be completed before metaphysics, etc. in a downward going derivation-and-enrichment movement. This is obviously not the case, given the directions of Peirce’s own research activities. Why, now, did Peirce add Phenomenology or Phaneroscopy to the sciences around the turn of the century, giving it the privileged place of second only to mathematics, and making the first and central result of the Kantian logic-metaphysics derivation, the doctrine of categories, the central matter of it? And what does it imply as to the relation between Phenomenology and Logic? Even if the derivation of the categories firmly follows the logic-metaphysics trajectory, it seems to be Peirce’s increasing realism which makes him realize that even if discovered in logic, the status of the categories may be more general than that. In the mid-1880s—developed at length in the 1887 “Guess at the Riddle” book synopsis—the categories which began their career as a classification of predicates, are generalized and hypostatically abstracted into metaphysical properties of the universe itself. Now, they are redescribed as indeterminacy, haecceity, and intelligibility—traceable in different shapes across an ordered ser-

228

Chapter 13: Phenomenology and Logic in Peirce

ies of disciplines, from reasoning, metaphysics, and psychology, over physiology, biology, physics, to sociology and theology, that is, a central selection from the ladder of all sciences lower than mathematics.¹⁸⁷ This omnipresence of categories in the sciences forms the germ of Peircean phenomenology—giving the idea they inherited this structure from logic and ultimately mathematics. The Logic of Relations had established the fact that there were three classes of predicates defined by valencies, 1-, 2- and 3-valent, respectively, apart from a nullclass of full saturation or non-relatedness. In what has later become known as the Reduction Theorem (Burch 1991), Peirce argued that predicates of all valencies higher than 3 would be analyzable into combination of the three basic predicate categories. This formal structure increasingly appeared to Peirce to be motivated not only by logic, but also directly by mathematics, as being a structure to the same degree informing logic and metaphysics—“metaphysics being an imitation of geometry”, so “A Guess at the Riddle” (EP I, 246; CP 1.354). This became the subject of explicit reflection already in 1896, six years before the launching of the new discipline of Phenomenology in the Minute Logic. Here, Peirce made an attempt to “develop my categories from within”, that is, providing for them their own foundation, not dependent upon logic in which they were discovered, and pertaining to all possible universes. Here, he writes: The questions which are here to be examined are, what are the different systems of hypotheses from which mathematical deduction can set out, what are their general characters, why are not other hypotheses possible, and the like. (…) This much, however, is indisputable: if there are really any such necessary characteristics of mathematical hypotheses as I have just declared in advance that we shall find that there [are], this necessity must spring from some truth so broad as to hold not only for the universe we know but for every world that poet could create (“Logic of Mathematics: An attempt to develop my categories from within”, 1896, CP 1.417).

Thus, the Categories are now taken to be not only logical and metaphysical principles for reality, but principles for every possible world conceivable, and so being sources also of mathematical axiom systems. As such, their investigation is independent of logic and metaphysics alike, pertaining to phenomena of any kind, as he continues: “We remark among phenomena three categories of elements” (CP 1.418). Despite this mathematical-sounding introduction, Peirce proceeds, as so often in phenomenology, not by mathematical proof or analogy, but by exemplifying the three categories in real-world phenomena, Firstness primarily by sense-qualities, Secondnesses by facts and resistance, Thirdnesses by laws and thoughts—that is, he takes his beginnings materially rather than formally, in the material offered from ordinary experience and special sciences from below, rather than from formal structures offered by mathematics from above. As to

Methods and Findings of Phenomenology

229

facts, e. g., he gives a long “promiscuous list of properties of fact” in order to be able to connect facts to “duality” by means of comparison (“Logic of Mathematics: An attempt to develop my categories from within”, CP 1.440). The formal, mathematically informed description of the categories—as monads, dyads, triads—rather appears as the end result of this investigation, forming, as it were, an example of abstracting phenomenological structure from below and only, in the next step, attempting to connect them to mathematical principles from above. For the same reason, Peirce emphatically distinguishes it from pure mathematics: “It is not a mathematical inquiry; because the business of the mathematician is to frame an arbitrary hypothesis, which must be perfectly distinct at the outset, so far, at least, as concerns those features of it upon which mathematical reasoning can turn, and then to deduce from this hypothesis such necessary consequences as can be drawn by diagrammatical reasoning. The present problem is one of logical analysis” (“Logic of Mathematics: An attempt to develop my categories from within”, CP 1.443). Six years later, finally, in the first chapter of the Minute Logic, the issue of the categories still seems to be firmly logical, but the third chapter introduces the standard notion of Phenomenology as autonomous. This beginning is developed further in 1903, in the Pragmatism and Lowell lectures, the Syllabus, and later in the last Monist paper series.

Methods and Findings of Phenomenology In order to get a more detailed picture of the methods of Phenomenology, let us survey what Peirce actually does in addition to the standard introductory claims of describing the given, aided, if at all, only by mathematics. In the Pragmatism Lectures, the standard position is presented as follows: “… what we have to do, as students of phenomenology, is simply to open our mental eyes and look well at the phenomenon and say what are the characteristics that are never wanting in it, whether that phenomenon be something that outward experience forces upon our attention, or whether it be the wildest of dreams, or whether it be the most abstract and general of the conclusions of science” (Harvard Lectures on Pragmatism, 1903, EP II, 147; CP 5.41). Already here, however, we find the idea that there should be considerably more to be found in Phenomenology than the three Categories: “I find that there are at least two distinct orders of categories, which I call the particular and the universal. The particular categories form a series, or set of series, only one of each series being present, or at least predominant in any one phenomenon. The universal categories, on the other hand, belong to every phenomenon,

230

Chapter 13: Phenomenology and Logic in Peirce

one being perhaps more prominent in one aspect of that phenomenon than another but all of them belonging to every phenomenon” (Harvard Lectures on Pragmatism, 1903, EP II, 148; CP 5.43). Peirce gets this idea from Kant’s 4x3 table of categories, taking the four categories to be universal and present in all phenomena while the three orthogonal categories rather describe different realms of being.¹⁸⁸ This ambitious idea is developed further in the Syllabus: “Phenomenology studies the Categories in their forms of Firstness. It ought to be followed by a science which should study them in a general way as they present themselves throughout common experience. This seems to be approximately though not exactly, what Hegel intended in his Encyclopädie. This study may be termed, in advance of any serious undertaking of it, Encyclopedeutics. Then, and only then, should succeed the Normative Sciences” (Sundry Logical Conceptions, 1903, EP II, 272). This ambitious idea that Phenomenology should contain two branches—one about the three categories taken in nuce, and one about the categories as they appear in the vast, encyclopedic array of different fields of human endeavors, makes it understandable why Peirce very often—already in “A Guess at the Riddle”—argues from examples. Some manuscripts—e. g., R 1135 “A Classification of Ideas and Words”, 1897—seem to be aborted attempts at this encyclopedic part of Phenomenology. This, then, provides quite another source for Phenomenology than either Mathematics, Logic, or Phenomenology: the vast empirical variety of facts, which is, of course, what we really meet at a first glance when we attempt to describe the Phaneron. So, pure and applied Phenomenology: Categories and Encyclopedeutics. This idea is connected to the methodological idea developed by Peirce from 1903 – 1905 that there must be two steps in the investigation of the Phaneron, a formal and a material or an a priori and an a posteriori step: “The principles and analogies of Phenomenology enable us to describe, in a distant way, what the divisions of triadic relations must be. But until we have met with the different kinds a posteriori, and have in that way been led to recognize their importance, the a priori description means little;—not nothing at all, but little” (Nomenclature and Divisions, 1903; EP II, 289; CP 2.233).¹⁸⁹ Still, Peirce thinks that the a priori description should come, also sequentially, first: Having thus settled what the Phaneron is, we have to undertake the examination [of] its indecomposable constituents. But before undertaking the actual work of observation, it is indispensable that we should begin by considering what is possible. For otherwise we would be exploring without any definite field to explore. We should idly wander without accomplishing anything. The preliminary examination of the possibilities, on the other hand, will furnish us with definite questions to answer (“The Basis of Pragmaticism”, 1905, R 284, 39).

Methods and Findings of Phenomenology

231

The first, a priori step, is informed by Peirce’s logic of relations: “Among the preliminary questions the first (which is only rendered necessary on account of our [stating?] of medads, monads, dyads, etc.) will be, Can a posable element of this phaneron be a medad? The answer must be, no. For a medad is a proposition, and a proposition essentially contains two elements, its subject and predicate. This is true even of the simple proposition ’It rains’, that is, the environment is rainy./ After this come a series of questions as to whether the indecomposable element can be a monad, a dyad, a triad, a tetrad, etc.” (“The Basis of Pragmaticism”, 1905, R 284, 39). This argumentation is given in a bit more detailed fashion in “The Basis of Pragmaticism in Phaneroscopy” (1905), where the role of the a priori part is considerably upgraded: I invite the reader to join me in a little survey of the Phaneron (which will be sufficiently identical for him and for me) in order to discover what different forms of undecomposable elements it contains. This so will be a work of observation. But in order that a work of observation should bring in any considerable harvest, there must always be a preparation of thought, a consideration as definite as may be, of what it is possible that observation should disclose. That is a principle familiar to every observer. Even if one is destined to be quite surprised, the preparation will be of mighty aid (EP II, 362).

Interestingly, the assumedly a priori investigation immediately goes into arguing from analogy, as already hinted at in the Syllabus—this time an analogy not with logic but with chemistry. Peirce, of course, was a chemist by training, and it is well-known how his logic of relations was originally inspired by the notion of the different valencies of the elements which, in Peirce’s time, gave rise to Mendeleyev’s periodic table of elements. Here, his argument goes as follows:¹⁹⁰ A doubt may, however, arise whether any distinction of form is possible among indecomposable elements. But since a possibility is proved as soon as a single actual instance is found, it will suffice to remark that although the chemical atoms were until quite recently conceived to be, each of them, quite indecomposable and homogeneous, yet they have for half a century been known to differ from one another, not indeed in internal form, but in external form. Carbon, for example is a tetrad, combining only in the form marsh gas), that is, with four bonds with monads (such as is H) or their equivalent; boron is a triad, forming by the action of magnesium on boracic anhydride, and never combining with any other valency; glucinum is a dyad, forming Cl G Cl, as the vapor-density of this salt, corroborated by many other tests, conclusively shows, and it too always has the same valency; lithium forms LH and LI and L3N, and is invariably a monad; and finally helion, neon, argon, crypton, and xenon are medads not entering into atomic combination at all. We conclude, then, that there is a fair antecedent reason to suspect that that the phaneron’s indecomposable elements may likewise have analogous differences of external form. Should we find this possibility to be actualized, it will, beyond all dispute, furnish us with by far the most important of all divisions of such elements (EP II, 363).

232

Chapter 13: Phenomenology and Logic in Peirce

This introduction of material from a (much) lower-order science by analogy immediately gives Peirce principle headaches—in a long ensuing paragraph he appeals to the reader not to assume he here makes “reasoning by analogy” for that would be “demilunatic stuff” (EP II, 363)—concluding: “But though I do not offer such a crude argument, it is certainly true that all physical science involves (I do not say, depends upon) the postulate of a resemblance between nature’s law and what it is natural for a man to think, and moreover, the success of science, affords overwhelming proof that that postulate is true; and consequently, sound logic does distinctly recommend that the hypothesis of the indecomposable elements of the Phaneron being in their general constitution like the chemical atoms be taken up as a hypothesis with a view to its being subjected to the test of an inductive inquiry” (EP II, 363). The argument from analogy between chemistry and logic is explicitly rejected—but immediately the connection found is supported by the general claim of a much stronger analogy, that between natural laws and human thought propensities. Actually, what returns here in a new guise is a general, naturalized version of the old Kantian logic-metaphysics connection, now granting the right to argue from chemistry in the a priori investigation of Phenomenology. It is remarkable that Peirce, in the brackets, underlines that he does not claim that the relation is one of dependence—that would violate the dependence hierarchy of the sciences. The next argument, however, is decidedly a priori. It presents two unacceptable pictures of the Phaneron—one in which it consists entirely of uncombined elements and one in which it consists of one intrinsic, unanalyzable whole. In the former case, we would be unable to form any idea of the Phaneron at all— in the latter case, we would be unable to have any compound experiences such as those of propositions (interrogations and judgments are offered as examples). The assumption, then, is that we actually have access to something like the Phaneron, and, again, the argument from logic that we do have access to propositions. From these premises, Peirce argues that the very idea of combination must be part of the Phaneron—and that it must, itself, be indecomposable (for if it was composed of other things, it would, in itself, be a result of combination). Having thus proved the existence of combination—Thirdness—Peirce proceeds to derive Secondness and Firstness from Thirdness, using the principle that anything involved in a part of the Phaneron must, itself, be part of it as well—a version of the Nota Notae principle. And as Secondness and Firstness are involved in Thirdness, they too must be indecomposable elements of the Phaneron.¹⁹¹ This, then gives rise to a long argument against the indecomposability of Fourthness, that is, for the Reduction Thesis. Peirce first presents an argument ad oculos—a drawing with a number of Monads, Dyads, Tetrads, Pentads, Hexads etc. constructed out of Triads—a sort of intuitive lattice theory (EP II, 364). Here, at

Plurality of Paths to the Phaneron

233

last, a sort of mathematical argument is given for the basic structure of Phenomenology.¹⁹² Then he presents an argument that a Tetrad organizing its four elements is really proceeding by means of triadic combinations (EP II, 365), and finally, again, he resorts to a chemical argument for triadic reduction: “But those who do not see the force of this reason had better try to build up a chemical triad, that is, a connected group with three free bonds, out of chemical dyads, while observing the law of valency” (EP II, 366). Only after this a priori investigation establishing monads, dyads, and triads as the indecomposable elements of the Phaneron, Peirce turns to the actual observation of the Phaneron which plays center stage in most principle claims about Phenomenology. This observation immediately is involved with material examples from perception (color), linguistics (word sounds), action (opening a door), etc.

Plurality of Paths to the Phaneron Thus, Peirce’s own argumentations for the contents of the Phaneron as the result of phenomenological investigation are considerably more plural than the austere picture of Phaneron observation aided by mathematics which the classification of sciences may indicate. Arguments with results from lower sciences, such as chemistry or logic, come in even already at the supposedly a priori level of the investigation, and the observational level—as already prefigured in the grand tour of the sciences in “A Guess at the Riddle”—clothes the categories in material stuff taken from the special sciences as well as everyday experiences. But except for the unfulfilled wishes for the development of a longer series of particular, encyclopedic categories, the central inventory of Phenomenology remains restricted to the naked system of the three well-known categories. Its reliance upon mathematics seems restricted to a spontaneous lattice theory, and mathematical formalization and references in the development of Phenomenology are generally sparse. In that sense, being the second-most general science, the subject matter of Phenomenology remains curiously restricted—the three formal categories coming out of the logic of relations—as compared to the enormous, manifold, and detailed subject matters of mathematics or of logic on each side of it in the Classification of the Sciences. We may imagine, of course, that the yet undeveloped encyclopedic part of Phenomenology might make use of far more mathematical tools. Of course, the well-known centrality of the three categories in Peirce’s system and their generality makes their description no small task. It seems as if Phenomenology arises by a partition of the broad notion of logic, so that categories, hypostatically abstracted, are simply lifted out of logic (and their realist reinter-

234

Chapter 13: Phenomenology and Logic in Peirce

pretation in metaphysics) to receive their own discipline. The motivation may have been its proximity to (a very small part of) mathematics and Peirce’s growing realization, most lately through the work with classification of the sciences, of the ubiquity of triadic distinctions, which made him insist on their special a priori status. Still, it seems a bit strange with a whole discipline, the next most general of all, inheriting only a very tiny subset of the formalisms offered by its single superior discipline, mathematics, while the rich scientific use of math belong to lower disciplines. In detailed descriptions of the categories—e. g., “A Guess at the Riddle” or the 1896 paper mentioned—Peirce’s actual investigation process seems to be a much more liberal back-and-forth activity between examining concrete examples from lower sciences, abstracting and generalizing them—not unlike Husserlian Wesenschau—and making them fit parts of mathematical number structure from arithmetic and set theory. Simply “examining the phaneron” may sound as if it were an autonomous process supported by Phenomenology’s own principles only—bracketing their origin in the formal parts of logic. But Peirce’s own investigation practices when constructing his Phenomenology show a much more many-sided investigation pattern, revealing dependences or connections in a much broader sense than the Comtean ontological dependences claimed by the classification of the sciences. With respect to logic, in particular, Phenomenology seems to stand in continuous interaction with it, abstracting central principles from it which, in turn, appear as legislating their appearance in logic as well as in the lower sciences in Peirce’s classification.

Chapter 14 A Peirce for the 21st Century Theoretical Development as Key to Peirce’s Semiotics The Mazes of the Development of Peirce’s Semiotics Francesco Bellucci’s 2017 book Peirce’s Speculative Grammar is great news to those many who take some interest in Peirce’s semiotics—be they intellectual historians, Peirce scholars, logicians, philosophers, semioticians, or pragmatists.¹⁹³ It constitutes a great leap forward in understanding the intricacies, depths, problems, and possibilities of that doctrine. This is a point where the amount of work which Hartshorne and Weiss put into Peirce’s Collected Papers (CP) in the 1930s has really been a source of confusion rather than enlightenment. The semiotics chapters of volume two of the CP focus upon the icon-index-symbol distinction especially, and it mixes up, from §§ 2.219 – 2.308, a lot of shorter and longer definitions ranging from 1893 to 1910, Peirce’s most explosive period of theory development, as if those text bits obviously referred to one and the same thing. What is worse, the representation of Peirce’s classic articulation of his sign theory—three trichotomies of sign aspects, resulting by combination in ten classes of signs—developed during the composition of the 1903 Syllabus manuscript, is cut up and disseminated over no less than three volumes of the book, namely §§ 2.219 – 226, 2.233 – 272, 2.274– 277, 2.283 – 284, 2.292– 294, 2.309 – 331, 3.571– 608, and 4.394– 417. Particularly troubling is that the two substantially different Syllabus drafts of the very same theory, otherwise known as “Sundry Logical Conceptions” (§§ 2.274– 277, 2.283 – 284, 2.292– 294, 2.309 – 331) and “Nomenclature and Divisions of Triadic Relations” (§ 2.233 – 272) appear in this mix with the more developed version (the “Nomenclature” with the three trichotomies) appearing before the scattered parts of the less developed version (“Sundry …” with its two trichotomies only). Surely, the publication of the CP was pioneering work making a wealth of valuable stuff available for the first time, and many scholars were able to gather a rough idea of the three-trichotomies-ten-signs theory from the jigsaw puzzle of the Collected Papers. But what they could not get at all—or at least not without quite a considerable amount of work—is any idea of how that theory quickly developed in the course of Peirce’s annus mirabilis 1903, nor the larger issue of how it had evolved out of Peirce’s many other semiotic sketches and speculations, all https://doi.org/10.1515/9783110793628-016

236

Chapter 14: A Peirce for the 21st Century

the way down from his early ideas of the 1860s, and how it fed into the grandiose, unfinished draft vistas of the post-Syllabus years of the 1900s. This state of things has been the root of many unfounded or even mistaken uses of Peirce’s semiotics where—to put it bluntly—readers have been able to project their own prejudices and folk theories about signs into some selected crumb of text about icons and indices from Volume II of the CP rather than striven to understand what that theory, as a whole, really aims at—namely the analysis of propositions and inferences. This condition considerably improved, however, with the publication of the two chronological volumes of Essential Peirce by the Indianapolis Peirce Project in the 1990s which brought together large parts of the central Syllabus documents in Volume II, Chapters 18 – 21, making it considerably easier to get a good grasp of the classic theory. Still, the obvious selection pressure on the two volumes naturally precluded them from giving any clear picture of the overall development of the sign theory. This condition only really improved by the publication of Tom Short’s monograph Peirce’s Theory of Signs from 2007 with its more than 30-page second chapter on “The Development of Peirce’s Semeiotic” covering the whole period from 1865 to 1907. The Peirce Project’s grandiose chronological project of publishing Peirce’s Writings has, since its inception in the 1970s, covered the period up to the early 1890s only and will not reach 1902 and beyond within any conceivable timeframe. So, navigating the mazes of Peirce’s semiotics and its developments—not a small task in itself—has been unnecessarily further complicated by the mazes of publication of it. But many of these problems evaporate with the publication of the Italian scholar Francesco Bellucci’s magisterial monograph Peirce’s Speculative Grammar. Bellucci picks as his title Peirce’s systematic definition of his semiotics— “Speculative Grammar”—as the first, semiotic part of logic dealing with the description and analysis of sign aspects and types necessary to understand, in turn, the composition of propositions, their interrelations in arguments and their truth conditions, which are studied by Formal Logic or Logic Proper, finally to form the basis for Speculative Rhetoric or Methodeutic studying the philosophy of science issue of how actually to put to use logical structure in pragmatic scientific research with the aim of gaining new knowledge. Bellucci focuses upon the development during Peirce’s lifetime of the first part of this trichotomy of logic, that is, Peirce’s semiotics. I have no reason to hide that I find Bellucci’s endeavor as going in the same overall direction as my own 2014 book Natural Propositions: The Actuality of Peirce’s Doctrine of Dicisigns—in the sense that both of us insist upon the narrow ties between semiotics and logic in Peirce, so that the whole of Peirce’s enormous work with sign definitions is directly intended to serve the analysis of proposi-

The Mazes of the Development of Peirce’s Semiotics

237

tions and arguments which remained the primary analytical target throughout his career. So, all of Peirce’s definitions and descriptions of icons, indices, and much more, are intended to make reasoning processes understandable in an overarching “Physiology of Arguments”. In my book, I focused upon the generalized proposition doctrine of Dicisigns as developed by Peirce in and after his classic 1903 doctrine—and some further developments on that basis. Bellucci, of course, paints a much broader picture of the whole development of Peirce’s theory over his more than 40-year period of scientific activity, giving us an understanding of the detail of that development which sets new standards for scholarship. Bellucci’s overall argument claims that there are basically eight phases in the development of Peirce’s semiotics, the “classic” and most well-known 1903 phase constituting number seven among them, and he devotes a whole, detailed chapter to each phase in his chronological and systematic charting of the development of Peirce’s semiotics. The phases do not hold equal importance. The first phase is that of the 1860s where a surprisingly large bundle of Peirce’s basic and original ideas as to Speculative Grammar is articulated with the aim of analyzing and understanding assertions and arguments. By comparison, the second phase of the 1870s around Peirce’s never published 1873 logic book introduces medieval realism, the idea that the proposition separately represents its object, and the basic ideas of pragmatism, only marginally belonging to Speculative Grammar. The third period brings another large step forward in the Speculative Grammar repercussions of the important Algebra of Logic formalizations of the early 1880s, particularly the idea that all propositions need all of the three sign types of symbol, index, and icon in order to be expressed. The fourth “How to Reason” period of the early 1890s again appears as a minor period, even if both the Short Logic and the book of the chapter title, also nicknamed Grand Logic, are worked on here. The fifth, mid-to-late 1890s saw crucial discoveries like the Existential Graphs and the metaphysical category of “would-bes”, but again appear as a minor period in the development of Speculative Grammar, even if the development of certain problems now tend to make the early theory unstable. The sixth period centered upon the 1902 Minute Logic appears as a pretty important period, characterized by the emergence of Peirce’s new idea of defining sign types from a combination of simpler sign aspect types—signaling what Bellucci calls the First Reform of Speculative Grammar. Still, it is dwarfed by the seventh period of Peirce’s annus mirabilis of 1903 when he seems to have been virtually boiling—writing both the Pragmatism Lectures, the Lowell Lectures, and the various Syllabus sketches to accompany the latter, and which is characterized by Bellucci’s Second Reform of Speculative Grammar—arguably the most important

238

Chapter 14: A Peirce for the 21st Century

phase since the founding period of the 1860s. The final, eighth period introduce the Third Reform of subdividing the Object and Interpretant categories and is characterized by Peirce’s further attempts to extend the three-trichotomy theory of 1903 to first six, later ten trichotomies (and with 28 and 66 combined signs as the result, respectively). Much of that work exists in unfinished sketches only, particularly in his letters to Lady Welby; so, even if bubbling with new ideas, this final phase impresses with its imaginary utopias rather than the finalized system with established results of the preceding period.

The Birth of Peirce’s Semiotics—The 1860s Let us run through these phases. The first phase is that of the 1860s with the Harvard papers and the American Academy papers including the famous 1867 “New List” article with the first presentation of Peirce’s three categories. Surprising it is to find how many of the central semiotic issues of the later years are already introduced here—even more surprising it may appear that the evident root of the whole of the semiotic program is found in the basically logical issues of how to analyze propositions, inferences, and types of arguments. The classic Aristotelian term-proposition-argument triad—numbered the third trichotomy in the 1903 “classic” semiotics doctrine—emerges here as Peirce’s starting point, rather than the icon-index-symbol trichotomy often considered basic. Bellucci quotes Murphey for the two parts of that base: (1) the elementary identification of the notion of inference with that of sign—so that the premises function as a sign of the conclusion, and (2) the strive for generalizing the types of syllogism to a distinction between types of arguments in general. These two bases combine to give the idea that types of arguments should really be described as types of signs. This classification, in turn, was what gave rise to the abstraction of Peirce’s three categories in the “New List” paper. Already from the beginning, Peirce’s anti-psychologistic stance informed the sign notion: he saw no difference between external and internal signs, the two of which incarnate but one and the same logical structure. It is in this context that the icon-index-symbol distinction makes its first appearance, here not as a classification of signs or of sign aspects, but as types of truths, in the guise of a trichotomy between copies, signs, and symbols. They thus refer to different workings of propositions, copies (icons) use “sameness of predicates”, signs (indices) are individual objects denoting other individual objects, and are thus defined by reference, while symbols are general and thus the only properly logical one among the three truth types. This is why the logical study of terms-propositions-arguments is a study of symbols with respect to their logical properties, “objective symbolistic”. That is the

The Birth of Peirce’s Semiotics—The 1860s

239

only of the three which may embody truth or falsity. A bit later, they are defined in terms of different logical quantities using concepts inherited from the Port-Royal school, denotation (Peirce also: breadth) and connotation (Peirce also: depth) respectively.¹⁹⁴ Thus, copies (icons) are pure connotations without denotation; signs (indices) are pure denotations without connotation; while full, logical symbols have both and denote by connoting. From this, it also already follows that icons and indices can be parts of full, propositional symbols, performing within that frame their connotative and denotative functions, respectively. And already here, we also see the root of the later symbol concept defined as general signs, natural or acquired—thus not defined by convention, as indexical “signs” may also be conventional, and not all symbols need to be. It is as subtypes of symbols, then, that the classic Aristotelian term-proposition-argument triad is conceptualized. Already here, a proposition is a rudimentary argument, and a term a rudimentary proposition. In the classification of arguments, the central goal of this early theory, the leading principle of inferences becomes central. It is the ineliminable basis of the argument and should be expressed as economically as possible. The leading principle of an argument is isolated when, if used as a premise in a further argument, that argument will have the same leading principle as the first one. As arguments are signs, and as there are three kinds of truths, the classification of leading principles must also be triadic and be defined in terms of these truths. The very ratio for constructing the first version of the icon-index-symbol triad is thus to serve the typology of arguments, of symbols, so that, expressed in the later terminology, hypotheses (abductions) are arguments which function iconically, inductions are arguments which function indexically, and deductions are arguments which function symbolically. So, the copy-sign-symbol triad is used, in turn, to subdistinguish the argument subtypes of the symbol category. Already here, remarkably, Peirce insists that the generality of symbols—that is, of terms, propositions, and arguments, cannot be reduced to any sum of singulars like presumed by Aristotle. And already here, then, lies the root of Peirce’s “extreme realism” which teaches that the extension of general terms comprises also all merely possible things to which they may apply—an idea which would later lead Peirce’s deep interest in the mathematical continuum as an entity larger than any finite or infinite set, even transgressing the Cantorian transfinite hierarchy. As to logical proof, Peirce also already had the essentially computational idea that all steps of a proof take place by the substitution of signs. Thus, a hypothesis (abduction) is the substitution of a conjunctive term (uniting several predicates) with a symbol of which it is an icon. Induction is the substitution of an enumerative term (uniting several subjects) with a symbol of which it is an index; deduction is the substitution of a symbol with another symbol of the same object. These results are

240

Chapter 14: A Peirce for the 21st Century

what gives rise, in turn, to the three metaphysical categories by the use of the central Kantian principle of metaphysical deduction eternally dear to Peirce: the hypostatic abstraction of logical forms to metaphysical regularities—in this case, the three basic ways of “reducing sensuous impressions to unity”, to express it in Kantese. Quality, Relation, and Representation, the later Firstness, Secondness, and Thirdness, were the result of that abstraction, and from their interrelations also Peirce’s triad of distinction types—Dissociation, Prescission, and Discrimination, were derived. On this basis, §15 of the 1867 “New List” emerges as Peirce’s first systematic version of the Grammatica Speculativa, presenting taxonomies of signs, symbols, and arguments. But—as Bellucci concludes—the categories were reached only from the division of signs and the division of arguments, i. e., Peirce’s standard way of derivation, from logic to metaphysics.

From Semiotics to Pragmatism—The 1870s The second phase, focused upon the planned logic book of 1873, brings less surprise, if not by its relatively small focus upon semiotic and speculative grammar issues. As so often in his career, Peirce wished to bring his different results in logic and philosophy together in one volume. One book plan enumerated five chapters, on doubt and belief; inquiry and reality; the categories; signs; and inference, respectively. Another plan added more chapters, e. g., on space in logic, breadth and depth, probabilities, maxims of reasoning, but not all of these chapters seem to have been written (Bellucci 2017, 81). As is evident from these chapter titles, the book plans focus more upon logic proper and especially on what was later called rhetoric or methodeutic, that is, on philosophy of science and inquiry. Some of the ideas seem to have been discussed in the Metaphysical Club in the early 1870s and, as the logic book never coalesced, central sections actually written finally flowed into the important series of Illustrations of Science papers of 1877– 1878, among which “The Fixation of Belief” and “How to Make our Ideas Clear”, the birth certificates of pragmatism. Bellucci quotes Max Fisch for an explanation of the almost absolute absence of theories of signs in these papers: they were aimed at a more popular audience—he adds the further reason that the semiotic issue was already thoroughly dealt with in the 1868 – 1869 papers. An important generalization taking place in this phase is the step from taking all reasoning to take place in signs to all cognition to take place in signs. The groundwork of this idea lies in the anti-Cartesian papers “Questions Concerning Certain Faculties Claimed for Man” and “Some Consequences of Four Incapacities” of 1868 – 1869, refusing intuition and introspection as well as thoughtswithout-signs and the existence of an incognizable Ding an sich reality. The latter

The Johns Hopkins Years—The 1880s

241

gave rise to the first thorough articulation of Peirce’s “medieval” realism (that is, realism as to universals) in the 1871 review of Berkeley, to reappear in the 1873 logic. In that planned book, the semiotic focus is on symbols exclusively. Here, a stable feature of Peirce’s analysis of propositions appears, that they separately represent an object—a first germ of Peirce’s later, complicated “deduction of the Dicisign” in the 1903 Syllabus: “A representation is such only so far as it is conceived to be one. It is represented as representing a certain object. This object must therefore be indicated in the representation independently of that part of the representation which represents it to exist in a certain way. Or we may express ourselves thus:—There must be connected with any representation of an object another representation which represents that object independently & there must be a representation that the one represents whatever the other represents” (“On Representations”, 1873, W 3, 64; Bellucci 2017, 95). A representation— a proposition—is thus complete; a term incomplete, while the argument is perfect. Both term and proposition are thus “wanting” versions of the full-blown argument, anticipating Peirce’s doctrine of degeneracy. But overall, the logic of 1873 brought little new in speculative grammar, leaving the effects on that doctrine to Peirce’s progress in the logic of relations from around 1870 to his 1880 – 1885 formalizations of propositional and predicate logic.

The Johns Hopkins Years—The 1880s The third phase, then, is that of these algebras of logic, here called “The Johns Hopkins years” after Peirce’s position there from 1879 – 1884 and his collaboration with a number of illustrious students to produce those important steps, the first linear formalizations of propositional and predicate logic, respectively (Frege was the first, of course, in 1879, to formalize both in a graphical, non-linear formalism).¹⁹⁵ They particularly provide a new analysis of propositional and predicate logic as a whole and, spectacularly in the introduction to the formalization of predicate logic in 1883 – 1885, a bundle of new results in speculative grammar. As to the former, Peirce takes the relation of inclusion or inference as the basic notion of logic—as opposed to Boole’s choice of equality which Peirce analyzes as bidirectional inclusion. Here Peirce distinguishes illation, the drawing of a conclusion, (“P, therefore Q”) from the leading principle, the controlled, truth-preserving character of certain inferences. Leading principles may be expressed as conditional propositions (“If P, then Q”) which is why they are now taken to be fundamental, and categorical propositions but a derivative form of conditional propositions. As Bellucci says (2017, 103), Peirce’s first algebra of logic is, for that reason, simultaneously “[…] an algebra of classes (in-

242

Chapter 14: A Peirce for the 21st Century

clusion), an algebra of propositions (implication), and a system of logical consequences (illation)”. This is why he prefers the asymmetrical and transitive notion of inference as basic to his logic, rather than other possibilities like Boolean equality or “joint denial” which he discovered in 1880 (30 years before it become known as “Sheffer’s Stroke”). This will shape Peirce’s many analyses of propositions for the rest of his career. Peirce’s second “Algebra of Logic”—predicate logic using quantification—builds on explicit influence from his talented student Oscar Howard Mitchell, who formalized existential and universal quantification as well as proposed the reduction of all illative operations to two: erasure and copulation: “Take the logical product of the premises and erase the terms to be eliminated” (O.H. Mitchell 1883, 72; Bellucci 2017, 110). Peirce generalized this idea to the first version of the prenex formula where the quantifiers assemble at the left (sometimes called the “Hopkinsian” part of the expression) while the predicate proposition with free variables over which they quantify (the “Boolean” part) is isolated on the right side of the expression. It is this system, which is presented within a speculative grammar framework, in Peirce’s second “On the Algebra of Logic” paper in 1885. In that frame, called “Three Kinds of Signs”, Peirce develops a new version of his Speculative Grammar. As Bellucci insists, that doctrine is a result of the many new logical results of the 1880 – 1885 period, while it is presented as a prolegomenon to the final fruit of it, his predicate logic formalization. In the new speculative grammar, the notion of degeneracy is introduced, borrowed from the geometry of conic sections where generic sections like ellipses and hyperbolas are bordered by rarer, singular, degenerate cases where one or several variables vanish, like parabolas, circles, points, and intersecting lines. This principle is now generalized to relative predicates, of which Peirce count 0-, 1-, 2-, and 3-valent relations; all higher plural relations may be reduced to combinations or products of these predicates (Peirce’s famous “reduction theorem” analyzed by Robert Burch). Thus, dyadic relations come in genuine forms which cannot be expressed in the combination of two monadic ones: “A is the benefactor of B”, as well as degenerate forms which can be so expressed: “A is taller than B” which can be reduced to monadic statements of the respective heights of A and B. “A gives B to C” is a genuine triadic relation, while there are two levels of degeneracy for triadic relations. One is a combination of genuine dyadic relations, “A parts with B and C receives B”, another of degenerate dyadic relations: “A is taller than B and than C”. This doctrine of degeneracy is now applied to Speculative Grammar. Signs as such are genuinely triadic, but they admit of two degrees of degeneracy. One degenerate triadicity is the genuine dyadic relation of sign to object—which corresponds to indices; another is the degenerate dyadic relation of resemblance— which corresponds to icons. The non-degenerate sign, then, is a symbol which

How To Reason—Early 1990s

243

is truly triadic, and it is general in that it represents whatever it is represented to represent. Having presented this structural analysis interconnecting symbols, indices, and icons, Peirce goes to the next step: to show that every assertion and logical argument must make use of all these three sign types. Symbols makes possible the generality of propositions; indices make possible the proposition’s indispensable direct reference to its object, and icons are necessary to depict logical relations in order for them to be reasoned about. This latter may come as a surprise to many who conceive of icons as implying immediate visual resemblance. It is the reason why algebra here counts as a prime example of iconicity in Peirce: in order for relations to be reasoned about, they must be represented iconically, “for reasoning consists in the observation that when certain relations subsist others are found” (CP 3.363; Bellucci 2017, 117), and such observation requires that relations must be iconically accessible. This is simultaneously the reason that this is the birthplace of Peirce’s diagrammatology: the manipulation of such diagrammatic icons is the road to logical proofs. The notion of “iconicity” should not be developed until 15 years later, but its root, the discussion of which logic representations captures most iconically logical structure, is planted here.¹⁹⁶ As Bellucci insists, these results come from Peirce’s appropriation of F.A. Lange’s spatial interpretation of Kant’s idea that mathematical concepts must be constructed—this must take place in spatial icons, potentially to be manipulated temporally.¹⁹⁷ Consequently, Peirce calls his five algebraically expressed axioms of predicate logic “icons”. As Bellucci succinctly sums up “We interpret symbols and we are referred to objects by indices, but the form in which symbols and indices are connected (the syntax of a formula) can only be observed in iconic signs” (Bellucci 2017, 123). The requirement of these three sign types in the expression of all propositions is thus a main Speculative Grammar result of Peirce’s logically fertile Johns Hopkins phase.

How To Reason—Early 1990s The fourth phase occurs in the mid-1890s after Peirce’s strongly cosmological period around 1890 of “A Guess at the Riddle” and the “Law of Mind” series of Monist papers. Here, Peirce rewrote a number of early papers, including “New List” and “Fixation”, to go into a planned book titled How to Reason: A Critick of Arguments, also sometimes called the Grand Logic. It was refused by the publisher Ginn & Co. in 1894, after which Peirce planned a Short Logic, the only extant chapter of which is a summary of the grammatical parts of How to Reason, titled “Of Reasoning in General”—which was also not accepted for publication. It is here that Peirce for the first time consistently uses his early 1860s terminolog-

244

Chapter 14: A Peirce for the 21st Century

ical proposal of “Speculative Grammar” about that part of logic which analyzes propositions and arguments into their constituent signs, the “modi significandi” of the scholastics. Chapters I, II and VI of the first book of How to Reason treats Speculative Grammar issues, particularly Chapter 2, “What is a sign?”. Here, he gives a new rendering of the icon-index-symbol triad, now called likeness-indication-symbol. Symbols are defined after Greek “sym-ballein” as conventional signs or signs by habit, but Peirce simultaneously puts emphasis on his difference visà-vis Aristotle in taking such habits to embrace both external and mental signs, of which the former are imputed but the latter natural. Here, the important insight dawns that symbols are not only general signs in that they have a general meaning and thus are applicable in true assertions about many objects, but also in the sense that they are themselves general objects (a first germ of what was later developed into the qualisign-sinsign-legisign trichotomy). Based on the 1885 realization that reasoning needs all three kinds of signs, Peirce now articulates his “Symbols grow” doctrine—in the process of research, symbols may grow in extension by becoming applicable to new objects or in comprehension by acquiring more detailed meaning. As to assertion, Peirce now sets out to analyze the difference between signs such as “monkeys speak” and “speaking monkeys” which obviously cannot be an issue of composition only. Influenced by the hieroglyphic assertion sign meaning “which”, Peirce gives up the standard idea of an assertion as consisting of saturated terms interconnected by the “is” copula. Instead, what used to be terms are now reanalyzed as unsaturated “rhemes” incorporating the copula (“_is red”), able to be saturated by being somehow attached to an object, either directly or by means of an intervening index which points out the object. So, the assertion now combines an indicative and a symbolic sign, and pointing figures, pronouns and quantifiers may, in different ways, perform the indicative function. The symbolic signs of the assertion, in turn, are able to invoke an idea characterizing in some way the object or set of objects indicated. Finally, the analysis of inference highlights that it necessitates some kind of “monstrative” sign of illation meaning “follows from”. Even if we make explicit an inference’s leading principle and add it among its premises, as Bellucci says, that will never free us from stating explicitly what is the conclusion drawn. Such monstrative signs must be icons, because they show the relation between premises and conclusion, even in such simple cases as spatial juxtapositions of propositions. This develops Peirce’s 1885 idea that all deductions are diagrammatic, for monstrative, “showing” signs are essentially diagrammatic. As Bellucci summarizes, indices only indicate objects, but it takes icons “to demonstrate or show what is true about those objects”. Even if in many senses an intermediary phase which sums up and details the 1885 achievements, the

Grammatica Speculativa—Late 1890s

245

mid-1890s phase sets the table for the ensuing explosive development of Existential Graphs and all the new semiotic reflections connected to that.

Grammatica Speculativa—Late 1890s The fifth phase is characterized by precisely that. Bellucci argues that this phase takes its beginnings with the two reviews which Peirce wrote of the German logician Ernst Schröder who had become influenced by Peirce’s 1880s Algebras of Logic and published his own further developments in the monumental three-volume Vorlesungen über die Algebra der Logik. In October 1896 and January 1897, Peirce reviewed the First and Third Volumes of Ernst Schröder’s work (of 1890 and 1895, respectively). In these two papers, Peirce restates his Speculative Grammar vis-à-vis Schröder and embarks on his first graphical logic system, the “Entitative Graphs”. The first paper, “The Regenerated Logic” again focus upon the analysis of assertions, with particular emphasis on semiotics in its draft version “That Categorical and Hypothetical Propositions are One in Essence” which Bellucci makes central to his analysis of this phase. Here, Peirce argues against Schröder’s idea (from Sigwart), that deductive necessity is one of thinking, a “Denknotwendigkeit”, claiming it is rather a necessity of fact. How is such necessity to be analyzed? The task of the Grammatica Speculativa —as against Logic proper and Speculative Rhetorics—is to investigate the nature of assertions. The logical truth of assertions is the subject of logic proper, but before that, Grammatica Speculativa should investigate the meaning of assertions which is the precondition for their possible truth. Thus, Grammatica Speculativa must be the study of the significations, the “modi significandi” of assertions— both Latin terms stemming from the title of Thomas of Erfurt’s treatise which was believed, in Peirce’s time, to be by John Duns Scotus (De modis significandi sive grammatica speculativa). In the accompanying manuscript R 787, Peirce sketches a double investigation strategy of assertions: one is a priori, deducing consequences of the theoretical determination of assertions; the other is a posteriori, based on empirical cases of conceived assertions and working its way “upwards” toward theory in abstraction, thus testing the a priori results. The assertion is a communication to a receiver, stating that, on a certain occasion, some idea is compulsory, truth being defined as “definitive compulsion of the investigative intelligence” in the objective, non-subjective sense mentioned. From this assumption, three elements are deduced as being needed in an assertion: “a sign of the occasion, a sign of the idea, and a sign of the fact that the idea is applicable to the occasion for the scientific intelligence” (Bellucci 2017, 157).

246

Chapter 14: A Peirce for the 21st Century

First, the idea must be communicated by a sign able to call up a similar sign in the receiver, that is, an icon. This icon may be communicated by means of a symbol, but then this symbol must, originally as well as effectively, be connected to an icon, picture, or diagram which it is able to conjure again, in the interpreter. The predicate of an assertion, then, must communicate the idea either directly, through an icon, or indirectly, through a symbol (Bellucci 2017, 158). Icons, again, may be of first intention, directly presenting some qualities of an object, or they may be second intention, regulating other icons, such as logical connectives. So, icons of first intentions may be synthesized into composite icons by means of second intention icons. This a priori analysis is then corroborated by a posteriori examples in “rhetorical” evidence (Schröder). So, all languages must contain an iconical fundament of predicates, including the important iconic device of syntax, juxtaposing signs to make composite signs (such as assertions). The resulting assertion, then, is iconic for the important reason expressed as follows: “[…] for a great distinguishing property of the icon is that by the direct observation of it other truths concerning its object can be discovered than those which suffice to determine its construction” (SWS, 63; CP 2.279; Bellucci 2017, 160). And assertions allow for deductive inferences which is exactly the procedure for making such discoveries. Second, the occasion must be communicated by a sign of the compulsory event happening here and now—which is why that sign must be an index, able to point out that individual event or object. Indices, again, may be direct, such as pointing fingers, demonstrative pronouns, etc. or they may be indirect, such as spacetime indications or quantifiers and related instructions of how to locate or delimit such objects. Assertions, then, may be compounded from two complexes: one is a Predicate complex, a set of First Intention Icons interconnected by Second intention icons, another is a Subject complex, a set of Indices selecting and constraining which objects about which the Predicate speaks. This is a meta-semiotic description of the “Algebra of Logic” formalization of 1885. Third, neither the Predicate nor the Subject suffice to constitute an assertion, which is why a third sign is needed. Here, Peirce identifies that sign with the classic copula, analyzed as a symbol (he should later give a different analysis of the third sign, e. g., in the Syllabus “Deduction of the Dicisign”). It is the compulsion not of the occasion, but of the assertion sign itself. In formalized utterances, it is the main logical connective which undertakes the general, symbolic copula function (an “and” or an “implies”, etc.) in addition to its iconic meaning. But this function may be implicit: in many languages, the mere juxtaposition of Predicate and Subject may suffice to constitute an assertion. As a result, Peirce makes an explicit revision of the old Speculative Grammar account of the “New List”: the trichotomy of qualities, references, and represen-

Grammatica Speculativa—Late 1890s

247

tations should be generalized to “non-relative characters, dual relations, and plural relations” (R 787, 30; Bellucci 2017, 164), failing in 1868 to recognize the latter’s irreducibility to dual relations. Only those triadic relations are representations which brings the interpretant not only into a relation with the object, but also with “some representation of the object” (Bellucci 2017, 165; italics original). The recipient must know the object but also a representation of it. This is why weathercocks, photographs, maps, etc. are now considered symbols, for they may be true and thus able to state assertions. For that same reason, the definition of symbols as general habits can no longer be co-extensive with the definition of them as conventions which must be insufficient. “[…] some indices assert, and some symbols indicate”, as Bellucci says (2017, 166), and that is not accounted for by the state-of-the-art of Peirce’s 1896 semiotics, as he adds, having no taxonomic distinction between symbolic indices like the weathercock or photograph and indexical symbols like a quantifier or demonstrative pronoun. Bellucci makes a strong argument that this broadening of the mid-1890s Speculative Grammar and its resulting unclarities lie beneath the vast refurbishments of the doctrine in the ensuing sixth and seventh phases. In the article mentioned, this forms the backdrop of Peirce’s argument against Schröder’s distinction between categoricals and hypotheticals. They are really of the same essence—so Peirce’s title—because a categorical assertion can be seen as a hypothetical argument deprived of its inferential assertiveness: thus, every assertion is, at bottom, conditional. Categorical propositions like “All men is mortal” are expressed, in Peirce’s algebra, hypothetically: “If a man exists, then he is mortal”. Also, Peirce’s second Schröder review holds implications for Speculative Grammar. Here, Peirce introduces the notions of valency or adicity of relations: “medads”, “monads”, “dyads”, and “polyads”, for relations with 0, 1, 2 or more slots to be filled in with indices referring to Scotist “hecceities”, that is, existing individual events or objects. Full propositions, then, are 0-valent medads, like a logical atom where all loose ends or bonds are saturated. Based on this analysis, he goes on to develop his first complete graphical logic formalization, the Entitative Graphs, by adding the oval of negation to his first 1882 sketches of graphical representation of relations—and immediately after the publication of the review, he inverted the Graphs to the dyad notation of Existential Graphs which he preferred for simplicity and developed further for the rest of his career.¹⁹⁸ Peirce immediately thought the Entitative Graphs with their emphasis on the conditional were the “more philosophical” of the two, Existential Graphs being built on negation and conjunction.¹⁹⁹ Later, however he took the “scroll” sign of implication, combined from two nested negations, to be fundamental of the latter so it was deemed equally conditional, hence “philosophical”. As Bellucci says, many

248

Chapter 14: A Peirce for the 21st Century

of Peirce’s ensuing presentation of the Existential Graphs take their departure in an introductory sketch of Speculative Grammar motivating what follows. In R 484 (1898), Peirce realizes that no pure Icons nor Indices may exist; the former would be a “pure sense-quality” without any parts; the latter would be a “pure sense-reaction” of complete individuality, but all such reactions are instances of general patterns. So, the two are limit cases only. An icon represents its object as a “mere dream”, an index as an “active, existent thing”, and a symbol integrates these two in representing its object as having both the capacity of being iconized and of being indicated (quotations from Bellucci 2017, 175 – 176). All signs, then, are more or less symbolic, and all symbols assert. The subtypes of symbols, terms-propositions-arguments, then do not differ in their assertion, but rather in the “vagueness or explicitness of their parts” (Bellucci 2017, 177)—in a term, the “representative and reactive” aspects are left vague; in a proposition, the representative aspect, reason, is left vague, but the reactive is made explicit. The problems gradually developed in this phase, with the almost imperial rule of symbols understood as assertions, shall make Peirce’s early system finally explode in the sixth and seven phases.

The First Reform: Six Signs—1902 The sixth phase is centered around the drafts of the Minute Logic from 1901– 1902, comprising four large chapters—which were left unfinished and never published, after Peirce’s unsuccessful application for Carnegie support in the summer of 1902 in which Speculative Grammar issues are also developed. Planned chapters on the three branches of logic never materialized but the introductory synopsis of the book contains a new representation of them. Here, a complete reform of Speculative Grammar was proposed, that of taking the trichotomies of Term-Proposition-Argument and Icon-Index-Symbol no longer as classification of signs, but of semiotic parameters, simultaneously opening the issue of how those parameters combine. This initiative solves the riddle of the “symbolic indices” like the weathercock and the quantifier: the former now becomes an indexical proposition and the latter an indexical rhema. The new theory is developed on the basis of a changed conception of the logic-semiotic relation—earlier, logic was the objective part of the study of symbols, in itself a part of semiotic: logic as a branch of a branch of semiotics, as Bellucci says. Now, the two are all but identified: Logic as formal semiotics. Consequently, the related sign definitions dispense altogether with any reference to the human mind, broadening Peirce’s thoroughgoing anti-psychologism in logic to cover all of semiotics. Now, icons and indices become fully-fledged objects of

The First Reform: Six Signs—1902

249

logic, even if symbols remain the over-arching concept because arguments, resting on general leading principles as they are, must invariably be symbols. Furthermore, the analysis of inference types in terms of signs is changed, and finally, propositions other than symbols must be acknowledged. “Arguments are symbols that represent that certain icons (in abduction), indices (in induction), or symbols (in deduction) represent (and thus can be substituted by) certain other symbols” (Bellucci 2017, 193). In the Minute Logic, Speculative Grammar is preceded for the first time by a section on Phenomenology (the new generalized, hypothetical doctrine of the categories) providing the formal tools for the division of signs; now the three categories appear as Originality-Obsistence-Transuation, the latter two with one and two degenerate versions, respectively. The central reform of the Minute Logic is to pass from seeing Term-Proposition-Argument as a subdivision of the category of Symbols from the Icon-Index-Symbol trichotomy, to taking instead the two to be independent classifications of all signs. Only then, combinations like “indexical propositions” become possible. The issue now becomes: to what extent may icons and indices be terms-propositions-arguments?—“A proposition may either be a Symbol or an Index, but its Subject must either be an Index, or a Symbol referring in a particular indexical manner to an Index. A Rhema may be either Symbol, Index or Icon, but if not an icon, it must, at least, refer to Icons. Consequently, since Arguments are composed of Propositions, and Propositions of Rhemata, it follows that for a Proposition, Icons and Indices are required, and for an Argument Icons, Indices, and Symbols” (R 425; Bellucci 2017, 198). Thus, the two newly independent trichotomies are not so independent as to combine freely. Yet, only ad hoc rules are considered (such as: icons are too simple to function as propositions or arguments). In any case, six combined classes of signs are the result: (1– 3) rhemes—iconic, indexical or symbolic; (4– 5) propositions—indexical or symbolic; (6) arguments. As to the further subdivision of arguments, that task is double: their justification and strength is a matter of critical logic; only their purely semiotic definition belongs to Speculative Grammar. Here, an important inversion takes place: in 1867, deduction was symbolic and induction indexical—now the two change places; a conundrum that keeps occupying Peirce for the rest of his career. In 1867, deduction went from symbol to symbol, induction from index to symbol, and abduction from icon to symbol. Now, he claims that his original conception of Abduction confused two ideas: abduction proper and qualitative induction (induction from a sample to a whole, but regarding characters and comprehension rather than objects and extension). In 1901, he had introduced the idea that Ab-De-Induction were not only types of inferences but also stages of investigation, in that order. In the same period, he developed his bipartition of deduction into corollarial and theorematic,

250

Chapter 14: A Peirce for the 21st Century

of which he boasts in the Carnegie application, distinguishing between the direct and indirect drawing of consequences, the latter being more complicated and driven by formal experiment. Simultaneously, induction is now of three kinds, crude-qualitative-quantitative. The semiotic interpretation of the three now claims that they are Originary, Obsistent, Transuasive arguments, respectively. Abduction (cleansed for qualitative induction) remains iconic in the sense that it proposes a hypothesis so that the fact of the premises is an icon of the fact of the conclusion. Deduction is now indexical, because it forces its conclusion upon us (when we finally find that conclusion, as it were): the diagram of the premises is an index of the diagram of the conclusion. Induction now becomes symbolic: the premises in terms of a sample of observed data are symbols of their conclusion which follows by a (fallible) habit rule of thumb governed by the general conception of the (abductive) hypothesis they are built on. This inversion of the places of Deduction and Induction is further corroborated by the development of the mentioned binary-ternary subtypologies of the two. Already the next year, however, Peirce expressed doubt as to this new order of things, and from 1905 he is back to the 1867 position again. The First Reform step from trichotomies of signs to a combinatory trichotomies of sign aspects, however, came to stay, and will play center stage in the last two phases of Bellucci’s narrative.

The Second Reform: Ten Signs—1903 With the seventh phase, we reach the “classic” doctrine of the 1903 Syllabus mentioned in the beginning—with three trichotomies combined into ten sign classes, now guided by an explicit set of combination rules. This and the final, eighth, phase are extensively covered by Bellucci in last two, almost book-length chapters of the book. The Syllabus originated as an accompanying text to be disseminated to the audience of the Lowell lectures given by Peirce in Cambridge in the fall of 1903, and the printed version contained a classification of the sciences, an ethics of terminology and an intro to the Existential Graphs. But it did not contain what Peirce had struggled with the most, namely the new version of Speculative Grammar after the 1902 reform principles. As already mentioned, it was worked through twice during work on the Syllabus, first in “Sundry Logical Conceptions” (SLC), then in “Nomenclature and Divisions of Triadic Relations” (NDTR), with the latter adding the new trichotomy of Qualisigns-Sinsigns-Legisigns to give the “classic” ten-sign combinatory. As mentioned in the beginning, these papers would assume status of classics of semiotics through their central if scattered use in Volume II of the Collected Papers in

The Second Reform: Ten Signs—1903

251

the 1930s. Bellucci’s long chapter on the Syllabus provides an account of the origin and compositional history of these central documents which is unprecedented in detail. The former text seemingly took a long time to compose and exists in two parallel versions, while the latter, slenderer and more definitive, was composed on a short notice in Nov. 1903. We shall not here go into the fascinating intricacies of this story, suffice it to summarize its Speculative Grammar results. The first version of the SLC begins, as the Minute Logic, with a discussion of the categories in phenomenological terms including a restatement of the degeneracy theory and a presentation of the mature classification of the sciences: Mathematics-Phenomenology-Normative Sciences (Aesthetics-Ethics-Logic)-Metaphysics, where each of the three normative sciences has a physiological, classificatory, and methodical part—among which Speculative Grammar forms the physiological part of logic. In its presentation of the icon-index-symbol triad, already here it is emphasized that symbols exist in replicas only, a foreshadowing of the new trichotomy developed in the NDTR. As to the term-proposition-argument triad, Peirce now realizes that its generalization after the First Reform necessitates a new terminology, now that it is no longer a tripartition of symbols only: Sumisign-Dicisign-Suadisign is the new proposal, with one-two-three parts respectively—and of which “Dicisign” would survive longer than the other two terms. Already here, the Dicisign has the main focus, and the first version of Peirce’s “Deduction of the Dicisign” applies the a priori method to elucidating why it is that Dicisigns must have two parts. This is the case, because in order to represent the objects as real and independent of itself, the sign “represents a Secondness of its object, and represents it in the form of a Secondness” (R 478; Bellucci 2017, 220)—which requires two parts of the Dicisign, one representing the object and the other representing the sign’s own relation to the object, something which can be achieved only by representing it by an index. This analysis seemingly was not deemed sufficient, for it was considerably extended in the second version of SLC. What is further elaborated here is the proposition’s new-found necessity of representing itself. The second deduction of the Dicisign belongs to the most complicated parts of the Speculative Grammar in the whole of Peirce’s work, and Bellucci’s detailed and illuminating analysis forms a high point of his book and brings our understanding of Peirce’s fertile analysis of propositions much further.²⁰⁰ I shall not go through all its details here. The proposition is not only a sign that can be true or false, it is a sign that professes to be so, Peirce had said already in 1896, and it does so by means of implicitly referring to its own relation to its object. The proposition sign claims about itself that it is actually connected to the fact which is represents as true. Thus, it represents itself as an index of its object. Here, the object, the thing or event indexically referred to, importantly differs from the fact which the Dicisign represents. It is true

252

Chapter 14: A Peirce for the 21st Century

that the Dicisign depicts the fact that it represents and that the structure of the fact is the syntax of the Dicisign, but this is the result of a deeper meta-structure, namely the Dicisign’s reference to its own object-reference. This is possible because of the Dicisign’s interpretant, which claims that the Dicisign is an index of its object. But as Bellucci observes, this immediately adds new complexity to the notion of interpretant whose object, standardly, was the very same as that of the original sign. Now, the interpretant’s object is the sign’s relation to its object. This leads Peirce to a new distinction between the primary and secondary object of the Dicisign—the former being the standard object, the latter being the sign’s indexical relation to that object. Here, Bellucci claims that this distinction, never to appear again in this wording, is later solved by Peirce’s ensuing distinctions between kinds of interpretants. In the final SLC version, this is begun by the distinction between (1) interpretants of a proposition which may be anything which logically follows from it, and (2) the essential interpretant which interprets it as a proposition. This analysis of the Dicisign as a sign whose interpretant represents it as an index of its object is now taken as the premise of a proof that such a sign must be internally structured in two parts: this is because the sign can only be represented as an index if it is, in itself, structured like an index (if not, the interpretant could not represent it as such). Hence, it must have two parts, corresponding to the index and its object. The secondary object’s double structure is, as Bellucci says, projected onto the Dicisign itself (Bellucci 2017, 232). And as the secondary object’s two parts are the primary object and the sign itself, respectively, the Dicisign’s two parts must represent those two parts. Thus, what is called in brief the Predicate of a proposition is really “the representation of the way in which the proposition itself represents its object” (Bellucci 2017, 232; italics original). While the former part must be an index, this latter part must be or contain an icon, for that is the only sign which does not clearly distinguish its object and interpretant—but an icon of the Dicisign itself. This accounts for the double structure of predicate rhemata, including an iconic core branching into unsaturated slots. The predicate, then, is an icon of the character which this sign attributes to its objects (referred to by subject indices in the slots). Peirce now subjects this complicated a priori deduction of the Dicisign to the a posteriori—rhetoric—confirmation test, finding it to hold for categorical and hypothetical, dis-, and conjunctions, informational symbols as well as dito indices, etc. A final, important question here addresses the syntax of the dicisign:²⁰¹ what keeps Subject and Predicate together in order to form a proposition? Peirce’s answer here is that this is the very juxtaposition of the two parts—a syntax more general than linguistics since Dicisigns now embrace also non-symbolic material; cf. Chapter 5 on co-localization.

The Second Reform: Ten Signs—1903

253

All in all, Bellucci’s detailed analysis of Peirce’s deductions of the Dicisign surpasses all existing efforts pertaining to this in Peirce studies—and, more general, it also goes to emphasize the centrality of propositions-assertions-Dicisigns in the whole of Peirce’s semiotics. There is no “deduction of the icon” nor of the index—why? Because propositions and their interlinking in arguments simply form the central explanandum of the whole of Peirce’s semiotics, and all the subtle distinctions of Speculative Grammar serve the purpose of explaining them. Still, the most important innovation of the seventh phase awaits elucidation. The final SLC version is the locus also for the introduction of hypoicons and hyposemes (or subindices), that is, signs which are primarily icons or indices (given that no pure icons or indices exist). The disappearance of these terms in the final NDTR text signals that the existence of such general icons and indices is considered to be explained by the addition of a new, third, trichotomy. In the Lowell lectures manuscripts worked out in the course of summer and fall 1903, Peirce began systematically distinguishing e. g., Symbols and Graphs as such from their individual Replicas, a practice growing out of his development of Existential Graphs since 1896. In the NDTR, this observation is theoretically elaborated into an autonomous, new trichotomy, that of Qualisign-Sinsign-Legisign, on a par with the two standard trichotomies playing center stage in the Speculative Grammar ever since the 1860s. Bellucci interestingly shows how the introduction of this triad was prompted by Peirce’s ongoing development of the Gamma part of the Existential Graphs, the part transcending the propositional and predicate logics of the Alpha and Beta parts.²⁰² Gamma graphs, among many other things, should be able to represent hypostatic abstractions, that is, the deductive creation of new, higher-level subjects out of predicates (e. g., “Redness” out of “Red”). This involved a whole series of new abstract meta-signs able to characterize signs and their relata, such as “A is a medad” (a full proposition); “B is in the dyadic relation A to C”, and many more. In R 467 from Nov. 1903, such a list includes a special sign for the second-order proposition “A is a legisign”, further developed in R 508 with the distinction between a graph as a legisign and the individual replica instances of the same graph. The ambiguity of the term “graph” in Gamma thus necessitated the distinction between graphs formaliter (as repeatable legisigns) and graphs materialiter (as individual sinsigns or replicas). This distinction is now developed in NDTR and its draft in R 800—amounting to Bellucci’s Second Reform of Speculative Grammar—and it is also present in the later versions of some of the Lowell lectures. NDTR thus forms the final word on Speculative Grammar of the Syllabus; it was intended to replace SLC rather than continue it, and Bellucci finds indications it was meant to be printed as a final result of investigations. The two quick reforms—the 1902 combinatory

254

Chapter 14: A Peirce for the 21st Century

of sign aspects, and the 1903 addition of a new third trichotomy (numbered the first)—now necessitated the elaboration of a set of principles for trichotomy combination, which first appeared in NTDR. It has to do with the sequence of trichotomies which are meticulously presented in the order I. qualisign-sinsign-legisign; II. icon-index-symbol; and III. rheme-dicent sign/dicisign-argument. For their combination machinery, Bellucci cites and simplifies Robert Burch’s instructive summation in three rules: (1) each trichotomy has three consecutive, numbered members 1– 2– 3; (2) trichotomies are linearly ordered (like the I-II-III sequence mentioned); (3) combinations of the 3x3 sign aspects are allowed if they satisfy the ordering rule: first element ≥ second element ≥ third element, where the ordinals of elements refer to I-II-III, respectively, and the “greater than” sign refers to the number of the element in its trichotomy. This calculus results in the famous 10 combined signs of the Syllabus which Bellucci lays out and interprets in great detail. As these 10 signs have often been presented and discussed elsewhere, we shall not go further into them here.²⁰³ Important subdivisions not caught by this new a priori network of ten, however, include the three kinds of arguments (which started the whole Speculative Grammar crusade almost 40 years earlier) or their recently developed subtypes, nor rhemes distinguished after valency, nor the distinction between a proposition and its assertion, etc.

The Third Reform: Twenty-Eight or Sixty-Six Signs—1904 – 1908 After this demanding tour de force, both on the part of Peirce and of his intellectual biographer, the panoply of ideas of the last and eighth phase 1904– 1908 almost feels like a piece of relaxing entertainment. It is inaugurated by Bellucci’s Third Reform, the introduction of further subdistinctions between two types of Objects—Immediate and Dynamic—and three types of Interpretants, Immediate, Dynamic, and Representative, respectively (the term chosen for the latter varies; Eventual, Final, etc. are also used). Just like the three 1903 trichotomies are based on (1) the sign itself; (2) its relation to its object; (3) its relation to its interpretant, respectively, further subdivisions of the two latter naturally go on to form bases for further trichotomies. This takes place in two steps, up to six trichotomies in 1904– 1905 and two stabs at ten in 1905 – 1906 and 1908, respectively. Ordering these trichotomies linearly, then, is the indispensable premise for combining further sign types from them, potentially resulting in 28 or 66 classes of signs, respectively.²⁰⁴ Many interpreters have reveled in fantasies of the fertility of so many new sign types which were never listed, much less described by Peirce; fewer have looked into the difficult definitory problems of

The Third Reform: Twenty-Eight or Sixty-Six Signs—1904 – 1908

255

the proposals which received far less groundwork than the thorough and wellrounded 10-classes Syllabus taxonomy. Among those few Murphey, Short— and, of course, Bellucci. The six-triad model of 1904 adds to the three Syllabus trichotomies referring to the sign itself, its relation to its object, and its relation to its interpretant, respectively, three new divisions, referring to the signs’s relation to its immediate object, and to its immediate and its dynamic interpretants, respectively. Particularly the former occupies Bellucci who makes a controversial but as far as I can see correct interpretation of it.²⁰⁵ Part of the problem is to determine what the “immediate object” is, that defines the relevant trichotomy. Bellucci does a beautiful job in tracing the appearance of this term in Peirce, and Peirce’s definition of it as the object “as it is represented by the sign”. What in the world does that mean?—, as Bellucci asks. Here, he is a staunch defender of the point that the Immediate Object has to do with the identity of the object, not with any sort of description of it. I perfectly agree in this—as against many Peirce scholars who have taken the Immediate Object to be some sort of preliminary description or depiction of the Object.²⁰⁶ But such a thing would be an Interpretant category, not an Object category. The Immediate Object has to do with how the sign identifies and claims to establish contact with its real, Dynamic Object. Here, Bellucci runs into a minor problem, I think. He refuses that the distinction has anything to do with the Primary/Secondary Objects of the SLC discussed above, saying that the Secondary Object is “the representation that the sign is a sign […] of its object” while the Immediate Object is “that part of the sign that indicates the dynamic object” (Bellucci 2017, 288). I am not convinced the difference between the two is so crucial as to prevent the former from being a first stab at the latter. Moreover, the latter is also not a quite correct description, as far as I can see. Bellucci builds this on Peirce’s explanation of immediacy: “… to say that A is immediate to B means that it is present in B” (Bellucci 2017, 291). From this, Bellucci concludes that “to be present in a sign” can mean nothing else than to “be part of a sign” (Bellucci 2017, 291). Can it not? Could “present in” it not mean to be presented, or even “represented” in or by a sign, which Peirce says many times about the Immediate Object? “Represent” in Peirce is a reference relation, not a signification relation, so the idea that the Immediate Object is the Object as “represented by the sign” could be paraphrased as the Object as “referred to by the sign”, highlighting the indexical reference relation playing center stage in the “Deduction of the Dicisign”. Actually, Bellucci’s own interpretation of the resulting trichotomy also points in this direction. That trichotomy is the one grouping three sign types sometimes (among other terminological attempts) called “vague”, “singular”, and “general” signs. Bellucci rightly interprets this as the introduction in a

256

Chapter 14: A Peirce for the 21st Century

new guise of the age-old distinction between particular, singular, and universal propositions (present in e. g., Kant’s first Critique). This gives the implication, however, that this new distinction only holds between propositions, and that the Immediate Object is an issue of their quantification—existential, singular, and universal, respectively. The counterintuitive result follows immediately that only propositions have immediate objects—fitting well with Peirce’s old idea that propositions make their object reference explicit, by means of explicit Subjects such as indices, proper names, quantifications etc. I think Bellucci is completely correct in these conclusions—strangely, he does not stop to consider their implications for the resulting 28 signs of the 6-triad taxonomy combinatory. If one whole trichotomy pertains to propositions only, the resulting number of combined signs will be less than 28, the exact number depending upon the place of the trichotomy in the linear ordering of divisions. This interpretation also relativizes Bellucci’s idea that the Immediate Object is simply “part of” the sign. It is correct, of course, that Subject signs like pointing fingers, proper names, or quantifiers are part of propositions, but Peirce does not identify the Immediate Object with the Subject. Rather, he says, time and time again, that the Immediate Object is something which is “represented” by the sign. The Immediate Object is something referred to by the sign, but in another way than its external, dynamic Object—I think it is nothing but the famous claimed, indexical connection of the sign to its Object (so central in the Deduction of the Dicisign). Peirce sometimes describe quantifiers as retrieval recipes—they describe how to get from the sign to the object (via the selection by the sign utterer or by the receiver, as Bellucci repeats). I would say it is this indexical retrieval or identification process terminating in a Dynamic Object, claimed possible by the sign, which constitutes its Immediate Object. Be that as it may, as to the two additional interpretant trichotomies, the Immediate Interpretant gives rise to the trichotomy of Feelings, Experiences, Thoughts, while the Dynamic Interpretant has the subtypes of Interpretation by Definition, by Action, by Submission, respectively. In general, the three interpretant categories should come to be interpreted as follows: the initial interpretant is how the sign itself demands to be interpreted, the dynamic interpretant is how it is actually interpreted in a situation; the representative (or final, or normal, or eventual) interpretant is everything which the sign may ultimately be interpreted to mean in the final analysis (echoing Peirce’s convergence-to-truth epistemology). Bellucci interestingly discusses Short’s idea that the Dynamic Interpretant trichotomies may be used to distinguish the expression of and the assertion of a proposition and, more generally, the possibilities of generalizing to a series of other speech acts mentioned by Peirce in the 1901(?) “Kaina Stoicheia” article. In any case, the discovery of the distinction between a proposition and the asser-

The Third Reform: Twenty-Eight or Sixty-Six Signs—1904 – 1908

257

tion of it, presented in that article, is one motor driving the new division attempts, for it was not derivable from the three-division theory of the Syllabus. Regrettably, Bellucci does not pause to present a table of the 1904 – 1905 six trichotomies nor spends much time on their rules of combination, maybe because he hastens to continue to the first 10-trichotomy theory of 1905 – 1906. A revised table from October 1905 shows six trichotomies, now with a seventh (Abstract-Concrete-Collective) added as a subdivision of the middle, Singular sign category of the Immediate Object trichotomy and the dynamic interpretant trichotomy reformulated to signs interpreted by Sympathy, Compulsion, Reason, respectively—and on the same day, Peirce makes a note that four further divisions must be considered. So, that forms the start of the first ten-trichotomy period. The four further divisions result from an extension based on the standard genericity subdivision principle saying that Seconds admit one degenerate version while Thirds admit two. Thus, there should be two divisions according to the Dynamic Object, two divisions to the Dynamic Interpretant, and three to the Representative or Final Interpretant, all in all seven, which is four more than when each of these instances had only one division. Several drafts are developed in October, adding new ideas such as a speech act trichotomy of InterrogativeImperative-Significative pertaining to the Immediate Interpretant. A central problem should remain, however, over all the ten-division attempts up until 1908, namely that the rules for combination of divisions are never amended to fit the new more complicated situation, and even the canonical linear sequence of trichotomies, required to establish their combination, are never settled upon. As Bellucci says, this has the elementary reason that the six- and ten-division schemas depend upon the degeneracy calculus which gives a hierarchical tree structure whose linearization is never satisfactorily addressed. This is a main reason why all the six- and ten-division attempts of 1904 – 1908 remain an unfinished quarry of—very interesting, to be sure—hypotheses. Interpretants now account for no less than six of the ten trichotomies, and as interpretants are all concerned with various types of sign effects, Bellucci reasonably interprets the ten-division crusade as one primarily concerned with or even driven by the introduction of speech acts into the sign taxonomy. Thus, the 1906 terminological change from the established Rheme-Dicisign-Argument to Seme-Pheme-Delome is not one of mere substitution, but of further generalization, realizing that there are other speech acts to be performed on the basis of propositions than asserting Dicisigns—thus, Dicisigns remain the core subcategory of the more general “Pheme” category, also comprising other speech acts on the basis of Dicisigns than assertions. Bellucci ingeniously finds equivalents to Austin’s famous locutionary-illocutionary-perlocutionary distinction pertaining to speech acts in the ten divisions: the locutionary aspect corresponds to

258

Chapter 14: A Peirce for the 21st Century

the well-known Rheme-Dicisign-Argument of the representative interpretant; the illocutionary to the mentioned Interrogative-Imperative-Indicative of the immediate interpretant; the perlocutionary to the two dynamic interpretant divisions of resulting Feeling-Fact-Sign and Sympathy-Compulsion-Representation. In this reconstruction, four of the ten divisions are really speech act trichotomies, effectively refuting Austin’s famous quip that “With all his 66 division of signs, Peirce does not, I believe, distinguish between a sentence and a statement”.²⁰⁷ An early 1906 version again changes terminology and clarifies the two new among the Normal (Representative, Final) Interpretant divisions: Strange-Common-Novel, and Monadic-Dyadic-Triadic. A later 1906 version, after the famous Monist “Prolegomena” paper, makes many terminological changes, most notably TingeToken-Type for Quali-Sin-Legisign (later Tone-Token-Type)—but also moves trichotomies around and introduces the Ab-In-Deduction division, the mother of the whole Speculative Grammar adventure, as number 10, the final among the three Eventual Interpretant divisions—now remarkably revising its order back to the 1867 original. In the pragmatism papers of around 1907, a new division of interpretants, Emotional-Energetic-Logical, is introduced, and Peirce scholars have argued over whether it is but a terminologically new version of the standard Immediate-Dynamic-Final division; here, Bellucci sides with Short (correctly, I think) in claiming that it is indeed an independent and non-conflicting division adding new speech acts dimensions to Peirce’s late semiotics, as a further division of perlocutionary effects. It is also in those papers that Peirce makes explicit his important notion of “collateral observation”: the interpreter of a proposition must have some sort of previous experience, directly or indirectly, with the object of the proposition’s subject—otherwise the interpreter would not know at all what is talked about, and the interpretation effectively shrinks to an unsaturated rheme or, at best, a vague proposition. Finally, in the same papers, Peirce clarifies that the Final Interpretant cannot be a sign itself, but nothing but a “habit of action”; it cannot be just another conception in an infinite semiotic sequence of conception interpretants (cf. Chapter 2). That habit, of course, may concern both external action habits and thought habits. The final push forward of Speculative Grammar takes place in the 1908 rearticulation of the ten-division schema in a December letter to Lady Welby. Particularly the trichotomy pertaining to the Immediate Object now undergoes surprising changes, prompted by Peirce’s development of his doctrine of “continuous predicates”.²⁰⁸ Peirce’s idea is that predicates may be subjected to an analysis hypostatically abstracting all unanalyzed stuff in them so that what remains is but a naked, continuous, relational structure. His example is that “Cain kills Abel” may be hypostatically abstracted to “Cain stands in the relation of Killing

Semiotics in the World

259

to Abel”, effectively substituting the triadic relation “_stands in the relation of_to_” for the dyadic relation “_kills_”, simultaneously creating the new hypostatic object of “Killing”. Such analysis can only be performed a limited number of times until a rock bottom is reached because “_stands in the relation of standing in the relation of_ to_” means the same thing (cf. Peirce’s beloved quote “Nota notae est nota rei ipsius”, the property of the property is a property of the thing itself). Such a predicate is “continuous” in the sense that adding further relations adds nothing, just like adding a point or a line segment to a continuous line adds nothing to its continuity (see the following chapter). Now, in the 1908 ten-division scheme, the Immediate Object is redefined in the following manner: the sign must indicate the Dynamic object “[…] by a hint; and this hint, or its substance, is the Immediate Object” (Bellucci 2017, 336). A hint, of course, is an index. The corresponding division of signs is now changed into Designatives-Descriptives-Copulants where Designatives are standard subjects of propositions, Descriptives are standard predicates—while Copulants are continuous in the sense given. They are signs like “_possesses the character_”, “_stands in the relation of_to_”, “_ occurs concurrently with_”; other candidates could be “_is identical to_”, “_is teridentical to_and_”, “_implies_”, “_is co-localized with_”, etc. Of such signs Peirce says that “These signs cannot be explicated, they must convey Familiar universal elementary relations of logic. We do not derive these notions from observation, nor by any sense of being opposed, but from our own reason” (Bellucci 2017, 337; italics original; see also Chapters 15 and 18). Whether the Vague-Singular-General division is abandoned or should be resurrected as some additional subdivision of the new Immediate Object division, remains unclear. It must be admitted that some of the final 1908 versions of the ten-division schema, such as the polished and stark version of R 795, assume a clarity and seeming definitivity which is indeed alluring. Still, some of the trichotomies remain virtually unexplained and the solution to the issue of their compossibility continue to remain wanting. Bellucci’s final chapter on the eighth phase is rich and bewildering, as is its subject matter itself, but still it provides us with an orientation structure for understanding the intentions and aims taking Peirce to develop his final systems, primarily the experienced need for including a number of central speech act aspects into his taxonomies.

Semiotics in the World I have here discussed Bellucci’s results in some detail. A mere lauding of the book, however well-deserved, would convince no-one about the character of

260

Chapter 14: A Peirce for the 21st Century

its qualities. It goes without saying that the much more fine-grained presentation in the book itself is as indispensable as it is rewarding. In discussing its main results, I hope to convince the reader that there is no way around, for serious Peirce scholars, to get acquainted with the detail of Bellucci’s argument. If it gives us a Peirce for the 21st century it is not only because it presents the motivations for Peirce’s semiotic development in a new level of detail and with many hitherto unrecognized connections and motivations charted, but also because it convincingly rearticulates that semiotics in its proper place: as a tool box, unprecedented in detail, in order to analyze and understand propositions, arguments, and reasonings, theoretically as well as with respect to empirical signs expressing these logical structures. Doing so, it indirectly gives us, simultaneously, a picture of the world in which such logical structures play a far more prominent role and have a much more widespread appearance than normally assumed, in human as well as non-human nature.

Chapter 15 Blocking Evil Infinites A Note on a Note on a Peircean Strategy Schlechte Unendlichkeit Hegel famously coined the term “schlechte Unendlichkeit”—bad infinity—to address the issue of a proliferating process of repetitive thought without end— which should be avoided.²⁰⁹ A similar argument is often marshaled in philosophy in order to rule out excessive conceptuality. The reality of relations, thus, can be counterargued that if you accept real relations, then what about the relations between the relation and its relata? And what about the relations between those second-order relations and the first-order relation—that would call for third order relations and so on ad infinitum, ultimately constituting a potential infinity. But as reality is taken not to contain infinities, such processes are supposed to have no reality counterparts. In the case of relations then, better to avoid evil infinity by refusing to ascribe reality to any relations at all. In Peirce’s philosophy and semiotics—accepting the reality of relations—a recurring strategy appears to rule out such idling processes by reaching instead a rock bottom. That strategy, however, is not the Hegelian trick of Aufhebung. In what does it consist? Let us take a few examples to give the idea. In his mature deep-digging investigation of the structure of propositions (“Dicisigns”) taking its departure in the 1903 Syllabus,²¹⁰ one strategy is that of emptying a proposition for semantic content in order to reach its bare fundamental structure. Such emptying may be undertaken by means of hypostatically abstracting its predicates in order to constitute additional subjects.²¹¹ Thus “Cain killed Abel” may be translated into “Cain stands in the relation of Killing to Abel”. Instead of the two-place predicate “X kills Y”, a three-place predicate “X stands in the relation of Z to Y” plus a new hypostatic subject Z, “Killing”, undertake the same task of description. In principle, such transcription is indefinite—the next step would be to translate the three-place predicate into a four-place predicate: “X stands in the relation Z of standing in the relation Q to Y”. It is easy to see that this procedure may be continued into a schlechte Unendlichkeit. Instead, Peirce’s argument goes that there is absolutely no difference between standing in a relation to something and standing in the relation of standing in a relation to something.²¹² So here, already the first step reached rock bottom, and “X stands in the relation of Z to Y” must be accepted as a primitive, not accessible to further such analysis. https://doi.org/10.1515/9783110793628-017

262

Chapter 15: Blocking Evil Infinites

Another case is that of the leading principle of inferences. As a fundamental claim of the philosophy of logic, inferences are deemed valid reasonings only if they follow and acknowledge a general leading principle securing that in not only the particular case, but in a generic class of cases, like premises lead to like conclusions. The whole of Peirce’s logical trajectory began by distinguishing the three different leading principles of ab-, in-, and deduction, respectively. That leading principle is not counted among the premises of the inference but is rather the generic diagrammatic structure which makes evident that those premises do lead to the conclusion. A leading principle may be made explicit as a logical doctrine (e. g., Modus Ponens), but in most ordinary cases, the leading principle is accepted tacitly, yet subject to virtual self-control (here, Peirce is walking a knife’s edge). Would it be better if all reasoners were taught logical doctrine, becoming able to make explicit their leading principles? Not necessarily, so Peirce,²¹³ because the very act of making explicit the leading principle will itself depend upon a leading principle (already, e. g., “Algebra of Logic”, 1880, EP I, 203; CP 3.166). This fact, however, does not make logic obsolete, because dependent upon an infinite abyss of still deeper leading principles. Rather, the leading principle of a leading principle is but that leading principle itself. A further version of this rock-bottom principle pertains to the famous “unlimited semiosis”, so beloved by Derrida and deconstructivists: the principle that the interpretant of a sign is, in itself, a sign of the very same object. This basic definition makes the sign relation recursive and makes possible an indefinite chain of signs. Such a chain, however, is not autonomized and isolated from reality. Quite on the contrary, as the definition maintains, the single such chain pertains to the same object and potentially enriches the description of that object, ultimately to converge toward a final interpretant of that object (that is, if the sign using community stick to basic, overarching principles of sign development).²¹⁴ But, given the sign definition, how could there be a final interpretant not itself a sign? Here, Peirce’s pragmatism famously holds that the final meaning of a sign consists in the set of action habits which a rational person would adopt given that the conceived sum of effects of the sign is true.²¹⁵ And that set of action habits are not themselves a sign (even if signs of it may, of course, be made). Again, the habit of a habit is that habit itself.

Nota Notae All of these check blocks are particular versions of a general scholastic principle discussed by Peirce, the so-called “Nota Notae” principle, referring to the claim that “Nota notae est nota rei ipsius”: the predicate of a predicate is a predicate of

Nota Notae

263

the thing itself.²¹⁶ Originating in Aristotle’s Categories, the principle was later taken up by Wolff, Kant, and Stuart Mill. The Latin version just given Peirce finds in Kant.²¹⁷ Of course, here the notion “predicate” should be taken as referring to the meaning of the predicate, not the predicate word or expression itself. If it is taken to refer to the token or type of the predicate expression, the Nota Notae principle would be wrong (the fact that a predicate token is written with red ink does not imply that the object referred to is written with red ink; the fact that a predicate type stems from the 16th century does not imply that the object it refers to stems from that century, etc.). But if a certain color is very rare, it does follow that objects having that color are very rare. Or, Peirce’s standard example, if humans are mortal, and Enoch is human, it follows that Enoch is mortal. Here, the Nota Notae gives rise to a syllogism: “mortal” is a second-order predicate of the first-order-predicate “human”, also holding for those which the first-order predicate holds for. The particular use of the principle in Peirce addressed here, however, highlight special cases where the first and second-order predicates of the Nota Notae are the same. Oftentimes, such cases will be meaningless (the red color of the red color, etc.): many predicates do not apply to themselves. Other predicates unproblematically apply to themselves (an utterance of an utterance, leading to any level of quotations of quotations; a sign of a sign, leading to any level of description of the sign’s object). The issue of which predicates are thus self-applicable is not a formal one, decidable from formal criteria, but rather pertains to the regional ontology to which that predicate belongs. Here, Peirce’s use of the Nota Notae focuses on a subset of those special cases where 1) the predicate is self-applicable and 2) its self-application does not at all change its meaning. While the utterance of an utterance is a special utterance, namely a quotation, the habit of a habit is simply that same habit. The former still conforms to the Nota Notae principle (because being quoted is also a property of the first utterance), but the latter belongs to that special subset of self-applicable predicates where f2(x) = f(x), so to speak. All of those are continuous in the special sense Peirce used when picking the term “continuous predicates”: applying the predicate to itself gives but the same predicate, just like joining one continuous line to another gives a continuum of the same power. Thus, they form a rock bottom providing Peirce’s seemingly byzantine logic and semiotics with a fundamental inventory of formal ontology: relations, continuous predicates, leading principles, habits are not further analyzable and must be taken to belong to the basic furniture of ontology across all disciplines. If we accept Peirce’s argument, the next question follows: how much belongs to such furniture?

Chapter 16 Peirce and Cassirer—The Kroisean Connection Vistas and Open Issues in John Krois’ Philosophical Semiotics John Michael Krois was known as a leading Cassirer scholar, one of the world’s leading experts on Cassirer’s thought, and chief initiator of the impressive publication of Cassirer’s considerable Nachlass. Less known is the fact that he was also an important Peirce scholar, finding and cultivating many interesting points of connection between Peirce and Cassirer. I never discussed this explicitly with John Krois, but I think the two of us shared the assumption that what made Peirce and Cassirer and their virtual interconnections so interesting and fertile is that they incarnate, each on their continent, the final development of philosophy before the split between analytic and continental traditions developed during the first half of the 20th century. Both of them constructed extremely ambitious systems with grand metaphysical ambitions—at the same time as they insisted on the close connectedness of philosophy to the ongoing development of the sciences, taken in a very broad sense—such close connections between sciences and metaphysics being one of the ties often cut on both sides of the analytic-continental split. Both of the two could be described as a sort of Neo-Kantians, at the same time vigorously transgressing the Kantian framework in order to found comprehensive theories addressing the general semiotic access to and shaping of the world—Peirce in his pragmatism and semiotics, Cassirer in his doctrine of symbolic forms. Both, furthermore, aimed at founding these ambitious doctrines on systematical ontological assumptions, Peirce in his phenomenological list of categories, Cassirer in his little-known theory of Basisphänomene, basic phenomena, which became a special focus field for John Krois. This short chapter aims at outlining the basic lines in John Krois’ connecting Peirce and Cassirer—and some open issues made visible by these connections. Five main themes stand out: that of sign categorizations, that of pragmatism, that of images, that of semiotic evolution, and that of embodiment. As Krois emphasized, there are also points where the two of them integrate less easily—here could be mentioned mythic thought, generality, and the relations between semiotic taxonomy and evolution.

https://doi.org/10.1515/9783110793628-018

Pragmatism and Embodiment

265

Sign Categorizations and Basic Phenomena The sign categorizations of Peirce and Cassirer agree in taking human language to be an important special case—but far from the only or even the central example of sign systems. Furthermore, both agree that signs/symbolic forms do not form an arbitrary external vehicle for thought; rather, all thought is in signs (Peirce) or all thought is mediated by symbolic forms (Cassirer). Both of them also share the idea there are no simple beginnings, no initial, simple intuitions on which to build semiotic forms. To Peirce, the process of growing reason and the gaining knowledge is one with the evolution of the universe and thus took its beginnings long before human beings and their civilizations accelerated it.²¹⁸ To Cassirer, the first meaning-bearing symbolic forms are Ausdrücke, “expressions”, natural symbolisms—a special interest to Krois—but they are never simple and constitute, from the outset, complex phenomena with a perceptive as well as a meaning aspect, saturated with secondary and tertiary qualities which may only subsequently be distinguished and isolated. At the basis of the two philosophers’ systems, Krois never ceased to emphasize their predilection for triadic distinctions: Peirce’s “triadomany” as, e. g., in the icon-index-symbol distinction and Cassirer’s Ausdruck-Darstellung-Reine Bedeutung categories. At the forefront of Krois’ research until his last moment was the critical comparison of Peirce’s basic phenomenological trichotomy of Firstness/Secondness/Thirdness to the overlooked triad of Cassirerian “Basisphänomene” of Life/Action/Work developed towards the end of Cassirer’s career and only recently being published—Krois emphasizing how early versions of Peirce’s triad built on three personal pronomina in the singular, I-It-Thou—just like Cassirer’s “basic phenomena” did. Important problems in synthesizing the sign categorizations of the two, however, remain—we shall address a couple of them discussing semiotic evolution below.

Pragmatism and Embodiment Pragmatism was another connecting line between the two investigated by Krois— defining it in terms of embodiment as the “embodiment of thought in signs, of beliefs in habits of actions, and the “mind” in the body”.²¹⁹ Pragmatism, of course, is most often used as the historical classification of the American philosophies of Peirce, James, Dewey, and their intellectual descendants—but Krois made a strong case for the extrapolation of the term to cover also Cassirer, based on his idea of objects as being the “sum of possible and actual effects” (quoted from Krois 2011, 97), and his claim that the basic schema of causality

266

Chapter 16: Peirce and Cassirer—The Kroisean Connection

is not a primitive of understanding but is derived from action experience with tool use (Krois 2011, 97). Peirce’s “pragmatic maxim” of 1878, cultivated further during his last large creative burst after the turn of the century, claimed that the meaning of a statement is equivalent to the conceived effects of it, similarly connecting meaning to conception of action—belief as “that upon which you are prepared to act” (Peirce quoting Alexander Bain). A related connecting line is the focus upon functions and relations at the expense of substance in both Peirce and Cassirer. Peirce was, parallel to Frege, the discoverer of polyvalent logic of relations, while Cassirer emphasized functional correlations as the center of modern science at the expense of substance. The last of the Aristotelian categories, relation, was thus substituted for the first one, substance, which should be relegated to a remote and provincial “Nantucket of thought” (Peirce). Thus, to both Peirce and Cassirer, the relational connecting of objects in action forms the central node of semiotic and scientific meaning and world-orientation—the relation of conceiving and acting to objects being a special case of functional relation.

Images and Symbolic Pregnance A central semiotic issue highlighted by John Krois is that of the status of images. The preoccupation with individual images, artists, and currents in art history, on the one hand, and the emphasis on conceptual and linguistically expressed meaning in philosophy, on the other, were, to Krois, significative for an important academic shortcoming: the lack of a proper, general study of images as such. Here, again, the Peirce-Cassirer connection appeared as a pledge: Peirce’s basic notion of iconicity as a function present in the majority of signs, on the one hand, and Cassirer’s insistence upon the prominence of Ausdrücke, expressions, on the other, most often saturated with image-like qualities. Krois, of course, realized that this connection also involved “the greatest difference” (Krois 2011, 106) between the two: while Peirce’s iconicity notion is very general and, what is more, involved in his semiotic doctrine of the growth of generality in the ongoing research process (as indicated in one of Krois’ favorite Peirce quotations that “individualism and falsity are one and the same”²²⁰), Cassirer’s notion of expression is tied to specific, bodily, ritual practices. At the bottom of Cassirer’s whole doctrine of symbolic forms lay the important notion of “symbolic pregnance”, defined in another among Krois’ favorite quotations: Unter ‚symbolischer Prägnanz‘ soll also die Art verstanden werden in der ein Wahrnehmungserlebnis, als ‚sinnliches‘ Erlebnis, zugleich einen bestimmten nicht-anschaulichen

Semiotic Evolution

267

‚Sinn‘ in sich faßt und ihn zur unmittelbaren konkreten Darstellung bringt (Cassirer 1929, Volume III, 235).

A perceptual experience immediately implying a non-conventional meaning which it brings to concrete representation (“Darstellung”, in Cassirer implying propositional representation with truth-claims). This convoluted description was the target of Krois’ repeated reconstructions. A recurrent example, in Cassirer, of “symbolic pregnance” was the phenomenon of blushing of shame (“Schamröte”). It is, of course, an immediate sign of shame in the person blushing and thus permits the immediate inference to the proposition “He is shameful”. The redness in the face has immediate Peircean icon qualities—the intensity of the red being roughly proportional to the intensity of shame—but the relation between the red color and connected social emotion is not immediately one of similarity.²²¹ The blushing of shame as an example is intriguing—it is an involuntary, automatic, general, bodily sign by no means subject to human convention (even if the situations prompting it are, of course, subject to such conventions). Still, Cassirer—and Krois—took it as a very basic example of natural symbolism, thereby extending the notion of “symbolicity” beyond the limits of human culture. This idea is in conformity with the Peircean idea that symbols are defined by “habit”—of which human convention forms but only one, especially developed type. Expression and interpretation habits acquired in the slow adaptation process of biological evolution (cf. the blushing example) form another type of symbols—for instance the typical perceptual appearance of a species by which it is recognizable for fellow specimens (and for related predator and prey species). Just like blushing of shame, the striping of the zebra or the flashing pattern of a firefly have an immediate iconic quality—and the inference it makes possible to the concept of the zebra species with all its stable characteristics of behavior is a piece of natural symbolism.²²² Thus, the core Krois-Cassirer concept of symbolic pregnance embeds iconicity in primitive symbolism facilitating stable inferences.

Semiotic Evolution Cassirer’s concept of evolution is to some degree what could be called secularized Hegelianism—it mainly addresses the development of human civilization through history—finding, below that, an abrupt jump between closed animal Umwelten characterized by signals only and human freedom beyond it.²²³ Cassirer’s notion of mythic thought is the fertile ground of all such subsequent semiotic development in civilization—characterized by the ubiquity of expressive function and symbolische symbolische Prägnanz, emotionality, ritual, built from bodily orienta-

268

Chapter 16: Peirce and Cassirer—The Kroisean Connection

tion and action, immediate “moodiness” of the natural symbolism of all things perceived. Only later in the process, the aesthetic aspects of mythic thought may become independent as art and the qualitative individuality of artworks (just like the other symbolic forms only gradually become institutionally independent during civilization). With respect to semiotic evolution, Peirce, by contrast, is a continuist pan-evolutionist Darwinist seeing no limits between biological evolution and physical evolution “below” it and historical evolution “above” it. An important difference here between the two is the relation between semiotic taxonomy and history. Cassirer’s Ausdruck-Darstellung-Reine Bedeutung triad is, at the same time, conceived of as a schema for large phases in the historical development of humanity. Expressions are taken to be pre-(or proto‐)propositional, pre-conventional, rooted in mythical thought as expressed in bodily action and ritual, only secondarily given shape in linguistically shaped mythical thought systems. Full propositions are taken to arise only in the Darstellung phase with language, facilitating the distinguishing between subject and predicate and so introducing the disputed notion of substance—which is, later again, disappearing in favor of Reine Bedeutung focusing upon function only in the development of science. Peirce, in return, does not project his semiotic triads onto large-scale semiotic development.²²⁴ To Peirce, by contrast, pre-propositional meaning exists only marginally, if at all: “… no sign of a thing or kind of thing—the ideas of signs to which concepts belong—can arise except in a proposi1on; and no logical operation upon a proposi1on can result in anything but a proposition; so that non‐propositional signs can only exist as constituents of propositions” (“An Improvement on the Gamma graphs”, 1906, CP 4.583; emphasis added). The Peircean idea that all thought is in signs implies that thought signs are propositions which connect by means of logical inferences²²⁵—even much of what is usually, by psychologists, called “associations” are analyzed as inferences, importantly broadening the Peircean concept of inference to encompass thought processes using non-linguistic sign types like images, gestures, diagrams, etc. Many Peirce scholars fail to realize the central place played by propositions in Peirce’s semiotics. Even John Krois sometimes tended to underrate the central role of logic in Peirce’s semiotics.²²⁶ The important thing to learn from Peirce is not that semiotics transcends logic—rather the conception of “logic as semiotics” gives Peirce a broader, semiotic conception of logic than most other logicians, especially with regard to which signs are able to embody logical relations and functions. This is especially important regarding propositions, or “Dicisigns” in Peirce’s terminology. The proposition “… must, in order to be understood, be considered as containing two parts. Of these, the one, which may be called the Subject, is or represents an Index of a Second existing independently of its

Embodiment as Extended Mind

269

being represented, while the other, which may be called the Predicate, is or represents an Icon of a Firstness [or quality or essence]” (Syllabus, 1902, EP II, 177; CP 2.312). Importantly, this analysis immediately includes images: Dicisigns may consist of a picture with a legend, of a diagram with text, of two combined gestures, or even, in some cases, of one picture only—one and the same picture fulfilling the S and P functions of a Dicisign (this requires the observer is able to recognize the subject of the picture from “collateral knowledge”). If we go back to Cassirer’s much-quoted definition of “symbolic pregnance”, we recall it gave rise to “immediately, concrete Darstellung” (propositional representation). So, also Cassirer realized that the mythic, emotional, immediate “expressions” incarnated implicit propositions (which, it is true, were only later made linguistically explicit in his second, Darstellung, category). If that is the case, we might propose the following welding of the semiotic systems of the two, with an attempt to translate Cassirer’s categories into Peircean terms:²²⁷ ‒ Ausdrü cke—implicit propositions ‒ Darstellungen—explicit propositions ‒ Reine Bedeutungen—propositions translated into formal representations

Embodiment as Extended Mind Cassirer’s concept of “symbolic forms” emphasizes the external storage of human endeavors embodied in ritual, myth, language, sciences, institutions, books, artworks, technology, etc.—with the corollary that the individual’s access to general insights and actions (and thus the transgression of his or her individuality) goes via individual reintegration of such results of civilization. This constitutes an early version of what is now called the “extended mind”—the dependence of individual minds on external storing and action technologies for its functioning. As Krois realized, Peirce has a partially similar doctrine of the embodiment of signs: reasoning is supported by diagrams with which we interact by means of (bodily or imagined) experimentation. Diagrams comprise graphs, maps, algebras, schemas, linguistic syntax … all sign structures offering experiments as a road to gaining information. Diagrammatically represented knowledge provide experimental devices, and, when externalized, expand their scope considerably as well as become collectively accessible by many subjects. The issue of embodiment—as investigated during recent decades of cognitive science—was a special field for John Krois’ unification of Peirce and Cassirer. Peirce insisted that universals must be conceivably embodied in facts, ideas in signs, and signs in replicas—while Cassirer added an emphasis on the specific-

270

Chapter 16: Peirce and Cassirer—The Kroisean Connection

ities of the human body, taken as a basic reference system for the construction of symbolic forms. Krois’ notion of Embodiment is wide and encompasses both the necessary incarnation of meaning in symbols—the most widespread embodiment notion in Peirce and Cassirer taken together—and the connection of signs to the human body processing them. This latter doctrine, however, is rarely, if ever, addressed in Peirce²²⁸—while figuring prominently in Cassirer, especially in his doctrine of expression and mythical thought. This comes forward in another of Krois’ favorite quotations: “Der menschlichen Körper und seine einzelnen Gliedmassen erscheinen gleichsam als ein ’bevorzugtes Bezugssystem’ auf das die Gliederung des Gesamtraumes und all dessen, was in ihm gehalten ist, zurückgefürhrt wird” (Cassirer 2009, 45)–the human body and its members form the privileged reference system to which the entirety of space and all of its contents refer back. In this connection, Krois often refers to Cassirer’s example of cosmic directions in Australian aboriginals being defined not abstractly but with reference myths pertaining to bodily practices like the orientation of burial processions, the location of the afterlife in cosmos, etc. This example is revealing: the Australian cosmic directions do not spring directly from the physiology of the human body but is mediated by mythic and ritual bodily activity. In general, Krois refused embodiment doctrines entailing relativism and their taking structures of the human body to determine or even constrain knowledge to such a degree that changes in bodily abilities would completely overturn knowledge. What interested Krois was rather the immediacy of expression interpretations coming as ingrained capacities of the human body: our ability to decode the symbolic pregnance of blushing of shame—and, in general, the enormous semiotic foundation inherent in such expressive natural symbolisms, easily quoted and brought to functioning in iconic signs like images.

The Krois Perspective John Krois’ much-too-early death in 2010 cut short his ambitious program of developing a unified doctrine of signs, images, and bodies, based on an integration of Peirce’s and Cassirer’s philosophies. Both Peirce and Cassirer, however, insisted that human knowledge is a collective phenomenon—as implied by Cassirer’s integration of I, Thou, and It in his doctrine of “basic phenomena”. As quoted by Krois: “Das Wissen von ’mir’ ist nicht vor und unabhängig vom Wissen des ‘Du’ und ‘Es’, sondern dies alles konstituiert sich nur miteinander” (unpublished manuscript quoted, e. g., in Krois 2011, 181); knowledge about myself is not inde-

The Krois Perspective

271

pendent of the knowledge about you and it, rather all three of them are constituted in interrelation. John Krois set some important milestones, pointing out a direction of research which I hope many of us will be able to continue.

Chapter 17 The Riddle of Dependences How to Connect Entities across Pragmatism, Phenomenology, and Structuralism It is a strange fact that several important scholars of the 19th – 20th centuries preoccupied with issues of meaning and existence placed, at the center of their doctrines, calculi of dependences. The immediate reason for that is the recognition that in the world, in meanings claiming to refer to it, or in both, phenomena exist which are possible only if other phenomena exist with them. Thus, the relation between such phenomena is one of dependence, and an attempt to formalize this relation is seen, by Peirce, Husserl, Jakobson, Hjelmslev, and Ingarden— to take them chronologically—as a crucial theoretical endeavor, located at the epicenters of their respective doctrines. The special place of the five may be indicated by the fact that none of them clearly belong to neither the analytic nor the continental schools of thought diverging through the 20th century. Dependence calculi would soon seem too formal to continentals, and their overarching theories too ambitious or metaphysical to detail-oriented analytics. A central locus connecting ontology and meaning in dependences is Husserl’s 3rd and 4th Investigations in his 1900 classic Logische Untersuchungen, introducing an elementary triad of dependence types which went on to strongly influence Ingarden, to some degree Jakobson, and maybe, more indirectly, Hjelmslev, while Peirce, as in many other respects, was working independently. I shall begin by briefly running through Husserl’s argument for an elementary triad of dependence relations which can be found, in different garbs, in all of the gang of five. But my main issue in this chapter is to scrutinize how three of the figures mentioned, namely Peirce, Hjelmslev, and Ingarden, went on to take this elementary triad much further, each in their idiosyncratic way, to form more complicated and ambitious systems of dependences and dependence-related categories in logic, linguistics, and ontology. It should immediately be cautioned that the relations charted are not those of temporally extended cause-and-effect chains which might, sometimes, also be called “dependences” in another use of the word. In all of the five, the relevant dependences are structural, simultaneous, or synchronous relations, e. g., between a thing and its properties, or between a sentence and its constituents.

https://doi.org/10.1515/9783110793628-019

Husserlian Dependences

273

Husserlian Dependences Husserl’s early masterwork Logische Untersuchungen consists of a large prolegomena and six investigations.²²⁹ The former lays out Husserl’s fundamental antipsychologism: what he aims at is general, logical, and phenomenological structure, not properties of the human psyche in particular.²³⁰ The six investigations form one overarching argument: beginning by 1) distinguishing signs endowed with meaning form signs merely indicating objects, Husserl goes on to 2) consider abstractions as a special subclass of the former, and 3) to make a crucial distinctions among abstract concepts, that between parts and moments. The former, also called “genuine” parts, are characterized by being separable, such as a leg of a table. The latter, “unechte Teile”, or moments, are inseparable, such as the surface of a table. The latter, as against Aristotle, include what is normally called properties, simple or relational, describable by predicates. These distinctions give rise to three different possibilities relations between different parts and wholes: they may be independent, unilaterally dependent, or mutually dependent. ²³¹ A moment is unilaterally dependent upon the object of which it is a part; to put it otherwise, it is founded on that object. This theory of formal ontology is immediately put to use to frame a novel theory of the a priori, namely that a priori conditions are relations of foundation. This Husserlian theory of the a priori radically differs from the Kantian idea that the a priori consists in general, subjective conditions of thought, placing instead a priori conditions in the object. This is why, simultaneously, we may be in the wrong about a priori structures.²³² As objects have form and matter, this paves the way for Husserl’s distinction between formal and material (or regional) ontologies—the former charting a priori structures of all possible objects; the latter charting a priori structures of specific regions or domains of existence.²³³ Special sciences, then, are founded on structures of regional ontological concepts which develop and are clarified along the development of those sciences, ultimately organized in foundation or dependence structures. In investigation 4), Husserl immediately puts to use this new ontological theory in a sketch of the ontology of linguistic grammar with noun and sentence as the units on which other linguistic phenomena depend; in investigation 5) the same conceptual machinery gives birth to the first version of his theory of intentionality with the conscious, intentional act possessing four defining moments, its quality, matter, representative content, and object. The whole starting spark of Ingarden’s momentous philosophical work could be said to problematize whether the object is really a moment of the intentional act (leading to subjective idealism), or whether it is rather a genuine part of the act (leading to objective realism). So, the part/moment distinction may carry huge metaphysical implications. The long investigation 6) develops a whole phenomenological epistemology

274

Chapter 17: The Riddle of Dependences

based on these prerequisites and was subject to a series of later revisions by Husserl, much contested exactly by Ingarden. The relation to this foundation of founding in the other four protagonists is different. Peirce had developed his own doctrine of dependences and categories long before, ever since the 1860s, but he got hold of a copy of the Logische Untersuchungen briefly after publication and taking over Husserl’s term “phenomenology” (later “phaneroscopy”, and much else) he rearticulated his category and dependence doctrine as an investigation of elementary categorical possibilities, bracketing existence in a phenomenological reduction (cf. Chapter 13). In the mature version of his three-category doctrine beginning in the 1880s, Peirce enriched that structure by a theory of “degeneracy”, boosting it to hold six categories all in all, with ripe consequences for semiotics and metaphysics alike. Jakobson was influenced by Husserl’s third and fourth investigations in his linguistic structuralism, as has been argued by Elmar Holenstein.²³⁴ He coined the notion of “structuralism” in the late 20s, and his conception of structure, particularly his asymmetric binarism summed up in his and Trubetskoy’s marked/unmarked distinction, became informed by Husserl’s dependence calculus. Hjelmslev, of course, was Jakobson’s friend—and antagonist—in the nascent international linguistic structuralism of the 1920 – 1930s, and it is well-known that his increasingly more austere, formal, and would-be autonomous version of structuralism inspired by logical positivism was inimical to Jakobsonian binarism as well as to his wide-ranging metaphysical inspirations counting both Husserl and Peirce among his inspirators. Still, Hjelmslev’s Omkring sprogteoriens grundlæggelse of 1943 (Prolegomena, 1953/1961) happened to repeat exactly the same triad of dependences as in Husserl’s third investigation—as pointed out, inter alia, by Paul Diderichsen. Hjelmslev does not refer to Husserl, so it is not known whether he got the idea from indirect inspiration or whether he independently came to the same result. Already in his works of the 1930s, like Sprogsystem og sprogforandring (“Language System and Language Change”) and Catégorie des cas, Hjelmslev had elaborated further on dependences, and in the fullblown theory (only being published, in an English version, in the 1975 Resumé of a Theory of Language), to which Prolegomena was the prolegomena, his dependence calculus had diversified into a complicated structure with seven different opposition categories, to which we shall return below.²³⁵ Finally, Ingarden was a direct pupil of Husserl during the 1910s, in which period he gradually diverged from his master’s increasing idealism, and most of Ingarden’s impressive work springs out of an attempt to refute, from within the phenomenological tradition, that idealism. Bringing with him from that tra-

Peircean Distinctions

275

dition, however, was the dependence calculus which he, in the wartime first volume of his masterwork Der Streit um die Existenz der Welt—“The Clash over the Existence of the World”—elaborated to diversify into four different “existential” dependence types. So, both Peirce, Hjelmslev, and Ingarden radically developed and diversified an originally simple three-dependences theory. Why did they do that, and how do their improvements compare?

Peircean Distinctions Peirce famously took as the metaphysical basis of his philosophical system three basic categories developed by him already in the 1860s, one of its first versions being Quality, Relation and Representation, respectively, oftentimes generalized to First-, Second- and Thirdness. Their structure was derived from the Predicate, Subject, and their interconnection in Propositions, respectively, following the Kantian idea that the development of metaphysical concepts should be permissible on the basis of logical concepts only.²³⁶ Ontologically, the three categories chart three different kinds of being, sometimes called possibility, actuality, and reality, later may-bes, existents, and would-bes. Importantly, the ability to tell apart these categories lies in a capacity of distinctions of which Peirce very early named three (“On a New List of Categories”, 1867): dissociation, prescission, and discrimination. ²³⁷ The idea is that there are three modes of separation which may be undertaken in the analysis of a phenomenon, going from 1) the coarsest, being able to distinguish independent qualities, e. g., red from blue (dissociation), over 2) one able to distinguish what may be supposed to exist without the other, e. g., space from color (prescission) to 3) the most subtle being able to distinguish what may only be represented or thought of separately, e. g., color from space (discrimination). This terminology remains constant in Peirce, and in the Syllabus (1903), the three modes are directly connected to the definition of the three categories: In order to understand logic, it is necessary to get as clear notions as possible of these three categories and to gain the ability to recognize them in the different conceptions with which logic deals. Although all three of them are ubiquitous, yet certain kinds of separations may be effected upon them. They correspond to the three categories. Separation of Firstness, or Primal Separation, called Dissociation, consists in imagining one of the two separands without the other. It may be complete or incomplete. Separation of Secondness, or Secundal Separation, called Prescission, consists in supposing a state of things in which one element is present without the other, the one being logically possible without the other. Thus, we cannot imagine a sensuous quality without some degree of vividness. (…) Separation of Thirdness, or Tertial Separation, called discrimination, consists in representing one of the

276

Chapter 17: The Riddle of Dependences

two separands without representing the other. If A can be prescinded from, i. e. supposed without, B, then B can, at least, be discriminated from A (EP II, 270).²³⁸

So, dissociation distinguishes independent parts, prescission distinguishes a founding part from a founded part, while discrimination distinguishes all that can be represented in isolation, such as founded parts, be they in unilateral or mutual dependences—to rephrase Peirce’s distinction types in Husserlian foundation lingo. Not only are the three distinction types defined 1– 2– 3 with reference to the categories; these distinguishing abilities are also themselves what make the very separation of Peirce’s three basic categories possible in the first place. None of the three may be dissociated; however: “It is possible to prescind Firstness from Secondness. We can suppose a being whose whole life consists in one unvarying feeling of redness. But it is impossible to prescind Secondness from Firstness. For to suppose two things is to suppose two units; and however colorless and indefinite an object may be, it is something and therein has Firstness, even if it has nothing recognizable as a quality. Everything must have some nonrelative element; and this is its Firstness. So likewise it is possible to prescind Secondness from Thirdness. But Thirdness without Secondness would be absurd” (EP II, 270). So, as there is a foundation relation between first and second, and between second and third, the lower categories can be prescinded from the higher while the higher may be discriminated from the lower only. Even if presented in quite a different clothing and with the emphasis on the epistemological-logical tools to track dependences, the structure of the dependence calculi at the bottom of Peirce’s metaphysical categories and Husserl’s refoundation of the a priori, in short, are identical. Peirce, however, went on to refine this category table by an additional apparatus of genericity. As we heard above, it is mentioned already in his first formalization of predicate logic, the second of the “Algebra of Logic” papers from 1880/ 1885, and is raised into ontological prominence in his first comprehensive sketch of a metaphysics in A Guess at the Riddle from 1887, when they become a standard part of his architectonic, continuing, e. g., in the Harvard Pragmatism Lectures of his annus mirabilis 1903, his Letters to Lady Welby 1904– 1908, etc. A concise way of presenting the conceptual machinery can be found in the Guess at the Riddle: “… the whole book being nothing but a continual exemplification of the triad of ideas, we need linger no longer upon this preliminary exposition of them. There is, however, one feature of them upon which it is quite indispensable to dwell. It is that there are two distinct grades of Secondness and three grades of Thirdness” (EP I, 253; CP 1.365). Peirce goes on to explain how he generalizes the notion of genericity from the geometry of conic sections (ellipses,

Peircean Distinctions

277

hyperbola, circles, parabola, etc.). Here, the generic cases are ellipses and hyperbola, while parabola and circles only appear as limit cases with singular variables of conic equations, and still more “rare” or degenerate are the single point or two intersecting lines which may appear when still more variables vanish. The more degenerate cases form singularities on the borderlines between the more generic cases. So, there are degrees of degeneracy. Peirce continues to develop this analogy: “Nearly in this same way, besides genuine Secondness, there is a degenerate sort which does not exist as such, but is only so conceived. The medieval logicians (following a hint of Aristotle) distinguished between real relations and relations of reason. A real relation subsists in virtue of a fact which would be totally impossible were either of the related objects destroyed; while a relation of reason subsists in virtue of two facts, one only of which would disappear on the annihilation of either of the relates. Such are all resemblances …” (EP I, 253; CP 1.365). Peirce mentions the example of two persons being alike in being Americans. This fact may be dissolved into two independent facts, each of them being an American. Not so the relation of Cain killing Abel—it may not be dissolved into two independent facts of killing and being killed. So, the former is degenerate, the latter not so. Contrasts and comparisons similarly are degenerate relations of reason. Going to Thirdness, now, “… there are two degrees of degeneracy. The first is where there is in the fact itself no Thirdness or mediation, but where there is true duality; the second degree is where there is not even true Secondness in the fact itself” (EP I, 254; CP 3.166). A pin fastening together two things is degenerate in the first degree—if either of the two is annihilated, the pin and the other will still exist in a real, dual relation. All sorts of mixtures are of this same nature, socalled “accidental thirds”. Even more degenerate are … thirds degenerate in the second degree. The dramatist Marlowe had something of that character of diction in which Shakespeare and Bacon agree. This is a trivial example; but the mode of relation is important. In natural history, intermediate types serve to bring out the resemblance between forms whose similarity might otherwise escape attention, or not be duly appreciated. In portraiture, photographs mediate between the original and the likeness. In science, a diagram or analogue of the observed fact leads on to a further analogy. The relations of reason which go to the formation of such a triple relation need not be all resemblances. Washington was eminently free from the faults in which most great soldiers resemble one another. A centaur is a mixture of a man and a horse. Philadelphia lies between New York and Washington. Such thirds may be called intermediate thirds or thirds of comparison (EP I, 254; CP 3.166).

Even if obviously the most degenerate of cases, these examples go to show that they are highly regarded by Peirce for their possible role in processes of reasoning and investigation.

278

Chapter 17: The Riddle of Dependences

This extension of Peirce’s elementary category list of three to one of six, which may be numbered 1.0, 2.0, 2.1, 3.0, 3.1, 3.2, respectively, proved to become an important motor, not only in classifying and relating empirical sciences such as in the Riddle, but also in theory development within Peirce’s own doctrine. Thus, Peirce’s classic trichotomy of Icon-Index-Symbol may be reinterpreted so that Indices and Icons are first and second degree degenerates of Symbols, respectively, or that propositions and terms (Dicisigns and Rhemes) may be first and second degree degenerates of Arguments.²³⁹ The degeneracy apparatus may even drive theoretical innovation, particularly in the fertile years after 1903, such as when Peirce derives, from genericity categories, the idea that while there is only one main type of Abduction, there must be two of Deduction (corollarial and theorematic)²⁴⁰ and three of Induction (simple, quantitative, and qualitative)—or when he elaborates further his semiotics by saying that a sign must have two objects (immediate and dynamic) and three interpretants (immediate, dynamic, and final). In Husserlian terms, the degenerate cases would be those in which no real founding dependence relation is at stake despite the fact that it seems, on the surface, to be the case. Really, the relata of degenerate relations are independent. But that does not imply they are but surface phenomena to be brushed aside—they are still brought together by generic forms and play important roles in thought and research. Rather, they give rise to the idea that all Secondness and Thirdness phenomena must have two and three subtypes, respectively. To sum up, Peirce’s development of his elementary dependence calculus from yielding six instead of three categories is a formal move motivated by entering a new constraint into the system, that of genericity. It is formal in the sense that it does not, in itself, predict the content matter of the new subcategories which derives, rather, from the specific semantic domains of Second- and Thirdness concepts subjected to the enlarged dependence calculus.

Hjelmslevian Dependences While Peirce generalized his categories from the structure of logical propositions —and the dependences followed in deciding the relations between those categories—Hjelmslev’s use of the three dependences is directly thematized as a central descriptive tool of glossematics. The classic locus for the presentation of them is the Prolegomena from 1943 where it is couched in a proliferation of new terminology even surpassing Peirce in the amounts of new vocabulary. To Hjelmslev, linguistic form is sharply distinguished in two independent fields, expression and content, and each of these two fields should be charted by analyz-

Hjelmslevian Dependences

279

ing them into systems of units, so-called functives, connected by dependence functions. Exactly as in Husserl, three possible dependences between two functives are listed: determination, interdependence, and constellation, respectively (cf. Hjelmslev 1975, 60), the latter being independence or the absence of dependence). Simple dependence is at stake when one part requires another for its presence, but not vice versa. Interdependence appears when two parts mutually require the presence of each other and consequently only appear together. Constellation, finally, occurs when the occurrence of two parts is free, and both of them, one of them, or none of them are possible appearances. The identity of this dependence calculus with Husserl’s 1900 system is striking.²⁴¹ The central role of dependences is evident from the central idea that objects are really “nothing but intersections of bundles of dependences” (Hjelmslev 1969, 23). Hjelmslev further applies this three-dependence system in two variants, pertaining to process and system, respectively. Process and system are defined by both-and and either-or relations, respectively, that is, what is traditionally referred to as syntagmatic and paradigmatic relations.²⁴² In these two fields, the three-dependence system is specified as selection, solidarity, combination, and specification, complementarity, autonomy, respectively (Hjelmslev 1969, 37, and 1975, 60). Selection, one-sided dependence in linguistic linearization, may be at stake, for instance, in the relation between main clause and relative clause (a relative clause may not occur without a main clause, while the opposite is not the case). Solidarity, two-sided dependence, occurs for example at the sentence level between noun phrase and verb phrase, and combination, pure compatibility, is found e. g., between two main clauses or the two parts of a compound noun. Linguistic analysis is pursued, now, by beginning with the discourse as an undivided whole, going through successive phases of partitioning discourse into invariant parts—functives— registering the internal functions holding between them. Having exhausted this description at a given level, analysis goes on to repeat the procedure as to the internal structure of those elements, and the open inventory of possibilities at the higher levels gives place for smaller, closed paradigms of correlated morphemes and syntagmatic relations at the lower levels inside sentences, and the procedure is supposed to go on until a bottom of simple “figurae” are reached in each of the two domains, a level where the clear distinctions of bound articulation again cease to hold. In Hjelmslev’s thoroughgoing parallelism between content and expression, the whole of this descriptive apparatus is taken to be pertinent to both. The very first partitioning is supposed to give the two functives expression and content, mutually dependent, thereafter would follow (e. g.) periods, sentences, paradigms, morphemes,

280

Chapter 17: The Riddle of Dependences

etc. The systems of paradigm morphemes on the content side of language, however,—like in his large study of case—particularly occupied Hjelmslev. This distinct triad of dependences, however, is only the superficial and derivative upper level of an underground of much more complicated structures informed by participation, Hjelmslev’s career-long insistence that languages, even if possessing logical features and, among other things, facilitating reasoning, are not at all logical through-and-through but are informed by what some have called magical thinking. Hjelmslev took the notion of participation from the French anthropologist Lucien Lévy-Bruhl and, influenced by his notion of “prelogical” thought, Hjelmslev coined the notion of “sublogic” to refer to linguistic structure making logic as well as prelogic possible. In Lévy-Bruhl, “prelogical” thought was exemplified in the idea that some person may be, simultaneously, identical and non-identical with some particular parrot in the woods. In Hjelmslev, participation is defined by the phenomenon that opposed terms may share content—and making it a general prerequisite to linguistic dependences, he stripped the term for Lévy-Bruhl’s evolutionism (supposing a development from primitive pre-logic to more sophisticated logic) to make it an elementary synchronic phenomenon in the basis of all language and thought.²⁴³ Participation, again, holds for both content and expression, and in the content side of language, the participation idea is formalized in a calculus of socalled “concept zones”, developed in books such as Sprogsystem og Sprogforandring and Catégorie de Cas in the early thirties. Hjelmslev was particularly interested in understanding the implicit semantics of the large morphological categories of languages, such as case, tempus, gender, number, aspect, etc. Such concept zones are approximately corresponding to “semantic domains”, and Hjelmslev’s Saussurean idea is that such zones are basically grasped by means of oppositions, charted by elementary logic: they are divided into opposing end zones framing a middle neutral zone. This partitioning, however, is now subjected to a series of possibilities of weighting with different emphases such subsets of the concept zone. The whole of the concept zone is seen as a sort of “ballot” which may be filled out in different ways, resulting in terms with different emphases across the zone. As Lorenzo Cigana has convincingly showed in his 2014 Ph.D. dissertation and ensuing publications that the formalization of these “sublogical” participation phenomena occupies a central axis of Hjelmslev’s summing up of glossematics in the spartan algebra of his compact chefd’œuvre Resumé of a Theory of Language (originally in Danish, published only in 1975 in an English translation). We cannot do full justice to the details of this complicated theory with hundreds of definitions in this context (see Cigana 2014) but let us give an outline focusing upon the relation between participation and dependences.

Hjelmslevian Dependences

281

In the Resumé, the more concrete linguistic analyses of the 1930s are left behind in a generalized theory of linguistic categories, and the theory is presented in a long series of sparse definitions interrupted only by rules and notes with only very rare linguistic exemplifications, and the book, even if providing a concentrate of Hjelmslev’s mature theory counting as the central manifestation of the glossematic system, was published late and never achieved a huge following, appearing as it did when Chomskyanism and other currents had long since overtaken structuralism as cutting edge linguistics. Rather, it counts as a hidden bible of formal glossematics. Here, a long development of “sublogical” structure is followed by a briefer development of the more unanimous, well-defined level resulting from passing from a primordial level of “free articulation” to “bound articulation”. In this step, free sublogical participation phenomena may be reduced by “exclusions” where shared content between opposites is ruled out. In the analytical procedure, however, the starting point is always the more restricted, bound articulations. Cigana, arguably the most thorough interpreter of this fundamental part of glossematic theory, aptly calls the relevant paragraphs *Ggb3.1– 2 in the first half of the Resumé a “path through a labyrinth” (2014, 457). Sublogical participation, however, is not a diffuse swamp of floating content, but possesses its own structures to be described. This description takes place in five steps, and we cannot go into deep detail but shall attempt to give a picture of the relation of the dependence calculus to participation phenomena. The steps are as follows: 1) Three possible parts of the concept zone are described by the Latin letters a and b for opposed contents, and c for the intermediary neutral zone. Then, 2) two levels of emphasis on different parts of the zone are indicated by “filling in the ballot” by striking through the related concept zone part by a diagonal if covered, by two crossing diagonals if covered with insistence. This calculus of semantic weightings, 3) gives seven different possible types of structuring the concept zone named by the Greek letters α, Α, β, Β, γ, Γ, Γ2, as follows (Fig. 57)²⁴⁴:

Fig. 57: Seven structurings of the same concept zone.

282

Chapter 17: The Riddle of Dependences

The first two, the Alphas, taken together, indicate the opposition between a simple concept covering center and one end of the zone vs. a complex one, covering all parts of the zone with equal insistence. If the former is the adjective “poor” and the second “rich”, participation is given by the fact that “rich” may be taken in a simple sense (“He’s rich”, covering one end of the zone) as well as a complex sense which covers the whole zone including its opposite of poverty (as in “How rich is he?”—Hjelmslev’s example from Forelæsninger over Sprogteori; cf. Cigana 2014, 498). This overlap in the semantics of “poor” and “rich” is participation.²⁴⁵ “Extreme participation” is the participation in which the “Participants have the highest possible number of common Variants” (Hjelmslev 1975, 25). In extreme participation, it cannot be decided whether the neutral middle zone is included or not. The two Beta categories taken together, in turn, signify a symmetric, contrary opposition of participation (not exhausting the zone); the two first Gamma categories signify a contradictory, exhaustive opposition of participation, while Γ2 indicates a change between emphasis on a and b in different contexts. All of them, however, remain “sublogical” because signification still is shared between terms over parts of the concept zone, even if with more emphasis in certain zones. These seven types of sublogical forms, in turn, 4) may be coupled in different combinations in order to give possible paradigm systems with any number of members, pertinent for different morpheme systems across languages, e. g., the different case systems of Catégorie des cas which seem to be the empirical examples in the background, motivating the much more general theory of the Resumé. In the Sprogsystem og Sprogforandring, such combinations up to paradigms with six members are listed; in the Resumé, combination possibilities up to 13 members are meticulously computed.²⁴⁶ The seven types combine after solidarity laws restricting free combination, that is, certain among the seven elements necessarily occur together and certain couples of elements occur along with other couples.²⁴⁷ Moreover, 5) another further development gives the further result that the pairwise combination of content types into “polarities” which define linguistic categories, yield nine such possible pairs. Such concept zones articulated by participation, however, may be simplified and made “logical-exclusive” (in parts of languages themselves, not as a result of linguistic analysis) by the important process of exclusion: “Any participation (participant-correlation) can be transformed into an exclusion (field-correlation)” (Hjelmslev 1975, 23). In the transition from the vast amount of sublogical possibilities in free articulation and to the narrower sets of possibilities of bound articulation, all participation is reduced to exclusion characterized by clear category members no longer sharing content. Thus, “Any contradictory exclusion can be transformed into a contrary participation, and any contrary par-

Hjelmslevian Dependences

283

ticipation into a contradictory exclusion”, just like the converse transformation between contrary exclusion and contradictory participation holds (Hjelmslev 1975, 24– 25). In this way, sublogical categories where contents overlap, flow into each other, and share content may be cleansed by exclusion, creating more clear and isolated categories. At bottom, importantly, all correlates are by principle assumed to remain participative (Resumé, Reg 11, 12, 23), While the sublogical “Free Articulation” takes place without reference to any particular dependence function, “Bound articulation” now takes place with reference to one among the three dependence functions, and the step from sublogical Free to logical Bound articulation implies that the “most” sublogical pair, with extreme participation, α and Α, is excluded completely, while, in the Beta-Gamma elements, reduction to exclusive content zone boxes not sharing content with other such boxes gives a much simpler picture. The main such reduction results in the simple set of four possibilities β-Γ of three-content zone emphasis only (Fig. 58):

Fig. 58: Reduced logical concept zone combinations.

(Hjelmslev 1975, 50 – 51; simplified graphics adopted from Cigana 2014, 559).²⁴⁸ Now, these elements chart the four logical possibilities of a, non-a, both a and non-a, neither a nor non-a. Here, the first three elements may directly show the relation between the three main dependence types of interdependence, constellation, determination, plus the fourth, the non-applicability of any function. Furthermore, each of the three dependence functions may be mapped after the same four-category scheme, such that functives involved in selection (determination in the process realm) may be sorted after: 1) selected, 2) selecting, 3) both selecting and selected, 4) neither, respectively. The resulting “bound articulation” is, as Cigana says, the field for the standard glossematic methodology (Cigana 2014, 551) with its logical-exclusive correlations between members of paradigms.²⁴⁹ But it is only pertinent 1) from a point in the ongoing analysis process where the open series of chapters, sections, sentences, with an indefinite amount of the members, in larger text parts, ceases to prevail and closed, finite paradigms appear in the analysis and 2) until the utmost point of analysis where

284

Chapter 17: The Riddle of Dependences

the final level of glossemes are again subject to free articulation. So, the realm where bound articulation with the three simple dependences holds forms a sort of mesoscopic realm of sentence grammar, bounded from above by the more open macroscopic, transphrastic realm, and from below by microscopic realm of the final inventory of elements. At this level we do not consider which functive presuppose the other, but how functives distribute within a category. Thus, at this intermediary level of bound articulation only, with exclusive concept zone boxes and with bound paradigms with a small, finite number of interrelated category members, the standard three dependences operate, and after the arduous, sublogical description of participation types in the Resumé, the standard system of dependences across process and system, relation and correlation, is derived as a result (51) and summed up schematically (60). Thus, in Hjelmslev, the dependence calculus shared with Husserl is presented as logically exclusive and pertinent to a mesoscopic level of analysis addressed by traditional linguistics, but possible only as nested within a more basic, comprehensive foundation of sublogical participation. A central issue in this amazing theory is that clear principles for which concept zone combinations are rendered possible are never made explicit (that is, step 2 above), just like clear such principles for which combinations of sublogical contents into systems of paradigm members (step 4 above) may be given but are not clearly motivated. These systems thus remain a seductive and challenging torso. If bound articulation to be studied by means of the three dependences is indeed the main glossematic analytical approach, it must, however, yield to participation whenever it proves insufficient; cf. the rule Rg 24 of the Resumé (Hjelmslev 1975, 49): “If it is impossible to identify unambiguously each correlate under a category through bound articulations, the result of the free articulation provides the only designation of the correlates”. Thus, the designation of correlates as sublogical participants “can be introduced everywhere where it is impossible to identify each correlate unambiguously through a bound articulation” (Hjelmslev 1975, 49). So, it cannot be determined beforehand how much of linguistic structure will obey clear dependence relations between exclusive units—participation phenomena like syncretisms, overlapping, gradualism, etc. may, in many cases, prove ineradicable. Precisely for this reason, extreme participation is postulated as the default state of any system, since participation “can” be reduced to exclusion, but not vice versa. While sublogical structuring is taken to be basic and giving rise to logical dependence structuring as a secondary derivative, analysis has to proceed in the opposite direction, charting as much structure as possible by exclusive logic, ready to admit participation whenever failing to make exclusive definitions.

Hjelmslevian Dependences

285

This is not the place to go deeply into the difficult issue of the transformation from free to bound articulation and vice versa in Hjelmslev’s algebra, occupying hundreds of pages in Cigana’s reconstruction. Suffice it to say that the three dependence types so central to Hjelmslev’s system are not, unlike the case in Peirce or Husserl, each in their way, taken as primitives, but rather are taken to be the derivative result of a theoretically crucial process of emergence taking us from the vast fauna of sublogical systems to the much more restricted set of logical possibilities between which clear dependences hold. In a certain sense, however, on a very general level, some resemblances between Peirce’s and Hjelmslev’s doctrines may be noted. Both of them find, beyond the level of clear categories between which dependences hold, a level of more primitive categories defined by a relaxation of restrictions required at the upper level. In Peirce: degeneracy, in which parts of the definitions of Secondand Thirdness concepts cease to hold and give place for vaguer, but still indispensable concepts; Hjelmslev: the realm of sublogic where exclusion ceases to hold and gives space for participation in all of its proliferating subtypes. In Peirce, degeneracy yields simpler subtypes of generic notions (such as icons and indices from symbols) which, at the same time, may form parts of those generic notions (icons and indices typically forming parts of symbols). Taken in isolation, doubly degenerate concepts such as icons, if considered in isolation, are but vague, and the distinction between them and their object may become fluid. Moreover, Peirce’s general insistence upon the metaphysical priority of continuity over discrete phenomena²⁵⁰ indicates the possibility of continuous transformations between concepts referring to the latter—in a certain sense corresponding to the fusion and merging phenomena in Hjelmslevian sublogic. In Hjelmslev, the relaxation of exclusion gives rise to participation phenomena appearing in discourse even if not subject to strict dependence relations—syncretisms, intersections, polarities within a category. A decisive difference, however, remains that Peirce the logician studying how people ought to think would take the degenerate categories to be understandable only on the background of their generic “ancestors” derived from logic, while Hjelmslev the descriptive linguist would see logic as a derivative product of the primitive, non-normative, condition of participative thought and language, such structures facilitating all thought including its many non-logical varieties. Still another development of the three dependences may be found in one of Husserl’s closest disciples, Roman Ingarden.

286

Chapter 17: The Riddle of Dependences

Ingardenian Dependences As mentioned, the backbone of Ingarden’s long career as a philosopher grew out of a disagreement which he developed with his phenomenological master already when in Germany in the 1910s. The first generation of Husserl scholars— Ingarden, Adolf Reinach, Edith Stein, and others—seem to have immediately experienced Husserlian phenomenology based in the Logische Untersuchungen as a realist position and so were surprised to glimpse indications in a more subjective idealist direction with the publication of Husserl’s Ideen in 1913. Over the next years, Ingarden became convinced that he had to develop phenomenology in a realist direction as against Husserl’s nascent “transcendental phenomenology”, and so his first book Essentiale Fragen (“Essential Questions”, 1925) began what should be a lifelong struggle with the realism/idealism issue. The idealism which Ingarden felt compelled to attack was not objective idealism, the issue of the reality foundation of general concepts, but modern, post-Cartesian, subjective idealism claiming that what appears as the real world is really, at bottom, the product of subjective intentional acts. Ingarden’s most well-known work, the 1931 Das literarische Kunstwerk, “The Literary Work of Art”, forms a major argument in this strife: by developing the regional ontology of purely intentional objects, with a main example in fictitious objects as presented in artworks, Ingarden wished to show that their ontological structure differs on a number of counts from those of real world objects—so that the latter could not be, like the former, mere products of intentions.²⁵¹ So, apart from proving to be one of the seminal works on literary theory of the 20th century, Das literarische Kunstwerk develops the general notion of “pure intentional objects” to cover objects understood as moments—rather than parts—of intentional acts. That theory, in turn, would continue to inform the central achievement of Ingarden’s career, the magisterial, if unfinished, multivolume work of Der Streit um die Existenz der Welt—“The Clash over the Existence of the World”.²⁵² The first two volumes of that book were written in Polish during the extreme conditions of WW2 in Poland, only to be rewritten in German by the author himself and appearing in Germany in the 1960s, while an English version of the first volume came out in 1964, and the remaining volumes are only currently being translated. The overall layout of the book is structured after a number of basic Ingardenian distinctions, namely those of Existential Ontology, Formal Ontology, and Material Ontology, respectively. Every possible object has an existential mode, a formal structure, as well as material qualities. The two latter concepts, of course, are Husserl’s from the Logische Untersuchungen, where they address structures shared by all possible objects vs. structures shared by objects belonging to a certain region of being, a material or regional ontology. Existential Ontology, Ingarden’s own addition, has nothing

Ingardenian Dependences

287

to do with existentialism, nor indeed with ontology in the narrow sense of a doctrine of what actually exists, rather it approaches eidetic phenomenology or Peircean phaneroscopy, or, again, conceptual analysis in analytic philosophy, in the sense that it scrutinizes the totality of merely possibly existing object categories—under a phenomenological bracketing of existence, as it were. All of the project’s initial two volumes, then, pertains two what may exist, while metaphysics proper, the general description of what really exists in this world, was the purported task of the third volume which never properly came into being.²⁵³ A large chunk of it, however, appeared much later, in 1974, dealing with the causal structure of the real world. In the first volume of the Streit, however, the main thrust of Ingarden’s argument rests on a generalization and further subarticulation of Husserl’s dependence calculus from the 3rd Logical Investigation. Possibly existing objects must be defined, so Ingarden, after which dependence relations they span to other objects. Their place in such dependence relations defines which types of “existential moments” they possess. This is developed in the first part of the book, adding, in the second part, an analysis of time, with Ingarden claiming that the past, present, and future must be described as all of them existing but endowed with different modes of being: Actuality, Post-Actuality, Empirical Possibility, and Non-Actuality, just like he distinguishes between three kinds of temporal entities: enduring objects, extended processes, and momentaneous events. Furthermore, distinctions pertaining to types of temporal existence are drawn between the monadic moments of Fissuration, Non-Fissuration, Fragility, and Persistence.²⁵⁴ Finally, Ingarden distinguishes three types of ontological domains: ideal qualities, individual objects, and ideas—remarkably close to Peirce’s three realms of Firstness qualities, Secondness individual objects or reactions, Thirdness general ideas or patterns.²⁵⁵ All of these different possibilities of existential moments, of course, are partially independent and may be combined; the resulting ontology is impressive in its width and its detailed categorization of possible types of existence.²⁵⁶ Here, we shall focus upon the elementary calculus of dependences from the first half of Streit’s Volume I. Let us go directly to discussing the four different versions of three-type dependences, which Ingarden found it necessary to develop to chart all possibly existing objects.²⁵⁷ He distinguishes between; 1) Autonomie vs. Heteronomie— which is an entity having its whole foundation of being within itself, vs. an entity being dependent for its existence and its entire repertoire of qualities on another entity. 2) Ursprünglichkeit vs. Abgeleitetheit—which is the inability of an entity to be created or destroyed by another entity, vs. the dependence of an entity on another in order to come into existence; 3) Selbständigkeit vs. Unselbständigkeit— which is the lack of requirement, in an entity, to form a whole with other entities

288

Chapter 17: The Riddle of Dependences

in order to be existent, vs. the dependence of an entity that can only exist if it coexists with something else within the confines of a single whole; and, finally 4) Unabhängigkeit vs. Abhängigkeit—which is when an entity is not only selbständig but also does not require the existence of any other selbständige objects, vs. the dependence of an entity on another in order to remain in existence. I initially present the four dependence types in German, as they have been translated in different ways in English.²⁵⁸ Here; I shall stick to the English translations of Ingarden 1964: 1) autonomy vs. heteronomy; 2) originality vs. derivation;3) separateness vs. inseparateness; 4) self-dependence vs. contingency. The first distinction comes out of the ontological effort undertaken in Das literarische Kunstwerk in so far as “heteronomy” is what characterizes “purely intentional objects”, like that of fictional characters or, indeed, all objects as they are immanently described in and by intentional acts. Heteronomy is also the form of being of future, empirical possibilities. All heteronomous objects are characterized by Ingarden’s famous “Unbestimtkeitsstellen”, that is, spots of indeterminacy. There are a lot of properties of Donald Duck or of the cake I am about to bake tomorrow which are indeterminate. Properties of Donald not mentioned in the canon of cartoons by Walt Disney, Carl Barks, etc. are simply indeterminate, just like the issue whether my apple pie will be burnt in the oven or not—given that the future needs not, on the ontological level, be determinist (whether that is the case in reality is an issue for later, metaphysical investigations). Thus, heteronomous objects are in a sense the “weakest” among dependent objects; even dependent objects in the other three dependencies are autonomous, such as, for instance, the contingent moment of red color in an object which, by the first dependence character, are autonomous. In the next dependence type, “originality” pertains to objects which cannot have been created. Examples are the personal God, or a Platonic idea of the Good (the examples are Johansson’s), other examples may be ideal relations such as those of mathematics. Objects lacking such originality are derived. This dependence relation largely distinguishes ideal objects, states-of-affairs, and relations from actual, empirical dito, the latter taken to be dependent upon the former. In the third dependence type, “separate” entities may exist in themselves, while inseparate objects are dependent upon some other objects for their existence. This comes close to Husserl’s original distinction between parts and moments where the latter comprehend properties of objects. Properties and events, e. g., are inseparate from objects and processes, respectively. Finally, in the fourth dependence type, any organism possesses, as such, the moment of “self-dependence”. The very same organism, however, conceived as a parent holds the opposite moment of contingency, because its parenthood de-

A Metalanguage of Dependences

289

pends upon the existence of offspring. As Johansson says, this is an ontological way of distinguishing monadic from relational, polyadic predicates. Past, present, and ideal objects are self-dependent. These four versions of dependence contribute a large deal of structure to Ingarden’s ontological zoo of possible beings. The only possible entities being independent in all the four senses of dependence are monotheist deities, maybe Spinoza’s universe of which everything else is but modes. Ingarden’s ontology, however, does not attempt to decide the metaphysical issue whether such absolute beings exist, only that they belong to the realm of the ontologically possible. The general combination of the four dependences with Ingarden’s series of other existential modes gives rise to four overall categories of entities, again, without taking it to be the task of ontology to decide whether any of them actually exists in our world. They may exist “(A) Absolutely (and thus be absolute entities), (B) Extratemporally (or ideally, and thus be ideal entities), (C) Temporally (or really, and thus be real entities), (D) Purely Intentionally (and thus be fictional entities)” (Johansson 2009, 3). They are only, however, the general framework for a much more detailed fauna of possible ontological beings adding further distinctions. Thus, dependences are taken as a very central tool by Ingarden in order to chart elementary relational predicates of possible forms of being— while temporal and endogeneous properties of the same beings are taken care of by monadic predicates.

A Metalanguage of Dependences The three scholars discussed here take their overlap with Husserl’s elementary triad of dependences in very different directions. However, in all of them, the dependence calculus remains at the heart of their doctrines, and further developments of it are crucial to the sophistication and idiosyncratic character of all the three of them. Peirce’s combination of dependences, charted by his triad of attention-focusing abstraction types, with the degeneracy idea permitting the partial relaxation of relational characteristics of dependence-defined categories, gives him a tool which serves at least two purposes: to integrate the growing number of triadic distinctions of his theory as not just the repetition of the same metaphysical schema over many different areas and problems, but also an internal, rational, generation of subtypes of Secondness and Thirdness phenomena. In Peirce’s monism, those categories are immediately taken to be relevant for mind as for nature alike, finding the six resulting categories both in nature and in its representations. Peirce stuck to the Kantian principle that metaphysical categories

290

Chapter 17: The Riddle of Dependences

should be derived from logic only, granting that the six-category scheme with its roots in mathematics and logic would immediately deliver categories applicable in metaphysics as well as in the empirical special sciences. Hjelmslev rarely, if ever, spoke explicitly about ontological issues, and with his inspiration from logical positivism, he obviously sought to minimize ontological commitments. Still, forming part of the linguistic turn, he elevated language and linguistic distinctions to a high and central position with no little ontological prominence, particularly as when he, in his famous, ambitious conclusion to the Prolegomena, predicts that glossematic linguistics will form the very entrance gate to all other fields of articulated knowledge and thereby realize the goal of “humanitas and universitas”. So, elementary distinctions drawn at the bottom of glossematics still may end up as crucial structures if not of the world itself, then in any possible understanding of it.²⁵⁹ To Ingarden, Husserl’s disciple, nevertheless taking his philosophy in a realist direction not so alien to Peirce, Husserl’s dependences of the Logische Untersuchungen remain a central tool in the construction of ontology and hence, any possible metaphysics. His diversification of dependence relations into four elementary types bears witness to an attempt to rationally distinguish between possible ontological domains such as deities, ideas, objects, properties, purely intentional objects, and much more, requiring specified dependence types with different scope and strength for their description. The wanting metaphysical part of material ontology of his investigation, however, leaves open how these dependences would prove to incarnate in the real world of metaphysics and the special sciences. A vain hope of this chapter would have been to reach a synoptical, common level of description where the dependence theories of Peirce, Hjelmslev, and Ingarden might be articulated in a metalanguage making possible if not their integration, then at least their clearer comparison. Such a Grand Unified Theory of Dependences remains, for now, a desideratum. Suffice it to say that with the continental and analytic schools seemingly being about to exhaust their separated development possibilities and, after a century apart, approaching mutual communication if not ecumenical reunification, dependence calculi for the charting of what is and what could be, in reality, signs, or both, provide a resource in the archives of 20th century thought which might once again prove valuable.

Chapter 18 Conscious Self-Control as Criterion for Reasoning … the faculty which has served to elevate man above all the rest of the fauna of our globe is the power of self-control. “Diversions of Definitions”, R 650, July 20 – 23, 1910, LoF I, 169

In his mature, creative period from around 1902, Peirce put a large emphasis on the principle that reasoning proper must be subjected to conscious control. Automatized inferences, be they undertaken by machines, animals, or unconscious human mental processes, do not, in this perspective, count as reasoning because there is no control to grant the validity of the results of the process. This does not imply that such processes cannot be trusted; most often they can, but it implies that whenever reason leaves its foundations in such automatic and quasi-automatic processes in order to chart new territory, its inferences must be self-controlled, in the sense of subjected to scrutiny by a conscious self. In modern parlance, you might say such automata may be able to produce true belief—but not justified true belief. A concise example of Peirce’s argument goes like this: Reasoning cannot possibly be divorced from logic; because, whenever a man reasons, he thinks that he is drawing a conclusion such as would be justified in every analogous case. He therefore cannot really infer without having a notion of a class of possible inferences, all of which are logically good. That distinction of good and bad he always has in mind when he infers. Logic proper is the critic of arguments, the pronouncing them to be good or bad. There are, as I am prepared to maintain, operations of the mind which are logically exactly analogous to inferences excepting only that they are unconscious and therefore uncontrollable and therefore not subject to criticism. But that makes all the difference in the world; for inference is essentially deliberate, and self-controlled (Harvard Lectures on Pragmatism, 1903, EP II, 188; CP 5.108).

This doctrine of philosophy of logic involves a diverse handful of prerequisites: the mature Peirce’s theories of consciousness, of ethical conduct, of self-control. Even if Peirce’s mature development of self-control beginning in 1902 does have connections to a host of his logical and semiotic innovations of the period, like different types of interpretants, hypostatic abstraction, theorematic reasoning, continuous predicates, etc., Peirce’s ideas in this field do not form a well-rounded, finished result like several other mature achievements, such as his 1903 sign theory or his system of Existential Graphs. So, in order to get a grasp of Peirce’s conception of self-controlled reasoning, we have to situate it on a brief investigation of its bases in these diverse presuppositions. Peirce’s deep originality probably lies primarily in his logic, semiotics, and pragmatism—yet his more experhttps://doi.org/10.1515/9783110793628-020

292

Chapter 18: Conscious Self-Control as Criterion for Reasoning

imental and, at times, extravagant endeavors in the philosophy of mind and cosmology intervene in the former on important and sometimes surprising points requiring examination.²⁶⁰ The discussion of conscious self-control, therefore, also involves some of Peirce’s rather ambitious cosmological ideas—which is not, however, to say that his idea of self-control necessarily implies such ideas.

Peirce’s Doctrine of Consciousness The basis of self-controlled reasoning in consciousness is precarious for a number of reasons. Peirce was—along with Frege and Husserl—leading the wave of strong anti-psychologism in logic and epistemology in late 19th century philosophy and beyond, which became crucial in both analytic and continental philosophy to this day.²⁶¹ From his earliest sketches of the 1860s to his last papers around 1910, Peirce never vacillates on the principle that logic is normative and should not be confused with how people actually think, nor with the psychological or neurological conditions supporting thinking processes in particular species. So, the appearance of the psychological or psychophysical notion of consciousness in the definition of reasoning forms an important challenge to Peirce’s strict anti-psychologism. But, also for the reason that consciousness, in Peirce’s pragmatist opinion, is not at all definitory for mind, self, or personality and plays but a relatively weak and marginal role in human behavior and activity in general, as compared to many contemporary ideas. Peirce’s description of consciousness is founded on his three categories developed on the basis of logic already in his 1867 On a New List of Categories. Using these categories, he redefined the standard tripartition of consciousness found in many 19th century philosophers and psychologists: feeling, will, and reason. An early version of Peircean categorization of consciousness goes as follows: It seems, then, that the true categories of consciousness are: first, feeling, the consciousness which can be included with an instant of time, passive consciousness of quality, without recognition or analysis; second, consciousness of an interruption into the field of consciousness, sense of resistance, of an external fact, of another something; third, synthetic consciousness, binding time together, sense of learning, thought (The Triad, 1885, CP 1.377).²⁶²

Feeling comprises all possible quality appearances in consciousness; this does not cover elementary sense or emotion qualities only but also e. g., the feeling of appreciating a complex artwork or the feeling of understanding a mathematical proof.²⁶³ Consciousness of interruption, clash, or error, by contrast, necessarily involves more than one feeling, and a particularly important type of this is

Peirce’s Doctrine of Consciousness

293

the involuntary change of feeling, which is what introduces the unconditionality of the external world and reveals the self to have been in error. Synthetic consciousness, finally, involves the fusion of several contents, typically into propositions, arguments, habits, and all larger complexes of feeling, struggle, and thought. All consciousness is intrinsically time consciousness and is extended in time and space. The three consciousness types of feeling, brute existence, and cognition merge in continuous experience, and every single act of consciousness will contain all three aspects—however, they have different relations to time. The former is momentaneous only, the middle involves at least a timespan sufficient to record the clash between two feelings and introduce the ego/non-ego distinction, while the latter, involving syntheses of the former two, ranges from simple propositions and inferences and all the way up to larger constructions of habit and thought, developing over longer timespans. Just like European Gestalt theorists of the period (Stumpf, Ehrenfels, etc.), Peirce may cite the example of the melody—or the inference chains of a mathematical proof—as example of synthetic consciousness transcending the briefer timespans of feeling or brute clash experience.²⁶⁴ The simplest consciousness type of Feeling occupies a special position: all mental activity is in need of Feeling in order to appear as conscious; simultaneously, however, the mind has no direct access to Feeling as it belongs to the fleeting moment exclusively, and every reflection upon it is already at a distance, potentially falsifying it. Thus, Peirce does not subscribe to what Sellars would later criticize as “the myth of the given”; cf. his lifelong skepticism against introspection as a reliable source of information about mental or psychical issues. The inferences subject to self-control belong to the latter of the three, the synthetic type of consciousness. This theory of consciousnesses makes Peirce an opponent to empiricist theories seeking to build psychology on the idea of elementary, immediate sense data as a basis of later, higher-level cognitive processing. Such ideas keep popping up, however, both in lay people and the discipline of psychology, because humans entertain a spontaneous and partly erroneous naïve psychology, an “instinctive theory” of their own psychological processes.²⁶⁵ It is correct, Peirce claims, that consciousness considered in the moment will consist of feeling or quale exclusively, but that does not imply that feeling or immediate sense data are elementary input to consciousness. Rather, isolated feelings or immediate sense data are post-hoc abstract constructions only, artificially isolating them from the ongoing chain of inferences forming the lifeline of consciousness. Consciousness, always involving all of the three aspects mentioned, rather takes “percepts” as input, involving feelings, existence, as well as cognition; such percepts are invariably signs about external objects or events, not of internal psychical ideas. Consciousness is primarily con-

294

Chapter 18: Conscious Self-Control as Criterion for Reasoning

scious about aspects of the external world which is a further reason why introspection is barred and credible information about the internal world is possible only by hypothetical reconstruction beginning with external percepts. Particularly, immediate consciousness—be it presented in “sense data”, feelings, or quale consciousness—is fleeting, disappearing with the moment and is not at all accessible to introspection, but to retroactive, hypothetical reconstruction only, both to the ordinary person’s own experience and to the scientific investigator of consciousness.²⁶⁶ Such reconstruction invariably involves the third, synthesizing kind of consciousness. A couple of further peculiarities, as against naïve, “instinctive” psychology, in Peirce’s theory must be mentioned. A corollary, particularly developed through the 1890s, is that generality is part and parcel of perceptual judgments. It is possible directly to observe some generalities, that is, they are not derived, higher-level psychical phenomena only but may form aspects of the external world directly perceived: We can understand one habit by likening it to another habit. But to understand what any habit is, there must be some habit of which we are directly conscious in its generality. That is to say, we must have a certain generality in our direct consciousness. Bishop Berkeley and a great many clear thinkers laugh at the idea of our being able to imagine a triangle that is neither equilateral, isosceles, nor scalene. They seem to think the object of imagination must be precisely determinate in every respect. (…) I can see no way of escaping the proposition that to attach any general significance to a sign and to know that we do attach a general significance to it, we must have a direct imagination of something not in all respects determinate (1893 addition to the 1877 Fixation of Belief in a draft of How to Reason, R 407; CP 5.371, n.).

As inferences involve generality at several levels, in their predicates, in their structure, in their logical principles, this is important for their control undertaken by the third kind of consciousness. Another, more extravagant aspect of Peirce’s theory is his speculations that consciousness may not be confined to the individual. As we shall see below, his broader concept of mind comprises large swathes of the individual’s unconscious activities, but also general aspects of the external world. The much narrower concept of consciousness, however, may also go beyond the individual to include pairs or groups of persons, even larger social groups and organizations. Here an expression of the idea from Peirce’s most romantic and spiritualistic period in the early 1890s around the first Monist paper series: “… there should be something like personal consciousness in bodies of men who are in intimate and intensely sympathetic communion. It is true that when the generalization of feeling has been carried so far as to include all within a person, a stopping-place, in

Consciousness and Unconscious Mind

295

a certain sense, has been attained; and further generalization will have a less lively character. But we must not think it will cease. Esprit de corps, national sentiment, sympathy, are no mere metaphors. None of us can fully realize what the minds of corporations are, any more than one of my brain cells can know what the whole brain is thinking” (Man’s Glassy Essence, 1892, EP II, 348; CP 6.271). Later, Peirce even extended this hypothesis to cover large parts of the cosmos; cf. around the same time as his intensive insistence on self-control: “Analogy suggests that the laws of nature are ideas or resolutions in the mind of some vast consciousness, who, whether supreme or subordinate, is a Deity relatively to us” (Harvard Lectures on Pragmatism, 1903, EP II, 184; CP 5.107). The degree of extension of consciousness beyond the individual continued to engage Peirce, but he never really settled on how to determine the exact scope or character of such extensions. The upshot, however, is that conscious, self-controlled reasoning is not necessarily a privilege of the individual but may also be undertaken by at least some human collectives; cf. Peirce’s insistence on science as a collective endeavor across generations. Conscious agents, then, be they individual or collective, are able to causally control, channel, and restrict reasoning: Finally, ascribing to consciousness the ability of self-control is possible only when assuming its causal efficiency, rejecting epiphenomenalism. But while I say this, it must not be inferred that I regard consciousness as a mere “epiphenomenon”; though I heartily grant that the hypothesis that it is so has done good service to science. (…) … it exercises a real function in self-control, since without it, or at least without that of which it is symptomatic, the resolves and exercises of the inner world could not affect the real determinations and habits of the outer world (A Survey of Pragmaticism, 1907, EP II, 419; CP 5.493).

Despite the rather marginal role which Peirce is willing to admit for consciousness in the larger perspective, it—or the process of which it is a part—is assumed to possess causal powers put to use in self-control.

Consciousness and Unconscious Mind Given the expansive notion of mind in Peirce’s objective idealism, the role of consciousness shrinks by comparison. Peirce aggressively attacked doctrines tending to identify mind or the psyche as such with consciousness, and, correlatively, he saw reason, however important, as paling in comparison to habit, instinct, and, in general, the unconscious parts of mind.²⁶⁷ Such ideas have two aspects: one is that individual as well as collective minds in humans are taken to vastly exceed their conscious parts or aspects. The other is that, in Peirce’s objective idealism, the external world itself has a strong mental aspect, residing in the

296

Chapter 18: Conscious Self-Control as Criterion for Reasoning

general laws, regularities, patterns active there, appearing to the individual mind in the shape of general predicates, so to speak objective mind dripping into the local mind of the individual.²⁶⁸ Vis-à-vis this truly ambitious conception of mind, the role of conscious reason seems to have reached an absolute low in Peirce’s spiritual period around 1890: “Swarming facts positively leave no doubt that vivid consciousness, subject to attention and control, embraces at any one moment a mere scrap of our psychical activity. (…) three propositions may be laid down. (1) The obscure part of the mind is the principal part. (2) It acts with far more unerring accuracy than the rest. (3) It is almost infinitely more delicate in its sensibilities” (Logic and Spiritualism, 1890, CP 6.569). Even if not remaining that pessimistic after his spiritual awakening began to wane in the mid-1890s, Peirce continued to judge the unconscious parts of mind to be larger and more important for everyday conduct than logic and reasoning, finding support in Eduard von Hartmann’s 1869 notion of the unconscious:²⁶⁹ Almost all the psychologists still tell us that mind is consciousness. But to my apprehension Hartmann has proved conclusively that unconscious mind exists. What is meant by consciousness is really in itself nothing but feeling. (…). But I do not believe that psychology can be set to rights until the importance of Hartmann’s argument is acknowledged, and it is seen that feeling is nothing but the inward aspect of things, while mind on the contrary is essentially an external phenomenon (Minute Logic 1902, CP 7.364).²⁷⁰

Humans typically overestimate their conscious powers and efforts, neglecting in their instinctive theories of psychology the vast amount of neural and mental processes preceding and conditioning consciousness. This is part and parcel of Peirce’s famous Humean conservative sentimentalism giving passions priority over reason on everyday matters, thus advising people to go with established gut feelings in ordinary life, unless in cases where there are strong experiential reasons to doubt those feelings and seek new ways: Invariably follow the dictates of Instinct in preference to those of Reason when such conduct will answer your purpose: that is the prescription of Reason herself. Do not harbor any expectation that the study of logic can improve your judgment in matters of business, family, or other departments of ordinary life. (…) But fortunately (I say it advisedly) man is not so happy as to be provided with a full stock of instincts to meet all occasions, and so is forced upon the adventurous business of reasoning, where the many meet shipwreck and the few find, not old-fashioned happiness, but its splendid substitute, success. When one’s purpose lies in the line of novelty, invention, generalization, theory—in a word, improvement of the situation—by the side of which happiness appears a shabby old dud—instinct and the rule of thumb manifestly cease to be applicable. The best plan, then, on the whole, is to base our conduct as much as possible on Instinct, but when we do reason to reason with severely scientific logic (Minute Logic 1902, CP 2.177– 178).

Consciousness and Unconscious Mind

297

With respect to consciousness in particular, this implies a complete reversal of received relations between consciousness and thought: “Only one must not take a nominalistic view of Thought as if it were something that a man had in his consciousness. Consciousness may mean any one of the three categories. But if it is to mean Thought it is more without us than within. It is we that are in it, rather than it in any of us” (Peirce to James, Nov. 25, 1902, CP 8.256). Here Peirce is writing against his friend James and against the psychologist’s notion that thoughts be completely private to the individual. Thought is vastly superior to consciousness, and individual unconscious thought shades into the general, mental aspects of the exterior. In the individual, the vast majority of mental processes, then, are not only unconscious, but involuntary, that is, beyond control. That ranges from the unconscious neural control of important physiological processes in the body and to the majority of acquired habits sunk to rehearsed automatisms:²⁷¹ Of excessively simple reasonings a great deal is done which is unexceptionable. But leaving them out of account, the amount of logical reasoning that men perform is small, much smaller than is commonly supposed. It is really instinct that procures the bulk of our knowledge; and those excessively simple reasonings which conform to the requirements of logic are, as a matter of fact, mostly performed instinctively or irreflectively. Reasoning, properly speaking, cannot be unconsciously performed. A mental operation may be precisely like reasoning in every other respect except that it is performed unconsciously. But that one circumstance will deprive it of the title of reasoning. For reasoning is deliberate, voluntary, critical, controlled, all of which it can only be if it is done consciously. An unconscious act is involuntary: an involuntary act is not subject to control; an uncontrollable act is not deliberate nor subject to criticism in the sense of approval or blame. A performance which cannot be called good or bad differs most essentially from reasoning (Minute Logic 1902, CP 2.181– 182).

What does this unconscious instinct comprise, dominating human mental life? Peirce made an ambitious attempt to list human instincts, unsurprisingly sorted in three large categories, pertaining to the individual, culture, and the human species, respectively: 1) health, food, house, collecting; 2) progeny, morals, magic, war; 3) imitation, play, conversation, clothes—just to give an idea of exactly what kinds of activities Peirce took to be primarily instinct-driven and involuntary, only resorting to conscious reasoning for innovation and science.²⁷² Not only instincts and habits, however, may be unconscious, that also hold for sensations. Peirce, together with his student Joseph Jastrow, was the first to experimentally investigate what was later called “subliminal perception”. They found that standard psychophysical claims about the existence of an “Unterschiedsschwelle”, a threshold of difference, below which human beings were unable to distinguish two almost identical stimuli, did not hold. Quite on the

298

Chapter 18: Conscious Self-Control as Criterion for Reasoning

contrary, they found that the distinguishing ability persisted into very small differences—albeit with no conscious insight in what subjects themselves experienced as mere guessing. The results of guesses, however, showed an ability of sensation below another threshold, that of consciousness. Thus, Peirce and Jastrow (1885, 83) concluded that “… it gives new reason for believing that we gather what is passing in one another’s minds in large measure from sensations so faint that we are not fairly aware of having them, and can give no account of how we reach our conclusions about such matters”. The two of them found this might explain current claims about telepathy. In our context, it also feeds into how Peirce thought that selves do not possess clearly distinct boundaries but may influence each other without noticing. The overall distinction between unconscious abilities and conscious reason, however, could not be sharp, but is subject to Peirce’s continuism: … anti-synechistic thinkers wind themselves up in a factitious snarl by falsifying the phenomena in representing consciousness to be, as it were, a skin, a separate tissue, overlying an unconscious region of the occult nature, mind, soul, or physiological basis. It appears to me that in the present state of our knowledge a sound methodeutic prescribes that, in adhesion to the appearances, the difference is only relative and the demarcation not precise (Issues of Pragmaticism, 1905, EP II, 347– 348; CP 5.440 – 441).

There is no strict borderline between un/consciousness, thought elements may drift back and forth between the two, and one may strive to become conscious, to some degree, of one’s unconscious habits, constituting the bulk of the Self.

The Self of Self-Control In this picture, with consciousness but a small part of the mind’s overall activities, which status is assigned to the Self? It is well-known that Peirce, as with his downplaying of consciousness, also attempted to give definitions of Self and Personality which largely deconstruct them as unitary substances, already from his early ideas of humans as signs (cf. below). Colapietro 1984 did much to establish a coherent doctrine out of Peirce’s scattered comments on the self, and he is right that the many famous places where Peirce defines the self negatively—by means of its errors or insufficiencies—are not necessarily negative in an evaluative sense of the word.²⁷³ This can be illustrated by Peirce’s famous detailed lake metaphor for the individual mind which he develops over a whole page:

The Self of Self-Control

299

Consciousness is rather like a bottomless lake in which ideas are suspended, at different depths. Percepts alone are uncovered by the medium. The meaning of this metaphor is that those which [are] deeper are discernible only by a greater effort, and controlled only by much greater effort. These ideas suspended in the medium of consciousness, or rather themselves parts of the fluid, are attracted to one another by associational habits and dispositions,—the former in association by contiguity, the latter in association by resemblance. An idea near the surface will attract an idea that is very deep only so slightly that the action must continue for some time before the latter is brought to a level of easy discernment. Meantime the former is sinking to dimmer consciousness. There seems to be a factor like momentum, so that the idea originally dimmer becomes more vivid than the one which brought it up. In addition, the mind has but a finite area at each level; so that the bringing of a mass of ideas up inevitably involves the carrying of other ideas down. Still another factor seems to be a certain degree of buoyancy or association with whatever idea may be vivid, which belongs to those ideas that we call purposes, by virtue of which they are particularly apt to be brought up and held up near the surface by the inflowing percepts and thus to hold up any ideas with which they may be associated. The control which we exercise over our thoughts in reasoning consists in our purpose holding certain thoughts up where they may be scrutinized. The levels of easily controlled ideas are those that are so near the surface as to be strongly affected by present purposes. The aptness of this metaphor is very great (Untitled, probably c. 1896, CP 7.554).²⁷⁴

Another variant adds the idea of a constant rain over the lake adding new percepts to the consciousness of its surface layers. The lack of bottom in the other end goes into unconscious mind, further into its physiological base and pre-individual biological origin, thereby also connecting it to other such lakes. Consciousness is located in the top layers of the lake and diminishes with depth. This fits with a different liquid metaphor, that “the ego is a mere wave in the soul” (Principal Lessons on the History of Science, 1896, CP 1.112). The lake metaphor is couched in Peirce’s 1890s practice of speaking of “ideas” in the mind, as in the first Monist papers; in most other periods before and after, Peirce would speak of signs, symbols, or propositions. Ideas or signs, they coalesce to form connected networks of habits and dispositions—signs pragmatically being oriented towards conceived practical effects and actions. And in the unconscious, pre-critical depths of the lake, such networks of signs follow the classic associationist laws of similarity and proximity. Within this network of signs, the self is characterized by Peirce’s description of personality as a “bundle of habits”.²⁷⁵ As a habit is a general rule of action of the shape: ’if such-and-such a situation occurs, then do so-and-so’, this continues the inferentialist idea of the self, but now with the emphasis that most such habits are not conscious (cf. Chapter 2). As says Colapietro: “The conception of the personality as a coordination of ideas (6.155; 1892) was replaced in this third moment by the conception of it as a unity of habits (6.228)”, and he goes on to quote what he finds the single most seminal description of the self in Peirce:

300

Chapter 18: Conscious Self-Control as Criterion for Reasoning

Two things here are all-important to assure oneself of and to remember. The first is that a person is not absolutely an individual. His thoughts are what he is “saying to himself,” that is, is saying to that other self that is just coming into life in the flow of time. When one reasons, it is that critical self that one is trying to persuade; and all thought whatsoever is a sign, and is mostly of the nature of language. The second thing to remember is that the man’s circle of society (however widely or narrowly this phrase may be understood), is a sort of loosely compacted person, in some respects of higher rank than the person of an individual organism. It is these two things alone that render it possible for you but only in an abstract, and in a Pickwickian sense—to distinguish between absolute truth and what you do not doubt (What Pragmatism Is, 1905, EP II, 338; CP 5.421).

Just like Peirce’s shrinking of the role of consciousness in the mind, his description of personality in terms of bundled networks of habits forms a radical reduction as compared to more substantialist conceptions of personality, and Peirce has but scorn against what he considers too exaggerated and indeed selfish notions of personality. Most of the personality habit bundle is unconscious, and the self is subjected to an important tension between unity and dispersion. Its unity Peirce originally conceived along the lines of Kant’s famous “I think” accompanying all conscious acts, and later he described it in yet another metaphor: a map of a landscape placed in that very landscape.²⁷⁶ Here, the topological theorem that a mapping of a manifold upon itself has at least one constant point gives Peirce the idea to consider that the map, of course, contains a copy of itself, that copy again a copy, and so on in infinity. The constant point through all the maps of maps of maps, then, is an image of self-consciousness being a constant point, a self-referential sign, through successive phases of the self. This notion of unity, however, is weak in at least two senses. It does not entail that the bundles of habit form one whole rather than several, nor that those bundles possess any clear boundary. Selves may have different degrees of connectedness, and Peirce refers to contemporary research into multiple personalities: “Perhaps it may be thought that hypnotic phenomena show that subconscious feelings are not unified. But I maintain on the contrary that those phenomena exhibit the very opposite peculiarity. They are unified so far as they are brought into one quale-consciousness at all; and that is why different personalities are formed. Of course, each personality is based upon a ‘bundle of habits’, as the saying is that a man is a bundle of habits. But a bundle of habits would not have the unity of self-consciousness. That unity must be given as a centre for the habits” (Logic of Events 1897, CP 6.228). So, the unity of the individual self is not only weak; there may even be several of them, more or less interconnected, in the same body. The bundle-of-habits idea of the self may also make it clearer why the borders of consciousness and self are so porous: the individual bundle of signs and habits may be shared, to a large degree, with other individuals. And the bundle

Self-Control and Reasoning

301

of the individual may be defective and wanting as compared to the larger networks he or she is connected to, not to speak of the even larger such sign networks of groups or cultures, humanity as a whole, or the cosmos. So, this is a root of Peirce’s recurring definitions of the self by means of lack or error, originating in the basic ur-experience of the ego when one feeling is denied by the forceful external imposition of another; later in life generalized by the realization that one’s own sign network is defective as measured on many other such networks with which it connects. A final important consideration leads in the direction of self-control: the rather minuscule roles of consciousness and self within the mind are not necessarily understood by themselves. To Peirce, that is the root of many flattering, much too ambitious theories of the two, but also the root of overblown personal vanity, self-overestimation, and selfishness in the individual. Individuals, therefore, are urged to realize their close interconnectedness and quasi-identity with other individuals, one the one hand, as well as to struggle to perfect their lamentable, quasi-disconnected selves by means of a lifelong process of increasing self-control, on the other, leading them out of egoism and pointing them towards higher, ideal aims (cf. the following chapter). It may appear as quite surprising that such weak, loosely connected, and deliquescent conscious selves on the thin surface of the mind and merging into their more able semiotic surroundings should really be able to come together to take a stand as strict controllers of reasoning. That is a central Peircean riddle to which we now eventually turn.

Self-Control and Reasoning Peirce emphasized the role of self-control in ethics already in the 1860s but only beginning in the late 1880s did he focus on the issue of the normative control of logical inferences.²⁷⁷ In a 1893 manuscript revisiting the associationist tradition, he continues the “Law of Mind” idea that the basis of thought is the synthesis or clustering of ideas, so that the origin of logical processes are here seen as a sort of bottom-up thermodynamics of ideas connecting by means of largely unconscious associations: Such inferences are beyond the jurisdiction of criticism. It is the part of psychology to explain their processes as it can; but, as long as they are out of the focal plane of consciousness, they are out of our control; and to call them good or bad were idle. The ordinary business of life is, however, best conducted without too much self-criticism. Respiration, circulation, and digestion are, depend upon it, better carried on as they are, without any meddling by Reason; and the countless little inferences we are continually making,—be they ever so defective,—are, at any rate, less ill performed unconsciously than they

302

Chapter 18: Conscious Self-Control as Criterion for Reasoning

would be under the regimen of a captious and hypochondriac logic. Quite otherwise is it with the actions which carry out our grander purposes. Here all must be voluntary, thoroughly conscious, based on critical reflection. Logic is wanted here, to pull inferences to pieces, to show whether they be sound or not, to advise how they may be strengthened, to consider by what methods they ought to proceed (Association of ideas, 1893, CP 7.448 – 449).

The vast majority of human everyday life is governed by unconscious associations and habits—governing it well—while the “grander purposes” breaking with everyday routines must be, by contrast, governed by logical self-control. The decisive questions now: how can such self-control “pulling inferences to pieces” be described, which forms may it take, how does it proceed? Here we shall address a number of issues: 1) the relation of logical self-control to ethical self-control; 2) self-control, inhibitory or creative; 3) the details of self-control processes of internal dialogue; 4) levels of self-control—the role of hypostatic abstraction; 5) machine and animal counterexamples; and finally, 6) the role of consciousness in the execution of self-control.²⁷⁸

Ethics and Logical Self-Control In his strong semiotic-philosophical push in the first years of the 20th century, Peirce realizes that logical self-control is but a species of the more encompassing genus of ethical self-control—leading him to elevate ethics (and even higher, aesthetics) to sciences superior to logic in his flowering classifications of sciences (e. g., in the 1902 Carnegie application). Thus, “Ethics, or the science of right and wrong, must appeal to Esthetics for aid in determining the summum bonum. It is the theory of self-controlled, or deliberate, conduct. Logic is the theory of self-controlled, or deliberate, thought; and as such, must appeal to ethics for its principles” (“Classification of the Sciences”, Syllabus, 1903, EP II, 260; CP 1.191). In ethics, self-control is taken to be not only what permits humans to pursuing their aims in thought-out action sequences, it is also what leads humans out of narrow selfishness to pursue higher ideals, over a never-ending lifetime process, simultaneously developing and strengthening personality: “Man comes from the womb in actuality and animal little higher than a fish; by no means as high as a serpent. His humanity consists in his destination. He becomes not actual man until he acquires self-control and then he is so in the measure of his self-control” (The Argument for Pragmatism Anachazomenally or Recessively Stated, R 330, c. 1907, no pagination).²⁷⁹ Self-control is thus required for controlled action in the moment, but also an overall, ethical, character-building endeavor on a larger scale: “At any rate, our power of self-control certainly

Ethics and Logical Self-Control

303

does not reside in the smallest bits of our conduct, but is an effect of building up a character. All supremacy of mind is of the nature of Form” (Some Amazing Mazes, 1908, CP 4.611).²⁸⁰ In the particular case of logic, self-control builds on an ideal of rule-following: “… reasoning is a species of controlled conduct and as such necessarily partakes of the essential features of controlled conduct. (…) every inference forces itself upon us irresistibly. That is to say, it is irresistible at the instant it first suggests itself. Nevertheless, we all have in our minds certain norms, or general patterns of right reasoning, and we can compare the inference with one of those and ask ourselves whether it satisfies that rule” (What Makes a Reasoning Sound?, 1903, EP II, 250; CP 1.606). Such rules do not, however, generate inferences which rather appear spontaneously, uncontrolled, bottom-up, to be controlled post-hoc. The thermodynamics of associative idea-generation of the 1890s is supplied with an ensuing control phase weeding out bad results—a quasi-Darwinian schema of variation-followed-by-selection often employed by Peirce. The 1900s are also the period where Peirce develops his general idea of diagram experiments as source of knowledge, and they add a more controlled aspect also to the generation of inferences: … the secret of rational consciousness is not so much to be sought in the study of this one peculiar nucleolus, as in the review of the process of self-control in its entirety. The machinery of logical self-control works on the same plan as does moral self-control, in multiform detail. The greatest difference, perhaps, is that the latter serves to inhibit mad puttings forth of energy, while the former most characteristically insures us against the quandary of Buridan’s ass. The formation of habits under imaginary action (see the paper of January, 1878) is one of the most essential ingredients of both; but in the logical process the imagination takes far wider flights, proportioned to the generality of the field of inquiry, being bounded in pure mathematics solely by the limits of its own powers, while in the moral process we consider only situations that may be apprehended or anticipated (Issues of Pragmaticism 1905; CP 5.440, EP II, 347).

The original birth certificate of pragmatism, the 1878 “How to Make our Ideas Clear” is now reinterpreted and recruited as a doctrine of self-control. The notion of “Formation of habits under imaginary action” refers to the idea of imagining fictitious situations and actions before they occur so as to be ready for thought or action if and when such situations should appear for real. But is self-control thus creative or is it rather a mere sieve to strain away acritical inferences created elsewhere?

304

Chapter 18: Conscious Self-Control as Criterion for Reasoning

Self-Control: Inhibitory or Creative? There seems to be a certain tension in Peirce’s descriptions of self-control. One the one hand, we may find claims that the action of self-control is purely inhibitory: it only serves the role of weeding out emerging examples of bad reasoning, but not at all otherwise contributing to the furthering of reasoning. On the other hand, we may find repeated insistence that diagram experiments in the imagination of future action possibilities is part and parcel of the process of self-control. The former argument appears in the interesting context of a phenomenology of logic attempting to answer the issue of the origin of logical forms of inference, a bit like Husserl’s Erfahrung und Urteil. As to the matter or content of inferences, it is dealt with by referring to the idea that at some point, the chain of inferences must have begun with premises not themselves the result of conscious inference, but rather stemming from “the uncontrolled parts of the mind”—deeper in the lake, as it were. But such an argument would not solve the even deeper issue of the origin of the very form of inference schemas themselves, the “leading principles”: But as to the logical form, it would be, at any rate, extremely difficult to dispose of it in the same way. An induction, for example, concludes a ratio of frequency; but there is nothing about any such ratio in the single instances on which it is based. Where do the conceptions of deductive necessity, of inductive probability, of abductive expectability come from? Where does the conception of inference itself come from? That is the only difficulty. But self-control is the character which distinguishes reasonings from the processes by which perceptual judgments are formed, and self-control of any kind is purely inhibitory. It originates nothing. (…) What can our first acquaintance with an inference, when it is not yet adopted, be but a perception of the world of ideas? In the first suggestion of it, the inference must be thought of as an inference, because when it is adopted there is always the thought that so one might reason in a whole class of cases. But the mere act of inhibition cannot introduce this conception. The inference must, then, be thought of as an inference in the first suggestion of it. Now when an inference is thought of as an inference, the conception of inference becomes a part of the matter of thought. Therefore, the same argument which we used in regard to matter in general applies to the conception of inference (Harvard Lectures on Pragmatism, 1903, CP 5.194).

In order to be able to judge inference candidates appearing before the mind, selfcontrol has to be acquainted with the elementary forms and rules of inferences to be able to see whether those candidates fit the pattern, so to speak. It cannot itself be responsible for generating or discovering those rules. Inferences and their forms must be there before any self-control of them. Peirce attempts to solve the problem by means of self-reference in the appearance of the very first inference: when self-control thinks of an inference as an inference, that inference passes

Self-Control: Inhibitory or Creative?

305

from form to becoming the matter of a higher-order inference. This makes it amenable to the same argument as the matter of inferences, he claims—the upshot must be that it, too, derives from some uncontrolled region of the mind.²⁸¹ This would fit with Peirce’s insistence that humans have an innate, if not perfect, pre-self-control capacity for reasoning and understanding the world, assumedly supported by Darwinian arguments. Such an imperfect capacity could then be fine-tuned by self-control of self-control; cf. below on levels. This is developed further in Peirce’s late 1908 doctrine of “continuous predicates”.²⁸² They are predicates so to speak emptied of all non-logical content, so that what remains are signs like “_possesses the character_”, “_stands in the relation of_to_”, “_ occurs concurrently with_”; other candidates could be “_is identical to_”, “_is teridentical to_and_”, “_implies_”, “_is co-localized with_”, etc. Of such signs, Peirce says that “These signs cannot be explicated, they must convey familiar universal elementary relations of logic. We do not derive these notions from observation, nor by any sense of being opposed, but from our own reason” (Letter to Lady Welby, Dec. 25, 1908, EP II, 184; CP 8.352). So, they form existing rational structures for inhibitive self-control to work with. But how does this idea of self-control as merely inhibitive or selective fit with the description of its “fancied reiterations” which facilitate the creation of new action habits, determining future behavior? Many times, we hear about how repeated practicing will shape and strengthen habits of self-control, both in morality and logic, and how this practicing, in both cases—but particularly in logic— may take place in the imagination so that a well-practiced habit sits ready to give rise to premeditated action if the relevant situation arises: Moreover,—here is the point,—every man exercises more or less control over himself by means of modifying his own habits; and the way in which he goes to work to bring this effect about in those cases in which circumstances will not permit him to practice reiterations of the desired kind of conduct in the outer world shows that he is virtually well-acquainted with the important principle that reiterations in the inner world—fancied reiterations,—if well-intensified by direct effort, produce habits, just as do reiterations in the outer world; and these habits will have power to influence actual behaviour in the outer world; especially, if each reiteration be accompanied by a peculiar strong effort that is usually likened to issuing a command to one’s future self (Pragmatism, 1907, R 318, 57).

This obviously also holds for the establishment of that important subset of habits which are habits of thought and reasoning. The solution to the enigma of inhibition versus creation, I think, must be sought in two different uses of the notion of self-control, one narrow, stepwise, inhibitory, and one broader, of which inhibition is a basic component, but which describes its nesting within an overarching process of voluntary, purposive habit-forming and habit-change.

306

Chapter 18: Conscious Self-Control as Criterion for Reasoning

These two meanings of self-control may be combined so that the former constitute steps in the overarching purpose-orientation of the latter. Importantly, this feeds into Peirce’s epistemological discussion of how a series of single, simple, logically necessary steps may combine to form an overall chain of thought that is original. His example is mathematical proofs, which are not automatic algorithms but rather driven by the intention of reaching the goal of proving a particular theorem, seeking to attain this aim by a series of exploratory steps not pre-determined. Peirce considers the possibility of automatization of such deductions: … that necessary reasoning takes a course from which it can no more deviate than a good machine can deviate from its proper way of action, and that its future work might conceivably be left to a machine—some Babbage’s analytical engine or some logical machine (of which several have actually been constructed). (…) … the tendency of the logic of relations itself—the highest and most rational theory of necessary reasoning yet developed—is to insinuate the idea that in necessary reasoning one is always limited to a narrow choice between quasi-mechanical processes; so that little room is left for the exercise of invention (Some Amazing Mazes, 1908, CP 4.611).

This, however, is erroneous, according to Peirce, and he claims that even the great 19th-century English-American mathematician James Joseph Sylvester falls prey to such self-misunderstanding when he almost apologizes for failing to always reach his conclusions by way of apodictic procedures. Sylvester may refer to the correct fact that accidental experience or a happy guess can lead to the solution of a mathematical problem, Peirce says, but still it remains correct that “all genuine mathematical work, except the formation of the initial postulates (if this be regarded as mathematical work) is necessary reasoning” (Some Amazing Mazes, 1908, CP 4.611). Peirce here, implicitly, seems to distinguish the context of discovery from the context of justification; cf. Reichenbach’s later terminology, the former may be accidental, while the latter is necessary. This takes Peirce to this important observation that: The mistake of Sylvester and of all who think that necessary reasoning leaves no room for originality—it is hardly credible however that there is anybody who does not know that mathematics calls for the profoundest invention, the most athletic imagination, and for a power of generalization in comparison to whose everyday performances the most vaunted performances of metaphysical, biological, and cosmological philosophers in this line seem simply puny—their error, the key of the paradox which they overlook, is that originality is not an attribute of the matter of life, present in the whole only so far as it is present in the smallest parts, but is an affair of form, of the way in which parts none of which possess it are joined together (Some Amazing Mazes, 1908, CP 4.611).

The Self-Control Process

307

Originality lies in the overall construction of the whole of a mathematical proof, not in any of its single steps, but in their combination. Peirce exemplifies and generalizes this by the following brief analysis of Napoleon’s particular genius (cf. on “Great Men” in the following chapter): Every action of Napoleon was such as a treatise on physiology ought to describe. He walked, ate, slept, worked in his study, rode his horse, talked to his fellows, just as every other man does. But he combined those elements into shapes that have not been matched in modern times. Those who dispute about Free-Will and Necessity commit a similar oversight (Some Amazing Mazes, 1908, CP 4.611).

Peirce concludes this argument with the quote about self-control above, that it resides in the overall build-up of character in the individual.²⁸³ In the same way, the single, inhibitory steps of self-control combine to form an overarching process of self-control, aiming to shape future conduct of action and thought after some purpose. The mathematical proof serves as a generalizable example here: the theorem to be proved is already known, and the aim of the whole self-controlled proof process is to somehow logically get there. This purpose so to speak recruits the single building-blocks of inhibitory self-control in a combination which may not be mechanically predicted, until the theorem is (maybe) finally proved. Peirce here implicitly relies upon his contemporary development of the important distinction of corollarial and theorematic deductions, the former a version of Kantian deduction where the conclusion is merely making explicit what was already there in the premises, while the latter is taken to cover more difficult mathematical proofs requiring the introduction of material not present in the premises, like auxiliary lines in geometry. Such introduction is an original, abductive step and de-banalizes the understanding of deduction, such as Jaakko Hintikka argued.²⁸⁴ This unpredictability of the investigation process is one of the things that sets self-control apart from automatized inference processes; cf. about machines and instincts below. This doubleness of inhibitory and creative is also involved in the detailed sequencing of the larger self-control process.

The Self-Control Process The mature Peirce gives a number of shots at the more elaborate description of the phases of the self-control process, a task he initiated in detail through 1903 – 1906. A brief version goes like this: “… its essential features are review, critical comparison with previous decisions or with ideals, rehearsal in the imagination of future conduct on various possible occasions, and the formation or modifica-

308

Chapter 18: Conscious Self-Control as Criterion for Reasoning

tion thereby of habits or dispositions of the occult something behind consciousness” (Notes on Portions of Hume’s Treatise of Human Nature, 1905, R 939, 3 – 5). Here, inhibition initiates the first step of “… review, critical comparison with previous decision or with ideals”, the idea being that if such comparison turns out to be unfavorable, the inference subject to control will be ditched. After this first inhibitory phase follows the subsequent use of inferences having passed the first phase in habit formation. Here comes the imagination-of-future-conduct phase, spreading over different subtypes of occasions where the inference is relevant. Such imagination practices, essentially a version of diagram experiments, must involve the full test of abductions (let us try our new insight on this type of occasion), followed by deductions (in that case, such and such implications would follow), and inductions (would such implications, again, fit with other collected knowledge of such situations)—leading to higher-level inhibitions to weed out conclusions not fitting the relevant ideal.²⁸⁵ Only the results of this test, presumably, will give rise to action resolutions, aiming to instill a new habit, possibly automatized by subsequent mental or real repetition training, thereby possibly affecting non-conscious habit patterns so as to stay ready if a situation of the imagined kind should occur. As always, “habit” and “action” comprise not only external, physical behavior but just as well the action type of future thought. This process also involves considerations in case an inference or action candidate did not pass the inhibitory control phase, just like it involves training or preparation of self-control in itself, as in this more detailed account of the process: After every occasion on which one has acted in any marked manner, one will, if not too pressed, review one’s conduct, and tell oneself how one likes it. If one is highly satisfied, one will go over it again; and imaginary performances are nearly as effective as real ones in establishing habits. But if one blames oneself, one proceeds to analyze and to determine wherein one erred by comparison either with one’s resolutions or with one’s ideal. One considers how the errors might be avoided. One resynthetizes, and enacts another proposed line of conduct before the imagination. Perhaps several. When one’s selection is made one rehearses in imagination the future performances again and again, as if one were committing it to memory, putting particular stress on the passages where one is liable to be surprised by a sudden impulse. Perhaps one says to oneself (all meditation being in dialogue): why did I not behave as I intended to behave, and how am I to make sure of doing so next time? Or perhaps one says: I acted as I had resolved to act. How did I ever come to suppose such conduct would meet any approbation? These are mentioned as specimens of possible complications. All self-control is affected by self-preparation. Its essential parts are, four; viz:—1st, the review of past conduct, 2nd, esthetic valuation of that conduct, 3rd, analytic criticism of the faulty parts and of how they might be mended; 4th, synthesis and imaginative rehearsal of proposed future conduct tending even to a habit of so behaving (Materials for Monist Article: The Consequences of Pragmaticism, 1905, R 288, version I, 25 – 33).

The Self-Control Process

309

The final formation of such a new habit, importantly, is seen as a form of mechanization or automatization. Thus, conscious self-control is, in a sense, but an intermediary update check of the human machinery of largely unconscious mind. In itself, this phase has at least three steps, first a resolve, an inference conclusion of the imaginary future experiments, then the addressing of oneself in a determination, and finally the result of that decision in the shape of a more or less complete automatization of an action sequence or thought sequence relevant to the situation types investigated:²⁸⁶ The power of self-control is certainly not a power over what one is doing at the very instant the operation of self-control is commenced. It consists (to mention only the leading constituents) first, in comparing one’s past deeds with standards, second, in rational deliberation concerning how one will act in the future, in itself a highly complicated operation, third, in the formation of a resolve, fourth, in the creation, on the basis of the resolve, of a strong determination, or modification of habit. This operation of self-control is a process in which logical sequence is converted into mechanical sequence or something of the sort. How this happens, we are in my opinion as yet entirely ignorant. There is a class of signs in which the logical sequence is at the same time a mechanical sequence and very likely this fact enters into the explanation (Letter from Peirce to F.C.S. Schiller, probably 1906 like 8.321, CP 8.320).

Self-control of habits, thus, is a sort of self-induced programming of the human mind utilizing the computational possibility of transforming a logical sequence into a mechanic sequence.²⁸⁷ In “What Makes a Reasoning Sound?”, the first of the 1903 Lowell Lectures (EP II, 245 ff.; CP 1.591 ff.), Peirce goes into some detail about the self-control process. Here, he isolates no less than eight overall phases: 1) Adoption of an ideal, more or less developed 2) An intention to shape one’s conduct according to that ideal 3) The articulation of a rule of action for some future occasion, simultaneously minimizing the “wiles of the devil” in the person 4) The anticipation of a specific future occasion where that rule will be relevant, and the gathering of forces considering how one will then act, resulting in 5) A resolution to act in a certain way on the imagined occasion, in the shape of a diagram or a plan 6) The imprinting of that resolution on oneself 7) The resulting determination to act, the establishment of a persistent action habit which is now the “really efficient agency” (246) for the future action once it arrives.

310

Chapter 18: Conscious Self-Control as Criterion for Reasoning

8) A capacity for post-hoc comparing the resulting actions with the 1) ideal, potentially giving rise to a new 8-step sequence (cf. Atkins 2016, 184 f.). As Atkins emphasizes, the resulting determination is the actual efficient agency of conduct—that role is not played by desire which may accompany or motivate some of the phases and components of self-control or not (thus, this constitutes Peirce’s argument against hedonism and its claim that desires desiring their own gratification be the motors of action; Atkins 2006, 191). An important issue remains here: as the future is necessarily underdetermined, determination cannot foresee future action sequences in all possible detail. It could not be completely correct, then, as Atkins says, that determinations are not general (2006, 189). They are considerably less general than desires, indeed, but being habits, they must remain on some level of generality. Maybe this conundrum was the reason Peirce continued to take interest in further specification of the action sequence in the self-imprinting of determinations, so to speak the deliberate diminishing the degree of generality in order to enhance control over single sub-phases of future events. The investigation of the self-training phases establishing the action habit (bullets 4– 7 in the 1903 scheme) reaches its largest detail in a very late sketch titled “Self-government”: “He establishes this government; and then he is bound. But only by his own free and reasonable act, which is world-wide apart from being bound by nature. It is a free government” (A Sketch of Logical Critic, 1911, R 675, Second Draft, 18 – 20).²⁸⁸ Kant’s notion of autonomy as self-legislation lurks in the background. Here, Peirce lists nine steps as follows, almost in the shape of a self-help training manual for habit improvement, now with the emphasis on fleshing out in detail the imagined conduct, associating each of those details with imagined feelings and imprinting the result so as to form a determination, all of it subjected to training by repetition: 1) “… self-critiques of conduct must be regularly kept up” 2) Repetition of an act in imagination 3) Rendering vivid all details 4) Attention to feelings accompanying those details 5) Focusing especially on difficult parts of the act 6) Making a resolution—by a strenuous self-command 7) Repeating this, again, half a dozen times 8) Make determination strong, so as to performing it almost unconsciously, automatically 9) Making a “movement of the soul” accompanying determination²⁸⁹

The Self-Control Process

311

The overall scheme remains the same already established, yet detailing subarticulations of the imagination and determination phases, with special respect to imagining and memorizing details of the action sequence and repeating these as well as the determination to oneself. Particular emphasis is here put on how the general rule established in step 4) of the 1903 scheme is now detailed with respect to a more specific, even if still to some degree general, action sequence in an imagined future occasion. Each phase, moreover, here is expressed in a way so as to overcome a certain inertia or counterargument. Peirce’s phase dissections of the self-control procedures immediately pertain to deliberate activity in general, subject to moral assessment. But they carry over to that important subspecies of deliberate action which is reasoning. First, the whole process of imaginary self-training regarding future action is, in itself, a piece of reasoning, inferring a number of implications from an ideal. Second, when the object of self-training is reasoning itself, self-control extends itself to not only checking inferences already made, comparing them to more or less explicit standards of leading principles, but to improving future inference procedures by imagining them in logical step-by-step detail. In that sense, the “creative”, not only inhibitory version of self-control implies the self-critical exercising of inference steps to stay ready for future challenges for reason. An important upshot of this development of the syntax of self-control is the idea that it takes place in a sort of constant dialogue with one’s future self, in no less than two senses: 1) the immediate proposing/inhibiting interaction within the ongoing dialogue of thinking where the future self is that of the immediate next moment, ready to voice a counterargument. And 2) the more remote future self at the unknown later time, supposedly being prompted to perform the action trained. The former is a special version of the mature Peirce’s more overall analysis of reasoning to take place in a constant feedback between a “utterer” and an “interpreter”, that is, a proposer and a critic, or a verifier and a falsifier, taking turns in roles opposed vis-à-vis each other—in the conduction of proofs in the Existential Graphs nicknamed a “Grapheus” and a “Graphist”.²⁹⁰ Each step in Peirce’s process descriptions of self-control, then, has the shape of countering imagined objections by an Advocatus Diaboli in an ongoing ping-pong. A much slower dialogue, then, is the second one with the remote future self, possibly reporting back when occasion rises to test the newly-established habit in practice, comparing actual action results with action rules and their motivating ideal.

312

Chapter 18: Conscious Self-Control as Criterion for Reasoning

Levels of Self-Control and Hypostatic Abstraction This process description of self-control in its pro-and-con phases forms a, so to speak, horizontal issue of self-control. Quite another, then, is the vertical issue of how one control may take another, already established control, as its object. Also, in 1905, Peirce considered this relation: “… control may itself be controlled, criticism itself subjected to criticism; and ideally there is no obvious definite limit to the sequence” (Issues of Pragmaticism, 1905; EP II, 349; CP 5.543). The idea is illustrated with the example, often cited in later cybernetics literature, of how 19th century steam engines were equipped with a “governor” facilitating feed-back control by the letting out of steam at a certain pressure threshold to avoid a too fast working pace, which might potentially damage machinery.²⁹¹ That governor, in turn, may be controlled by a further higher-level governor so as to avoid the former’s kicking in too suddenly and making too abrupt a velocity brake, also threatening the machine: … man’s machinery is provided with an automatic governor upon each and every governor to regulate it by a consideration otherwise not provided for. For while an automatic governor may be attached to any governor to prevent any given kind of excess in its action, yet each such attachment complicates the machine; and not to speak of the impossibility of ever planning an infinite multitude of distinct contrivance, the disadvantages of complication in artificial machinery are so serious, that the automatic government of the governor of a governor is, I suppose, a thing hardly to be seriously considered, while in the human machine,—or, at least, in the cortex of the brain, or in whatever part it be whose action determines of what sort the man’s conduct shall be, there seems, as far as we can see no limit to the self-government that can be and will be brought to bear upon each such determining action, except the lack of time before the conduct which was to be determined must come into actual play (On Definition and Classification, 1910, R 649, 20 – 21; LoF III, 399).

Here, a distinction between human and machine is proposed based on the idea that the series of governors governing governors must reach an end due to ensuing complications of mechanisms, while humans supposedly are able to construct an indefinite number of levels of conscious self-control. That is hardly a strong argument, empirically dependent on the development of machines as it remains; cf. the following section. Stronger is a first sketch Peirce gave of the details of these levels in the central self-control year of 1905: To return to self-control, which I can but slightly sketch, at this time, of course there are inhibitions and coördinations that entirely escape consciousness. There are, in the next place, modes of self-control which seem quite instinctive. Next, there is a kind of self-control which results from training. Next, a man can be his own training-master and thus con-

Levels of Self-Control and Hypostatic Abstraction

313

trol his self-control. When this point is reached much or all the training may be conducted in imagination. When a man trains himself, thus controlling control, he must have some moral rule in view, however special and irrational it may be. But next he may undertake to improve this rule; that is, to exercise a control over his control of control. To do this he must have in view something higher than an irrational rule. He must have some sort of moral principle. This, in turn, may be controlled by reference to an esthetic ideal of what is fine. There are certainly more grades than I have enumerated. Perhaps their number is indefinite. The brutes are certainly capable of more than one grade of control; but it seems to me that our superiority to them is more due to our greater number of grades of self-control than it is to our versatility (Consequences of Critical Common-Sensism, 1905, CP 5.533).

We 1) 2) 3) 4)

may summarize these seven levels as follows: Unconscious controls in the mind²⁹² Instinctive self-control (not necessarily completely unconscious) Self-control resulting from training (upbringing, education, coaching, etc.) Self-control resulting from self-training (cf. the process descriptions above involving imagination), aiming at some selected goal 5) Improving the goal already set 6) Involving some guiding moral principle 7) That principle, in turn, reconstructed after some aesthetic ideal Peirce muses that the number of such levels may be indefinite. The recursive mode of definition by level n controlled by metalevel n+1, however, seems to entail that level numbers remain describable by an integer. Peirce’s seventh level— an aesthetic norm—is taken to stem from the uppermost normative discipline of aesthetics in Peirce’s idiosyncratic definition of that term (the study of those ultimate aims or values which are valid in and by themselves). For that reason, level 7) seems to be the ultimate level, even if different aesthetic values may compete.²⁹³ This does not preclude, however, that intermediate levels may multiply by subdivision facilitating more detailed, articulated, and easier manageable control procedures. Peirce’s bottom-up description of the levels of meta-controls seems to indicate that the rise in levels is also, to some degree, a process of cultivation, domestication, civilization, also in the German sense of a personal Bildung, of character construction and growing conscious self-insight, ranging from biological, cultural, and to individual developments, also having the character of a discovery procedure aiming to gradually revealing and realizing higher values not explicit in the beginning of the process. Interestingly, while the 1903 sketch of the horizontal process of self-control began with the assumption of an ideal governing the whole process, the vertical process of controls of controls terminates

314

Chapter 18: Conscious Self-Control as Criterion for Reasoning

with the reorganization of the columns of controls after some aesthetic ideal finally reached. If the former process takes place on every single level of nested controls, we must assume that there are lower-level ideals, one for each level, while the uppermost, “esthetic” ideal is articulated late or never, and if it is indeed reached, it may exert at downward restructuring of lower-level ideals. Such downward reconstruction, of course, may be possible at each n/n+1 level step. Continuing the quoted sketch of the column of meta-levels of controls of controls, Peirce draws a crucial connection to the semiotic device of hypostatic abstraction, developed since 1902, but also culminating in the self-control year of 1905. Hypostatic abstraction is a generalization of Duns Scotus’ observation that while some entities are real objects (like actual things or processes), on the basis of such an ens realis, a new ens rationis may be defined. One of Peirce’s staple examples is that from the existence of white things, the hypostatic abstraction of “whiteness” may be constructed.²⁹⁴ Continuing the dialogue above where Peirce claimed that human superiority was the result of self-control, his fictive interlocutor asks: “Doctor Y. Is it not due to our faculty of language? Pragmaticist: To my thinking that faculty is itself a phenomenon of self-control. For thinking is a kind of conduct, and is itself controllable, as everybody knows. Now the intellectual control of thinking takes place by thinking about thought. (…) One extremely important grade of thinking about thought, which my logical analyses have shown to be one of chief, if not the chief, explanation of the power of mathematical reasoning, is a stock topic of ridicule among the wits. This operation is performed when something, that one has thought about any subject, is itself made a subject of thought. (…)” (Consequences of Critical Common-Sensism, 1905, CP 5.534).²⁹⁵

This is the idea that the ladder climbed by the ensuing steps of meta-control levels is constructed from corresponding steps of the semiotic tool of hypostatic abstractions. Following the quote, Peirce gives the example of hypostatic abstraction in mathematics, giving rise to a series of ever more abstract conceptions, from entities to the abstraction of a set, to the cardinality of that set, to the cardinal number, to the cardinal sequence, etc.—each new abstraction introducing the variability—and hence controllability—of a lower level within a higher one.²⁹⁶ While much other semiotic machinery is deemed accessible to higher animals like parrots, finches, dogs by Peirce (including symbols, arguments, prescission, etc.), hypostatic abstraction not so. This ability of thinking about thought by means of making an n-order thought an object of n+1-order thought and thus exercising self-control seem to be a candidate for a Peircean missing link between higher animals and human beings.²⁹⁷ It is also a good candidate, then, to what distinguishes humans from other machines.

Machine and Animal Counterexamples

315

Machine and Animal Counterexamples Reasoning validated by conscious self-control can be contrasted to Peirce’s analyses of machines and animals, both of them able to process inferences but not to crucially control them. In Peirce’s time, simple mechanic syllogism-computing devices were being constructed, such as Jevons’ 1869 “Logical Piano” and Peirce’s Johns Hopkins student Allan Marquand’s “New Logical Machine” presented in 1883 – 1885, both of which were referred to by Peirce in his 1887 paper on “Logical Machines” (W 6, 66 – 73).²⁹⁸ Peirce even himself counts as one of the early developers of computer architecture, proposing in a brief letter from Dec. 30, 1886, to Marquand a machine built no longer from rods, levers, and springs, but from electrical circuits instead (W 5, 421– 423) with a drawing suggesting electrical representation of “logical multiplication and addition”, that is, universal and existential quantifiers (Fig. 59): I think you ought to return to the problem, especially as it is by no means hopeless to expect to make a machine for really very difficult mathematical problems. But you would have to proceed step by step. I think electricity would be the best thing to rely on.

Let A, B, C be three keys or other points where the circuit may be open or closed. As in Fig 1, there is a circuit only if all are closed; in Fig. 2. there is a circuit if any one is closed. This is like multiplication & addition in Logic. Yours faithfully C. S. Peirce P.S. If you will send me a copy of your last paper on your machine, I will act as Devil’s Advocate, by attacking it. Fig. 59: Peirce’s 1886 letter to Marquand with a sketch of how to implement universal and existential quantification in electric circuitry (W 5, 422).

Peirce thus seems to have been the first to propose electricity-based computer architecture. An 1890 diagram model of a general, electromagnetic computing design is found in Marquand’s papers, and may be the result of his and Peirce’s collaboration:

316

Chapter 18: Conscious Self-Control as Criterion for Reasoning

Fig. 60: Sketch of the design of an electrical logical machine, found among Marquand’s papers, c. 1890.

Information is here represented by the electrical charge in each of the 16 magnetic coils. Successive premises would be encoded and the conclusion then computed. In that sense, the two of them may count as the first actual inventors of an electrical computer, (cf. W 6, xliv).²⁹⁹ Already in the 1860s, Peirce had marketed the argument that the ability of logical machines to process inferences parallel to the human mind provided a strong argument against psychologism in logic: it does not require a human psyche to draw logical conclusions.³⁰⁰ Peirce, however, denied that mechanical

Machine and Animal Counterexamples

317

devices could ever become able to achieve consciousness nor self-control. In that sense, he constitutes a link in the intellectual history from Leibniz’ famous mill argument from the 1714 Monadologie and to Searle’s Chinese Room argument of 1980.³⁰¹ Both of these arguments imagine the details of the cognitive process magnified, showing that the mechanical movements closely scrutinized would not show any sign of consciousness. Leibniz, of course, did this in order to show that perception was not mechanical, Searle in order to argue that Turing architecture computers could never achieve consciousness (whereas other machine types like human brains might do so). Peirce shares some features with both: anti-necessitarianism as a prerequisite to consciousness (Leibniz) and the ensuing rejection of consciousness in any logical machine (Searle). Let us look at Peirce’s arguments on the capabilities of logical machines. In his 1887 paper on “Logical Machines”, Peirce asked the open question of “Precisely how much of the business of thinking a machine could possibly made to perform, and what part of it must be left for the living mind, is a question not without conceivable practical importance; the study of it can at any rate not fail to throw needed light upon the nature of the reasoning process” (W 6, 65). After discussing the structures of Jevons’ and Marquand’s machines and arguing for the superiority of the latter, Peirce concludes: Every reasoning machine, that is to say, every machine, has two inherent impotencies. In the first place, it is destitute of all originality, of all initiative. It cannot find its own problems; it cannot feed itself. It cannot direct itself between different possible procedures. […] This, however, is no defect in a machine; we do not want it to do its own business, but ours. […] In the second place, the capacity of a machine has absolute limitations; it has been contrived to do a certain thing, and it can do nothing else. For instance, the logical machines that have thus far been devised can deal with but a limited number of different letters. The unaided mind is also limited in this as in other respects; but the mind working with a pencil and plenty of paper has no such limitation. It presses on and on, and whatever limits can be assigned to its capacity today, may be over-stepped tomorrow. This is what makes algebra the best of all instruments of thought; nothing is too complicated for it. And this great power it owes, above all, to one kind of symbol, the importance of which is frequently entirely overlooked—I mean the parenthesis (Logical Machines, 1887, W 6, 70 – 71).

Funnily, the supposed superiority of the mind over machine is taken to be due to the former working with formal algebra with pen and paper, where the parenthesis is the sign that makes possible a clear, stepwise computation procedure. So, the difference does not lie in clarity nor in the single steps. The difference lies in that the machine has neither initiative nor originality, it does only what it has been built to do; human researchers by contrast are taken to possess “original initiative”, selecting their own problems. Another complaint often made by Peirce is that existing machines, inspired by syllogisms, deliver one conclusion

318

Chapter 18: Conscious Self-Control as Criterion for Reasoning

only, while the logic of relations shows that to any set of premises, any number of different conclusions may follow. Peirce, of course, wrote almost two generations before the concept of a universal Turing machine, but still he later realized that the one-purpose or one-answer shortcoming is not principal. He now points the to the fact that all of arithmetic follows from six assumptions about numbers (Peirce indirectly referring to Peano’s axiomatization of arithmetic of 1889), and now continues: “The logical machines hitherto constructed are inadequate to the performance of mathematical deductions. There is, however, a modern Exact Logic which, although yet in its infancy, is already far enough advanced to render it a mere question of expense to construct a machine that would grind out all the known theorems of arithmetic and advance that science still more rapidly than it is now progressing” (Reasoning and Instinct, 2, 1900, R 831, 8).³⁰² So, here, Peirce is very optimistic in terms of which theorems computers will be able to prove. Interestingly, Peirce here subscribes to the optimism also voiced in Hilbert’s famous second question of 1900 about the consistent derivation of the whole of arithmetic, much later to give rise to Hilbert’s Entscheidungsproblem of 1928 and Church and Turing’s subsequent proofs of its impossibility in 1936, elaborating on Gödel’s 2nd incompleteness theorem of 1931. Despite this optimism as to proofs, Peirce still insists on the deficiencies of machines, but now they are differently argued: In genuine reasoning, we are not wedded to our method. We deliberately approve it, but we stand ever ready and disposed to reëxamine it and to improve upon it, and to criticize our criticism of it, without cessation. (…) If a machine works according to a fixed principle involved in the plan of it, it may be a useful aid in reasoning; but unless it is so contrived that, were there any defect in it, it would improve itself in that respect, then, although it could correctly work out every possible conclusion from premises, then the machine itself would afford no assurance that its conclusions would be correct. Such assurance could only come from our critical examination of it. Consequently, it would not be, strictly speaking, a reasoning machine. Self-criticism can never be perfectly thorough for the last act of criticism is always itself open to criticism. But as long as we remain disposed to self-criticism and to further inquiry, we have in this disposition an assurance that if the truth of any question can ever be got at, we shall eventually get at it (Reasoning and Instinct, 2, 1900, R 831, 10 – 12).

Now, the arguments against the machine are: 1) It is unable to repair errors and defects in itself 2) Machines may perform correct inferences but are unable to provide explicit assurance of why they are correct—an early version of what is now called explainability in computer science

Machine and Animal Counterexamples

319

3) By contradistinction humans, thanks to self-control, may criticize their own conclusions, criticize criticism in an open-ended dialogue, each step taking the former result as its object of investigation The two crucial shortcomings of machines here, inability to detect and correct errors, and inability to make explicit their own procedures, are two sides of the same coin. Knowledge of its own principles would be needed for the machine to perform error-correcting, and it is the further development of this knowledge which would constitute “original initiative”.³⁰³ These 1900 reflections on the limitations of machines seem to feed directly into the new emphasis and further development of Peirce’s notion of self-control from around the 1902 Minute Logic. The decisive difference is the ensuing criticism exercised by humans in their self-controlling dialogue, within or among themselves; in a certain sense, the yet-uncontrolled inferences of humans are just as mechanic as are the machines: “Say, if you like, that thinking has everything to do with the life of reasoning; I still insist that it has nothing to do with the logical criticism, which is equally applicable to the machine’s performances and to the man’s” (Minute Logic, 1902, CP 2.56 – 59). Translated into current scholarly vernacular, what Peirce is addressing is that machines and humans alike may produce true beliefs, but in lack of selfcontrol, none of them are able to produce justified true belief, in the language of philosophers—or provide explainability of their results, in the terminology of computer scientists. Nowadays, a central problem for the latter is explainability of the automatized results by deep machine learning used in a growing number of “smart” devices: the involved neural-network architecture yields impressive results, e. g., in pattern recognition, but its black-box architecture remains unable to make explicit why those results are tendentially true. Moreover, their results are statistical only, not realizing full logical validity of “old-fashioned” AI programs. Related doubts have been raised about large computer-aided proofs, such as Andrew Wiles’ famous 1994 proof of Fermat’s last theorem. Peirce’s self-control criterion thus forms an important early version of this persistent issue of artificial intelligence, recently having given rise to the research programs of “XAI”, explainable artificial intelligence.³⁰⁴ We already heard how Peirce, in 1908, now aware of the ongoing further work upon Charles Babbage’s analytical engine,³⁰⁵ much more capable than the Jevons and Marquand machines, finds that originality of thought may coexist with logical necessity in its single steps, still refusing such originality for machines due to their lack of explicit self-control. Animals provide quite another contrast case. Humans themselves are mammals, and there is little doubt that many higher animals possess some degrees of

320

Chapter 18: Conscious Self-Control as Criterion for Reasoning

consciousness. Animals, to Peirce, are not Cartesian machines, and animal instinct is no blind, mechanical procedure but is subjected to some degrees of self-control: When the minds of the lower animals first began to be studied, it was the unchangeableness of animals’ methods that led observers to draw a sharp line of demarcation between Instinct and Reason. But facts subsequently came to light showing that that fixity was only relative, that bees in a clime of perpetual summer, after some generations, give up storing vast quantities of honey; that beavers, provided with new materials, gradually evolve new styles of architecture; that sheep, carried to valleys where poisonous hellebore grows, learn not to eat it; that birds sometimes take to unaccustomed food, and come to prefer it; (…). Such phenomena evince an element of self-criticism, and therefore of reasoning (Reasoning and Instinct 2, 1900, R 831, 10 – 13).

This argument points to a sort of reasoning at the collective level of populations of a species changing behavior in a rational way in the face of changing environmental conditions—supposedly too swiftly to be explained by evolution. Peirce, however, also found quasi-rational behavior on the level of individual creatures: “All thinking is by signs; and the brutes use signs. But they perhaps rarely think of them as signs. To do so is manifestly a second step in the use of language. Brutes use language, and seem to exercise some little control over it. But they certainly do not carry this control to anything like the same grade that we do. They do not criticize their thought logically” (Consequences of Critical Common-Sensism, 1905, CP 5.534). Animals share with human beings some of the elementary levels of self-control, and so are able to reason, also in the elementary pragmatic sense of letting arguments influence behavior changes. Many higher animals have the ability of becoming trained to pretty particular tasks and action series, that is, at least level 3 in Peirce’s seven-step hierarchy above. What they lack is thinking about thought, that is, the ens rationis step of hypostatic abstraction. Again, this ability of creating new abstract objects out of aspects of experience is taken to be a semiotically central device for logical self-control. Given the progress in ethology since Peirce, where not only skills and intelligence but also sign processing capabilities of apes, whales, parrots, corvids and many higher genera, but also surprisingly smart non-vertebrate species like bees, spiders, octopi etc. are now rated considerably higher than in Peirce’s day, it is an interesting thought experiment to imagine which kinds and degrees of self-control Peirce would now be ready to ascribe to them.³⁰⁶

The Role of Consciousness in Self-Control

321

The Role of Consciousness in Self-Control An important issue to which Peirce does not seem to furnish any definitive answer is the more precise role played by consciousness in self-control. It is obvious that he finds the relevant kind of self-control in logic to be deliberate or voluntary, mirroring his mature theory of assertions which refers to the assumption of responsibility in making truth claims; cf. Chapter 3. The central argument here is that actions of which you are not conscious, that is, more or less automatized behavior sequences in act or thought, cannot count as deliberate and thus not be criticized as being good or bad. An initial general issue is how consciousness—or the larger mind of which it is a part—is able to influence future concrete action at all. Peirce thinks that all physical events are directly caused by other physical events only, just like all mental events are immediately caused by other events of the mind. Still, he refuses to admit any dualist doctrine of parallelism between the two. This is why he assumes the two realms may interact indirectly: … we must understand by final causation that mode of bringing facts about according to which a general description of result is made to come about, quite irrespective of any compulsion for it to come about in this or that particular way; although the means may be adapted to the end. The general result may be brought about at one time in one way, and at another time in another way. Final causation does not determine in what particular way it is to be brought about, but only that the result shall have a certain general character (On Science and Natural Classes, 1902, EP II, 120; CP 1.211).³⁰⁷

We already saw how, in the process of self-control, determination is assumed to possess causal efficacy in bringing about concrete actions. The argument cited leads into Peirce’s recurrent metaphor with the court and the sheriff. The court refers to the law, but the law being general cannot act to catch the perpetrator. That requires the strong arm of the sheriff. Similarly, the mind guides concrete events by general, final causation, while those actual events determine the particular way the aim is realized, by efficient causation. Psychologist logicians do not understand this, Peirce claims: So, those logicians imagine that an idea has to be connected with a brain, or has to inhere in a “soul.” This is preposterous: the idea does not belong to the soul; it is the soul that belongs to the idea. The soul does for the idea just what the cellulose does for the beauty of the rose; that is to say, it affords it opportunity. It is the court-sheriff, the arm of the law (On Science and Natural Classes, 1902, EP II, 120; CP 1.216).

Even if consciousness is a physical effect of the physiology of the brain, it is simultaneously guided by final, ideal causation, just like the sheriff by the law:

322

Chapter 18: Conscious Self-Control as Criterion for Reasoning

… though matter cannot act immediately upon mind or t’other way it may act all the same upon it. That self-control, self-consciousness, involve endless series is clear. There are other modes of application, not merely other applications (Letter to Royce, May 27, 1902, CP 8.122, n.).

It is not, however, the first aspect of consciousness, instantaneous feeling, that guides self-control: “Rationality is being governed by final causes. Consciousness, the feeling of the passing instant, has, as such, no room for rationality. The notion that logic is in any way concerned with it is a fallacy closely allied to hedonism in ethics” (Minute Logic, 1902, CP 2.55). Final causes, like the pursuit for truth animating logic, are to be found in the third, synthetic aspect of consciousness, more particularly in the self-conscious self or ego part of it: “I use the word ‘self-controlled’ for ‘controlled by the thinker’s self’, and not for ‘uncontrolled’ except in its own spontaneous, i. e., automatic, self-development, as Professor J. M. Baldwin uses the word” (A Neglected Argument, 1908, 6.454– 455). It is not thought controlling itself, it is a self controlling thought. The map-of-map metaphor of self-consciousness through time makes of it the center of consciousness, referring to itself by all of the time taking itself as its object in the self-controlling chain of self-criticism: “My dear Professor Royce, I wish you would tell me precisely why it is that you object to making anything its own purpose, or the sign of itself. It seems to me clear that that is just what consciousness is …” (Letter to Royce, May 28, 1902, CP 8.122 n.). To Peirce, it is a definitory aspect of consciousness that it, all of the time, dialogically addresses itself. But what is covered by its self-criticism? An important reason for its activity seems to be that its object is not merely simple deductions of the Kantian type where the conclusion contains nothing but what was already there in the premise. We already heard how “theorematic” deductions were argued to transcend mechanizability. Rather, the object of conscious self-control of reasoning is the whole of the ongoing, recursive investigation process, comprising abduction, theorematic deduction, induction, including self-correcting error-detection, all of it interconnected by the aim of truth continuously recruiting these capabilities. In one of Peirce’s many attempts at a proof of pragmatism in the 1900s, he mentions, as the seventh out of fourteen steps: “7. And the very first steps in all reasoning,—which is retroduction,—consists in the manipulation of signs of a certain sort, and an attentive and observational manipulation, self controlled & selfconscious” (The Argument for Pragmatism Anachazomenally or Recessively Stated, c. 1907, R 330, unpaginated). Abduction—the qualified guess constructing possible hypotheses to explain a surprising fact—as the first step in investigation must be covered by self-control, just like every subsequent step in an indefinite chain of inferences. This also ex-

The Role of Consciousness in Self-Control

323

plains the distance Peirce saw from full scientific investigation processes to simple syllogism-proving machinery. This ambitious scope of what is supposedly covered by self-conscious self-control, however, should not be confused with an idea that such self-control should be expected to possess insight in each minute detail of the actual process of thinking. Here, another principle of economy considerably minimizes what self-control must be able to make explicit in order to perform this duty. Reasoning is distinguished from acritical inference because of the fact … that it is always accompanied by the belief that it, the special inference, is only an instance of a type, or genus of inference. I do not agree with Hume that the line should be drawn between cases where the “check or controul” actually is resorted to. It suffices that the mind should appeal to the possibility of such confirmation, just as the moral difference between lawful and lawless action consists, not in the case being carried into court, but in the agent’s confidence that a court would sustain him (Notes on Portions of Hume’s Treatise of Human Nature, 1905, R 939, 3 – 4).

Again, the court/sheriff metaphor is invoked: control requires the consciousness that the inference controlled is a token of a general type of valid inference structure, which may, if necessary, be made explicit, just like every single legal activity does not have to be tried at court, but might be so tried, if necessary. So, self-control is rather standing back, ready to step in at a given ocasion. Other times, Peirce likens the relation with a contract: you do not have to be conscious about every word of a contract, nor, a forteriori, how its text psychologically came into being as a piece of writing—what you need to know is which general obligations the contract imposes upon the contracting parties.³⁰⁸ Likewise, the role of consciousness here should not be confused with an idea that all details of the psychological thinking process should be consciously present or even accessible; not even in the idea that every single logical step of the process should be so accessible. That lies in Peirce’s revival of the medieval distinction of the logica utens and the logica docens—the former being the spontaneous use of logic taking place in scientific and other practice, put to use, e. g., by practicing mathematicians or other scholars, or in everyday reasoning. Scientists need not take logic courses nor be fluent in logical doctrine—but they should be conscious of what they are doing in the minimal sense of realizing that every step they take is “an instance of a type” of inference, and that that inference, if challenged by errors, insufficient results, or by counterarguments, could be made explicit. Finally, the conundrum of human versus general intelligence. Is it not strange, Peirce basing his whole logic on the principle of universality, normative principles holding for every possible intelligence—while simultaneously invok-

324

Chapter 18: Conscious Self-Control as Criterion for Reasoning

ing for its control the peculiar psychophysical property of consciousness in higher animals and humans? In one of the main loci of Peirce’s general account of diagrammatical reasoning, R 292a from 1906, a parallel version of the Prolegomena paper called “ Πλ “, he underlines this: “Those whom we hear all-confidently asserting that anything like reasoning is a phenomenon peculiar to human consciousness or to the specific type of consciousness to which the human variety appertains, have not sufficiently considered the subject, and in particular fail to recognize that the question is not what happens to be extant but what the essential nature of reasoning allow” (Πλ, draft of the Prolegomena, R 292a; LoF III, 187). Peirce assumes, in short, that every possible intelligence able to exert selfcontrol will have to make use of some type of consciousness—not necessarily exactly like the variety known on this planet—serving the construction of a selfconscious self, implying the ability to measure its own activity against the elementary standards of logic.

Windows and Freedom Peirce’s long struggle with the conceptual cluster of self-control, consciousness, mind, self, machines, animals, humans, reasoning, and logic gives result less clear that one may have wished for—and probably also than what Peirce himself would have wanted. Still, it is thought-provoking to follow his struggle. Not only new aspects appear of what animated Peirce in his last fertile philosophical explosion through the 1900s—much of the reflection on conscious self-control appears intertwined with the definitive developments of semiotics, pragmatism, Existential Graphs in the years 1902– 1906, through Peirce’s Annus Mirabilis of 1903. One clear result appears to be two levels of self-control. One local, stepwise, inhibitive self-control, built on the simple measuring of inferences by some minimal degree of consciousness of their general leading principle, developed in constant ping-pong with oneself characteristic of dialogic Peircean reasoning. And one global, habit-forming self-control, oriented towards a more or less remote future, stitching together a series of inhibitory steps, utilizing imaginary thought experiments, attempting by training to command a future version of oneself, guided by some more or less explicit overarching purpose, personal, social, or universal. Both of them, of course, take place in the third mode of consciousness, the cognitive, temporally extended, learning ability of synthesis. The two aspects of self-control mentioned simultaneously display the enormous range of that synthetic ability required for self-control.

Windows and Freedom

325

The first of them pertains to what could be called the immediate window of consciousness—related to the ongoing synthesis capability in what psychologists call short-term memory or working memory. We heard Peirce’s claim that consciousness is both temporally and spatially extended. Its possibility of critically reviewing the simplest step of thought—the inference step from one proposition to the next—seems to rely upon an elementary ability of surveying, in one glance, as it were, a limited spatiotemporal domain covering the way a proposition combines subject and predicate. The synthesis of those two components or aspects of a proposition into one, truth-claiming sign arguably forms the most elementary step among the logical endeavors of the third, synthetic consciousness. Combining an icon and an index in that specific way so as to make them function as predicate and subject, respectively, is a different kind of synthesis than that of the melody or of gestalts of the visual field, to be sure, but still a synthesis most often spontaneously accomplished, with the result that a sign is processed as professing a truth by claiming two aspects of itself being involved with the very same object. Most probably, that is a process facilitated by brain architecture in many higher species (cf. Stjernfelt 2014, Chapter 5). But viewed from the consciousness inside, this synthesis is made possible by the co-localization of the subject and predicate token parts of the proposition within a pretty narrow spatio-temporal window. There could be no far spatiotemporal distance between subject and predicate, neither in thought nor in external propositions representations, in order for the unity of the proposition to be established (cf. Bellucci 2014, Stjernfelt 2014; this volume, Chapter 5). Simultaneously, that synthesis involves the structure of a proposition—one aspect, the subject, referring to some object, and another, the predicate, describing that same object.³⁰⁹ The assumption about that object, then, is what unites the specific propositional use of the space-time consciousness window. Hence, this is a more or less implicit knowledge which self-control must put to use when critically examining the validity of a proposition: does the claimed predicate actually hold for the object pointed out by the subject? A similar synthesis is repeated for the next step—the relation between premises and conclusion of an elementary inference, be it ab-, de-, or induction. Their synthesis also requires co-localization of inference parts in a spatio-temporal window of consciousness.³¹⁰ Again, that is not to say that all propositions or inferences in that window are necessarily fully conscious; probably most of them are acritical and below the level of consciousness. But when the critical examination of them is performed by a conscious act, that must involve a synthetic overview which is, simultaneously or in short sequence, conscious of all relevant parts, now measuring it, as Peirce says, on the leading principle of the inference. Those must form the two elementary, nested windows of logical conscious con-

326

Chapter 18: Conscious Self-Control as Criterion for Reasoning

trol. The internal or external dialogue between the “utterer” and the “interpreter” in self-control must be stepwise comprehensible or overviewable so as to be able to immediately compare pro-con-pro sequences, even if the total argument may easily have a scope so as to escape one synthetic glance.³¹¹ The size of those windows in human beings, of course, is an empirical issue of psychology. For all his emphasis, however, on conscious self-control of reasoning, Peirce’s argument is philosophical and general, as we saw in the R 292a quotation above. As no conscious, reasoning agent could be omniscient nor all-seeing, any possible consciousness must work in some consciousness window able to synthesize a spacetime slot, smaller or larger, its scope dependent upon biological species, individual talent, culture, education, situation, intoxication, etc.³¹² The other end of self-control, the cumbersome struggle to teach oneself new habits, also belongs in the other end of the third mode of synthetic consciousness. Here, the immediate window is transgressed and the whole process only kept together by the overarching purpose, recruiting any number of the small proposing-inhibiting steps of the former kind. This synthesis is possible only with the intense use of both short-term, semantic, and episodic memory, fueling imaginations of future acts with memories of what went wrong in earlier past attempts at that act, diversifying future act in subtypes after type of purpose and type of situation, synthesizing whole narrative scenarios in short-term memory but relying upon the small immediate window anytime some detail of the process requires special scrutiny—just like the whole of the action sequence should be overviewed in one, albeit vaguer and more general glance. Obviously, in developing this distinction, we are extemporizing on indications only briefly given, primarily in Peirce’s 1905 developments of conscious-self-control. But Peirce’s important reinterpretation of the Kantian notion of human freedom certainly belongs to the latter. Peirce rarely uses the important Kantian notion of “autonomy”, but aspects of his doctrine of self-control obviously addresses exactly this issue: … the propositions that the laws of nature are not absolute and that important physical events are due to human reasoning are far from proving that human action is (in any important degree) free, except in the sense that a man is a machine with automatic controls, one over another, for five or six grades, at least. I, for my part, am very dubious as to man’s having more freedom than that, nor do I see what pragmatic meaning there is in saying that he has more (Letter from Peirce to F.C.S. Schiller, probably 1906 like 8.321, CP 8.320).

In a certain sense, Peircean self-control forms an attempt at analyzing further Kantian autonomy, also in the sense of its involving the building of character, human dignity, capability of ethical judgment, the strive for ideal goals etc.—

Windows and Freedom

327

the famous capacity of moral self-legislation which, to Kant, was a source of awe paralleled only by the starry skies above.³¹³ In that sense, Peircean conscious self-control, initially seeming so fragile, contested, and marginal, may end up preserving and even further developing a central Kantian Enlightenment notion—but deprived of the large-scale Kantian metaphysical dualism of Realms of Freedom and Necessity which no continuist pragmatist would be ready to accept. Peircean self-control rather takes freedom by self-control as a fragile, contested, and never fully achieved result of human perfectibility rather than a given metaphysical reality. We shall return to this in the final chapter.

Chapter 19 Limited Individuals and Unlimited Aims Peirce’s Philosophical Anthropology The mature Peirce’s idea about the specificity of human beings vis-a-vis other animals is—as we have seen—characterized by two interconnected ideas: selfcontrol and hypostatic abstraction. The sign type of abstraction, making new, higher-level abstract objects out of fleeting experiences and their predicates, allows for human beings the explicit access to an expanding world of general ideas and meanings which remain implicit—if at all—in other animals. The procedure may be repeated indefinitely, so as to construct hierarchies of still more abstract concepts to be investigated. Applying this semiotic mechanism upon their own activity, human beings may exert self-control also constituting hierarchies, a given level controlling the next-lower level of self-control. Peirce did not, however, restrict these abilities to the actual biological species of homo sapiens. Oftentimes, he speculates how future or interplanetary nonhuman species may achieve similar capacities in order to continue or overtake human achievements; conversely, higher animals participate, to some degree, in the same abilities. In a certain sense, then, Peirce’s conception of humans is transhuman: it points into an open future of potential further improvement and evolution of humanity.³¹⁴ This optimistic side of Peirce’s anthropology, it is true, is counterbalanced by his very low evaluation of individual human beings as defined primarily by error: “… individualism and falsity are one and the same”, as he would say in 1893.³¹⁵ It is when committing error, so Peirce, that individuals discover their own existence in their ability to be in the wrong, correctable by something else different from themselves: external reality. In this chapter, we shall investigate deeper Peirce’s philosophical anthropology with its biological, semiotic, metaphysical, even theological connection lines. What are the conditions framing these human creatures, the main carriers of complicated signs in this corner of the universe? Remarkably, Peirce continued developing these reflections all through his trajectory as a philosopher, and even if his results are hardly conclusive, they throw an important light on his more precise and crisp results in logic and semiotics. We shall follow an overall chronological line, beginning with Peirce’s early and surprising comparison between human beings and words under the headline of “Man, a Sign”.

https://doi.org/10.1515/9783110793628-021

Man, a Sign

329

Man, a Sign Already in his first fertile period of 1866 – 1868, the young Peirce describes his conception of human beings by a surprising comparison: Human beings are like words or signs. The idea is that just like signs, human beings connect references to whatever objects they are attending to, on the one hand, with the ascription of meanings describing those objects on the other: “A man denotes whatever is the object of his attention at the moment; he connotes whatever he knows or feels of this object, and is the incarnation of this form or intelligible species; his interpretant is the future memory of this cognition, his future self, or another person he addresses, or a sentence he writes, or a child he gets” (“Lowell Lecture” XI, 1866, W 1, 498; CP 7.591). Propositional meaning, composed from denotation and connotation, is communicated to some future communication partner, self or other.³¹⁶ Humans and signs share the same triadic structure. To compare man and word, then, is no mere metaphor, Peirce argues. The implication is that individual human beings form a subspecies of the more general category of signs. This semiotic analysis of the human mind immediately leads into an early version of Peirce’s extended mind doctrine. For if humans thus possess the capacity to spread their mind in the shape of signs, they are not confined to the immediate biology of their carnal bodies: “But are we shut up in a box of flesh and blood? When I communicate my thought and my sentiments to a friend with whom I am in full sympathy, so that my feelings pass into him and I am conscious of what he feels, do I not live in his brain as well as in my own— most literally? True, my animal life is not there but my soul, my feeling thought attention are” (“Lowell Lecture” XI, 1866, W 1, 498; CP 7.591). If humans are indeed signs, they may, just like them, exist in multiple token copies at one and the same time: “There is a miserable material and barbarian notion according to which a man cannot be in two places at once; as though he were a thing! A word may be in several places at once, Six Six, because its essence is spiritual; and I believe that a man is no whit inferior to the word in this respect” (“Lowell Lecture” XI, 1866, W 1, 498; CP 7.591). In a swift inference, the young Peirce takes this semiotic quality of human beings to constitute the very spiritual identity of the individual person—generalizing from his initial perception-interpretation example to assume that the whole of one’s semiotic activity comes together to constitute one complex sign. The person, then, is equal to his or her semiotic activity taken as a whole. Moreover, in the lack of any possibility of trustworthy introspection, the overall meaning of this complex sign lies well beyond the grasp of the individual itself: “Each man has an identity which far transcends the mere animal;—an essence, a meaning subtile as it may be. He cannot know his own essential significance; of his eye it is eyebeam. But that he truly has

330

Chapter 19: Limited Individuals and Unlimited Aims

this outreaching identity—such as a word has—is the true and exact expression of the fact of sympathy, fellow feeling—together with all unselfish interests—and all that makes us feel that he has an absolute worth” (“Lowell Lecture” XI, 1866, W 1, 498; CP 7.591).³¹⁷ Simultaneously, then, this property is what provides the basis for Peirce’s version of the Kantian idea of the dignity of the individual. While the well-known Kantian idea rests upon moral autonomy, such autonomy is no given thing to Peirce, intellectual and moral self-control rather being a lifelong quest to be pursued, as discussed above, and elementary dignity rather consists in this initial, basic ability of human signs to spread to other recipients. This notion of the semiotic self is strongly idealist in the sense that it makes of sign use the core of what gives human beings their special value, over and beyond their elementary animal life. As to human specificity, it must be noted that most of what Peirce says about humans as signs in this early piece, may also be extrapolated to higher animals.³¹⁸ They would also combine attention-direction with interpretation and action into signs and thus possess a similar existence over and above their mere biological being, spreading signs even if maybe in more restricted amounts. So, these first sketches of a philosophical anthropology in Peirce do not immediately imply any sharp distinction between humans and other higher animals, such as is often taken to be crucial to theories of humanity, but rather a difference of degree. Pertaining to both humans and other animals, the important distinction is rather that between their animal being as individual carnal organisms on the one hand, and their participation in semiotic networks on the other. Two years after, in the closing chapter of the important paper “Some Consequences of Four Incapacities” (1868), arguing against the existence of anything absolutely incognizable, Peirce generalizes his idea under the headline of “Man, a Sign”.³¹⁹ Here, Peirce’s idea is developed in a compact presentation of hasty cocktail of an inferentialist theory of mind, fallibilism, truth as the convergent limit of collective investigation, Scotist realism of universals—all of which would later be developed at length to form central threads of Peircean epistemology: “At any moment we are in possession of certain information, that is, of cognitions which have been logically derived by induction and hypothesis from previous cognitions which are less general, less distinct, and of which we have a less lively consciousness” (EP I, 52; CP 5.311). Such chains of inference signs may present us with true or untrue claims—the former referring to independent reality and to be vindicated by future collective investigation, the latter not so. Thus, the semiotic activity of the individual “man-sign” forms but a tiny part of the overall quest of humanity for truth, ranging far into an uncharted future. An argument against Peirce’s man=sign hypothesis might be that the former possesses consciousness, the latter not so. In order to counterargue this objec-

Man, a Sign

331

tion, Peirce considerably marginalizes the role of consciousness even in individuals. Individual consciousness is but a weak way of signifying the consistency of sign use, a manifestation which is, moreover, due to the biological, material aspect of humanity: “But this consciousness, being a mere sensation, is only a part of the material quality of the man-sign. Again, consciousness is sometimes used to signify the I think, or unity in thought; but the unity is nothing but consistency, or the recognition of it. Consistency belongs to every sign, so far as it is a sign; and therefore every sign, since it signifies primarily that it is a sign, signifies its own consistency” (EP I, 53; CP 5.313). The logical, formal qualities of the “mansign”, by contrast, are assumed to be central. A much stronger similarity between humans and signs is added as a counterargument—namely, that both are able to increase information: “The man-sign acquires information, and comes to mean more than he did before. But so do words. Does not electricity mean more now than it did in the days of Franklin?” (EP I, 53; CP 5.313).³²⁰ This sets the scene for a daring extension of the “mansign” comparison: each of the two is impossible without the other, rather, they mutually support each other, and their interaction is what makes the growth of information possible in each of them: Man makes the word, and the word means nothing which the man has not made it mean, and that only to some man. But since man can think only by means of words or other external symbols, these might turn round and say: “You mean nothing which we have not taught you, and then only so far as you address some word as the interpretant of your thought.” In fact, therefore, men and words reciprocally educate each other; each increase of a man’s information involves and is involved by, a corresponding increase of a word’s information (EP I, 53; CP 5.313).

Signs are like the Sphynx answering the naïve interrogator: they are the easily overlooked external vehicle for the development of human knowledge. It is a compact analysis of the enlightenment process: by elaborating external signs which are the only means available for humans to gather information, those signs simultaneously grow to educate humans: “For, as the fact that every thought is a sign, taken in conjunction with the fact that life is a train of thought, proves that man is a sign; so, that every thought is an external sign, proves that man is an external sign” (EP II, 54; CP 5.314). Thus, humans are also signs in the sense that they may be read and interpreted from the outside, opening for the possibility, discussed in the previous chapter, that persons do not have a fixed boundary but flow into other persons, potentially constituting larger-scale persons in the shape of groups, organizations, etc. ³²¹ Importantly, thus, Peirce’s motto “Man, a Sign” is equivocal, referring simultaneously to the individual human being whose total semiotic activity constitutes him or her as a personal

332

Chapter 19: Limited Individuals and Unlimited Aims

sign—and to humanity as a transgenerational whole of humanity whose overall semiotic activity pattern is equal to its progress in knowledge and activity. The individual aspect of the collective “man-sign”, however, is difficult for many to realize because they tend to identify themselves rather with their individual will, power, or force as felt in the present now: “That is to say, the man and the external sign are identical, in the same sense in which the words homo and man are identical. Thus my language is the sum total of myself; for the man is the thought. It is hard for man to understand this, because he persists in identifying himself with his will, his power over the animal organism, with brute force” (EP II, 54; CP 5.314). The individual naturally emphasizes his or her concrete activity in the present moment, mostly unable to grasp its potential long-term semiotic general effects. This collective aspect of it, however, is the dominant level to Peirce, for the individual semiotic self is possible only using signs handed down in the overall semiotic process across generations. Seen from this vantage point, however, the contribution and status of each individual are all but negligible. Peirce concludes this brief and tense brainstorm of philosophical anthropology with a discouraging analysis of individual human beings: The individual man, since his separate existence is manifested only by ignorance and error, so far as he is anything apart from his fellows, and from what he and they are to be, is only a negation. This is man, … proud man, Most ignorant of what he’s most assured, His glassy essence (EP II, 55; CP 5.317).

Quoting, as so often, Shakespeare’s “Glassy Essence”, Peirce finds that the pride of humans is vastly and unjustly exaggerated.³²² The individual typically does not at all realize the grander semiotic scheme of which he or she forms a part. It has the particularly humiliating consequence that individual idiosyncrasies and identities, celebrated by romantics through Peirce’s century, are revealed as nothing but error in the larger perspective. Oftentimes, Peirce will say that the existence of reality really dawns on individuals only when they realize their first mistake, so that a split between true and false becomes evident in their sign use—the same experience making them discover, simultaneously, themselves as the point of origin of that error. The individual may strive to recuperate from this in the longer run, but at the outset, the individual is in no powerful position. Peirce’s idealist philosophical anthropology here shows a strong intellectualist bent, due to his inferential theory of the self: the sign use constituting the individual person consists but of logical inferences connecting signs. Misrepresentations of this constitution of the self in terms of individual will, power, or

Limited Individuals with Unlimited ideals

333

force—focusing only on the intention and activity of the moment and not its longer-term involvements—may tempt the individual with a wholly unreasonable self-pride, the implication being that such inflated self-images ought to be fought and kept under control. We shall return to some religious connections of this idea. Peirce’s denigration of the individual, it should be added, is hardly without a certain collectivist or even totalitarian danger. The overall emphasis on the transgenerational semiotic process of the whole of humanity, modeled on the progress of science, may lead to the ignorance, devaluation, or even disregard of individual predicaments, needs, or experiences. This tension would continue to haunt Peirce’s philosophical anthropology. The closest he came to explicitly addressing what could be called the central chasm of his anthropology was probably the concluding lines of his long review essay of Fraser’s edition of Berkeley in 1871, the paper in which he decisively opted for realism as to universals: The question whether the genus homo has any existence except as individuals, is the question whether there is anything of any more dignity, worth, and importance than individual happiness, individual aspirations, and individual life. Whether men really have anything in common, so that the community is to be considered as an end in itself, and if so, what the relative value of the two factors is, is the most fundamental practical question in regard to every public institution the constitution of which we have it in our power to influence (“Review of Fraser’s Works of Berkeley”, 1871, EP I, 105; CP 8.38).

Limited Individuals with Unlimited ideals In his famous 1877– 1878 series of articles launching the classic formulations of pragmatism in “Fixation of Belief” and “How to Make Our Ideas Clear”, Peirce also takes his initial sketches of a philosophical anthropology several steps further. In the conclusion of “Fixation”, Peirce looks back on the paper’s discussion of the three attitudes to acquiring knowledge competing with the scientific method: the a priori, authority, and tenacity methods, respectively. The former—to which he would later warm considerably in his last large philosophical thrust around 1900—is quickly dismissed as a mere trick to simply adopting what one is already uncritically inclined to believe. The latter he claims to admire for its “strength, simplicity, and directness”, simply clinging to the first idea to appear to the mind, and often accompanying brilliant but unlasting success. Hence, its victories remain on the short run only: “It is impossible not to envy the man who can dismiss reason, although we know how it must turn out at last” (EP I, 122; CP 5.386). Thus, the two serve to illustrate elementary but erroneous human possibilities: intellectual prejudiced indolence and the brutality of ill-considered, immediate action, respectively.

334

Chapter 19: Limited Individuals and Unlimited Aims

The non-scientific method most deeply analyzed here, however, is that of authority: “The method of authority will always govern the mass of mankind; and those who wield the various forms of organized force in the state will never be convinced that dangerous reasoning ought not to be suppressed in some way” (EP I, 121; CP 5.386). Most humans will never rise to scientific rigor and will remain prone to readily accept authorities of their times.³²³ This fact, however, heralds bad conditions for free speech and free inquiry: “If liberty of speech is to be untrammeled from the grosser forms of constraint, then uniformity of opinion will be secured by a moral terrorism to which the respectability of society will give its thorough approval. Following the method of authority is the path of peace. Certain non-conformities are permitted; certain others (considered unsafe) are forbidden. These are different in different countries and in different ages; but, wherever you are, let it be known that you seriously hold a tabooed belief, and you may be perfectly sure of being treated with a cruelty less brutal but more refined than hunting you like a wolf” (EP I, 122; CP 5.386). This echoes Mill’s On Liberty (1859) where he added to state or church suppression of free thought and speech that of social conformity. You do not have to be persecuted by threats of institutional penalties or such “grosser forms” of repression; the majority of human beings will prove capable of “moral terrorism” against dissenting voices which might well do the job. Their argument is that of social peace. Peirce sees that security will typically trump all other considerations and allow for moral terrorists to silence dissenters. This somber aspect of philosophical anthropology has, to Peirce, a corollary in intellectual history: “Thus, the greatest intellectual benefactors of mankind have never dared, and dare not now, to utter the whole of their thought; and thus a shade of prima facie doubt is cast upon every proposition which is considered essential to the security of society” (EP I, 122; CP 5.386). This hypothesis anticipates Leo Strauss’ 1952 idea that in the vast majority of human history, you can never trust philosophers on their word, for they will have used all sorts of cunning strategies attempting to fool censors, appear correct and pious, conform to power, and signaling their real viewpoints by indirect means only, if at all.³²⁴ Peirce even extends this predicament to his own time. Of course, such a condition gives rise to self-censorship, admitted or not: “Singularly enough, the persecution does not all come from without; but a man torments himself and is oftentimes most distressed at finding himself believing propositions which he has been brought up to regard with aversion. The peaceful and sympathetic man will, therefore, find it hard to resist the temptation to submit his opinions to authority” (EP I, 122; CP 5.386). One wonders which among his own viewpoints Peirce may have found it wise to submit to such self-tormenting.

Limited Individuals with Unlimited ideals

335

This analysis adds a couple of important further pessimist notes to Peirce’s 1860s anthropology. There, the overall historical movement of humanity was the measure-stick against which the errors of individuality stood out. Now, those erroneous individuals are able to come together to form the overall mob-like mass of humanity, succumbing to authorities, willingly sheltering under temporal powers in order to preserve peace and deliberately participating in moral outrage campaigns against the few brave enough to utter even a subset of their dissenting views.³²⁵ No nice picture of the majority of human beings. The 1878 “Doctrine of Chances” adds further dark notes to this overall picture of the human condition. Statistically, even the most perfect empirical regularity will admit of counter-examples—which is why Peirce may conclude that “If man were immortal he could be perfectly sure of seeing the day when everything in which he had trusted should betray his trust, and, in short, of coming eventually to hopeless misery. He would break down, at last, as every good fortune, as every dynasty, as every civilization does. In place of this we have death.—” (EP I, 149; CP 2.653). So, death is what spares humans from seeing their every hope and belief crushed by events. This gloomy, proto-Spenglerian doctrine, however, is taken in a surprising turn as the premise for a construction of long-term social, if not cosmological optimism. The mortality of individuals necessarily makes the number of their risks taken and inferences drawn but finite— but probability requires that number to be infinitely great in order to approach certainty. So, the process of reasoning must transgress the narrow limits of individual lives. This argument, of course, may be repeated given any other temporal limit of groups, countries, civilizations, planets, and so on. Those restrictions on the condition of individuals as of civilizations, then, are what pushes Peirce into a veritable transhumanist claim: “It seems to me that we are driven to this, that logicality inexorably requires that our interests shall not be limited. They must not stop at our own fate, but must embrace the whole community. This community, again, must not be limited, but must extend to all races of beings with whom we can come into immediate or mediate intellectual relation. It must reach, however vaguely, beyond this geological epoch, beyond all bounds” (EP I, 249; CP 2.654).³²⁶ Not even geological epochs, counted in millions of years, constitute any limitation, nor does the very existence of the human species itself: all possible races of beings with which we may enter into more or less direct semiotic communication are to be counted as partners in taking further the development of sign-supported reasoning.³²⁷ Peirce’s philosophical anthropology here deepens the tension between empirical human beings here and now, hidebound by complacency, immediate success, pride, subjection to authority and moral terrorism, on the one hand, and their long-term involvement in the realization of the grand ideals of logic on

336

Chapter 19: Limited Individuals and Unlimited Aims

the other. From this increasing tension, it becomes clear that Peirce’s version of Enlightenment optimism is not at all based on any Rousseauist ideal anthropology of the noble savage or the unspoiled child, of human beings as innately or inherently innocent, good, or benevolent in any sense of the word. Rather, empirical human beings fall, most often, far below what ideals would require of them, and Peirce’s anthropology offers no guarantee that such persons will really be able, in the long run, to support the high ideals of logic. Enter theology as a possibility, in the cosmological sketch of the same year, “The Order of Nature” (1878).³²⁸ The existence of a superior being might be a factor able to bridge the distance between empirical humans and their ideal task: “One way of accounting for it, certainly, would be to suppose that the world is ordered by a superior power. But if there is nothing in the universal subjection of phenomena to laws, nor in the character of those laws themselves (as being benevolent, beautiful, economical, etc.), which goes to prove the existence of a governor of the universe, it is hardly to be anticipated that any other sort of evidence will be found to weigh very much with minds emancipated from the tyranny of tradition” (EP I, 170; CP 6.395). Peirce realizes that divine guidance might play the conceptual role of mending the strong tension inherent in his anthropology, but he does not seem to hold great hope in the lawlike aspects of the universe to convince free minds—like himself—about the existence of such a power, and his deeper involvement of metaphors or aspects of theology in his philosophical anthropology had to await his personal crisis and awakening of the early 1890s. These lawlike aspects of the universe, however, will grow to a veritable bridge between humans and their long-term aims; cf. below. Thus, an interesting cosmological implication becoming clear in this discussion is how Peirce ascribed a great logical, cosmological, if not theological signification to the existence of regularities of the universe; cf. his Scotist realism of universals.³²⁹ As to Laplace’s famous rejection of God—reputedly, he said to Napoleon in 1801 that he saw no use for such a hypothesis in his explanation of the structure of the solar system—Peirce remarks that there is really nothing atheistic in Laplace’s argument at all, for his argument builds on the existence of regularities (EP I, 172; CP 6.398).³³⁰ So, cosmic regularities are more important than actual deities in theologically judging a position. Other times, Peirce sees lawlike regularities as simply one and the same thing as mental characteristics of the universe— cf. the ideas of order and super-order discussed below. So, Peirce naturally considers the issue whether truly universal regularities can be found, or whether all empirical regularities rather remain “of limited range”, as a very deep metaphysical question still awaiting clarification (EP I, 171; CP 6.397). This argument builds on an abridged version of the standard theological “argument from design” that

“Great Men”

337

the difference between an ordered universe and a purely chaotic universe constitutes a sign of the divine character of the former. Here Peirce does not, however, take the extra step of pointing to some responsible deity but remains satisfied with the more pantheist idea that the very regularity itself constitutes a sort of divine aspect of the universe. These metaphysical and cosmological issues will turn out also to have a bearing on Peirce’s philosophical anthropology. In 1878, he adds the argument that the arbitrary, chaotic world feared by theologians would be indistinguishable from the present, ordered world if considered from the point of view of some being with a minimal intelligence only. Such organisms, it follows, would be spontaneous atheists. Human beings, however, are able to appreciate—to some degree, at least—the order of the present universe, and in general “The interest which the uniformities of Nature have for an animal measures his place in the scale of intelligence” (EP I, 176; CP 6.406). So, a continuous measure of intelligence is proposed where different beings may be judged according to their ability to detect and appreciate regularities in the cosmos.

“Great Men” Interestingly, around the same time, Peirce also contemplated an alternative candidate who might bridge the chasm between authoritative, error-prone individuals and their grand ideals—namely supermen.³³¹ When teaching his logic class at Johns Hopkins in the last academic year of his brief stay there 1879 – 1884, he picked as a central exercise the construction of a list of “Great Men” since the fall of Constantinople in mid-15th century³³² and the classification of them in four levels of greatness, a bit like Ptolemy’s six classes of stars after brightness which Peirce had recently studied as an astronomer with the Coast Survey.³³³ Peirce argues he picked this example to show the relevance of mathematical method even in a field where our judgment is both unprecise and constrained by the lack of exact knowledge. Simultaneously, however, he is intervening in a standing debate. Thirty years earlier, Carlyle had written his famous “Hero-Worship” book emphasizing the role of great men, while Spencer, more recently, had countered him emphasizing such figures as mere products of their social environments. Francis Galton, by contrast, claimed that eminent characters were hereditary.³³⁴ Peirce seems to have struck a middle road between these extremes, but he certainly ascribed to great figures a strong impact on societal development, and through the 1890s, he kept returning to the issue. Twenty years after the Johns Hopkins class, now planning to write a piece on the intellectual achievements of the 19th century, he went back and resumed these results, of

338

Chapter 19: Limited Individuals and Unlimited Aims

which his general reflections on method were published (CP 7.256 – 261).³³⁵ In the unpublished parts, you find Peirce going into detailed considerations of hundreds of great persons of sciences, philosophy, poetry, arts, music, politics, and much more, of the 19th century all up to his own time of 1901, as well as statistical reflections on the variation of frequencies of great persons in the four 19th century generations considered. It is a virtual intellectual history of main drivers of modernity. Even a few women such as Jane Austen and George Eliot make the hit lists.³³⁶ In 1883, Peirce and his class had settled on a list of 288 “Great Men” over the four centuries since 1453, to be ranked in four classes.³³⁷ Of first-order magnitude great persons through the period, however, Peirce and his class counted a mere 16: Michelangelo, Shakespeare, Goethe, Beethoven, Wagner; Columbus, Luther, Peter the Great?, Washington, Napoleon; Galileo, Kepler, Newton, Kant, Hegel, Darwin—sorted in three groups after Feeling-Action-Thought, roughly artists, politicians, and scientists-philosophers (the question mark with Peter the Great is Peirce’s). Peirce knew well that clear criteria as well as deep information about these persons were lacking; his point being that even given such limitations, his class proved able to pretty clearly organize the empirical material in four classes after magnitude. Our point here, of course, does not concern neither the method nor the exact results of Peirce’s exercise; rather that this interest in “Great Men” of history in general, as of intellectual history in particular, may be seen as an alternative way of bridging the gaping chasm at the center of his anthropology. How would the human species, consisting for the most part of fallible, authority-seeking, vain and self-centered individuals, live up to its long-term enlightenment task of scientific progress and social amelioration prescribed by logic? One possibility considered (but discarded) in 1878 was, as we saw, divine guidance—another seems to have been the occurrence of grand historical figures capable of transcending their own selfish, petty occupations and assume the historical task of pushing inert humanity into the future. As the conclusion of his 1901 publication on great men of science of the 19th century, Peirce wrote: “Emancipation from the bonds of self, of one’s own prepossessions, importunately sought at the hands of that rational power before which all must ultimately bow—this is the characteristic that distinguishes all the great figures of the nineteenth-century science from those of former periods” (Peirce 1901, no pagination). Peirce speculates that such great figures must be endowed with more convoluted brains than the average persons—increasing their distinction abilities and making them “less the slave of ordinary traditional associations”—and muses that even if many people with such special brains never achieve greatness this only goes to show that most people with certain abilities are “crushed by circum-

“Great Men”

339

stances” (R 1132, 14) anyway. But in addition to such external limitations, even eminent men may also be inhibited by personal, “inward” defects such as “Vanity and lack of audacity, which often go hand in hand, waste of time and letting slip the forelock of opportunity, defect of perseverance, discouragement, bad judgment, being drawn into small pursuits, vices …” (14). Persons of the top tier, of very high genius, by contrast, easily control such internal factors of error, but then they are subject to the mercy of external conditions, and nine out of ten of them will be “squelched”. After Peirce’s approximate statistics, only one birth in 320 million is naturally capable of reaching the highest grade of greatness, that is, but one per generation in all of Europe. But among the 16 top figures of Peirce and his class, all of them appeared in “generations of high popular aspiration and hope”, while they were completely absent from periods of “popular depression”, showing the dependence of even such “demigods” on the external vagaries and social conditions of their times (16). In “barren times” such talents would simply be kept back by the “lack of stimulus and of opportunity” (17). In any case, however, such geniuses could not have been produced by any sum of small causes but must rather “be considered as quite another variety of the genus homo, results of [a] cause which very rarely operates at all” (18). Still, this variety must be but a matter of detail, he adds, “since the greatest men are the most human of human beings” (18) So, they virtually belong to a new and more advanced subspecies, even more human than the average human beings. Peirce must admit that, among the 16 of supreme magnitude, three of them, Newton, Peter the Great, and Hegel do “appear at times inhuman and bad”, but still he thinks such stains may be explained away in the larger perspective. So, here Peirce introduces an evaluative scale according to which greatness and humanity are normative measures, directly linked and in some sense proportional,. More greatness, more humanity. The superior race to which these top figures belong seems to be developing and realizing more fully humanity’s potential than do average human beings. Thus, humanity is a norm which most if not all present human beings only partially satisfy, and which is subject to further future evolution. And so, conversely, some existing human beings may fail the test of humanity in this normative sense. We shall not go deeper into Peirce’s charting of Great Men or his speculations about their rise. But it is clear that Peirce contemplates, in his 1883 class exercise and again in his retrospective 1901 piece of intellectual hero-worship, an alternative candidate than a transcendent deity for filling the strange gap at the center of his philosophical anthropology. As mentioned, he even calls his top class of greatness “demigods” at the same time as he declares them to be the “most human of human beings”. So, the further you approach the divine, the more you develop humanity, and vice versa. This class of semi-divine super-

340

Chapter 19: Limited Individuals and Unlimited Aims

men emerging with statistical rarity among standard, even eminent human beings, seem to be capable of doing the job of filling the anthropological void and connecting the inert mass of erroneous, egotistic individuals with their historical task. But even if the needs of their times seem to call forth such great figures, as Peirce says, there does not seem to be any Hegelian necessity that such calls will always be heeded. Peirce the statistician knows that with the rarity of top candidates and their acute dependence on social initial conditions, there is no guarantee that the right person will always be there to rise for the occasion. Their immediate function, obviously, is to push forward the evolution of the networks of signs constituting culture. Even if taking them to be a superior variant of the genus homo, Peirce does not follow their long-term destiny, though: do they also constitute the first harbingers of a biologically superior future humanity? Around the same time, Peirce considers a third solution to the riddle: the stepwise increase of human spheres of interest. In a review of his disciple Josiah Royce’s Religious Aspect of Philosophy from 1885, he describes a possibility implying neither divine guidance nor great men: “For altruism is but a developed egoism; that same sensitiveness which in its lowest state is selfishness, first transforms itself into esprit de corps or collective selfishness; then, passing from feeling for others collectively to feeling for them individually, it becomes philanthropy, pity, sympathy tossed hither and thither rudderless on the ocean of human misery; finally, steadying itself by the conception of an ideal humanity and a divine providence, it passes into christian charity, which gathers up all selfishnesses and all pities and is ready to give each its due measure” (EP I, 239; CP 8.49).³³⁸ That is, an individual process of Bildung, an ongoing biographical sophistication of the moral character of the person, a bit like Ciceronian humanitas: a disposition requiring lifelong intellectual cultivation. In a typically Peircean move, a continuous development line from initial, narrow egoism to the final, assumedly generalized charity of Christians is drawn, taking the shape of an ongoing extension of beings regarded worthy of participating in the moral community of an ideal humanity. Such humanity and divine providence, however, are not posited as existing, active, mechanical forces, rather as “conceptions”, as guiding ideals serving the extrapolation of moral dignity in the individual.

1880s–1890s: Biological Instinct and Objective Idealism On the animal scale of intelligences mentioned, humans in general possess “special aptitudes for guessing right”, Peirce claimed in “A Theory of Probable Infer-

1880s–1890s: Biological Instinct and Objective Idealism

341

ence”, 1883 (CP 2.753). If that were not the case, even the greatest of men, as he adds, would have knowledge the level of an idiot. This aptitude Peirce would connect to the inference type of retroduction or abduction, creating hypotheses faced with a surprising fact. An infinity of such hypotheses to be investigated, however, are possible given any particular fact to be explained, which could be said to form the general riddle of abduction: why is it that human beings guess right in this vast pool of possibilities most of the time, or, in any case, sufficiently many times for scientific development to prove possible? Abductive guesses, of course, must be investigated further by deduction and induction to gain evidence, but why is it that scientists do not waste their time on such further investigation in the large majority of abduction possibilities but are, most often, able to quickly zoom in on a few selected fertile hypotheses candidates for further scrutiny? Here, Peirce’s argument is evolutionary: “… in point of fact, not man merely, but all animals derive by inheritance (presumably by natural selection) two classes of ideas which adapt them to their environment. In the first place, they all have from birth some notions, however crude and concrete, of force, matter, space, and time; and, in the next place, they have some notion of what sort of objects their fellow-beings are, and of how they will act on given occasions” (CP 2.753). Naive physics and naive sociology, as it were. Organisms are born with certain competences regarding elementary physics and relevant parts of the biology and sociology of their own species: “Man has thus far not attained to any knowledge that is not in a wide sense either mechanical or anthropological in its nature, and it may be reasonably presumed that he never will” (CP 2.753). This idea feeds into what would become a standard assumption of the mature Peirce, that human knowledge is necessarily “anthropomorphist”, and he aggressively sticks to this idea in the face of contemporary critics claiming that it be an important goal to cleanse human knowledge from anthropomorphisms; cf. below. Such an idea, Peirce claims, is simply impossible, as it is the human anthropomorphist instinct for guessing right which leads us on the track selecting correctly, as a tendency, among the plethora of possible abductive guesses. Not only does abduction form part of human instinct; the same goes for deduction itself: We usually conceive Nature to be perpetually making deductions in Barbara. This is our natural and anthropomorphic metaphysics. We conceive that there are Laws of Nature, which are her Rules or major premisses. We conceive that Cases arise under these laws; these cases consist in the predication, or occurrence, of causes, which are the middle terms of the syllogisms. And, finally, we conceive that the occurrence of these causes, by virtue of the laws of Nature, results in effects which are the conclusions of the syllogisms. Conceiving of nature in this way, we naturally conceive of science as having three tasks—

342

Chapter 19: Limited Individuals and Unlimited Aims

(1) the discovery of Laws, which is accomplished by induction; (2) the discovery of Causes, which is accomplished by hypothetic inference; and (3) the prediction of Effects, which is accomplished by deduction. It appears to me to be highly useful to select a system of logic which shall preserve all these natural conceptions (“A Theory of Probable Inference”, 1883, CP 2.713).

The three concepts, central to scientific explanations of many sorts, of laws, causes, and effects, are analyzed as metaphysical corollaries to the logic concepts of major-minor premises, and conclusions, respectively. As such, they exemplify Peirce’s Kantian doctrine of inference to metaphysics from logic, and here, this logical basis forms part of human instinct—cf. the discussion of the phenomenology of logic in Chapters 12 and 18. At the same time, they are taken to legitimize the adoption and formalization of all three Peircean steps of inquiry: ab-, de-, and induction. Thus, Peirce’s vast efforts to formalize logic as well as scientific methodology form an attempt to make explicit and clear what already lies implicit and less precise in human instinct; cf. the distinction between logica utens and logica docens—logic implicit in use versus logic as the explicit object of study.³³⁹ This naturalist embodiment theory thus finds certain biological, instinctive bases for the development of human knowledge. Such restrictions, however, come to stand in a certain tension to the growth of Peirce’s objective idealism in the ensuing period. The idea that regularities of the cosmos, as described in general predicates and investigated in scientific laws, form a sort of mental aspect of nature itself is further boosted in Peirce’s spiritual “Law of Mind” period in the early 1890s, in the wake of a personal religious crisis.³⁴⁰ In parallel, the idea that the semiotic activity of individuals makes up their personality is further hypostatized to a system of general habits: “Habit tends to coordinate feelings, which are thus brought into the order of Time, into the order of Space. Feelings coordinated in a certain way, to a certain degree, constitute a person; on their being dissociated (as habits do sometimes get broken up), the personality disappears” (“Logic and Spiritualism”, 1890, W 6, 393; CP 6.585).³⁴¹ This doctrine makes clearer some ambiguous aspects of Peirce’s early theory: the claim that the sign use of individuals makes up his or her personality. Now, feelings, that is, elementary quale consciousness, enter the picture as that which is coordinated by the inference chains of habits, while Peirce also places a stronger emphasis on the stable, general parts of that sign use which constitutes the individual’s system of habits across individual sign actions. Unlike the 1878 idea of pragmatism where the aim of making ideas clear, involving awareness, seemed to embrace most if not all of human ideas, most habits are now unconscious and with them the individual’s personality. So that personality is now identical to

1880s–1890s: Biological Instinct and Objective Idealism

343

the system of habits regulating most everyday action and in need of no further check by reasoning—in contrast to scientific investigations transgressing and challenging such habits, necessitating logical and epistemological control. This habit personality, however, has no more fixed boundaries than the “mansign”. Quite on the contrary, most of the habit signs of a person is shared with other humans so that what remains really private in each of them is but a tiny part of the person. In 1891, Peirce wrote a number of comments on James’s Principles of Psychology that had appeared the year before. Here, his 31st question strongly opposes James’s Cartesian-like claim for the complete privacy of the inner life of each individual, resumed here before Peirce’s counterargument: No thought even comes into direct sight of a thought in another personal consciousness than its own. Absolute insulation, irreducible pluralism, is the law. Is not the direct contrary nearer observed facts? Is not this pure metaphysical speculation? You think there must be such isolation, because you confound thoughts with feeling-qualities; but all observation is against you. There are some small particulars that a man can keep to himself. He exaggerates them and his personality sadly (“Questions on William James’ The Principles of Psychology”, 1891, CP 8.81).

Thus, to Peirce’s theory of Personhood, much of the semiotic person is public, even more of it shared with other persons, and only a small part remaining private in the sense of kept inaccessible to others. A few years later, Peirce may even doubt references to reason which are often nothing but ex post rationalizations dressing up inferences which are not really rational but rather motivated by some unconscious habit: “Men many times fancy they act from reason when, in point of fact, the reasons they attribute to themselves are nothing but excuses which unconscious instinct invents to satisfy the teasing “whys” of the ego. The extent of this delusion is such as to render philosophical rationalism a farce” (“Philosophy and the Conduct of Life”, 1898, EP II, 32). Simultaneously with this piece of hermeneutics of suspicion, the very motor of the whole man=sign anthropology—cognition—is relativized considerably: “It is the instincts, the sentiments, that make the substance of the soul. Cognition is only its surface, its locus of contact with what is external to it” (Reasoning and the Logic of Things, 1992 (1898), 110)—cf. the rainy surface of the lake metaphor of the human mind in the previous chapter. Instincts, most of them unconscious networks of habit-signs of action and thought, now constitute the bulk of personality. The intellectualism of the early theory of personhood is considerably reduced. With this more detailed notion of personality, reference back to the man=sign equation of the 1860s now makes possible a similar, if surprising, mirror idea of the personification of general ideas per se: “… a person is only a partic-

344

Chapter 19: Limited Individuals and Unlimited Aims

ular kind of general idea. Long ago, in the Journal of Speculative Philosophy (Volume II, 156), I pointed out that a person is nothing but a symbol involving a general idea; but my views were, then, too nominalistic to enable me to see that every general idea has the unified living feeling of a person” (“Man’s Glassy Essence”, 1892, W 8, 182; CP 6.270).³⁴² It is the doctrine of general regularities as the mental aspects of the universe which is now taken to an almost panpsychic extreme: such ideas are now also supposed to have a sort of emotional inside to them, a sort of personal consciousness of their own. It is the same period in which Peirce may famously declare his “Schelling-fashioned idealism which holds matter to be mere specialized and partially deadened mind” (“Law of Mind”, 1892, W 8, 135; CP 6.102), and in contrast to the early period, such mind now even seems to be endowed with consciousness which undergoes quite a rehabilitation in this period. Consciousness will wane again in his mature period after 1900 (cf. below), but its prominence in Peirce’s spiritual interlude cannot be ignored. Here, humans, by entertaining general ideas, so to speak participate in the personalities inherent in the habits of the universe. While the anthropomorphism idea may, at a first glance, appear as a biological, serious, even narrow constraint upon human knowledge, this principle now rather makes of human beings a sort of cosmic agents directly participating in the mental development of the universe itself. In “The Law of Mind” where Peirce counterposes mechanical laws with the general mental law that ideas influence each other continuously, Peirce directly connects this broadened doctrine of personality with the notion of a personal deity. There is a … teleological harmony in ideas, and in the case of personality this teleology is more than a mere purposive pursuit of a predeterminate end; it is a developmental teleology. This is personal character. A general idea, living and conscious now, it is already determinative of acts in the future to an extent to which it is not now conscious. This reference to the future is an essential element of personality. Were the ends of a person already explicit, there would be no room for development, for growth, for life; and consequently there would be no personality. The mere carrying out of predetermined purposes is mechanical (W 8, 155; CP 6.157).

Open-ended teleological growth is now a crucial feature of the semiotic network of personality, and its final telos escapes grasp. But this development of the personality hypothesis is immediately taken to harbor consequences for the philosophy of religion: “… a genuine evolutionary philosophy, that is, one that makes the principle of growth a primordial element of the universe, is so far from being antagonistic to the idea of a personal creator, that it is really inseparable from that idea; while a necessitarian religion is in an altogether false position and is destined to become disintegrated. But a pseudo-evolutionism which enthrones

From Anthropomorphism to the Celebration of Error

345

mechanical law above the principle of growth, is at once scientifically unsatisfactory, as giving no possible hint of how the universe has come about, and hostile to all hopes of personal relations to God” (W 8, 155; CP 6.157). What may now serve to unite personality and theism, biology and objective idealism, in Peirce’s early 1890s spiritual anthropology, is his vast generalization of evolution. ³⁴³ Arguing that the central role of evolution in biology after Darwin must exalt evolution to an elementary process of the universe as a whole, Peirce effectively extends evolution in two directions, as it were: to the pre-biological development of the physical universe whose laws are regularities adopted by habit-taking (as he had already mused in the 1887 “Guess at the Riddle”) and to the scientific community’s quest for truth across generations as he had claimed since the 1860s. All this might now come together in a bracing evolutionism claiming the whole of the universe to be alive and evolving. Peirce’s mystifying claim that the living universe and the personal god are inseparable, however, is not resolved in any clear way: is it a pantheist claim that the whole of the universe is identical to the divine person—or is it a theistic claim that this deity remains separate from the living, ordered universe he created and through which he and humans may communicate? Evolution points in the former direction, theism in the latter. Peirce seemed to cool down somewhat after his intensely spiritual period of the early 1890s, particularly when he came back to intensive formal work with his logic graphs from around 1896, but the idea of a special, divine place for human-like beings in the universe would keep on lurking in the background into his last large creative explosion of the 1900s. In 1893, he asked: “What is it, then, that the whole people is about, what is this civilization that is the outcome of history, but is never completed?” and immediately gave the answer: “We may say that it is the process whereby man, with all his miserable littlenesses, becomes gradually more and more imbued with the Spirit of God, in which Nature and History are rife”.³⁴⁴

From Anthropomorphism to the Celebration of Error Such an idea paves the way for the reference to ideas inspired by theology—theist, deist, panpsychist, or pantheist—in the philosophical anthropology of the mature Peirce. Peirce, however, continued to harbor large doubts as to the relevance of any established theological dogma: In my opinion, the present infantile condition of philosophy, (…) is due to the fact that during this century it has chiefly been pursued by men who have not been nurtured in dissecting-rooms and other laboratories, and who consequently have not been animated by the

346

Chapter 19: Limited Individuals and Unlimited Aims

true scientific Eros, but who have on the contrary come from theological seminaries, and have consequently been inflamed with a desire to amend the lives of themselves and others, a spirit no doubt more important than the love of science for men in average situations, but radically unfitting them for the task of scientific investigation (“Philosophy and the Conduct of Life”, 1898, EP II, 29).³⁴⁵

So, we should hardly expect the teachings of any particular Christian confession to directly step in to account for the human role in cosmology. Theological inspiration takes a more indirect character. This constant refusal to admit explicit theological teachings into metaphysics has a special reason in Peirce. To him, religion is primarily a practical issue, rather than an issue of theoretical dogma. The role of a church is important not for developing doctrine or teaching theological truths, but in organizing the moral social life of believers and guiding their common practical activities.³⁴⁶ Theologians, by contrast, are guilty in mixing up this eminently practical task with theoretical metaphysics which they do not understand and should rather leave to scientists and philosophers: “They swamp religion in fallacious logical disputations” (“What is Christian religion?”, 1893, CP 6.438). The key to the involvement of religious themes and metaphors in Peirce’s anthropology is his repeated embrace of anthropocentrism, interpreted more and more in the direction of being closely related to human god-likeness, the classic homo imago dei argument. Anthropomorphism, in different guises, had been conceived as a scientific fallacy through most of the modern period ever since Francis Bacon, later analyzed by luminaries like Hume and Kant. Peirce’s contrarian embrace of the concept, however, is of a much more general version than the standard interpretation of anthropomorphism as the erroneous ascription of uniquely human properties to nature or divine beings (like souls to things, particular human feelings or intentions to animals, or human body shape or psychology to deities). Rather than defending what is traditionally attacked for anthropomorphism, Peirce provocatively adopts the pejorative very explicitly, so as to market his particular idea of the special role of human beings in the universe. In his mature period around and after the turn of the century, a number of different arguments attach to the concept: ‒ Quasi-tautologically: anything shaped by humans must eo ipso, in some general sense, be anthropomorphic ‒ Humans can reach insights based on their anthropomorphic instincts only, but among those instincts, reason itself forms a part ‒ Humans have an instinct for guessing right (cf. the riddle of abduction)—as this is a human capacity, it forms a central part of anthropomorphism

From Anthropomorphism to the Celebration of Error

‒ ‒

347

Anthropomorphism is not at all a source of falsity but rather an asset, a privileged capacity—in a version of the theological god-likeness argument Finally, anthropomorphism is connected to the problem of evil, the human participation in ongoing creation, and the possibility of intelligent life elsewhere in the universe—ambitiously connecting theological and cosmological issues which may only, however, be drafted in abductive guesses with little scientific evidence

The first, quasi-tautological version of anthropomorphism, may sound like this: “If I were to attach a definite meaning to ‘anthropomorphism,’ I should think it stood to reason that a man could not have any idea that was not anthropomorphic, and that it was simply to repeat the error of Kant to attempt to escape anthropomorphism” (“PAP” 1906 – 1907; NEM IV, 313). What is it that grants this sweeping notion of anthropomorphism? “’Anthropomorphic’ is what pretty much all conceptions are at bottom […]. And in regard to any preference for one kind of theory over another, it is well to remember that every single truth of science is due to the affinity of the human soul to the soul of the universe, imperfect as that affinity no doubt is” (Harvard Lectures on Pragmatism, 1905, EP II, 152; CP 5.47). So, no matter which competing theory will eventually turn out to be the better, it will be anthropomorphic in the sense of resulting from the affinity of two souls, that of humans and that of the universe. Thus, anthropomorphism in Peirce’s sense is granted by a sort of preestablished mental harmony between human beings and the cosmos. This renaissance-like idea, of course, should be tempered by what we know about Peirce’s anti-substantialist analyses of souls or personalities as but fuzzy, oriented networks of habit signs. Again, the connection between these two “souls” consists in their ability to incarnate the same general, “mental” ideas. And again, this connection, even if in some sense soulful or mental, has little if anything to do with consciousness; cf. below.³⁴⁷ Eventually, it has come into being through evolution granting the intellectual fitness of humans to their surroundings. The very conclusion of the whole, ambitious Harvard pragmatism lecture series of 1903 zooms in on exactly anthropomorphism: It will be asked whether he will not have a shocking leaning toward anthropomorphic conceptions. I fear I must confess that he will be inclined to see an anthropomorphic, or even a zoömorphic, if not a physiomorphic element in all our conceptions. But against unclear and nonsensical hypotheses, [of] whatever ægis [he will be protected]. Pragmatism will be more essentially significant for him than for any other logician, for the reason that it is in action that logical energy returns to the uncontrolled and uncriticizable parts of the mind. His maxim will be this:

348

Chapter 19: Limited Individuals and Unlimited Aims

The elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action; and whatever cannot show its passports at both those two gates is to be arrested as unauthorized by reason (Harvard Lectures on Pragmatism, 1905, EP II 241; CP 5.212).

Here, anthropomorphism is generalized to zoo- or even physiomorphism, signaling the human embeddedness in regularities of the universe on several levels. Knowledge, on all these levels, is granted by pragmatist perception-action cycles weeding out, as if in passport control, false or erroneous conceptions. Importantly, action as pragmatist control of knowledge should not be confused with any idea that action be the primary or even only goal of knowledge, nor any interpretation of pragmatism in the direction of utilitarianism. Here, Peirce is on guard against such tendencies in his fellow pragmatists in the years around 1900, after James had popularized the term pragmatism in the late 1890s. When reviewing Karl Pearson’s The Grammar of Science in 1901, Peirce remarks on Pearson’s claims that the “stability of society” should be a noble ethical aim: To demand that man should aim at the stability of British society, or of society at large, or the perpetuation of the race, as an ultimate end, is too much. The human species will be extirpated sometime; and when the time comes the universe will, no doubt, be well rid of it. Professor Pearson’s ethics are not at all improved by being adulterated with utilitarianism, which is a lower motive still. Utilitarianism is one of the few theoretical motives which has unquestionably had an extremely beneficial influence. But the greatest happiness of the greatest number, as expounded by Bentham, resolves itself into merely superinducing the quality of pleasure upon men’s immediate feelings. Now, if the pursuit of pleasure is not a satisfactory ultimate motive for me, why should I enslave myself to procuring it for others? (8.141).

Peirce steadfastly refuses to admit neither the stability of society nor general happiness as relevant ultimate aims of action. What those general aims might be he does not address here but would return to it later in his mature period. Here, he even predicts a time when the role of earthling humans in co-creating the universe may have reached its end. But if anthropomorphism makes of reason a human instinct, it differs from most animal instincts in being much more plastic and hence also capable of a much larger degree of error.³⁴⁸ Already in 1893, he had hailed ignorance and error as virtual “sacramenta” that he would never give up,³⁴⁹ and in the years after 1900, Peirce develops this idea in detail: One of the most remarkable distinctions between the Instinctive mind of animals and the Rational mind of man is that animals rarely make mistakes, while the human mind almost

From Anthropomorphism to the Celebration of Error

349

invariably blunders at first, and repeatedly, where it is really exercised in the manner that is distinctive of it. If you look upon this as a defect, you ought to find an Instinctive mind higher than a Rational one, and probably, if you cross-examine yourself, you will find you do. The greatness of the human mind lies in its ability to discover truth notwithstanding its not having Instincts strong enough to exempt it from error. This comes out strongly in almost any concrete instance. Frederic the Great is a notable example. Kant’s power of making use of confused conceptions and working out so much truth as he did in spite of them illustrates this virtue. Hardly any really great inventor thoroughly comprehends his own invention until long after it is achieved (Minute Logic, 1902, CP 7.380; he adds in the margin that “This is the marvel and admirable in it; and this essentially supposes a generous portion of capacity for blundering”).³⁵⁰

This re-evaluation of error and mistakes as a necessary, even benign component of reasoning forms a new way of bridging the anthropological chasm: errorprone individuals really just incarnate what now appears to be a major virtue of human instincts—their plasticity: “But fortunately (I say it advisedly) man is not so happy as to be provided with a full stock of instincts to meet all occasions, and so is forced upon the adventurous business of reasoning, where the many meet shipwreck and the few find, not old-fashioned happiness, but its splendid substitute, success. When one’s purpose lies in the line of novelty, invention, generalization, theory—in a word, improvement of the situation—by the side of which happiness appears a shabby old dud—instinct and the rule of thumb manifestly cease to be applicable” (Minute Logic, 1902, CP 2.178). In the same movement, new, more general ideal aims of reasoning are made explicit: novelty, invention, generalization, theory. The year after, in the Harvard lectures, this doubleness of reason—plasticity/ error—is redescribed in Darwinian terms: It is a truth well worthy of rumination that all the intellectual development of man rests upon the circumstance that all our action is subject to error. Errare est humanum is of all commonplaces the most familiar. Inanimate things do not err at all; and the lower animals very little. Instinct is all but unerring; but reason in all vitally important matters is a treacherous guide. This tendency to error, when you put it under the microscope of reflection, is seen to consist of fortuitous variations of our actions in time. But it is apt to escape our attention that on such fortuitous variation our intellect is nourished and grows. For without such fortuitous variation, habit-taking would be impossible; and intellect consists in a plasticity of habit (The Harvard Lectures on Pragmatism, 1903, CP 6.86).

The plastic tendency to error is reanalyzed as fortuitous variation, the Darwinist concept of natural variety being the presupposition to natural selection. Individual organisms not passing the survival test during selection are akin to scientific errors weeded out. Both form an indispensable part of the evolutionary process. So, the human instinct of reason quickly produces fortuitous variation, including

350

Chapter 19: Limited Individuals and Unlimited Aims

lots of errors, in ontogenetic time, instead of awaiting the slow production of and selection among such variation in phylogenetic time.

Human Participation in Creation In Peirce’s most explicit and most-quoted theological effort, the Neglected Argument for the Reality of God (1908), the reason-as-instinct theory is taken to new heights: “Animals of all races rise far above the general level of their intelligence in those performances that are their proper function, such as flying and nestbuilding for ordinary birds; and what is man’s proper function if it be not to embody general ideas in art-creations, in utilities, and above all in theoretical cognition?” (EP II, 443; CP 6.476). The central instinct of humans simply amounts to externalize general ideas in all sorts of exterior signs of an extended mind doctrine: art, technology, and science. Far from being a threat against scientific truth, then, anthropomorphism in Peirce’s sense forms its very condition of possibility, it is an asset which permits humans a degree of fit into the universe, both implicitly, unconsciously, and more explicitly in the growth of externalized embodiments of ideas mentioned. Thus, anthropomorphist reason and the external embodiment of general ideas are but two sides of the same coin. This finally leads to the involvement of certain theological conjectures or abductions. It must immediately be added that the Neglected Argument for the existence of God is less than convincing. It claims that in the course of the Schillerian free “play of musement”, that is, the sort of free daydreaming considering the compatibility of possibilities without or before any obligation to truth and method, the idea of a deity will invariably appear and foster a certain interest, growing along with increasing musement. In short, it is nothing but an abduction.³⁵¹ Here, the abduction-as-anthropomorphic-instinct theory comes in handy, for it makes it probable, so Peirce, that this attractive theological complex of ideas be true. It remains, however, as he says, a “strictly hypothetical God” (EP II, 440; CP 6.467). Peirce, however, is so convinced by his “humble argument” that it makes him revise the self-control demand of arguments. Now, he distinguishes “argumentation”, with explicit premises and subjected to full self-control, from the broader notion of “argument”, referring more vaguely to “any process of thought reasonably tending to produce a definite belief” (EP II, 435; CP 6.456). We get no criteria for when a mere “argument” in this sense is performed “reasonably”. Sometimes, however, he claims to be willing to submit the hypothesized idea of a deity to the full pragmatist method and hence deduct certain necessary inferences from it for inductive testing—such as the liveliness or understandability of the universe, as when saying that mus-

Human Participation in Creation

351

ing is “… resulting in a hypothesis of the very highest Plausibility, whose ultimate test must lie in its value in the self-controlled growth of man’s conduct of life” (EP II, 446; CP 6.480). As Cheryl Misak dryly remarks, however, he “… seems to have been aware of the sogginess of his argument, for each time he begins to talk about ‘tracing out a few consequences of the hypothesis’, he quickly changes subject”.³⁵² The “neglected argument” contains pretty little about the more precise character of the hypothesized deity, and you might be tempted to ask which underpinning of understanding or of consolation any entity that vague and hypothetical would really offer. A text like Answers to Questions Pertaining to My Belief in God of 1905 gives considerably more detail, in which Peirce lists his position on each of the traditional properties ascribed to the Christian deity. The conclusion, however, is similar to the vagueness of the “neglected argument” in its insistence that people who refuse God do so because they make a much too precise concept of him. “God” can be a very vague concept only and must remain so, accessible to instinct rather than argument—Peirce here implicitly relying upon a version of the standard idea of God’s mysterious ways.³⁵³ Even if admittedly guesswork, such theological improvisations may throw some further light upon the mature Peirce’s understanding of the human condition. In 1905, Peirce repeats his general anthropomorphism, now connecting it with humans as children of God: I hear you say: “This smacks too much of an anthropomorphic conception.” I reply that every scientific explanation of a natural phenomenon is a hypothesis that there is something in nature to which the human reason is analogous; and that it really is so all the successes of science in its applications to human convenience are witnesses. They proclaim that truth over the length and breadth of the modern world. In the light of the successes of science to my mind there is a degree of baseness in denying our birthright as children of God and in shamefacedly slinking away from anthropomorphic conceptions of the universe (Harvard Lectures of Pragmatism; 1905, EP II, 193; CP 1.316).

So, the flip side of anthropomorphism is really the age-old god-likeness argument, homo imago dei, that humans are created in the image of God. The reason why anthropomorphism may be thus turned around 180 degrees is really that it is but another word for theomorphism. Both universe and humans bear the same divine stamp, and the former may, hence, be understood by the latter.³⁵⁴ And the scientific discovery of regularities is nothing less than reading parts of the divine mind. In the next step, this is connected to Peirce’s purported solution to that central riddle of the centuries of the Enlightenment, the theodicée. How could an omniscient, omnipotent, and benevolent deity have created a universe ripe

352

Chapter 19: Limited Individuals and Unlimited Aims

with evil and misery? Leibniz famously claimed to solve this conundrum with his doctrine of “the best possible world”, but Peirce seeks a different way. In a small quip without dating (but probably late), Peirce defined “evil” in the following way: “Evil: That which men in general ought to resist. The well-being of mankind demands that there should be pain and evil; and he ought to thank God for permitting them to exist. For so man is permitted to have a part in the creation” (R 1177, 6). Evil must be there because it urges humans to resist it, to indulge in ameliorating activity, to enter into their lifelong quest of reasoning and selfcontrol. So, the instinct of reason is not sufficient. Humans must be nudged forward by the existence of pain and evil—and the award, in the other end, is becoming thereby collaborators of the deity in the ongoing creation of the universe. So, pain and evil now appear as further means to bridge the anthropological chasm. Peirce’s evolutionist universe, of course, is never finished, it is a living, mental being whose ultimate end has hardly yet been disclosed. But humans are privileged co-creators in this process: As for the ultimate purpose of thought, which must be the purpose of everything, it is beyond human comprehension; but according to the stage of approach which my thought has made to it—with aid from many persons, among whom I may mention Royce (in his World and Individual), Schiller (in his Riddles of the Sphinx) as well, by the way, as the famous poet (in his Aesthetische Briefe), Henry James the elder (in his Substance and Shadow and in his conversations), together with Swedenborg himself—it is by the indefinite replication of self-control upon self-control that the vir is begotten, and by action, through thought, he grows an esthetic ideal, not for the behoof of his own poor noddle merely, but as the share which God permits him to have in the work of creation (“Issues of Pragmaticism”, 1905, CP 5.402, n. 2; the “famous poet” is Friedrich Schiller, not to be confused with the eponymous F. C. S. Schiller mentioned).

Humans participate in cosmological evolution even if its long-term aim lies beyond human understanding. They do so by developing still further externalizations of general ideas, underpinned by their simultaneous grasping new levels in the hierarchy of self-controls. Interestingly, Peirce here spills a bit of his theological beans. The father of his friends William and Henry, Henry James Sr., is given as the source of Peirce’s solution to the problem of evil:³⁵⁵ “As for the ‘problem of evil,’ and the like, I see in them only blasphemous attempts to define the purposes of the Most High,—or rather that is what I think of such disturbances of religious consciousness generally; but that particular problem has received the most beautiful and satisfactory solution in Substance and Shadow” (Letter to William James, July 23, 1905, CP 8.263). The book title is James Sr.’s Swedenborgian treatise of 1863. So, what is this grand solution? In an “Additament” to the Neglected Argument article, Peirce further explains: “… bless God for the law of growth with all the fighting it imposes upon him—Evil, i. e.,

Human Participation in Creation

353

what it is man’s duty to fight, being one of the major perfections of the Universe” (1908, EP II, 445; CP 6.479). Peirce’s evolutionary, growing universe also inherits the Darwinist property of struggle, now theologically reinterpreted as necessitated by the occurrence of evil. Evil is here, quasi-Leibniz, interpreted as one of the major perfections of the universe because driving further its living, evolutionary process.³⁵⁶ The vir of James Sr. to which Peirce referred above, then, is the individual aim for which the mere homo should strive in his or her life-long process of increasing self-control. In 1898 he had, in a rare interest in the concept of sin, portrayed this process of learning through the metaphor of sinning: “But just as it is not the self-righteous man who brings multitudes to a sense of sin, but the man who is most deeply conscious that he is himself a sinner, and it is only by a sense of sin that men can escape its thraldom; so it is not the man, who thinks he knows it all, that can bring other men to feel their need of learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning” (“The First Rule of Logic”, 1898, EP II, 47; CP 5.583). Comparing ignorance with sin and knowledge with repentance, increased self-control and learning are taken as two aspects of the road from homo to vir, from selfpride to humility. Much later, in 1910, Peirce will identify this mature vir phase with the “real self” of humans: “When I speak of a man’s Real Self, or True Nature, I mean the Very Springs of Action in him, which I mean how he would act, not when in haste, but after due consideration; and by “due consideration”, I mean such deliberation as shall give him time to develop, to grow up to his proper Manhood, which many a man never does actually attain in this world, scarce any of us, fully” (“How to Define”, 1910, LoF 3.1, 401). Here, he compares the idea of infant baptism that the child’s “sponsors at the font” grant that it will receive the proper education so as to acquire the habits of feeling of a proper Christian, on the one hand, with Baptists claiming the child must await actually having acquired those feelings before he becomes “a new man”, on the other. Here, Peirce’s conception of human maturation is that the Real Man consists in how he would act if given due time to grow up and develop “proper Manhood”, which many never actually achieve. Thus, Peirce’s ideas of personal maturation are shaped by exploiting Christian metaphors, rather than e. g., Ciceronian ideas of humanitas with related ideas of individual cultivation of personality.³⁵⁷ In the same 1905 letter to James, Peirce ties the knot on a handful of these connections between anthropomorphism and theology: … I prefer the word “anthropomorphism” as expressive of the scientific opinion. […] And in particular if it implies theism, I am an anthropomorphist. But the God of my theism is not

354

Chapter 19: Limited Individuals and Unlimited Aims

finite. That won’t do at all. For to begin with, existence is reaction, and therefore no existent can be clear supreme. On the contrary, a finite being, without much doubt, and at any rate by presumption, is one of a genus; so that it would, to my mind, involve polytheism. In the next place, anthropomorphism for me implies above all that the true Ideal is a living power, which is a variation of the ontological proof due, I believe, to Moncure Conway’s predecessor, William Johnson (not James) Fox. That is, the esthetic ideal, that which we all love and adore, the altogether admirable, has, as ideal, necessarily a mode of being to be called living. […] Now the Ideal is not a finite existent. Moreover, the human mind and the human heart have a filiation to God. That to me is the most comfortable doctrine. At least I find it most wonderfully so every day in contemplating all my misdeeds and shortcomings (CP 8.262).

Peirce’s deity must be infinite, for a finite god would exist, that is, enter into actual action-reaction events on the level of other existing, individual objects. This, of course, goes against James’s version of pragmatism according to which everything is finite. To Peirce, by contrast, this implies that this god does not exist as an individual at all but rather has the character of a general “living power”. The original ontological argument of Anselm, of course, claimed that as God is a perfect being He must exist, for non-existence would contradict His perfection. The version Peirce embraces is infused with evolutionism: the most admirable ideal must be living—if it were not living, it would not be admirable. It is to this living but non-existing deity that human beings are claimed to have a “filiation”. But it is a strange kind of divine life, and the mature Peirce’s deity moves in mysterious ways indeed: How, for example, can we ever expect to be able to predict what the conduct would be, even of [an] omniscient being, governing no more than one poor solar system for only a million years or so? How much less if, being also omnipotent, he be thereby freed from all experience, all desire, all intention! Since God, in His essential character of Ens necessarium, is a disembodied spirit, and since there is strong reason to hold that what we call consciousness is either merely the general sensation of the brain or some part of it, or at all events some visceral or bodily sensation, God probably has no consciousness. Most of us are in the habit of thinking that consciousness and psychic life are the same thing and otherwise greatly to overrate the functions of consciousness (“Additament”, 1908, EP II, 447; CP 6.489).³⁵⁸

God is a living ideal, a necessary being, yet without existence nor consciousness, with no experience, desire, nor intention. He is also not omniscient, nor bound by morality.³⁵⁹ We are almost approaching a negative God, the apophatic deity of the mystics, of which most if not all characterizations are false. Peirce’s difficult —and indeed, anti-anthropomorphic (in the standard sense of the word)—conception also approaches a Spinozist idea of God simply consisting in the regularity of the universe. Still, in contrast to Spinoza, Peirce’s idea seems to be that his

Humans, Aliens, and Purposes of the Universe

355

deity would still remain separate from the universe whose existent, material embodiment could not be part of the deity, and, in particular, whose “evil perfections” would also hardly form such parts.³⁶⁰

Humans, Aliens, and Purposes of the Universe If God has no consciousness, he has, or rather is, mind. In the Minute Logic (1902), a few years before, Peirce had connected his idea of mind closely to an analysis of the concept of purpose, or, more generally, to an interpretation of the Aristotelian final cause: “It is, as I was saying, a widespread error to think that a ‘final cause’ is necessarily a purpose. A purpose is merely that form of final cause which is most familiar to our experience” (EP II, 120; CP 1.211). This argument is aimed against the contemporary tendency to take ascriptions of purposes to non-human matters to be an anthropocentric error. To Peirce, final causes are leading the evolution of the universe, and it is only the tiny subset of them occurring to human or other consciousnesses which appear as purposes. Those final causes, now, are put to use to describe the regularities of the universe: “A class, of course, is the total of whatever objects there may be in the universe which are of a certain description. What if we try taking the term ‘natural,’ or ‘real class’ to mean a class of which all the members owe their existence as members of the class to a common final cause?” (EP II, 117; CP 1.204).³⁶¹ Peirce finds the theory of evolution has proved the existence—and shown the process of their realization—of such final causes in nature.³⁶² Far from all such final causes, now, may be known by humans, but way may be able discover some of them, e. g., in biology: Mind has its universal mode of action, namely, by final causation. The microscopist looks to see whether the motions of a little creature show any purpose. If so, there is mind there. Passing from the little to the large, natural selection is the theory of how forms come to be adaptive, that is, to be governed by a quasi purpose. It suggests a machinery of efficiency to bring about the end—a machinery inadequate perhaps—yet which must contribute some help toward the result. But the being governed by a purpose or other final cause is the very essence of the psychical phenomenon, in general (Minute Logic, 1902, CP 1.269).

This development of a generalized notion of final causes can be seen as yet another attempt to build the bridge between human individuals and their grand aims. All of the regularities of the universe which are being discovered by science, have a mental quality, and that quality is now further interpreted as generalized purposivity. An equation: regularity = mind = final cause is claimed, and

356

Chapter 19: Limited Individuals and Unlimited Aims

if God is indeed mind, this permits to see science as simply charting God’s truth through the regularities of the universe: “I recognize two branches of science: Theoretical, whose purpose is simply and solely knowledge of God’s truth; and Practical, for the uses of life” (EP II, 117; CP 1.239). With science studying the purposes of the universe, it simultaneously charts fragments of the divine. Thus, this notion of divinity is intimately wed to reason. In 1902, Peirce outlined a fourth degree of clearness in addition to the third of the Pragmatic Maxim, this higher degree tied to how a conception serves the ongoing development of “concrete reasonableness”: … a still higher grade of clearness of thought can be attained by remembering that the only ultimate good which the practical facts to which it directs attention can subserve is to further the development of concrete reasonableness; so that the meaning of the concept does not lie in any individual reactions at all, but in the manner in which those reactions contribute to that development (“Pragmatic and Pragmatism”, Baldwin’s Dictionary of Philosophy and Psychology, 1902, CP 5.3).

This development, again, is simply one and the same thing as the continuous creation of the universe: “The creation of the universe, which did not take place during a certain busy week in the year 4004 B.C., but is going on to-day and never will be done, is [the] development of Reason. I do not see how one can have a more satisfying ideal of the admirable …” (“What Makes a Reasoning Sound?”, 1903, EP II, 255; CP 1.615). And the human ideal of conduct is nothing but participating in this grand cosmological story: “… the ideal of conduct will be to execute our little function in the operation of the creation by giving a hand toward rendering the world more reasonable whenever…it is ‘up to us’ to do so” (“What Makes a Reasoning Sound?”, 1903, EP II, 255; CP 1.615). So, the whole network of signs of which individuals, groups, societies, intelligent species, form a part, comes together in one sign which is the universe itself: “… the universe is a vast representamen, a great symbol of God’s purpose, working out its conclusions in living realities” (“The Basis of Pragmaticism in the Normative Sciences”, 1906, EP II, 393; CP 5.119). That is about as close as we get to Peirce outlining his idea of the admirable, the supreme aesthetic value, supposed to constitute the highest level of the self-control hierarchy and of human behavior in general. Interestingly, God’s thoughts as incarnated in the universe are considerably more accessible to human investigation than is the deity itself who remain the object only of the vaguest of abductions. Peirce’s theological improvisations have important implications for how he conceives of the role of humanity and intelligence in the universe. We already mentioned how he extended reason to “all races of being” in 1878; now he returns to this issue, initially correcting himself, claiming now that the human

Security, Uberty, and Humanity

357

race is on the brink of extinction within generations, and it may be illusory that any future intelligences will prove able to continue its achievements. Still, … there is a bare possibility, which it is quite beyond our forces to evaluate, that among the millions of stars our telescopes descry, there may be a sufficient number not too far away, that have planets on which the to us wholly unknown conditions are present for the formation of something like living protaids, and it may be that in some cases these develope into intellectual beings; and it may not be absolutely beyond the bounds of possibility that some of them may visit the earth, may detect the vestiges of human occupation, and may ascertain something of human science. There is a religious faith that the universe was not made entirely for inanimate things, and that it somehow preserves the good qualities of the soul. For my own part, I think I should be willing to stake my whole personal felicity, at long odds, upon its being so; although of course I cannot be sure of this until the occasion actually arises, if it ever should. At the same time, I am forced to acknowledge that this has not one grain of scientific weight (R 601, undated, late; Robin’s guess: between 1902– 1908).³⁶³

Hope is deposited in interplanetary intelligence, granted by the existence of some affinity of the universe to animate beings. Just like the deity of the Play of Musement, the optimism of the existence of alien, non-human intelligences, however, remains but an alluring, hypothetical abduction without any evidence.³⁶⁴ But Peirce would bet.

Security, Uberty, and Humanity Thus, Peirce is perfectly clear that such ideas about the central role of humans and human-like beings in the universe are but guesses at the riddle whose only underpinning is really the supposed anthropomorphism of abduction. But are there any clear borderlines between unchecked abduction and mere hope? In his very last finished paper, An Essay toward Reasoning in Security and Uberty (1913), written at a point where Peirce would probably have known he was moribund, he returns to this idea in his final pronouncements on philosophical anthropology.³⁶⁵ He used to think that the human race “… would become extinct before any great number of future centuries. But in the first place further consideration has pretty nearly balanced that inclination of judgment; and in the next place, if it be so, I incline toward guessing that another and more intelligent race may supplant us to advantage; though this the merest dream” (EP II, 466). That the universe should be somehow conducive to the growth of intelligent races remains but a vague belief. In any case, the noble ideas for which humanity may strive remain beyond the reach of pragmatism as a method. For pragmatism “… certainly aids our ap-

358

Chapter 19: Limited Individuals and Unlimited Aims

proximation to security of reasoning. But it does not contribute to the uberty of reasoning, which far more calls for solicitous care. […] … the Maxim of Pragmatism does not bestow a single smile upon beauty, upon moral virtue, or upon abstract truth, the three things that alone raise Humanity over Animality” (EP II, 465). In this final text, virtually Peirce’s intellectual testament, he thus adds to defining humanity by the semiotic and intellectual means it employs—self-control, hypostatic abstraction, semiotic communities, externalization of ideas,—the central aims of using those means in the shape of the age-old triad of the beautiful, the good, and the true—aesthetics, ethics, and logic, Peirce’s three “normative sciences”. Yet, they are not beyond the reach of human reason more generally, rather, they are supposedly the ultimate aims of reasoning, innovation, generality and their ongoing externalizations in art, technology, and science. Peirce here argues against Bacon’s claim that the subtilities of nature will forever transcend, by far, the subtilities of human senses and reason (for how could Bacon then know about the existence of such subtilities in the first place, given his own method?) and, as a current scientific counterexample, Peirce substantiates his scientific optimism by pointing to how the puzzling, recent Michelson-Morley experiment has already received one exact interpretation.³⁶⁶ Peirce’s final optimism is based on the plasticity of human instinct: “Like animals we may be betrayed by our instincts. But even animals like bees and toads may learn to modify their instincts, and human instincts are far more ‘mutable’” (EP II, 468). This plasticity is visible in the “extraordinary variety of languages, customs, institutions, religions, as well as the many revolutions [these] have undergone in the brief half-dozen of millennia to which our acquaintance with them is as yet limited, as compared with the almost insignificant anatomical variations …” (EP II, 468). Such large human cultural variety on the basis of the tiny biological variety of the species homo confirms that you cannot possibly infer from the lack of instinctive reason to any lack of historical improvement of reasoning abilities. That would be old-fashioned and with no appeal to “a modern”, as Peirce says. Human progress of 6,000 years is the empirical fact grounding Peirce’s final modernist optimism and its cosmological guesses, after all. This would be Peirce’s final word on the riddle of how the sad condition of individual reason needs not imply the impossibility of an optimistic destiny of humanity.

The Human Predicament What makes humans differ from animals? Summing up, human beings master the sign type hypostatic abstraction; they have more levels of self-control; human reason is prolonging instinct and becoming entrenched as part of

The Human Predicament

359

human instinct itself; humans have a far larger plasticity of instincts and, correlatively, a far larger capacity for blundering but for that same reason also a capacity for correcting error; the ability to reach the admirable values of beautygoodness-abstract truth by the ongoing externalization of such general ideas in media like art, technology, science. All these features are more or less metaphorically or abductively described by humans being children of God, created in the image of the unconscious deity, partaking in creation in an evolving, still more regular universe being somehow friendly or receptive to the evolution of intelligences—all of it with its final future purposes unknown or at best vaguely glimpsed. In this most intoxicating version of the picture, humans are but unfinished and busy working on a transhuman evolutionary trajectory of improving themselves and the universe with them, far into a divine future beyond the understanding of humanity’s present incarnation. But are humans really capable of this? This is the question posed by the internal structure of Peirce’s conception of humanity: What may solve the gaping chasm at the center of Peirce’s anthropology, connecting radically imperfect individuals with the high-reaching aims of humanity and beyond? A number of proposals are investigated: 1) divine guidance, 2) the emergence of great personalities, 3) the gradual extension of human ethical sensibility to cover all human and transhuman intelligences, 4) the ongoing externalization and making explicit the fleeting results of thought and action, 5) an integrated conception of humanity modeled upon the transgenerational scientific community; 6) evolution, encompassing pre- as well as postbiological development of cosmos and society, involving individuals in an overarching living, creative universe; 7) the plasticity of human instinct making it fallible but simultaneously capable of ongoing ontogenetic learning and personal development; 8) the nudging of imperfect individuals by pain and evil, these thus constituting ultimately benevolent if not sacred forces; and 9) anthropomorphism, in Peirce’s special sense, granting humans and similar transhuman intelligences favorable conditions in the universe and its overarching finality. To what degree these different connections between restricted individuals and their infinite aims are mutually exclusive—or whether they are rather interlinked or maybe even constitute the very same state of things on different levels of description—is harder to establish. For an approach like that of the present book whose interest lies primarily in the safer waters of Peirce’s logic, semiotics, and philosophy of science, what could be learned from these more extravagant parts of Peirce’s reflections? One is that signs and individual semiotic entities and acts such as diagrams, assertions and inferences continuously interlink and constitute large network complexes. This is facilitated by Peirce’s elementary insistence that the purpose of

360

Chapter 19: Limited Individuals and Unlimited Aims

signs is to be interpreted in other signs, that propositions are there to make possible inferences to further propositions. A further important issue is Peirce’s attempt to semiotically redefine a series of traditionally psychological or sociological entities as smaller and larger networks of signs. Persons and their personalities, texts and corpuses of texts interconnected by dialogical structures, social groups, communities, institutions, all the way up to civilizations, the whole of humanity, even the embeddedness of humanity in the physico-biological world on the one hand and in the evolution of future intelligent races, on the other hand. A human specificity is the instinct and growing ability to incarnate signs of all sorts in hypostatized external structures able to outlast the lives of their creators. This ambitious conceptual usage of networks of signs on all levels of size and complexity, it is important to emphasize, are intended to explain and replace more substantialist standard metaphysical definitions of notions like personality, science, community, culture, etc. Pragmatism has a strong anti-metaphysical aspect, evident in the reductionist claims in every single one among Peirce’s multiple versions of the maxim of pragmatism: the meaning of signs is nothing but the conceived effects, behaviors and actions following from their assumed truth. What is left in metaphysics after this radical cleansing, however, is no small residue. Peirce’s Scotist realism emphasizing the reality reference of predicates of true claims takes these growing networks of signs as a bedrock of what may, in turn, claim metaphysical existence. Seen from the inside of Peirce’s logic and semiotics, then, this growth and aims of semiotic networks pertain most clearly to concepts addressing the boundary conditions of his theory, such as scientific community, dynamic object, final interpretant, convergence to truth in the limit, self-control as grant of reasoning, etc. Obviously, it was a crucial interest to Peirce that these networks of signs develop according to certain norms, of which he most thoroughly investigated those of logic and epistemology—late in his career realizing the dependence of those cognitive, scientific norms on ethical and, in a very broad sense, aesthetic, norms. Peirce’s home-made theological improvisations testify to an intense urge of searching to find something to grant that limited, fallible, selfish, even evil and deplorable humans will actually prove able to rise to incarnate and develop those norms. The partial clothing of these hopes in religious garb indirectly demonstrates an important fact: that Peirce did not see human progress—as witnessed by 6,000 years of progress—granted for even the near future, rather resting but on a hope, a daydream, or pipe dream as strong or frail as religion or superstition. Thus, Peirce as an enlightenment thinker committed to the advancement of truth, good, and beauty, in short, to the development of Reason,

The Human Predicament

361

remained immensely anxious, even frightful that this project might eventually falter. Resting on the weakest abductions only, these many attempts to bridge the chasm between the limitations of the vast majority of individual human beings and the grand aims projected by the normative sciences are anything but definitive, even probable. Rather, they do little more than encourage to dig deeper in the attempts to understand and further that possibility, with little obvious grant of success.

Coda Finishing a book, as a writer or a reader, is reaching the limit of one finite series of signs. Peirce, from the very beginning, insisted that “all thought is in signs” which would serve as no bad headline of his whole endeavor. In particular, he realized, as an early proponent of the Extended Mind hypothesis, that “… it is much more true that the thoughts of a living writer are in any printed copy of his book than they are in his brain”. Expressing one’s thought in a book is not only transporting to another medium what was already there in the person, the psyche, or the brain. It is, rather, creating an external artifact containing much more than could ever be present in any individual mind, not to speak about any individual consciousness.³⁶⁷ This is why books may be fancied to be vaguely alive. But the book itself is finite, and so subject to other types of limitations: “… death makes the number of our risks, of our inferences, finite, and so makes their mean result uncertain. The very idea of probability and of reasoning rests on the assumption that this number is indefinitely great”. This is why Peirce hopefully insists that the individual writer, appearing in any number of books, really belongs to a larger continuum: “… our interests shall not be limited. They must not stop at our own fate, but must embrace the whole community. This community, again, must not be limited, but must extend to all races of beings with whom we can come into immediate or mediate intellectual relation. It must reach, however vaguely, beyond this geological epoch, beyond all bounds”. I do share this hope—as well as the nagging apprehension it may fail.

https://doi.org/10.1515/9783110793628-022

Literature Peirce References (see detailed references below) CP: EP I: EP II: LoF: NEM: PM: R:

Collected Papers (references by volume and paragraph number) The Essential Peirce, Volume I The Essential Peirce, Volume II Logic of the Future: Writings on Existential Graphs New Elements of Mathematics Philosophy of Mathematics Peirce manuscripts, microfilmed and numbered in accordance with the Robin Catalogue SS: Semiotics and Significs: The Correspondence Between Charles S. Peirce & Victoria Lady Welby SWS: Selected Writings on Semiotics 1894 – 1912 W: Writings of Charles S. Peirce: A Chronological Edition Amani, Majid (2008): “Logical Machines: Peirce on Psychologism.” In: Disputatio 2. No. 24, 335–348. Ambrosio, Chiara (2016): “The Historicity of Peirce’s Classification of the Sciences.” In: European Journal of Pragmatism and American Philosophy 8. No. 2. https://journals. openedition.org/ejpap/625, last accessed on March 11, 2022. Anellis, Irving H. (1995): “Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other’s Work in Logic, and an Assessment of Russell’s Accuracy and Role in the Historiography of Logic.” In: Modern Logic 5, 270 – 328. Anellis, Irving H. (2012): “How Peircean Was the ‘Fregean’ Revolution in Logic?” Working Paper. http://arxiv.org/pdf/1201.0353.pdf, last accessed on March 11, 2022. Atkins, Richard (2016): Peirce and the Conduct of Life: Sentiment and Instinct in Ethics and Religion. Cambridge: Cambridge University Press. Austin, John L. (1961): Philosophical Papers. Oxford: Oxford University Press. Bain, Alexander (1870): Logic, London and New York: Longmans and D. Appleton & Co. Bateman, John, Wildfeuer, Janina, and Hiippala, Tuomo (2017): Multimodality: Foundations, Research and Analysis—A Problem-Oriented Introduction. Berlin and Boston: de Gruyter. Beeson, Robert J. (2008): Peirce on the Passions: The Role of Instinct, Emotion, and Sentiment in Inquiry and Action. Graduate Theses and Dissertations. https://scholar commons.usf.edu/etd/134, last accessed on March 11, 2022. Bekoff, Mark, Allen, Colin, and Burghardt, Gordon M. (Eds.) (2002): The Cognitive Animal. Empirical and Theoretical Perspectives on Animal Cognition. Cambridge: MIT Press, 41 – 45. Bellucci, Francesco (2013): “Peirce’s Continuous Predicates.” In: Transactions of the Charles S. Peirce Society 49. No. 2, 178 – 202. Bellucci, Francesco (2013a): “Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange.” In: Bellucci, Francesco: History and Philosophy of Logic 43. No. 4,

https://doi.org/10.1515/9783110793628-023

366

Literature

293 – 305. https://doi.org/10.1080/01445340.2013.777991, last accessed on March 11, 2022. Bellucci, Francesco (2014): “Peirce and the Unity of the Proposition.” In: Transactions of the Charles S. Peirce Society 50. No. 2, 201 – 219. Bellucci, Francesco (2015): “Exploring Peirce’s Speculative Grammar: The Immediate Object of a Sign.” In: Sign Systems Studies 43. No. 4, 399 – 415. Bellucci, Francesco (2015a): “Peirce on Phaneroscopical Analysis.” In: Journal Phänomenologie 44, 56 – 72. https://www.academia.edu/11664897/Peirce_on_Phaner oscopical_Analysis, last accessed on March 11, 2022. Bellucci, Francesco (2017): Peirce’s Speculative Grammar. Logic as Semiotics. New York and London: Routledge. Bellucci, Francesco (2019): “Peirce on assertion and other speech acts.” In: Semiotica 228, 29 – 54. https://www.degruyter.com/document/doi/10.1515/sem-2018-0081/, last accessed on March 11, 2022. Bellucci, Francesco (in press): “Rhemata” Bellucci, Francesco, Chiffi, Daniele, and Pietarinen, Ahti-Veikko (2021): “Assertion, conjunction, and other signs of logic: A contribution to the philosophy of notation.” In: Transactions of the Charles S. Peirce Society 57. No. 2, 270 – 287. Ben-Jacob, Eshel, Becker, Israel, Shapiro, Yoash, and Levine, Herbert (2004): “Bacterial Linguistic Communication and Social Intelligence.” In: Trends in Microbiology 12. No. 8, 366 – 372. Benacerraf, Paul and Putnam, Hilary (Eds.) (1989): Philosophy of Mathematics. Cambridge: Cambridge University Press. Boler, John F. (1963): Charles Peirce and Scholastic Realism: A Study of Peirce’s Relation to John Duns Scotus. Seattle: University of Washington Press. Bostrom, Nick (2014): Superintelligence: Paths, Dangers, Strategies. Oxford: Oxford University Press. Bredekamp, Horst (2010): Theorie des Bildakts. Berlin: Suhrkamp. Brent, Joseph (1998): Charles Sanders Peirce: A Life. 2nd ed. Indianapolis: Indiana University Press. Brower, Lincoln P. (Ed) (1988): Mimicry and the evolutionary process. Chicago: University of Chicago Press. Brøndal, Viggo (1928): Ordklasserne, Copenhagen: Munksgaard Brunning, Jacqueline and Forster, Paul (Eds.) (1997): The Rule of Reason. The Philosophy of Charles Sanders Peirce. Toronto: University of Toronto Press. Burch, Robert (1991): A Peircean Reduction Thesis: Foundations of Topological Logic. Lubbock: Texas Tech University Press. Cajori, Florian (1928 – 1929, 1993): A History of Mathematical Notations. New York: Dover. Cantens, Bernardo (2005): “Prolegomena to Peirce’s Philosophy of Religion”, https://www. unav.es/gep/SeminarioCantens.html, last accessed on March 27, 2022 Carlyle, Thomas (1841, 1885): On Heroes, Hero-Worship, and the Heroic in History. In: Complete Works, I – XX. https://www.gutenberg.org/files/1091/1091-h/1091-h.htm, last accessed on March 11, 2022. Cassirer, Ernst (1923): Philosophie der symbolischen Formen. Erster Teil: Die Sprache. Berlin: Bruno Cassirer. Translated as: Cassirer, Ernst (1955): The Philosophy of Symbolic Forms. Volume One: Language. Ralph Manheim (Trans.) New Haven: Yale University Press.

Peirce References (see detailed references below)

367

Cassirer, Ernst (1925a): Philosophie der symbolischen Formen. Zweiter Teil: Das mythische Denken. Berlin: Bruno Cassirer. Translated as: Cassirer, Ernst (1955): The Philosophy of Symbolic Forms. Volume Two: Mythical Thought. Ralph Manheim (Trans.). New Haven: Yale University Press. Cassirer, Ernst (c. 1928 – 1929 [written], 1995): Zur Metaphysik der symbolischen Formen. Hamburg: Felix Meiner. Cassirer, Ernst (1929): Philosophie der symbolischen Formen. Dritter Teil: Phänomenologie der Erkenntnis. Berlin: Bruno Cassirer. Translated as: Cassirer, Ernst (1957): The Philosophy of Symbolic Forms. Volume Three: The Phenomenology of Knowledge. Ralph Manheim (Trans.). New Haven: Yale University Press. Cassirer, Ernst (1940 [written], 1957, 1991): Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit. Von Hegels Tod bis zur Gegenwart (1832 – 1932). Volume IV. Hildesheim: Georg Olms. Cassirer, Ernst (1942): Zur Logik der Kulturwissenschaften. Göteborg: Göteborgs Högskolas Årsskrift 47. Translated as: Cassirer, Ernst (1961): The Logic of the Humanities. Clarence Howe (Trans.). New Haven: Yale University Press. Cassirer, Ernst (2009): “Die Begriffsform im mythischen Denken.” In: Cassirer, Ernst: Schriften zur Philosophie der symbolischen Formen. Marion Lauschke (Ed.). Hamburg: Felix Meiner, 3 – 62. Champagne, Marc (2018): Consciousness and the Philosophy of Signs How Peircean Semiotics Combines Phenomenal Qualia and Practical Effects. Cham: Springer. Champagne, Marc and Pietarinen, Ahti-Veikko (2020): “Why Images Cannot be Arguments, But Moving Ones Might.” In: Argumentation 34. No. 2, 207 – 236. Cigana, Lorenzo (2013): “The linguistic crucible: the role of the deuxième ‘Congrès International des Linguistes’ in Hjelmslev’s theory of participative oppositions.” In: Travaux du 19eme CIL. https://www.academia.edu/11566646/The_linguistic_crucible_ the_role_of_the_deuxième_Congrès_International_des_Linguistes_in_Hjelmslev_s_theo ry_of_participative_oppositions, last accessed on March 11, 2022. Cigana, Lorenzo (2014): La nozione di “Partecipazione” nella Glossematica de Louis Hjelmslev. Universitá della Calabria and Université de Liège: Unpublished Ph.D. Dissertation. Cigana, Lorenzo (2014a): “La notion de “participation” chez Louis Hjelmslev: un fil rouge de la glossématique.” In: Cahiers Ferdinand de Saussure 67, 191 – 202. Cigana, Lorenzo (2019): “The formalisation of grammatical meanings in Copenhagen structural linguistics. Some remarks.” In: History and Philosophy of the Language Sciences. https://hiphilangsci.net/2019/06/14/formalisation_copenhagen, last accessed on March 11, 2022. Clark, Andy (1997): Being There. Putting Brain, Body, and World Together Again. Cambridge, MA: MIT Press. Clark, Andy (2008): Supersizing the Mind: Embodiment, Action, and Cognitive Extension. Oxford: Oxford University Press. Cobley, Paul (1994): “Enhancing survival by not enhancing survival: Sebeok’s semiotics and the ultimate paradox of modelling.” The American Journal of Semiotics 30. No. 3/4, 191 – 204. Cobley, Paul, and Stjernfelt, Frederik (2015): “Scaffolding development and the human condition.” In: Biosemiotics 8. No. 2, 291 – 304.

368

Literature

Cohen, Hermann (1877): Kants Begrü ndung der Ethik. Berlin: Dü mmler. Cohen, Hermann (1904): Ethik des reines Willens. Berlin: Bruno Cassirer. Colapietro, Vincent M. (1989): Peirce’s Approach to the Self: A Semiotic Perspective on Human Subjectivity. Albany: State of New York University Press. Colapietro, Vincent M. (2009): “Habit, competence, and purpose: How to make the grades of clarity clearer.” In: Transactions of the Charles S. Peirce Society 45. No. 3 348 – 377. Copeland, Jonathan and Lloyd, James E. (1983): “Male firefly mimicry.” In: Science 221, 484 – 485. Currie, Adrian (2018): Rock, Bone, and Ruin. An Optimist’s Guide to the Historical Sciences. Cambridge: MIT Press. Darwin, Charles (1880): The Power of Movement in Plants. London: Murray. Dau, Frithjof (2011a): “Ligatures in Peirce’s Existential Graphs.” In: Semiotica 186. No. 1/4, 89 – 109. Dau, Frithjof (2011b): “Die Ikonizität der Peirceschen Existentiellen Graphen aus der Sicht der Formalen Logik.” In: Zeitschrift für Semiotik 31. No. 3/4. Deacon, Terrence (1997): The Symbolic Species. New York: W.W. Norton & Co. Deacon, Terrence (2012): Incomplete Nature: How Mind Emerged from Matter. New York: W.W. Norton & Co. Debrock, Guy (1996): “Information and the metaphysical status of the sign.” In: Colapietro, Vincent M. and Olshewsky, Thomas M. (Eds.): Peirce’s Doctrine of Signs—Theory, Applications, and Connections. Berlin: Mouton de Gruyter, 80 – 89. De Mesa, Juliana Acosta López (2019): “A semiotic theory of self-control.” In: Cognitio Revista de Filosofia 20. No. 2, 217 – 229. De Tienne, André (2003): “Learning qua Semiosis.” In: S. E.E.D. Journal—Semiotics, Evolution, Energy, and Development 3, 37 – 53. De Tienne, André (2004): “Is Phaneroscopy as a Pre-Semiotic Science Possible?” In: Semiotiche 2, 15 – 30. De Waal, Cornelis (2006): “Science Beyond Self: Remarks on Charles S. Peirce’s Social Epistemology.” In: Cognitio 7. No. 1, 149 – 163. Diderichsen, Paul (1966): Helhed og struktur. Copenhagen: Gad. Diderot, Denis (1769 [D’Alembert’s Dream written], 2011): Rameau’s Nephew/ D’Alembert’s Dream, London: Penguin. Dijkstra, Trude, and Jagersma, Rindert (2014): “Uncovering Spinoza’s Printers by Means of Bibliographical Research.” In: Quaerendo 43(4), 278 – 310. Dipert, Randall (1997): “Peirce’s Philosophical Conception of Sets.” In Houser et al. (eds.) 1997, 53 – 76. Donald, Merlin (2001): A Mind So Rare: The Evolution of Human Consciousness. New York: Norton. Duncker Karl (1945): “On problem-solving processes.” In: Psychological Monographs 58. No. 5 i–113. https://doi.org/10.1037/h0093599, last accessed on March 11, 2022. Eco, Umberto (1976): A Theory of Semiotics. Bloomington: Indiana University Press. Eco, Umberto (1999): Kant and the Platypus. London: Secker. Ehrenfels, Christian von (1890): “Über Gestaltqualitäten.” In: Vierteljahrsschrift für wissenschaftliche Philosophie 14, 249 – 292. El-Hani, Charbel Niño, Queiroz, João, and Stjernfelt, Frederik (2010): “Firefly Femmes Fatales. A Case Study in the Semiotics of Deception.” In: Journal of Biosemiotics 3 No. 1, 33 – 55.

Peirce References (see detailed references below)

369

Emerson, Ralph Waldo (1841): “The Sphynx.” https://poets.org/poem/sphinx, last accessed on March 11, 2022. Farias, Priscila and Queiroz, João (2006): “Images, diagrams, and metaphors: Hypoicons in the context of Peirce’s Sixty-six-fold classification of signs.” In: Semiotica 162, 287 – 307. Fisch, Max H. (1967): “Peirce’s progress from nominalism towards realism.” In: Fisch, Max (1986): Peirce, Semeiotic, and Pragmatism: Essays by Max H. Fisch. Kenneth Laine Ketner and Christian J. W. Kloesel (Eds.). Bloomington: Indiana University Press, 184 – 200. Fisch, Max (1986): Peirce, Semeiotic, and Pragmatism: Essays by Max H. Fisch. Kenneth Laine Ketner and Christian J. W. Kloesel (Eds.). Bloomington: Indiana University Press. Fortis, Jean-Michel (2011): “On Localism in the History of Linguistics.” http://htl.linguist.univparis-diderot.fr/_media/fortis/fortis_on_localism.pdf, last accessed on Sept. 26, 2018. Frege, Gottlob (1879): Begriffsschrift. Halle: Louis Nebert. Frisch, Karl von (1993): The Dance Language and Orientation of Bees. Cambridge: Harvard University Press. Fuller, Steve (2019): Nietzschean Meditations: Untimely Thoughts at the Dawn of the Transhuman Era. Berlin and Basel: Schwabe Verlag Galton, Francis (1869): Hereditary Genius. An Inquiry into its Laws and Consequences. London: MacMillan & Co. https://galton.org/books/hereditary-genius/1869-FirstEdition/ hereditarygenius1869galt.pdf, last accessed on March 11, 2022. Gilman, Benjamin Ives (1892): “On the properties of a one-dimensional manifold.” In: Mind 1, 518 – 526. Godfrey-Smith, Peter (1998): Complexity and Function of Mind in Nature. New York: Cambridge University Press. Goodman, Nelson (1976): Languages of Art. Indianapolis: Hackett Publishing Company. Gray, Jeremy (2009): Plato’s Ghost: The Modernist Transformation of Mathematics. Princeton: Princeton University Press. Hartimo, Mirja (2007): “Towards completeness: Husserl on theories of manifolds 1890 – 1901.” In: Synthese 156, 281 – 310. Hartmann, Eduard von (1869): Philosophie des Unbewussten: Versuch einer Weltanschauung. Berlin: Carl Duncker. Hegel, Georg Wilhelm Friedrich (1830): Enzyklopädie der philosophischen Wissenschaften im Grundrisse. http://www.zeno.org/Philosophie/M/Hegel,+Georg+Wilhelm+Friedrich/Enzy klopädie+der+philosophischen+Wissenschaften+im+Grundrisse, last accessed on March 11, 2022. History Computer Staff (2021): “Charles Peirce and Allan Marquand: First Electrical Logical Machine.” https://history-computer.com/charles-peirce-and-allan-marquand-first-elec trical-logical-machine/, last accessed on March 11, 2022. Hjelmslev, Louis (1928): Principes de grammaire générale. Copenhagen: Høst og Søn. Hjelmslev, Louis (1934, 1972): Sprogsystem og sprogforandring. Copenhagen: Nordisk Sprogog Kulturforlag. Hjelmslev, Louis (1935): La catégorie des cas. Étude de grammaire générale. Première partie. Acta Jutlandica VII, 1. Aarhus: Universitetsforlaget. Hjelmslev, Louis (1943): Omkring sprogteoriens grundlæggelse. Copenhagen: Munksgaard. English Version: Hjelmslev, Louis (1969): Prolegomena to a Theory of Language. 2nd ed. Madison: The University of Wisconsin Press.

370

Literature

Hjelmslev, Louis (c. 1943a, 1975): Resumé of a Theory of Language. Copenhagen: Nordisk Sprog- og Kulturforlag. Hilpinen, Risto (1992): “On Peirce’s Philosophical Logic: Propositions and Their Objects.” In: Transactions of the Charles S. Peirce Society, 28. No. 3 (Summer), 467 – 488. Hintikka, Jaakko (1983): “C.S. Peirce’s ‘First Real Discovery’ and Its Contemporary Relevance.” In: Freeman, Eugene (Ed.): The Relevance of Charles Peirce. La Salle: The Hegeler Institute, 107 – 118. Hintikka, Jaakko (1997): Lingua Universalis vs. Calculus Ratiocinator. An Ultimate Presupposition of Twentieth-Century Philosophy. Dordrecht: Kluwer. Hoffmann, Michael (2006): “Seeing Problems, Seeing Solutions. Abduction and Diagrammatic Reasoning in a theory of Scientific Discovery”, Working Paper #2006.15, Georgia Institute of Technology. Hoffmeyer, Jesper (1996): Signs of Meaning in the Universe. Bloomington: Indiana University Press. Hoffmeyer, Jesper (2008): Biosemiotics. An Examination into the Signs of Life and the Life of Signs. Scranton and London: University of Scranton Press. Hoffmeyer, Jesper and Stjernfelt, Frederik (2016): “The Great Chain of Semiosis: Investigating the Steps in the Evolution of Biosemiotic Competence.” In: Biosemiotics 9. No. 1, 7 – 29. Holenstein, Elmar (1975): Roman Jakobsons phänomenologischer Strukturalismus. Frankfurt/ M: Suhrkamp. Holenstein, Elmar (1976): Linguistik Semiotik Hermeneutik, Frankfurt/M: Suhrkamp. Holmes, Larry (1966): “Peirce on Self-Control.” In: Transactions of the Charles S. Peirce Society Fall, 1966, 2. No. 2 (Fall 1966), 113 – 130. Hookway, Christopher (2002): “‘… a sort of composite photograph’: Pragmatism, Ideas, and Schematism.” In: Transactions of the Charles S. Peirce Society 38. No. 1/2, 29 – 45. Hookway, Christopher (2009): “Habits and interpretation: Defending the pragmatist maxim.” Paper presented at the conference Peirce and Early Analytic Philosophy, Helsinki, May 19 – 20, 2009. http://www.nordprag.org/papers/Hookway%20-%20Habits%20and%20In terpretants.pdf, last accessed on March 11, 2022. Horstbøll, Henrik, Langen, Ulrik, and Stjernfelt, Frederik (2020): Grov Konfækt: Tre vilde år med trykkefrihed 1770 – 73. Volumes I–II. Copenhagen: Gyldendal. Houser, Nathan (1983): “Peirce’s General Taxonomy of Consciousness. “ In: Transactions of the Charles S. Peirce Society 19. No. 4 (Fall 1983), 331 – 359. Houser, Nathan (2009): “Introduction.” In: Peirce, Charles Sanders (1982 ff.): Writings of Charles S. Peirce: A Chronological Edition. Volume VIII. Referred to as W 8. Bloomington: Indiana University Press, xxv-xcvii. Houser, Nathan, Don D. Roberts, and James van Evra (eds.) (1997): Studies in the Logic of Charles Sanders Peirce. Bloomington: Indiana University Press. Hurford, James (2007): The Origins of Meaning. Oxford: Oxford University Press. Hurley, Susan and Nudds, Matthew (Eds.) (2006): Rational Animals. Oxford: Oxford University Press. Husserl, Edmund (1968): Briefe an Ingarden mit Erläuterungen und Erinnerungen an Husserl. Roman Ingarden (Ed.). Den Haag: Martinus Nijhoff. Husserl, Edmund (1970): Logical Investigations. John N. Findlay (Trans.). London and Henley: Routledge and Kegan Paul.

Peirce References (see detailed references below)

371

Husserl, Edmund (1971): Ideen zu einer reinen Phänomenologie und Phänomenologischen Philosophie. Book III [Ideen III]. Husserliana V. Tü bingen: Max Niemeyer. Husserl, Edmund (1973): Experience and Judgment. London: Routledge and Kegan Paul. Husserl, Edmund (1975): Logische Untersuchungen I [LU I]. Husserliana XVIII. Den Haag: Martinus Nijhoff. Husserl, Edmund (1980): Ideen zu einer reinen Phänomenologie und Phänomenologischen Philosophie [Ideen]. Tü bingen: Max Niemeyer. Husserl, Edmund (1984): Logische Untersuchungen II [LU II]. Parts I–II. Husserliana XIX/1 – 2. Hamburg: Felix Meiner. Husserl, Edmund (1985): Erfahrung und Urteil [EU]. Hamburg: Felix Meiner. Husserl, Edmund (1991): Ideen zu einer reinen Phänomenologie und Phänomenologischen Philosophie. Book II [Ideen II]. Husserliana IV. Tü bingen: Max Niemeyer. Ingarden, Roman (1925): “Essentiale Frage. Ein Beitrag zu dem Wesensproblem.” In: Jahrbuch fü r Philosophie und phänomenologische Forschung 7. Halle a. d. Saale: Max Niemeyer, 125 – 304. Ingarden, Roman (1931, 1965): Das literarische Kunstwerk. Tü bingen: Max Niemeyer. English Version: Ingarden, Roman (1973): The Literary Work of Art. Evanston: Northwestern University Press. Ingarden, Roman (1937, 1974): “Psychologism and Psychology in Literary Scholarship.” In: New Literary History 5. No. 2 (Changing Views of Character, Winter 1974), 213 – 223. Ingarden, Roman (1964): Time and Modes of Being. Springfield: C.C. Thomas. Ingarden, Roman (1964a): “Artistic and aesthetic values.” In: British Journal of Aesthetics 4. No. 3, 198 – 213. Ingarden, Roman (1965 – 1974): Der Streit um die Existenz der Welt. Volumes I-III. Tü bingen: Max Niemeyer. Israel, Jonathan (2001): Radical Enlightenment. Oxford: Oxford University Press. Israel, Jonathan (2006): Enlightenment Contested. Oxford: Oxford University Press. Israel, Jonathan (2011): Democratic Enlightenment. Oxford: Oxford University Press. Israel, Jonathan (2020): The Enlightenment that Failed. Oxford: Oxford University Press. Jablonka, Eva (2002): “Information: Its interpretation, its inheritance, and its sharing.” In: Philosophy of Science 69, 578 – 605. James, Henry (Ed.) (1920): The Letters of William James. Boston: The Atlantic Monthly Press. James, Henry, Sr. (1863): Substance and Shadow, Or Morality and Religion in Their Relation to Life; An Essay upon the Physics of Creation. Boston: Ticknor and Fields. James Sr., Henry (1869): The Secret of Swedenborg: Being an Elucidation of his Doctrine of the Divine Natural Humanity. Boston: Fields, Osgood & Co. James, William (Various): The James Collection. Cambridge: Harvard, Houghton Library, MS Am 1092.9 – 1092.1. James, William (1890, 1918): The Principles of Psychology. Volumes I–II. New York: Henry Holt & Co. Johansson, Ingvar (2006, 2009): “Proof of the Existence of Universals—and Roman Ingarden’s Ontology.” https://www.researchgate.net/publication/225561945_Proof_of_the_Ex istence_of_Universals-and_Roman_Ingarden%27s_Ontology, last accessed on March 11, 2022. Preprint version of a paper published in Metaphysica. International Journal for Ontology & Metaphysics 10, 65 – 87.

372

Literature

Johansson, Ingvar (2013): “The Basic Distinctions in Der Streit.” In: Semiotica 194, 137 – 157. https://doi.org/10.1515/sem-2013-0025, last accessed on March 11, 2022. Kammerzell, Frank and Peust, Carsten (2002): “Reported Speech in Egyptian: Forms, Types and History.” In: Gü ldeman, Tom and Roncador, Manfred von (Eds): Reported Discourse: A Meeting Ground for Different Linguistic Domains. Amsterdam and Philadelphia: John Benjamins, 289 – 322. Kant, Immanuel (1762) Die falsche Spitzfindigkeit der vier syllogistischen Figuren. Königsberg: J.J. Kanter; https://books.google.de/books?id=a5dZAAAAcAAJ&printsec=frontcover&hl= da&source=gbs_ViewAPI&redir_esc=y#v=onepage&q&f=false, last accessed 24 April 2022. Kant, Immanuel (1771, 1787): Kritik der reinen Vernunft. Riga: Hartknoch. Kant, Immanuel (1784): “Was ist Aufklärung?” In: Berlinische Monatsschrift 4, 481 – 494. https://de.wikisource.org/wiki/Beantwortung_der_Frage:_Was_ist_Aufklärung%3F, last accessed on March 11, 2022. Karmiloff-Smith, Annette (1992): Beyond Modularity: A Developmental Perspective on Cognitive Science. Cambridge: MIT Press. Kauffman, Stuart and Clayton, Philip (2006): “On Emergence, Agency, and Organization.” In: Biology and Philosophy 21. No. 4 501 – 521. Ketner, Kenneth Laine and Arthur F. Stewart (1984): “The Early History of Computer Design: Charles Sanders Peirce and Marquand’s Logical Machines.” In: The Princeton University Library Chronicle 45, 187 – 224. Kitcher, Philip and Varzi, Achille (2000): “Some Pictures are Worth 2Aleph-0 Sentences.” In: Philosophy 75. No. 3, 377 – 381. Koerner, E. F. K. (1997): “Remarks on the Sources of R. Jakobson’s Linguistic Inspiration”, Cahiers de l’ILSL, N° 9, 151-168 Komárek, Stanislav (2003): Mimicry, aposematism and related phenomena. Mimetism in nature and the history of its study. Munich: Lincom Europa. Kress, Gunther and Van Leeuwen, Theo (2001): Multimodal Discourse: The Modes and Media of Contemporary Communication. Oxford: Oxford University Press. Krois, John Michael (1994): “C.S. Peirce and philosophical ethics.” In: Parret, Herman (Ed.): Peirce and Value Theory. Amsterdam and Philadelphia: John Benjamin, 27 – 38. Krois, John Michael (2011): Körperbilder und Bildschemata. Aufsätze zur Verkörperungstheorie ikonischer Formen. Horst Bredekamp and Marion Lauschke (Eds.). Berlin: Oldenbourg Akademieverlag. Krolikowski, Walter P. (1964): “The Peircean Vir”. In: Moore, Edward C. and Robin, Richard S. (Eds.): Studies in the Philosophy of Charles Sanders Peirce. Second Series. Amherst: University of Massachusetts Press, 257 – 270. Kull, Kalevi (2018): “Retorik i biologien.” KRITIK 155 – 156, 98 – 100. Kull, Kalevi (2018a): “On the Logic of Animal Umwelten: The Animal Subjective Present and Zoosemiotics of Choice and Learning.” In: Marrone, Gianfranco and Mangano, Dario (Eds.): Semiotics of Animals in Culture: Zoosemiotics 2.0. Cham: Springer, 135 – 148. Kull, Kalevi, Deacon, Terrence, Emmeche, Claus, Hoffmeyer, Jesper, and Stjernfelt, Frederik (2011): “Theses on Biosemiotics: Prolegomena to a Theoretical Biology.” In: Emmeche, Claus and Kull, Kalevi (Eds.): Towards a Semiotic Biology: Life is the Action of Signs. London: Imperial College Press, 25 – 41.

Peirce References (see detailed references below)

373

Kusch, Martin (1995): Psychologism: A Case Study in the Sociology of Philosophical Knowledge. London: Routledge. Landgrebe, Jobst and Smith, Barry (2021): “Making AI Meaningful Again.” In: Synthese 198, 2061 – 2081. https://doi.org/10.1007/s11229-019-02192-y, last accessed on March 11, 2022. Lane, Robert (2009): “Persons, Signs, Animals: A Peircean Account of Personhood.” In: Transactions of the Charles S. Peirce Society 45. No. 1, 1 – 26. Lane, Robert (2018): Peirce on Realism and Idealism. Cambridge: Cambridge University Press. Lange, Friedrich Albert (1877): Logische Studien: Ein Beitrag Zur Neubegrundung Der Formalen Logik Und Der Erkenntnisstheorie. Iserlohn: J. Baedeker. Langen, Ulrik and Stjernfelt, Frederik (2022): The World’s First Full Press Freedom: The Radical Experiment of Denmark-Norway 1770 – 73. Berlin: De Gruyter. Lassègue, Jean (2020): Cassirer’s Transformation: From a Transcendental to a Semiotic Philosophy of Forms. Dordrecht: Springer. Lauritzen, Anne Mette and Stjernfelt, Frederik (2020): Your Post Has Been Removed: Tech Giants and Free Speech. Dordrecht: Springer Open. Leibniz, Gottfried Wilhelm (1714, 1978): La monadologie. Paris: Librairie Delagrave. http://clas siques.uqac.ca/classiques/Leibniz/La_Monadologie/leibniz_monadologie.pdf, last accessed on March 11, 2022. Lessing, Gotthold Ephraim (1766): Laokoön oder Über die Grenzen der Malerei und Poesie. Berlin: Voss. Levy, Stephen H. (1997): “Peirce’s Theoremic/Corollarial Distinction and the Interconnectedness between Mathematics and Logic.” In: Houser, Nathan, Roberts, Don D., and Van Evra, James (Eds.): Studies in the Logic of Charles Sanders Peirce. Bloomington: Indiana University Press, 85 – 110. Lewis, Sara and Cratsley, Christopher (2008): “Flash signal evolution, mate choice, and predation in fireflies.” In: Annual Review of Entomology 53, 293 – 321. Lloyd, J. E. 1965, “Aggressive mimicry in Photuris: firefly femmes fatales” Science, 149, 653 – 654. Lloyd, J. E. 1975, “Aggressive mimicry in Photuris fireflies: signal repertoires by femmes fatales”, Science, 187, 452 – 453. Lloyd, J. E. 1980, “Male Photuris fireflies mimic sexual signals of their females’ prey”, Science, 210, 669 – 671. Lloyd, J. E. 1981, “Firefly mate-rivals mimic their predators and vice versa”, Nature, 290, 498 – 500. Lloyd, James E. (1986): “Firefly communication and deception: ‘Oh, what a tangled web.’” In: Mitchell, Robert W. and Thompson, Nicholas S. (Eds.): Deception: Perspectives on human and nonhuman deceit. Albany: SUNY Press, 113 – 128. Mancosu, Paolo, Zach, Richard, and Badesa, Calixto (2009): “The development of mathematical logic from Russell to Tarski, 1900 – 1935.” In: Haaparanta, Leila (Ed.): The development of modern logic. Oxford: Oxford University Press, 318 – 470. Marquand, Allan (1883): “A Machine for Producing Syllogistic Variation” and “Note on an Eight-Term Logical Machine.” In: Peirce, Charles Sanders (Ed.): Studies in Logic. Boston: Little, Brown and Company, 12 – 15; 16. Metcalfe, Janet and Weibe, David (1987): “Intuition in insight and noninsight problem solving.” In: Memory & Cognition 15, 238 – 246.

374

Literature

Milkov, Nikolay (2002): “Lotze’s concept of ‘states of affairs’ and its critics.” In: Prima Philosophia 15, 437 – 450. Mill, John Stuart (1859): On Liberty. London: John W. Parker & Son. Millière, Raphaë l (2016): “Ingarden’s combinatorial analysis of the realism-idealism controversy.” In: Richard, Sébastian and Malherbe, Olivier (Eds.): Form(s) and Modes of Being. The Ontology of Roman Ingarden. Bern and New York: 67 – 98. https://philpapers. org/archive/MILICA-6.pdf, last accessed on March 11, 2022. Millikan, Ruth (2006): “Styles of Rationality.” In: Hurley, Susan and Nudds, Matthew (Eds.): Rational Animals. Oxford: Oxford University Press, 117 – 126. Misak, Cheryl (2004): Truth and the End of Inquiry: A Peircean Account of Truth. Oxford, Oxford University Press. Mitchell, Oscar H. (1883): “On a New Algebra of Logic.” In C. S. Peirce (Ed.) (1883). 72 – 106. Mitchell, Robert W. and Thompson, Nicholas S. (Eds.) (1986): Deception: Perspectives on Human and Nonhuman Deceit. Albany: SUNY Press. Mitchell, William J. T. (1994): Picture Theory. Chicago: University of Chicago Press. Mitchell, William J. T. (2005): What do Pictures Want? The Lives and Loves of Images. Chicago: University of Chicago Press. Moore, Matthew E. (Ed.) (2010): New Essays on Peirce’s Mathematical Philosophy. Chicago and La Salle: Open Court. Morris, Charles (1938): “Foundations of the Theory of Signs.” In: Neurath, Otto (Ed.): International Encyclopedia of Unified Science. Volume 1. No. 2. Chicago: University of Chicago Press. Morris, Charles (1946): Signs, Language, and Behavior. New York: Prentice-Hall. Mulligan, Kevin, Simons, Peter M., and Smith, Barry (1984): “Truth-Makers.” In: Philosophy and Phenomenological Research 44, 287 – 321. Mulsow, Martin (2012): Prekäres Wissen. Eine andere Ideengeschichte der Frühen Neuzeit. Berlin: Suhrkamp. Munck, Thomas (2019): Conflict and Enlightenment: Print and Political Culture in Europe, 1635 – 1795. Cambridge: Cambridge University Press. Murphey, Murray (1961): The Development of Peirce’s Philosophy. Cambridge: Harvard University Press. Murphy, Sean (2013): “Irish Historical Mysteries: Molly Malone.” http://homepage.tinet.ie/ ~seanjmurphy/irhismys/molly.htm, last accessed March 11, 2022. Nöth, Winfried (1990): Handbook of Semiotics. Bloomington: Indiana University Press. Nöth, Winfried (2010): “The criterion of habit in Peirce’s definitions of the symbol.” In: Transactions of the Charles S. Peirce Society 46. No. 1, 82 – 93. Ohlsson Stellan (1992): “Information-processing explanations of insight and related phenomena.” In: Keane, Mark T. and Gilhooly, Kenneth J. (Eds.): Advances in the Psychology of Thinking. London: Harvester-Wheatsheaf, 1 – 44. Østergaard, Svend, and Stjernfelt, Frederik (2013): “FONK! HONK! WHAM! OOF! Representation of Events in Carl Barks—and in the Aesthetics of Comics in General.” In: Pedri, Nancy and Petit, Laurence (Eds): Picturing the Language of Images. Newcastle: Cambridge Scholars Publications, 483 – 508. Parker, Kelly A. (1998): The Continuity of Peirce’s Thought. Nashville: Vanderbilt University Press. Peirce, Charles Sanders (1878): Photometric Researches, Leipzig: Wilhelm Engelmann

Peirce References (see detailed references below)

375

Peirce, Charles Sanders (Ed.) (1883): Studies in Logic by Members of the Johns Hopkins University. Boston: Little, Brown and Company. Peirce, Charles Sanders (1887): “Logical Machines.” In: The American Journal of Psychology 1, 165 – 170. Included in W 6, 65 – 73. Peirce, Charles Sanders (1931 – 1958; 1998): Collected Papers. Volumes I-VIII. Charles Hartshorne, Paul Weiss, and Arthur W. Burks (Eds.). Referred to as CP; references given by volume and paragraph numbers. London: Thoemmes Press. Peirce, Charles Sanders (1976): New Elements of Mathematics. Volumes I–IV. Carolyn Eisele (Ed.). Referred to as NEM. The Hague: Mouton. Peirce, Charles Sanders (1977): Semiotic & Significs: The Correspondence Between Charles S. Peirce & Victoria Lady Welby. Charles S. Hardwick and James Cook (Eds.). Referred to as SS. Bloomington: Indiana University Press. Peirce, Charles Sanders (1982 ff.): Writings of Charles S. Peirce: A Chronological Edition. Volumes I–IV; VIII. Referred to as W. Bloomington: Indiana University Press. Peirce, Charles Sanders (1992): The Essential Peirce. Volume I (1867 – 1893). Eds. Nathan Houser and Christian J. W. Kloesel (Eds.). Referred to as EP I. Bloomington: Indiana University Press. Peirce, Charles Sanders (1998a): The Essential Peirce. Volume II (1893 – 1913). Nathan Houser and Christian J. W. Kloesel (Eds.). Referred to as EP II. Bloomington: Indiana University Press. Peirce, Charles Sanders (2010): Philosophy of Mathematics. Selected Writings. Matthew Moore (Ed.). Referred to as PM. Bloomington and Indianapolis: Indiana University Press. Peirce, Charles Sanders (2020): Selected Writings on Semiotics 1894 – 1912. Francesco Bellucci (Ed.). Referred to as SWS. Berlin and Boston: De Gruyter Mouton. Peirce, Charles Sanders (2020 – 2022): Logic of the Future: Writings on Existential Graphs. Volumes I–III. Ahti-Veikko Pietarinen (Ed.). Referred to as LoF. Berlin and Boston: De Gruyter (referred to as LoF). Peirce, Charles Sanders (Various, partially undated): Manuscripts at the Houghton Library. Referenced by Ms. numbers in the 1966 microfilm edition (The Charles S. Peirce Papers. Microfilm Edition. Thirty Reels with Two Supplementary Reels Later Added. Cambridge: Harvard University Library Photographic Service); numbers refer simultaneously to the Robin catalogue of the manuscripts (1967, 1971). Referred to as R. Peirce, Charles Sanders and Jastrow, Joseph (1885): “On Small Differences in Sensation.” In: Memoirs of the National Academy of Sciences 3, 73 – 83. https://psychclassics.yorku.ca/ Peirce/small-diffs.htm, last accessed on March 11, 2022. Penrose, Roger (1989): The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics. Oxford: Oxford University Press. Pepperberg, Irene (2002): The Alex Studies: Cognitive and Communicative Abilities of Grey Parrots. Cambridge: Harvard University Press. Petry, Edward S. (1992): “The Origin and Development of Peirce’s Concept of Self-Control.” In: Transactions of the Charles S. Peirce Society 28. No. 4, 667 – 690. Pietarinen, Ahti-Veikko (2005): “Cultivating habits of reason: Peirce and the Logica Utens versus Logica Docens Distinction.” In: History of Philosophy Quarterly 22. No. 4, 357 – 372. Pietarinen, Ahti-Veikko (2005a): “Compositionality, relevance and Peirce’s logic of Existential Graphs.” In: Axiomathes 15, 513 – 540.

376

Literature

Pietarinen, Ahti-Veikko (2006): Signs of Logic. Dordrecht: Springer. Pietarinen, Ahti-Veikko (2007): “Abductive issues in Peirce’s proof of pragmaticism.” In: Pombo, Olga and Gerner, Alexander (Eds.): Abduction and the Process of Scientific Discovery. Lisboa: Centro de Filosofia das Ciências da Universidade de Lisboa, 303 – 320. Pietarinen, Ahti-Veikko (2010a): “Which philosophy of mathematics is pragmaticism?” In: Moore, Matthew E. (Ed.): New Essays on Peirce’s Mathematical Philosophy. Chicago and La Salle: Open Court, 59 – 79. Pietarinen, Ahti-Veikko (2010b): “Pragmaticism as an anti-foundationalist philosophy of mathematics.” In: Van Kerkhove, Bart, De Vuyst, Jonas, and Van Bendegem, Jean Paul (Eds.): Philosophical perspectives on mathematical practice. London: College Publications, 156 – 183. Pietarinen, Ahti-Veikko (2011): “Existential Graphs: What a Diagrammatic Logic of Cognition Might Look Like.” In: History and Philosophy of Logic 32, 265 – 281. Pietarinen, Ahti-Veikko (2011a): “Moving pictures of thought: Graphs, games, and pragmaticism’s proof.” In: Semiotica 186, 315 – 331. Pietarinen, Ahti-Veikko (2019): “Semeiotic completeness in the theory of signs.” In: Semiotica 228, 237 – 257. Pietarinen, Ahti-Veikko and Bellucci, Francesco (2016): “Habits of reasoning. Grammar and critics of logical habits.” In: West, Donna and Anderson, Myrdene (Eds.): Consensus on Peirce’s concept of Habit: Before and beyond consciousness. Cham: Springer. Pietarinen, Ahti-Veikko and Chevalier, Jean-Marie (2015): “The Johns Hopkins Metaphysical Club and Its Impact on the Development of the Philosophy and Methodology of Sciences in the Late 19th-Century United States”, http://www.commens.org/papers/paper/pietar inen-ahti-veikko- chevalier-jean-marie-2014-johns-hopkins-metaphysical-club- and; latest accessed 24 April 2022 Pietarinen, Ahti-Veikko and Snellman, Lauri (2006): “On Peirce’s late proof of pragmaticism.” In: Aho, Tuomo and Pietarinen, Ahti-Veikko (Eds.): Truth and games. Volume 78. Helsinki: Acta Philosophica Fennica, 275 – 288. Pietarinen, Ahti-Veikko and Stjernfelt, Frederik (2015): “Peirce and Diagrams: Two Contributors to an Actual Discussion Review Each Other.” In: Synthese 192. No. 4, 1073 – 1088. Pietarinen, Ahti-Veikko and Stjernfelt, Frederik (In Press): “Semiotics of Mathematics and Logic.” In: Pelkey, Jamin (Ed.): Bloomsbury Companion to Semiotics. London: Bloomsbury Academic. Pöppel, Ernst and Bao, Yan (2014): “Temporal Windows as a Bridge from Objective to Subjective Time.” In: Arstila, Valtteri and Lloyd, Dan (Eds.): Subjective Time: The Philosophy, Psychology, and Neuroscience of Temporality. Cambridge: MIT Press, 241 – 262. Putnam, Hilary (1982): Realism with a Human Face. Cambridge: Harvard University Press. Queiroz, Joaõ and Stjernfelt, Frederik (Eds.) (2011): Semiotica 186. Special issue on “Diagrammatical Reasoning and Peircean Logic Representations”. Quine, Willard V. O. (1948): “On What There Is.” In: The Review of Metaphysics 2. No. 1, 21 – 38 Quine, Willard V. O. (1953): From a Logical Point of View. New York: Harper.

Peirce References (see detailed references below)

377

Raposa, Michael L. (1984): “Habits and essences.” In: Transactions of the Charles S. Peirce Society 20. NO. 2, 147 – 167. Ribeiro, Sidarta, Loula, Angelo, Araújo, Ivan de, Gudwin, Ricardo, and Queiroz, João (2007): “Symbols are not uniquely human.” In: Biosystems 90, 263 – 272. Roberts, Don D. (1970): “On Peirce’s Realism.” In: Transactions of the Charles S. Peirce Society 6. No. 2, 67 – 83. Roberts, Don D. (1973): The Existential Graphs of Charles S. Peirce. The Hague: Mouton. Robin, Richard (1967): Annotated Catalogue of the Papers of Charles S. Peirce. Amherst: University of Massachusetts Press. Robin, Richard (1971): “The Peirce Papers: A Supplementary Catalogue.” In: Transactions of the Charles S. Peirce Society 7. N. 1, 37 – 57. Rosenthal, Sandra B. (1982): “Meaning as habit: Some systematic implications of Peirce’s pragmatism.” In: The Monist 65. No. 2, 230 – 245. Rowling, J.K. (1997): Harry Potter and the Philosopher’s Stone. London: Bloomsbury. Sandu, Gabriel and Hintikka, Jaako (1999): “Tarski’s guilty secret: Compositionality”, In: Wolenski, Jan and Kölher, Eckehart (Eds.): Alfred Tarski and the Vienna Circle. Dordrecht: Kluwer Academic Publishers, 217 – 230. Schwartz, Daniel L. (1995): “The emergence of abstract representations in dyad problem solving.” In: The Journal of the Learning Sciences 4. No. 3, 321 – 354. Searle, John (1980): “Minds, Brains and Programs.” In: Behavioral and Brain Sciences 3, 417 – 457. Sebeok, Thomas (1979): “Prefigurements of art.” In: Semiotica 27. No. 1 – 3, 3 – 74. Sebeok, Thomas (1989): The sign and its masters. New York: University Press of America. Shakespeare, William (1604). Measure for Measure. https://www.sparknotes.com/nofear/ shakespeare/measure-for-measure/, last accessed on March 11, 2022. Shapiro, Gary (1973): “Habit and meaning in Peirce’s pragmatism.” In: Transactions of the Charles S. Peirce Society 9. No. 1, 24 – 40. Shin, Sun-Joo (1994): The Logical Status of Diagrams. Cambridge: Cambridge University Press. Shin, Sun-Joo (2000): The Iconic Logic of Peirce’s Graphs. Cambridge: MIT Press. Shin, Sun-Joo (2010): “Peirce’s Two Ways of Abstraction.” In: Moore, Matthew E. (Ed.): New Essays on Peirce’s Mathematical Philosophy. Chicago and La Salle: Open Court, 41 – 58. Shin, Sun-Joo (2013): “Visualization of Quantificational Logic.” Paper presented at the conference Extended Problem Solving, Aarhus University, January. Short, Thomas L. (1982): “Life among the Legisigns.” In: Transactions of the Charles S. Peirce Society 18. No. 4, 265 – 310. Short, Thomas L. (1997): “Hypostatic abstraction in self-consciousness.” In: Brunning, Jacqueline and Forster, Paul (Eds.): The Rule of Reason: The Philosophy of C.S. Peirce. Toronto: University of Toronto Press, 289 – 321. Short, Thomas L. (2007): Peirce’s Theory of Signs. Cambridge: Cambridge University Press. Singh, Simon (1999): The code book. The secret history of codes and code breaking. New York: Doubleday. Smith, Barry (1979): “Roman Ingarden: Ontological Foundations for Literary Theory.” In: Odmark, John (Ed.): Language, Literature & Meaning. Volume I. Amsterdam: John Benjamins, 373 – 390.

378

Literature

Smith, Barry (1980): “Ingarden vs. Meinong on the Logic of Fiction.” In: Philosophy and Phenomenological Research 16, 93 – 105. Smith, Barry (Ed.) (1982): Parts and Moments. Munich: Philosophia. Smith, Barry (1992): “An Essay on Material Necessity.” In: Hanson, Philip and Hunter, Bruce (Eds.): Return of the A Priori. Canadian Journal of Philosophy. Supplementary Volume 18, 301 – 322. Smith, Barry (1994): Austrian Philosophy. Chicago and La Salle: Open Court. Smith, Barry (1996): “In Defense of Extreme (Fallibilistic) Apriorism.” In: Journal of Libertarian Studies 12, 179 – 192. Smith, Barry (1999): “Truthmaker Realism.” In: Australasian Journal of Philosophy 77. No. 3, 274 – 291. Smith, Barry (2005): “Against Fantology.” In: Reicher, Maria E. and Marek, Johann C. (Eds.): Experience and Analysis. Vienna: ÖBV & HPT. Sonesson, Göran (1999): “Aniconic visual signs.” https://www.academia.edu/492229/The_In ternet_Semiotics_Encyclopaedia, last accessed on March 11, 2022. Sowa, John (2015): “Signs and Reality.” In: Applied Ontology 10. No. 3 – 4, 273 – 284. Spencer, Herbert (1873): The Study of Sociology. London: Henry S. King & Co. https://oll.lib ertyfund.org/title/spencer-the-study-of-sociology-1873, last accessed on March 11, 2022. Spiegelberg, Herbert (1956): “Husserl’s and Peirce’s phenomenologies: Coincidence or interaction?” In: Philosophy and Phenomenological Research 17, 164 – 185. Spiegelberg, Herbert (1969): The Phenomenological Movement. A Historical Introduction. 2 Volumes. The Hague: Martinus Nijhoff. Stephen, Damian G., Boncoddo, Rebecca A., Magnuson, James S., and Dixon, James A. (2009): “The dynamics of insight: Mathematical discovery as a phase transition.” In: Memory & Cognition 37 No. 8, 1132 – 1149. Stjernfelt, Frederik (2000): “Diagrams as a Centerpiece of a Peircean epistemology.” In: Transactions of the Charles S. Peirce Society 36. No. 3, 357 – 384. Stjernfelt, Frederik (2000a): “Die Vermittlung zwischen Anschauung und Denken bei Kant, Cassirer und Peirce.” In: Zeitschrift für Semiotik 22. No. 3 – 4, 341 – 368. Stjernfelt, Frederik (2002): “Tractatus Hoffmeyerensis: Biosemiotics as Expressed in 22 Basic Hypotheses.” In: Sign Systems Studies 30 No. 1, 337 – 345. Stjernfelt, Frederik (2007): Diagrammatology. An Investigation on the Borderlines of Phenomenology, Ontology, and Semiotics. Dordrecht: Springer. Stjernfelt, Frederik (2008): “Spatial Cognition Strategies in Map and Diagram Reasoning.” In: Brandt, Per Aage and Carstensen, Claus (Eds.): The Map is Not the Territory. Esbjerg: Esbjerg Kunstmuseum, 167 – 173. Stjernfelt, Frederik (2008a): Admiral, Bitumen, Zodiak. Lille Klaus Høeck Encyklopædi. Copenhagen: Gyldendal. Stjernfelt, Frederik (2009): “Simple Animals and Complex Biology. The double von Uexküll inspiration in Cassirer’s philosophy.” In: Synthese 179. No. 1, 169 – 186. Stjernfelt, Frederik (2011): “Peirce’s Notion of Diagram Experiment. Corollarial and Theorematical Experiments With Diagrams.” In: Heinrich, Richard, Nemeth, Elisabeth, Pichler, Wolfram, and Wagner, David (Eds.): Papers from the 33rd International Wittgenstein Symposium in Kirchberg am Wechsel 2010. Frankfurt and Lancaster: Ontos. Stjernfelt, Frederik (2011a): “Authenticities and Their Conflicts. Genuine Challenges of Museology.” In: Ravn, Thomas Bloch and Aasted, Elsebeth (Eds.): Authenticities and

Peirce References (see detailed references below)

379

Relevance. Report from the 24th Conference in the Association of European Open Air Museums, Den Gamle By, Aarhus, Denmark 2009. Aarhus: Den Gamle By, 40 – 59. Stjernfelt, Frederik (2011b): “On operational and optimal iconicity in Peirce’s diagrammmatology.” In: Semiotica 186. No. 1, 395 – 419. https://doi.org/10.1515/semi. 2011.061, last accessed on March 11, 2022. Stjernfelt, Frederik (2012): “The Evolution of Semiotic Self-Control.” In: Deacon, Terrence, Schilhab, Theresa, and Stjernfelt, Frederik (Eds.): The Symbolic Species Evolved. Dordrecht: Springer, 39 – 63. Stjernfelt, Frederik (2013): “The Generality of Signs. Anti-Psychologism in the Foundations of Semiotics—and Its Actual Relevance.” In: Semiotica 194, 1 – 33. Stjernfelt, Frederik (2013a): “Forgotten Twins. Reason and Visuality.” In: Kristensen, Tore, Michelsen, Anders, and Wiegand, Frauke (Eds.): Transvisuality. Liverpool: Liverpool University Press, 75 – 86. Stjernfelt, Frederik (2013b): “From Diagrams to Poetry.” In: Elleström, Lars, Fischer, Olga, and Ljungberg, Christina (Eds.): Iconic Investigations. Amsterdam: John Benjamins, 121 – 140. Stjernfelt, Frederik (2014): Natural Propositions: The Actuality of Peirce’s Doctrine of Dicisigns. Boston: Docent Press. Stjernfelt, Frederik (2014a): Dicisigns and Cognition: The logical interpretation of the ventraldorsal split in animal perception. In: Cognitive Semiotics 7. No. 1, 61 – 82. Stjernfelt, Frederik (2015): “Dicisigns.” In: Synthese 192. No. 4, 1019 – 1054. Stjernfelt, Frederik (2015a): “Green War Banners in Central Copenhagen: A Recent Political Struggle Over Interpretation—And Some Implications for Art Interpretation as Such.” In: Bundgaard, Peer and Stjernfelt, Frederik (Eds.): Investigations into the Phenomenology and the Ontology of the Work of Art. What are Artworks and How Do We Experience Them? London: Springer Open, 209 – 224. Stjernfelt, Frederik (2017): “Diagrammatic and Iconic Imagery in Science.” In: Philipsen, Lotte and Kjærgaard, Rikke Schmidt (Eds.): The Aesthetics of Scientific Data Representation: More than Pretty Pictures. London: Routledge, 16 – 21. Stjernfelt, Frederik (2017a): “Essay sur le Don: An aphorism offered for Don Favareau’s 60th birthday.” In: Cobley, Paul and Kull, Kalevi (Eds.): Biosemiotics in the Community: Essays in Honour of Donald Favareau. Tartu: University of Tartu Press, 103 – 106. Stjernfelt, Frederik (2021): “Review of ‘Logic of the Future: Writings on Existential Graphs. Volume 1: History and Applications.’” In: Transactions of the Charles S. Peirce Society 57. No. 1, 114 – 127. Stjernfelt, Frederik (2022): “The Epistemology of Secrecy: The Roles of Abduction in the Investigation of Deep State Issues”, in Lorenzo Magnani (ed.) (2022), Handbook of Abductive Cognition, Cham, Switzerland: Springer, forthcoming. Stjernfelt, Frederik (2022a): “Abduction in Diagrammatical Reasoning”, in Lorenzo Magnani (ed.) (2022), Handbook of Abductive Cognition, Cham, Switzerland: Springer, forthcoming. Strauss, Leo (1952): Persecution and the Art of Writing. Glencoe: The Free Press. Struhsaker, Thomas T. (1967): “Auditory Communication among Vervet Monkeys (Cercopithecus aethiops).” In: Altmann, Stuart A. (Ed.): Social Communication among Primates. Chicago: University of Chicago Press. Stumpf, Carl (1883 – 1890): Tonpsychologie. Volumes I – II. Leipzig: S. Hirzel.

380

Literature

Suhler, Christopher and Churchland, Patricia (2010): “Control: Conscious and Otherwise.” In: On the Human, a project of the National Humanities Center. https://nationalhumanities center.org/on-the-human/2010/05/control-conscious-and-otherwise/, last accessed on March 11, 2022. Talmy, Leonard (2000): “The Windowing of Attention in Language.” In: Toward a Cognitive Semantics. Cambridge: MIT Press. Tetens, Johann Nicolas (1777): Philosophische Versuche über die menschliche Natur und ihre Entwickelung. Leipzig: Weidmann. https://www.deutschestextarchiv.de/book/view/tet ens_versuche01_1777?p=5, last accessed on March 11, 2022. Thom, René (1975): Stabilité Structurale et Morphogénèse. Paris: Ediscience. English Version: Thom, René (1977): Structural Stability and Morphogenesis. Reading: Benjamin. Tiercelin, Claudine (1984): “Peirce on Machines, Self Control, and Intentionality.” In: Torrance, Steven (Ed.): The Mind and the Machine. Chichester: Ellis Horwood. Tomasello, Michael (1999): The Cultural Origins of Human Cognition. Cambridge: Harvard University Press. Tomasello, Michael (2008): Origins of Human Communication, Cambridge: MIT Press. Tomasello, Michael, Carpenter, Malinda, Call, Josep, Behne, Tanya, and Moll, Henrike (2005): “Understanding and sharing intentions: The origins of cultural cognition.” In: Behavioral and Brain Sciences 28, 675 – 691. Trammell, Richard L. (1973): “Charles Sanders Peirce and Henry James the Elder”. In: Transactions of the Charles S. Peirce Society 9. No. 4, 202 – 220. Tylén, Kristian, Fusaroli, Riccardo, Bjørndahl, Johanne S., Rączaszek-Leonardi, Joanna, Østergaard, Svend, and Stjernfelt, Frederik (2014): “Diagrammatic Reasoning: Abstraction, Interaction, and Insight.” In: Pragmatics & Cognition 22. No. 2, 264 – 283. Uexküll, Jakob von (1928): Theoretische Biologie. Berlin: J. Springer. Viola, Tullio (2020): Peirce on the Uses of History. Berlin and Boston: De Gruyter. Wachter, Daniel (2005): “Roman Ingarden’s Ontology: Existential Dependence, Substances, Ideas, and Other Things Empiricists Do Not Like.” In: Chrudzimski, Arkadiusz (Ed.): Existence, Culture, and Persons: The Ontology of Roman Ingarden. Frankfurt: Ontos, 55 – 82. Welby, Victoria (1903): What is Meaning? Studies in the Development of Significance. London: Macmillan & Co. Whittle, Michael (2014): “Romantic Objectivism: Diagrammatic Thought in Contemporary Art.” Kyoto City University of Arts: Ph.D. Dissertation. www.michael-whittle.com/uploads/1/1/ 1/3/11134083/romantic_objectivism.pdf, last accessed on March 11, 2022. Wilson, Aaron B. and Brunson, Daniel J. (2017): “The Transhumanist Philosophy of Charles Sanders Peirce.” In: Journal of Evolution and Technology 27. No. 2, 12 – 29. Wood, David, Bruner, Jerome S., and Ross, Gail (1976): “The role of tutoring in problem solving.” In: Journal of Child Psychiatry and Psychology 17 No. 2, 89 – 100. Zeman, Joseph J. (1964): The Graphical Logic of C. S. Peirce. University of Chicago: Ph.D. Dissertation.

Earlier Versions of Chapters of This Book Chapter 1. 2011. “Signs Conveying Information: On the Range of Peirce’s Notion of Propositions: Dicisigns.” In: International Journal of Signs and Semiotic Systems 1. No. 2, 40 – 52. Chapter 2. 2016. “Dicisigns and habits: Implicit propositions and habit-taking in Peirce’s pragmatism.” In: West, Donna and Anderson, Myrdene (Eds.): Consensus on Peirce’s Doncept of Habit: Before and Beyond Consciousness. Cham: Springer, 241 – 264. Chapter 3. 2021. “Peirce’s Theories of Assertion.” In: Transactions of the Charles S. Peirce Society 57. No. 2, 248 – 269. Chapter 4. 2019. “The Identity of Sweet Molly Malone: Dicent Indexical Legisigns—A New Element in the Periodic Table of Semiotics?” In: Transactions of the Charles S. Peirce Society 55. No. 2, 175 – 184. Chapter 5. 2019. “Co-localization as the Syntax of Elementary Propositions: An Amazing Peircean Idea and Some Implications for the Semiotics of Truth.” In: Jappy, Tony (Ed.): Bloomsbury Companion to Contemporary Peircean Semiotics. London: Bloomsbury Academic, 419 – 458; 482 – 485. Chapter 6. 2022 “Sheets in the Wild.” In: Tempo da colheita: homenagem à Lucia Santaella [Harvest time: Festschrift for Lucia Santaella]. São Paulo: Filoczar. Chapter 7. 2012. “How Do Pictures Act? Two Aspects of Picture Activity.” In: Feist, Ulrike and Rath, Markus (Eds.): Et in imagine ego. Berlin: Akademie, 16 – 29. Chapter 8. 2019. “Dimensions of Peircean Diagrammaticality.” In: Semiotica 228, 301 – 331. Chapter 9. 2015. “Iconicity of logic—and the roots of the ‘iconicity’ concept.” In: Hiraga, Masako, Herlofsky, William J., Shinohara, Kazuko, and Akita, Kimi (Eds.): Iconicity: East Meets West. Amsterdam: John Benjamins, 35 – 56; https://benjamins.com/catalog/ill.14. 02stj. Chapter 10. Østergaard, Svend and Stjernfelt, Frederik (2016): “Diagrammatic Problem Solving.” In: Ljungberg, Christina and Krämer, Sybille (Eds.): Thinking with Diagrams. Boston and Berlin: Mouton de Gruyter, 103 – 119. Chapter 11. 2018. “Schematic Aspects of an Aesthetics of Diagrams.” In: Ritchie, Matthew (Ed.): The Temptation of the Diagram. Los Angeles: Getty Research Institute. Chapter 12. 2021. “Peirce as a Truthmaker Realist: Propositional realism as backbone of Peircean metaphysics.” In: Blityri. Studi di storia delle idee sui segni e le lingue 9. No. 2, 123 – 136. Chapter 13. 2016. “Phenomenology and Logic in Peirce.” In: Journal Phänomenologie 4, 21 – 38. Chapter 14. 2019. “A Peirce for the 21st Century.” Review of Bellucci, Francesco: Peirce’s Speculative Grammar. In: Sign System Studies 46. No. 4, 590 – 616. Chapter 15. 2016. “Blocking Evil Infinites: A Note on a Note on a Peircean Strategy.” In: Sign Systems Studies 42. No. 4, 518 – 522. Chapter 16. 2012. “Peirce and Cassirer—The Kroisian Connection: Vistas and Open Issues in John Krois’ Philosophical Semiotics.” In: Bredekamp, Horst, Lauschke, Marion, and Arteaga, Alex (Eds.): Bodies in Action and Symbolic Forms: Zwei Seiten der Verkörperungstheorie. Berlin: Akademie, 37 – 46. Chapter 17. In Press. “Dependences: How to connect entities, across pragmatism, phenomenology, and structuralism” (abbreviated version). In: Cigana, Lorenzo and https://doi.org/10.1515/9783110793628-024

382

Earlier Versions of Chapters of This Book

Gregersen, Frans (Eds.): StructuralismS. Copenhagen: Det Kongelige Danske Videnskabernes Selskab. Chapter 18. 2021. “Conscious Self-Control as Criterion for Reasoning” (abbreviated version). In: Cognitive Semiotics 14. No. 1, 71 – 99. Chapter 19 was written for this volume.

List of Illustrations Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.

1: : : : : : : : : : : : :

Fig. Fig. Fig. Fig.

: : : :

Fig. : Fig. : Fig. Fig. Fig. Fig.

: : : :

Fig. : Fig. Fig. Fig. Fig.

: : : :

Fig. : Fig. : Fig. Fig. Fig. Fig. Fig. Fig.

: : : : : :

Australian road sign, Wikimedia Commons: Bahnfrend—Own work, CC BY-SA . Peirce’s pre- sign taxonomy Peirce’s combinatorial -sign taxonomy of the  Syllabus; CP . A photographic print of Andreas Achenbach, , @ villa-achenbach.de Dauthage’s  portrait of Andreas Achenbach, Wikimedia Commons Two Beta graphs; Roberts (),  “No Admittance” sign, Wikimedia Commons King Den ivory tablet, Abydos.@ CaptMondo, license CC BY . Decipherment of the King Den tablet. @ Kammerzell and Peust Introductory Donald Duck image sequence, © Disney Diagram of a geometrical triangle The Cartesian Plane Segment of a topographical map of southern Germany. @ Creative Commons Attribution-Share Alike . Unported license. Attribution: Thomas Römer Library sign The cover of Harry Potter and the Philosopher’s Stone. @ Bloomsbury The Peirces’ tombstone, Milford PA (author’s collection) Woodcut sheet reporting on the execution of Danish Prime Minister Struensee and his alleged accomplice Count Brandt, Copenhagen , @ Royal Library, Copenhagen Anatomical chart of the thorax with selected parts, Wikimedia Commons Title page of Spinoza’s Tractatus Theologico-Politico, anonymous publication, Amsterdam , Wikimedia Commons Department of Semiotics sign, Estonia “Gone with the Wind” poster,  “Putin and the Pussygrabbers” poster, US , @ WTFToto New Orleans Michel-Marie Carquillat: Portrait of Joseph-Marie Jacquard, , woven silk, . x . cm, @ Wikimedia Commons Screenshot from the newscast of the Ergenekon case at www.thedailybeast.com, May ,  Map of Manhattan; Kitcher and Varzi  Algebra of Logic expression of “Everybody loves someone” Beta graph of “Everybody loves someone” London Underground map (central segment), developed from Harry Beck’s  original Map of Bakerloo line, London Underground  Commutation diagram used in the proof of the “Five Lemma”; Wikipedia article “Five Lemma” Peirce notation and modern notation of elementary signs of propositional logic Examples of existential and universal quantification in Peirce’s Algebra of Logic Universal and existential quantifier signs in the Algebra of Logic Frege, Peirce, and modern notation of existentially quantified expressions Frege, Peirce, and modern notation for universally quantified expressions Alpha Graphs for propositional logic, Wikimedia Commons

https://doi.org/10.1515/9783110793628-025

384

List of Illustrations

Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Fig. : Figs.  – :

Alpha Graph for disjunction Beta Graphs with linguistic and modern interpretations Beta Graph with trivalent predicate Linear and Beta Graph versions of “All that is good is ugly” Equivalent Beta Graphs with Identity Lines vs. Selectives Linear logic representation and Beta Graphs compared Triangle diagram with auxiliary lines in a proof of the angle sum Target elements in insight problems Example of a Cog Wheel problem. Which lever to pull in order to save the rabbit? Reaction time development over successive trials, Group  Reaction time development over successive trials, Group  Gesture-language combinations Flow chart over typical developments across groups Average reaction times for different solution strategies Final reaction time for individuals and pairs “The Temptation of the Diagram” (El Segundo Museum of Art, California,), © Matthew Richie, reproduced with permission. “The Demon in the Diagram” (Moody Center for the Arts at Rice University, Houston, Texas, ), © Matthew Richie, reproduced with permission. The top tiers of Peirce’s classification of the sciences c.  Metaphysical parts of the object, “New List”,  Seven structurings of the same concept zone, Hjelmslev () Reduced logical concept zone combinations, Hjelmslev () Peirce’s  letter to Marquand with a sketch of how to implement universal and existential quantification in electric circuitry, W ,  Circuit Diagram for an Electromagnetic Logical Machine, found among Allan Marquand’s papers, c. ; quoted from Ketner and Stewart () Contradiction version of the β-Γ bound articulation, Hjelmslev () Realms of Being after Ingarden, @ Peter Simons

Fig. : Fig. Fig. Fig. Fig. Fig.

: : : : :

Fig. : Fig. : Fig. :

Notes  The origin and, correspondingly, the amount of versions and parts of the Syllabus during the fall of 1903 is a complicated issue (covering at least Robin numbers 477– 478, 508, 538 – 541, maybe more, not of all which have been published; cf. Bellucci 2017, Chapter 7). Prominent versions are the “Sundry Logical Conceptions” and the “Nomenclature of Triadic Divisions”, the latter appearing as the most final version. They were cut into smaller pieces and scattered in the CP but restored as intact chapters in the EP II along with two briefer Syllabus-related pieces, “An Outline Classification of the Sciences” and “Ethics of Terminology” (cf. also Chapter 14 below). Here, we shall generally refer to the Syllabus, while going into further detail when necessary.  Further examples include the following: Stjernfelt 2008a, El-Hani, Queiroz, and Stjernfelt 2010; Stjernfelt 2011a; Østergaard and Stjernfelt 2013; Stjernfelt 2013b; Cobley and Stjernfelt 2015; Stjernfelt 2015a; Hoffmeyer and Stjernfelt 2016; Stjernfelt 2017.  A more detailed discussion of the notion of Dicisigns may be found in Stjernfelt 2014, Chapter 3, and in Stjernfelt 2015. Chapter 1 of the present book serves as an intro to the further discussions of a Peircean theory of propositions in Chapters 2– 5.  Peirce’s main development of the Dicisign doctrine falls in his late period from around 1903, e. g., in the Harvard Lectures of Pragmatism (in the CP as well as the EP II), and in the Syllabus of Certain Topics of Logic which has never been published in its entirety, but appears in large parts in the CP and the EP II, etc. I pronounce “Dicisign”: “Dee-see-sign”, after the standard way of pronouncing Latin “c” as an “s” when it appears before front vowels like “i” and “e”.  It is an intriguing fact that this counts as one of the spectacular cases of parallel discovery in the history of science, a bit like the famous Leibniz-Newton case with calculus. Frege famously undertook a complete formalization of predicate logic in his 1879 Begriffsschrift, while Peirce did the same thing in his two “Algebra of Logic” papers from 1880 – 1885 but had already initiated the study of relational predicates in his 1870 “Logic of Relatives”. Neither of the two referred to the other nor seems to have known the other’s work.  For a discussion of the iconicity of different logic representations, see Chapter 9.  Oftentimes in his early period until the 1890s, Peirce will use “assertion” for “proposition”, before he conceived of the Dicisign to be independent of both the mental representation of it, of the assent to it by some agent, and of the assertion of it by some actor (cf. below).  The Peircean analysis takes Dicisigns claiming to refer to actually existing singular objects to be basic. Hence, even if crucial to logic, quantified Dicisigns form derived cases of vague (existential quantification) and general (universal quantification) Dicisigns.  Of course, such photographs may be forged or subject to Photoshop manipulation, etc.—but possibilities of falsity on many levels will affect all types of Dicisigns.  Rhemes are often thus identified with isolated Predicates outside of propositional contexts. Strictly speaking, as the Rheme-Dicisign-Argument triad is taken to be exhaustive, also isolated Subjects outside of propositional contexts must be classified as Rhemes. The tension between these two clashing definitions of Rhemes, see Bellucci (in press).  The second, “dynamic” interpretant will then be the meaning actually realized in each single case of interpreting the Dicisign; as to interpretants, see also Chapter 3; Chapter 14.  Peirce would claim such a Dicisign is meaningless (his example is “Any Phoenix, when rising from its ashes, sings Yankee Doodle”) but must be classed with true Dicisigns because no possible perception can make it false. We would rather classifiy it as without any immediate truth value. https://doi.org/10.1515/9783110793628-026

386

Notes

 Peirce’s idea that Dicisigns refer to a Universe of Discourse rather than directly to reality makes it easy, it seems to me, the connect his Dicisign doctrine with accounts for fictitious propositions like Roman Ingarden’s; cf. Stjernfelt 2007, Chapter 16.  Another issue, which we may only mention in the passing, is Peirce’s 1903 subdivision of Dicisigns which comprise the following types: ) Propositions proper—Dicent Symbols (characterized by involving a general idea) ) Quasi-Propositions—Informational Indices a) Dicent Sinsigns (a Weathercock, some photographs, some paintings … but presumably also all sort of empirical occurrences offering information about their particular cause or motivation) b) Dicent Indexical Legisigns (Peirce’s example: a street cry identifying the individual shouting, or expressions identifiying individuals like “This is him”, “That is Napoleon”); cf. Chapter . These three categories appear as numbers , , and , respectively, of Peirce’s famous ten-sign classification based on the combination of the three trichotomies of the Syllabus (EP II,  ff.; see Fig.  below). It is an contested issue whether the biosemiotic examples discussed below should be categorized as proper Dicent Symbols or rather as Dicent Sinsigns. The apparently simpler status of the latter might immediately tempt one to opt for that choice, but the automatized character of most of the biosemiotic examples rather point in the direction of the generality of Dicent Symbols—E. Coli is probably not concerned with the particularity of this and that lump of sugar, but more interested in its general character of nutrient carbohydrate. Thus, very simple signs are also very general.  This points to an important issue of plasticity in Peirce’s Dicisign doctrine: the exact dividing line between the S and P aspects of one and the same Dicisign may differ with interpretation. This does not indicate the dividing line is arbitrary nor that it may vanish completely—but merely that many Dicisigns, especially nonlinguistic or only partially linguistic Dicisigns may be parsed into S and P parts in different ways, depending upon the immediate purpose of the interpreter, and that no fixed location of the line could be said to exist. Peirce says: “Take the proposition ‘Burnt child shuns fire.’ Its predicate might be regarded as all that is expressed, or as ‘has either not been burned or shuns fire’ or ‘has not been burned,’ or ‘shuns fire’ or ‘shuns’ or ‘is true’; nor is this enumeration exhaustive. But where shall the line be most truly drawn? I reply that the purpose of this sentence being understood to be to communicate information, anything belongs to the interpretant that describes the quality or character of the fact, anything to the object that, without doing that, distinguishes this fact from others like it; while a third part of the proposition, perhaps, must be appropriated to information about the manner in which the assertion is made, what warrant is offered for its truth, etc. But I rather incline to think that all this goes to the subject. On this view, the predicate is, ‘is either not a child or has not been burned, or has no opportunity of shunning fire or does shun fire’; while the subject is ‘any individual object the interpreter may select from the universe of ordinary everyday experience” (“A Survey of Pragmaticism”, 1907, CP 5.473). Hilpinen (1992, 476) also discusses this quote and rightly remarks that this idea takes Peirce far away from the logical atomism of Russell and Wittgenstein, according to whom there is only one complete analysis of the proposition. As to the relativity of the S-P distinction, see also Chapter 4. Again, this plasticity depends on the Universes of Discourse referred to by the utterer and the interpreter. Another interpreter of the Australian warning sign might include the sender of the sign and read it as follows: “So, these are the sole three animal species acknowledged by the Australian traffic authorities”.  Cf. the arguments in Stjernfelt 2007, Chapter 11, pertaining to Peirce’s discussions of the abilities of dogs and parrots where he seems to ascribe to them abilities to deal with Dicisigns. Peirce claims that “All thinking is by signs, and the brutes use signs. But they perhaps rarely

Notes

387

think of them as signs. To do so is manifestly a second step in the use of language. Brutes use language, and seem to exercise some little control over it. But they certainly do not carry this control to anything like the same grade that we do. They do not criticize their thought logically” (“Consequences of Critical Common-Sensism”, c. 1905, CP 5.534). So what animals lack, according to him, is rather the ability to subject their own Dicisigns and Argument to explicit and critical scrutiny. See Chapters 18 – 19; cf. also Stjernfelt 2012 and 2014.  From another perspective, Hurford 2007 makes a similar argument, see Stjernfelt 2014 Chapter 5.  Critics have argued that Alex was only an example of the “Kluge Hans”-effect where the animal guesses the answer after subtle cues from its trainer. Against this, however, counts the fact that Alex was able to answer questions from other people in the absence of its trainer.  The relation of Dicisigns to habits and action, see Chapter 2  An important corollary is that Dicisign structure as such is not a conventional component of human cultures (even if particular use patterns of Dicisigns may follow such conventions); cf. the discussion of “culturalism” as the exaggeration of culture as an explanatory category for human behavior (Eriksen and Stjernfelt 2012). The sophistication of Dicisign use during evolution must be a central issue for evolutionary biosemiotics; cf. Hoffmeyer and Stjernfelt 2016.  Cf. the roles of conscious binding, short-term working memory, and medium-term memory discussed by Donald 2001.  The “or” in the claim is not an exclusive-or—a sign may be both an icon, an index, and a symbol, but no sign may belong to a fourth category.  Bellucci has convincingly argued (2017) that the 1906 trichotomy of Seme-Pheme-Delome is not identical to Rheme-Dicisign-Argument but constitutes a further generalization, covering all the different acts which may be enacted on the bases of terms, propositions, and arguments. Phemes, thus, comprise acts undertaken on the basis of a Dicisign, such as assertions, beliefs, questions, imperatives etc.  The “New List” was presented in a lecture at the American Academy of Arts and Sciences 14 May 1867 and published the year after.  As observed by Colapietro 2009, 368.  Even late in life, Peirce continued to refer to this idea in his discussions of habit: “For our present purpose it is sufficient to say that the inferential process involves the formation of a habit. For it produces a belief, or opinion; and a genuine belief, or opinion, is something on which a man is prepared to act, and is therefore, in a general sense, a habit” (Minute Logic, 1902, CP 2.148).  “Thus, when you say that you have faith in reasoning, what you mean is that the belief habit formed in the imagination will determine your actions in the real case. This is looking upon the matter from the psychological point of view. Under a logical aspect your opinion in question is that general cognitions of potentialities in futuro, if duly constructed, will under imaginary conditions determine schemata or imaginary skeleton diagrams with which percepts will accord when the real conditions accord with those imaginary conditions” (Minute Logic, 1902, CP 2.148). Cf. Stjernfelt 2007, Chapter 4.  In the background here lies Peirce’s intense occupation with the mathematical concept of the continuum and its possible metaphysical implications; cf. Parker 1998; Stjernfelt 2007.  In the Robin catalogue, the Kaina stoicheia or New Elements is dated to 1904. Bellucci, Chiffi, and Pietarinen (2021, 286) question this dating, arguing that as it fails to refer to the conceptual novelties of the 1903 Syllabus, it must be earlier. Other circumstantial evidence points to late

388

Notes

1901 as the most probable dating. In this book, we assume this dating, marking it with a question mark.  “… for it is the belief men betray and not that which they parade which has to be studied” (“Issues of Pragmaticism”, 1905, EP II, 349, n.).  An important variant idea occurring several times in Peirce is that beliefs, pragmatically defined, are at odds with propositions of science (despite the fact that the maxim was originally conceived of as a meaning clarification procedure in scientific terms). Thus, in 1898, he says (“Cambridge Lectures on Reasoning and the Logic of Things: Philosophy and the Conduct of Life”, CP 1.635) the following. “… I hold that what is properly and usually called belief, that is, the adoption of a proposition as a {ktéma es aei} to use the energetic phrase of Doctor Carus, has no place in science at all. We believe the proposition we are ready to act upon. Full belief is willingness to act upon the proposition in vital crises, opinion is willingness to act upon it in relatively insignificant affairs. But pure science has nothing at all to do with action. The propositions it accepts, it merely writes in the list of premisses it proposes to use. Nothing is vital for science; nothing can be. Its accepted propositions, therefore, are but opinions at most; and the whole list is provisional. The scientific man is not in the least wedded to his conclusions”. A similar argument is repeated five years later (“Telepathy”, 1903, CP 7.606). The idea seems to distinguish the definition of conceptions by the sum of conceived effects of their objects, on the one hand, and the action consequence inferred from (some of) those effects—so that the latter is reserved for “vital” issues only, remote from the cool, detached relation of the scientist to his results. In this variant idea, then, “beliefs” differ from scientific propositions, radically narrowing the explicitly broad definition of “belief” so as to cover any assent, of some endurance, to a proposition.  Add to this idea the later result that the sharp distinction between phylogeny and ontogeny holds for higher animals with gendered reproduction only; for bacteria which comprise the vast majority of the biosphere, DNA exchange is not confined to meiosis but takes place continuously even across species so that phylogeny and ontogeny are rather aspects of the same process.  Of course, “human” should be construed with some caution here; we only know human realizations of such processes, but it is in no way precluded that other organisms or automata could satisfy the relevant criteria.  Following Peirce’s definition of a fact: “What we call a ‘fact’ is something having the structure of a proposition, but supposed to be an element of the very universe itself. The purpose of every sign is to express ‘fact,’ …” (“Kaina Stoicheia”, 1901(?), EP II, 304), it is evident that physical laws are general facts and thus have the structure of propositions—but that is not the same thing as saying that they are themselves propositions, as only the semiotic or scientific representation of them are.  As was the case as late as in 1878 when Peirce wrote: “As for deduction, which adds nothing to the premisses, but only out of the various facts represented in the premisses selects one and brings the attention down to it, this may be considered as the logical formula for paying attention, which is the volitional element of thought, and corresponds to nervous discharge in the sphere of physiology” (“Deduction, Induction, and Hypothesis”, 1878, CP 2.643).  Of course, this is equivalent to Hilbert’s Entscheidung problem, which was, famously, proved to be undecidable by Church and Turing thirty years later, following Gödel. The implication of this for pragmatism is that for certain conceptions, not only the sum of conceivable effects may be practically unattainable, but in some cases not even principally attainable. Consequently, the same holds for the related action habits. In most cases, however, this makes the concept of number no less pragmatically clear.

Notes

389

 “The Scotistic form or essence functions in precisely the same manner that Peirce’s habit does; it determines how a thing “would be” disposed to behave under certain specifiable conditions” (Raposa 1984, 157).  In the original paper, here followed a section of the structure of self-control. This has been left out, this discussion unfolding in larger detail in Chapter 18.  But probably not more than a clue—the generalization to the non-sign, action habit character of the final interpretants of all concepts is probably equivalent to the much sought-after “proof of pragmatism”.  CP 5.543; variant in R 599, 5: “An assertion is an act by which a person makes himself responsible for the truth of a proposition”.  This may sound trivial, but it proved a classic problem of picture theories of propositions like Russell’s or Wittgenstein’s to account for false or mendacious propositions. It would not be wrong to call Peirce’s theory of propositions a picture theory, but it makes room for false propositions due to its distinction between the reference and signification of the proposition, and for lies with its distinction between assertion and assent.  Even far into his period of technically defining “assertion”, Peirce may still use the term in the non-technical way as a synonym of “proposition”, e. g., in “On Logical Graphs”, 1903, CP 4.354  In a parallel draft, Peirce expands the copula to include, more generally, the “asserting verb” (R 787, 1896)  This tripartition poses some problems, couched in the non-technical terms of “compulsion” and “occasion”. Is the triad simply identical with 1) subject, 2) predicate; 3) an early version of the immediate object? Or is it rather a new, illocutionary trichotomy so that 1) “the enforced idea” is the whole of the proposition; while 2) is the act of claiming the proposition in a certain situation, and 3) the situation-bound intention of the utterer? In the latter case, it is a new analysis of the pragmatics of asserting.  The weathercock-type example mentioned here would develop into the subtype of “informational index” (as opposed to non-informational indices) and “Dicent Indexical Sinsign” (in the 1903 ten-signs system) in the development of the Syllabus a couple of years later.  The Syllabus “Deduction of the Dicisign” is so named by Bellucci; see Bellucci 2013, 2014 and 2017, Chapter 7; see also Stjernfelt 2014, Chapter 3.  Properly, “Replicas” are such incarnations of general sign types; Replicas being a particular sort of Sinsigns or Tokens more generally.  Peirce’s problems with awareness of habits, see Chapter 2 above.  Peirce’s notion of self-control, see Chapter 18; cf. also Stjernfelt 2012, 2014.  In Stjernfelt 2014 (Chapter 7), I use the definition in this way on a couple of examples to substantiate my claim that many multimodal expressions are, actually, asserted propositions which can be seen from the fact that severe penalties may befall those uttering them in case of falsity or fraud.  Bellucci 2017, 266.  Thus, it does not appear in the “Sundry Logical Conceptions” draft of the Syllabus where Peirce still clings to a two-trichotomies theory, which has given rise to some confusion. The “Nomenclature” appears to be the final version of the Syllabus sign theory, introducing both the Qualisign-Sinsign-Legisign trichotomy and the ten-sign combinatory. As to the chronology of the composition of the Syllabus during the fall of 1903, see Bellucci 2017, Chapter 7.  Cf. Bellucci 2017, Chapter 6.

390

Notes

 The most famous of Mendeleyev’s predictions concerns those named eka-Boron, eka-Aluminium, eka-Manganese, and eka-Silicon, where the prefix “eka” means “one” (that is, one step higher, in the same group of elements, than the element after the prefix), and they proved to be good predictors of the approximate properties of the elements Scandium, Gallium, Technetium, and Germanium, respectively.  I am here quoting the famous Irish ballad “Molly Malone” (also known under titles such as “Cockles and Mussels” and “In Dublin’s Fair City”) for its example of a famous, if fictitious, street-vendor announcement cried out in the streets of Old Dublin. The first reference to the song, complete with music and text, is from 1883 – 1884; a London source describes it as written and composed by James Yorkston, quoting an earlier Scottish publication; see Murphy 2013.  See also the previous chapter.  Peirce, in a few words, added a third, enigmatic example: “A third variety may be a premiss of an argument” (EP II, 297; CP 2.265). No further explanation follows. A premise is normally considered a proposition, a full-blown standard Dicent Symbol. Maybe Peirce here intimated that when that proposition enters an argument, as a premise, it changes status and what appears there is really a general name, making it possible to identify the proposition behind it. When, in propositional logic, we abbreviate propositions as p or q, those names are indeed Indexical Legisigns and they refer to Dicent Symbols, but they are not, in themselves dicent. I remain open to further elucidations of this third example of Dicent Indexical Legisigns.  This implies that the category of Rhematic Indexical Legisigns, with its prototypical representative being proper names, covers a much wider range of signs than linguistic names, namely all those signs that permit the unique identification of an object or set of objects, if the Rheme is saturated by some other Index to form a Dicent Indexical Legisign. They will comprise the “timbre or theme” of a voice, the characteristic look of a face, a DNA profile, but also all other sorts of general iconic or indexical information that may potentially be used to identify an object in a particular Universe of Discourse. It is true that icons or description in isolation cannot single out an object and that some indexical information (knowledge by acquaintance) must lie at the bottom of any identification, but this indexical connection may be many signs away and overtaken in trust from some source (I need not have seen ex-president Trump myself in order to be able to identify him from the orange skin color, yellow hair, and other characteristics).  I first proposed a version of this interpretation in Stjernfelt 2014, Chapter 3.  This may throw further light upon Peirce’s disputed category of “immediate objects”. Propositions not only have an object, referred to by the subject of the proposition, but also an immediate object, which concerns the way in which that object is identified by the sign (see Stjernfelt 2014, 85 f., 97 ff.; Bellucci 2017, 288 f., 324 ff.). Many authors have misidentified the immediate object as some preliminary description of the object, but in that case, it would be a meaning or interpretant category, not an object category. In Peirce’s extended taxonomy of signs, he developed a trichotomy of signs based on their immediate objects. As discussed above, that trichotomy thus refers to what connects the proposition to its dynamic object. Here are three possibilities: vague, singular, and general signs—which may be formalized by the three different quantifiers “some”, “this”, and “all”. Taken in isolation, these quantifiers, indexical in nature, are Rhematic Indexical Legisigns. Like proper names, they serve to identify what objects are spoken about. The Dicent Indexical Legisigns involving the “street cry” and “Farragut”, in this trichotomy, would be singular signs, but this implies that we should also expect Dicent Indexical Legisigns that are vague and general when the quantifiers are used to address names rather than descriptions: “Some elements of group 7 are called Halogens”, and “All elements of group 7 are called Halogens”, respectively. In the Morning Star and Evening Star example, the identity claim

Notes

391

made identifies two names, each having its own Singular Immediate Object, as pertaining to one and the same Dynamic Object.  Thus, the development of this idea may address some of the deep structures of the ongoing research into multimodality as it appears, e. g., in Kress and van Leeuwen 2001 and Bateman et al. 2017.  On Oct. 12, 1904, he repeats the example when illustrating his ten-sign taxonomy of the 1903 Syllabus in a letter to Lady Welby: the seventh sign category comprises ‘Dicent Sinsigns (as a portrait with a legend)’ (CP 8.341).  Ms. 1147; cf. the larger quote below.  “Kaina Stoicheia”, 1901(?), EP II, 310; cf. below.  I originally realized the fertility of Peirce’s idea while working on a number of papers that ultimately came together in the book Natural Propositions (2014) about Peirce’s theory of propositions. Pages 62– 75 of that book reconstruct Peirce’s argument; pages 108 – 114 contain some initial proposals for further development of his basic idea.  The combination principle depends on two ordering sequences: in each trichotomy, the sign aspects are ordered 1– 2– 3 after Peirce’s three categories, and the trichotomies, in turn, are ordered based on the Sign-Object-Interpretant sequence in the sign definition (so that QualisignSinsign-Legisign is first, Icon-Index-Symbol is second, and Rheme-Dicisign-Argument is third). Based on these two sequences, a certain combination of sign aspects is possible if the number of the element from the first trichotomy ≥ the number of the element from the second ≥ the number of the element from the third. Adding new trichotomies, then, it is important in order to generalize this schema that they be sequentially ordered after some principle further extending the Sign-Object-Interpretant sequence. Peirce chose his extended division of Objects and Interpretants for that purpose (Immediate vs. Dynamic Object; Immediate, Dynamic, vs. Final Interpretant), so that trichotomies were defined after which of these they address in which way. We cannot go further into these issues here. The figure is quoted from EP II, 296.  Peirce famously continued that strategy by adding further trichotomies to the combinatory; cf. Queiroz and Stjernfelt 2019.  The name of “Deduction of the Dicisign” for Peirce’s argument is Bellucci’s; for more thorough discussions, see Stjernfelt 2014, Chapter 3, and 2015; and Bellucci 2017, Chapter 7.  I add a plural possibility in brackets: ‘Object(s)’, ‘Subject(s)’ for the simple reason that just like Frege, Peirce extended his doctrine of Predicates to relational Predicates taking more than one Subject, thus referring to more than one Object. In the following, I shall just say ‘Object’ and ‘Subject’, implicitly suggesting both possibilities.  Dicisigns combined from picture predicates and text subjects are so widespread that it is strange that this particular proposition type has often escaped notice: paintings with legends, newsreel with voiceover speech, photos with text, diagrams with explanations, in print, on TV, on homepages, etc. In Stjernfelt 2014, I analyze a number of examples of how such signs are, in actual social practice, taken as truth claims, with serious consequences for utterers if the relevant proposition turns out to be false. One of the reasons such signs have semiotically escaped notice may be that picture semiotics has often referred to examples which may actively derive their effect from rebelling against simple co-localization syntax: ads and modern art. Since the mid-nineteenth century, much modern art has, as a deliberate esthetic strategy, dispensed with referential titles and instead has made the relation artwork-title to one of experiment. Dispensing totally with any title (‘Ohne Titel’) may be a strategy for urging the observer to supply some reference him/herself; developing strange, not immediately understandable titles may serve as deliberate artistic alienation (surrealism was a strong influence in such ti-

392

Notes

tles)—also motivated by the fact that modern art downplays the interest in truthful representation with a preference for other aims like experiment, shock, subjective experience, etc. A semiotic focus upon the special, sophisticated strategies of modern art may thus serve to occlude the basic role of picture-text propositions in much ordinary human communication. It would be a bit like making general linguistics on the basis of experimental poetry only.  Cf. Hookway 2002.  “It may be asked what is the nature of the sign which joins ‘Socrates’ to ‘_is wise’ so as to make the proposition ‘Socrates is wise.’ I reply that it is an index. But, it may be objected, an index has for its object a thing hic et nunc, while a sign is not such a thing. This is true, if under ‘thing’ we include singular events, which are the only things that are strictly hic et nunc. But it is not the two signs ‘Socrates’ and ‘wise’ that are connected, but the replicas of them used in the sentence … No other kind of sign would answer this purpose; no general verb ‘is’ can express it” (“Kaina Stoicheia”, 1901(?), EP II, 310).  Peirce’s many writings on the EGs are scattered over the CP, NEM, and the two EP volumes; a comprehensive publication of all of Peirce’s writings on the issue is appearing in the LoF (2020 – 2022).  The proposition in this case is no assertion, but rather an imperative. In Peirce’s germ-like speech act theory, he realizes that one and the same proposition may be put to use in different speech acts, assertion, assent, interrogative, imperative, etc.; cf. Stjernfelt 2014, 102. Here, my use of ‘proposition’ also covers such speech acts, even if most of my examples are assertions. Bellucci 2017, 315 ff., argues that the further generalization of the Term-Proposition-Argument triad to Seme-Pheme-Delome in 1906 is intended to cover this so that Phemes comprise Dicisigns which are assertive, imperative, etc.  An immediate issue of course: what is “direct” taken to mean here? As often in Peircean semiotics, the distinction between labels and standard propositions referring to their object at a distance is not discreet but rather involves a continuum. Labels may simply be expressed by significant features of the very object itself (such as shapes or forms by which conspecifics recognize each other); they may be imposed directly onto the surface of their object (tatoos, print), they may be temporarily put there (clothings, packaging, etc.), they may shade into standard propositions (gesture, smell, sound expressions, signs in some degree of vicinity of their object). The legend of a painting, e. g., may be directly glued or nailed to the picture object, located on the frame, or it may be at shorter and larger distances from it, in the latter case typically supported by subject indices (arrows, directions, etc.).  “Label” in an archaeological sense of the term which differs from (if overlapping with) the technical notion of the same name developed in the previous section. The British Museum, “King Den’s sandal label,” in Smarthistory, August 2, 2016, accessed April 16, 2022, https://smarthistory.org/king-den-sandal-label/.  Cf. Kammerzell and Peust 2002. The illustration stems from Kammerzell’s presentation at the Humboldt University 2017 conference “Pictures and Texts—Pictures as Text: Iconicity and Indexicality in Graphic Communication” organized by the linguists Gisela Fehrmann and Silvia Kutscher, and the egyptologist Aleksandra Lapčić. The debates at this amazing interdisciplinary conference were a central inspiration for the present chapter. Kammerzell and I discussed multimodality and co-localization at the conference, and he was so kind as to permit me to reproduce this slide from his talk, titled ‘The Polycentric Origin of the Egyptian Script’. I thank him for both.  Reading directions in Ancient Egyptian is subject to variability, even within the same picture or text sequence. Right to left is most common, but local reading direction is most often indicat-

Notes

393

ed by which way the hieroglyphs face—animal hieroglyphs typically facing towards (against) the reading direction; here, they face right, so reading direction is towards left (Kammerzell, personal communication).  In medieval art, both in Europe and Mesoamerica, graphic techniques were developed to indicate speech uttered by depicted persons, such as lines from the speaking mouths to the relevant written expressions, the addition to the picture surface of scrolls, ribbons, flags, banderols, and paper sheets, etc., with texts displayed. Modern speech balloons seem to have appeared in eighteenth-century Western political cartooning of the Enlightenment. In the ensuing comparison of the Den label with Disney comics, it is important to emphasize that the propositions represented by the two differ in the sense that the reference of the former is real, Egyptian history, while the reference of the latter is the fictitious world of Duckburg. So, the propositions refer to different types of Universes of Discourse, and in the fictive case, they may be classified by Ingarden’s notion of quasi-propositions, their truth-value being restricted to the closed world of Duckburg.  Thus, they properly belong to the special type of propositions which Peirce called ‘Dicent Indexical Legisigns’. They are not symbols, but they are general signs because of the generality of the name use claimed by them. Such signs, see Chapter 4.  These propositions are labels: they function by the proximity of the names a, b, c, and so on to the objects they refer to. And they are simultaneously Dicent Indexical Legisigns (cf. Chapter 4), for they do not describe those objects but rather name them so as to be easily referred to in the accompanying text.  It is well known that when he began his development of the “Existential Graphs” around 1896, Peirce picked the very simple convention that placing two propositions side by side would express their conjunction—one of the two defining conventions, along with the enclosure for negation (or the double enclosure for implication), for the Alpha version of the EGs formalizing propositional logic. And, of course, those two conventions were inherited by predicate logic of the Beta Graphs and the different sketches to further extensions of the Gamma Graphs. A bit earlier, he had attempted the converse convention in the aborted first version called “Entitative Graphs” where the simple juxtaposition of two propositions should be interpreted as their disjunction. As it is well known that disjunction and conjunction are definable in terms of each other, it might seem a trivial discussion which one to prefer. Not so for Peirce who argued that it was more natural and iconic for “AB” to mean “A and B”, rather than “A or B”. This naturalness of the “invisible” notation of simple juxtaposition to mean conjunction seems to have two rather different roots: algebra and sign use in the wild. The development from “Entitative” to “Existential” Graphs is charted by the Peirce papers published in LoF, Volume I, 2020, particularly with the founding paper “On Logical Graphs” (R 482, LoF I, 211– 261) from 1896 and the immediately ensuing mss. Peirce’s first s logic notation—the first root to the notation still used today—explicitly had the name of an “Algebra of Logic”, and that, of course, is a sign of the Boolean roots of that notation. George Boole had taken over the use of algebraic notations for simple arithemetic operations and redefined them in his algebra of logic. Stemming from here is the proto-computer idea of admitting two values of variables of the algebra only,  and , meaning false and true. Thus, Boole was able to write equations like x(-x) =  which expresses the Law of Contradiction. Here, x is any proposition, -x is it negation, so the product of the two being zero means that both of them cannot take the value  at the same time: they cannot both be true. Here, Boole employs the established notation for multiplication by simple apposition: ab (otherwise often expressed as a+b, a×b, or a+b). It is interesting that in the long and byzantine de-

394

Notes

velopment of mathematical notation, there seems to have been one occasion only when ab was considered as a sign for a+b, while interpreting ab as a sign for multiplication of a and b was in use at Leibniz’ time and propagated by him: “Multiplication we are commonly content to indicate by simple apposition: thus, ab signifies a multiplied by b” (Leibniz’ “Miscellanea Berolinensia” (), here quoted from a translation in Cajori , ). Leibniz was against the x sign for multiplication and rather used a comma or a dot as alternatives to simple apposition) This usage was widely accepted at Boole’s time. So, Boole, in his logical algebra, took multiplication to signify logical conjunction and addition to signify logical disjunction. Peirce inherited this idea, generalizing it when, inspired by his pupil O.H. Mitchell, introduced quantifiers in his second “Algebra of Logic” paper. Here, existential quantification is analyzed as a sum and universal quantification as a product of truth values (again,  for false and  for true), so that Πx meant “For all x”, and Σx meant “There exists an x”. Π and Σ were chosen as abbreviations of “Product” and “Sum”, respectively, the idea being that universal quantification refers to the situation where the ensuing proposition was true for all x’s (so that the product of truth values for all x’s ⋅⋅⋅ … = >), while existential quantification refers to the fact that the proposition is true for at least one variable (so that the sum of truth values for all x’s +++++ … >). For that reason, Peirce also wrote the assertion of full quantified propositions like this: “Πx bx >” and “Σx bx >”, all x’s are blue; there exists a blue x, respectively. It was Mitchell’s and Peirce’s idea to separate quantified propositions in two parts, the indexical quantification, so-called “Hopkinsian” part and the iconical predication, so-called “Boolean” part. Interestingly, these two parts, again, are simply coupled by juxtaposition, in a certain sense repeating multiplicative conjunction on the higher level of predicate logic: “It is true both that there exists an x and that that x is blue”. So, in his first logic notation, Peirce not only inherits Boole’s convention that simple juxtaposition equals conjunction, he further elaborates it in his quantification notation. If we pass from propositional to predicate logic, a further reason appears. We noted that Peirce’s algebra for quantified propositions coupled the two Subject and Predicate parts by means of juxtaposition. Here, juxtaposition entails that the variables in the Subject part refer to the same objects as the same variables in the Predicate part. Here, the co-localization of the two simpler signs grants that, taken together, the two fuse to form a proposition. In a certain sense, this convention is a weakened form of conjunction. It unites the two vague, unsaturated propositions “There exists something …” and “… something is blue” into one, saturated proposition. Thus, it would be strange that co-localization at this level meant claiming the simultaneous truth of both of the vague sub-propositions while the same device on the propositional level should mean the disjunction between whole propositions. In the algebra of logic, of course, the notation is read linearly, in sequence from left to right; in the existential graphs, there is no preferred reading direction. This puts stronger conditions on which meanings can be referred to by the “invisible” convention, for now the relation must be symmetric which is not the case in an oriented notation. In the linear notation, ab might be used to mean a=>b (even if it would seem strange), because the sequence is given, but in the EGs ab is immediately identical to ba so it could not represent any asymmetrical logical function. It could mean “and”, “or”, “iff”, but not “if…then”. That is one reason, stemming from the mathematical-logical tradition, for taking the same “invisible” convention as basic in the Existential Graphs. Another, I would argue, can be found in the widespread use of co-localization as conjunction in the wild; cf. the arguments in Chapters  – . The book cover uniting a number of proposition signs in logical conjunction (cf. above) appears as a wild form of Peirce’s formalized “Sheet of Assertion” or “Phemic Sheet” with the particular addition that this sheet is, as a label, directly attached to the object to which it refers.

Notes

395

You can also find—rarer—cases where Sheets of Assertion in the Wild conforms to the conventions of Peirce’s Entitative Graphs where co-localized propositions appear as alternatives, that is, in disjunction. This, in particular, may be found in lists of alternative choices, like, e. g., lists of different gambler’s options with odds. Typically, however, this mode of representing disjunction most often require additional information, such as, e. g., the context of choice, the ordering of the alternatives in a menu list of options, etc. So, the standard in Sheets in the wild seems to be co-localization as conjunction. Thus, Peirce’s final choice of Existential conjunction over Entitative disjunction may be motivated both by mathematical-logical history and by Sheets in the wild.  The Figure shows the first edition of the book with UK adult cover, 1997. The book cover forms a label in the sense discussed here. When presented in isolation from the book—as in our illustration or in a book advertisement—it is, of course, no longer a label, but typically additional subject indices will express its relation to the book text behind it. In very simple labels— cf. about biosemiotics below—there will be no need for a topological propositional field, because the sign label is part of or immediately connected to the Object. As soon as the Object is not present, however, some Subject index must be added to indicate the whereabouts of the Object, and this addition of an explicit Subject sign necessitates a propositional field in which to unite the Subject and Predicate signs. Once constructed, however, a propositional field may be used also in labels, as the book cover example shows.  The picture shows the tombstone of the Peirces in Milford Cemetery, PA. The grave was made only after Juliette’s death in 1934, including Peirce’s urn which she had kept until then. Juliette’s birth year was never known. The tombstone has recently been supplemented by a more elaborated memorial monument.  Which was, of course, what permitted Champollion’s decoding of the hieroglyphs on the Rosetta Stone. More about cartouches in Stjernfelt 2015a.  Cf., for instance, Talmy 2000.  See Hoffmeyer 2008, the short introduction to Stjernfelt 2002; see also Hoffmeyer and Stjernfelt 2016.  Isolated icons would display similarities to a vast range of possible objects but not predicating anything about them in lack of an indexical connection to some of them; isolated indices may be able to point out objects but not to say anything about them for lack of descriptive, iconic predication. Uniting icons and indices in descriptions of denoted objects is the function of propositions—that is, in the Peircean meaning of those concepts. Of course, scholars are free to propose competing definitions of “icon” and “index” etc., but in that case, they should do so explicitly in contrast to existing, Peircean definitions. Primitive biological propositions would probably most often be holophrastic, cf Brøndal’s idea that the simplest sentences are unartculated interjections (Brøndal 1928). They implicitly contain, however, the essential referential and semantic functions.  See the relevant chapters of Stjernfelt 2007 and 2014. Peirce took “anthropocentrism” to be inevitable in human understanding and aggressively redescribed it as a positive concept; cf. Chapters 18 – 19 below.  A bit more can be found in Stjernfelt 2014, Chapters 5 – 6 and the references there given.  See the discussion in Stjernfelt 2007, Chapter 9; see also Ben-Jacob et al. 2004.  Cf. El-Hani, Queiroz, Stjernfelt 2010, building upon Lloyd 1965, 1975, 1980, 1981, 1986.  On deception, cf. Mitchell and Thompson 1986  This time window in human semiotics seems to be equivalent to the time window permitting rhythm perception: if more than five or ten seconds endures between each beat, it becomes im-

396

Notes

possible to synthesize the sequence of beats into one coherent melodic-rhythmic unity and the beats separate into isolated events, just like very swift beats with less than some fraction of a second between beats also lose musical coherence and rather will be perceived as a sort of quivering or buzzing than an articulated rhythm.  Neurobiological evidence seems to point to a hardwired organization of proposition-processing parts of the brains of many higher animals in order for them automatically to parse perceptual content into Subject (where is something happening right now?) and Predicate (what is the general character of that happening?), see the summary and argument in Stjernfelt 2014, Chapter 5.  See Stjernfelt 2007, Chapter 2.  Cf. Smith 1999.  “What we call a ‘fact’ is something having the structure of a proposition, but supposed to be an element of the very universe itself. The purpose of every sign is to express ‘fact,’ and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the perfect Truth …” (“Kaina Stoicheia”, 1901(?), EP II, 304).  “… an act of assertion supposes that, a proposition being formulated, a person performs an act which renders him liable to the penalties of the social law (or, at any rate, those of the moral law) in case it should not be true, unless he has a definite and sufficient excuse …” (Syllabus, 1903, EP II, 278; CP 2.315), see Chapter 3.  In Stjernfelt 2014, Chapter 7, I analyse some recent Danish cases. The backbone of the infamous ‘Cartoon Crisis’ of 2006 was that the Danish newspaper Jyllands-Posten actually claimed, in an accompanying text, that a bundle of drawings depicted Islam’s claimed founder Muhammad, effectively asserting a set of multimodal propositions. The sacking of a Danish TV news journalist (Nybro, 2007) had the background that there was a mismatch between footage and voiceover speech as a joint proposition in a report on the Iraq war that he broadcasted. And the case against a Danish neuroscientist (Penkowa, 2011) from the University of Copenhagen had the background that she had (among other things) falsely combined immune-histological images with text to make scientific claims which were not true. In all these cases, multimodal, co-localized propositions were judged by different observers to be false, with severe consequences for the originators of those propositions.  Peirce “Logical Tracts. No. 2. On Existential Graphs, Euler’s Diagrams, and Logical Algebra”, 1903, CP 4.430. A complete collection of Peirce’s writings on Existential Graphs is the LoF (2020 – 2022).  Cf. Chapter 9. It is a deep issue, why simple co-localization should be the most iconic representation of logical conjunction. Peirce famously toyed with the dual system of “Entitative Graphs” in the mid-1890s, in which juxtaposition of propositions was taken to mean disjunction rather than conjunction. Francesco Bellucci, commenting this chapter, argues the reason for preferring conjunction may be that asserting two isolated propositions is equal to asserting their conjunction (⊢(p∧q) = (⊢p ∧ ⊢q)), while asserting each of two disjunct propositions is not equal to asserting their disjunction (⊢(p∨q) ≠ (⊢p ∨ ⊢q)). Another issue is why a proposition on a sheet in the wild is immediately interpreted as an assertion, rather than as an imperative, an optative, an interrogative, an assent, or any other elementary speech act. Sheets of such other speech acts would, of course, be possible (and Peirce took some steps in that direction in his Gamma graphs), but assertion seems to retain a privileged position among speech acts in the wild, maybe because of the simple fact that the realization of any speech act entails the truth of that speech act being realized, but not vice versa. If you give an order, it is true that you give an order—if you express a truth, however, it is not necessarily imperative, wishful, questionable, assented to, etc. that you do so.

Notes

397

 Cf. Peirce, R 1147, c. 1900 (the largest of several drafts of the article ‘Exact Logic’ for the Baldwin Dictionary), 12; cf. also Chapter 4.  To the development of Peirce’s general theory of propositions, see Stjernfelt 2014 and 2015a; Bellucci 2017  I recently had the occasion to analyze a number of such woodcut-with-text prints in Horstbøll, Langen, and Stjernfelt 2020; cf. the English version Langen and Stjernfelt 2022.  In Peirce’s Beta graphs, identity lines may branch so as to represent multivalent Predicates with more than one Subject slot—in principle as many as you may wish, even if Predicates with valency > 3 arguably may be decomposed into combinations of elementary predicates of valency 3 or less (the “Reduction Thesis”). Such branching identity lines appear to be rare in Sheets in the Wild, even if their appearance cannot be precluded.  These propositions may be regarded as definitions and thus being “Dicent Indexical Legisigns”; cf. Chapter 4.  It may even be argued that such maps, due to their continuous representation, involve an infinity of potential propositions, e. g., pertaining to the distances between any two points in the landscape.  On the political implications of this book, see Israel 2001.  The discovery of Israel de Paul as the printer of the Tractatus was only made in 2013 by the two book history Ph.D. students Trude Dijkstra and Rindert Jagersma; see their (2014).  On this definition of “label” propositions, see Chapter 5  What is said here, pertains to the movie poster as a type. The single tokens of that type may add further important signification: posted outside a cinema, the poster token will, as a Dicent Indexical Sinsign, make the propositional claim that the movie advertised can actually be watched in that very movie house on which it sits as a label.  On aspects of the cultural evolution of cartouches and frames, see Stjernfelt 2015; on comic frames, see Østergaard and Stjernfelt 2013.  Negation may sometimes be indicated by the crossing out or the dismemberment of a content; part-whole by vertical subordination, disjunction by a list of choice possibilities (like a menu of options), implication by a temporal or spatial sequence of propositions (cf. the preceding chapter; see also Champagne and Pietarinen 2020)—corresponding to the fact that proofs, in the Existential Graphs, are conducted by a sequence of sheets, displaying the steps of the proof as so many sheet snapshots. This list is open to further input of empirical evidence from the wild, both as to further representation devices of such elementary semantic functions, and as to further functions to find representation. Please do not hesitate to contact the author with good examples.  On the important sign type of diagrams, much used in scientific propositions as in everyday reasoning, see Stjernfelt 2007 and the next section below. The development of a semiotics of propositions charting their occurrence in the wild forms an important addition to current research in multimodality of representations, such as Kress and van Leuwen 2001, and Bateman et al. 2017.  On the problems of policies against fake news on the internet, see Lauritzen and Stjernfelt 2020. The analysis of propositions claimed by political “dark ads” on the net and what to do about them constitutes a most pressing issue for current semiotics and politics.  Mitchell, What Do Pictures Want?, 2005.  Bredekamp, Theorie des Bildakts, 2010.  “… daß von Bildern zu sprechen ist, sowie Naturdinge ein Minimum an Spuren menschlicher Bearbeitung aufweisen” (Bredekamp 2010, 35).

398

Notes

 Jonathan Israel, in his impressive pentalogy on the Enlightenment, places the insistence on the spontaneous activity of matter at the core of “radical Enlightenment” as opposed to “moderate Enlightenment”, to which matter is inert and its movement the effect of divine intervention. The hylozoism central to radical proponents of the Enlightenment like Spinoza or Diderot thus has a strongly anti-theological impetus, taking all activity to be immanent to this world. See Israel 2001, 2006, 2011, and 2019.  Peirce’s diagram doctrine is discussed at length in Stjernfelt 2007. See also Queiroz and Stjernfelt 2011.  Kitcher and Varzi 2000.  Stjernfelt 2014 ch. 10.  The same obviously holds true for algebraic diagrams, for instance equations. Fermat’s theorem, which took more than 300 years of intensive scrutiny to be proven, evidently kept this implicit information quite hidden. It is well known that subject-like qualities have often been attributed to written texts as well—one need only think of the relation of believers to sacred texts or holy books. Nevertheless, pictures often seem more strikingly subject-like than texts. One reason may be the immediately continuous quality of (most) pictures, which allows them to display their implicit information in a more striking way than is the case for algebras or texts.  Such as I argued in a 2000 paper and later in Stjernfelt 2007.  A possible way might be to insist that images are those icons which particularly realizes the fact that “Icons are so completely substituted for their objects as hardly to be distinguished from them” (“On the Algebra of Logic”, 1885, W5, 163, 3.362), so that in images, icon and object almost merge, in diagrams the two are distinct, and in metaphors, they connect via an intermediary. That would remain approximate only; Peirce does not go in this direction, and it also does not seem to grasp the essence of diagram signs.  Bellucci 2017, 211; 285  This is due to an important reformulation of what it means for a sign to be iconic, namely the following: “For a great distinguishing property of the icon is that by the direct observation of it other truths concerning its object can be discovered than those which suffice to determine its construction” (“That Categorical and Hypothetical Propositions are one in essence, with some connected matters” c. 1895, SWS, 63; CP 2.279)—which I have called the “non-trivial icon definition”.  After Peirce’s Johns Hopkins student O. H. Mitchell who was the first to propose the sorting of quantifiers and predicate expressions into two separate parts of the linear formalism.  Oftentimes, the erroneous idea is met that Peircean symbols should be defined by being conventional signs. That is not the case. Peirce explicitly, many times, says that symbols may be conventional or natural—the superordinate concept of the two being “habit”. Bellucci has insistently pointed to the fact that symbols are defined by being general signs—in the double sense that they are signs general in themselves (Legisigns) which, moreover, have a general meaning and refer to general objects (e. g., Bellucci 2017, 65 ff.).  You may indeed wonder how those two, initial and final symbolic interpretants relate to their diagrammatic bases. Peirce was happy to cite, working on “How to Reason” in 1893, the quote “Omne symbolum de symbolo” (“Symbols”, 2.302), all symbols come from symbols, which seems not to cover the two cases mentioned where two diagrams have a symbolic interpretant, so that symbols in these cases come from diagrams. In his mature period, after the development of the EGs, it seems to have dawned on Peirce that diagrams may, themselves appear in propositions making general claims, so emphasis shifts toward propositions; cf. “… no sign of a thing or kind of thing—the ideas of signs to which concepts belong—can arise except in a proposition; and no logical operation upon a proposition can result in anything but a proposition; so

Notes

399

that non-propositional signs can only exist as constituents of propositions” (“An Improvement on the Gamma graphs” 1906, 4.583). In order to function as propositions, of course, diagrams are unsaturated predicates which need to be saturated by the addition of subjects in the shape of indexical signs pointing out which object they refer to, thus constituting a symbolic proposition.  R 914 is undated in the Robin catalogue, but as it speaks of a combinatory of six sign trichotomies, it must be from around 1904– 1906 when Peirce went from three to six trichotomies, only to expand to ten in 1908.  The “phenakistoscope” was a 19C technology to animate a simple sequence of pictures of a movement by means of displaying them on a turning wheel seen through a slit.  Cf. Champagne and Pietarinen 2020.  Another example is the fact that the 2D representation of propositional logic in Peirce’s Alpha graphs may be linearized to a series of 1D graphs.  The choice of terminology here is inspired by Peirce’s use of “degeneracy” to refer to relations between categories; he took the terminology, again, from the geometry of conic sections (“On the Algebra of Logic”, 1885, EP I, 225; CP 3.359; “A Guess at the Riddle”. 1887– 1888, EP I, 253; CP 1.365),  As mentioned, Peirce does not use the concept of “co-localization” but I find it apt to describe the elementary procedure he is considering; cf. above. When discussing the co-localization of linguistic units on the page, Peirce uses the standard English notion “collocation” (meaning the idiomatic connection of words): “It is impossible for a word to have much of the iconic element. Syntax alone, and the collocation of words and sentences, can build up this sort of sign” (Ms. 409, 1893, from the “How to Reason” Project 106). “Co-localization” seems to me to generalize that idea also to non-linguistic signs, including diagrams.  Cf. Stjernfelt 2011b, 2014, Chapter 10.  Cf. Pietarinen and Stjernfelt, in press.  Cf. Pietarinen and Stjernfelt 2015.  In his initial musings on how to construct logic graphs in 1896, Peirce toyed with representing predicates not by some version of their natural language names but by depicting them by “direct ideographs” in the formalism, that is, as icons (diagrams or direct samples of the predicate quality): “Each unanalyzed verb is to be represented by a special ideograph, direct (i. e., a picture or other directly suggestive icon) or indirect (as by an initial letter, which is a direct suggestive icon of the word); … “ (R 483, 1896, published as Text 9 in LoF, Volume I, 302). He did not, however, develop this idea further and stayed with using “indirect ideographs”: “A direct ideograph is one directly suggestive of the idea; an indirect one is an ideograph suggestive of the word that expresses that idea. Such, for example, is an initial letter” (R 483, 1896, published as Text 9 in LoF, Volume I, 295). That is, writing “Red” or “R”, instead of directly applying a patch of red color to the Sheet.  I have often discussed this issue with my friend Ahti Pietarinen (see Pietarinen and Stjernfelt 2015) who maintains that as second-order Existential Graphs may be used to express virtually any content whatsoever, there is no need to consider other diagrams. I claim this is wrong, for two reasons. One is that a semiotic theory should be able to study how people actually reason, in the sciences as well as in everyday life—and they do that, to a large extent, by using diagrams which do not depict logical relations but rather depict selected phenomena of the object field of interest. Another is that even if the use of, e. g., a topographical map might be translated somehow (even if I cannot, for the time being, imagine how) into a second-order EG representation, my guess would be that actually finding your way in an area will be helped more by a good topographical map or GPS rather than by an ever so versatile EG representation.

400

Notes

 In R 15, “On Quantity” (c. 1895, NEM IV, 275): “… a diagram, or visual image, whether composed of lines, like a geometrical figure, or an array of signs, like an algebraical formula, or of a mixed nature, like a graph …”  Like symbols typically involving icons and indices; arguments involving rhemes and dicisigns, etc.  For example: “The concept of iconicity was first proposed by Morris” (Nöth 1990, 123). Also, the idea of “degrees of iconicity”, so central to Peirce’s introduction of the notion, is routinely ascribed to Morris 1946. A similar urban legend seems to pertain to Peirce’s notion of “aniconicity”: “The concept of aniconicity was first introduced by T. A. Sebeok (1979) as the “complementary obverse” of iconicity” (Sonesson 1999). In both cases, we may add, the very ideas or “concepts” referred to may have been discussed long before Peirce, Kratylos coming to mind as an early example. It was Peirce, however, not Morris or Sebeok, who introduced the notions of “iconicity” and “aniconicity” to address those concepts.  This chapter was originally given as a paper at the “9th International Symposium on Iconicity in Language and Literature”, held in Tokyo, 2013.  See also LoF III, 327.  In R 229 (NEM II, 595), from around 1897 (personal comm. André de Tienne), a small text on the “logic of number”, Peirce discusses his definition of mathematics as the science that studies hypotheses. Here, he addresses the idea of the contemporaneous Scottish mathematician George Chrystal that mathematics is defined by the “definiteness” of mathematical conceptions and their “finite number of specifications”. Peirce remarks upon the low degree of definiteness of topology, likening it to other, non-mathematical conceptions which may also display degrees of definiteness. This leads him to the remark: “I incline to suspect that Prof. Chrystal has confounded definiteness with iconicity, or the palpability of being represented in a diagram”. In Peirce’s philosophy of mathematics, diagram tokens form the access to diagram types, incarnating selected mathematical properties. Thus, the iconicity of diagrams is what makes possible knowledge about mathematical objects. Thus, the use of “iconicity” here addresses mathematical representation devices, just like the CP use addresses logical representation systems.  E. g. “iconize”: Syllabus 1903 (EP II, 277; CP 2.312); “iconical” already in the 1885 “On the Algebra of Logic” (CP 3.393); “iconic” seems largely if not completely to take over to become the preferred adjective form from the mid-1890s (e. g. the 1897 “Logic of Relatives”, CP 3.523) with ensuing multiple occurrences in the 1900s. “Iconically” appears as the adverbial form of both “iconical” and “iconic”. As to the “icon” notion itself, in Peirce’s early period of the 1860s, icons were called “copies” or most often “likenesses” (e. g. in the 1867 “New List of Categories”), but “icon” definitely takes over from the 1880s.  Stjernfelt 2007, 123 f.  Cf. Bellucci 2013.  Actually, two dual systems, “Entitative Graphs” and “Existential Graphs”, respectively. Now documented in detail in the three vols. of the LoF (2020 – 2022).  Cf. the LoF project.  Much interesting scholarship has emerged investigating Existential Graphs in recent decades—see references to Roberts, Zeman, Shin, Pietarinen, Dau, etc., and Queiroz and Stjernfelt 2011. Most recently, Ahti Pietarinen has published Peirce’s extensive writings on Existential Graphs in the LoF project (Peirce 2020 – 2022).  Peirce was the first to realize that all logical connectives could be defined in terms of one sign only, that for “neither-nor” (later called “Sheffer’s Stroke” after the logician who rediscovered it in 1913)—for perspicuity, however, he preferred the EG Alpha version with two connec-

Notes

401

tives—maybe because it does not seem easy to come up with a simple iconic sign for “neithernor”; Peirce used what has sometimes been called “Peirce’s Arrow”, a vertical arrow pointing down.  The system may also be expressed with the double cut signifying implication, in which case negation ceases to be primitive and becomes a derived notion. A heated discussion has recently been raging as to which of these two versions is original, final, preferable, etc. We shall not here go into this.  Chronologically, however, Beta Graphs for Predicate Logic were developed by Peirce first, while Alpha Graphs followed as a simplification pertaining to Propositional Logic.  You may add a further feature of iconicity not implied directly by the Alpha and Beta conventions, which is the stepwise structure of logical proofs as an iconic sign of the dialogic structure of logic (see Pietarinen (2006) and further references). Thus, Peirce takes this stepwise structure as referring to the alternate efforts by an utterer and his opponent—in Peirce, a Graphist and a Grapheus—taking turns in making changes on the Existential Graph, one trying to prove, the other to disprove it. Connected to this idea is his reinterpretation of Existential and Universal Quantifiers as the right to select an instantiation by the defender or the attacker of a proposition.  As mentioned above, there is an earlier (1897) occurrence of the term, but the 1905 occurrence is the first one supported by a thorough discussion of iconicity and degrees of iconicity of different representation devices.  He might have, at first, have imagined that the EGs would also constitute also a quick and easy calculus for practical purposes, but he soon gave up that idea; cf. the early papers in LoF I.  See, e. g., “PAP”, in NEM IV, 316 ff, see also Stjernfelt 2007, Chapter 4.  Even in this case, however, it could be argued that something is added—namely the points of departure and destination and the line routes explored between them. In this sense, the distinction we are making is rather one of a continuum between less and more manipulation/addition.  E. g. Minute Logic, 1902, CP 4.233; see also Stjernfelt 2014, Chapter 10.  An attempt at this can be found in Stjernfelt 2014, Chapter 10.3.  An equation is a diagram because the spatial arrangement determines what manipulation can be done.  The experiment was conducted with Kristian Tylén and Riccardo Fusaroli; cf. also Tylén et al. 2014.  These provisional data were collected at a public performance at the “Science in the City” festival at the ESOF conference, Copenhagen, June 2014.  Cf. Stjernfelt 2014, Chapter 5.  After Lessing’s 1766 Laokoön; to this principle in comics, see Østergaard and Stjernfelt 2013.  Among important contributions on Peirce’s realism could be mentioned Boler 1963, Fisch 1967, Roberts 1970, Murphey 1993, Misak 2004, Short 2005, Pietarinen 2006, Lane 2018. As to Peirce’s philosophy of propositions, see in particular Bellucci 2014, 2017; Stjernfelt 2012, 2014, 2015a.  Mulligan et al. 1984.  At the same time, he offered his analysis of the transcendental method: “The method was the invention of Kant, and in his hands it consists in showing, by some ingenious argument— different in every case—that the logical analysis of the process which the mind must go through shows that the proposition which is to be defended is involved in the a priori conditions of the possibility of practical everyday experience. If Kant had performed all the work which a thorough, scientific application of his method demanded, he would have to postpone the publica-

402

Notes

tion of his “Critic of the Pure Reason” for another century, at least, which would have been regrettable. It would be radically contrary to Kant’s principles to base logic (in the sense in which the word is used in the present book) upon the transcendental method. On the contrary, his whole critic of the understanding is deliberately based upon a scientific logic supposed to be already established” (Minute Logic, 1902; R 425; CP 2.31).  “Er erscheint noch heute so dü rftig, jener Inhalt der transscendentalen Methode: die Erfahrung ist gegeben; es sind die Bedingungen zu entdecken, auf denen ihre Mö glichkeit beruht” (Cohen 1877, 24).  “Alle Philosophie ist auf das Faktum der Wissenschaft angewiesen. Diese Anweisung auf das Faktum der Wissenschaft gilt uns als das Ewige in Kants System” (Cohen 1904, 65).  This, of course, is no news to historians of Peirce’s development: “It is not an exaggeration to say that the subject-predicate theory of the proposition is one of the fundamental premises of Peirce’s philosophy in the late 1860’s” (Murphey 1961, 152). In some important respects, Peirce was an American neo-Kantian, in some respects even anticipating his German counterparts of which he seems to have known nothing.  See Boler 1963; Stjernfelt 2007, Chapter 2.  This subject realism argument was inherited by Quine in his famous claim for ontological commitment: “A theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true” (Quine, 1948, 33; the article was reprinted in Quine, 1953, 1– 19). Quine thus takes over Peirce’s subject realism but not his predicate nor representation realism: to him, all that exists are individuals referred to by the index signs of bound variables. Smith 2005 takes Quine’s example to be the root of the poverty of current analytic philosophy metaphysics: taking his departure in a reading of surface features of the logical formalism of first order predicate logic, Quine arrives at a naked “fantology” (from “F(a)-ontology”). Smith’s paper implies an important question: which features of logic merit the derivation of metaphysical categories and which do not? Peirce was certainly a maximalist on this question, but I am not certain Peirce did ever articulate explicit criteria to determine the answer. An important further task would be to check if any such criterion could be implied in his many examples  It may be objected that subject indices do not refer to reality but merely to existence. This is indeed correct, but Peircean reality, as a whole, is made up of three modes of being, based on the three categories, of which the second pertains to existence while the two others, pertain to qualities and laws, or, in Peirce’s mature version, may-be’s and would-be’s, respectively. In the 1903 Syllabus, for instance, Peirce may articulate subject realism as follows: “This shows that a Dicisign must profess to refer or relate to something as having a real being independently of the representation of it as such, and further that this reference or relation must not be shown as rational, but must appear as a blind Secondness” (EP II, 276; CP 2.310). Here, we use the notion of realism in a broad sense to cover the status of all three modes of being.  Actually, Peirce seems to have begun using “states-of-things” as the real correlate of true propositions earlier than the Austro-German tradition for “Sachverhalte”, initiated by Lotze (1874) and further developed by Stumpf in the 1880s (cf. Smith, 1994; Milkov, 2002). Peirce used “state of things” as that which a true proposition represents already in the 1860s—e. g., in the 1868 “Questions Concerning Certain Faculties” and “Four Incapacities” papers (e. g., EP I, 24, CP 5.254; EP I, 37, CP 5.279). Initially, however, Peirce does not seem to have explicitly defined “state of things” as a technical term, but he should definitely be included in the early history of states-of-affairs realism and “truthmaker” realism.

Notes

403

 Peirce addresses this in a phenomenological rebuke of Kant’s more atomist-associationist theory of synthesis: “Kant gives the erroneous view that ideas are presented separated and then thought together by the mind. This is his doctrine that a mental synthesis precedes every analysis. What really happens is that something is presented which in itself has no parts, but which nevertheless is analyzed by the mind, that is to say, its having parts consists in this, that the mind afterward recognizes those parts in it” (“A Guess at the Riddle”, 1888, W 6, 449; CP 1.384).  A brief version of that argument is: “Looking upon the course of logic as a whole we see that it proceeds from the question to the answer—from the vague to the definite. And so likewise all the evolution we know of proceeds from the vague to the definite” (“Logic of Continuity”, 1897, CP 6.191).  Even if the “Epokhé” terminology appeared only later, Husserl, already in the LI had the idea of a pure phenomenology bracketing existence: “Es handelt sich dabei aber nicht um grammatische Erörterungen im speziellen, auf irgendeine historisch gegebene Sprache bezogenen Sinn, sondern um Erörterungen jener allgemeinsten Art, die zur weiteren Sphäre einer objektiven Theorie der Erkenntnis und, was damit innigst zusammenhängt, einer rein deskriptiven Phänomenologie der Denk- und Erkenntniserlebnisse gehören. Diese ganze Sphäre ist es, die zum Zweck einer erkenntniskritischen Vorbereitung und Klärung der reinen Logik durchforscht werden muß; in ihr werden sich daher unsere nächsten Untersuchungen bewegen” (from the introduction to Volume II of the Logical Investigations, Husserl 1984, 5). Already here, Husserl marshals the idea that the dependence of logic upon phenomenology implies that logical conceptions are abstracted from more concrete, phenomenological experiences: “Die logische Begriffe als geltende Denkeinheiten müssen ihren Ursprung in der Anschauung haben; sie müssen durch Abstraktion auf Grund gewisser Erlebnisse erwachsen und im Neuvollzuge dieser Abstraktion immer wider neu zu bewähren, in ihrer Identität mit sich selbst zu erfassen sein” (Husserl 1984, 10). As we shall see, abstraction in Peirce rather goes in the opposite direction, from logic to more general phenomenology. The comparison between Peirce’s and Husserl’s phenomenologies was initiated by Spiegelberg 1956, and his history of phenomenology (1969) includes Peirce’s version.  Each of the two physical and psychichal sides, now, fall in Nomological, Classificatory, and Descriptive branches, respectively, where all of the Special Sciences will be located. The classifications of 1902 evolve out of a long process with simpler schemes; cf. Ambrosio 2016, also Viola 2020, Chapter 2.  See Stjernfelt 2007, Chapter 6. Here, I shall use “phenomenology” and “phaneroscopy” interchangeably. “Phenomenology” became a standard notion in Peirce scholarship primarily due to Hartshorne and Weiss’s use of it in the publication of Peirce’s Collected Papers in the 1930s where they took the term as headline of the third section (out of four) of Volume I.  “I admit that one thing involved in this idea of the supreme certainty of one’s own personal existence is a thing that logic must admit, namely that what he seems to perceive he does perceive,—I mean that the propositions which, though entirely unlike percepts, he deliberately finds himself forced to admit, are truly representing elements of his percepts, are beyond criticism, since they are beyond control” (“Reason’s Conscience”, 1904, R 693, 152).  As when he says that biology could only take the step from description to classification after it was informed by the step-higher science of physiology; cf. Viola 2020, 57.  “Thus, intelligibility, or reason objectified, is what makes Thirdness genuine” (“A Guess at the Riddle”, 1888, EPI, 255; CP 1.366); “Indeterminacy, then, or pure firstness, and hæcceity, or pure secondness, are facts not calling for and not capable of explanation” (“A Guess at the Riddle”, 1888, EPI 275; CP 1.405).

404

Notes

 Peirce argues that Kant’s four general categories, Quantity, Quality, Relation, and Modality are universal because assumed present in all phenomena—while the tripartite subsections of each of them (Unity, Plurality, Totality; Reality, Negation, Limitation; Inherence, Causation, Reaction; Possibility, Necessity, Actuality, respectively) are particular because not present in all phenomena (EP II, 148). This gives him the idea of a similar partition of his own Categories.  It is the same, final version of the Syllabus in which Peirce constructs his a priori ten-sign taxonomy, subsequently striving to assign empirical, a posteriori sign types to the theoretically predicted categories, cf. also Chapter 4– 5.  The “Glucinum” of the quote is an earlier name of the element Beryllium.  Thus, Secondness, and, in turn, Firstness, are derived from Thirdness. This corresponds to the general analysis of the relation between the three in terms of genericity, already developed in the “On the Algebra of Logic” and “A Guess at the Riddle”. The idea is taken from the geometry of conic sections where generic such sections comprise ellipses and hyperbolas while less generic—degenerate—cases comprise parabolas, circles, intersecting lines and a point; cases where some of the variables are fixed or vanish. Analogously, Secondness and Firstness are but degenerate forms of Thirdness. In “The Basis of Pragmaticism in the Normative Sciences” not much later (early 1906), this idea is taken as a general principle in phaneroscopic analysis: “The same phenomenon presents itself in the realm of phaneroscopy to such an extent that the only successful way of analyzing any of the concepts which belong peculiarly to this realm is not to begin by considering that concept in all its breadth, but rather to confine oneself, at first, to its highly characterized form, and when that has been thoroughly comprehended, to inquire by what modifications the bordering forms attach themselves to it. But this rule must not be understood as conflicting with the plan of examining the highest and most general concept first. However, until special instances are before us, abstract descriptions can hardly be understood” (EP II, 390). The latter conclusion may also give us a hint why exemplification taken from “lower” sciences remains a steady practice in Peirce’s phaneroscopic investigations.  Bellucci 2015a gives a strong argument that the singling out of Phenomenology as the study of the categories is motivated in taking the most formal part of logic—the logic of relatives—as the phenomenological realization of mathematical structure.  This chapter reviews the book Bellucci, Francesco (2017): Peirce’s Speculative Grammar: Logic as Semiotics. New York and London: Routledge.  In Port Royal, the relevant notions were “extension” and “comprehension”; the reinterpretation “denotation-connotation” is due to John Stuart Mill; the “extension-intension” version to Gottfried Wilhelm Leibniz; the “breadth-depth” to William Hamilton; later Gottlob Frege would use “reference-sense” for a related distinction. Mill’s “denotation-connotation”, thus, should not be confused with the later use of the same notions to signify primary and secondary signifiés in structural linguistics and semiotics. See also Stjernfelt 2014, Chapter 9.  Peirce’s classes seem to have been virtually boiling with geniuses: Christine Ladd (later married Franklin), O. H. Mitchell, Allan Marquand, John Dewey, Thorstein Veblen, Joseph Jastrow, etc. Ladd-Franklin’s 1916 recollection calls them “a not unimportant handful”. See Pietarinen and Chevalier 2015.  Cf. Chapter 9 on the origin of the “iconicity” concept.  Covered in more detail in Bellucci 2013a.  This step is documented and analyzed by Pietarinen in LoF I.  The manuscript R 482 “On Logical Graphs” of 1896 seems to be the breakthrough paper of the new graphs systems. Here, the development from Entitative to Existential Graphs can be traced, and the paper seems to have been a sort of open quarry of ideas from which Peirce de-

Notes

405

veloped many EG papers of the ensuing years. The ms. seems to have existed in a finished version which Peirce unsuccessfully tried to persuade Paul Carus to publish and which later disappeared. See Text 5 of the LoF I and Pietarinen’s accompanying commentary.  I myself discuss the Deduction of the Dicisign in Stjernfelt 2014, Chapter 3.  Bellucci treats this under the headline of the “unity” of the proposition in his 2014.  After developing the Alpha version of EGs which formalize propositional logic, Peirce added new signs in order to capture predicate logic in Beta. Gamma became the headline of a whole bundle of unfinished further additions aming to cover temporal logic, speech act logic, second order logic, three-value-logic, abstractions, etc..  Here, I disagree with Bellucci on a fine point, namely the interpretation of the seventh of the ten Syllabus sign classes, the “Dicent Indexical Legisign”, see Chapter 4.  Queiroz and Stjernfelt (2019) collects a set of investigations on the “Extended Peirce” of Bellucci’s Phase Eight.  See also Bellucci 2015.  I make a similar argument in Stjernfelt 2014, Chapter 3.  Austin 1961, 87, n. 1; see also Stjernfelt 2014, 101.  Bellucci treats this issue also in his 2013b; see the next chapter.  “Etwas wird ein Anderes, aber das andere ist selbst ein Etwas, also wird es gleichfalls ein Anderes, und so fort bis ins Unendliche. Diese Unendlichkeit ist die schlechte oder negative Unendlichkeit, indem sie nichts ist, als die Negation des Endlichen, welches aber ebenso wieder entsteht, somit ebensosehr nicht aufgehoben ist—oder diese Unendlichkeit drückt nur das Sollen des Aufhebens des Endlichen aus. Der Progreß ins unendliche bleibt bei dem Aussprechen des Widerspruchs stehen, den das Endliche enthält, daß es sowohl Etwas ist als sein Anderes, und ist das perennierende Fortsetzen des Wechsels dieser einander herbeiführenden Bestimmungen” (Hegel , §§  – ).  The Syllabus was never published in its entirety, but various selections can be found scattered in the CP and more collected in EP II, Chapters 18 – 23.  In a letter to Lady Welby, Dec. 14, 1908, SS, 396 – 397.  Stjernfelt 2014, 88 – 89.  As argued by Pietarinen and Bellucci 2016.  Cf. Stjernfelt 2014, Chapter 11.  To these aspects of Peirce’s habit concept, see Chapter 2 as well as Pietarinen and Bellucci 2016.  In 1901, Peirce writes in a small article on the Nota Notae in Baldwin’s Dictionary of Philosophy and Psychology: “The logical principle Nota notae est nota rei ipsius, that is, the predicate of the predicate is the predicate of the subject, which is laid down in several places by Aristotle as the general principle of syllogism. The principal passages are as follows: ‘When one thing is predicated of another as its subject, whatever is said of the predicate can also be said of the subject’ (Categ., iii. 1 b 10). ‘Whatever is said of the predicate will hold also of the subject’ (Categ., v. 3 b 4)” (“Nota Notae”, 1901, 2.590). Othertimes, Peirce simply identifies the Nota Notae with the transitivity of the copula: A=B, B=C → A=C.  In his first logical publication, the 1762 Falsche Spitzfindigkeit.  One of Krois’ favorite Peirce quotation is the brief claim that “… the idea of manifestation is the idea of the sign”. A backbone of this short paper will be such preferred quotes in Krois. The context of this quote is as follows: “There is a recognition of triadic identity; but it is only brought about as a conclusion from two premisses, which is itself a triadic relation. If I see two men at once, I cannot by any such direct experience identify both of them with a man

406

Notes

I saw before. I can only identify them if I regard them, not as the very same, but as two different manifestations of the same man. But the idea of manifestation is the idea of a sign” (“Thirdness”, 1903, CP 1.346).  In Krois 2011, 94.  The more complete quote goes as follows: “When we come to study the great principle of continuity and see how all is fluid and every point directly partakes the being of every other, it will appear that individualism and falsity are one and the same. Meantime, we know that man is not whole as long as he is single, that he is essentially a possible member of society. Especially, one man’s experience is nothing, if it stands alone. If he sees what others cannot, we call it hallucination. It is not “my” experience, but “our” experience that has to be thought of; and this “us” has indefinite possibilities” (A footnote added to Peirce’s reworking of his 1878 pragmatism papers, 1893; CP 5.402, n. 1)—see also Chapter 19.  Which was probably one of the reasons why Krois tended to reject Peirce’s repeated definition of iconicity by similarity between a sign and its object. Krois pointed to a quote where Peirce says there is not similarity in representing a call for sobriety by means of the picture of a drunkard: “It may be questioned whether all icons are likenesses or not. For example, if a drunken man is exhibited in order to show, by contrast, the excellence of temperance, this is certainly an icon, but whether it is a likeness or not may be doubted” (2.282)—but immediately after that, Peirce adds that “The question seems somewhat trivial” (probably because the example mentioned can be analyzed as similarity plus the rhetorical device of inversion). Krois, sometimes, took the radical consequence of seeing instead iconicity as pertaining to the material qualities of the sign vehicle, taken in isolation, apart from any connection to the sign object. I do not find this interpretation helpful—in that case, all signs will be iconic per definition.  The analysis of the blushing of shame/ striping of zebra examples might focus upon the whole of which the appearing sign is a part: the totality of the psychophysical shame event has the blushing as an aspect, just like the whole of two zebras interacting has their striping as an aspect. In that analysis, the blushing and the striping may be seen, immediately, as an icon of the whole. Cf the discussion of “labels” in Chapter 5.  As to Cassirer’s inspiration from von Uexküll and his “Umwelt” notion, see Stjernfelt 2009.  Even if Krois at some points follows Terrence Deacon in taking icon-index-symbol to be projectable onto semiotic development so the three sign functions should appear, in the course of evolution, in that order, with symbols as a special human privilege.  “Such being the nature of reality in general, in what does the reality of the mind consist? We have seen that the content of consciousness, the entire phenomenal manifestation of mind, is a sign resulting from inference. Upon our principle, therefore, that the absolutely incognizable does not exist, so that the phenomenal manifestation of a substance is the substance, we must conclude that the mind is a sign developing according to the laws of inference” (“Some Consequences of Four Incapacities”, 1868, CP 5.313).  Even to the extent of claiming that Peirce “… broke with the belief that philosophy is based upon logic …” (Krois 2011, 101).  We do not, however, thereby solve the evolutionary issue of projectability of semiotic taxonomy on history.  A traversal of the Peirce Mss. gathered in the Collected Papers, for instance, shows a wide use of the notion of “embodiment”. The term here covers three things: the embodiment of general laws in particulars; the embodiment of thoughts in signs, and the embodiment of signs (e. g., symbols) in material replicas of those signs. In all cases, thus, Peirce’s embodiment notion refers to the fact that general notions of all kinds must (at least possibly, conceivably) incarnate

Notes

407

in particulars if not to be void. Peircean “embodiment” thus does not refer to the human body; indeed the wording “human body” is a hapax in the CP; the one time it appears is in a discussion of scholastic terminology.  Husserl 1975, 1984; English version Husserl 1970. Holenstein 1976 charted some of the surprisingly different intellectual influences of the Logical Investigations, cf. also Stjernfelt 2007, Chapter 7.  This section summarizes parts of Chapters 7– 8 and 11 of my dissertation Diagrammatology (2007) where I claimed, in Chapter 7, that Hjelmslev’s further dependence calculi “… necessitates further research surpassing the scope of this chapter”. In a sense, this old debt is what I hope to pay a part of in the present chapter.  Husserl 1984, 264– 265; cf. also Smith 1979 and 1994.  Cf. Smith’s “fallibilistic apriorism”, Smith 1996.  Husserl himself distinguished, top-down, three large fields of regional ontology, the physical, the biological, and the psychical, while some of his important students rather worked bottom-up in devising regional theories of “social acts”, particularly judicial utterances (Adolf Reinach) or pure intentional objects, particularly fictions (Ingarden). As to Husserl’s notion of the a priori; cf. Smith 1996.  Cf. Holenstein 1975. The degree and timing of the influence of the Logische Untersuchungen on Jakobson, however, is contested. Koerner 1997 argues that explicit references to Husserl is found in Jakobson only beginning in the late 1930s so that the influence may be one of affinities discovered by Jakobson post hoc after the development of his own brand of structuralism in the 1920s–1930s (Koerner 1997, 156).  The original Danish version Forelæsninger over Sprogteori of 1942 (a stenography of Hjelmslev’s lecture series of that title) is finally under publication by Una Canger and Lorenzo Cigana.  Cf. Stjernfelt 2021. As to criteria for relations between logical formalisms and ontology, Smith 2005. On Peircean logic representations, Pietarinen 2006.  Cf. CP 1.549. References to Collected Papers are given by CP plus volume and paragraph, references to Essential Peirce by EP plus volume and page.  Such abstractions in the sense of attention focusing signs differ from Peirce’s “hypostatic” abstraction creating a new, second order object out of a predicate; see Stjernfelt 2007, Chapters 11 and 18.  Cf. Chapters 1– 6; Bellucci 2017.  Cf. Stjernfelt 2014, Chapter 10.  There is no mention in Hjelmslev as to the roots of his triad of dependences which is merely “predicted” in the quasi-logical language of the Prolegomena. While the co-founder of the Copenhagen circle and opponent Viggo Brøndal may refer to Husserl, just like their common disciple Paul Diderichsen would do decades later, there is no mention of any phenomenological inspiration in the Prolegomena. Diderichsen several times remarks upon the similarity between the “three main types of grammatical connexion” in structural linguistics and Husserl’s mereological analyses from Logische Untersuchungen (Diderichsen 1966, 107 (1947); 137 (1948); 207 (1952)) but he gives no indication as to any relationship between Husserl and Hjelmslev, and the only early reference to Husserl in Hjelmslev is pejorative. Three possibilities (at least) seem to compete. One is, of course, that Hjelmslev came upon the idea of a dependence grammar independently; another is that the absence of references is due to the radical and autonomyclaiming linguistics he strives about to found. Unlike his companion Brøndal, much more Jakobsonian in spirit in his reference to the philosophical tradition and to a multiplicity of sources for his version of structuralism, Hjelmslev wants to free himself from any metaphysics, inspired as

408

Notes

he is by logical positivism, especially in Carnap’s version. Maybe he would see too much metaphysical heritage in references to phenomenology? A third possibility would be influence via an intermediate (so as for instance Anton Marty; both Jakobson and Brøndal seem unlikely in that role) or from a common source of inspiration (Brentano?).  Hjelmslev would call such relations “functions”; for the sake of comparison, we stick to the notion of “relations”.  This step in Hjelmslev may be compared to contemporary ideas such as in Cassirer whose system of primitive, mythological “Ausdrücke” only give rise to clear, truth-claiming propositions with the development of “Darstellung” to achieve scientific status in “Reine Bedeutung”. Also here, the “Ausdrücke” corresponding to a mythical worldview, will never be left behind in the development of civilization but remains as an indispensable prelogical basis for all further articulations; cf. Cassirer 1923 – 1929; Stjernfelt 2000.  (Resumé, 29). The three vertical dots notation indicates the units considered are in the system side of language built from correlations, vs. “R” indicating the process side built from relations.  Thus, this example is a version of Jakobson’s marked-unmarked distinction. Hjelmslev denied the overachinbg binarism stemming from generalizing such two-term systems and insisted on non-binary derivation of multi-term systems.  The resulting lists, however, differ considerably; cf. Cigana 349. Here the possible combinations members of categories of the Resumé, up to seven members: 1) Γ2; 2) α A; 3) α A Γ2, βB γ, β B Γ, 4) β B γ Γ, β B γ Γ2, β B Γ Γ2; 5) α A β B γ, α A β B Γ, β B γ Γ Γ2; 6) α A β B γ Γ, α A β B γ Γ2, α A β B Γ Γ2; 7) α A β B γ Γ Γ2.  Rg. 16 in the Resumé, rendered like this in Cigana 349: “(α ↔ A) ∣ (β ↔ B) ↔ (γ∣Γ)∣Γ2”, where “↔” is solidarity and “∣” the converse, autonomy, meaning that the Alphas must be present both, as must the Betas, while the Gammas may occur together or not. A level higher, the Betas and Gammas, as pairs, must appear together, while their relation to the Alphas is optional. The motivation for this crucial “Law of solidarity” is not easy to fathom.  A simpler, contradictory version with four possibilities β-Γ of two-content zone combinations needs not occupy us here (Resumé, 51):

Fig. 61: Contradiction version of the β-Γ bound articulation.  Cigana compares bound and free articulation, in a strong metaphor, with macroscopic Newtonian physics and microscopic quantum mechanics: the former holds sway in standard analysis but must yield when a microphysical level is reached in which quantum phenomena necessitate other descriptions. In the same sense, dependence descriptions of bound articulation is taken to be the standard procedure having to yield, however, to sublogical-participation description when necessary.  Cf. Stjernfelt 2007, Appendix.  Ingarden 1965; see also Smith 1979, 1980, Stjernfelt 2007, Chapter 17.  Ingarden 1965 – 1974.

Notes

409

 On this phenomenology-metaphysics issue, Ingarden resembles Peirce who also took phenomenology to generally study all what could possibly appear, while metaphysics was a narrower, dependent endeavor studying general aspects of this world; cf. Chapter 13.  Cf Johansson 2009, 2013, Millière 2016; the distinction fissuration/non-fissuration refers to whether an object’s existence is takes place in the flow of time or not, while fragility/persistence pertains to whether an object—like multi-cellular organisms—will perish.  Ingarden 1965 – 1974 I, 39; II, 1, 60. As in Peirce, ideas—or representations—are two-sided and possess an aboutness regarding some content.  Peter Simons has synthesized all of Ingarden’s distinctions and ontological subtypes in one impressive, drop-shaped diagram, “Ingarden’s Tear”, with 15 interdefined regions of possible being, summing up the products of all of the distinctions mentioned. The diagram is published as an appendix to Johansson 2009 (Fig. 61):

Fig. 62: Realms of Being after Ingarden.

410

Notes

 Ingarden 1965 – 1974, English version of Volume I, Time and Modes of Being.  Ingarden 1965 – 1974, 27– 30.  Any attempt at “epistemologizing” away ontological issues ends by facing the issue of the very nature of the devices of knowledge they claim lie behind what is naively conceived as real. Be it language as in Hjelmslev and much of structuralism, be it societal structures as in social constructivism, be it cultural norms in social anthropology, be it inherited brain structures in evolutionary psychology – the positing of such sources of knowledge invariably exalts a particular selection of reality to ontological prominence: language, society, culture, biology. Bottom line, such attempts are no less ontological than the assumedly naive realism they started out attacking; rather, they are reductionist ontologies because they presume that all of reality really depends on one of its subsets only: language, or society, or culture, or biology. Moreover, they are dependence theories themselves in their claim that knowledge depends upon language, society, culture, or biology exclusively. The upshot seems to be that no matter how many epistemological manoeuvres one might make, you still will not be able to escape ontological dependences.  Both consciousness, mind, and self are complicated issues which undergo developments through Peirce’s career, and we cannot here cover all details but aim to highlight the aspects most relevant to conscious self-control of reasoning.  Cf. Stjernfelt 2014, Chapter 1. On the European debate over psychologism in the period, see Kusch 1995.  In the late Essays on Reasoning (R 654, R 680), 1910, LoF1, Peirce furthermore distinguishes three kinds of awareness; sensations, perception of difference, and intentional attention (135; 139 – 144).  Cf. also: “The quale-consciousness is not confined to simple sensations. There is a peculiar quale to purple, though it be only a mixture of red and blue. There is a distinctive quale to every combination of sensations so far as it is really synthetized—a distinctive quale to every work of art—a distinctive quale to this moment as it is to me—a distinctive quale to every day and every week—a peculiar quale to my whole personal consciousness” (Logic of Events, 1897, CP 6.223). Peirce’s notion of feeling thus transgresses the reduction of feeling to pleasure and pain found, e. g., in Kant; instead, he refers back to the Danish-German philosopher J.N. Tetens and his definition of Feeling as “whatever is directly and immediately in consciousness at any instant” (“Forms of Consciousness”, 1896, CP 7.540; cf. Tetens’ Philosophische Versuche from 1777). Peirce’s idea of “quale”, of course, lies at the root of the present concept of “qualia” as referring to the qualitative aspects of conscious experience.  Cf. the description of the third kind of consciousness in the large metaphysical panorama of A Guess at the Riddle where psychology is the last and supposedly lowest of the descending series of special sciences to be illuminated by the three categories: “This is a kind of consciousness which cannot be immediate, because it covers a time, and that not merely because it continues through every instant of that time, but because it cannot be contracted into an instant. It differs from immediate consciousness, as a melody does from one prolonged note. Neither can the consciousness of the two sides of an instant, of a sudden occurrence, in its individual reality, possibly embrace the consciousness of a process. This is the consciousness that binds our life together. It is the consciousness of synthesis” (A Guess at the Riddle, 1887, EP I, 260; CP 1.381). Melodies in early gestalt theory, see e. g., Ehrenfels 1890, Stumpf 1883 – 1890; cf. also Smith 1994. Thus, Peirce distinguishes the cognitive, synthetic processing of a melody or a proof, taking place in synthetic consciousness, from the resulting, momentaneous, and simple feeling accompanying such syntheses.

Notes

411

 Cf. “A part of this instinctive science, as we may call it, is that events succeed one another in time, that the past, when not too remote, is remembered, that the future, when not too remote, can be with some probability conjectured or anticipated, and that a single moment between the past and the future, (that is, some facts belonging to that moment), is directly before the mind” (“Association of Ideas”, 1893, CP 7.422).  For more elaborate discussions of Peirce’s doctrines of consciousness, see Houser 1983 and Champagne 2018.  Peirce seems to have used the notions “unconscious” and “subconscious” interchangeably, the latter occurring, e. g., in the 1902 Minute Logic. Here, we use “unconscious”, closest to von Hartmann’s notion.  It may even be seen as dominating the material aspect of the world; cf. Peirce’s Schellingian idea of matter as just “effete mind”. Based on the idea around 1890 that matter follows mechanical causes while mind follows teleological causes, it may even extend to speculations as that the mental aspects of the external world may be guided by overarching purposes.  In the quote here, Peirce identifies consciousness with its “feeling” part only, as is sometimes the case. Peirce never quoted Freud, and his notion of unconscious does not involve anything resembling the Id, repressed drives, infantile sexuality, and so on, but rather insists that most of normal mental processes, including inference processing and habit-taking, takes place below the level of consciousness. Thus, Peirce dethroned consciousness in a move which is now and again triumphantly repeated by cognitive psychologists and neuroscientists in our day as if it was a complete novelty; cf., e. g., Suhler and Churchland 2010.  Again, this quote displays a recurrent tendency to use “consciousness” in a narrower sense, comprising only the first among three broader consciousness types, that of quality feelings in the moment.  “There are mental operations which are as completely beyond our control as the growth of our hair. To approve or disapprove of them would be idle. But when we institute an experiment to test a theory, or when we imagine an extra line to be inserted in a geometrical diagram in order to determine a question in geometry, these are voluntary acts which our logic, whether it be of the natural or the scientific sort, approves” (The Harvard Lectures on Pragmatism, 1903, CP 5.130).  “Of the Classification of the Sciences, Second Paper, Of the Practical Sciences”, 1902, R 1342, 46 – 48, including an attempt to derive such empirical instincts as a sort of surface phenomena from a set of deeper, more technically defined instincts.  Peirce interchangeably speaks of “the self”, “the ego”, “personality”, etc. to address the same central issue. For a more thorough discussion of Peirce’s notions of the self, see Colapietro 1984, particularly Chapters 4 and 5.  There are two undated variants of the lake metaphor piece (R 1112 and R 1113; CP 7.553 – 554). The only other locus mentioning this metaphor is a brief passage in “Forms of Consciousness” of 1896 (CP 7.547), so it seems probable the two undated pieces stem from the same period.  Already in “Some Consequences of Four Incapacities” of 1868, Peirce had the idea that “… my language is the sum total of myself; for the man is the thought” (W 2, 241; CP 5.314). Later, the notion of language as definitory of the self is broadened to concern “a bundle of habits” (“Logic of Events”, 1897, CP 6.228)  The map metaphor: “Draft of review of Royce’s World and Individual, Volume II”, 1902, CP 8.122.  Petry 1992 covers four phases of Peirce’s development of the concept of self-control. The first is his early writings of the 1860s where the concept is inspired by Schiller and Swedenborg;

412

Notes

the second the 1880s where he oftentimes attacked self-control as allied with moral absolutism; the third later in the decade where he began to see self-control as a condition for deliberate reasoning. The fourth phase from around 1902 “… consists in the integration of the concept of selfcontrol with the rest of his philosophy” (668). This is certainly correct; unfortunately, Petry stops short of detailing this final and decisive phase.  We may add that self-control is one of the few technical terms of Peirce’s philosophy which has a deep biographical connection to his own sad destiny, both as a person and an academic. Towards the end of his life, in late 1910 when he was increasingly ill and weak, Peirce looked back on his life: “The writer, in his long life, has found out for himself, what had often been told him while he was under tutelage, but which he then never would sufficiently realize, that chances are large that any given young boy will become a miserably unhappy man,—however he may try to lie to himself for consolation,—because he had not worked hard enough in his youth upon the work of his own self-development and self-government. That is the reason that so many successful and happy men have had the lowest origins. For they could not help seeing from the first, that that must be true of them which is really true of the highest born, as well, namely, that their education and training must be their own work, being due to their own nice observation, their own strenuous attention and other endeavours, and their own useful habits” (“The Art of Reasoning Elucidated”, late in 1910, R 678 , 22– 23 in the second set). Peirce, implicitly, finds the reason for his youthful lack of self-control in the fact that he himself did not have lowly origins. Rather, he was indeed one of the “highest born”, growing up at the top of US academia and celebrated as a prodigy in early age. This late self-criticism—after his development of his theoretical conception of self-control a few years earlier—is corroborated by his old friend James in a letter we have no reason to believe that Peirce ever saw: “… Peirce has never constrained himself in his life. Selfish, conceited, affected, a monster of desultory intellect, he has become now a seedy, almost sordid, old man, without even any intellectual residuum from his work that can be called a finished construction, only ‘suggestions,’ and begging old age” (William James to Dickinson S. Miller, March 31, 1903. William James Collection; cf. James, Henry (Ed.) 1929, 178 where Peirce is anonymized as “Z”). In many ways, James behaved like an angel towards his old friend and pragmatist brother-in-arms, granting the old bum a sort of private pension from around 1907 (Brent 1998, 306 – 307, 315 – 316) but in private, James was unanimous in his moral condemnation of his life for his lack of self-control.  Peirce adds that self-control must master man’s evil passions, and those passions are loved by God exactly because they indirectly serve to strengthen self-control. Cf. the following chapter.  Peirce does not definitively address the issue of the degree of connection between self-control in ethics and in logic, respectively, particularly what could be called the “mad scientist” problem: could a person be well-versed in logical self-control, but wanting in other, more general levels of ethical behavior? Maybe he would consider this a case of multiple personality—cf. also the note above on his own mature self-interpretation.  It is strange, however, that Peirce does not here consider his own ideas of consciousness beyond the individual or indeed the pragmatist idea of the society of scientists informing its simple members of its achievements. Obviously, Peirce here entertains a thought experiment of the very first appearance of inference forms in order to find their original conditions of possibility. Even within this experiment, one cannot help to feel a sort of bootstrap trick being pulled: making an inference take itself as an object is hardly a sufficient explanation of its appearance to the mind.  Cf. Chapter 15.

Notes

413

 Cf. Peirce when introducing his newly-constructed Existential Graph logic representation system in the “Peripathetic Talks” of 1898: “It will be found that by piling truism upon truism we arrive at last at deeply interesting and important results” (LoF I, 348).  Cf. Hintikka 1983, se also Stjernfelt 2011 and 2014, Chapter 10. A result reached by theorematic reasoning is necessary and the whole of the structure of the process one of deduction; yet it involves, in the context of discovery, abductive trial-and-error steps such as the selection of which auxiliary objects to instantiate and put to use; cf. Shin 2010.  Barry Smith, commenting this chapter, asked if this picture leaves no room for the creative discovery of new types of objects in mathematics. Peirce, I think, categorized such scientific events under the subtype of “theorematic” deduction, calling for the further study and typologization of forms of theorematic reasoning.  Peirce illustrates the resolve concept by this anecdote: “I remember that one day at my father’s table, my mother spilled some burning spirits on her skirt. Instantly, before the rest of us had had time to think what to do, my brother, Herbert, who was a small boy, had snatched up the rug and smothered the fire. We were astonished at his promptitude, which, as he grew up, proved to be characteristic. I asked him how he came to think of it so quickly. He said, ‘I had considered on a previous day what I would do in case such an accident should occur.‘ This act of stamping with approval, ‘endorsing‘ as one’s own, an imaginary line of conduct so that it shall give a general shape to our actual future conduct is what we call a resolve” (“Reason’s Rules”, 1902, CP 5.538). Herbert Peirce later had a strong career as a US foreign diplomat, probably exploiting self-control to a larger degree than his elder brother.  This transformation, simultaneously, is what explains the ability of thought to influence action, or more generally, mind to influence matter. Thus, the passage from “resolution” over “determination” to “action” breaks mind-matter parallelism, grants consciousness its causative powers, and instantiates a general plan in a particular act here-and-now.  Peirce rarely uses the notion of “autonomy”, he rather sticks to notions like “self-government”, but it is clear that the centrality of “self-control” in Peirce’s ethics sketches are close to that of autonomy in Kant’s ethics.  See Atkins 2016, 182– 185. Due to such a list of identifiers, Atkins says that “We are all sufficient familiar with self-controlled actions so as to differentiate them from actions or behaviors that are not self-controlled” (183). That may be true as a general statement even it does not necessarily imply that we are able to distinguish the two in each particular case.  Cf Pietarinen 2006, as well as Pietarinen’s introduction texts in the LoF.  On Peirce and cybernetics, Holmes 1966.  Even recently, the existence of unconscious controls may be celebrated as a pathbreaking discovery in neuroscience and neurophilosophy—that is, e. g., the main point of Suhlers and Churchland’s 2010 paper.  Aesthetic ideals being the ultimate governors of self-control also seems to lie behind this late piece of philosophy of life advice: “This consideration shows the great advantage of man’s making the best use of his time in deciding that supreme and difficult question, what sort of Attainment would prove most satisfactory to himself;—say, wealth, or the power of reading men’s minds, or power to compel this or that body of men to obey him, or magnetic power, or self-approval, or what else, to give a few of the least complex and crudest examples of what I mean by ‘Attainments’” (“On Definition and Classification”, 1910, R 649, 21). A further level might be that of selecting between such competing “esthetic” norms.

414

Notes

 Strictly speaking, a step of “prescission” is taken from “white thing” to “white” before the next, hypostatic step from “white” to “whiteness”. A longer discussion of “hypostatic abstraction” and its different types, see Stjernfelt 2007, Chapter 11; cf. also Stjernfelt 2012, 2014.  Omitted here is a long quote of Peirce’s favorite example of a hypostatic abstraction, Molière’s “Virtus dormativa”, the sleep-inducing power of opium, which he ridicules in his last play Le malade imaginaire as an idle medieval abstraction. Peirce, by contrast, defends the scholastic virtus dormativa for constituting a small but important step in reasoning: it highlights it is no accident that opium puts to sleep; there must be something in opium inducing sleep, calling for further research to identify that something; cf. Stjernfelt 2007, Chapter 11.  Peirce here uses his partially home-made set-theory terminology: “In order to get an inkling —though a very slight one—of the importance of this operation in mathematics, it will suffice to remember that a collection is a hypostatic abstraction, or ens rationis, that multitude is the hypostatic abstraction derived from a predicate of a collection, and that a cardinal number is an abstraction attached to a multitude. So an ordinal number is an abstraction attached to a place, which in its turn is a hypostatic abstraction from a relative character of a unit of a series, itself an abstraction again”. So, this generation of still higher-level concepts in set theory is taken as a formal parallel to the still higher levels of self-control also in other domains of thought and action; cf. Barry Smith’s question above.  Cf Stjernfelt 2012; 2014, Chapter 6.  Marquand published two brief papers on his logical machine research in the 1883 book Studies in Logic, edited by Peirce and presenting papers by himself and his Johns Hopkins students (12– 15; 16). Images of Marquand’s machine and later models of it can be found in Ketner and Stewart 1984, Figs 1– 5.  Cf. Ketner and Stewart 1984; the 1890 diagram is quoted from there.  Harvard Lecture I, W 1, 166 – 167; see also Amani 2008.  “On est oblige´ d’ailleurs de confesser que la perception et ce qui en de´pend est inexplicable par des raisons me´caniques, c’est-a`-dire par les figures et par les mouvements. Et feignant qu’il y ait une Machine dont la structure fasse penser, sentir, avoir perception, on pourra la concevoir agrandie en conservant les mê mes proportions, en sorte qu’on y puisse entrer, comme dans un moulin. Et cela pose´, on ne trouvera en la visitant au-dedans que des pie`ces qui se poussent les unes les autres, et jamais de quoi expliquer une perception. Ainsi c’est dans la substance simple, et non dans le compose´ ou dans la machine qu’il la faut chercher” (Leibniz 1714, §17).  R 831 is undated in the Robin catalogue, but as Edward S. Holden refers to the ms. in a letter to Peirce 21 May 1900, this seems to be its year of origin (André de Tienne, personal comm.).  In a vague sense, this idea might be said to anticipate the Lucas-Penrose argument against the abilities of “strong AI”, based on Gödel’s incompleteness proof (Penrose 1989). The fact that all axiomatizations of arithmetic will contain true statements not provable by the system is taken to indicate the superiority of the human observer able to realize those unprovable truths. Gödel’s proof famously rests upon the coding of arithmetical propositions so as to admit a double reading, both as simple claims about numbers and as self-referring expressions. Peirce’s insistence that self-referential consciousness is required for devising meta-controls of control might be said to anticipate Gödel’s self-referential step in a less formal sense (just like his “Deduction of the Dicisign” makes self-reference a crucial property even of simple propositions.) There is little agreement, however, on whether Gödel’s proof actually merits Penrose’s skepticism.  Cf. also Tiercelin 1984.

Notes

415

 Babbage had sketched the design already in the 1830s, while his son Henry Babbage undertook a much-publicized attempt of actually constructing a working fragment of it in the decades around 1900.  I discuss this a bit in Stjernfelt 2012; 2014, Chapter 6.  Several times, he toys with strange sorts of nested vortice movements involving different “ethers” on different size scales as a proposal of such indirect matter-mind interaction.  Cf. “What we call a reasoning is something upon which we place a stamp of rational approval. In order to do that, we must know what the reasoning is. In that sense, it must be a conscious act, just as a man is not bound by a contract if it can be proved that he signed it in his sleep. It must be his conscious act and deed. But for that purpose he only needs to know the character of the relation between the premisses and the conclusion. He need not know precisely what operations the mind went through in passing from the one to the other. That is a matter of detail which is not essential to his responsibility. The mind is like the conveyancer who has drawn up a deed. What books he looked into in choosing his verbiage is no concern of the person who signs, provided he knows what the paper binds him to doing” (“A Classification of the Sciences”, 1903, CP 2.183).  That this synthesis itself is predicative, iconic, was Peirce’s idea with the “continuous predicates” mentioned above—such predicates being extended structures not further analyzable.  This proximity, juxtaposition, or co-localization is not metric, rather topological in the sense of belonging to the same, connected space-time frame; cf. Chapters 5 – 6.  How big is that window? Some empirical guidelines here may be the average maximum size of a period in spoken (time) or written (space) language. Another indication may come from the more general (not only logical) window of consciousness—the maximum timelapse between two ensuing notes of a melody or beats of a rhythm. As soon as that present now is transgressed, the melody dissolves into isolated notes, the thought into independent signs, and we must pass to the realm of short-time memory in order to maintain synthesis.  Some might claim God would not be subject to such limits to synthesizing consciousness; yet Peirce would doubt God has any consciousness at all: “Since God, in His essential character of Ens necessarium, is a disembodied spirit, and since there is strong reason to hold that what we call consciousness is either merely the general sensation of the brain or some part of it, or at all events some visceral or bodily sensation, God probably has no consciousness” (“Additament to “A Neglected Argument””, 1908, CP 6.489); cf. the following chapter.  Self-control even appears at a similarly prestigious point in some of Peirce’s draft attempts to enlarge the finished three-trichotomy 1903 theory to a ten-trichotomy theory, primarily by enlarging in the direction of speech-act issues (Bellucci 2017, Chapter 8). His newfound distinctions between two types of objects and three types of interpretants of a sign, would result, for instance, in the following trichotomy of the purpose of the final interpretant, that is, the final meaning of a sign in the limit: “VIII. According to the Purpose of the Eventual Interpretant: Gratific; To produce action; To produce self-control” (Letter to Lady Welby, Dec. 24, 1908, EP II, 490; CP 8.372). Here, the aim of producing action—a standard goal for sign development ever since “How to Make Our Ideas Clear”, is surpassed by signs with that most noble aim of producing self-control.  The literature on transhumanism over the last half-century is vast; suffice it to refer to one of the recent statements of that tradition’s philosophical interpreters, Steve Fuller’s 2019 Nietzchean Meditations.  In an addition to an updated version of the 1878 “How to Make our Ideas Clear” (CP 5.402, n. 2).

416

Notes

 Already around the same time, Peirce had articulated the idea that in propositions, denotation and connotation (or, extension and comprehension, or breadth and depth) are not, like in isolated terms, inversely proportional. Rather, the two are independent, varying with each of the two components of a proposition. Their product, he terms “information”: “comprehension X extension = information” (“Harvard Lectures on the Logic of Science. Lecture X: Grounds of Induction”, 1865, W 1, 276). Thus, information of a proposition grows with increase of reference, of objects referred to, as well as with increase of meaning, of descriptions made of those objects. In the next lecture, we find the variant “Connotation X Denotation = Information” (“Harvard Lectures on the Logic of Science. Lecture XI”, 1865, W 1, 288); cf. Stjernfelt 2014, Chapter 9. As simple terms have also de- and connotation, however, why are humans not merely terms? When the early Peirce speaks of “signs” or “symbols”, he most often means propositions whose truth claim forms the center of logic. It thus seems most probable than the “man=sign” idea concerns propositions. Humans are signs because they constantly claim something, explicitly or not, knowingly or not.  The eye-eyebeam expression is one of Peirce’s frequent references to Emerson’s 1841 poem “The Sphynx”. Peirce quotes the Sphynx’s final answer to an interrogating poet:”The old Sphinx bit her thick lip,– / Said, “Who taught thee me to name? / I am thy spirit, yoke-fellow, / Of thine eye I am eyebeam. // Thou art the unanswered question; / Couldst see they proper eye, / Alway it asketh, asketh; / And each answer is a lie. / So take thy quest through nature, / It through thousand natures ply; / Ask on, thou clothed eternity; Time is the false reply”. Thus, Peirce’s references most often indicate the lack of introspective insight into the mental structures or capabilities involved in one’s own activities (https://poets.org/poem/sphinx, last accessed on March 27, 2022).  At the other end of his career, Peirce will give this definition of a person: “By a ‘person,’ […] I suppose we mean an animal that has command of some syntactical language” (R 659, 1910; cf. Lane 2009, 1) with the weight more on the competence than the performance of that animal. But it remains that the definition comes close to Cassirer’s “animal symbolicum”, yet, in Peirce, it is not given beforehand that this definition will pick out Homo sapiens exclusively.  This constituting the fourth and last of the four incapacities: We have no power of 1) introspection, of 2) intuition (in the sense of first impressions or first premises), of 3) thinking without signs, of 4) conceiving anything absolutely incognizable.  On Peirce’s early concept of information, cf. the note above.  Interestingly, two promiment Peirce scholars judges this extension of the person very differently. Lane 2009 takes his point of departure in the tension between individual animal being and general semiotic competence in a construction of a Peircean theory of personhood, giving both these determinations their due in a compromise definition: “… a person is an animal whose nervous system functions in a specific way, viz. to engage in a continuous process of sign-interpretation” (8). He rejects, however, Peirce’s extension of such personhood to larger composite entities like groups, companies, societies, etc. De Waal  also reconstructs Peirce’s theory of personhood, here in the light of his social epistemology, being more favorable to ascribe personhood to collective entities like the ones mentioned, remarking, e. g., how pieces of knowledge may be a property of the scientific institution as such rather than of particular individuals belonging for some time to that institution.  Shakespeare 1604, Measure for Measure, Act 2, Scene 2: “ISABELLA: Could great men thunder / As Jove himself does, Jove would ne’er be quiet, / For every pelting, petty officer / Would use his heaven for thunder; / Nothing but thunder! Merciful Heaven, / Thou rather with thy sharp and sulphurous bolt / Split’st the unwedgeable and

Notes

417

gnarled oak/ Than the soft myrtle: but man, proud man, / Drest in a little brief authority, / Most ignorant of what he’s most assured, / His glassy essence, like an angry ape, / Plays such fantastic tricks before high heaven / As make the angels weep; who, with our spleens, / Would all themselves laugh mortal”.  The reflection on this chasm will later be continued in terms of the difference between the mass of unreflective habits in everyday behavior on the one hand, and consciously controlled reasoning on the other; cf. Chapter 3.  Strauss, Leo (1952): Persecution and the Art of Writing. Current intellectual historians tracing the many devices of such “cunning” strategies through the Enlightenment comprise Martin Mulsow (2012) and Thomas Munck (2019).  Colapietro is right (cf. above) that the definition of the individual by falsity is not necessarily negative in a moral sense, but the ability of individuals to form mobs further enhancing and engraining falsity is certainly a negative propensity in humans, according to Peirce.  Peirce even goes so far as demanding of the fragile individual the willingness to sacrifice him- or herself to this transgenerational collective of transhumans: “He who would not sacrifice his own soul to save the whole world, is, as it seems to me, illogical in all his inferences, collectively. Logic is rooted in the social principle” (“The Doctrine of Chances”, 1878, CP 2.654).  The transhumanist aspects of Peirce’s pragmatism have been emphasized by Wilson and Brunson 2017. They compare him to transhumanist Nick Bostrom and conclude: “Peirce offers a consistent vision of the human, a natural being, both limited by bodies and already transcending them, on a trajectory of communal inquiry that is also a project of self-overcoming in order to know all that is knowable, and to experience all that can be experienced. Thus, Peirce deserves to be regarded as one of the great philosophical predecessors to contemporary transhumanism”. They are certainly right. When they restrict this conclusion, however, by stating that “Of course, Peirce never says explicitly that we should enhance our basic capacities through technological means—a task that was practically unheard of during his time”, they are not completely correct. Not only did Peirce see his philosophy of science making explicit logic in artificial formalisms as enhancing human capacities, he also—as we heard in the previous chapter—played a role in the early invention of computer technology expecting strong future results like automatical proofs of all theorems of arithmetics, echoing Hilbert’s mathematical optimism. Not coincidentally, he thought of his logical results as pertaining to the “Logic of the Future” which Ahti Pietarinen recently picked as the headline for his edition of Peirce’s writings on Existential Graphs.  To some degree, religion had been there in the background all along, the Peirce family being Unitarians—the anti-trinitarian Enlightenment theology not far from deism—even if Charles himself had changed confessions to Episcopalianism prior to his wedding to Melusina in 1863. Notes by the young Peirce confirms that he had, already in the 1860s, articulated the goal of uniting science and religion, inspired by authors such as Louis Agassiz and William Whewell, both of whom saw science as the investigation of the thoughts of God, an idea to which the mature Peirce would return (Viola 2020, 12 ff.).  Cf. Boler 1963; Stjernfelt 2007, Chapter 2.  To support his idea that religions do not necessarily involve the claim of existence of a deity, Peirce refers to the contemporary French freethinker Étienne Vacherot who, in Peirce’s portrait, is as earnest as can be: “He worships the Perfect, the Supreme Ideal; but he conceives that the very notion of the Ideal is repugnant to its real existence. In fact, M. Vacherot finds it agreeable to his reason to assert that nonexistence is an essential character of the perfect, just as St. Anselm and Descartes found it agreeable to theirs to assert the extreme opposite” (CP 6.396). Peirce adds that he finds either position more religious than that of “theologians

418

Notes

of evidence” who will only admit God in their system after he has identified himself and delivered his credentials for their scrutiny. Three decades later, Peirce will directly, in one of his few religious texts, make of scientific discoveries the charting of parts of God’s thoughts: “… the discoveries of science, their enabling us to predict what will be the course of nature, is proof conclusive that, though we cannot think any thought of God’s, we can catch a fragment of His Thought, as it were” (1905, 6.502); cf. below.  Of course, the two need not be mutually exclusive alternatives. A supreme being might see fit to pursue its ways be means of employing geniuses. Peirce does not, however, consider this.  It seems like Peirce took the 1453 fall of Constantinople as the starting point of modernity. A series of lists of great characters from 1883 – 84 can be found in W 5, sorted into different categories. as well as questionnaires to organize the knowledge of each selected candidate so as to serve the comparison between them and calculate relative importance of each.  Cf. his 1878 Photometric Researches.  Carlyle 1885 [1841]; Galton 1869; Spencer 1873. See Houser’s intro to W 8; cf. Viola 2020, 185 – 191.  “The Productiveness of the Nineteenth Century in Great Men”, 1901, R 1123; published, with a deletion, as CP 7.256 – 261 (1– 11); cf. the Robin catalogue.  Around 285 names are considered as candidates for “Great Men” of the long 19th century, 1791– 1901. The scientific parts of the list he singled out in a publication the same year, 1901, “The Century’s Great Men in Science”, in Annual Report of the Board of Regents of the Smithsonian Institution, Washington. It may need a remark that when speaking about “Men”, Peirce do not refer to males only; his usage, standard of the times is that of “men” being unmarked vis-avis “women” as marked (in Jakobsonian terms). So “Great Men” equals “Great Humans”. But great women in his various lists are few, primarily political figures like Jeanne d’Arc or Queen Elizabeth or authors of literary fiction.  In 1901, Peirce remembers the investigation and its limitations as follows: “I was desirous of having this include substantially all the great men of history. Yet I was less concerned that it should omit none whom it ought to contain than that those that it did contain should form a fair sample of what great men were like. Since we were all students, no doubt we had a bias in favor of men of intellect; but against this we were on our guard. There was naturally some moral leaning, and the social atmosphere of Baltimore must have affected our judgments. Moreover, it is humanly impossible in such a selection to do justice to contemporaries, compatriots, and acquaintances, whose greatness we are too close by to discern. I could now improve the list in details, besides doing something toward bringing it down to date. But it was formed with so much care that I would not venture to touch it short of a good six months solid preparatory study” (CP 7.257).  Peirce obviously develops this idea from Henry James Sr.’s 1863 Substance and Shadow, to which he refers, several times, with reverence: “Man’s destiny on earth, as I am led to conceive it, consists in the realization of a perfect society, fellowship, or brotherhood among men, proceeding upon such a complete Divine subjugation in the bosom of the race, first of self-love to brotherly love, and then of both loves to universal love or the love of God, as will amount to a regenerate nature in man, by converting first his merely natural consciousness, which is one of comparative isolation and impotence, into a social consciousness, which is one of comparative omnipresence and omnipotence; and then and thereby exalting his moral freedom, which is a purely negative one, into an aesthetic or positive form: so making spontaneity and not will, delight and no longer obligation, the spring of his activity” (James Sr. 1863, 6). On James Sr. and his Swedenborgianism, cf. below.

Notes

419

 A few years later, this idea is extended from the reason of humans and of the universe to embrace the thought of God himself: “For I hold that even the thought in Nature goes through a process of self-development or growth, which is what in the human mind, we call, reasoning and as I venture to believe it must be that the thought of God himself does, and at any rate I find it to be quite inconceivable that thought should, in itself, without accretions from without, go through a process of self-development or growth (without which a “moving picture” could mean nothing), otherwise than by its taking a dialogic form, which suggestion is confirmed by the careful observation of our own solitary thinking” (“Phaneroscopy (φαν)”, 1906, LoF III/1, 254).  In the early 1890s, Peirce entered a tumultuous period of his life. After being sacked from the Coast Survey, he would never again, despite many attempts, acquire a stable salaried position. It is well known that in his hour of darkness, he accidentally stumbled into St. Thomas Church on Fifth Avenue in New York on April 24th, 1892. In a letter the same day to the reverend, Peirce relates how God received him and he had a mystical experience (W 8, lxxvi). In the letter— if it was ever sent we do not know—Peirce also explains how he, as a man of science, has kept away from the church even if never really abandoning an elementary faith in the truth of Christianity. The “Law of Mind” articles appearing after that date display a markedly spiritual turn in Peirce’s thought, only to recede again in the mid-late 1890s.  Cf. the idea that a “Person is mind whose parts are coördinated in a particular way”, ((Evolution], 1892– 1893, R 954; cf. also Lane 2009, 3)  Peirce will continue to refer back to his original Man=Sign philosophical anthropology also in his last creative burst of the 1900s: “We can now see what judgment and assertion are. The man is a symbol. Different men, so far as they can have any ideas in common, are the same symbol. Judgment is the determination of the man-symbol to have whatever interpretant the judged proposition has. Assertion is the determination of the man-symbol to determining the interpreter, so far as he is interpreter, in the same way”. (“Kaina Stoicheia” 1901(?), EP II, 324). Here, the sign type of symbol—characterized by having a general object—is selected to describe the doctrine, supposedly because the entirety of a human being’s general habits may be fused into one, general, if complicated sign.  In the Monist “Law of Mind” papers from the period, Peirce even distinguishes three aspects of evolution after his three categories, attempting to enrich what Peirce saw as the insufficient Darwinian version of the former two aspects only: “Three modes of evolution have thus been brought before us: evolution by fortuitous variation, evolution by mechanical necessity, and evolution by creative love. We may term them tychastic evolution, or tychasm, anancastic evolution, or anancasm, and agapastic evolution, or agapasm” (“Evolutionary Love”, 1893, EP I, 362, CP 6.302– 303).  Additional footnote to an 1893 reworking of “How to Make our Ideas Clear”, 5.402, n. 1.  An even harsher verdict can be found in “Logic of Events”, 1897, 6.3: “I once bought and read through Dr. Schaff’s three volumes upon the Creeds of Christendom for the purpose of ascertaining whether the theologians, who composed them, had ever once, from the first to the last, inserted a single clause in one of them by way of recognition of the principle of love; and I found that such a thing had never been done. But then we must remember that, that principle being fully admitted by all Christians, its insertion would not have served to damn anybody. Now the principal business of theologians is to make men feel the enormity of the slightest departure from the metaphysics they assume to be connected with the standard faith. Upon their religious side, however, I will not pretend to any opinion about the influence of theologians. But since theology pretends to be a science, they must also be judged as scientific men. And in that

420

Notes

regard I must say that another so deplorably corrupt an influence as theirs upon the morals of science I do not believe has ever been operative”.  E. g., religion is seen as a “Way of Life” rather than a belief (“What is Christian Faith”, 1893, CP 6.439 – 440); “… essentially a social, a public affair (…) claiming a supremacy in the determination of all conduct, private and public” (“Science and Religion”, 1893, 6.429). Cf. also Cantens, Bernardo (2005): “Prolegomena to Peirce’s Philosophy of Religion”, https://www.unav.es/gep/ SeminarioCantens.html, last accessed on March 27, 2022. The idea that the main if not only role of religion is to organize the social and moral life of believers goes back to Spinoza’s 1670 Tractatus. A remote source to Peirce’s rejection of theological dogma in favor of heartfelt religious practice may be pietism; cf. below.  Peirce’s intense obsession with consciousness of the early 1890s seemed to be considerably tempered through the latter part of the decade.  On the enlarged fallibility of humans, cf. Trammell 1973, 209.  “What is the use of Consciousness?”, 1893, CP 7.564.  In the same paper, Peirce adds an interesting reflection on the relations between Instinctive and Rational minds, surprisingly seeing the latter as more infantile than the former. Still, the latter must have developed out of the former, animals being more instinct-governed than human beings: “… let me say, at once, that I doubt very much whether the Instinctive mind could ever develop into a Rational mind. I should expect the reverse process sooner. The Rational mind is the Progressive mind, and as such, by its very capacity for growth, seems more infantile than the Instinctive mind. Still, it would seem that Progressive minds must have, in some mysterious way, probably by arrested development, grown from Instinctive minds; and they are certainly enormously higher. The Deity of the Théodicée of Leibniz is as high an Instinctive mind as can well be imagined; but it impresses a scientific reader as distinctly inferior to the human mind. It reminds one of the view of the Greeks that Infinitude is a defect; for although Leibniz imagines that he is making the Divine Mind infinite, by making its knowledge Perfect and Complete, he fails to see that in thus refusing it the powers of thought and the possibility of improvement he is in fact taking away something far higher than knowledge. It is the human mind that is infinite”. Peirce’s new reevaluation of the role of error makes him refuse perfection and completion as relevant properties of a mind which would then cease to be alive, developing, and able to achieve still more growth.  What is more, it is an abduction based on Peirce’s individual musement experience only, without making explicit any criteria for which among the many possible results of musing should be taken seriously in that way. When other musers may foster and develop other, competing ideas, why would they not possess a validity equal to Peirce’s deity? Another issue worthy of remark is the absence of Jesus Christ from the “Neglected Argument” and many other among Peirce’s theological musings. The trinity holds no special role, despite Peirce’s “triadomany” in so many other respects. As mentioned, his family was Unitarians, an Enlightenment theology current rejecting the trinity for scriptural reasons: it is not mentioned in the Bible. Peirce refers to the teachings of Christ in the “Law of Mind” period of the early 1890s where he opposes it to the Gospel of Greed which he finds in 19th century philosophy in general and in Darwin in particular. Both are judged as doctrines of progress rather than theologicsl doctrines, the former claiming empathy between individuals as the road to progress, the latter claiming the struggle for existence among individuals (“Evolutionary Love”, 1893, 6.294). In other periods, he mostly mentions Christ when discussing the possibility of miracles (on which Peirce does not seem to have a definite position).  Misak 2004, 32.

Notes

421

 In this text, Peirce follows Hume in substituting for “God” the notion of “Supreme Being”, which is taken to be more precise but also more comprehensive because it does not presuppose infinity and the series of traditional divine “omni-” attributes which Peirce may then go through and question one by one, in most of them avoiding subscribing to the classical definitions and simultaneously claiming that the Supreme Being really remains beyond grasp: “But we only wildly gabble about such things” (CP 6.509). He compares the existence of a Supreme Being to the existence of order in the universe, which is also but vague, however, with nobody thinking of refusing or disproving its existence. It is but the pedantry of learned, primarily male scholars that make them refuse God, Peirce critically adds. The most important property of God in the “Answers” paper is creativity whose open-endedness also forms a main reason for his vagueness and ungraspability: “”Do you believe this Supreme Being to have been the creator of the universe? “Not so much to have been as to be now creating the universe …” (CP 6.505), followed by: “I think we must regard Creative Activity as an inseparable attribute of God” (CP 6.505). This continuous process of creation comprises human beings: “In general, God is perpetually creating us, that is developing our real manhood, our spiritual reality” (CP 6.507), thus including our increasing self-control; cf. about the vir below.  In the 1906 “PAP”, Peirce says: “The thought of God,—if the anthropomorphism is too distasteful to you, you can say the thought in the universe, …” (LoF III/1, 278). Such an idea, however, seems panpsychist, even pantheist, and thus going against Peirce’s 1890s claims for theism with a God independent of the universe.  This “Vir” is a hapax legomenon in Peirce’s work, but that did not prevent Krolikowski from addressing a whole paper to this word: Krolikowski 1964. It derives from a complicated distinction in Henry James Sr.’s interpretation of Swedenborg, between the general species of homo and the more specific vir which is the virtuous, autonomous individual, arguably possible only if at all, as the eventual result of the long strive for self-control. In his Secret of Swedenborg, James Sr. wrote: “… so far as I am vir, and therefore morally and personally conscious, being formerly individualized from all lower existence, and identified only with man, I am God’s veritable son, being spiritually begotten of him through his living absorption in the homo, and am consequently endowed with conscience, which is the faculty of discerning between good and evil, or, what is the same thing, of freely compelling myself away from a finite and illusory good to one which is infinite and real, and so coming at last into the deathless fellowship of his perfection […]” (James Sr., (1869), 138). Interestingly, Peirce’s concept of self-control thus has an important root in Swedenborg’s spiritual mysticism. Swedenborg was originally a disciple of one of the main proponents of German radical pietism, Johann Konrad Dippel who took self-refutation and the struggle against the immediate demands of the self to be central to reformed religion. Dippel turned strongly against Lutheran orthodoxy and the idea that explicit dogma, orthodoxy, church institutions, participation in prescribed ceremony, the persecution of heretics, should be central to Christianity. Dippel, by contrast, found true redemption in the individual’s personal struggle with itself, supported by non-formalized communities or brotherhoods of likeminded believers outside the church involved in social amelioration initiatives—even involving believers from very different, even non-Christian confessions, provided they partook in the same moral struggle. In short, a practical rather than theoretical conception of religion not far from Peirce’s. Thus, Peircean self-control seems to inherit a strand of radical pietism via Swedenborg. Peirce hardly, however, bought into the latter’s famous spiritualism claiming the possibility of communication with deceased spirits, even if he did pay a remark to it on some occasion (Harvard Lectures on Pragmatism, 1903, CP 5.47, n.).

422

Notes

 Even if evil would thus count as one of the perfections of the universe, Peirce later regrets his identification of it with pain. He refers to a contemporary case with some Russian countess involved in sado-masochism, enjoying pain, and, in a more theoretical vein, he sketches an antiEpicurean proof “that pain per se cannot be considered as an Evil”, the argument being that pain is but a quality of feeling while good and evil are relative to some purpose or end (“How to Define”, 1910, LoF III.1, 403 – 404). In themselves, pain and pleasure provide no guideline for action, even though they may function as “rational motives as being veridical signs of real needs” (“How to Define”, 1910, LoF III/1, 402) and thus serving us well. In the same context he ridicules contemporary theologians claiming that the invention of anaesthetics is ungodly and intervening in God’s scheme, particularly regarding women in childbirth. Peirce quotes an anonymous theologian for claiming that such practice is but “… a decoy of Satan which though speciously […] offering to bless women, will in the end rob God of the deep and earnest cries for help that rise to Him in the time of their trouble” (“How to Define”, , LoF III/, ). Peirce defends the soothing of pain, admitting that he himself is a softie in such matters: “Now, for my part, I thought then, as I do now, that their tender solicitude lest their poor darling little Almighty should find all this dearly cherished schemes frustrated by the clever dentist, or be at least forced to resort to extraordinary and revolutionary measures to avert that dire result was as richly comical as anything well could be” (“How to Define”, , LoF III/ , ).  Again, Peirce’s theological improvisations seem his own rather than informed by any deep study of the dogmas of competing confessions: “I have studied my full share of theology, for a layman. But I confess that most of it, and particularly the differences between the dfferent Protestant denominations, runs off from me like holy water from the back of an heretical duck. I ought to have a religious cyclopedia always at hand. If I had one I would study it with diligence. Until I can afford to purchase one, I must regret, and sincerely regret, that the only religious ideas of which I can venture to speak without an humble apology for my ignorance are those of the high church party of the Protestant Episcopal Church, or perhaps only a section of that” (“How to Define”, 1910, LoF III/1, 401). Surprisingly, Peirce refers to high church Episcopalianism (the US branch of Anglicanism) whose standard theism may indeed be compared to the personal god of his “Law of Mind” period around 1890 but seems to have pretty little resemblance with the strange deity painted by Peirce in the 1905 letter.  Peirce adds a reference to William: “See James’s paper ‘Does “Consciousness” Exist?’ in Jour. Phil., Psy., and Sci. Meth. I, 477; 1904, Sep. 1. But the negative reply is, in itself, no novelty”.  “’Do you believe Him to be omniscient?’ […] I do not see why we may not assume that He refrains from knowing much” (“Answers”, 1905, CP 6.508); “… it seems to me that the very meaning of the word “God” implies, not surely morality, for He seems to me to be above all self-restraint or law, but to imply aesthetic spiritual perfection” (1905, CP 6.510).  This deity seems to be pure general Thirdness. It remains difficult to understand, though, given Peirce’s frequent insistence that the general ideas of Thirdness have no efficiency at all if not incarnated in Secondnesses, in his standard metaphor like the Law is in need of the strong arm of the Sheriff to be imposed. Is humanity equivalent to the Sheriff or a part of his activity? In the 1908 “Additament”, Peirce makes precise his idea of thought and mentality as inherent in ordered aspects of the cosmos: “Order is simply thought embodied in arrangement; and thought embodied in any other way appears objectively as a character that is a generalization of order, and that, in the lack of any word for it, we may call for the nonce, “Super-order”. It is something like uniformity. The idea may be caught if it is described as that of which order and uniformity are particular varieties. Pure mind, as creative of thought, must, so far as it is manifested in

Notes

423

time, appear as having a character related to the habit-taking capacity, just as super-order is related to uniformity” (CP 6.490). Maybe the Peircean divine, then, relies in this super-order uniformity coordinating, on a higher level, regularities of the universe. Here, we are approaching arguments like the “fine-tuned universe” and Wheeler’s “anthropic principle” that basic constants of natural laws fit together to constitute a universe making human existence possible.  The idea that all natural classes are purposive are connected to Peirce’s intensional theory of classes in his version of set theory. No merely extensional set of arbitrarily combined elements is really possible—the set theoretic examples to prove the contrary will be selected for that very purpose and so also be purposive. Cf. Dipert 1997; Stjernfelt 2007. Peirce will stick to this theory also in his final years: “The essence of anything lies in what it is intended to do” (“Some Amazing Mazes. Fourth Curiosity”, 1907, CP 4.659).  Many Darwinists, of course, would count it a central virtue of the doctrine of evolution that it gave a general recipe for translating apparent final causes to strings of small efficient causes, thereby eradicating the former. Peirce accepts the description but not its reductionist conclusion; he takes the string of small efficient causes to show how final causes operate.  In his “Answers to Questions Concerning my Belief in God” (1905), Peirce abducts the existence of intelligences in the universe from Olbers’ paradox (that if the universe is infinite and stars evenly distributed in it, the night sky would be luminous), seeing its darkness as a sign of a plenitude of planets, many of which supposedly are inhabited: “The fact that the heavens do not show a sheet of light proves that there are vastly more dark bodies, say planets, than there are suns. They must be inhabited, and most likely millions of them with beings much more intelligent than we are. For on the whole, the solar system seems one of the simplest; and presumably under more complicated phenomena greater intellectual power will be developed. What must be the social phenomena of such a world!” (CP .)  Peirce’s cosmological optimism—which he time and time again emphasizes is but a dream rather than supported by scientific evidence—may be contrasted with his portrayal of pessimism in the 1908 “Neglected Argument”: “I do not admit that pessimists are, at the same time, thoroughly sane, and in addition are endowed in normal measure with intellectual vigour; and my reasons for thinking so are two. The first is, that the difference between a pessimistic and an optimistic mind is of such controlling importance in regard to every intellectual function, and especially for the conduct of life, that it is out of the question to admit that both are normal, and the great majority of mankind are naturally optimistic. (…) In order to present my other reason, I am obliged to recognize three types of pessimists. The first type is often found in exquisite and noble natures of great force of original intellect whose own lives are dreadful histories of torment due to some physical malady. Leopardi is a famous example. We cannot but believe, against their earnest protests, that if such men had had ordinary health, life would have worn for them the same colour as for the rest of us. Meantime, one meets too few pessimists of this type to affect the present question. The second is the misanthropical type, the type that makes itself heard. It suffices to call to mind the conduct of the famous pessimists of this kind, Diogenes the Cynic, Schopenhauer, Carlyle, and their kin with Shakespeare’s Timon of Athens, to recognize them as diseased minds. The third is the philanthropical type, people whose lively sympathies, easily excited, become roused to anger at what they consider the stupid injustices of life. Being easily interested in everything, without being overloaded with exact thought of any kind, they are excellent raw material for littérateurs: witness Voltaire. No individual remotely approaching the calibre of a Leibnitz is to be found among them” (“Neglected Argument” 1908, EP II, 449; CP 6.484). A full argument, however, would require the proof of pragma-

424

Notes

ticism, he adds. As an argument against pessimism, Peirce’s remarks are hardly convincing, and his own optimism, ultimately relying in the vague conviction that the universe is somehow made for intelligent beings, is little more persuasive.  In 1909, Peirce was diagnosed with abdominal cancer, and he progressively weakened during the following years. Peirce’s final attempt to deal with traditional theology and religion seems to have taken place through 1911. All of Mss. R 846 – 856 are attempts through 1911 to write a small book with a logical criticism of the doctrines of Christianity or of religion in general, with titles such as “First Rough Draught of the Substance of A Logical Examination of theChristian Creed in Brief Summary”. Yet, most of the Mss. only achieve introductions of elements of logic or of Peirce’s own biography, both of which he seemed to have considered necessary prerequisites to the daunting task. Only a couple of times, the declared subject matter shines through. R  has regrets “that the darker and more cruel parts of religious faith have not had justice done to them nor brought into so high relief as they ought”. R  has the claim that Peirce is “… a scientific man to the core; and the early Christians did not exhibit a more thorough abhorrence for the impurities of the paganism of their childhood, than I entertain for the utterances I used to hear from the pulpit about the “plenary inspiration” of the Bible, etc.”. The scene seems to be set for a tough clash between logic and established religion, but unfortunately, we never learn about the fruits of this late endeavor. R  has “… there is a pretty widely spread impression that the tendency of scientific work is to produce scepticism, if not disbelief, regarding religion, as distinguished from a deistic philosophy”. This might give the idea that Peirce may have seen his own achievements as a “deistic philosophy”, and with its home-made, anti-dogmatic character with strong bonds to science, it may not be erroneous to sum up Peirce’s scattered ideas as a version of natural religion, of deism. Indeed, his theological musings have many deist features: the rare references to Jesus, even rarer to the Bible, the emphasis on God creator of the universe and the sciences as the reader of his thoughts.  Albert A. Michelson and Edward W. Morley’s famous experiment of 1887 was the surprising empirical finding triggering the vast development of physics after 1900. By an ingenious arrangement of half-transparent mirrors, the two American physicists were able to disprove the existence of an ether—traditionally supposed to be the medium in which light waves spread. Simultaneously, this result made improbable the existence of any given, stable reference frame against which movement could be measured. The result mentioned interpreting these finding is the Lorentz transformations by the Dutch physicist Hendrik Lorentz, the immediate precursor and even co-articulator of Einstein’s 1905 special relativity—a couple of pages later, Peirce refers to Lorentz for the possibility of adding spatial to temporal units in the frame of, if not space-time, then time as a fourth dimension. Lorentz’ interpretation of the Michelson-Morley experiment thus counts to Peirce as a contemporary example of the progress of science. Peirce did not seem to be acquainted with, however, Einstein’s famous batch of 1905 papers on special relativity, the photo-electric effect, Brownian motions, and the mass-energy equivalence.  The quotations in this brief Coda have been cited earlier in the book. They stem from “Questions Concerning Certain Faculties”, 1868, W 2, 113; CP 5.253/ Minute Logic, 1902, CP 7.364/, and “The Doctrine of Chances”, 1878, EP I, 249; CP 2.654.

Name Index The index includes names of fictive characters, institutions, etc. Names also refer to their adjectivized and substantivized forms (“Darwinian”, “Darwinist”, etc). “f” indicates mention on the following page; “ff” several following pages.

Achenbach, Andreas 74 – 77 Agassiz, Louis 417 Alex the Grey Parrot 18, 21, 387 Amani, Majid 414 Ambrosio, Chiara 403 Anellis, Irving H. 168 Anselm of Canterbury 354, 417 Antonioni, Michelangelo 129 Aristotle 8, 34, 72, 140, 212, 214, 238 f, 244, 263, 266, 273, 277, 355, 405 Atkins, Richard 310, 413 Augustine of Hippo, 39 Austen, Jane 338 Austin, John L. 257 f, 405 Babbage, Charles 125, 306, 319, 415 Babbage, Henry 415 Bacon, Francis 277, 346, 358 Baer, Karl Ernst von 106 Bain, Alexander 25, 44, 266 Baldwin, James Mark 75, 322, 356, 397, 405 Barks, Carl 87 f, 108, 288 Bateman, John 391, 397 Beethoven, Ludwig van 338 Bellucci, Francesco 4, 24, 41, 43, 46, 59, 62 f, 65 f, 137, 142, 159, 212, 235 – 260, 325, 385, 387, 389 – 392, 396, 398, 400 f, 404 f, 407, 415 Bentham, Jeremy 348 Berkeley, George 29, 34, 213, 241, 294, 333 Biden, Joe 117 Bismarck, Otto von 125 Bloomsbury Publishers 95, 99 Boler, John F. 401 f, 417 Boole, George 107, 132, 137, 166, 242, 393 f Brandt, Enevold 111 https://doi.org/10.1515/9783110793628-027

Bredekamp, Horst 123, 397 Brent, Joseph 412 Brentano, Franz 408 Brøndal, Viggo 395, 407 f Brown, Robert 19, 424 Brunson, Daniel J. 417 Burch, Robert 228, 242, 254 Butler, Rhett 116 Caesar and Brutus 59 Cain and Abel 258 f, 261, 277 Canger, Una 407 Cantens, Bernardo 420 Cantor, Georg 239 Cardano, Gerolamo 185 Carlyle, Thomas 337, 418, 423 Carnap, Rudolf 407 Carnegie, Andrew 151, 219, 248, 250, 302 Carquillat, Michel-Marie 127 Cartesian, see Descartes Carus, Paul 58, 388, 404 Cassirer, Ernst 4, 264 – 271, 406, 408, 416 Catholic Church 52 Champagne, Marc 397, 399, 411 Champollion, Jean-François 395 Chevalier, Jean-Marie 404 Chiffi, Daniele 387 Chomsky, Noam 281 Chrystal, George 400 Church, Alonzo 318, 388 Churchland, Patricia 411, 413 Cicero, Marcus Tullius 340, 353 Cigana, Lorenzo 280 – 285, 407 f Coast Survey, USA 154, 338, 419 Cohen, Hermann 212 f, 402 Cobley, Paul 385 Colapietro, Vincent 298 f, 387, 411, 417 Columbus, Christopher 338

426

Name Index

Comte, Auguste 219, 226 Conway, Moncure 354 D’Arc, Jeanne 418 Darwin, Charles 33, 268, 303, 305, 338, 345, 349, 353, 419, 421, 423 Dau, Frithjof 400 Dauthage, Adolf 76 f Deacon, Terrence 18, 406 Defoe, Daniel 95 Den (Pharaoh) 84 – 87, 94, 392 Department of Semiotics, University of Tartu 116 Derrida, Jacques 262 Descartes, René 12, 90, 99, 103, 157, 201, 206, 240, 286, 319, 343, 417 Devil, the 309, 315 Dewey, John 265, 404 Diderichsen, Paul 274, 407 Diderot, Denis 397 Dijkstra, Trude 397 Diogenes 423 Dipert, Randall 423 Dippel, Johann Konrad 421 Disney, Walt 87 f, 143, 288, 393 Donald, Merlin 387 Duck, Donald 11, 15, 87 ff, 108, 117, 288 Duncker, Karl 182, 185 Eckstein, Adolf 77 Ehrenfels, Christian von 293, 410 Einstein, Albert 424 El-Hani, Charbel 20, 385, 395 Eliot, George 338 Elizabeth I of England 418 Emerson, Ralph Waldo 416 Epictetus 123 Episcopal Church 423 Epicurus 422 Ergenekon Case 126, 128 Eriksen, Jens-Martin 387 Escher, Maurits 205 Euclid of Alexandria 129, 150 f, 180 f, 181, 185, 197 Euler, Leonhard 138, 151, 164, 396 Farias, Priscila

135

Farragut, David 67 f, 390 Fehrmann, Gisela 392 Fermat, Pierre de 319, 398 Fisch, Max 240, 401 Fox, William Johnson 354 Franklin, Benjamin 331 Fraser, Alexander Campbell 34, 213, 333 Frederick the Great of Prussia 349 Frege, Gottlob 8 f, 78, 164 – 167, 170, 241, 266, 292, 385, 391, 404 Freud, Sigmund 411 Frisch, Karl von 18 f Fuller, Steve 415 Fusaroli, Riccardo 401 Gable, Clark 116 Galileo Galilei 338 Galton, Francis 337, 418 God; gods 98, 112, 288, 336, 339, 345 f, 350 – 356, 412, 415, 417 ff, 421 – 424 Gödel, Kurt 318, 388, 414 Goethe, Johann Wolfgang von 338 Green, Nicholas St. John 26, 44 Grice, Paul 60 Hamilton, William 404 Hartmann, Eduard von 296, 411 Hartshorne, Charles 64, 236, 403 Harvard University 50, 57, 159, 218, 221, 229 f, 238, 276, 295, 304, 347 ff, 351, 385, 411, 414, 416, 421 Hebb, Donald 30 Hegel, G. W. F. 220, 230, 261, 267, 338 ff, 405 Hilbert, David 59, 318, 388, 418 Hilpinen, Risto 10, 386 Hintikka, Jaakko 15, 307, 413 Hjelmslev, Louis 4, 272, 274 f, 278 – 285, 290, 407 f, 410 Hoffmeyer, Jesper 385, 387, 395 Holden, Edward S. 414 Holenstein, Elmar 274, 407 Holmes, Larry 413 Holmes, Oliver Wendell 44 Hookway, Christopher 40, 392 Horstbøll, Henrik 396 Houser, Nathan 411, 418

Name Index

Hume, David 296, 308, 323, 346, 421 Hurford, James 387 Husserl, Edmund 14, 28, 215, 219 f, 227, 234, 272 – 276, 278 f, 284 – 290, 292, 304, 403, 407 Ingarden, Roman 4, 203, 272 – 275, 287 – 290, 386, 407 – 410 Israel, Jonathan 397 Jacquard, Joseph-Marie 124 f Jagersma, Rindert 397 Jakobson, Roman 272, 274, 407 f, 418 Jakurjan 85 f, 88, 102 James, Henry Jr. 352, 412 James, Henry Sr. 352 f, 418, 421 James, William 44, 106, 151, 265, 297, 343, 348, 352 ff, 412, 422 Jastrow, Joseph 297 f, 404 Jesus Christ 420, 424 Jevons, William Stanley 315, 317, 319 Johansson, Ingvar 288 f, 409 Johns Hopkins University 241 ff, 315, 337, 398, 414 Kammerzell, Frank 84 ff, 87, 89, 392 f Kant, Immanuel 9, 51, 81, 197, 140 f, 151, 199, 211 – 214, 217 f, 221 – 227, 230, 232, 240, 243, 256, 263 f, 273, 275, 289, 300, 307, 310, 322, 326 f, 330, 338, 342, 346 f, 349, 401 ff, 410, 413 Karmiloff-Smith, Annette 186 Kepler, Johannes 338 Ketner, Kenneth L. 414 Kitcher, Philip 128 f, 397 Kluge Hans the horse 387 Koerner, E. F. K. 407 Köhler, Wolfgang 182 Kress, Gunther 391, 397 Krois, John Michael 4, 264 – 271, 405 f Krolikowski, Walter P. 421 Kull, Kalevi 105 f Künrath 115 Kusch, Martin 410 Kutscher, Silvia 392 Ladd(‐Franklin), Christine

404

427

Lane, Robert 211, 216, 401, 416, 419 Langacker, Ronald 102 Lange, Friedrich Albert 164, 243 Langen, Ulrik 397 Lapčić, Aleksandra 392 Laplace, Pierre-Simon 58, 336 Lauritsen, Anne Mette 397 Leeuwen, Theo 391, 397 Leibniz, Gottfried Wilhelm 317, 352 f, 394, 404, 414, 420, 423 Leigh, Vivian 116 Leopardi, Giacomo 423 Lessing, Gotthold Ephraim 197, 401 Lévy-Bruhl, Lucien 280 Lloyd, James E. 395 Lorentz, Hendrik 424 Lotze, Hermann 215, 402 Lowell Institute 25, 37, 50, 133, 140 f, 144, 159, 229, 237, 250, 253, 309, 329 f Lucas, John 414 Lucretius 123 Luther, Martin 338, 421 McDuck, Scrooge 87 ff, 108 Malone, Molly 62 – 69, 390 Marlowe, Christopher 277 Marquand, Allan 315 ff, 319, 404, 414 Marty, Anton 408 Meinong, Alexius 14 Mendeleyev, Dmitri 64, 231, 390 Metaphysical Club, The 25, 28, 44, 240 Michelangelo Buonarotti 338 Michelson, Albert A. 358, 424 Milkov, Nikolay 402 Mill, John Stuart 263, 334, 404 Miller, Dickinson S. 412 Millière, Raphaël 409 Misak, Cheryl 351, 401, 420 Mitchell, Margaret 116 Mitchell, Oscar H. 242, 394, 398, 404 Mitchell, Robert W. 395 Mitchell, W. J. T. 123, 397 Molière (Jean-Baptiste Poquelin) 414 Mona Lisa 128 Morgan, Augustus de 107 Morley, Edward W. 358, 424 Morris, Charles 101, 162, 399 f

428

Name Index

Muhammad 396 Mulligan, Kevin 401 Mulsow, Martin 417 Munck, Thomas 417 Murphey, Murray 238, 255, 401 f Napoleon Bonaparte 58, 307, 336, 338, 386 Newton, Isaac 338 f, 385 Nietzsche, Friedrich 415 Nöth, Winfried 24, 399 Nybro, Jeppe 396 O’Hara, Scarlett 116 Obama, Barack 15 Ockham, William of 213 Ohlsson, Stellan 182, 184, 186 Olbers, H. W. 423 Østergaard, Svend 98, 179 – 190, 385, 397, 401 Parker. Kelly 387 Paul, Israel de 115, 397 Peano, Giuseppe 9, 132, 164, 167 f, 318 Pearson, Karl 348 Peirce, Herbert 413 Peirce, Juliette (Juliette Froissy Pourtalai) 395 Peirce, Melusina (Melusina Fay) 417 Penkowa, Milena 396 Penrose, Roger 414 Pepperberg, Irene 21 Peter the Great of Russia 338 f Petrie, Flinders 84 Petry, Edward S. 411 f Peust, Carsten 84 ff, 87, 89, 392 f Pietarinen, Ahti 24, 41, 133, 387, 397, 399, 401, 404 f, 407, 413, 417 Plato 203, 288 Pöppel, Ernst 105 Porphyry 94 Port Royal School 239, 404 Potter, Harry 95 f Putin, Vladimir 119 Putnam, Hilary 168

Queiroz, João 135, 385, 391, 395, 397, 400, 405 Quine, Willard van Orman 9, 222, 402 Reichenbach, Hans 306 Reinach, Adolf 286, 407 Ritchie, Matthew 198, 207 Roberts, Don D. 400 Robin, Richard S. 357, 385, 387, 398, 414, 418 Rosenthal, Sandra B. 26 Rousseau, Jean-Jacques 336 Rowling, J. K. 95 f Royce, Josiah 322, 340, 352, 411 Russell, Bertrand 9, 15, 78, 108, 132, 164, 167 f, 170, 386, 389 Ryle, Gilbert 94 Satan 422 Saussure, Ferdinand de 280 Schaff, Philip 419 Schelling, Friedrich von 344, 411 Schiller, F. C. S. 309, 326, 352 Schiller, Friedrich 350, 352, 411 Schilling, L. 77 Schopenhauer, Arthur 423 Schröder, Ernst 1 f, 9, 63, 132, 164, 167 f, 245 ff Scotus, John Duns 34 f, 213, 245, 247, 314, 330, 336, 360, 389 St. Thomas Church, New York 419 Searle, John 317 Sebeok, Thomas 400 Sellars, Wilfrid 293 Selznick, David 116 Shakespeare, William 277, 332, 338, 416 f, 423 Sheffer, Henry M. 242, 400 Shin, Sun-Joo 400, 413 Short, Thomas L. 65, 237, 255 f, 401 Sigwart, Christoph von 245 Simons, Peter 409 Smith, Barry 9, 396, 402, 407 f, 410, 413 f Smithsonian Institution, Washington 418 Socrates 164, 392 Sonesson, Göran 400 Spencer, Herbert 337, 418

Name Index

Spengler, Oswald 335 Sphynx, The 331, 416 Spiegelberg, Herbert 403 Spinoza, Baruch de 114 f, 289, 354, 397, 420 Stephen, Damian G. 183, 189, 192 Stewart, Arthur F. 414 Strauss, Leo 334, 417 Struensee, Johann Friedrich 111 Struhsaker, Thomas T. 20 Stumpf, Carl 14, 215, 293, 402, 410 Suhler, Christopher 411, 413 Supreme Being 418, 421 Swedenborg, Emmanuel 352, 411, 418, 421 Sylvester, James Joseph 306 Talmy, Leonard 102, 395 Tetens, J. N. 410 Thomas of Erfurt 245 Tienne, André de 400, 414 Tiercelin, Claudine 414 Timon of Athens 423 Tomasello, Michael 12 Trammell, Richard L. 420 Trubetskoy, Nikolai 274 Turing, Alan 317 f, 388 Trowbridge, John 58 Trump, Donald 119, 390 Tylén, Kristian 402

Uexküll, Jakob von

429

103, 406

Vacherot, Étienne 417 f Varzi, Achille 128 f, 397 Veblen, Thorstein 404 Venn, John 16 Viola, Tullio 403, 417 f Voltaire, François de 424 Waal, Cornelis de 416 Wagner, Richard 338 Washington, George 277, 338 Wegener, Alfred 128, 185 f Weiss, Paul 64, 236, 403 Welby, Victoria 23, 26, 51, 59 f, 238, 258, 276, 305, 391, 405, 415 Wheeler, John A. 423 Wilson, Aaron B. 417 Wittgenstein, Ludwig 14 f, 73, 108, 215, 386, 389 Whewell, William 417 Wiles, Andrew 319 Wolff, Christian 263 Wright, Chauncey 44 Yorkston, James Zeman, Jay

400

390