Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition [1st ed. 2019] 978-3-030-25799-6, 978-3-030-25800-9

Table of contents :
Front Matter ....Pages i-xii
Front Matter ....Pages 1-1
Mutual Insights on Peirce and Husserl (Ahti-Veikko Pietarinen, Mohammad Shafiei, Frederik Stjernfelt)....Pages 3-15
Logical Construction and Phenomenological Reduction (Kuno Lorenz)....Pages 17-42
Thoughts, Things and Logical Guidance (Angelina Bobrova, Ahti-Veikko Pietarinen)....Pages 43-58
Front Matter ....Pages 59-59
Philosophy of Notation in the 19th Century. Peirce, Husserl, and All the Others on Inclusion and Assertion (Francesco Bellucci)....Pages 61-75
Symbolic Knowledge in Husserlian Pure Logic (Manuel Gustavo Isaac)....Pages 77-96
Peirce’s Existential Graphs as a Contribution to Transcendental Logic (Mohammad Shafiei)....Pages 97-122
Front Matter ....Pages 123-123
Husserl and Peirce and the Goals of Mathematics (Mirja Hartimo)....Pages 125-137
A Receding Parallelism: Husserl and Peirce from the Perspective of Logic of Probability (Carlos Lobo)....Pages 139-174
Front Matter ....Pages 175-175
On Peirce and Husserl on Intentionality (Yi Jiang)....Pages 177-184
On the Arising of the I in Peirce and Husserl (Susi Ferrarello)....Pages 185-197
Phaneroscopy and Theory of Signs as Theory of Cognition (Ahti-Veikko Pietarinen, Jelena Issajeva)....Pages 199-219

Citation preview

Logic, Epistemology, and the Unity of Science 46

Mohammad Shafiei Ahti-Veikko Pietarinen   Editors

Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition

Logic, Epistemology, and the Unity of Science Volume 46

Series Editor Shahid Rahman, University of Lille III, Villeneuve d’Ascq, France Managing Editor Nicolas Clerbout, Universidad de Valparaíso, Valparaíso, Chile Founding Editor John Symons, The University of Texas at El Paso, El Paso, TX, USA Editorial Board Jean Paul van Bendegem, Free University of Brussels, Belgium Johan van Benthem, University of Amsterdam, The Netherlands Jacques Dubucs, CNRS/Paris I, France Anne Fagot-Largeault, Collège de France, France Bas van Fraassen, Princeton University, USA Dov Gabbay, King’s College London, UK Tony Street, Divinity College, Cambridge, UK Graham Priest, CUNY, USA Gabriel Sandu, University of Helsinki, Finland Göran Sundholm, Universiteit Leiden, The Netherlands Heinrich Wansing, Ruhr-University Bochum, Germany Timothy Williamson, Oxford University, UK

Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light on basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity. For inquiries and submissions of proposals, authors can contact Christi Lue at [email protected].

More information about this series at http://www.springer.com/series/6936

Mohammad Shafiei Ahti-Veikko Pietarinen •

Editors

Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition

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Editors Mohammad Shafiei Department of Philosophy Shahid Beheshti University Tehran, Iran

Ahti-Veikko Pietarinen School of Humanities and Social Sciences Nazarbayev University Astana, Kazakhstan

ISSN 2214-9775 ISSN 2214-9783 (electronic) Logic, Epistemology, and the Unity of Science ISBN 978-3-030-25799-6 ISBN 978-3-030-25800-9 (eBook) https://doi.org/10.1007/978-3-030-25800-9 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The aim of the present book is to provide a further step into the paths less trodden in the scholarship of two prominent philosophers, Peirce and Husserl, and to bring these two fairly discordant temperaments into a creatively disruptive interplay. The proposed exercise to parallel Peirce and Husserl is hoped to help identify elements in the prevailing scholarship that have potential for a further systematic exploration of certain fundamental notions that are found both in Peirce’s and in Husserl’s writings, especially as concerns methods and logic of science, theory of knowledge and the role of the mind in these investigations. This can be done both by drawing a parallelism between their works and by identifying a number of differences and tensions. Both approaches can offer new insights for scholars to reorient their further explorations. Needless to say, most of those similarities, differences and tensions are the tasks that ultimately the readers and the future communities of investigators are invited to work out from the material provided at their disposal. The present volume collects eleven papers on these themes. It begins with two contributions particularly appropriate to set the agenda. An introductory piece “Mutual Insights on Peirce and Husserl”, written by the editors together with Frederik Stjernfelt, outlines some of the central historical and systematical themes arising out of the recent scholarship on Peirce and Husserl. Next, Kuno Lorenz’s contribution “Logical Construction and Phenomenological Reduction: Towards a Dialogical Reconstruction of Experience with Special Reference to Peircean and Husserlian Methods” consists of two parts, an account of “Historical Relations” around Pragmatism and Phenomenology followed by a treatment of “Systematic Issues” connected with the two methodologies involved. It proposes a dialogical framework from which one could develop mutual approaches of Peirce and Husserl as two and somewhat complementary perspectives to the issues encountered in foundational explorations of science and inquiry. In the next chapter, “Thoughts, Things and Logical Guidance”, Angelina Bobrova and Ahti-Veikko Pietarinen study Peirce’s notion of guiding principle of reason and its central role in his logic. The authors provide an analysis of the guiding principle and its evolution grounded in the primitive forms of the method of

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existential graphs. The chapter then contains some comparison between Peirce and Husserl as regards the status of logic in their philosophical methods. The next three chapters are dedicated to the philosophy of logic. Francesco Bellucci’s contribution entitled “Philosophy of Notation in the 19th Century. Peirce, Husserl, and all the Others on Inclusion and Assertion”, which pertains to the new and emerging area of the philosophy of notation, discusses the relevance of notation and its conceptual significance for logic and reasoning in the nineteenth century focusing on the work of the philosophers under consideration in our volume. The author discusses two important notational devices that were embedded in Husserl’s and Peirce’s notations, the sign of inclusion and the sign of assertion. In “Symbolic Knowledge in Husserlian Pure Logic”, Manuel Gustavo Isaac studies symbolic knowledge in Husserl’s philosophy and compares it stepwise with the conceptualizations offered by Peirce. The author develops his discussion by focusing on the question, “How can the subjective operating with symbols be justified in the process of obtaining objective contents of knowledge?” Mohammad Shafiei in “Peirce’s Existential Graphs as a Contribution to Transcendental Logic” studies some criteria required by a phenomenological logical framework and then shows how those criteria are fulfilled by existential graphs. According to Shafiei, Peirce’s existential graphs offer explanations of meaning which are neither truth functional nor inferential. Thus, existential graphs respect the Husserlian distinction between consequence level and truth level. The next two chapters concern the philosophy of mathematics. In “Husserl and Peirce and the Goals of Mathematics”, Mirja Hartimo discusses the aims of mathematics in both Peirce and Husserl. Hartimo pinpoints the common ideas of these philosophers in relation to the delimitation of mathematics. After discussing the main similarities, the authors elaborated an important difference. Hartimo explains that while for Husserl the goal of mathematics is to characterize definite manifolds, for Peirce it is to discover the real potential world as expressed by his conception of continuum. Carlos Lobo’s paper “A Receding Parallelism: Husserl and Peirce from the Perspective of Logic of Probability” concerns the foundations of the theory of probability on the basis of a parallelism between Peirce’s and Husserl’s ideas and guiding principles, a parallelism which according to the author goes beyond the determinate similarities and invites us to enlarge the general scope of such studies. In his thorough exploration, Lobo investigates the roots of the logic of probability focusing on the contributions of Peirce and Husserl. The next two chapters, “On Peirce and Husserl on Intentionality” by Yi Jiang and “On the Arising of the I in Peirce and Husserl” by Susi Ferrarello, involve the notion of intentionality and consciousness. The contribution of Jiang Yi elaborates Husserl’s notion of intentionality comparing it with the one of Peirce. The author argues that although the two philosophers had different motives from which the problem of intentionality arises, they shared common concerns of intentionality as the first state of consciousness.

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Ferrarello discusses how the ego arises within the lived experiences of the concrete human being. Ferrarello’s chapter provides a comparative examination of Husserl’s genetic phenomenology and Peirce’s category of secondness. The chapter compares Husserl’s notion of awakening of the ego with Peirce’s psychological notion of ego reaction. In contrast to Spiegelberg’s (1956: 170) claim according to which the “Heraclitean” picture of Peirce’s system is a “major obstacle to a full-scale comparison between the two phenomenologies”, Ferrarello argues that it is precisely this Heraclitean image of the soul that makes Peirce and Husserl’s systems, after all, so surprisingly similar. In the final chapter, Ahti-Veikko Pietarinen and Jelena Issajeva provide an extended glossary of the most central terms of Peirce’s theory of phaneroscopy, explaining key terms of Peirce’s theory from the viewpoint of the theory of cognition. The chapter shows how the theory of signs is influenced by phaneroscopy, the science of phenomenology that prepares ground for the sign-theoretic study of mind. The glossary serves as an aid to both Peirce’s theory of signs and its phenomenological underpinnings, illustrating the unique character of this early method for the theory of cognition. Tehran, Iran Astana, Kazakhstan

Mohammad Shafiei Ahti-Veikko Pietarinen

Acknowledgements

We thank the funding agencies of the projects 12786, PUT267 and PUT1305 (Academy of Finland and Estonian Research Council, “Diagrammatic Mind (DiaMind): Logical and Cognitive Aspects of Iconicity”, “Abduction in the Age of Fundamental Uncertainty”, PI Pietarinen); Russian Academic Excellence Project “5–100”; and also Iran’s National Elites Foundation (INEF) for the funding support of the first editor’s postdoctoral research at Shahid Beheshti University, during which time he also worked on the current volume. Our special expression of gratitude goes to Shahid Rahman for his support throughout the years that it took to bring the present volume into its final shape.

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Contents

Part I

Methods

1

Mutual Insights on Peirce and Husserl . . . . . . . . . . . . . . . . . . . . . . Ahti-Veikko Pietarinen, Mohammad Shafiei and Frederik Stjernfelt

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2

Logical Construction and Phenomenological Reduction . . . . . . . . . Kuno Lorenz

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Thoughts, Things and Logical Guidance . . . . . . . . . . . . . . . . . . . . . Angelina Bobrova and Ahti-Veikko Pietarinen

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Part II 4

Logic

Philosophy of Notation in the 19th Century. Peirce, Husserl, and All the Others on Inclusion and Assertion . . . . . . . . . . . . . . . . Francesco Bellucci

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Symbolic Knowledge in Husserlian Pure Logic . . . . . . . . . . . . . . . . Manuel Gustavo Isaac

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Peirce’s Existential Graphs as a Contribution to Transcendental Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohammad Shafiei

Part III

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Mathematics

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Husserl and Peirce and the Goals of Mathematics . . . . . . . . . . . . . 125 Mirja Hartimo

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A Receding Parallelism: Husserl and Peirce from the Perspective of Logic of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Carlos Lobo

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Part IV 9

Cognition, Consciousness and Intentionality

On Peirce and Husserl on Intentionality . . . . . . . . . . . . . . . . . . . . . 177 Yi Jiang

10 On the Arising of the I in Peirce and Husserl . . . . . . . . . . . . . . . . . 185 Susi Ferrarello 11 Phaneroscopy and Theory of Signs as Theory of Cognition . . . . . . 199 Ahti-Veikko Pietarinen and Jelena Issajeva

Part I

Methods

Chapter 1

Mutual Insights on Peirce and Husserl Ahti-Veikko Pietarinen, Mohammad Shafiei and Frederik Stjernfelt

What are the points of contact between Peirce’s and Husserl’s thoughts? Ever since the rather negative conclusions of Herbert Spiegelberg’s 1956 evaluation of the commonalities in Peirce’s and Husserl’s systems of thought, virtually no comprehensive studies have appeared on the mutual insights that could be obtained from the works of these two influential philosophers, despite the fact that some of their fundamental 1 ideas germinated under similar conditions, contexts, influences and predecessors. It is perhaps only the book Diagrammatology (Stjernfelt 2007), which mainly focused on the cognitive, philosophical and semiotic significance of Peirce’s diagrammatic logic, that referred extensively also to Husserl’s notions. Among those 2 one could highlight the notion of categorial intuition. The goal of Diagrammatology, however, was to open the discussion by pointing to a number of important similarities rather to arrive at any comprehensive, let alone conclusive, perspective that would 1 For example the recent book Essays on Husserl’s Logic and Philosophy of Mathematics (Centrone 2017) contains no chapter on Peirce and Husserl, and Centrone & Minari (2017) on Husserl and Schröder no mention on Schröder’s indebtedness to Peirce. 2 “kategoriale Anschauung” in German. This can be translated into “categorical intuition” as some Husserl scholars have chosen to do. However, we here follow the choice of those who, in accordance with Dorion Cairns’ suggestion in his Guide for Translating Husserl, translate “kategoriale” into “categorial” and reserve “categorical” for the German term “kategorisch”.

A.-V. Pietarinen (B) School of Humanities and Social Sciences, Nazarbayev University, Astana, Kazakhstan e-mail: [email protected] M. Shafiei Shahid Beheshti University, Tehran, Iran e-mail: [email protected] F. Stjernfelt Department of Communication, Aalborg University Copenhagen, AC Meyers Vænge 15, 2450 Copenhagen SV, Denmark e-mail: [email protected] © Springer Nature Switzerland AG 2019 M. Shafiei and A.-V. Pietarinen (eds.), Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition, Logic, Epistemology, and the Unity of Science 46, https://doi.org/10.1007/978-3-030-25800-9_1

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position the thoughts of the two thinkers according to their views on science, logic, knowledge or signs. The present volume is calculated to begin to fill those lacunae in the received scholarship.3 One of the reasons is probably that both Peirce and Husserl proved, over the first half of the 20th century, to become fountainheads of two very different traditions: Peirce originated pragmati(ci)sm, sem(e)iotics and phaneroscopy, Husserl that of phenomenology. Writing before the continental–analytic split eventually ossified, they might have become targets of a somewhat unfortunate and premature tagging along that split: Peirce as an ancestor of the analytic tradition and Husserl of the continental tradition. This simplification occludes many of the ideas, thoughts, and historical influences they both had in common. Both were philosophizing mathematicians, both wanted to gain a fundamental understanding of the validity of logical reasoning, and both of them were famously building their philosophies on a very principled stance against psychologism. And both of them were, in the medieval sense of the word, realists in philosophy. Another and perhaps a more fruitful distinction that can be drawn to aid an examination of the nature of the fundamental thoughts of a philosopher is that of Jaakko Hintikka’s generalization of the distinction between logic as a universal language and logic as a calculus—Lingua Universalis versus Calculus Ratiocinator, to use Leibniz’ terminology. Hintikka argued that the former leads to imprisonment within one universal means of expression; the dire implication is that it becomes impossible to investigate the world in any other way than via that language. Included in this conception is that semantics becomes ineffable and ultimately impossible to be formalized, as any attempt to capture one’s semantical relations is bound to be exercized in terms of using the very same language as one which is set out to be the target of the formalization. Only a purely formal syntax would remain attainable, and relativism threatens as no language-free vantage point is available from which to evaluate and criticise vital linguistic distinctions. Ultimately, no truth-definitions may be given from the points of views of the position which is suspended in that very language one is to evaluate. In Hintikka’s work, this distinction is seen to cut across the analytic–continental distinction: Frege, Russell, Wittgenstein, the young Carnap and Quine all fall in the Lingua Universalis category—as do, remarkably, some central figures such as Heidegger or Derrida typically regarded as continental philosophers. The calculus model, on the other hand, maintains that there is a plurality of perspectives and methodologies, including cognitive, semiotic, linguistic and logical tools and representations that are at one’s disposal in order to evaluate language and its meaning. It is this methodological pluralism that is consistent with realism: different approaches triangulate answers one hopes to gain when addressing the same objects of investigation. What is more, different representational tools may be used to analyze each other’s up and downsides, avoiding the circularity that bewitches the Univer3 The

secondary literature investigating both Peirce and Husserl is few and far between; we can single out Atkins (2018), Broekman (2010), Petrilli (2010) and Ransdell (1989) in addition to the references found in the individual chapters of the present volume.

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sal Language model. Notably, among the philosophers that belong to the calculus tradition one counts Boole, Schröder, Gödel, the later Carnap, and surely Hintikka himself—as well as those of Husserl and Peirce. Peirce’s semiotics is an open-ended collocation of a plurality of methods and conceptual approaches (just take the famous icon-index-symbol triad as representing three different ways of investigating the same object). In Husserl we find similar ideas along the lines of intentionality that may be presented in many different subtypes. A central relatedness between the two is their realism. Applied to universals, for instance, the implication is that each of them must, in their respective systems, possess an epistemology that addresses how it is possible to intend such universals while also coming into possession of knowledge about them. In Peirce, such a task is undertaken by diagrammatic reasoning. The semantics of a general symbol is taken to involve a ‘stylized’ icon of the object, and the diagram thus formed paves the way to reason about the general object involved in the diagram. A diagram token, which may be drawn, printed, sit on a table, on appear on a computer screen makes it possible, provided that a set of abstract reading directions are given, to gain a perceptual access to such general objects. This happens most conspicuously with geometrical diagrams. Once a diagram of a general conception is attained it is possible to reason about that object by manipulating and experimenting with the diagram according to certain rules of the system. Husserl, half a generation younger than Peirce, was influenced by the emerging critiques on the use of diagrams that we see emanating from the works of Pasch and Hilbert in Germany, and for such reasons was inclined to meet claims made in favour of the epistemological centrality of diagrams with a great deal of skepticism. Husserl would rather consider diagrams instrumentally, as auxiliary tools of philosophical theorising and mathematical proof. Still, he maintained the presence of a central method in his epistemology, and in that sense something that plays a similar role to that of Peircean diagrams, namely kategoriale Anschaaung—“categorial intuition”. Husserl famously claimed that knowledge could evolve only from direct acquaintance, not only regarding empirical objects, but also with general, categorial structures, such as numbers, grammar, logic or general concepts. The ability that we have in order to evaluate such objects is “categorial intuition”. Working with such an intuition by experimenting with its structure goes under the name of “eidetic variation”. It plays a similar role to Peirce’s idea of manipulation with diagrams.4 Thus what Husserl claims to be our competence to categorically intuit objects and structures also became a theoretical underpinning of the developments of the 20th century philosophy commonly regarded as “conceptual analysis”. Such an approach, of course, is common across broad sections of the ill-named continental and analytic communities alike. 4 In the book Diagrammatology (Stjernfelt 2007), Stjernfelt focused on the cognitive, philosophical

and semiotic significance of Peirce’s diagrammatic logic, and initiated the comparison with Husserl’s notions, particularly as found in his early phase of Logical Investigations (1900–01) and especially in relation to that of categorical intuition. The double review of Stjernfelt & Pietarinen (2015) also offers some pointers to the notions deserving further investigation see also Pietarinen (2016).

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A very important commonality here between the two is that “intuition” is no simple feat. No immediate, snapshot-like or direct access to the gates of Platonic heavens is to be expected. Rather, both Peirce and Husserl insist that intuition5 is logical investigation. It involves a process that takes the cognition of a general object as its input or premise, not as its result. The process of intuition itself is the laborious task of tracing the implications of that premiss, in the imagination or by following the figures and relationships drawn on a paper, depicted on a computer screen, or reproduced with the mind’s eye. A corollary common to Peirce and Husserl is that in this sense intuition addresses objects which—due to the fact that they are composite wholes— do not display all of their relational qualities on that representative medium. They possess depths of implicit structure which may—and only ever so often—become explicit by such variation, manipulation and experimentation. A closely related similarity between the two is derived from the fact that neither diagrams nor categorical intuitions can be simple objects in any sense of the word. A diagram is a whole composed of interrelated parts, which is the prerequisite for experimenting with those parts in order to gain insight into their relations, dynamics and composition. Similarly, eidetic variation presupposes that the category in question is not immediately evident but has a compositional complexity which can only be investigated through a procedure of variation. For both philosophers, this implies a mereology in their respective theories (even if neither of them knew or used this term which rather comes from Lesniewski). It is the doctrine of parts and wholes. Husserl investigated such a doctrine in his third Logical Investigation where he distinguished between two kinds of parts: genuine parts or moments and non-genuine parts. The latter may be “cut off” from their whole, such as a leg can be cut-off from a table, while the former is not so, as a surface cannot be cut off from the table without ceasing to be a table. This, in turn, gave rise to three ontological dependence relations: independence, one-sided dependence and mutual dependence. Husserl took these to be involved in all definitions and descriptions of any ontological importance. Importantly, Peirce’s definition of his three famous categories, Firstness, Secondness, and Thirdness is also resting upon a certain calculus of dependencies—witness his essential semiotic claims, already present in his 1885 “Algebra of Logic” paper, such as that diagrams necessitate the collaboration of icons, indices and symbols as parts of one and the same diagrammatic whole. To Husserl, the calculus of dependencies would be put to use in any ontological investigation, be it general, formal ontology or material, regional ontology as found in the base of every special science. Similarly, Peirce’s categories would furnish the ontological framework of all special sciences as already hinted at in his 1888 “Guess at the Riddle” and further developed in his later work on the classification of sciences. Thus, the development of a “dependence ontology”, both in its general and applied versions connecting to the special sciences, lie as a central project to be further developed in both philosophers. 5 We

take the liberty here to refer to both Peirce’s diagram manipulations and Husserl’s intuitional variations by the headline “intuition”. This is not in the least meant to neglect Peirce’s early refusal of intuition in its immediate, originary sense as a possible source of knowledge (Peirce 1869). Here, however, neither of the two philosophers need presupposing the presence of any revelatory idea of how conceptual knowledge may be achieved.

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We should not, however, expect to find any easy one-to-one translatability between Peirce’s and Husserl’s vocabularies. Nor, a fortiori, are we likely to find any marked affinity in the details in which they proposed to carry out the analysis in their respective philosophical systems. In order to grasp what the important similarities and dissimilarities between them may be, it is necessary to place oneself in the birds-eye perspective in order to gain an overview of the general ambitions of their respective philosophical thoughts. Indeed Peirce and Husserl make a highly attractive duo of original and unforgiving thinkers. When reading Husserl, a Peirce scholar is liable to undergo some experiences of déjà vus just as much as genuine puzzlement and alienation. A devoted Husserlian is likewise susceptible to find much in Peirce, especially in his phenomenology (phaneroscopy) and in the philosophy of mathematics, that could sharpen the focus of that side of the story.6 So what, if any, are the connections and contrasts between Peirce’s and Husserl’s thoughts? As Stjernfelt’s book had presented the case, one commonality is the motivation of both Peirce and Husserl to exploit diagrammatic features of cognition and thought in their philosophical quest for meaning and signification.7 Reasoning that is based on the activities associated with diagrammatic representations—namely experimentation on diagrams and making general observations on the outcomes of such activities—characterizes inquiry and its progress. As far as Peirce is concerned, the case is rather clear, but to show that Husserl was also a diagrammatic thinker would require two major bridges to be built: (1) to link categorial intuition to the general concept of diagrams, and (2) to see eidetic variation, which Husserl developed later in Ideas (1913), as an adequate counterpart to the idea of experimentation on diagrammatic relationships. What is Husserlian phenomenology, after all, one might ask here? In its early version, it seems to stand or fall with the consistency of the details of categorical intuition.8 Building new bridges would thus at the same time be a major undertaking in phenomenology as well as a source for novel contributions to the theory. For Husserl, categorical intuition was the faculty of human beings experiencing ideal and general entities, including mathematical entities, by “intuiting” them or being given them directly in consciousness. But what is idealization? One could take it as a form of abstraction from sense data or from particular cases (cf. Husserl’s 2nd Logical Investigation), but also something that often adds to abstraction by bringing 6 Peirce

famously vacillated in his terminology for that elementary task of philosophy which is to investigate the inventory of aspects of any possible phenomenon that may appear to any possible mind—just like Husserl bracketing reality assumptions during that investigation. In the years after 1900 he called it “phenomenology”, probably directly inspired by Husserl’s Logical Investigations, only some years later to replace it with notions like “phaneroscopy” or even “phanerochemy” (cf. e.g. Bellucci 2017). 7 Despite Husserl’s “official” Hilbertian stance that diagrams are mere auxiliary devices, Diagrammatology analyzed a number of Husserl’s examples of objects of categorial intutions in the Investigations to show that they shared important features with Peirce’s broader notion of diagrams. 8 We do not go into Husserl’s later development, during the 1910s, of so-called “transcendental phenomenology” reshaping his doctrine to begin with the assumption of a “transcendental ego”.

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in implicit theoretical commitments. It seems that idealization, or experiencing ideal entities by intuiting them and working on the basis of that intuition, adds to these mathematical or ontological entities—and this in turn is something which Peirce strived to explain in terms of his notion of theorematic deduction.9 The content differs from perceptually realized sensory content. But precisely how is that supposed to be achieved? To what degree do Husserl’s ideal entities agree with Peirce’s relational schemes, his icons and diagrams? Do they do the same type and amount of work? Husserl speaks about the “grasping” of essences, and as such those activities may be, first of all, related to abstraction, both in the prescissive and hypostatic senses of Peirce’s theory of abstraction. Experimentation, or Wesenschau, is then quite another matter. How do we grasp or hypostatize objects that are constituted in consciousness, rather than constructed as autonomous subjects for further inquiry? These autonomous subjects are introduced in Peirce’s theory by hypostatization, which is important in order to potentially and occasionally open up entirely new lines of inquiry. The idea that scientific discoveries largely consist in the ability of applying methods developed for the purposes of some other fields to a new area of inquiry forms the cornerstone of Peirce’s philosophy of science. “The higher places in science in the coming years are for those who succeed in adapting the methods of one science to the investigation of another”, he proclaimed in a lecture at Johns Hopkins University as early as in 1882 (W4: 378–82). This, perhaps more than ever before, holds true in modern sciences, which advance by cross-pollination of fundamentally diverse methods, approaches and figments of imagination abduced in the minds of scientists. It was then Peirce’s need to reply to William James’s ‘stream of consciousness’ proposal, namely the problem of fixing the transitory elements of thought, which explains some of Peirce’s renewed interest in abstraction in his later years and which made him further elaborate his theory of abstraction. Under this light, it becomes understandable that the constitutive approach of later “trasnscendental” Husserl could be closer in spirit to James’s radical empiricism than to Peirce’s later logical theory of abstraction. That Peirce would disagree with James on these matters is shown in his public reply to James’s question during one of the Lowell Lectures he held in 1903: “A Thought, being of the nature of a Representation, cannot be ‘present’ to consciousness. A thought is something that has to be enacted, and until it is enacted, its meaning has not been given, even to itself” (R 478). In the light of the Lingua Universalis versus Calculus Ratiocinator distinction, one sees that James would fall in the camp away from Peirce, because in James’s version of pragmatism (as well as Dewey’s, among others), it is actual action that constitutes the meaning of our expressions and concepts, hence relativizing meaning to actual practices. Peircean meaning, by contrast, always implies a continuum of not-yet-actualized potential— just like the continuous infinity of Husserllian eidetic variation. This shows, among other things, that pigeonholing Husserl’s thought is no easy matter. Since under Peirce’s calculus conception entities of mathematics, for example, would give rise to new kinds of objects, entia rationis, their logical analysis would 9 Cf

Stjernfelt (2014, Chap. 10).

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also need a novel type of second-order graphical (diagrammatic) logic to analyse them. In the same 1903 lecture series Peirce termed it the logic of potentials. In mathematics, hypostatic abstraction happens when turning “adjective elements of thought into substantive objects of thought” (R 462), when operations become subject of operations, and so on. Such abstraction “gives mathematics half its power”, he concludes two years later (EP2: 352, 1905, Issues of Pragmaticism; see also Pietarinen 2010). Today we would recognize much of what propels sciences as having to do with potentials of this kind: we find mathematical collections, physical notions of gauges, electric potentials, centres of gravity, or talk on market economies, persons, personal identities, ideas of self, free will, and so on, which may not actually exist in any simple, empiricist sense of the word, yet have been developed to function as important objects both of our thoughts and the evolution of scientific theories. The very act of making important observations necessarily involves an application of hypostatic abstraction. Peirce in fact went on to suggest even some proof-theoretic transformation rules for his ‘enactment theory of thoughts’, which he formalized in his second-order logic of potentials. He even notes that the resulting system remains to be “incompletely conceived” (R 508: Syllabus B.6). This has to be regarded as a pertinent observation, since as we now know, full second-order logic in which all mathematics can in principle be done is semantically incomplete. Yet its proof rules are categorical—the notion which was conceived by Peirce’s colleague and correspondent Edward V. Huntington and the name of which Oswald Veblen credits to Peirce’s student John Dewey (Mancosu et al. 2009, p. 326). Interestingly enough, categoricity (“definit”) has also been argued to be an important notion discernible in Husserl’s writings (Gray 2009, p. 206). While the mature Peirce had the fruits of abstraction ripening in his logic of potentials, Husserl in his later years cultivated what was distinctly a transcendental, or universal-empiricist, notion of logical reasoning. For Peirce, second-order logic of abstraction was ‘mathematics in a diagram’s clothing’, cutting across the thought to expose us of its essential structure. For the later Husserl, categorial intuition was the faculty of human beings experiencing ideal and general entities, including mathematical entities, by “intuiting” or presenting them directly in consciousness, and catching them in the process of thinking midstream. One further bit of history to enhance our historical awareness is that Peirce used the graphical logic of potentials to express sequences, including ordered sets and relations such as posteriority and anteriority. This is historically noteworthy because such sequences can be expressed by one-dimensional manifolds. This mathematical fact in turn becomes a highly relevant result because one-dimensional manifolds had been the topic of Peirce’s another Johns Hopkins student, Benjamin Ives Gilman, who wrote a paper about them in 1892 and published it in the first volume of The Mind. His paper soon caught Husserl’s interest, so much so that he embarked on studying the subject of manifolds himself (on this, see Hartimo 2007, p. 294), Hartimo 2018. The outcome was his theory of manifolds marking the beginning of his fascination in phenomenological affairs and playing a central role in his major statement of antipsychologism, the magisterial 300-pages introduction to the Logical Investigation.

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We can thus find an unbeaten path straddling from Peirce’s logical investigations to Husserl’s later thought. Husserl and Peirce surely also had some common contemporaries that influenced their thinking. Peirce attributed the idea that logical inference is iconic and diagrammatic to the German logician Friedrich Albert Lange’s posthumous Logische Studien (1877). Husserl also took good note of this book. Logische Studien, which has since passed into a virtual oblivion (but see Bellucci 2013), ought to be regarded as one of those important common origins to the kind of ‘diagrammatology’ practiced in the late 19th and early 20th centuries. The other mutual influence comes from Alexander Bain, whose book Logic (1870) both Husserl and Peirce carefully studied. Peirce, while deeply inspired in his pragmatism by Bain’s idea that belief is “that upon which a man is prepared to act”, was relatively dismissive about the details of Bain’s presentation of logical and scientific reasoning, but Husserl was much taken by the book’s accomplishments. Interestingly, Peirce and Husserl both refer to the same parts and topics of Bain’s book that discuss the nature of propositions. Husserl refers to Bain’s “Part first, Appendix B”, Hua XII: 372, and Peirce to “Logic, Pt. I, Bk. I, Chap. III, Sect. 27”. (See CP 2.551, where Peirce quotes from Bain 1870, pp. 109–110. The word “called” should be “named”.) Now Peirce was the likely author of the review on Bain’s Logic which was published in the Nation 11, 4 August 1870, 77–78. The reviewer attacks Bain for “ignoring all logical writings not English”, which is “the more reprehensible, as logic has by no means received its greatest development in England”. For Peirce, Bain nevertheless deserved the title of the grandfather of pragmatism, for reasons that are well known. Husserl’s 1891 “On the Logic of Signs (Semiotic)” should not go without mention, either, as it here that Husserl presents his early approach to meaning and signification. At this moment, Husserl had his review on the first volume of Ernst Schröder’s Algebra der Logic (1890) out, and his referencing and commenting upon Peirce as a precursor of what Schröder had presented testifies a recognition of what the origins of that algebraic way of thinking might have been, however dimly. Peirce was of course unhappy with Schröder’s distorted presentation of his original ideas and what he saw as ill-conceived attempts by Schröder to develop the dyadic algebra of logic into the directions in which it was unlikely to go. Peirce’s own remedies were poised to lead into the much improved and in a sense ultimate formulation of logic in the form of the graphical logic of existential graphs.10

10 The enigmatic “Remark on the Gamma Rims” (R 478), which concerns the modal and higherorder logic of the gamma part of the logic of existential graphs, incidentally contains an important criticism of Schröder in being an early recognition of the differences between the standard and nonstandard interpretations of second-order logic. Peirce takes Schröder to be an advocate of potentials that quantify over the “whole universe of logical possibility”. However, this made Peirce to conclude that his dyadic algebra of logic which had been “Schröder’s pet”, is “faulty from every point of view”. The following distinction between expressing something to be “true of the collection of all men” and something being “one of the possible collections of men” was not, Peirce presumes, something that his own algebra would be capable of drawing. Thus new logics and new signs and

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It is also clear that Husserl’s use of the term ‘sign’ now differs considerably from Peirce’s, and that we do not find in his later classifications for example anything corresponding well to Peirce’s important class of sign, namely icons. Some might argue that Husserl’s phenomenological semiotics resonates better with the Saussurean and structuralist accounts of meaning and signification, but Husserl’s continued investigation of signs in the 1st Logical Investigation certainly involves reflection upon both meaning and reference while the latter is all but bracketed by Saussureans. If signs are “public things” (Sokolowski 2002), that account is unlikely to agree well with Saussure’s mental character of the signification relation which has a clear bent in the direction of psychologism. On the other hand, one should recall what Husserl might have meant when he stated that communication is possible “if the listener also understands the speaker’s intention. He does this inasmuch as he takes the speaker to be a person, who is not merely uttering sounds but speaking to him, who is accompanying those sounds with certain meaning-giving acts” (the 1st Logical Investigation, Hua XIX, p. 39/1970a, p. 277). This, in its own terms, could anticipate modern pragmatics and especially that of Paul Grice’s influential theory of meaning, in which intentions to mean something are primary and the task of interpretation is to abduce those intended meanings. The matter is made all the more curious as it has recently turned out that Grice was strongly influenced by Peirce’s general theory of signs, even before writing his 1957 paper “Meaning” (Pietarinen and Bellucci 2015).11 Historically and biographically speaking, perhaps the most significant connection was set up by Christine Ladd-Franklin, also Peirce’s gifted student from Johns Hopkins University (Pietarinen 2013). When she worked in Europe in 1901–1902, she wrote to Peirce about having met many of the leading philosophers, psychologists, mathematicians and logicians of the time, among them Edmund Husserl (R L 237, Ladd-Franklin to Peirce, 22 November 1902). In her exchange with Peirce, Ladd-Franklin had complained, a year earlier, how Husserl had remained “unchallenged” by him so far (R L 237, 20 October 1901). What was Peirce about to do? To answer this we must ponder a little on what gave Peirce such a high estimate of “the distinguished” Husserl in one of his unpublished manuscripts (R 298). In fact, in an earlier draft the praise “distinguished” is in fact absent. Peirce writes: Yet how many writers of our generation (I will name Husserl, if I must instance one among the hurdles), after underscored promises that their discourse shall be of logic, and not of psychology, forthwith become intent upon these elements of the process of thinking which are special to the human mind, as we find it, to the utter neglect of those elements which equally belong to every mode of embodying the thought. (R 298, 1906, Phaneroscopy)9

Peirce here echoes a common criticism of the time, that the later parts of the Investigations fell prey to the psychologism so strongly attacked in its introduction. To notations are needed, which is the task for the Gamma graphs and rightly seen as “a labor for generations of analysts, not for one”. 11 The connection of that Husserl’s early paper on semiotics to Philosophy of Arithmetic has recently been studied in Byrne (2017). On the evolution of Husserl’s semiotics see Byrne (2018), among many others.

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what degree this is correct remains a matter of contention, but this passage conveys the gist of Peirce’s engagement with Ladd-Franklin’s challenge. The paper in which the previous quotation appears was delivered as his November 1906 address at the National Academy of Sciences meeting, entitled in full “Phaneroscopy, or Natural History of Signs, Relations, Categories, etc.: A method of investigating this subject expounded and illustrated”. The passage and its context reveals that Peirce was quite aware of the fact that Husserl, like most logicians of the time, portrayed himself to be anti-psychologistic about logic, but that Husserl did not practice what he preached. Husserl attempted to carry out his project, insofar as Peirce would interpret it, with reference to “those elements of the process of thinking” that are peculiar to the human mind. Peirce, however, did not approve that mathematical entities could be characterized by reference to any singular concept of the human mind and its peculiarities, and that the nature of mathematical reasoning, as far as it concerns creations of the mind must take into account any “sign-creatory” capable of uttering signs, in Peirce’s other words any “mode of embodying the thought” (R 318: 18, 1907). To push this historical story to its ultimate culmination, it is immediately after the Husserl-passage quoted above (R 298; CP 4.7) that Peirce proceeds to showcase his newly-founded logic of Existential Graphs (Roberts 1973; Peirce 2019). The attempt takes place within the broad context of his attempts at a proof of pragmaticism, which he by 1905 argued to be best exemplified by the full use of such graphs. He takes graphs to be the “moving pictures of thought” (Pietarinen 2006; Stjernfelt 2007), and believes them to provide precisely the medium needed for both (i) the proof of his general philosophy of pragmaticism to be delivered, and (ii) a logic that is independent of psychological accidents of human mind and conventional accidents of human speech. That (i) and (ii) jointly define the desiderata for nearly all that Peirce endeavours to do after 1905 is due to logical rather than the general (such as cognitive, visual or psychological) characteristics of the category of diagrammatic signs. A candid summary of Peirce’s achievements is found in his 1909 Christmas Day letter addressed to William James: Then my Algebra of Dyadic Relatives with which Schroeder fell in love and which is certainly very pretty, though he exaggerated its value (not so unjustly however as Whitehead’s positively silly objection to it). Then my Universal Algebra of Logic, which I consider the most convenient to use as a calculus of any, and though not particularly pretty, very powerful and pretty deep.12 Finally my triumph in that line, my Existential Graphs, by which all deduction is reduced to insertions and erasures, and in which there are no connecting signs except the writing of terms on the same area enclosed in an oval or parentheses (which will do instead of ovals) and also heavy lines to express the identity of the individual objects whose signs are connected by such lines. This ought to be the Logic of the Future. (R L 224, Dec 25, 1909, cf. Ma and Pietarinen 2018; Peirce 2019)

What was this new graphical method of logic calculated to accomplish? In the same letter, Peirce would plan what the agenda for the future research might look like, 12 This

passage could also be taken to imply that those who were commenting upon the state of logic as given in its explicitly algebraic outfit, such as represented e.g. by Schröder, would not get into the heart of the matter of what logical analysis consists of.

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which among others was “to show … that concepts are capable of such phaneroscopic analysis, or in common parlance ‘logical analysis’”.13 It behooves upon us to make our interpretations of these early thoughts along the lines that respect this fundamental alliance of phaneroscopy and logic, and to seek that alliance in those notational advantages that Peirce had every reason to be particularly proud of. Husserl, even if committed to investigating the phenomenological foundations of logic (as in the Erfahrung und Urteil volume), never, unlike Peirce, articulated logical representation systems to support his reasoning. Still, the insistence in both that logic and phenomenology should be developed in concert, that this connection possesses deep ontological implications, and that such implications are inherited by the special sciences—all of this, despite their many differences in detail, makes the two philosophers important head figures of a program that is deeply relevant in the face of psychologism reappearing in new guises of the 21st century. Acknowledgements Work of the first author was supported by the Estonian Research Council Research Grant PUT1305 (Abduction in the Age of Fundamental Uncertainty, Principal Investigator A.-V. Pietarinen).

References Atkins, R. (2018). Charles S. Peirce’s phenomenology: Analysis and consciousness. Oxford: Oxford University Press. Bain, A. (1870). Logic. London/New York: Longmans/D. Appleton & Co. Bellucci, F. (2013). Diagrammatic reasoning. Some notes on Charles S. Peirce and Friedrich A. Lange. History and Philosophy of Logic, 34(4), 293–305. Bellucci, F. (2017). Peirce on phaneroscopical analysis. Journal Phänomenologie, 44, 56–72. Broekman, J. M. (2010). Firstness and phenomenology—Peirce and Husserl on attitude change. In A. Wagner & J. Broekman (Eds.), Prospects of legal semiotics. Dordrecht: Springer. Byrne, T. (2017). Husserl’s early semiotics and number signs: Philosophy of arithmetic through the lens of “On the Logic of Signs (Semiotic)”. The Journal of the British Society for Phenomenology, 48(4), 287–303. Byrne, T. (2018). The evolution of Husserl’s semiotics: The logical investigations and its revisions (1901–1914). Bulletin d’analyse Phénoménologique, XIV, 5. Centrone, S. (ed.) (2017). Essays on Husserl’s logic and philosophy of mathematics. Dordrecht: Springer. Centrone, S., & Minari, P. (2017). Husserl and Schröder. In S. Centrone (Eds.), Essays on Husserl’s logic and philosophy of mathematics. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science) 384. Dordrecht: Springer. Gilman, B. I. (1892). On the properties of a one-dimensional manifold. Mind, 1, 518–526. 13 In 24 January 1910 Peirce writes that “The system of Existential Graphs, whose fidelity in the iconization of thought is such that I have found in it precious help in logico-phaneroscopic analyses, expresses this well” (R 646, pp. 41–42, emphasis added). What Peirce means by “this” is the property of duality, in other words the phenomenon of polarity, which shows up in the distinctions between positive and negative terms, in the separation of oddly and evenly enclosed areas of graphs by cuts, and in the opposite nature of the characters that for instance rhemas have. Such dualities have fundamentally phenomenological roots.

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Gray, J. (2009). Plato’s ghost: The modernist transformation of mathematics. Princeton: Princeton University Press. Hartimo, M. (2007). Towards completeness: Husserl on theories of manifolds 1890–1901. Synthese, 156, 281–310. Hartimo, M. (2018). Husserl on completeness, definitely. Synthese, 195(4), 1509–1527. Husserl, E. (1891). Besprechung von: E. Schröder, Vorlesungen über die Algebra der Logik, vol. I, Leipzig 1890, Göttingische gelehrte Anzeigen, pp. 243–270. [English translation in Husserl (1994), pp. 52–91]. Husserl, E. (1952). Ideen zu einer Reinen Phänomenologie und Phänomenologischen Philosophie Bd. II: Phänomenologische Untersuchungen zur Konstitution. Husserliana (Vol. IV). Den Haag: Martinus Nijhoff. Husserl, E. (1970a). Philosophie der Arithmetik. Mit ergänzenden Texten. HUA XII, ed. Lothar Eley. Den Haag: Martinjus Nijhoff. [Trans. Dallas Willard as Philosophy of arithmetic. Psychological and logical investigations with supplementary texts from 1887–1901, Collected Works X, New York: Springer, 2003]. Husserl, E. (1970b). Zur Logik der Zeichen (Semiotik). In Philosophie der Arithmetik. Mit ergänzenden Texten. HUA XII, ed. Lothar Eley, 340–373. Den Haag: Martinjus Nijhoff. [English translation in Husserl (1994), pp. 20–51]. Husserl, E. (1984). Logische Untersuchungen: Untersuchungen zur Phänomenologie und Theorie der Erkenntnis, HUA XIX, ed. Ursula Panzer. Dordrecht: Springer. [Trans. J. N. Findlay as Logical Investigations, New York: Routledge, 1970]. Husserl, E. (1994). Early writings in the philosophy of logic and mathematics. Collected Works V. [Trans. Dallas Willard. New York: Springer]. Lange, F. A. (1877). Logische Studien: Ein Beitrag Zur Neubegrundung Der Formalen Logik Und Der Erkenntnisstheorie. Iserlohn: J. Baedeker. Ma, M., & Pietarinen, A.-V. (2018). Peirce’s calculi for classical propositional logic. The Review of Symbolic Logic. https://doi.org/10.1017/S1755020318000187. Mancosu, P., Zach, R., & Badesa, C. (2009). The development of mathematical logic from Russell to Tarski, 1900–1935. In L. Haaparanta (Ed.), The development of modern logic (pp. 318–470). Oxford: Oxford University Press. Peirce, C. S. (1869). Some consequences of four incapacities. Journal of Speculative Philosophy, 2(4), 193–208. Peirce, C. S. (1931–1958). In C. Hartshorne, P. Weiss & A. W. Burks (Eds.), Collected papers of Charles Sanders Peirce (Vol. 8). Cambridge, MA: Harvard University Press. Cited as CP by volume and paragraph number. Peirce, C. S. (1967). Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin, “Annotated Catalogue of the Papers of Charles S. Peirce”, Amherst: University of Massachusetts Press, 1967, and in “The Peirce Papers: A supplementary catalogue”, Transactions of the C. S. Peirce Society 7 (1971): 37–57. Cited as R followed by manuscript number. Peirce, C. S. (1980). Writings of Charles S. Peirce: A Chronological Edition. 7 Vols., ed. by Moore, E. C., Kloesel, C. J. W. et al. Bloomington: Indiana University Press. Cited as W followed by volume and page number. Peirce, C. S. (1998). The essential peirce, selected philosophical writings, Vol. 2, (1893–1913) ed. Peirce Edition Project. Bloomington: Indiana University Press. Peirce, C. S. (2019). Logic of the future: Writings on existential graphs. Vols. 1–3, ed. by A.-V. Pietarinen, Peirceana. Mouton De Gruyter. Petrilli, S. (2010). Image and primary iconism: Peirce and Husserl. Semiotica, 2010(181), 263–274. Pietarinen, A.-V. (2006). Signs of logic: Peircan themes on the philosophy of language, games, and communication. Synthese Library 329 Dordrecht: Springer. Pietarinen, A.-V. (2010). Which philosophy of mathematics is pragmaticism? In M. Moore (Ed.), New essays on Peirce’s mathematical philosophy (pp. 59–79). Chicago: Open Court. Pietarinen, A.-V. (2013). Christine Ladd-Franklin’s and Victoria Welby’s correspondence with Charles Peirce. Semiotica, 196, 139–161.

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Pietarinen, A.-V. (2015). Peirce and diagrams: Peirce and Husserl in Professor Stjernfelt’s diagrammatology. Synthese, 192, 1073–1088. https://doi.org/10.1007/s11229-015-0658-8. Pietarinen, A.-V. (2016). Is there a general diagram concept? In S. Krämer & C. Ljundberg (Eds.), Thinking in diagrams: The semiotic basis of human cognition (pp. 121–138). Berlin: Mouton de Gruyter. Pietarinen, A.-V., & Bellucci, F. (2015). Paul Grice’s manuscript on ‘Peirce’s general theory of signs’. International Review of Pragmatics, 7, 128–175. Ransdell, J. (1989). Is Peirce a phenomenologist? Unpublished manuscript. Published in French translation by A. De Tienne, “Peirce est-il un phénoménologue?” Ètudes Phénoménologiques 9–10: 51–75. http://www.iupui.edu/~arisbe/menu/library/aboutcsp/ransdell/PHENOM.HTM. Roberts, D. D. (1973). The existential graphs of Charles S. Peirce. The Hague: Mouton. Sokolowski, R. (2002). Semiotics in Husserl’s Logical Investigations. In D. Zahavi & F. Stjernfelt (Eds.), One hundred years of phenomenology. Phaenomenologica (Series Founded by H. L. van Breda and Published Under the Auspices of the Husserl-Archives) 164. Dordrecht: Springer. Spiegelberg, H. (1956). Husserl’s and Peirce’s Phenomenologies: Coincidence or interaction. Philosophy and Phenomenological Research, 17(2), 164–185. Stjernfelt, F. (2007). Diagrammatology. An investigation on the borderlines of phenomenology, ontology, and semiotics. Synthese Library 336. Dordrecht: Springer. Stjernfelt, F. (2014). Natural propositions. The actuality of Peirce’s Doctrine of Dicisigns. Boston: Docent Press. Stjernfelt, F., & Pietarinen, A.-V. (2015). Peirce and diagrams: Two contributors to an actual discussion review each other. Synthese, 192(4), 1073–1088.

Chapter 2

Logical Construction and Phenomenological Reduction Towards a Dialogical Reconstruction of Experience with Special Reference to Peircean and Husserlian Methods Kuno Lorenz Abstract In Part I, an outline of the relations with respect to questions of method is made that hold between some of the most important philosophical movements in the first half of the 20th century and the Pragmatism of Peirce as well as the Phenomenology of Husserl. Attention is focused on methodological difficulties that arise when the difference of word and object including its specialization of mind and body gets questioned. Neither side can subsist in separation; signs and what they stand for depend on each other. It turns out that constructions in the spirit of Peirce as well as reductions in the spirit of Husserl depend on each other, too. Any attempt at reconstructing experience is bound to fail as long as the dialogical polarity of actions—in I-role an action while acting is executed, in You-role it is cognized—is not explicitly taken into account. In Part II, the dialogical organization of such a reconstruction is sketched, and it is shown how logical constructions and phenomenological reductions have to interact in order to achieve such a result. Yet, to do so would have been unlikely without the observation, due to Cavaillès, that there is a duality between objects (of procedures) and procedures (of making objects available) such that actions as procedures, i.e., actions while acting, rather than as objects show openly their dialogical polarity.

2.1 Historical Relations 2.1.1 Historical Setting of Pragmatism and Phenomenology Philosophy at the turn of the 20th century may be characterized by the appearance of two new kinds of fundamental opposition against classical tradition—besides the two previous ones, in the 19th century, already, initiated by K. Marx’ Materialism and S. Kierkegaard’s Existentialism—as represented by its culmination in German K. Lorenz (B) University of Saarland, Saarbrücken, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2019 M. Shafiei and A.-V. Pietarinen (eds.), Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition, Logic, Epistemology, and the Unity of Science 46, https://doi.org/10.1007/978-3-030-25800-9_2

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Idealism from I. Kant to G. F. Hegel. On the one hand, I refer to the uprising of Analytical Philosophy with its two branches of Logical Empiricism and Linguistic Phenomenalism which has its origin in their inception by B. Russell and G. E. Moore, respectively, and, on the other hand, to the foundation of that kind of Phenomenology that owes its set-up and influence to the work of E. Husserl. Analytical Philosophy reproaches traditional philosophy for its neglect to investigate into the qualifications of the linguistic means for treating matters of fact; hence its call for a ‘logical analysis of language’. The corresponding reproach of Husserl is contained in his slogan ‘Back to the things themselves!’ In both cases it is these methodological tenets that keep philosophical work in Analytical Philosophy and in Phenomenology going though they suffer from two respective presuppositions that undermine the very intentions of their implementation. In case you ask for a logical analysis of linguistic expressions you depend on standards in order to distinguish correct analyses from incorrect ones, and both Russell and Moore obviously believe that it is formal structure and material content of our world, respectively, that are, without interference of any, linguistic or other, means, accessible to be used as standards of judging the correctness of logical analyses of linguistic expressions. In case you call for a move to investigate into the nature of objects that you deal with rather than into the words used for such a purpose, you dispel any upcoming distrust of their qualification for disclosing this nature by holding the belief that training the ability of oneself and of others to report on evidences of introspection will enhance the reliability of verbal representation.1 Yet, at the time when both Analytical Philosophy and Phenomenology appeared on the scene, i.e. around 1900, another two philosophical movements that seemed to have nothing in common, were in full blossom, already. They were based on different methodological principles while fighting with philosophical tradition, that were less prone to doubt regarding their sound applicability, though only much later they became influential in the development of Analytical Philosophy and Phenomenology: It is the Pragmatism of C. S. Peirce—he himself, after 1905, called it ‘Pragmaticism’ in order to reduce the chance of misleading identifications with the Pragmatism of his friend W. James—as based on his Pragmatic Maxim for determining the meaning of linguistic expressions by non-linguistic activity,2 and the Historicism of W. Dilthey who asked to pay attention to the Hermeneutic Circle, because understanding a way of life by using verbal language for its articulation is a way of life by itself,3 i.e. 1 In

the Introduction to his “Logische Untersuchungen, II.1” (Logical Investigations I-II, London/New York 1970, repr. 2001), Husserl discusses extensively the difficulties involved, especially those of representation [Darstellung] and of communication [Übermittlung an andere], when turning from performing an act, e.g., of perceiving (an object), to performing an act of reflection on the original act, now having become an object and not being anymore a performance in the course of performing. 2 Contained in Peirce’s programmatic paper, “How to make our ideas clear” (cf. Collected Papers 5.402); it should be read together with the preceding abbreviation (5.400): “what a thing means is simply what habits [= schemata of action] it involves”. 3 Dilthey’s generalisation of a well-known observation that understanding a text is dependent on understanding its context and vice versa, is contained in various treatises where he uses ‘Erleben’ instead of ‘living’ and ‘Verstehen’ instead of ‘articulating living’, i.e., on both levels, opposite to

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mental activity will never be prior to just living, it is part and parcel of the ways of life. Peirce as well as Dilthey try to take account of the fact that making an experience and articulating an experience are dependent on each other, in the sense that, using the terminology of L. Wittgenstein in his “Tractatus”, the relation between world and language is an internal and not an external one. This means that both sides of the relation do exist only in terms of that relation and cannot be investigated separately, apart from giving an account of their relation. Both Peirce and Dilthey proceed with an attempt to fulfill this task by establishing a common ground for both world and language.4 Unfortunately, it was done only halfway, by reducing language and other sign-systems to verbal and other activities that use signs, but not the world of objects wholly to the world of actions dealing with objects, though, at least in Pragmatism, the Pragmatic Maxim might be read as envisaging such a radical step. We have arrived at a substitution of the difference between language and world – >word and object< in the terminology of W. V. O. Quine—by the difference of the world of signactions and the world of actions, yet with another world of objects beyond actions and sign-actions that, once more, are considered to exist independently from dealing with them, a reminder of I. Kant’s >Dinge an sichsuffering< an action rather than >doing< it; e.g., in “Der Aufbau der geschichtlichen Welt in den Geisteswissenschaften” (cf. Gesammelte Schriften VII, 79–188, p. 145f.) he writes: “…[das] Grundverhältnis von Erleben und Verstehen [ist ein] Verhältnis wechselseitiger Bedingtheit … Die Dunkelheit des Erlebnisses wird verdeutlicht, die Fehler, die aus der engeren Auffassung des Subjekts entspringen, werden verbessert, das Erlebnis selbst erweitert und vollendet im Verstehen anderer Personen, wie andererseits die andern Personen verstanden werden vermittels der eigenen Erlebnisse … So entsteht …eine Zirkulation von Erleben, Verstehen und Repräsentation der geistigen Welt in allgemeinen Begriffen”. 4 In classical philosophical tradition, and that includes authors like Peirce and Husserl as well, the term ‘language’ is often missing, because it is thought of as denoting the means of ordinary communication by natural language, only, under exclusion of the full power of language when used to conceptualize experience and to judge its adequacy by reasoning. Hence, on occasions like this one, you will regularly find ‘reason’ and its cognates instead of ‘language’, quite in line with the use of λO υ γoς in classical antiquity. 5 Cf. B. N. Rao, A Semiotic Reconstruction of Ryle’s Critique of Cartesianism, Berlin/New York 1994. The frequent terminological reference to Husserl’s phenomenological method by Carnap in his early work—“Der Raum” (1921) and “Der logische Aufbau der Welt” (1928)—that has

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asks primarily for programs of construction of objects, i.e., for poietic procedures on the level of iconic signs for objects that you deal with by any kind of activity,6 whereas Husserl’s method is primarily concerned with programs of description of objects of a special kind, i.e., with perceptual procedures of intuition that are self-reflective mental acts directed at universals that he calls ‘eide’.7 Now, Pragmatism and Historicism follow different strategies to overcome the remaining difference between the world of actions and the world of sign-actions. Basically, Pragmatism treats sign-actions as being just a kind of actions. This feature belongs to the consequences of identifying the meaning of a sign with the sequence of its interpretants, i.e., its effects on the mind, where, according to Peirce, on three levels of an emotional, an energetic, and an intellectual or logical interpretant, a sequence of ever more developed signs of one and the same object is generated, such that in practice each sequence will be finite, because it stops at some place and time. Hence, the arising last logical interpretant being the (linguistic) meaning of the sign, cannot be a sign anymore, but has, in accordance with the Pragmatic Maxim, to be identified with a habit, i.e., an action competence, with respect to the open set of possible dealings with the original object.8 Historicism follows the opposite procedure of treating each and every activity as a kind of language for the simple been investigated thoroughly by G. E. Rosado Haddock (The Young Carnap’s Unknown Master. Husserl’s Influence on Der Raum and Der logische Aufbau der Welt, Farnham 2008) did not develop into a lasting influence of Husserl within Logical Empiricism for the simple reason that Carnap, around 1930, exchanged his phenomenalism, i.e., rational reconstruction of experience on the basis of sentences that articulate >Ähnlichkeitserinnerungen< about >Elementarerlebnisse< , for a version of physicalism that starts with >Protokollsätze< about veridical empirical observations; this did happen, although M. Schlick, the spiritual head of the Vienna Circle, in his “Allgemeine Erkenntnislehre” (Frankfurt/M 2 1925) had outlined a way from >knowledge by acquaintance< to >knowledge by description< that avoids the hidden pitfalls in both Dilthey’s and Husserl’s procedures, i.e., presupposed respectively postulated transsubjectivity, by de facto following a version of Peirce’s Pragmatic Maxim. But, due to various methodological shortcomings, Schlick’s way was eventually overshadowed by the success of Carnap’s further work, cf. my paper “Erleben und Erkennen. Stadien der Erkenntnis bei Moritz Schlick” (Grazer Philosophische Studien 16/17 (1982), 271–282; in: K. Lorenz, Philosophische Variationen, Berlin/New York 2011, 153–164). 6 In the philosophy of science that follows the maxims of Logical Empiricism, such constructions, having passed at least some sort of logical analysis of language, are in general restricted to linguistic objects that are presented autonymously, a trivial way of iconic signification, rather than under inclusion of non-linguistic objects, as in the case of technical constructions where other devices like, e.g., drawings, are needed. 7 Cf. Husserl’s definition of ‘eidos’ in § 3 of “Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie I [Jahrbuch für Philosophie und phänomenologische Forschung 1, Halle 1913]/Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy I [Collected Works I, Den Haag 1976]”, and, in addition, to op.cit. §24, where Husserl refers to a >principle of all principles< that he identifies as being the primordial right of the given in intuition to count as true knowledge. 8 Cf. A Survey of Pragmatism, Collected Papers 5.467–469, p. 476; as this paper is only one of five versions of an unpublished article, being MS 318 in R. Robin’s Annotated Catalogue of the Papers of Charles S. Peirce (Amherst Mass. 1967), one should consult its partial publication in: The Essential Peirce. Selected Philosophical Writings [= Essential Papers] II (1893–1913) under the title ‘Pragmatism (1907)’, 398–433. It contains an extensive discussion—in Peircean terms: experiments of thinking—about an adequate analysis of the term ‘logical interpretant’ without restriction to its

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reason that it is bound to be understood. In each case the difference between the world of actions and the world of sign-actions lost its fundamental importance. However, another conspicuous difference between both procedures deserves closer scrutiny. Pragmatism, on the one hand, treats actions basically with respect to >doing< that is, by using the Aristotelian category of poieÙn a performance from the perspective of the person who executes the performance, being the agent in I-role, and not in the You-role of cognizing the performance that is the perspective of an agent with respect to >suffering< an action, i.e., by using the Aristotelian category of p©scein , the agent as >patientevents that make sense< (in German: Sinngeschehen), they befall us and are not produced, if producing is understood as considering an individual person to be the source of its activity with respect to its being meaningful. Only in reflecting on what a person is doing, this person will have a chance to identify the sense of what she or he is doing. Not by observation alone the sense of activities will be grasped, it needs participation, too. It is the You-role, the agent as patient while being active, second-order activities like observations of actions included, that stands in the focus of Dilthey’s investigations. Besides, a striking similarity to Husserl’s method of phenomenological description comes to the fore, though Dilthey and Husserl seem to apply it to totally different areas of >objectstheory of the transcendental constitution of an objective world< (§ 57), uses the concept of pairing Ego and alter ego (§ 51) such that within Ego alter ego constitutes itself and is turning Ego into a community of monads that is called ‘transscendental intersubjectivity’

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Buber did not only follow the two moves by Pragmatism and Historicism of treating sign-actions as actions and actions as sign-actions, respectively, in order to avoid the traditional cleavage between epistemology and ontology, but they even took the outstanding radical step of reducing objects to the open set of actions dealing with them. Besides, both Wittgenstein and Buber appear to be completely aware of the methodological implications that arise from distinguishing systematically I-role and You-role as soon as actions, respectively sign-actions, are performed. Wittgenstein is never just taking account of the I-role of acting without including the You-role as represented by the agents as patients. A language game is, strictly speaking, not an affair of one person only, it, rather, is a dialogical model of acquiring an action competence with >I< teaching and >You< learning, switching roles from repeating the action—performance in I-role—to imitating the action—performance in You-role— and vice versa, included.15 Due to the treatment of sign-actions as mere actions, there is no conceptual differentiation between linguistic and ordinary activity within a language game.16 Buber, likewise, gives equal weight to the You-role of receiving a sign-action (= understanding its performance) and to the I-role of sending a signaction (= giving its performance a meaning) with nature considered to be an agent and a patient as well. He even invokes a >dialogical principle< the essence of which is a plea for acknowledging the mutual dependency of I-role and You-role, such that the relation between I and You that in English translations of Buber’s writings is usually rendered by ‘I-Thou’, should be treated as being—in Wittgenstein’s terms— an internal one that has carefully to be distinguished from external relations that may obtain between objects of whatever kind, human individuals included.17 Buber (§ 56). This construction of his should meet the charge of having fallen victim to transcendental solipsism (§ 42), yet remains, nevertheless, dependent on assuming the identity of the world of alter ego with the world of Ego (§§ 47–49) as, in the eyes of Husserl, this identity is confirmed and evermore reconfirmed by daily life: Transcendental intersubjectivity is merely an intended one by the privileged >Urmonade< of the author of intentions (§§ 60–62), and cannot, by its very construction, account for transsubjectivity. 15 The terms ‘repetition’ and ‘imitation’ correspond conceptually to ‘assimilation’ and ‘accommodation’ within genetic epistemology devised by Piaget as an empirical theory of origin and development of the ability to acquire knowledge in childhood and adolescence of humans, cf. J. Piaget, Introduction à l’épistémologie génétique, I-III, Paris 1950. Cf. notes 10 and 11. 16 Wittgenstein says: “[…] eine Sprache vorstellen heißt, sich eine Lebensform vorstellen/[…] to imagine a language means to imagine a form of life”. Philosophische Untersuchungen/Philosophical Investigations. London, New York 1953, § 19. 17 Buber has published a collection of four essays together with a postscript “Zur Geschichte des dialogischen Prinzips” for the first time 1954 under the heading “Die Schriften über das dialogische Prinzip” that were reedited together with an additional postscript from 1957 to “Ich und Du”, as “Das dialogische Prinzip” (Heidelberg 1962). The rough sketch of the history of the dialogical principle contains a reference to “Daniel”, an early treatise of his that appeared 1913 in Leipzig [Berlin 2011], where he had made the distinction of two attitudes, a representing [vergegenwärtigenden] one that serves orientation, i.e., a knowing-how, and an objectifying [vergegenständlichenden] one that serves realization, i.e., a knowing-that, and Buber suggests that this distinction is his first attempt to articulate the difference between the two relations of ‘I-You’ and ‘I-It’ (cf. Das dialogische Prinzip, 4 1979, p. 309).

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contrasts the inseparable ‘I-You’-relation with the separable ‘I-It’-relation including the ‘I-He/She’-relation as its specialization. But, unfortunately, neither Wittgenstein nor Buber renounce the previous step of eliminating the difference between actions and sign-actions that had been taken, respectively, by Peirce in favor of actions, only, and by Dilthey in favor of signactions, only. Wittgenstein keeps to treating sign-actions basically as ordinary actions, conversely alike Buber who takes actions to be basically sign-actions. By, thus, barring an investigation into nature and origin of this distinction, they both forego the chance to develop the full power of the dialogical polarity that characterizes the realm of actions in general, and extends to a way of establishing the very difference between sign-actions (word) and actions (object). Of particular importance are the consequences of such investigations with respect to solving the paradox of man who is, on the one side, by bodily and mental activity, part of a common world, and who occupies, on the other side, during self-reflection becoming conscious of this embedment, a place opposite to the world around him that seems to be impenetrable from the outside.18 As a result, in the work of both Wittgenstein and Buber we are faced with simplifications of how signification works that runs counter an adequate understanding of the inseparability of thinking and acting, or, even more general, of theory and praxis beyond their merely conceptual, i.e. theoretical, separation. By treating sign-actions as ordinary actions that has led Wittgenstein to entrust language games as a piece of praxis with the theoretical task of acting as measuring-rods vis-à-vis the use of language without, hereby, acknowledging their role as full-fledged sign-actions on a par with ordinary verbal activity19 —they function, in the terminology of Peirce, as iconic presentations and not as symbolic representations of the world around us, language included—he is unable to differentiate between actions being used as signs and actions being sign-actions. In the opposite case of treating actions as sign-actions, Buber cannot anymore distinguish between the dialogical polarity of doing and suffering when performing an action, and the dialogical polarity of saying something by doing something, namely speaking, and understanding something by suffering something, namely listening; doing >means< saying, and suffering >means< understanding, praxis is turned into a case of theory. There is no chance anymore for somebody in You-role to suffer what somebody else in I-role does beyond understanding what the latter >said< by performing an action. Interaction, then, deteriorates into an essentially mental affair among the two participants as it would be in the case of exchanging speech acts where the action of uttering the sounds is restricted to just 18 H. Plessner refers to this paradox by attributing to man an >eccentric position< being man’s specific character that Plessner studies under the heading of >three fundamental laws of anthropology< in his “Die Stufen des Organischen und der Mensch” [1928] (= Helmuth Plessner. Gesammelte Schriften, I-X, ed. by G. Dux/O. Marquard/E. Ströker, vol. IV, Frankfurt/Main 1981, Chap. 7, pp. 360–415). 19 When Wittgenstein refers to grammar in stating: “Der Begriff der übersichtlichen Darstellung ist für uns von grundlegender Bedeutung. Er bezeichnet […] die Art, wie wir die Dinge sehen/The concept of a perspicuous representation is of fundamental significance for us. It earmarks […] the way we look at things” (Philosophical Investigations, § 122), he actually treats grammar to be part of the rules that regulate the ways of life and not as a self-contained system.

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serving as a carrier of its meaning, without any further functions a voice might be able to serve, e g., rhetorical ones like inciting or pacifying the other party, sometimes even unintentionally. Essentially two programs were drawn up for solving the ensuing problems: the program of naturalizing language and the program of symbolizing objects. Both are carried out in distinctly different ways. The one of naturalizing language appears basically in two competing versions, the behavioristic one as proposed by B. F. Skinner,20 or, in a logically purified form, by Quine with his stimulus-response-theory of language acquisition as part of a naturalized epistemology,21 and the mentalistic one as initiated most forcefully by N. Chomsky’s critique of Skinner22 and later on expanded by him in into a naturalistic notion of cognition that permits to defend Cartesianism without subscribing to the dualism of matter and mind.23 The program of symbolizing objects shows up, again basically, in two consecutive versions, a traditional one as worked out by E. Cassirer with the result of a theory of >symˆ´ bolic forms< that, in tune with the ancient Greek term ‘πραγμα’ (derived from ‘πραττειν’, ˆ i.e., intentionally doing something) for ‘object’, accounts for the role that objects play in human life,24 and a modern one that appears as a theory of culture in the frame-work of modern semiotics, paradigmatically displayed in the work of U. Eco.25 But neither program, be it the one of naturalization or the one of symbolization in any of their versions, is sufficient to establish a uniform account of the world of objects together with the ways of dealing with them by ordinary and verbal activities, the interactions among the agents included. The only way out is an attempt to combine the two procedures of Buber and Wittgenstein, that is, the treatment of actions as sign-actions, a case of symbolizing objects, and the treatment of sign-actions as actions, a case of naturalizing language, together with the dialogical context that both authors make use of systematically, in such a way that sign-actions will keep their character of being ordinary actions, and actions will show the character of being signs as well. The latter case occurs intentionally, when, e.g., an action is performed on stage thereby showing itself which amounts to having performed the sign-action of presentation in addition. The danger of falling prey to simplifications will be met by carefully paying attention to the dialogical polarity connected with performances of any kind of action, especially 20 Cf.

B. F. Skinner, Verbal Behavior, New York 1957.

21 Cf. W. V. O. Quine, Word and Object, Cambridge Mass. 1960; a comprehensive descriptive theory

of natural sign processes, but without Quine’s embedding of such an account in a theory of holistic evolution as envisaged by Peirce, had been presented earlier in: Ch. W. Morris, Signs, Language, and Behavior, New York 1946. 22 Cf. N. Chomsky, A Review of B. F. S. ‘s “Verbal Behavior”, Language 35 (1959), 26–58. 23 Cf. N. Chomsky, Cartesian Linguistics. A Chapter in the History of Rationalist Thought, New York/London 1966. 24 E. Cassirer, Philosophie der symbolischen Formen I-III, Berlin 1923–1929 [The Philosophy of Symbolic Forms I-III, New Haven Conn/London 1953–1957]. 25 Cf., among many others, Eco’s Trattato di semiotica generale, Milano 1975 [Theory of Semiotics, Bloomington Ind./London 1976] and Semiotica e filosofia del linguaggio, Torino 1984 [Semiotics and the Philosophy of Language, Bloomington Ind./London 1984].

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to those that are needed in an attempt to reconstruct experience that seems to be actually available, though without knowing how it came about, by constructing a possible model under the guidance of reducing the actual system of articulations by dispensing with available experiences that are irrelevant for the respective step of construction. In fact, the very difference of the I-role in doing and the You-role in suffering while performing an action, will become the gateway to the distinction between actions and sign-actions that eventually leads to a reconstruction of the common world of natural and cultural objects amidst individual and social activities that account for such an >objective< world being split into >subjective< perspectives. The chance to follow this way is dependent on paying attention to another crucial feature connected with speaking of objects and dealing with objects irrespective of their kind. It belongs to the consequences of the fact mentioned earlier and explicitly recognized from Peirce to Wittgenstein and from Dilthey to Buber that making an experience and articulating an experience are inseparably tied together. Whoever deals with or speaks of a well-determined (particular) object presupposes that, in principle, it may be identified to be the same object or a different one by anybody on other occasions, but everybody is likewise able to recognize that such a presupposition is in need of being justified, because misapprehensions abound. To secure the invariance of objects, their >samenessknownproving< their uniform availability. Actions in the role of experiencing objects by dealing with them, lead to stricto sensu >private< experiences, unless there is a way that makes other persons having like experiences of the same objects. In other words: How is it possible that reflection on one’s own activity is accessible to others? That it is possible cannot be questioned without entering a vicious circle, either on the level of actions, because reflecting on them makes use of sign-actions, usually verbal ones, or on the level of sign-actions, because in this case second-order sign-actions are used that lead to antinomies alike the one of the liar. Both Peirce and Dilthey evaded the issue by treating actions, respectively signactions, as invariant objects from the outset, whereas Russell and Husserl responded to the challenge by devising two methods of coping with the problem of transsubjective accessibility to objects: logical construction and, respectively, phenomenological reduction. Unfortunately, neither of them is sufficient to solve the problem generally. But a kind of partial solution may be attributed to either program. Russell succeeded in a certain sense with respect to actions in the active mode such that sign-actions follow suit, and Husserl in his turn succeeded in another sense with respect to sign-actions in the passive mode such that actions beyond acts of reflection will, as a means of scientific investigation, gain that kind of trustworthiness that is needed when empirical

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truths as well as schematic truths in formal sciences like Mathematics are at stake. Russell’s procedure of logical construction that was intended to justify his belief in logical atomism during a period of about twenty years (1905–1924), a position that he himself once called ‘analytical realism’,26 was based on the principle “Wherever possible, substitute constructions out of known entities for inferences to unknown entities”.27 The lowest level of known entities should consist of logically indivisible elements, logical >atomspure consciousnessbracketingepocheviewing universals< (in German: Wesensschau) as an area of eide—beyond what Husserl calls ‘material eide’,30 being the schematic forms of the formal sciences—that has to be discovered and investigated by phenomenology, is not anymore authored by an empirical ego, for this ego fell victim to phenomenological reduction, but by >the< pure ego, i.e. the pure presence of mental activity, to be called >the transcendental ego< being marked by instantaneity only as revealed by Husserl’s appeal to Kant’s dictum “Das ‘Ich denke’ muß alle meine Vorstellungen begleiten können”.31 Pure consciousness, being the >phenomenological residue< of ordinary consciousness, is staging the phenomena of the pure stream of experiences (reiner Erlebnisstrom) such that the ordinary world of objects that transcends consciousness is replaced by the feature of intentionality inherent in some but not all phenomena of consciousness. Now, the crucial division of act [directed at objects] and object [of an act] disguised by the terms ‘noesis’ and ‘noema’ is used by Husserl within the field of phenomenology, too. It is done without realizing that acts of reflection using sign-actions that are themselves dependent on general availability, introduce perspectives of phenomena in need of a principle of invariance in order to guarantee the identity of phenomena. The intended immediacy of phenomena that are displayed by the acts of reflection, Husserl’s >primordial right of the given in intuitionsynthetic< procedure by logical constructions, in order to get them fit for acting as a measuring rod of making and articulating experiences, there must exist an account of how what has happened, already, works. As a complement to logical constructions on the level of representation we need, on the other hand, an >analytic< procedure of deconstruction by phenomenological reductions, i.e., a rational procedure, on the level of objects that again is conceived dialogically and, together with logical construction, leads to a dialogical reconstruction of experience. Phenomenological reduction proceeds by using exactly the same actions and signactions that are gained as objects of logical constructions, in this case not as objects but as a means of dissolving the seemingly invariant objects of actual experience into individual perspectives that depend on the respective context of the objects of experience, i.e., the situations. But, these in turn have to be reconstructed with the help of the distinction between foreground and background in the field of experience such that experience of objects expands into an experience of both interior and exterior connections of objects. The fundamental duality of actions as objects and as a means that is well-known in mathematics, e.g., in two-dimensional projective geometry with respect to connection [of two points] and intersection [of two lines], and generalized as duality of >objet et opération< by J. Cavaillès,34 reappears in the dialogical approach to the task of reconstructing experience by logical construction and phenomenological reduction that, on the one hand, was initiated by Peirce with respect to sign-actions, and that, on the other hand, was not seen by Husserl as a way to substitute the mere claim that the realm of pure consciousness is transsubjectively accessible by the procedure that consists in counterbalancing phenomenologi34 Cf. G. Granger, Formal Thought and the Sciences of Man, Dordrecht 1983, Postface, 181–193; matter and manner in: N. Goodman, Ways of Worldmaking, Hassocks, Sussex 1978, play a similar role.

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cal reductions devoted to what is given and how, by logical constructions committed to what can be made and how, in order to provide for transsubjective availability. In order to grasp the importance of the condition that the elementary steps while deconstructing real experiences have to reappear as elementary items in the construction of ideal experiences, it is essential to realize that the actions within deconstruction and construction enjoy a different status: they occur as a means of deconstruction and as objects or results of construction. By way of caution, it should be added that the steps of construction will only be available on the sign level of (verbal) representation—that is the reason why the acts of construction count as objects—and, hence, without a guarantee that they are determined in an invariant way, independent of how they are represented. In order to provide for this feature, the corresponding steps of deconstruction on the ground level are needed, where the acts of construction have to reappear as a dialogically organized and, hence, at least I-You-invariant means of experience and not as objects of experience, though in a text like this one, deconstruction by reductions is, in turn, only represented and not actually performed. It belongs to the task of the reader to change the level of her or his activities by moving from the level of representation to the ground level and, in this way, to check by one’s own experience the adequacy of what is written here about the reconstruction of experience as a simultaneous affair of construction and reduction. Husserl was guided by the idea that real reductions of actual experiences exhibit ideal experiences, whereas Russell wanted to exhaust actual experiences by ideal constructions of possible experiences; Peirce, however, was aware of how praxis and theory of sign processes, i.e., semioses, might serve to intertwine reductions with constructions in order to understand what it means to make and to articulate experiences. In fact, Peirce observed that the classical distinction of ontology and epistemology together with the move from ‘what there is’ to ‘what is true’ being the leading questions of the respective sections of philosophy in the course of its development from antiquity via medieval times to enlightenment and modern times that had led philosophy into dealing with the methodological difficulties that accompany the difference of subject and object, does not apply simpliciter to the kind of questions that may be raised with respect to the realm of actions and sign-actions. To ascribe actions totally to subjects would neglect the internal and external conditions that have to be satisfied in order to produce a performance. It is action-competence, only, that may be treated as just being part of a subject, and not the performances as realizations of the competence. If, instead, actions would be considered to be nothing but a kind of objects, the concurrence of subjects, i.e., the agents as the source of their existence and themselves not merely objects, would be neglected. In this case, performances count as independent results of an action, the action >in statu agendithe same action once morein statu agendi< has lost its objecthood. You may observe that, while acting, being absorbed into one’s activity, no reference to it is possible, because there is no distance anymore >between< agent and her or his activity. Thus, the duality of actions as a means and as objects in the strict sense will be restored again. And it is performance of an action >in statu agendi< and not as an object, that exhibits the dialogical polarity of actions that was referred to earlier, already,35 using the objectival terminology of producing a token, i.e., an individual act, and imagining a type, i.e., a generic action, when the dialogic character of a performance had to be made explicit, in its primeval form of executing and cognizing an action. Executing and cognizing are not themselves full-fledged actions as it is the case with producing and imagining that are, like any object, dependent on activities that make them accessible, because there is no point in speaking of doing and suffering an execution or of doing and suffering a cognition. Or, rather, it will become the point of reflection, both to treat executions as if being objects by turning them into cognitions of actions associated with executions, and to treat cognitions as if being objects by turning them into executions of an action associated with cognitions. Hence, just the other way round, one should say that performing in (active) I-role is done by executing an action and performing in (passive) You-role is suffered by cognizing an action. These are the two dialogical sides of performing, and in order to avoid falling victim to an apparent alternative of following behaviorism or mentalism, it would be advantageous to use the technical terms of actualizing an action >in statu agendi< instead of executing it, and of schematizing an action >in statu agendi< instead of cognizing it. Neither actualizations nor schemata are ordinary objects, i.e., particulars, split into first-order tokens and second-order types, for the simple reason that actualizations are unique, unretrievable, and schemata simple, unduplicable, reference to them is out of question. They are codependent >immediate< entities, by means of execution as singular ingredients of an action in the case of actualization, and by means of cognition as the universal feature of an action in the case of schematization. Their immediacy is reflected by the fact that identity is not applicable to singularia, i.e., singular ingredients or actualizations,36 and diversity is not applicable to universalia, i.e., universal features or schemata.37 35 Cf.

note 10. pertinent slogan ‘no entity without identity’, under this title investigated by D. Gottlieb in: R. W. Shahan/C. Swoyer (eds.), Essays on the Philosophy of W. V. Quine, Norman, Oklahoma 1979, 79–96, that goes back to Quine’s claim that to be [an entity] means to be the value of a variable, in his early paper “Designation and Existence” (The Journal of Philosophy 36 (1939), 701–709) implies the denial of objecthood to singulars. 37 This is the background for Husserl’s banishment of material eide from the realm of eide that make up pure consciousness, because material eide are schematic forms, hence, special types that should 36 Quine’s

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Speaking, as we did in the beginning, in an objectival way of repeating and imitating an action as being the two dialogical roles that Wittgenstein and Buber had recognized independently from Peirce to be of systematical importance in making and articulating experience by means of actions and sign-actions, may now be refined by including the role of actions as a means >in statu agendi< that leads to a better understanding of repetition and imitation with respect to actions: The I-role of repeating derives from iterating singular actualizations, and the You-role of imitating derives from >seeing< these iterations as actualizations of >the same< universal schema.38 It is this dialogical polarity of actions as a means that explains how you do and suffer actions as objects and that will serve to solve the problem of how to combine logical construction and phenomenological reduction such that actions will be transsubjectively available. We have got to study how actions come about. They are neither objectively and actually present as individual acts nor subjectively and potentially as a generic act, i.e., as an action competence; they come about by having been learned, and it is irrelevant whether we ask for how to learn to perform an action or how to learn to acquire an action competence. Both questions ask for the same thing. For the process of learning we start with primary dialogical situations that are methodologically related to the procedure of language games as measuring rods with respect to any kind of actions, though without Wittgenstein’s renunciation of differentiating between actions and sign-actions, especially verbal ones. They qualify for judging whether, indeed, learning by repetition and imitation of performances takes place and not external training as in behavioristic approaches to learning processes, or internal knowledge transfer as in mentalistic approaches. The qualification is ensured by the crucial feature that a primary dialogical situation of learning to perform an action or to acquire an action competence, with the result of gaining actions as situation-bound objects, is at the same time using the action as a means by execution in I-role and cognition in You-role that, being, respectively, the pragmatic and the semiotic side of an action as an object, just take place and are not observable from the outside by a third party without making further steps of reflection that cause growing structural complexity of learning processes. In fact, the difference between action as an object and action as a means does not simply consist in two descriptions of the same matter, it originates from choosing the viewpoint towards the dialogical situation as a learning process. You look from the process of dialogically deconstructing a >real< action, being an individual act or a generic action, to the better not be called universals. Eide of pure consciousness, being universals that are not individuated into types, are claimed to be the same for all subjects. The term ‘schema’ is likewise equivocal, because besides being used as a synonym of ‘universal [as the characteristic of the indefinite series of indistinguishable singular actualizations]’ it is used instead of ‘type [of particular tokens]’ as well. 38 In the restricted contexts of sensory experience on the one hand and of truthful mental recognition on the other hand, Peirce—in “Some amazing mazes, fourth curiosity” (CP 6.318–6.343), 6.335, cf. 6.343—speaks of existents, when in executions an action exists (as a singular), and—in “What Pragmatism Is” (CP 5.411–5.437), 5.430—he speaks of reals, when in cognitions an action is understood (as a universal).

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process of constructing an >ideal< action as a prototype of real ones, dialogically by execution and cognition, or vice versa. We, thus, are able to observe how the initial stage of a dialogical reconstruction of experience exhibits the embryonic shape of the interdependence between sign [for an object] in the form of moves of deconstruction on the ground level, and object [of a sign] in the form of moves of construction on the level of representation. It can be shown, though not done in this paper, that even in historical perspective ontology outside the formal sciences (logic fighting psychologism in order to establish its independence from the non-formal sciences as far as formal truths are concerned, is a well-known special case) with its interdependent areas of mind and matter that evolved into the ongoing fight between psychologism, for some time under the label of rationalism, and physicalism, for some time under the label of empiricism, may be understood as an outcome of the interplay between epistemology in the framework of semiotics, and praxeology in the framework of pragmatics, both on the level of actions and on the higher level of sign-actions, a fortiori regarding objects of different logical levels. It will even be possible to arrive at an understanding of why both rationalism and empiricism show often a bipolar structure regarding the method of their scientific investigations: they proceed behavioristically or mentalistically in matters of psychology and the social as well as cultural sciences, and, respectively, by looking for efficient causes or for final causes in matters of physics and the other natural sciences, especially the life sciences. Back to the primary dialogical situation of two agents learning an action by repetition and imitation, we are faced with the fact that both agents partake in a common skill that is bound to the situation of learning common to both of them. In addition, we should note that neither the agent has the action fully at her or his disposal, because a perfect action competence would require the ability to produce a potentially infinite series of action-tokens with each token being an instance of the same action-type, which is obviously an impossibility. But even the acquisition of a restricted real action competence, that does include learning to identify the tokens (while being engaged in the learning process) as being tokens of the same type, e.g., climbing up a tree, is furthermore dependent on many conditions the situation of learning must satisfy in order to make learning possible, e.g., enduring bodily strength on the side of the agents, constant presence of a suitable tree, and innumerable others. And, still, there is not yet anything that would qualify such a primary learning situation as providing a prototype of, e.g., individual acts of climbing up a tree. By way of digression it should be remarked that, in case one of the agents is in the possession of a skill, already, the situation of learning by repetition and imitation loses its symmetry with respect to the two agents: one of them takes on the role of a teacher, the other becomes a student. But this additional feature is not sufficient to pass on a skill that B has learned from A, and a third agent C has learned from A, too, in such a way from B to C, that what C may learn from B coincides with what C has learned from A, because it is impossible to design a situation of learning for B and C in such a way that it will basically be either a situation of learning for A and B, or for A and C. Primary situations of learning are not comparative and, hence, not transitive: Transsubjective availability of actions without an everlasting

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first possessor of a skill who teaches, cannot be guaranteed. Hence, on this elementary level of learning, traditions including being aware of them—otherwise they would not be recognized as being traditions—cannot be established, either. In order to endow >real< primary dialogical situations, including the tokens and types of the actions that are learned by two agents in total dependence on the situation of learning, with a feature that permits to turn them into >ideal< primary dialogical situations that may count as the rock-bottom for constructing a prototype of the real actions, you have to change from >looking at< actions as objects to >looking at< actions as a means (unfortunately, the phrase ‘to look at’ implies, already, that it is objects that are looked at; it is obligatory to suppress those categories of grammar when describing the initial stage of reconstructing experience that presuppose the very distinctions that are described as being in need of introducing them). The process that leads from real actions in real learning situations to context-free ideal actions is one of deconstruction by phenomenological reductions in the spirit of Husserl. For this purpose, the agents as well as the situations together with all the conditions that the real situations have to satisfy, should not anymore be considered to be something separate from the actions. They all are treated as fused with each other that may be understood as the outcome of >bracketing< all the distinctions that make them appear as separate entities. Making distinctions within the primary dialogical situation is suspended rather than—on a logically higher level—exercising judgments on their existence as an indefinite number of matters of fact as Husserl had done, such that, for him, distinctions are kept, but as mere phenomena of consciousness, eventually of pure consciousness, only, that appear as the domain of study for phenomenologists. What, in our case, remains after having suspended the distinctions in the aforementioned way, such that learning an action counts as the only distinguishable feature of the primary dialogical situation being an otherwise undifferentiated object, is performing an action, not anymore as producing an action-token or as imagining an action-type, but in the active I-role as executing the action—Peirce says: it >exists< as an indefinite series of singular actualizations—and in the passive You-role as cognizing the action—Peirce says: it is >real< as a universal schema. The dialogically organized steps of phenomenological reduction consist in the appropriation of the real action by executing it, and in the detachment from the real action by cognizing it.39 Both actualizations and schema, being immediate in execution and cognition, respectively, are not proper objects, and should, therefore, better be called ‘quasiobjects’ that make up the ideal action >in statu nascendidoing< phenomenological reduction of real primary dialogical situations with respect to learning a real action by repetition and imitation, >suffers< 39 The reader should note that we do not follow Peirce’s usage of the terms ‘exist’ and ‘real’, cf. note 36; we rather follow the terminology that goes back to Plato by using ‘real’ when referring to particulars of whatever logical order, and ‘ideal’ when referring to what can be >seen< with the mental eye, only, i.e., a usage close to the one of Husserl, too, although it is unfortunate that Plato’s picture of calling first order particulars of a kind the imperfect copies of an idea, has lent support for thinking that ideas are objects as well, something that Aristotle, already, had criticized: Ideas being universals are means (of experience, but on the theoretical side, only, neglecting the singularia on the practical side), not objects.

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logical construction of ideal primary dialogical situations with respect to gaining the germ of an ideal prototype of the real action. To speak of a mere germ of an ideal prototype is due to the fact that the usual distinctions accompanying real learning situations are not yet available, e.g., the two agents appear as I-role and You-role of performances, only, and the distinction between individual act and general action is likewise dependent on further steps of reconstruction on the basis of singular actualizations (in I-role) and universal schema (in You-role). By phenomenological reduction we suspend not only the relations of consciousness with the external world as envisaged by Husserl, but each and every distinction effected by consciousness in the context of real primary dialogical situations as well, except those that are actually acquired: appropriation of an action and detachment from it. In an ideal primary dialogical situation there are neither action-tokens nor action-types but simply an action split into an indefinite series of singular actualizations and a universal schema bare of any separated context. Therefore, the two agents of the real situation that are learning the same action, are as yet indistinguishable in the ideal situation and have to be treated as an I-You-dyad of I-role and You-role in performing an action. The objectival view of producing (particular) action-tokens and imagining an (second-order particular) action-type in the real learning situation is changed into viewing at actions as a means that exhibits their dialogical polarity: In the ideal learning situation >there are< singular actualizations of an action by execution and universal schematization of an action by cognition. The traditional opposition of two realms of objects, of res extensa and res cogitans in Cartesianism as the objectival version and generalization of the original polarity of doing and suffering an action that we had discussed in the first part and used for starting the project of reconstructing experience with real primary dialogical situations for learning actions, has found its mirror image by referring to the basic duality of actions as objects and as a means, such that executing phenomenological reductions of the real learning situations appears as cognizing logical constructions of ideal learning situations. Reconstructions by using primary dialogical situations with respect to their dual character of being both objects (as real situations) and means (as ideal situations) may count as the prototype of reflective activity, be it ordinary activity or sign activity as in the special case of verbal activity.40 Again by way of caution, it is essential to distinguish between the object-meansduality of actions whatsoever, and the dialogical polarity of actions that does not apply when actions are treated as objects, i.e., as particular tokens—individual acts—of (second order) particular types—generic actions—related to each other by the wellknown operations of abstraction and concretion, unless the dialogical polarity is itself referred to as an object, such that the traditional categories of doing and suffering are understood as being objectival tools of recognizing actions to be one of the types of objects that are characterized by the ten different categories in Aristotle’s list.41 With respect to the special action of dialogical reconstruction of experience, being 40 With this concept of reflection the difficulties Husserl has discussed in his “Logische Untersuchungen”, cf. note 1 above, may be resolved. 41 Cf. Topica, 103b20–29.

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an action on the level of reflection that transcends the hierarchy of object-levels, because this hierarchy is itself an item that belongs to what is gained by reflection, the difference between reconstruction as an object and reconstruction as a means may be described as follows. As an object dialogical reconstruction is the twin procedure out of logical construction of an ideal object and phenomenological reduction of a real object being dependent on each other, because it comes about, on the one hand, by constructing possible experience, i.e., an experience that may be made, in using sign-actions as a means—their execution and cognition on the level of theoretical representation–, and, on the other hand, by deconstructing actual experience, i.e., an experience that is articulated, in using ordinary actions as a means—their execution and cognition on the level of practical activity–; dialogical reconstruction as a means, however, is simply cognizing logical constructions while executing phenomenological reductions. In this way, paying attention to the difference between reconstruction as a means and reconstruction as an object clarifies that, on the side of being a means, it turns a mere matter-of-fact experience of real objects into a comprehended experience, whereas, on the side of being an object, it takes place as a practical deconstruction of real objects that is dependent on being accessible by (deictic) sign-actions as a means— with respect to their cognition they appear in Husserl’s program under the label of >intentionality of consciousnessneurophilosophy< (P.S. Churchland) being the hybrid child of cognitive science and neuroscience.

2.2.2 Further Steps of Reflection by Following a Rule of Self-Similarity in Order to Cope with the Issue of How Making and Articulating Experience Are Intertwined The importance of distinguishing the two sides of reconstruction will become evident as soon as actions are to be released from being bound to the primary dialogic situations where they have been learned by two agents who alternate in taking on I-role and You-role, such that an arbitrary third agent will be able >from the outside< to identify the performances of either agent as being, indeed, performances of >the same< action. Hence, the next step of reconstructing experience on the way to a transsubjective experience asks for a transformation of the internal identity of actions, their local I-You-invariance—they are the same for just the two agents in

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the primary learning situation—into an external identity of actions, their general IYou-invariance, by introducing additional third agents exposed to primary learning situations being objects that have to be made accessible by actions of dealing with a primary action as it is learned in the primary learning situation. Of course, learning such an action of dealing with an action by its execution and cognition on the side of being a means to experience the action that is dealt with as an object (rather than to experience it by actually performing it) will be a more complex affair than in the primary case where executing and cognizing the primary action on the side of being a means is nothing but the other side, already, of an appropriation of the primary action and, respectively, of the detachment from it as an object, though only for the two primary agents, i.e., locally, and not yet, globally, for anybody. A further step of reflection by devising secondary dialogical situations for learning secondary actions of dealing with primary actions is asked for, such that these secondary actions may be used to establish different (subjective) perspectives of (objectively) the same primary action. We know, already, that primary situations of learning are not comparative. Hence, it is impossible to work with just one third agent to be confronted with many primary learning situations of the same action, because a concept of sameness of actions across different primary learning situations for them cannot be introduced. In order to achieve general I-You-invariance of actions secondary learning situations have to be set up by confronting arbitrary outsiders with just one primary learning situation such that the original agents in the role of an outsider are included. A secondary dialogical situation, therefore, has to consist of a primary dialogical situation of two agents learning an action enlarged by a third agent—the original agents as special cases of outsiders have to be included—who is learning an action of dealing with the original action by taking a two-fold external perspective towards the primary I-You-dyad, a secondary I-role towards the primary You-role and a secondary You-role towards the primary I-role. Of course, learning to view the primary learning situation from an external perspective includes internal perspectives by entering two new primary dialogical situations with either of the two original agents that yield variants of the primary action, because only one of the two roles coincides with one of the two roles of the primary action. The three agents in the role of outsiders who develop external perspectives towards the primary learning situation and its variants, acquire the ability both to change the I-role of executing the primary action (in either of its three variants) into the You-role of cognizing an action of >participating< in the primary action, and to change the You-role of cognizing the primary action into the I-role of executing an action of >observing< the primary action. We, thus, get two types of dealings with the original action, I-perspectives in the participation case by >cognizing the (primary) executionsexecuting the (primary) cognitionsindexical< – phrased paradoxically: ‘executing the primary action is cognized’—instead of pragmatically universal when considered to be a mere (secondary) action; in case of an aspect (primary You-role and secondary I-role!) such an action appears with respect to executing the action of cognizing the primary action as semiotically universal or >iconic< – phrased paradoxically: ‘cognizing the primary action is executed’—instead of pragmatically singular. No such differentiation happens, neither with respect to the execution of a phase nor with respect to the cognition of an aspect. They both remain on the pragmatical level. An execution of a phase, as it concerns the I-role of participating in the primary action (or one of its two variants), remains an execution of the primary action in an indirect way, mediated by the phase, such that, after the next step of reflection that turns executions of phases into cognitions of poietic actions vis-à-vis the primary action, these poietic actions contribute to the internal structuring of the corresponding primary action by determining parts (= the whole out of the singular ingredients of the mediating phase action) of the primary action; correspondingly, the cognition of an aspect, as it concerns the You-role of observing the primary action (or one of its two variants), remains the cognition of the primary action in an indirect way, mediated by the aspect such that, after the next step of reflection that turns cognitions of aspects into executions of perceptual actions vis-à-vis the primary action, these perceptual actions contribute to the external structuring of the corresponding primary action by being determined by properties (= the universal feature of the mediating aspect action) of the primary action. With the split, of cognitions concerning phases and of executions concerning aspects, into two levels, a pragmatic and a semiotic one, due to the second step of reflection, the distinction between actions as ordinary actions and actions functioning as signs, but not yet as full-fledged sign-actions, belongs to the items of experience that may have found a dialogical reconstruction by treating logical construction and phenomenological reduction as mutually dependent procedures. The agents, by learning to play the two secondary roles beyond the two primary roles, have, in traditional terminology, become >conscious< of their executions and cognitions. No wonder, then, that a way is cleared to attain the transsubjective availability of actions that was one of the problems to be solved when moving from real dialogical situations to ideal dialogical situations as dialogical reconstruction of experience by putting together phenomenological reduction and logical construction. We have reached a situation where the primary action, from being an internal object (for the two primary agents), only, that is guaranteed by the internal I-You-invariance of the real as well as ideal primary dialogical situation, can be turned into an external object that may be appropriated by phase actions and from which one may detach oneself

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by aspect actions. Objectification comes about by the identification of >all< dealings with the primary action with respect to their universal cognitions, i.e., as aspects, together with the summation of >all< dealings with the primary action with respect to their singular executions, i.e., as phases. Of course, a real primary action as an object will coincide to a certain degree, only, with its objectival reconstruction as an ideal primary action that consists out of the invariant of its aspects, its >formmatterall< aspects available, nor >all< phases, and the real agents will never be exhausted by their dialogical roles as they appear in the course of making steps of reflection while being engaged in the process of dialogical reconstruction. Learning both types of dealings with the primary action, phases and aspects, in a real secondary dialogical situation takes place as an affair of a third agent C with either one of the two original agents A and B, such that all three agents will eventually dispose of two further roles, a secondary I-role vis-à-vis the primary You-role and a secondary You-role vis-à-vis the primary I-role. Then, by executing phenomenological reduction of the real secondary situation you cognize the logical construction of an ideal secondary dialogical situation where, instead of real agents, only their roles occur: Besides the primary dialogical roles—those deriving from A and B lead to the primary action, the other two combinations, A and C as well as B and C, belong to mere variants of the primary action, as explained above—there are two secondary dialogical roles, connected with phases and aspects, that occur in secondary I-You-dyads where, in the case of a phase action, the primary dyad itself is replaced by the secondary dyad of primary I-role vis-à-vis secondary You-role, and, in the case of an aspect action, the primary dyad is replaced by the secondary dyad of primary You-role vis-à-vis secondary I-role. It is easy to recognize that in the first case, where the primary I-role, due to the loss of its partner, has to play the primary You-role, too, the primary You is internalized by the primary ego as >alter egoEgo< appears in I-and-You-role. In the second case, however, where the primary You-role is deprived of its co-player, because the primary I-role changed into the secondary I-role, the primary You is externalized by the primary ego as >Alter< and appears vis-à-vis the secondary Irole, in He/She-role. With the ability of playing the He/She-role in addition to the You-role an agent has done a step towards exercising self-distance (You as He/She, too), and, correspondingly, by being able to play the I-and-You-role in addition to the I-role, a step is done towards self-appropriation (I as I-and-You, too). If an agent forgets about the primary You-role by remaining in He/She-role, only, he follows a path towards a version of self-estrangement—a loss of the ability to show sympathy for the other–, if, however, he forgets about the primary I-role by remaining in I-andYou-role, only, he is on the way developing a kind of self-consciousness—a loss of the ability to show respect for the other. Universalizing the I-role by dropping the primary You-role leads to permanent self-appropriation, whereas objectifying the You-role by dropping the primary I-role leads to permanent self-distance. As generating selfdistance counteracts self-appropriation and vice versa, both universalization of Ego and objectification of Alter cannot stand side by side, either of them disavows the

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all-pervading dialogic character of our individual and social life in a common world split into different perspectives. Taking up the example of climbing up a tree, a phase action of participating in climbing up a tree might be in I-perspective the action of grasping a branch of the tree (eventually the basis for identifying the motor area of the brain); it will, after further steps of reconstruction, lead to the stipulation of calling the branch a part of the tree: trees as appropriated by phase actions get gradually equipped with an internal structure by turning each one of them as well as any group of trees, into wholes out of parts. The same action of grasping a branch of the tree may also be treated in You-perspective (eventually the basis for identifying the sensory area of the brain) to be an aspect-action of observing climbing up a tree; in this case, again after further steps of reconstruction, the tree appears as a particular unit with the property of being branched: trees as detached by aspect actions get gradually equipped with an external structure by turning them into particular units with properties they own.42 Phases and aspects as they have just been described, occur in their semiotic function; as mere actions, however, described with respect to their pragmatic function, they are actions in their own right, e.g., grasping a branch of the tree is to be treated as an action independent of any semiotic relation with climbing up a tree. Of course, the action of grasping a branch of the tree may enter all kinds of pragmatic relations with other objects, e.g. the instrumental relation as one of the causes that effects a performance of climbing up the tree. Dialogical reconstruction of experience that had been initiated as a, hopefully, more satisfactory answer than historically prior ones to the discovery that commonness of experience is a conviction without foundation—the Cartesian doubt—in need of being regained as a trustworthy conviction by procedures that are common by way of their introduction, is bound to go further ahead beyond primary and secondary dialogical situations. It is done by a hierarchically ordered sequence of steps of reflection that follow a rule of self-similarity which means that the cognition of an action on a certain level of reflection as well as an execution of an action on that level of reflection are turned, respectively, into an execution of an action on the next level of reflection (e.g., the cognition of a primary action into an execution of an aspect of it on the secondary level), and into the cognition of an action on that next level (e.g., an execution of a primary action into the cognition of a phase of it on the secondary level). This rule serves, on each level, as a procedure of objectifying the actions that are introduced, both, as a means of phenomenological reduction (by singular appropriation of objects and universal detachment from them, the way of their being objects of experience), and, at the same time, as quasi-objects of logical construction (out of the singulars of appropriation by summation and the universals of detachment by identification) in the preceding step of reflection. 42 After certain terminological adjustments it can be shown that the language of parts and wholes (out of parts) is equivalent with the language of objects and properties (of objects), cf. K. Lorenz, On the Relation between the Partition of a Whole into Parts and the Attribution of Properties to an Object, Studia Logica 36 (1977), 351–369 [reprinted in: K. Lorenz, Logic, Language and Method (note 20), 20–32].

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In this way, tertiary dialogical situations vis-à-vis the primary action, if used with respect to aspects and phases as secondary actions on their semiotic level—on their pragmatic level they permit to introduce both perceptual actions and poietic actions, as indicated above, already–, lead, with respect to aspects, to cognitions of iconic sign-actions, which means that while executing an observation of the primary action you cognize an iconic sign-action, and as, in this case, cognizing is a way of theoretical mediation by articulating the primary action, we are confronted with passing on theoretical experience that is gained by perceptual actions. With respect to phases, tertiary dialogical situations lead to executions of indexical partial actions, which means that while cognizing a participation in the primary action I execute an indexical partial action, and as, in this case, executing is a way of practical mediation by showing the primary action, we are confronted with passing on practical experience that is gained by poietic actions. Now, by a further step of reflection with respect to both executing and cognizing articulations, i.e., with respect to articulation pragmatically, as a mere action, and with respect to articulation semiotically, as a designation, two procedures are set going. On the one hand, executing an articulation on the pragmatic level is turned into cognizing a reception of signs, e.g., hearing a verbal articulation, and cognizing an articulation on the pragmatic level is turned into executing a production of signs, e.g., uttering a verbal articulation; on the other hand, executing a designation is turned into cognizing (an act of) signifying the primary action, and cognizing a designation is turned into executing (an act of) communicating the primary action.43 As with each step of reflection the previous action as a means is turned into an object, it is important to realize that with such an objectification the real dialogical situations of learning an action induce an individuation of these actions as objects that is beyond the scope of gaining logical constructions by phenomenological reductions. Primary actions as (ideal) objects had been introduced as units out of a universal as the result of identifying the (universal) cognitions of its aspects and the sum of singulars being the executions of its phases, in short: as the invariant of its aspects together with the whole out of its phases. But, a real primary action being an action type (generic action) that is usually considered to be an action competence, a mental entity, together with an indefinite sequence of action tokens (individual acts) as the (first order particular) instances of the (second order particular) action type that are usually called performances of the action being physical entities, may well occur as a different type-token-entity if different grainings of actions are taken into account, e.g. one performance of walking may be an individual whole out of many steps or out of few steps. Hence, the ideal primary action (and the consecutive ones) as an object should be treated as participating in the specific individuation of the real primary action as a type of tokens. Of course, particular objects of other categories but actions are included in the process of a dialogical reconstruction of experiencing 43 For further details, especially those that are concerned with procedures that yield symbolic articu-

lations out of iconic ones by rules of translations for them, and comprehensive practical mediations out of indexical partial actions by rules of construction for them, the reader may consult my paper ‘Pragmatic and semiotic prerequisites for predication’ (cf. note 11).

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them, as they may be constituted by actions of dealing with them in a Peircean fashion. The only difference: the process of reconstruction starts with the secondary actions of phases, i.e., appropriations of particulars, and aspects, i.e., detachments from particulars, instead of primary ones that are not available. With these additional features in mind, we may, finally, conclude that, indeed, the process of dialogically reconstructing experience by phenomenological reduction and logical construction demonstrates that making experiences and articulating experiences are two sides of the same coin. We have learned that phenomenological reduction of a real particular implies two steps, the step of appropriation of the particular by executing a phase action and the step of detachment from the particular by cognizing an aspect action: You are actualizing and schematizing the particular. The step of appropriation leads to making an experience, the step of detachment leads to articulating an experience. Appropriation takes place by >dissolving< the particular into singular executions of phases such that the cognitions of the respective phases appear as schematizations of generated partitions (parts are the means of poietic actions vis-à-vis the particular) of the particular. In this way, the logical construction of the ideal particular with respect to its matter, is, if cognized, (theoretically) understood as the whole out of the actualizations of its phases. The real particular, considered to be given by (subjective) sensation, has transsubjectively been reconstructed on the pragmatic level, and is, hence, pragmatically stabilized. Detachment from the particular, however, takes place by >enveloping< the particular in universal cognitions of aspects such that the executions of the respective aspects appear as actualizations of perceived distinctions (properties are the means of perceptual actions vis-à-vis the particular) of the particular. In this case, the logical construction of the ideal particular with respect to its form, is, if executed, (practically) understood as the identification of the schematizations of its aspects. The real particular, considered to be grasped by (subjective) intellection, has transsubjectively been reconstructed on the semiotic level, and is, hence, semiotically accessible.

Chapter 3

Thoughts, Things and Logical Guidance Angelina Bobrova and Ahti-Veikko Pietarinen

Abstract Peirce developed the theory of reasoning as a preferred instrument of the logical analysis of thoughts, while Husserl’s phenomenology took a turn to things we think about. The stark contrast between Peirce phaneroscopy and Husserl’s phenomenology shows up in Peirce’s insight that reasoning is guided by the leading or guiding principle of reason we form in imagination about the logical power of reasoning. Peirce further believed that the analysis of the processes of reasoning in their smallest movements is best accomplished by the methods of existential graphs. We provide an analysis of the guiding principle and its evolution grounded in the primitive forms of that method. We show that there is an evolution of the logical constant of negation from the paradisiacal implication (the scroll) and the blot, and explain the latter in terms of Peirce’s preferred interpretation as unscriptibility. These points establish Peirce’s logico-phaneroscopical analysis of reasoning having advantages not only over Husserl’s phenomenology but also over contemporary studies that have taken keen interest in cognitive aspects of reasoning and inference. Keywords Reasoning · Thought · Thinking · Guiding principle · Peirce · Husserl · Method of graphs · Phaneroscopy · Phenomenology · Paradisiacal implication · Scroll · Blot · Scriptibility

“Do not confound thought with thinking.” Peirce, R 499(s). A. Bobrova Russian State University for the Humanities, Moscow, Russia A.-V. Pietarinen (B) Nazarbayev University, Astana, Kazakhstan e-mail: [email protected] Research University Higher School of Economics, Moscow, Russia Tallinn University of Technology, Tallinn, Estonia © Springer Nature Switzerland AG 2019 M. Shafiei and A.-V. Pietarinen (eds.), Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition, Logic, Epistemology, and the Unity of Science 46, https://doi.org/10.1007/978-3-030-25800-9_3

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3.1 Introduction What is reasoning? Why do we reason? Over the centuries, these were the problems of philosophy and logic. However, in the middle of the 20th century, it was discovered, as if it were something surprising, that people in fact did not follow logical rules and that their behaviour was largely predicated on irrational, or perhaps procedurally rational, mental conduct. Logic had started losing its influence in these new domains, and today cognitive science studies human reasoning mostly from the perspectives of cognitive psychology. Logic has a supportive function, if any. Such appraisals seem widely held and shared by prevailing theories of reasoning. This semi-logical psychologism reminds us of the debates around logical psychologism at the turn of the 20th century. Psychologism in logic had claimed that in one way or another, logical laws are derived from psychological facts and mental laws. The founders of the modern logic, including Frege, Husserl and Peirce, did not quite accept this view, but their rejections were derived from vastly different reasons while not altogether abandoning the correlation between reasoning and cognition. This applies specifically to Husserl and Peirce. Both were charmed by the variety of epistemological questions posed by cognition and information flow, but both arrived at their respective proposals to solve these questions in altogether different manners.1 Husserl declined the relevance of logical methodology and encouraged us to go “back to the ‘things themselves”’ (Husserl 2001: 168), to retreat to the examination of the variety of ways in which things are actually given in experience. He uses logic only as an instrument and the first step from which to erect the phenomenological conception of philosophy. Peirce, on the contrary, wanted to reset the bounds of logic and see how a plurality of methods of reasoning and logics grows out of phenomenology. He did not accept Husserl’s premature retreat and would continue accusing him of being empiricist about logic after all. Is Peirce’s position, indeed, a more consistent of the two? In this paper, Peirce’s theory of reasoning is evaluated, demonstrating how that theory came to be developed as a preferred instrument of the logical analysis of thoughts, while not confusing that analysis with some other forms of studies concerning the way we think. Section 3.2 contrasts Husserl’s position with Peirce’s insight that reasoning is guided by what he termed the leading or guiding principle of reasoning (or, as he oftentimes also called them, the habit of reasoning). The guiding principle is the reason that we can constellate in imagination or with our mind’s eye. It gives reasoning its logical power. The guiding principle is also the reason that we can reach such logical powers ascertained by the analysis of the processes of inference in their smallest movement. Peirce further believed that this analysis is best accomplished by the methods of the theory of logic, especially those that he termed the graphical method of logic or existential graphs (EGs for short; see Pietarinen 2006b; Roberts 1973; Zeman 1964). EGs are briefly introduced in Sect. 3.3, followed by an analysis in Sects. 3.4 and 3.5 of the guiding principle and its evolution that is grounded in the primitive 1A

rich source of relevant information on Peirce–Husserl comparison of psychologism is found in Stjernfelt (2007).

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forms of the logic of EGs. The paper concludes by some summarizing thoughts on Peirce’s analysis of reasoning and its advantages not only over Husserl but also over contemporary studies that have taken keen interest in cognitive aspects of reasoning and inference.

3.2 Guiding Principle as the Core of Reasoning When treating logical reasoning as a formal structure, Husserl was clearly inimical to the admission of certain logical versions of psychologism, to something like weakly psychologistic conception of logic. Logic constituted only the first step towards achieving the overall goal of phenomenology: “Logical concepts, as valid thoughtunities, must have their origin in intuition: they must arise out of an ideational reconfirmation, and of recognition of their self-identity, on the reperformance of such abstraction” (Husserl 2001: 168). Husserl renounces formal logic in favour of the possibility of gleaning some protological evidence from intuitions. These intuitions are not logical per se; they only prepare grounds for what could become the foundation for logic. Peirce, however, would be unable to admit such a position as we can learn from his following sweeping dismissal of Husserl’s position: How many writers of our own generation ([…] let it in this case be the distinguished name of Husserl), after underscored protestations that their discourse shall be of logic exclusively and not by any means of psychology, forthwith become intent upon those elements of the process of thinking which seem to be special to a mind like that of the human race as we find it, to too great neglect of those elements which must belong as much to any one as to any other mode of embodying the same thought. (R 298, Phaneroscopy)2

What does Peirce offer instead? He does not reject the presence of logical underpinnings for connections between thoughts, as he looks for those connections even at the protological level. The American philosopher introduced the concept of the guiding principle that governs these connections in the capacity of that principle to govern reasoning. The principle constrains the ways in which information flows 2 An

alternative and slightly earlier draft of this passage reads as follows: “Yet how many writers of our generation (I will name Husserl, if I must instance one among the hordes), after underscored promises that their discourse shall be of logic, and not of psychology, forthwith become intent upon these elements of the process of thinking which are special to the human mind, as we find it, to the utter neglect of those elements which equally belong to every mode of embodying the thought.” These quotations have the following historical background. It was Christine Ladd–Franklin who in 1901 urged Peirce to critically engage with Husserl’s thought, especially his prevailing radical anti-psychologism. Ladd–Franklin would then meet Husserl and a number of other philosophers and scientists in 1902 during one of her frequent trips in Europe (Ladd–Franklin 2006). Husserl’s phenomenology, in turn, was inspired by Ladd–Franklin’s doctoral classmate, B. I. Gilman’s, paper on one-dimensional manifolds (Gilman 1892). Peirce’s engagement is found in his November 1906 address at the National Academy of Sciences meeting, entitled “Phaneroscopy, or Natural History of Signs, Relations, Categories, etc.: A method of investigating this subject expounded and illustrated,” of which R 298 is the testimony that is preserved in the archives. It is to appear in Peirce 2020 in full.

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in reasoning and how various conclusions are determined, secured and supported by their premises. Peirce uses this term on par with “rules of inference,” “habit of inference” or “leading principles”.3 He had explained the idea in one of his famous writings from 1877 as follows: That which determines us, from given premises, to draw one inference rather than another, is some habit of mind, whether it be constitutional or acquired. The habit is good or otherwise, according as it produces true conclusions from true premises or not; and an inference is regarded as valid or not, without reference to the truth or falsity of its conclusion especially, but according as the habit which determines it is such as to produce true conclusions in general or not. The particular habit of mind which governs this or that inference may be formulated in a proposition whose truth depends on the validity of the inferences which the habit determines; and such a formula is called a guiding principle of inference. (CP 5.367)

The guiding principle is the reason for reasoning to be valid and not only in its deductive manifestations. The principle is also responsible for the trustworthiness of induction as well as for the value of reasoning in the sense of its productivity (which Peirce termed “uberty”, Pietarinen 2019c), under the reasoning mode of abduction. The operation of guiding principles is thus not limited to the workings of deductive inference, although it is in deduction that we can see the function of the guiding principle becoming maximally transparent. Structurally, the guiding principle is expressed in deduction as the sign of the copula of inclusion (P C), in its capacity of perfectly mirroring the transitive and antisymmetric nature of inferential procedures. Indeed, as Peirce continues to develop the algebra of logic, it becomes a logic about the copula and its properties. The copula resembles implication. According to Bellucci and Pietarinen (2016), Peirce moved “away from Boole’s equational system and adopted an implicational one”. The motivation for the move had arisen from the fact that implication is simpler than identity, and that it hence yields considerably simpler proofs than those using the sign of identity would do. Beyond such expediency of calculation, copula of inclusion is the most analytic primary operation as it “alone is sufficient to express the whole logic of propositions” (Bellucci and Pietarinen 2016). Such implication is a primitive sign of the theory. It generates negation (as an implication of what is false), and other connectives may be reproduced after that. The process is irreversible, and this fact again is fully compatible with the irreversibility of inferential procedures. How does the guiding or leading principle of reasoning then operate? To demonstrate this, let us turn our attention to Peirce’s graphical project next.

3 There

are differences in meaning among these terms, but for the purposes of the present paper’s argument, we can safely ignore them.

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3.3 Evolution of Logical Guidance and the Theory of Existential Graphs As a logical system, EGs provide the sound and complete rules of deductive inference in the manner of ‘deep inference’ (Ma and Pietarinen 2017). Yet it is not the usual one either in notation or in terms of how logical constants acquire their meanings. Peirce also positions these systems as a cognitive resource that provides “a rough and generalized diagram of the Mind”; one which according to him “gives a better idea of what the mind is, from the point of view of logic, than could be conveyed by any abstract account of it” (R 490, in Pietarinen 2015: 900). By the mind, Peirce does not mean the human mind. As a representation of the mind, such generalized diagrams are connected to Peirce’s theory of signs. Indeed logic is his moniker for semiotic (CP 2.227). Peirce is seen to reset the boundaries of logic also in the sense of logic now growing into a general theory of cognition, where the mind is defined as the repository that produces signs. The sign is the object of the mind; or as Peirce preferred to termed it, the object of the “quasi-mind” (Pietarinen 2019a). Indeed, EGs presuppose the presence of a host of issues that much later have become the provenance of cognitive sciences. The basic units of EGs are the logical graphs, scribed upon the sheet of assertion as graph. Figure 3.1 gives two examples of graphs, one on the left a juxtaposition of two graphs, a, b, scribed upon the sheet, and the graph on the right an implication from a to b scribed upon the sheet. Graphs as instances scribed upon the sheet are propositional expressions “of any possible state of the universe” (CP 4.395). From the perspective of the most famous of Peirce’s division of signs, graphs may be thought to be icons. In EGs, however, they are predominantly symbols and possess indexical features as well, such as having to be connected to the universe of discourse as represented by the sheet. Graphs thus have their representative force as symbols and indices; still iconicity is what makes them unique when compared to many other and alternative logical systems and notations. Icons match logical structures with real conditions by association and likeness, and this connection demonstrates the necessity of certain presuppositions in logic. According to Peirce, logic is not an abstract science like mathematics. The fact that EGs admit of certain processes of evolution to take place provides additional evidence in support of his account of reasoning being a rather unique undertaking, whose importance may have remained somewhat undervalued. We will turn to this point in the next section. EGs include several separate theories, which Peirce coined the Alpha, Beta and Gamma parts, roughly corresponding to propositional, first-order and modal logics, respectively (for details, see e.g. Zeman 1964; Roberts 1973; Pietarinen 2006b; Ma and Pietarinen 2018a). For the purposes of the present argument, it suffices to review

Fig. 3.1

a

b

a b

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the basic version of EGs, the propositional Alpha theory.4 Its syntax consists of a sheet of assertion and cuts. The sheet is a basic tautology that means that everything that is scribed on it is asserted to be true. A simple way of interpreting cuts is as negative operations. Cuts are boundaries that partition the sheet into oddly and evenly enclosed areas. Such elements thus make up parts of the graphs that, in turn, are subject to transformations. There are three pairs of rules of transformation that are applied in Alpha graphs. Any graph may be scribed on any oddly enclosed area, and any graph may be unscribed whenever evenly enclosed (including unenclosed ones scribed on the sheet). Any graph on any area may be scribed on the same or any other area contained within it (iteration), and any graph that is the result of such iterations may be unscribed (de-iteration). If nothing else other than the blank space resides between two cuts, this double cut may be removed. Conversely, such a double cut may always be added around any graph, including blanks. These rules are sound and semantically complete and they define reasoning as a series of such activities of scribing and unscribing. The above rules characterize a sound and complete system, but Peirce is also careful in analysing the very origins of these rules. He finds for example that inserting and removing a double cut is not an “undeduced permission” (R S-30) but a result of some yet more fundamental considerations and observations. The important thing to notice is that, whatever these fundamental observations are from which the soundness of reasoning can then derive its justification from (on this, see Pietarinen 2019b), there are only two basic acts of transformation: those of scribing (insertions) and those of unscribing (omissions). This fundamental principle of reasoning which Peirce had repeatedly noticed (R S-30, R L 224, R 669)—namely that every operation can be reduced into one of these two—holds true also from the point of view of today’s general theories of proofs. Now consider an example. The following consequence holds in logic: {A → B, A}  B. After the initial graph (the colligated premises) is constructed, it starts moving about on the sheet according to the permissible transformations so defined: first, the inner a gets unscribed since it is a repetition of an outer token of that a, after which the remaining a is unscribed as it is evenly enclosed. Two cuts around b are then eliminated, and the conclusion b becomes as shown in the last graph of Fig. 3.2. When logical laws and axioms are being derived in such a fashion, the construction of the graph begins with the blank sheet of assertion. The proof that  A → A) begins with inserting a double cut around any blank of the sheet—just recall that the sheet is isotropic in all dimensions so all positions upon it are equivalent. After this, a is

Fig. 3.2

4 See

1. a a b

a

2.

b

3. b

4. b

Ma and Pietarinen (2018b) for ways of weakening the propositional Alpha part to various other ‘non-classical’ graphical logics.

3 Thoughts, Things and Logical Guidance Fig. 3.3

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0.

1.

2. a

3. a a

scribed on an oddly enclosed area and then scribed on the area inside the inner cut, as permitted by iteration (Fig. 3.3). These examples illustrate the value in Peirce’s assertion that graphs put before us “moving-pictures of thoughts”: it is these pictures that correctly introduce the leading principle of reasoning. The introduction is a formal one, pertaining both to the rules of the system as well as to the forms that the system speaks about. Dutilh Novaes (2011) refinement of MacFarlane’s (2000) thesis supports this way of seeing EGs as covering both procedural and schematic approaches to logical formality that we typically possess in today’s logics. Transformation rules testify that formality is dynamic, while pictures, as projections or snapshots of contents of thoughts as they become scribed on the sheet, represent the static conception. Although these two types of formalities are two different sides of the same underlying logical coin, it is more appropriate to present the workings of the guiding principle within the second approach. This attention to the formal side of reasoning gives a certain conceptual and logical superiority to Peirce’s project of ‘cognitive logic’ in comparison with Husserl’s empirical undertaking.

3.4 Scrolls and the Blot As represented by the graphical method, one novelty in Peirce’s conception of cognitive logic is its connection of the form of guiding principle to the interpretation of the sign of implication. In EGs, the implication is “the scroll”, namely a form in which there are two ovals one enclosed within the other, with one intersection point (Fig. 3.4, the graph on the left). This is typically shown in the shorthand notation with one continuous line (Fig. 3.4, the graph on the right). Scrolls are complete assertions of implication5 : whatever is placed in the outer compartment, including the blanks, is the antecedent, while whatever is situated in the inner compartment represents the consequent of the conditional. It is the scrolls that are the primitive signs of logical systems. The strategy of how we prove logical laws and axioms supports this. Any proof has to start with an insertion of a double cut on the blank sheet of assertion. Any such double cut is an implication from blank to blank. In Alpha graphs, this means an implication from Fig. 3.4

5 By

a b

a b

the scroll, we mean both the boundary and its contents, where the contents only contain the continuous sign of the blank.

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tautology to tautology. For example, we replace a and b in the graphs of Fig. 3.4 with the blank, that is, with the tautology or the top element. But the scroll does more than this. It is also the generator of the cut, in the sense of signifying how the oval boundaries come to mean negative assertions. Cuts also signify scopes of logical constants and are also punctuation marks. To demonstrate the working of this process, Peirce produces an elaborate argument which he intended to demonstrate the evolution of negation from the primitive sign of the scroll. For the sake of clarity, we will present two narratives that describe his argument. The 1st version. In order to ascertain whether [the cut] will have the effect of simply denying the entire Graph of its Area, let us reason somewhat as follows. Just as we have imagined that Adam and Eve, before the fall, were in a state of Innocency, trying to behave in fine and honorable ways although they had never dreamed that there was any such thing as Sin […], so we can equally well, perhaps more easily, imagine that there was once an intellectual state in which man had no conception of falsity. It would follow […] that there must have been a time when men used language with some syntax, and yet were not fully conscious of it; and as long as they were in that condition, they could hardly have had much notion of falsity, although they might very well have drawn simple inferences […]; but these would have furnished them no notion of falsity or even of contradiction. […] The idea of falsity, the serpent in their Eden, that could only cause them to eat of the fruit of the Tree of knowledge of Logical Good and Evil, could only come from noticing Words as being different from Things. When that came, they being already in the habit of uttering simple Conditional Propositions, might conceivably have formed such a Proposition as, “If A is true, everything is true”, and this might have suggested that [“]Not everything is true[”]. At any rate, the Scroll affords me no other means of denying any Graph, say A, than by scribing that [“I]f A be true, everything is true[”]. Now since it is impossible by any addition to increase Everything, this I can suitably express by completely filling with a blot the Inner Close of a Scroll that carries only A (and the Blank) in its Outer Close [Fig. 3.5b below], so that there shall be no more room in that Inner Close for anything else. I can then make this blackened Inner Close as small as I please [Fig. 3.5c below], at least, so long as I can still see it there, whether with my outer eye or in my mind’s eye (Horatio). Can I not make it quite invisibly small, even to my mind’s eye? “No”, you will say, “for then it would not be scribed at all”. You are right. […] it is my duty to say that this error of assuming that, because the blackened Inner Close can be made indefinitely small, therefore it can be struck out entirely, like an infinitesimal. That led me to say that a Cut around a graph-instance has the effect of denying it. I retract: it only does so if the Cut encloses also a blot, however small, to represent iconically the blackened Inner Close. I was partly misled by the fact that in the Conditional de inesse the Cut may be considered as denying the contents of its Area. That is true, so long as the entire Scroll is on the Place. But that does not prove that a single Cut, without an Inner Close, has this effect. On the contrary, a single Cut, enclosing only A and a blank, merely says: “If A”, or “If A, then” and there stops. If what? You ask. It does not say. “Then something follows”, perhaps; but there is no assertion at all. This can be proved, too. For if we scribe on the Phemic Sheet the Graph expressing “If A is true, Something is true”, we shall have a Scroll with A alone in the Outer Close, and with nothing but a Blank in the Inner Close. Now this Blank is an Iterate of the Blank-instance that is always present on the Phemic Sheet; and this may, according to the rule, be deiterated by removing the Blank in the inner close. This will do, what the blot would not; namely, it will cause the collapse of the Inner Close, and thus leaves A in a single cut. We thus see that a Graph, A, enclosed in a single Cut that contains nothing else but a Blank has no signification that is not implied in the proposition, “If A is true, Something is true. (R S-30, 1906)

A few years later, Peirce introduces the procedure of the evolution in the following terms:

3 Thoughts, Things and Logical Guidance Fig. 3.5

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a c

a c

a

a

The 2nd version. The Cut came to be thought of because of the immense frequency of occasions on which it was necessary to express the assertion “If X be true, then every assertion is true”. It was forced upon the logician’s attention that a certain development of reasoning was possible before, or as if before, the concept of falsity had ever been framed, or any recognition of such a thing as a false assertion had ever taken place. Probably every human being passes through such a grade of intellectual life, which may be called the state of paradisiacal logic, when reasoning takes place but when the idea of falsity, whether in assertion or in inference, has never been recognized. But it will soon be recognized that not every assertion is true; and that once recognized, as soon as one notices that if a certain thing were true, every assertion would be true, one at once rejects the antecedent that lead to that absurd consequence. Now that conditional proposition “If A is true, every proposition is true”, is represented, in the model of Fig. 3.5a, “If A is true, C is true” by blackening the entire inner close, as if there were no room, in reason, for any additional consequence. This gives Fig. 3.5b: “If A be true whatever can be asserted is true”, which is as much as to say that “A is not true and the inner close being cut very small”, we get, first Fig. 3.5c and finally Fig. 3.5d, in which the idea of flat falsity is first matured. (R 669, 1910; Pietarinen 2015: 920)

If we place a double cut on the sheet and scribe A on the antecedent area, we get the scroll “A implies the blank”. This would mean that “If A, then something is true”. The blank is a tautology, expressing ‘all truths’. Assuming uncountably many (or, as Peirce would say, “supermultitudinous”, R 28) truths that could be added in the blank area of the continuum however small, no addition, and not even of proper classes of individual truths, would increase its cardinality. That area could then just as well be blackened with the blot ‘ ’. As the size of that fully occupied area does not change the cardinality of truths included in it, it could just as well be atrophied until what was an inner loop of the scroll coincides with the boundary of the outer loop of that scroll. The result, now, is the sign for negation. In any expression of a negation of a proposition, signalled by a simple closed boundary around it, there is an indefinitely small (or, as Peirce would say, “infinitesimally small”, R S-30, R 450) boundary on which the blot rests that testifies of the evolutionary origins of the negation in a conditional. Without the blot residing on the boundary of the scroll the graph would be ill-formed, as it would express merely the antecedent of a conditional without any content as to its consequent, and would fail to express a denial or an assertion of anything at all. Peirce’s proof of the latter is, in turn—though he soon retracts this as an “unsatisfactory” proof (R S-30)—to apply the rule of deiteration to unscribe the entire blank of the inner close by virtue of the presence of another copy of the blank in its context which we can find on the sheet of assertion. This would, according to Peirce, now result in a vacuum in the area which would effect a collapse of the inner loop into the boundary of the outer loop. Effectively, the inner loop becomes the intersection point of the original scroll. This argument has a lot to recommend itself, and Peirce took some care in analyzing and criticizing it from several points of views. We focus only on one of those point, namely the meaning of the blot, as it has not been much discussed in

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the previous literature. The blot holds great deal of promise to be analyzed from the perspective of philosophy of logic. The easiest way to specify this sign would be to appeal to the constant falsehood (algebraically, the bottom element ⊥), and take the blot to be a representation of falsity. However, such meaning can hardly preserve the intended meaning since the blot is a positive rather than a negative assertion or denial. Peirce argues for the affirmative interpretation of the blot as follows: The simplest part of speech which this syntax contemplates, which, as scribed, I shall term a blot is itself an assertion. Ought it to be an affirmation or a denial? A denial is logically the simpler, because it implies merely that the utterer recognizes, however vaguely, some discrepancy between the fact and the speech, while an affirmation implies that he has examined all the implications of the latter and finds no discrepancy with the fact. This is a circumstance to be borne in mind; but since the denial implies recognition of the affirmation, while the affirmation is so far from implying recognition of the denial, that one might imagine a paradisaic state of innocence in which men never had the idea of falsity, and yet might reason, we must admit that affirmation is psychically the simpler. Now I think that upon this point we must prefer psychical to logical simplicity. I therefore make the blot an affirmation. (R L 376, 1911)

One might now be tempted to interpret the blot as a sign of tautology. This temptation to fall for the “psychically simpler” explanation could be explained as follows. If the sheet is an area of an uncountable number of existing elements, the blot signifies emptiness. Nothing can be added to a vacuum. Everything there is true as there is nothing to suggest us the possibility of asserting other kinds of meanings than positive ones. Assertions of falsity presume the presence of boundaries, as “the denial implies recognition of the affirmation”. The converse is not the case. But the blot, in so far as it is not placed somewhere else other than the sheet, in so far as it is unenclosed within any scrolls, it has no borders and, as a consequence, no opposition, no restriction, no constraints to control its expansion. The scroll creates an opposition, enclosing the blot within the boundaries of the inner loop of the scroll. The blot represents an infinite abyss of the kind of a black hole, from which nothing escapes, in which everything holds true and onto which nothing can be added without at once losing it. What was the boundless energy of the vacuum becomes bounded and confined to an enclosure, and the boundary of the blot is formed. So the blot is itself an assertion, a proposition according to its form, that is, it is not a sub-propositional element. It is capable of being considered as an affirmation or as a denial in its own right. This follows from noticing that “everything is true” is a proposition. Now a proposition may be an affirmation or a denial, that is, a positive or negative proposition according to its form. Peirce argues that psychically it is better to read absurdity or blot as a positive proposition, since we intend to define negation on the basis of absurdity, not the other way around. But epistemologically denial is simpler than affirmation. What would then the blot be in its negative form? Perhaps it says “there is no truth”, as “there is no truth” and “everything is true” may both serve as expressions of absurdities. Both are formally equivalent. However, since “There is no truth” involves negation it does not satisfy the aim of passing from a paradisiacal logic to a logic with a sign of negation. A clarification of the operation of opposition can be provided by Peirce’s notion of scriptibility, the possibility of scribing something on the sheet of assertion (R 501).

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The presence of the sheet (of assertion, affirmation or denial alike) presupposes scriptibility. Indeed, the utterer can undertake writing on the sheet any graph whatever he pleases. However, whenever there is the idea of scriptibility, there should be an opposite concept that signifies anti-scriptibility, an area on which “nothing at all can be scribed”. And so the very idea of unscriptibility emerges, which is realized by the blot which in Peirce’s terms is the “blackening [of] the entire inner close, as if there were no room, in reason, for any additional consequence” (R 669). Semantically, we should note, scriptibility does not mean having a truth-value. On the contrary, Peirce’s idea goes deeper than this as it suggests a possibility to generalize truth to other values besides truth and falsity (for details of how such proposals might come about in Peirce’s Dragon-Tail Logic see Ma and Pietarinen 2019). In logic, we can deal with values that do not contradict the fruitful presumption that both the sheet and the blot are tautologies. These values may be applied as soon as the sheet and the blot are duals of each other and as soon as there is the boundary (the cut) that can generate negation. Scriptibility does not equal truth, but it can be reduced to truth as soon as the sheet is what the classical, bivalent, Boolean logic professes it to be. And whenever that is the case, the interpretation of the areas of the sheets as tautologies and falsities ⊥ (the blots that are surrounded by the closed boundary) comes out as a natural one.

3.5 Logical Leading Principles, Logical Evolution, Logical Phaneroscopy As we can now see, Peirce’s concept of the leading principle is a logical and perfectly formalized tenet. He proposes how new signs of logic can evolve, arguing that such evolving processes are congenial in the very operation of the theory of EGs. These arguments thus also bring out the presence of two types of scrolls, signifying two kinds of implications, one without and the other with a conception of negation associated with it. This, we propose, is linked to evolutionary processes of intellectual thought. Those processes are interestingly similar to how the idea of grammatical elements of language may have developed in early homininis, among others. The first type represents is a primitive implication, which we call paradisiacal implication. We find it in Peirce’s two argumentative stories concerning reasoning. In the language that consists of scrolls alone, and which is the language of illative inferences, there is yet no conception of falsity or negation dawned upon those who discourse about the rationale of reasoning. Peirce is seen to draw a related conjecture in R 501 (c.1901): [A]state of mind is conceivable which should be capable of making judgments and yet should not have any such ideas as falsity and denial. Does such a state of mind exist? It is very nearly, if not quite, the state of mind of a horse. The phrase “horse sense” testifies to the general conviction of those who are acquainted with horses that they make judgments. But we rarely, if ever, observe in the horse, what is common enough in the dog, a state of doubt and deliberation as to whether a hypothesis an idea is true or not. But admitting that

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An implication is involved in the positive fragment of logic alone. It works at the level of paradisiacal logic, in which reasoning takes place but the idea of falsity has not yet been recognized. Paradisiacal implication is a primitive of one’s language, and in that language we see how the guiding principle of logic emerges. In contradistinction to Husserl, even at the ‘proto-logical’ level Peirce would analyse logical conceptions from the perspective of logic. A brief recourse into Peirce’s phaneroscopy, a version of phenomenology which Peirce developed independently from Husserl, will clarify the evolution of implication as the form of the guiding principle of logic. According to Peirce, phaneroscopy is an abstract science that structures the universe through the categories of our reality, while logic studies “the laws of signs so far as these denote things”(W3: 98). Bellucci (2015: 68) notes that “phaneroscopy investigates mental contents without making any distinction between truth and falsity, reality and fiction. […] Logic, by contrast, is bound to analyze mental contents only in so far as they relate to their objects, that is, it is bound to consider that which appears as a representation of something else.” Phaneroscopy deals with ideas and its concepts are considered as a pure appearance whereas logic needs signs as its concepts are seen as representations of something. In Peirce’s classification of the sciences (Pietarinen 2006a), phaneroscopy precedes logic but follows mathematics. Phaneroscopical analyses precede logical analyses. The former urge us to see a logical analysis also as a phaneroscopical analysis fulfilled with the idea of representation, since no logical concept is “considered as a mere appearance, but as a representation of something which is as it is independently of being represented as such” (Bellucci 2015: 69). The result is what Peirce once termed a “logico-phaneroscopic analysis” (R 646: 41–42, 1910). Its precise vehicle is the method of EGs, as that is the method that can iconize the thought, and hence also the inferential relations and the guiding principle, better than other methods do. The analysis from the classification of sciences is seen to provide a further reason to take the development of the conception of implication to have been an evolutionary process, protracted in evolutionary time. The guiding principle may have various logical forces which are not limited to deduction, and so it is only natural that it should be represented by implications with different logical powers. The variety can be reached when we admit that our logicophaneroscopic continuum is arranged in the way that allows some implications to carry analyses that are closer to phaneroscopical ones while others would fall under logical analyses and their rule-directed, interpretative modalities. It is the latter that

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concerns evolution. How can such inferences or judgments be presented in which the idea of the denial or falsity that has not yet been fully matured in one’s mind? One can see a dilemma arising here. Peirce takes mathematics to be science that at once gives rise to negation but mathematics also precedes phaneroscopy in the classification. This means that in phaneroscopy negation is somehow readily present, as it is the science that draws its validity from the validity of mathematics. The perspective of EGs provides a way out of this dilemma. When defining the blot, Peirce noticed that denial is logically a simpler operation than affirmation, while the latter is “psychically” the simpler. And if it is so, “we must prefer psychical to logical simplicity”, Peirce added (R L 376, 1911). This preference can be fixed in terms of the dialogues and cooperative practices of those “make-believe” agents that discourse upon the rationale of logic (R 280). In brief, although negation is a welldefined operation in phaneroscopy, the make-believe agents of the paradisiacal logic cooperate without recognizing its presence.6

3.6 Conclusion Both Peirce and Husserl were keen to understand the intellectual workings of cognition. They studied how information flows and how one thought is connected with another in a way it does in what we call reasoning. At the same time, though, they would propose doing that in a wholly different manner. Under the pretext of returning “to the things themselves”, Husserl would put logical structures aside—or rather bracket the methodology of logic as a normative science—and propose building phenomenological scaffolding on certain conceptions of mathematical forms of thinking. Peirce, on the contrary, conducts investigations into cognitive processes within a strict but expansive logical perspective that takes logic as a normative science that reposes on ethics and esthetics. When we observe informative processes, what we are observing are the consequences of a chain of thoughts that are governed by certain rules of inference, or in Peirce’s terminology a mental action that behaves according to the guiding or leading principles. Formally these principles are represented by logical schemata, while the present paper has proposed re-scribing them in terms of the more cognitively-friendly graphical forms of the theory of EGs. This theory shows particular advantages in this regard. It is not limited to the ordinary kinds of linear languages since the basic units of representation are the icons of logical relations, yet a well-defined consequence relation emerges from it. These iconically modified representations differ from non6 There

may be various processes or mechanisms at work that could prevent the recognition or awareness of an explicit negation, including the fact that what “the Phaneron” is cannot be directly observed (R 499(s)), and that its study must therefore be approached from the points of view of the graphicalization of logic. If that graphicalization does not permit a representation of cut as a negation, the latter needs to be gradually worked out from the presence of other signs, such as the scroll, which requires time and cognitive energy which should not be assumed to be at the initial disposal of these make-believe agents.

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graphical, linear, and predominantly symbolic ones in that the former makes it possible to actually observe the relations exhibited in that language. This, in turn, can be interpreted in the sense that the graphs provide the rules or percepts according to which certain other actions, explicated in terms of the dialogical or ‘social’ framework of engagement, become the rational course of action to be pursued. EGs thus embrace some deep-seated cognitive matters while admit an evolutionary approach to the meaning of inference. As the guiding principle has the form of a scroll, and as deduction makes this as transparent as possible, that principle literally illustrates how premises entail the conclusion. The guiding principle that the scroll provides in terms of its innate evolution is a continuous process starting with the paradisiacal logic (logic without negation). It is not necessary to try to enumerate all the advantages of Peirce’s conception over Husserl’s one or vice versa, which in any case would depend on areas of application. We think Peirce’s solution is quite understandable in the view of present-day cognitive investigations. Moreover, since it is formal, it can be used as a technical and transferable framework. For instance, positive paradisiacal implication agrees with results of psycholinguistics. Humans, manifested in such examples as homo erectus, infants below 14 months of age, most other primates, and so on, are unable to conceptualize negation, contradiction, or even that of absence, at least at the levels of grammar and in the dimension of illocutionary forces (see e.g. Clark and Clark 1977). Yet reasoning is present, admirably carried out in terms of thinking only of positive or affirmative instances. When the word–object relations break down and a subject becomes conscious of it, hypothetical conditionals emerge, and with the hypotheticals, axioms that suggest the hidden presence of a falsity. In closing, we remark that the correlation of two kinds of scrolls to dual-process theories of reasoning can be observed in important contemporary cases. Two scrolls remind us of the two-systems or the dual-process theories of reasoning developed e.g. by Evans and Over (1996), Sloman (1996), Stanovich and West (2000) and broadened to the decision-making theory by Kahneman and Tversky (2011), among others. They also confirm (Sperber and Mercier 2017) theory that criticizes the dual approach to reasoning, as the latter still relies on the idea of the presence of two types of intuitions. This adoption of our present framework has a couple of consequences. First, it explains why the intuitive associative connections that emerge from the operation of System 1 do look like inferences. Second, it specifies what is at issue in various cognitive biases, some of which are not fallacies at all. However, the details of the exposition of these consequences are topics of another work. Acknowledgements This work has been supported by the Academy of Finland (project 1270335) (DiaMind: Diagrammatic Mind), the Estonian Research Council (project PUT 1305) (Abduction in the Age of Fundamental Uncertainty), and the Russian Academic Excellence Grant “5–100” on Formal Philosophy. We thank the anonymous reader for very helpful remarks and suggestions on this paper.

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References Bellucci, F. (2015). Peirce on phaneroscopical analysis. Journal Phänomenologie, 44, 56–72. Bellucci, F., & Pietarinen, A.-V. (2016). Existential graphs as an instrument of logical analysis: part I. Alpha. The Review of Symbolic Logic, 9(2), 209–237. Clark, H., & Clark, E. (1977). Psychology and language: An introduction to psycholinguistics. NY, Chicago, San Francisco, Atlanta. Dutilh Novaes, C. (2011). The different ways in which logic is (said to be) formal. History and Philosophy of Logic, 32(4), 303–332. Evans, J. S. B., & Over, D. E. (1996). Rationality and reasoning. Hove, UK: Psychology Press. Gilman, B. I. (1892). On the properties of a one-dimensional manifold. Mind, 1, 518–526. Husserl, E. (2001). Logical investigations (Vol. 1). New York: Routledge. Kahneman, D., & Tversky, A. (2011). Thinking, fast and slow. New York: Farrar, Straus & Giroux. Ladd–Franklin, C., & Letter to Peirce, C.S. 20 October 1902 (R L). (2006). In A.V. Pietarinen, & J. Nikulainen (Ed.), Charles S. Peirce–Christine Ladd-Franklin Correspondence (1878–1904). Unpublished Transcription, 66 pages. Ma, M., & Pietarinen, A.-V. (2017). Proof analysis of Peirce’s alpha system of graphs. Studia Logica, 105(3), 625–647. https://doi.org/10.1007/s11225-016-9703-y. Ma, M., & Pietarinen, A.-V. (2018a). Peirce’s Calculi for Classical Propositional Logic. The Review of Symbolic Logic. https://doi.org/10.1017/S1755020318000187. Ma, M., & Pietarinen, A.-V. (2018b). A weakening of alpha graphs: quasi-boolean algebras. In P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, & F. Bellucci (Eds.), Diagrammatic representation and inference. Lecture Notes in Computer Science, 10871. Cham: Springer. https://doi. org/10.1007/978-3-319-91376-6_50. Ma, M. & Pietarinen, A.-V. (2019). Peirce’s logic of the dragon head, manuscript. MacFarlane, J. (2000). What does it mean to say that logic is formal? Ph.D. dissertation. Pittsburgh University. Peirce, C. S. (1931). The collected papers of Charles S. Peirce. (Vol. 1–8). Cambridge: Belknap Press of Harvard University Press, 1931–1958. (Cited as CP followed by volume and abstract number). Peirce, C. S. (1971). Manuscripts in the Houghton library of Harvard University, as identified by Richard Robin, annotated catalogue of the papers of Charles S. Peirce, Amherst: University of Massachusetts Press, 1967, and in The Peirce Papers: A supplementary catalogue, Transactions of the C.S. Peirce Society (Vol. 7, Issue 1971, pp. 37–57), 1967. (Cited as R followed by manuscript number and, when available, page number). Peirce, C. S. (1982). Writings of Charles S. Peirce: A chronological edition. (7 Vols.). In E.C. Moore, C.J.W. Kloesel, et al. (Eds.), Bloomington: Indiana University Press. (Cited as W followed by volume and page number). Peirce, C. S. (2020). Phaneroscopy (ϕαν). In A.-V. Pietarinen (Ed.), Charles S. Peirce: Logic of the future: Peirce’s writings on existential graphs. Mouton De Gruyter. Pietarinen, A.-V. (2006a). Interdisciplinarity and Peirce’s classification of the sciences: A centennial reassessment. Perspectives on Science, 14(2), 127–152. Pietarinen, A.-V. (2006b). Signs of logic: Peircean themes on the philosophy of language, games, and communication. Dordrecht: Springer. Pietarinen, A.-V. (2011). Existential graphs: What the diagrammatic logic of cognition might look like. History and Philosophy of Logic, 32(3), 265–281. Pietarinen, A.-V. (2015). Two papers on existential graphs by Charles Peirce. Synthese, 192(4), 881–922. Pietarinen, A.-V., & Issajeva, J. (2019a). Phaneroscopy and Peirce’s theory of cognition, this volume. Pietarinen, A.-V. (2019b). How to justify deductive reasoning: Peirce’s solution. British Journal for the History of Philosophy. Pietarinen, A.-V. (2019c). Abduction and diagrams. Preprint. Roberts, D. (1973). The existential graphs of Charles S Peirce. The Hague: Mouton.

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Sloman, S. A. (1996). The empirical case for two systems of reasoning. Psychological Bulletin, 119(1), 3–22. Sperber, D., & Mercier, H. (2017). The enigma of reason. Cambridge, MA: Harvard University Press. Stanovich, K. E., & West, R. F. (2000). Individual differences in reasoning: Implications for the rationality debate. Behavioral and Brain Sciences, 23, 645–726. Stjernfelt, F. (2007). Diagrammatology: An investigation on the borderlines of phenomenology, ontology, and semiotics. Dordrecht: Springer. Zeman, J. (1964). The graphical logic of C.S. Peirce, dissertation, University of Chicago, Online edition, 2002. www.users.clas.ufl.edu/jzeman/ (22 Feb 2019).

Part II

Logic

Chapter 4

Philosophy of Notation in the 19th Century. Peirce, Husserl, and All the Others on Inclusion and Assertion Francesco Bellucci

Abstract This paper focuses on two important notational devices that were embedded in Husserl’s and Peirce’s notations, the sign of inclusion and the sign of assertion. Husserl first criticizes, then follows Schröder in taking inclusion to be a simpler concept than equality, and endows his logical notation with a sign of inclusion. This was due to Peirce’s notational innovations and arguments, by which Husserl is indirectly influenced through of Schröder. Further, like Frege Husserl endows his notation with a sign of assertion, claiming that without some such sign it would be impossible to distinguish the assertion of a propositional content from its occurrence unasserted in some larger propositional context. Against this idea of Frege and Husserl, Peirce had a powerful argument—the compositional structure of a formula is de facto the sign of its assertion—, and Peirce’s algebraical and graphical notations can be seen as notational realizations of this principle.

In Sommersemester 1896 Husserl lectures on logic in Halle (Husserl 1896). A similar course was delivered in Göttingen in Wintersemester 1902/1903 (Husserl 1902). In both sets of lectures Husserl proposes a notation for the theory of propositional inferences (Theorie der propositionalen Schlüsse) and for the theory of predication and of conceptual inferences (Theorie der konzeptualen Schlüsse) which is largely 1 based on Schröder’s algebra of logic. While in his 1891 review of Schröder’s Vorlesungen über die Algebra der Logik Husserl had criticized Schröder’s claim that subsumption is a simpler concept than equality, in the 1896 and 1902 sets of lectures he employs Schröder’s sign of subsumption or inclusion (what we nowdays call a partial ordering relation) as the fundamental anti-symmetric operation of his calculus. Now, it is known that Schröder took the idea that inclusion is simpler than equality from Peirce. Thus, when Husserl criticizes Schröder, he is actually criticizing Peirce; and when, for precisely opposite reasons, he adopts Schröder’s notation, 1 See

Centrone (2010, pp. 128–147).

F. Bellucci (B) University of Bologna, Bologna, Italy e-mail: [email protected] © Springer Nature Switzerland AG 2019 M. Shafiei and A.-V. Pietarinen (eds.), Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition, Logic, Epistemology, and the Unity of Science 46, https://doi.org/10.1007/978-3-030-25800-9_4

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he is actually adopting Peirce’s. Schröder is thus the medius terminus of the indirect dialogue between Husserl and Peirce on the sign of inclusion. While profoundly influenced by Schröder’s logic, Husserl endows his notation with a sign that was absent in Schröder’s notation, and which was rather to be found in Frege’s: the sign of assertion. Frege had maintained that a sign of assertion is necessary in order to distinguish between the propositional content asserted and its assertion, for if these were not distinguished we would not know how to interpret a sentence in which a given propositional content occurs unasserted. Husserl provides a similar justification of his sign of assertion. Peano objected to Frege that a sign of assertion is unnecessary. Peirce did not know of Frege, but had a powerful argument to support the idea that an ad hoc sign of assertion, like Frege’s and Husserl’s, is notationally superfluous. Again, it is by means of the intermediation of Frege and Peano that we can reconstruct the indirect dialogue between Husserl and Peirce concerning the sign of assertion. Peirce and Husserl have often been compared as to their general conception of logic,2 but very little has been written on their “philosophy of notation.”3 This paper focuses on two important notational devices that were embedded in Husserl’s and Peirce’s notations, the sign of inclusion and the sign of assertion. I do not attempt to reconstruct Husserl’s and Peirce’s philosophies of notation in their entirety. What I attempt to do is to examine the philosophical and logical justification which each author gave for certain notational choices.

4.1 Inclusion While in the Operationskreis Schröder had followed Boole in adopting an equational approach (judgments are expressed as equations between classes),4 in the Vorlesungen he follows Peirce in adopting an inclusional approach (judgments are expressed as subsumption relations between classes). In this work Schröder distinguishes between identity (Gleichheit), symbolized by “=,” subordination (Unterordnung), symbolized by “⊂,” and subsumption (Einordnung), symbolized by “=(= .” In an assertion of the form “a = b” we state that a and b are different names 2 Stjernfelt

(2007, 2014), Pietarinen and Stjernfelt (2015).

3 The expression “philosophy of notation” was coined by Peirce to indicate the philosophical inves-

tigation of the properties of logical notations; cf. Peirce (1885). approach was based on equation. In The Laws of Thought he divided propositions into Primary, which relate to things, and Secondary, which relate to propositions, a distinction “nearly but not quite” co-extensive with that between categorical and hypothetical propositions. The propositions “The sun shines” and “The earth is warmed” are primary, the proposition “If the sun shines, the earth is warmed” is secondary. Both primary and secondary propositions can be symbolized in the same notation and subjected to the same laws. The difference between the two cases is only a difference in interpretation (as logic of classes or logic of propositions). Both kinds of proposition are expressed by an equation, symbolized in the notation by the sign “=” (Boole 1854, IV, 1, 53–54). Jevons had followed Boole in considering equation the “fundamental form of reasoning” (Jevons 1869, 14).

4 Boole’s

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of one and the same object of thought (1890, 128). In an assertion of the form “a ⊂ b” we state that a is strictly included in, or subordinated to, b (1890, 129–130). In an assertion of the form “a =(= b” we state that a is either subordinate or identical to b (1890, 132). Subordination and subsumption are strict and non-strict partial ordered relations, respectively.5 Although the sign of subsumption (Subsumtionszeichen) appears as a composite sign (zusammen-gesetztere Zeichen), i.e. as composed of the identity sign “=” and of the subordination sign “⊂,” yet it has the simplest meaning. The einfachen Zeichen do not express die einfachere Beziehung; rather, it is the composite sign that expresses the simpler relation (1890, 133). Subsumption is simpler because in asserting (1) we say less than in asserting either (2) or (3) (1) a =(= b (2) a ⊂ b (3) a = b. (2) and (3) are rendered by the conjunction of two assertions, namely (2a) All a are b, and not all b are a (3a) All a are b, and all b are a. which cannot be true at the same time. Thus, (1) expresses the simplest content because it asserts that either (2) or (3) is the case, but not both.6 It leaves open the possibility that a and b coincide (1890, 134). Thus, in (1) we express one thought, while in each of (2) and (3) we express two thoughts (1890, 136). For this reason, subsumption is the simplest and primary concept (ursprünglichere, 1890, 136), and the expression of a judgment as a subsumption (rather than as an equation, as Boole did) gives us the best and most general method for representing assertions in exact logic. Accordingly, in the second Vorlesung Schröder defines identity through subsumption (Definition I, 1890, 184),7 and in the seventeenth Vorlesung (in Band II) he defines subordination in the same way (1891, 109).8 Subsumption can have two interpretations, i.e., as a relation between classes in simple judgments or as a relation between judgments in composite judgments. As Schröder explains in “Signs and Symbols,” published in The Open Court in 1892: The fundamental sign in the present case was the symbol of inclusion or subsumption; viz., the symbol of the relation of a part to its whole, of the subject to the predicate, of a judgment, in other words, a symbol for the copula “is” or “are” of a judgment […] The same sign, placed between the judgments or statements a and b, admits of the following interpretations: “if a obtains, then b obtains,” “a conditions b,” “brings it in its train’; as a fact then, the class of occasions, of circumstances, in which the statement a is admissible, is contained in, is a part of, the class of circumstances or occasions, in which the statement b is true or admissible. The sign supplies the place therefore in syntax of the conjunctions “ergo,” “consequently,” “because” and “therefore” of general inference (Schröder 1892, 3464). 5 Cf.

Brady (2000, p. 145). Formel sagt nämlich als disjunktives Urteil aus: wenn A ⊆ B ist, so ist entweder A untergeordnet B; oder aber […] es ist A gleich B” (1891, 109). In formulas: A =(= B = {A ⊂ B} + {A = B}. 7 “Wenn a ⊂ = b und zugleich b ⊂ = a ist, so werde gesagt, es sei: a = b (gelesen a gleich b).” 8 Cf. Peckhaus (1990, p. 181), Brady (2000, p. 145), Grattan-Guiness (2000, p. 165). 6 “Die

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Interpreted in the logic of classes, the assertion in (1) can be rendered in words as “a is b” (when a is an individual and b a class), or “All a are b” (when both a and b are classes) (1890, 133). Interpreted in the logic of propositions, (1) can be rendered as “a implies b” (material implication) or “a, therefore b” (relation of illation). All this derives from Peirce. In his first published work on the logic of relatives, the “Description of a Notation for the Logic of Relatives” of 1870 (Peirce 1870), Peirce had introduced the “sign of inclusion” (“⤙”) to denote the transitive binary relation of “inclusion in” or “being as small as.” In a footnote, he gives reasons both for (i) the adoption of the relation of inclusion as primary in the calculus, and for (ii) the sign “⤙” as the sign of that relation. The reason why the relation of inclusion is primary is that a higher conception is logically more simple than a lower one under it. Whence it follows from the relations of extension and comprehension, that in any state of information a broader concept is more simple than a narrower one included under it. Now all equality is inclusion in, but the converse is not true; hence inclusion in is a wider concept than equality, and therefore logically a simpler one. On the same principle, inclusion is also simpler than being less than (1870, 318n* = W2, 360n1).

In a given state of information, the relation between the extension and the comprehension of a term are inversely proportional; the greater the extension, the lesser the comprehension.9 A conception “higher” in extension, i.e., a more extended concept, is “simpler” than a lower one: “animal” has a greater extension than “horse,” and thus it has a lesser comprehension, i.e., it is simpler in comprehension or meaning. Now, Peirce argues, all equality (symbolized by “=”) is inclusion (in fact, it is reciprocal inclusion), but not all inclusion is equality; this means that inclusion has a greater extension than equality, and thus, according to the law of inverse proportionality of these quantities, it has a lesser comprehension than the latter. Inclusion is conceptually simpler than equality. As he puts it in “On the Algebraic Principles of Formal Logic” of 1879, “all identity is inclusion but the reverse is not true. Hence, inclusion is a concept having a greater logical extension than identity. Hence, the logical comprehension of identity is greater than that of inclusion, or in other words inclusion is a simpler idea than identity” (W4, 21–23). Another way of saying this is that “an unsymmetrical relation can never be expressed as a complex or special case of a symmetrical relation; but a symmetrical relation may be expressible by means of an unsymmetrical relation” (MS 482, 1896). In the case in hand, inclusion, being unsymmetrical, cannot be expressed as a special case of equality, which is symmetrical, while the reverse is true. The same applies to “being less than,” or strict inclusion (symbolized by “