Semiotics and Philosophy in Charles Sanders Peirce [1 ed.] 9781443806992, 9781904303749

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Semiotics and Philosophy in Charles Sanders Peirce

Semiotics and Philosophy in Charles Sanders Peirce

Edited by

Rossella Fabbrichesi and Susanna Marietti

CAMBRIDGE SCHOLARS PRESS

Semiotics and Philosophy in Charles Sanders Peirce, edited by Rossella Fabbrichesi and Susanna Marietti This book first published 2006 by Cambridge Scholars Press 15 Angerton Gardens, Newcastle, NE5 2JA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2006 by Rossella Fabbrichesi and Susanna Marietti and contributors

All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN 1904303749

TABLE OF CONTENTS Acknowledgements.............................................................................................vii List of Abbreviations .........................................................................................viii Introduction..........................................................................................................ix

PART I - SEMIOTICS AND THE LOGIC OF INQUIRY Chapter 1 Peirce’s Contrite Fallibilism Nathan Houser ...................................................................................................... 1 Chapter 2 Semiotics of the Continuum and Logic of the Universe Carlo Sini ............................................................................................................ 15 Chapter 3 Peirce, Proper Names, and Nicknames Giovanni Maddalena ........................................................................................... 22 Chapter 4 Psychology and Anti-psychologism in Peirce Rosa M. Calcaterra.............................................................................................. 35

PART II - ABDUCTION AND PHILOSOPHY OF MATHEMATICS Chapter 5 The Analytic/Synthetic Distinction and Peirce’s Conception of Mathematics Michael Otte........................................................................................................ 51 Chapter 6 The Heuristic Exclusivity of Abduction in Peirce’s Philosophy Ivo Assad Ibri...................................................................................................... 89

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Chapter 7 Semiotics and Deduction: Perceptual Representations of Mathematical Processes Susanna Marietti ............................................................................................... 112

PART III – PEIRCE AND THE WESTERN TRADITION Chapter 8 Reflective Acknowledgement and Practical Identity: Kant and Peirce on the Reflexive Stance Vincent Colapietro ............................................................................................ 128 Chapter 9 The Importance of the Medievals in the Constitution of Peirce’s Semeiotic and Thought-sign Theory Claudine Tiercelin............................................................................................. 158 Chapter 10 Peirce and Plato Rossella Fabbrichesi ......................................................................................... 185 List of Contributors........................................................................................... 201 Indexes .............................................................................................................. 205

ACKNOWLEDGMENTS We wish to thank all of the participants in the “International Conference on Semiotics and Philosophy in C.S. Peirce” (Milan, Italy, April 2005), and particularly the Chancellor of the University of Milan, Professor Enrico Decleva, the Dean of the Faculty, Professor Elio Franzini, the Director of the Philosophy Department, Professor Renato Pettoello, who provided generous support to our project. We also wish to thank the chairmen of the sessions of the conference, namely Umberto Eco, Corrado Mangione and Giulio Giorello, who animated the discussion. Finally, our hearty thanks go to Paolo Bottazzini and Marco Meneghelli, the enterprising webmasters of our site on Peirce (www.filosofia.unimi.it/peirce/), who made every effort to advertise our initiative.

LIST OF ABBREVIATIONS The following commonly accepted abbreviations are used to refer to the standard editions of Peirce’s works: NEM - The New Elements of Mathematics. Ed. by Carolyn Eisele, 4 voll. The Hague: Mouton, 1976 (followed by volume and page numbers). CP - Collected Papers of Charles Sanders Peirce. Ed. by Charles Hartshorne and Paul Weiss, voll. 1-6. Cambridge: Harvard University Press, 1931-1935; ed. by Arthur W. Burks, voll. 7-8. Cambridge: Harvard University Press, 1958 (followed by volume and paragraph numbers). CN - Contributions to the Nation. Ed. by Kenneth L. Ketner and James E. Cook, 4 voll. Lubbock: Texas Tech Press, 1975-1987 (followed by volume and page numbers). RLT - Reasoning and the Logic of Things. Ed. by Kenneth L. Ketner and Hilary Putnam. Cambridge: Harvard University Press, 1992. EP - The Essential Peirce. Ed. by Christian J.W. Kloesel and Nathan Houser, vol. 1. Bloomington: Indiana University Press, 1992; ed. by Peirce Edition Project, vol. 2. Bloomington: Indiana University Press, 1998 (followed by volume and page numbers). W - Writings of Charles S. Peirce: A Chronological Edition. Ed. by Peirce Edition Project. Bloomington: Indiana University Press, 1982-2000 (followed by volume and page numbers). MS – Peirce manuscript, followed by a number identified in Richard R. Robin. Annotated Catalogue of the Papers of Charles S. Peirce. Amherst: University of Massachusetts Press, 1967, or in Robin, “The Peirce Papers: A Supplementary Catalogue”. Transactions of the Charles S. Peirce Society 7 (1971): 37-57.

INTRODUCTION This volume brings together the papers presented to the International Conference on Semiotics and Philosophy in C.S. Peirce held at the State University of Milan in April 2005. It also has, however, a more ambitious aim: scholars who were not present at the Conference were invited to send contributions so that some of the most authoritative voices in contemporary studies on Peirce, in particular from among those in Europe, could be included within a single collection. The intention is to encompass the reflections of philosophers in different fields–logic, philosophy of mathematics, theoretical philosophy, analysis of language. They were to present the results of their studies of this thinker and indicate new lines of research while giving the nonspecialist a clear idea of what it means today to address the many aspects of knowledge introduced by Peirce, without doubt the most prolific and versatile mind ever to have emerged in American culture. In short, this historical–but also in a broad sense ideal–figure is the focal point for all those who have generously contributed to this volume. They compose a complex polyphony in which each instrument interprets in its own way a score that in effect, as scholars well know, has always been incomplete but for this very reason open to many variations, some of them very fruitful. Charles Sanders Peirce (1839-1914) is now referred to with increasing frequency in the most varied fields, from logic to epistemology, semiotics to linguistics, and mathematics to law. Nevertheless, his ideas are little known due to the difficulty in accessing his writings, made up of thousands of often unordered pages not widely translated into other languages. The problem of being able to see Peirce’s own formulation of his ideas is being solved in part by the mammoth task of bringing out the collection of his Writings. But this involves sorting out more than 100,000 manuscript pages and the work is still far from completion. Peirce still appears to us in fragments; just think that he never got as far as publishing a single philosophical monograph. And also fragmented into a thousand currents are the studies dedicated to him in every part of the world, from Japan to Croatia, as a look at any bibliography on the subject will show. Yet it is a well-known fact that this philosopher is the father of pragmatism and founder of modern semiotics as well as the inventor of the logic of relations and the system of writing he called “Existential Graphs”. He was in fact the last philosopher able to master very different fields of study so that he is deservedly called the “American Leibniz” and stands out as the undoubtedly greatest American thinker. In his own country, however, his work

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is still widely neglected and people prefer to read his pupils, William James and John Dewey, who often distorted his thinking even though they developed it in other fertile directions. In Europe, Peirce is increasingly read and studied. As mentioned during the Conference, the example of Italy provides a good demonstration of this. Here, as far back as in the 1970s, the work of Umberto Eco (chairman of the first session) in the strictly semiotic field and that of Carlo Sini in theoretical philosophy made it possible for a complex and convoluted thought–“flashes of brilliant light relieved against Cimmerian darkness” as James put it–to become a powerful guiding beacon for a whole series of theoretical questions. This may well have happened for the very reason that though he put together a very solid and authoritative philosophical corpus, Peirce never presented it in a finished form and so left to those who followed in his wake a wide range of possible readings as well as the opportunity to indulge in free and varied interpretation–always irresistible for anyone engaging in philosophy. So it is semiotics and philosophy or, better, semiotics as philosophy and philosophy as semiotics, which emerge from a reading of these papers. At this point, therefore, it is worth saying something on semiotics as it is understood here. We believe that Peirce did not engage in the study of signs with a view to establishing a specialist technical discipline like the one that is now taught in many of the new degree courses. He understood semiotics as the study of the referential sign relation between sign, object and interpretant. This relation can activate an unlimited semiosis that is able to overwhelm both reference to an object outside interpretation and reference to a subject abstracted from the very form of life and communication that makes him what he is. His philosophy, then, reflects on one side a complex hermeneutical interplay between logic and ethics and, on the other, a pragmatics of a realist and universalist rather than empiricist kind. For Peirce, semiotics is philosophy in the broadest sense of the term: a theory of categories, an expression of modes of being, an analysis of knowledge and the question as to what the universe consists of, as well as a description of what we are and what we are prepared to do. And philosophy is semiotics: a fundamental reflection on the theme of reference and of distance, of symbolic mediation, of being present for something absent. We could go so far as to say that this has been the case since Heraclitus, who in fragment 93 attributes to the God Apollo the obscure ability of the semainein: “The Lord whose oracle is at Delphi neither speaks nor conceals, but gives a sign”. There is indeed a thread running through all of Peirce’s writings however diverse and inconsistent with one another they may appear to be. This thread consists of the brilliant intuition of the sign relation and its infinite references but also, and inseparably, of the question as to the relation that links man to nature, nature to its interpretant and the interpretant to the experience

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constituting it, which can be of both a logical and practical kind. This thread is Peirce’s tone–if we can put it like that–his tone of voice and the tone of his writing, imprinted on the page in letters of fire each time he embarks on giving expression to his thoughts whether on astronomy or algebra, economics or esthetics. It is our hope that this tone is also present in the contributions to this volume. To varying extents, they present this great thinker’s ideas not only and not so much putting the emphasis on his answers to the many questions posed by his time–in part also ours–but highlighting the questions that he posed to himself, full of meaning, torment and curiosity. They are questions that can serve today as a springboard for doing good philosophy, which it should be remembered is love of knowledge, hence endless questioning, and not investigation channeled into a school of thought, a set of problems with given solutions, notions to be reeled off, in the desperate attempt to be objective and methodical. Peirce was in this sense a true philosopher, who was able to engage with the technical languages of his time without losing sight of the only enquiry that could give them meaning. There are no contents that are philosophical in themselves and a philosophical doctrine only exists within the conventional a posteriori demarcations applied to certain historical events. To do philosophy does not mean dealing with being or acting or even the sign, addressing this or that theme but, instead, adopting the approach of the philosopher, of he who wants to be aware of his own gesture and is prepared to shift the question further and further back. Peirce undertook a radical epistemological investigation into the foundations of all knowledge, from the a priori kind that is mathematics and logic to that of the empirical sciences and of common sense. This line of enquiry was traced back to the extent of going beyond the usual distinctions at which traditional thought stopped, such as that between perceived and inferred knowledge or, even more, between matter and spirit. Although he very skillfully set down a methodology of knowledge–containing considerations that would still be of great value even when taken out of their philosophical context–he did not confine himself to this but pushed the question as to the possibility of knowledge to the extreme limit of a new cosmological conception. Now, this Peircean epistemology is entirely and authentically semiotic. Semiotic is the categorial starting point and semiotic is the awareness that reality is subject to being understood in and only in as much as mind and nature are two faces of the same coin, the two sides of the same sign process. Peirce absorbed the lesson of Kant with great perception but went further by understanding the semiotic value of the categories. This enabled him to abandon what he saw as dogmatic in Kant (the thing-in-itself as the hypothesis of a presign sensible manifold, but also the unity of apperception as the basis of objective knowledge). From its expression as a mode of the intellect, the idea of

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category soon became a mode of the sign, that is–as Peirce saw it–of being. Also many other notions underwent significant modification as his writings followed one after the other. The common fate of the conceptual tools forged by Peirce is to be put to the test in ever new theoretical contexts, used at every point to which they are able to lead us as jimmies to break open the old containers of ideas transmitted by tradition. Thus, the idea of habit, an operative-methodological notion, was brought within cosmology; that of abduction served to establish the affinity between man and the universe; and the continuity principle was not only introduced to explain Cantor’s sets but also became a quite powerful criterion for explaining all of reality. In our view, it is for this very reason that Peirce is still read today and not just by professional philosophers; his ideas are seen not only as applying to limited fields of knowledge but also as keys to open up the whole of experience. We then find out that many law scholars work with his concept of abduction, which has also demonstrated its usefulness in various other disciplines like history and computer science. Likewise, the continuity principle, or synechism, can migrate from mathematical to logical analysis and even touch upon theology. Peirce was also and above all a great logician and there are countless anecdotes on the number of original ideas he can boast of. But far more important is the fact that he made fundamental contributions to the algebra of logic, opening the latter up to analysis of the entire universe of relative terms. As is well known, the dominant tradition in logic during the twentieth century took a different path from that of algebra; nonetheless, we are still today reckoning with the work of Peirce. More than all of this, however, what we want to underline once again is that, hand in hand with his strictly logical research, Peirce never stopped reflecting intensely and radically on the meaning and foundation of this research. He contemplated the models of thought used in logic and mathematics and assigned to each of these disciplines its own place in the spectrum of the sciences. This is just one example–but a fundamental one in the philosophical debate–of what was said above regarding Peirce’s nonspecialist approach even to subjects that are more specialistic by definition. And again, Peirce’s analysis of the foundations of logical thought is carried out semiotically. It is from his study of the signs used in the deductive sciences that Peirce ends up by giving us acute and original answers to traditional questions in the philosophy of mathematics and logic: how does mathematics give us new knowledge? Where does the evidence in a demonstration come from? How can universal results be achieved? Peirce analyzed the graphic signs with which mathematicians work concretely and reread them in the light of the semiotic tools that he fashioned himself. Those same tools that were applied with mastery to identify a new table of categories as well as to follow a phenomenological path that can now help us to understand the legitimacy of logical thinking,

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which Peirce centers on the notion of diagram. In all logical-mathematical writing he saw diagrammatic writing, the material representation of abstract relational structures. He held that the mathematician cannot but think diagrammatically. It is starting from this consideration that his research arrived at the system of Existential Graphs, which many insist on seeing as a senile extravagance but which is underpinned by profound theoretical evaluation. Unfortunately, contemporary logic and philosophy of mathematics have inherited from the tradition in the 20th century a strong negative bias against diagrammatic reasoning. This prejudice tends to make us doubt, sometimes unconsciously, anyone who claims the right to base themselves on similar oddities. What sort of strange devices might diagrams be, which instead of ensuring that complete transparency that symbolic languages endeavor to achieve, are encumbered with all their concrete spatial qualities so that it is very difficult to distinguish what belongs to the essence of pure thought from what is superimposed on it incidentally? A widespread feeling tells us that reasoning should be represented linguistically and symbolically in order to guarantee its independence from the unessential instruments used to give it expression. As often happened, Peirce went against the general trend in this respect. Not only did he never strive to reach pure thought stripped of its chance coverings, he maintained rather that thought does not exist at all outside of the material signs which express it on each occasion. To reason means to transform the concrete sign of the premises to reasoning into the concrete sign of its conclusion, and nothing is left to analyze when we eliminate these signs under the illusion of grasping their ethereal content. Peirce’s teaching goes very deep and ends by encompassing not only the thought of men but also all of nature. Even nature, he tells us, evolves by transforming signs into other signs; it too embodies thought of an inferential kind. We believe that the papers presented here bear witness in the most direct way to the vitality of Peirce’s philosophical reflections. There is no celebratory homage to a great thinker but rather a keen and dynamic dialogue with his ideas. The authors talk to Peirce, discuss questions with Peirce in mind, sometimes arguing against his conceptions and pointing out their aporia, which in wideranging and fully philosophical thought are inevitable and also desirable. These papers display a vigorous approach to Peircean studies that is the true hallmark of philosophical enquiry. Philosophy–this great debate that unfolds through the centuries–grows and enriches its most deeply entrenched quality when it is truly able to listen and mingle, to contaminate itself internally and transfer cognitive tools from one part of its domain to another, readapting and reinterpreting them according to new requirements and the particular context. In our view, when we are given the possibility to take a writer outside himself, this is the clearest indication that he is still productive. It is gratifying to see in these papers that

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today philosophers use Peirce’s ideas to reach beyond him. What we find in them are not detailed comments on his writings or precise explanations of his notions but, instead, reflections and arguments that apply the philosophical tools learnt from him to the treatment of new problems and the formulation of new themes, both of which have arisen in the most varied areas as original theoretical necessities independent of Peirce. Thus it is that Peirce’s cultural approach and his single conceptions can help us to get our bearings when we reflect on human actions. They can guide us in going back over some of the stages in the history of mathematics and take us into a dialogue with contemporary philosophers or those in the distant past, providing us with a deeper understanding of the conceptions on which we ourselves were formed together with our entire thought. This is how Peirce, in his very person, gives truth to one of the most distinctive features of his thought: that general sharing of knowledge that for him lay at the root of all genuine progress in it. We all take part in research and this condition takes on an ethical dimension for which philosophy is able to account. Peirce, therefore, claimed a very elevated role for philosophy. This is because philosophy is not weak but strong knowledge, which can still teach the various scientific disciplines something and cross the rigid distinctions between them. Its strength is determined by the engagement of the question that moves it: the question as to the meaning of the practices that a certain society puts into effect and, hence, the question about this very questioning; the question about what is “meaning” and what is “practice” not in this or that theoretical operation but in general and from the very beginning. Meaning and practice, semiotics and pragmatism: this is what occupied Peirce throughout his entire life and we believe that he still has much to teach us on it. He therefore comes across as more of a teacher than an academic, reminding us like Socrates that the function of philosophers is to act as gadflies to culture, rather than to shut themselves up in the ghetto of “elegant conversation” to which our age would like to confine those who engage in pure thought. Rossella Fabbrichesi Susanna Marietti

CHAPTER 1 PEIRCE’S CONTRITE FALLIBILISM Nathan Houser My aim here is to reconsider the meaning and scope of Peirce’s doctrine of fallibilism. It may be helpful to begin by reviewing a contemporary account by Nicolas Rescher taken from his article on “Fallibilism” in the Routledge Encyclopedia of Philosophy. According to Rescher, fallibilism is a “doctrine regarding natural science” which holds that “scientific theories cannot be asserted as true categorically”. Fallibilism “does not hold that knowledge is unavailable” but only that “it is always provisional”. Rescher says that the doctrine of fallibilism is “most closely associated with Charles Sanders Peirce”. Rescher holds what might be regarded as a strong version of fallibilism, according to which we are to understand that any scientific theory or system will ultimately fail. A weaker version might hold only that any scientific theory or system might ultimately fail. The ultimate failure, or the possible failure, of any theory is explained by Rescher as follows: “Rational inquiry links the products [of] our understanding to the experienced conditions of a world in which chance and chaos plays an ineliminable role, so that there will always be new conditions and circumstances that ultimately threaten our rational contrivances”. Rescher believes that this situation lends itself naturally to a Kuhnian interpretation of scientific progress. Other than the role played by chance and chaos, principal grounds for fallibilism that Rescher gives are that available observational data underdetermine theories, and a similar but not equivalent point, that concrete realities are always experienced somewhat ambiguously. The ambiguity Rescher has in mind results from the need to interpret data, to put it into a theoretical context, in order to make sense of it. But, alas, since theories are underdetermined by observational data, any interpretation of data “carries in its wake the prospect of ambiguity, diversity, and discord”. According to Rescher, we occupy the predicament of the “Preface Paradox” exemplified by an author who apologizes in his or her preface for errors that have doubtless made their way into the work, while blithely remaining committed to all the assertions made in the body of the work itself. Fallibilism, historically and perhaps conceptually, is a doctrine closely aligned with scientific realism. This is probably because fallibilists are naturalists,

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generally speaking, who regard knowledge as an outgrowth of tested experience. Fallibilists have, therefore, generally been concerned with “protecting scientific realism”, to use Rescher’s terms. He says that Peirce’s stratagem was to adopt a convergence theory of inquiry according to which, though always fallible, scientific theories may be expected to “grow increasingly concordant and their claims less and less differentiated”. It seems, then, that according to Peirce we may expect science to increasingly approximate the truth, that state of information that is the limit toward which it is progressing. Rescher doesn’t believe Peirce’s account to be plausible. He claims that the fact that scientific progress “is not simply a matter of increasing accuracy” but is “genuinely revolutionary”, involving fundamental changes of mind about how things happen, “blocks the theory of convergence”. According to Rescher, “realistic fallibilists” have to be more radical than Peirce. We have to adopt a “Cognitive Copernicanism” and hold “that there is nothing cognitively privileged about our own position in time”. “A kind of intellectual humility is in order”, Rescher says, “a diffidence that abstains from the hubris of pretensions to cognitive finality or centrality”. We shall see that in fact Peirce is in agreement with this admonition. Rescher understands that his fallibilism has a decided skeptical impetus which he thinks Peirce failed to overcome with his convergentism. This appears to leave scientific realism at risk. Rescher mitigates his account of fallibilism by emphasizing that he regards the doctrine as applying to scientific knowledge but not necessarily, or at least not so radically, to the “knowledge of everyday life”. Because we are less committed to “detailed precision” in everyday life and, conversely, because in science we “deliberately court risk by aiming at maximal [...] informativeness and testability”, fallibilism is “a more plausible doctrine with respect to scientific knowledge”.

Margolis on Peirce’s Fallibilism Now I will turn to Peirce’s fallibilism but at first indirectly by considering the account given by Joseph Margolis in his 1998 article in the Transactions of the Charles S. Peirce Society. It was this article and Margolis’s more recent but less systematic treatment of fallibilism in his book Reinventing Pragmatism that led me to take a new look at Peirce’s fallibilism and its scope within Peirce’s system of philosophy.1 Margolis’s paper is disturbing and unsatisfying in many respects yet overall I find it insightful and quite helpful. Margolis begins with an observation 1

Significant portions of this section, as well as note 2, are taken from my 28 Dec. 2004 presidential address to the Charles S. Peirce Society (published in Transactions of the Charles S. Peirce Society, 2005).

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that I don’t remember hearing before: that Peirce’s doctrine of fallibilism is a linchpin of his philosophy. Certainly fallibilism is commonly regarded as one of the many interesting doctrines to be found in Peirce, even as a defining doctrine, but Margolis’s claim that it is a linchpin of his philosophy caught my attention in a new way. Margolis represents Peirce’s fallibilism, correctly I believe, as “an important but sprawling doctrine”, one that Peirce “never entirely domesticated”. He describes Peirce’s fallibilism as consisting of three “serially nested themes”: (1) fallibility, the “thesis that, with regard to any proposition, it is humanly possible to hold a mistaken belief”, which is “tantamount to a denial of Cartesian indubitability”; (2) self-corrective inquiry, the thesis that “it is both possible and likely that, for any mistaken belief, a society of inquirers can, in a pertinently finite interval of time, discern its own mistakes and progress toward discovering the true state of affairs”; and (3) a supporting metaphysics that marks Peirce’s fallibilism as more than just an epistemological doctrine (Margolis, 539). Margolis claims that Peirce failed in his defense of fallibilism. According to Margolis, Peirce’s failure “is extraordinarily important for the ultimate fate of many other contested theories that Peirce links to his doctrine”; in particular, Margolis says that “Peirce’s realism and conception of thirdness fail, if the doctrine of fallibilism fails” (Margolis, 536). So according to Margolis, what is at issue is the very heart of Peirce’s philosophy. Margolis’s case against Peirce’s fallibilism is based in part on his rejection of Peirce’s convergentism. But his chief complaint is that Peirce’s fallibilism fails because of paradoxes that beset its enabling metaphysics (Margolis’s third theme) and the unacceptable consequences of trying to resolve those paradoxes. It turns out that the most damaging paradox, one Margolis calls “the paradox of the known object”, simply dissolves on a careful reading of the relevant Peirce text.2 Although, in my opinion, none of Margolis’s 2

The Paradox of the Known Object (according to Margolis) results from two incompatible claims, both, Margolis says, made by Peirce and required by his fallibilism. Claim 1: “the act of knowing a real object alters it” (CP 5.555). Claim 2: “the real thing is as it is, irrespectively of what any mind or any definite collection of minds may represent it to be” (CP 5.565). Margolis argues that this incompatible dualism runs throughout Peirce’s doctrine of fallibilism and, effectively, destroys it. Margolis claims that “Peirce characterizes all of his principal notions—truth, reality, objectivity, mind, existence, thirdness, community, belief, knowledge, even pragmatism and fallibilism—in two distinct ways: in one, in accord with the consensual life of actual societies working in finite ways; in the other, in accord with the vision of the ideal limit of infinitely extended inquiry, in which the first is interpreted” (Margolis, 553-554). He goes on: “I hold that there is an analogous incompatibility involving each and every one of Peirce’s central notions and that the primary function of the full doctrine of fallibilism is to interpret and reconcile the double interpretation of all these notions. Effectively, the

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arguments against Peirce’s fallibilism fully hits the mark, what matters here is that his provocative treatment succeeds very well in showing Peirce’s fallibilism in a new light and in revealing it to be a key Peircean doctrine calling for attention. In gathering in the name of Peirce’s fallibilism all of the doctrines and principles that either directly or indirectly underwrite it (he links fallibilism with, at a minimum, Peirce’s evolutionism, his logic of relations, his realism, his doctrine of thirdness, his theory of thought and mind, and his views on progressivism in science), Margolis gives a new sense to the meaning of Peirce’s fallibilism and its centrality for Peirce’s pragmatism and for his thought in general.

What Peirce Says About Fallibilism Provoked by Margolis, I want to reconsider the scope of Peirce’s fallibilism and to begin working out a fuller picture of what it really amounts to. Let’s begin with a few background considerations. Recall that Peirce distinguishes between existence and reality, and that neither is absolute. Consider, for example, the

difference between the two is what obtains in particular, determinate, and finite human actions and what obtains in the single, all-inclusive ideal, evolutionary continuum viewed at the limit of the infinite sequence of all such finite actions” (Margolis, 554). Margolis concludes his case against Peirce’s form of fallibilism as follows: “Thus: the ‘real’ is altered by action, in the sense of finite human life; but the ‘real’ is, also, what it is ‘irrespectively of any mind,’ at the ideal limit of infinite inquiry. The Deweyan form of fallibilism jettisons Peirce’s third theme and holds to the first two themes. The price of such a retreat is to replace the would-be legitimation of a realism in science with a pious hope in favor of such a realism [...]. It’s no good insisting that Deweyan fallibilism ever recovers objectivity and realism: it has no regulative principle to offer; but then neither does Peirce’s fallibilism, since its regulative principle operates, per impossible, only at the ideal limit of inquiry. The dilemma cannot be overcome” (Margolis, 554). In dismissing Peirce’s fallibilism, Margolis has placed a lot of weight on the inconsistency of the two claims Peirce made in the so-called “paradox of the known object”. It is certainly interesting, if not revealing, that Peirce did not make both claims. Margolis missed the irony of the paragraph that contains the purported first claim. This is how Peirce put forward the alleged claim: “It appears that there are certain mummified pedants who have never waked to the truth that the act of knowing a real object alters it. They are curious specimens of humanity, and as I am one of them, it may be amusing to see how I think” (CP 5.555). Peirce then continues to elaborate the claim he is attributing to pragmatists who equate “the True” with “that in cognition which is Satisfactory”, a view he, as a selfproclaimed “mummified pedant”, rejects. So, on a more careful reading of the text in question, the paradox disappears—it disappears, anyway, assuming that Margolis is wrong in holding that Claim 1 is required by Peirce’s fallibilism (as Peirce obviously denies).

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following quotation from Peirce’s 1893 paper on “Fallibilism, Continuity, and Evolution”: If all things are continuous, the universe must be undergoing a continuous growth from non-existence to existence. There is no difficulty in conceiving existence as a matter of degree. The reality of things consists in their persistent forcing themselves upon our recognition. If a thing has no such persistence, it is a mere dream. Reality, then, is persistence, is regularity. In the original chaos, where there was no regularity, there was no existence. It was all a confused dream. This we may suppose was in the infinitely distant past. But as things are getting more regular, more persistent, they are getting less dreamy and more real (CP 1.175).

Now the infinite past when nothing was real and the infinite future when all reality will have a fixed existence are ideal limits and not assumed by Peirce to be historical absolutes. The upshot is that reality itself is in a continual state of growth. What about truth for Peirce. The standard view is that truth is belief at the ideal end of inquiry—but we should bear in mind that, from the side of logic, truth is the value of a proposition, which in Peirce’s philosophy is an intellectual sign that mediates between an object or state of affairs and an interpretant (an effect on an interpreter). This means that truth is always relative on the one hand to the conceptual resources of sign users and on the other hand is constrained by the pragmatic conditions that pertain between the object and sign users. As long as learning continues and pragmatic conditions change, truth in this sense cannot be fixed in eternal stagnation. In his Cambridge Conferences Lectures of 1898, Peirce rather notoriously made a distinction between matters of vital importance and the selfless advancement of knowledge and he considered whether our conception of truth varies accordingly: But whether the word truth has two meanings or not, I certainly do think that holding for true is of two kinds; the one is that practical holding for true which alone is entitled to the name of Belief, while the other is that acceptance of a proposition which in the intention of pure science remains always provisional. To adhere to a proposition in an absolutely definitive manner, supposing that by this is merely meant that the believer has personally wedded his fate to it, is something which in practical concerns, say for instance in matters of right and wrong, we sometimes cannot and ought not to avoid; but to do so in science amounts simply to not wishing to learn (EP2: 56).

With these background considerations in mind, let’s consider at last some of Peirce’s own expressions of his fallibilism. At the beginning of his 1893 article, Peirce argues that we can never hope to attain absolute certainty, absolute exactitude, or absolute universality, through reasoning. But then he says “if

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exactitude, certitude, and universality are not to be attained by reasoning, there is [...] no other means by which they can be reached” (CP 1.142): not by revelation, not through intuition of innate truths, not by direct experience, nor in any other way. So, “we can never be absolutely sure of anything, nor can we with any probability ascertain the exact value of any measure or general ratio” (CP 1.147). This seems mainly an expression of Margolis’s first theme of fallibilism but there are clear indications here of other parts of Peirce’s philosophy that will support the fallibilist stance. A statement that I particularly like is this one: “Fallibilism is the doctrine that our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and indeterminacy” (CP 1.171). This seems to connect Peirce’s metaphysical doctrines of synechism and tychism in a crucial way with fallibilism. In “The First Rule of Logic”, Peirce expresses his fallibilism indirectly in a passage leading up to his famous dictum: “Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy, Do not block the way of inquiry” (EP2: 48). The error of becoming so satisfied with what we already incline to think that we loose the will to learn is an offense that many metaphysicians are addicted to Peirce says, and it reveals itself in different ways: in absolute assertions, in claims that something or other can never be known, in claims that something is utterly inexplicable, and in claims that the final and perfect formulation of a truth has been achieved. This seems to be mainly a methodological and perhaps an ethical concern. An indication that Peirce may indeed have held the broad view of fallibilism that Margolis recommends can be found in a passage from Peirce’s 1893 fallibilism paper which the editors of the Collected Papers included in the autobiographical remarks gathered as a preface for the Harvard edition: For years [...] I used for myself to collect my ideas under the designation fallibilism; and indeed the first step toward finding out is to acknowledge you do not satisfactorily know already; so that no blight can so surely arrest all intellectual growth as the blight of cocksureness [...]. Indeed, out of a contrite fallibilism, combined with a high faith in the reality of knowledge, and an intense desire to find things out, all my philosophy has always seemed to me to grow [...] (CP 1.13-14).

Perhaps this is mainly a call for intellectual humility and the recognition that seeds of knowledge cannot any longer take root in minds that have become hardened and inhospitable to new ideas. That seems to be what he had in mind when he wrote, also in 1893, that “Nothing can be more completely contrary to a philosophy the fruit of a scientific life than infallibilism, whether arrayed in its old ecclesiastical trappings, or under its recent ‘scientistic’ disguise” (CP 8, G-c.1893-5, pp. 282-3).

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Peirce stated explicitly that he did not expect fallibilism to be attractive to conservative thinkers (those who dread consequences) but to radicals. Not to cocksure radicals, but to radicals who try experiments and who are eager to carry consequences to their extremes. Peirce believed that such radicals are animated by the spirit of science and that it is among them that fallibilism will find its supporters (see CP 1.148). There are many other characterizations of fallibilism in Peirce’s writings but these constitute a sufficient set of examples. One can see that there are intimations of the broad view that Margolis takes even though it is not explicitly stated and perhaps it wasn’t even fully recognized by Peirce.

Peirce’s Sprawling Fallibilism In what follows I want to begin developing Margolis’s insightful observation that Peirce’s fallibilism is “an important but sprawling doctrine, which Peirce never entirely domesticated” but which nonetheless is a linchpin of his philosophy. Which parts of Peirce’s philosophy support, or are crucially linked with, his fallibilism? How do they fit together? With his three “serially nested themes” Margolis has made a good start: Peirce’s fallibility thesis is wedded to the epistemological theory of self-corrective inquiry (Peirce’s convergence theory of truth), and these positions are supported by certain metaphysical doctrines. It will take a lot of work to get everything connected up in the right way—a lot more work than can be undertaken here. But I’m hoping that we can improve on Margolis and map out a path for future research. To begin making a better map of the territory, we might consider what different arguments from Peirce lead to the fallibilist conclusion? Susan Haack, in her “Fallibilism and Necessity” (Haack, 43), writes that “Some of Peirce’s arguments for fallibilism [...] stress the limitations of [our] human cognitive apparatus (no infallible intuition); others point to the weaknesses of our cognitive methods (error in measurement, uncertainty introduced by inductive reasoning); and others [...] appeal [...] to limitations as it were in the content of our knowledge (indeterminism)”. These add to the picture Margolis framed. Another approach is to consider sources of knowledge—not knowledge with a capital K, but our store of beliefs or, we might say, our information base. What are some of the candidates: instinct; perception; inference? Anything else? Insight, perhaps; intuition; inspiration; revelation; and, for Peirce, we don’t want to forget il lume naturale. And what about testimony? Of course I cannot here begin a proper analysis of each of these possible sources of knowledge but I will consider briefly whether any of these sources can be expected to provide more than a fallible

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ground on which to build our knowledge structures. I think this will be revealing even though for most of these alternatives we already know Peirce’s answer from the passages quoted in the previous section. I suppose instinct is a good place to start for perhaps it is there if anywhere that we might expect to find the bedrock we are looking for. In her illuminating study, “Peirce and Wittgenstein on Common Sense”, Rossella Fabbrichesi reminds us that both of these great thinkers used that very word and both believed in “a solid bedrock of indubitable beliefs (Peirce) or certainties (Wittgenstein) that [...] constitute[s] the solid ground of any possible knowledge” (Fabbrichesi, 188). This is the ground of common sense that has been inculcated in human thought over the ages, presumably through some kind of cognitive selection process, and its sanction, though it does not ask for sanction, is pragmatic. It is simply not questioned because it has served us so well. But as pragmatic habits of some sort, I think that we must regard instinctive beliefs as the ends of long-conducted rational or semiotic inquiries spread over centuries and, as such, there must have been an implicit inferential process that led to these long-established conclusions. Fabbrichesi points out that it is not only instinctive beliefs that bring inferential or, more generally, semiotic processes to a conclusion but, contrary to the perhaps prevailing view that for Peirce semiosis is never-ending, she accepts Peirce’s later pronouncement (and maybe earlier as well) that not only can semiotic inquiry reach conclusions (final interpretants) but that for all practical purposes it does so all the time. These conclusions, as Fabbrichesi tells us, are indubitable just as our instinctive beliefs are indubitable: the conduct of life demands that we carry on without doubt. But we know, do we not, that not even bedrock goes all the way down. Peirce gave a number of examples of when bedrock gives way to “events beyond human control”. Take the case of the long-settled belief that “heavy bodies must fall faster than light ones”. This really was bedrock for many centuries and, as Peirce noted, any competing views were regarded as “absurd, eccentric, and probably insincere”. “Yet”, Peirce continued, as soon as some of the absurd and eccentric men could succeed in inducing some of the adherents of common sense to look at their experiments—no easy task—it became apparent that nature would not follow human opinion, however unanimous. So there was nothing for it but human opinion must move to nature’s position. That was a lesson in humility (CP 5.385, n. 1).

Now I know that instinctive habits have been serving the species far longer than the once “long-settled” belief that “heavy bodies must fall faster than light ones”. But if the bedrock of instinctive beliefs runs deeper it may be only because these beliefs are so vague, as Fabbrichesi pointed out, and though that very vagueness helps give us the confidence we need to get on with life it is a weakness when it

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comes to elaborated intellectual thought. In fact it will support rational structures only by remaining silent. Much more could be said about instinct as a source of knowledge but to reach the end of this survey we must move on. As intellectual offspring of the late Enlightenment Epistemologists, isn’t it through perception that we expect most of our knowledge to be acquired? Remember Peirce’s claim that “[t]he elements of every concept enter into logical thought at the gate of perception and make their exit at the gate of purposive action” (CP 5.212; EP2: 241). So this must be the main source of what we call our scientific or our theoretical knowledge—our accumulated store of intellectual interpretants. But is there any avenue through perception that doesn’t lead past an inspection booth where “fallible” is stamped on all passports? Well, maybe there are no such inspection booths; in fact it may be that absence which has been the source of much confusion because perception does not own up to the fallibility of its own productions. But if we take the “fallible” stamp in hand are there any products of perception that we should be willing to exempt? Probably not. I have already indicated in passing that perception seems to encompass the sensory-cognitive process that begins in sense impressions and ends with perceptual judgments. Neither the sense impression nor the percept expresses anything that we can add to our encyclopedias or that we can reason from so we are left with the perceptual judgment as the source of knowledge that somehow begins in sensory experience. That is what introduces the intellectual component into perception; for convenience, I think of perceptual judgments as attaching the equivalent of text, at the propositional level, to sensations (but take note that even pictures and diagrams can represent facts, so not all propositions are linguistic entities).3 But perceptual judgments in whatever form are, after all, judgments, and judgments are the conclusions of inferences. I will spare you the analysis but, according to Peirce, “abductive inference shades into perceptual judgment without any sharp line of demarcation between them” so that “perceptual judgments, are to be regarded as an extreme case of abductive inferences” (CP 5.181). These judgments become the “first premisses”, from which, in the course of our experience, we are able to draw more and more remote conclusions and fill out our encyclopedias. But knowledge acquired in this way cannot be infallible unless abduction is an infallibly truth-functional process of inference. Of course it isn’t. In

3

We can think of perception something like Robert Frost thinks of poems: “A poem [...] begins as a lump in the throat, a sense of wrong, a homesickness, a lovesickness [...] It finds the thought and the thought finds the words” (Frost to L. Untermeyer, 1 Jan. 1916, Bartlett’s Familiar Quotations).

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fact abduction, though it may be the most fruitful form of inference, is also the weakest form. So perception cannot be a source of infallible knowledge.4 Because of the merging of perception with inferential processes I have already begun to consider inference as a possible source of knowledge. Peirce has taught us that there are three distinct varieties of inference: deduction, induction, and abduction. I am going to speed things up a little by asking the reader to admit with me that if any form of inference could be infallible it could only be deduction. We might say, I suppose, that a quantitative induction might similarly seem definite enough to be a candidate for infallibility, but I would argue that it is only because quantitative induction shades into deduction that this is so. But the point is moot because neither deduction nor induction is in fact a source of knowledge, according 4

This is not the place to go into detail about the structure and intricacies of Peirce’s theory of perception but for full disclosure I should point out that it is not unanimously accepted that Peirce succeeded in linking the sensory ground of perception, the percept, with the cognitive outcome, the perceptual judgment. At a recent conference on Pragmatism and Analytic Philosophy held in Rome (sponsored in March 2005 by Università Roma Tre Facoltà di Lettere e Filosofia and Centro di Studi Americani), John McDowell expressly stated that he doubts that Peirce could have succeeded in this and I believe that McDowell’s doubt that this link can be legitimately made is commonly shared by philosophers who belong to the ‘family’ that reveres Wilfrid Sellars as a forebear. Here is a problem that needs some volunteers. If among the readers of this paper there are students who are looking for a research project and are willing to take up this challenge, a good place to begin, after first going to Peirce’s own writings, is with a book with the strange title: “Kant and the Platypus”—well, that’s its title in English. I confess that I have not fully fathomed this profound work by Umberto Eco but I recommend it as the most stimulating examination of Peirce’s philosophy of perception I know of. I trust it is not out of place to give fair warning that Professor Eco’s book is not a book to pick up and breeze through and master in a single reading. I have tried that and failed. It came somewhat as a relief to me when I learned, although from a reviewer I don’t fully trust, that Professor Eco is recorded as having said that even a very smart reader should expect to spend two weeks on every page of Kant and the Platypus. There are 431 pages, including 38 pages of endnotes, which are very rich and must be read (although the typeface is smaller and will take more time, perhaps another week per page). So a very bright reader should expect to take 900 weeks (862 weeks for 431 pages plus an extra 38 weeks for the endnotes because of the small type). I calculate that it will take a bright reader about eleven and a half years to read this book, and for ordinary readers, or for relatively slow readers like me, whether bright or not, who knows how long it will take—anyway, I’ve only had five years so far to begin sinking my teeth into Eco’s Platypus. Peirceans who read Italian have a three year jump on those of us who must read the English translation. Of course the reason this book is so difficult to read is precisely because it is so rich with the history of ideas and with theoretical insights and interrelationships. That is why students would do well to go to it first after Peirce. Naturally it will not be possible to read Professor Eco’s book even in eleven and a half years without reading many other books and taking a few courses along the way, but for those who are familiar with Eco’s works that is to be expected.

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to Peirce: “Deduction Explicates; Induction evaluates: that is all” (CP 6.475). Every plank in the bridge we build over the “chasm that yawns” between our primitive yearnings and scientific knowledge is laid by abduction alone, so if abduction cannot give us infallibility then no other form of inference can. There should be no need for me to more than mention that even in the case of deduction, which does promise us that if we start out with infallible premisses at least we can be confident of preserving our infallibility, that in fact we can never be certain that we haven’t made a mistake. It seems to me that the three possible sources of knowledge just considered, instinct, perception, and inference, are the principal candidates and we have found that in each case Peirce’s fallibilist conclusion is compelling. Earlier I listed a few other possible sources: insight, intuition, inspiration, revelation, the light of nature, and testimony. It seems to me that in the cases of the first five of these candidates the situation is much the same as it is for instinct—except that some of us may not regard the beliefs that arise from insight, intuition, inspiration, revelation, or the light of nature, as conclusions of inferences, however extended; on the contrary, we may regard them precisely as direct non-semiotic implantings or else as the result of some kind of special vision (for example, the perception of natural relational forms due somehow to our natural attunement to them). Notice, if you please, that I am not suggesting that Peirce himself endorsed any of these means as possible sources of direct knowledge; on the contrary, we know that he rejected the idea of non-semiotic belief acquisition, what I call knowledge implantings (although, in passing, it might be worth considering whether someone else’s inferentially acquired interpretant could conceivably end up in your head). But the question is whether, nevertheless, any of these possible avenues to knowledge could underwrite infallibility and it seems to me that the clear answer is “no”. Either, as in the case of instinct, knowledge claims will be so vague as to be epistemically weightless, or else there will be doubts because of the nature of the knowledge acquisition itself. And you must see that testimony, our last hope, simply shifts to someone else all of the same uncertainties about knowledge acquisition that we have just considered. None of these sources can provide more than a fallible ground on which to build our knowledge structures.

Concluding Thoughts I doubt that anything in this paper is, by itself, very surprising. But hopefully, taken together, these considerations will begin to generate a growing conception of fallibilism as something deep and central for Peirce, a touch stone, in a sense, for everything else. Margolis’s three themes, beginning with Peirce’s commitment to anti-Cartesianism, then extending to his convergence epistemology, and finding

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support in metaphysical doctrines ranging from synechism to his evolutionary cosmology, together provide an initial framework for this broad view. But it is by searching more widely for everything in Peirce’s philosophy that supports his fallibilism or, conversely, depends on it, that we are able to begin filling in the picture. The principal grounds for fallibilism that Rescher gives also apply in Peirce’s case: (1) that chance and chaos play an ineliminable role in the world; (2) that available observational data underdetermine theories; and (3) that concrete realities are always experienced somewhat ambiguously. From Peirce, directly, we can add that reality itself is in a continual state of growth. Haack finds that Peirce’s arguments for fallibilism stress limitations and weakness in our human cognitive apparatus, in our cognitive methods, and in the content of our knowledge itself. Her concerns nicely highlight the three key correlates, the knower, the known, and the process of coming to know, as all involving limitations that underwrite fallibilism. Haack’s approach connects well with the one I’ve focused on here: that of considering sources of knowledge and whether any source can underwrite infallibility. My suggestion is that Peirce’s treatment of all of these topics is in one way or another a contribution to his theory of fallibilism. In drawing to a close, I want to look briefly at why Rescher and Margolis are so concerned with tying Peirce’s convergence epistemology so tightly to his fallibilism. They are both aware of the skeptical tendency of fallibilism and see, correctly, that Peirce’s adoption of a convergence theory of truth (and I would also add his later adoption of actual final interpretants in semiosis) is part of his strategy for “protecting scientific realism”. Neither Rescher nor Margolis believes that Peirce succeeded and I concede that to avoid skepticism a fallibilist will have to do some fancy stepping. This is not the place to argue that Rescher and Margolis are mistaken in holding that Peirce’s convergence theory fails. But, anyway, one has to go beyond convergence in Peirce to find his answer to skepticism. The fact is that Peirce was a far more radical fallibilist than either Rescher or Margolis seem to appreciate. This is illustrated in a passage Hilary Putnam has called the “first really antifoundationalist metaphor” (Borradori, 62) in which Peirce imagines us trying to make our way across an epistemological bog without ever having recourse to “the solid ground of fact”. [We] must [...] find confirmations or else shift [our] footing. Even if [we do] find confirmations, they are only partial. [We] still [are] not standing upon the bedrock of fact. [We are] walking upon a bog, and can only say, this ground seems to hold for the present. Here I will stay till it begins to give way” (CP 5.589; EP2: 55). We are all walking across this bog. Fallibilism is the understanding that no matter where we are in our journey and no matter how solid the ground may feel

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beneath our feet, at any time it may begin to give way. When we feel the ground beginning to shift what is it that guides us in taking our next steps (hopefully) to a new firm place? It could not be the convergence of inquiry; we would sink into the depths long before that. No, it is abduction alone, or perhaps even that protoabductive cognitive process we call perceptual judgment, that saves our hides. But I agree with Fabbrichesi that this is where our number one fallibilist, Charles Peirce, seems to deviate a little from the hard-nosed no-nonsense approach we usually associate with him. In her above referenced Cognitio article, Fabbrichesi made the point that in an important sense our working hypotheses always come at the beginning of inquiry, not at the end, and this is especially true for perceptual judgments (Fabbrichesi, 2004). If there is inference involved, as Peirce says there is (proto-abduction, anyway), there is also something very much like a gift from nature as well, something that we just somehow manage to see as if for the first time. Here we return to the Light of Nature and its gift to us of that little bit of cognitive content that lets us imagine where we are in the world and, maybe, where to safely take our next step. Fabbrichesi asks if this is in fact a “Copernican turning point for the main upholder of anti-intuitionism and antiCartesianism in the XIX century? Is Peirce really going back to some kind of innatism?” (Fabbrichesi, 189). She doesn’t think so, and neither do I. But it is true that Peirce’s Light of Nature requires us to be somehow attuned to nature through a combination of instinct and relational isomorphisms and I know that there is still much work to be done on this problem before doubters will be convinced that our “first judgments” are logical or semiotic products rather than the magical implantings I dismissed in the previous section. Of course these gift-of-nature abductions, or proto-abductions, are not really very dependable—Peirce calls them mere “guesses”—but they are sufficient to send us on our way and their ever-soslight tendency to be true is all that is needed to enable us, or enough of us, to keep from sinking into the bog. Peirce does not insist that this way of escaping skepticism is true but he says that there is reason to hope that it is true and he believes it is the only hope we have. My final words are about my title. Why contrite fallibilism? As far as I know Peirce used that expression, “contrite fallibilism”, only once, in the quotation I gave earlier where he said that it was “out of a contrite fallibilism, combined with a high faith in the reality of knowledge, and an intense desire to find things out”, that all of his philosophy had grown (CP 1.13-14). This adds a new dimension to fallibilism, humility, which Rescher also noticed. Remember Rescher’s admonition that “A kind of intellectual humility is in order, a diffidence that abstains from the hubris of pretensions to cognitive finality or centrality”. But the humility Peirce calls for is more contrite for it is a humility that nature demands of us, a hard lesson learned, when, for example, we must bow our heads and admit that heavy bodies do not fall faster than light ones notwithstanding the common sense of

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generations. If there is a slightly religious sound to this I believe it may be because Peirce thinks that in joining the quest for scientific truth one must undergo a conversion of a Kuhnian sort and recognize, deeply, that we can only make progress together as a community of dedicated investigators, that there will be many setbacks along the way, and that our own part will at most be small.

REFERENCES Borradori, Giovanna. The American Philosopher: Conversations with Quine, Davidson, Putnam, Nozick, Danto, Rorty, Cavell, MacIntyre, and Kuhn. Chicago: University of Chicago Press, 1994. Eco, Umberto. Kant and the Platypus. Translated by A. McEwen. New York: Harcourt Brace and Co. 1997. Fabbrichesi Leo, Rossella. “Peirce and Wittgenstein on Common Sense”. Cognitio 5 (2004): 180-193. Haack, Susan. “Fallibilism and Necessity”. Synthese 41 (1979): 37-63. Houser, Nathan. “The Scent of Truth”. Semiotica 153 (2005): 455-466. Houser, Nathan. “Peirce in the 21st Century”. Transactions of the Charles S. Peirce Society 41 (2005): 729-739. Margolis, Joseph. “Peirce’s Fallibilism”. Transactions of the Charles S. Peirce Society 34 (1998): 535-570. Rescher, Nicolas. “Fallibilism”. In Routledge Encyclopedia of Philosophy. Ed. by E. Craig, London-New York: Routledge, 1998.

CHAPTER 2 SEMIOTICS OF THE CONTINUUM AND LOGIC OF THE UNIVERSE Carlo Sini The relation of semiotics to cosmology is a nodal point in the later speculations of Charles Sanders Peirce. It is considered by his interpreters to be one of the most difficult and even obscure in his entire thought: something very fragmentary as well as conceptually incomplete. To apply the theory of signs and phaneroscopic categories to a hypothetical explanation of the universe’s evolution appears to most thinkers to be a theoretical undertaking that combines undoubted originality and logical-imaginative brilliance with a broad measure of conceptual thinking that is arbitrary and vague or even untenable. Particularly unacceptable is the application of an evolutionary criterion to phaneroscopic categories, whose distinctive character is purely logical and in no way chronological or evolutionary. As is known, phaneroscopic or phenomenological categories are not “derived” one from the other since they maintain a reciprocal independence despite being as a whole correlated in a circular fashion. In fact, how could we understand them without relating them reciprocally to one another? This does not at all mean, however, to “deduce them” or perhaps “resolve them” in the last of the three, which is exactly the difference from the triads in the Hegelian dialectic that Peirce expressly points out. If this is the case, how then do we understand the “spreading out” of these categories in a kind of cosmic evolution, a process stretching, for example, from the simple to the complex or from the vague to the determinate? These are notions typical of Spencer’s evolutionism and Peirce shows that he is aware of this, though at the same time he refers to Aristotle’s idea of possibility or potentiality (which, moreover, creates a further problem).1 But how to combine Spencer’s evolutionary

1

See Charles S. Peirce, The Logic of Continuity, in CP 6.185-213, translated in Italian and edited by Giovanni Maddalena, La logica della continuità, in Scritti scelti (Torino: UTET, 2005), 393-424.

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categories with Peirce’s logical, semiotic and mathematical thought is largely unclear and surprising, to say the least. In this regard, I will confine myself to quoting two well-known passages from 1891 and 1890 respectively: It would suppose that in the beginning-infinitely remote-there was a chaos of unpersonalized feeling, which being without connection or regularity would properly be without existence. This feeling, sporting here and there in pure arbitrariness, would have started the germ of a generalizing tendency. Its other sportings would be evanescent, but this would have a growing virtue. Thus, the tendency to habit would be started; and from this, with the other principles of evolution, all the regularities of the universe would be evolved. At any time, however, an element of pure chance survives and will remain until the world becomes an absolutely perfect, rational, and symmetrical system, in which mind is at last crystallized in the infinitely distant future (CP 6.33). I will begin the work with this guess. Uniformities in the modes of action of things have come about by their taking habits. At present, the course of events is approximately determined by law. In the past that approximation was less perfect; in the future it will be more perfect. The tendency to obey laws has always been and always will be growing. We look back toward a point in the infinitely distant past when there was no law but mere indeterminacy; we look forward to a point in the infinitely distant future when there will be no indeterminacy or chance but a complete reign of law. But at any assignable date in the past, however early, there was already some tendency toward uniformity; and at any assignable date in the future there will be some slight aberrancy from law [...]. We have therefore only to suppose the smallest spoor of it [the tendency toward uniformity] in the past, and that germ would have been bound to develop into a mighty and over-ruling principle, until it supersedes itself by strengthening habits into absolute laws regulating the action of all things in every respect in the indefinite future (CP 1.409).

The problems posed by such “conjectures”–though they be stimulating–are many. Not least is the one we could raise in respect of Peirce’s explicit position according to which in an infinitely distant past of pure potentiality, or even of pure chaos, there could be no time or logic at all. In the Cambridge Conference of 1898 on the "Logic of Continuity” he expressly states that time and logic are also products of evolution (CP 6.193) and also alludes in what is indeed at first sight a mysterious fashion to the punctuality of events that occur where there was no time (CP 6.200). Such drastic statements make us at the least cautious in taking Peirce’s cosmological conjectures literally. How can it be supposed that he was not fully aware of the at the very least apparent inconsistency of conceptions that speak of “pasts” and “futures”, however “infinitely” distant, but which–so it seems–lie outside time not to mention logic?

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At the nub of the Cambridge Conference is the theme of the continuous, put in relation to generality. These are two primary questions running through Peirce’s entire thought. It is well known that on this occasion he gave a stimulating illustration of the notion of continuous: the famous blackboard on which a ringshaped white line is traced in chalk. Without putting to one side the problems raised above and other ones as well, I want to use this example to try and suggest a different approach to the relation between semiotics and cosmology. As rightly pointed out by Giovanni Maddalena, two kinds of continuity seem to emerge in Peirce: one connected to Firstness and another to Thirdness.2 Maddalena says that all the ambiguities of the cosmological-metaphysical level in Peirce go hand in hand with the ambiguities of the concept of continuity: […] on one side, it is the final outcome of logic and phenomenological thirdness, on the other it is also the model of a reality that remains unitary by absorbing into itself random variables. Peirce’s cosmological explanation starts from the fact that the logic of relations has revealed that continuity is the highest type of generality. Within the evolutionary scheme it must be supposed that the continuity to which logic sets an end point (a continuity understood as habit) derives from a vaguer original generality. Hence there is an internally evolving, original idea that has to be filtered by experience in order to become habit. In other words, he passes here from a continuity-thirdness to a continuity-firstness.3

Two points in the above quotation seem to me to be particularly productive: the model of a reality that remains unitary (that is, embracing in itself the “first” and the “third” without thereby lacking differentiation) and the origin understood as “ideal”. I would like to present my way of illustrating them using the example of the blackboard. As you will recall, in this example the two-dimensional continuous blackboard is the sign of a continuum with an indefinite number of dimensions. The points on the blackboard are the possible sign exemplifying the indefinite dimensions. But these points are not actually on the blackboard taken as an example of the continuum; let us say that they are only “potentially” in it. This means that only when a circular sign is traced on the board with white chalk do these points appear. But in what sense? It is here that our “phaneroscopic” (and, I would add, “genealogical”) observation needs to be sharp.

2

Maddalena, Introduzione to Scritti scelti, 25-28. For this set of problems see also the Introduzioni by Rossella Fabbrichesi Leo to the two anthologies of Peirce’s writings edited by her: La logica degli eventi (Milano: Spirali, 1989) and Categorie (Roma-Bari: Laterza, 1992). 3 Maddalena, Introduzione to Scritti scelti, 28.

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First of all, we have to clarify the nature of the sign made with white chalk; for instance, how is it possible for this to happen? Evidently, under the sole condition that the surface of the blackboard, its being a “support”, continually sustains the act of tracing the sign and its material form in the deposited chalk: it is thus by drawing a figure on the blackboard as support that the trace occurs. In this way, says Peirce, the trace shows a “certain element of continuity” in it. “Where did this continuity come from? It is nothing but the original continuity of the blackboard which makes everything upon it continuous” (CP 6.203). Consequently, we also have an original difference between the black of the board-support, revealed as such by the contrasting white line, and the white trace itself. How should we think of this differentiating relation? That there is, of course, a “limit”, that is a “discontinuity”, between the black of the board and the white of the line and this is precisely the point. But we must stick close to the point and not make mistakes or be imaginatively naïve. The limit is not to be thought of as between the already traced white line and the rest of the blackboard which, so to speak, receives and supports it; the limit is in each point of occurrence of the white in its difference or in its differentiation from the black of the supporting continuum. A limit, Peirce specifies rightly and exactly, that "is neither black, nor white, nor neither, nor both” (CP 6.203). The white, therefore, occurs: a unique and primordial event as is the event, I would say, of every occurrence (that is of every dimension or original quality). But how does it occur? In the only possible and conceivable way; namely it occurs by being repeated “linearly” (or “dimensionally”). In the occurrence of its being traced, the white is repeated, that is it occurs in repetition and in this way establishes: 1. the underlying continuity from which the white stands out through difference; 2. its discontinuous continuity, that is the habit of whiteness repeated each time or stated generality that extends into the future; and 3. the “unitary” nature of the support that embraces and holds the sign’s origin and destination together (its “being made temporal” and “being localized”). A support for difference and for each single difference, as well as for every generality–that is for every possible dimension or quality–this unitary nature is not white; but neither is it black since the black emerges solely through difference from the white just as continuity emerges from discontinuity. And it is not even either one or the other or both of them as, in a certain sense, it is the possibility of both precisely because at the same time it excludes them from itself–it is the exclusion from the possible that renders them “existing” and so moving towards their “relational” reality or the repeated and reasserted generality of the white and the black. If you like,

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something similar to the chora in Plato’s Timaeus (but here is not the place to go into this reference which, as is known, raises what are not minor problems).4 We can see clearly, then, how and why continuity is “first” and “third”. As Firstness it is pure potentiality of continuity, that is of generality and of permanence. But it is such not in itself (which it would be ingenuous and mistaken to think) but only in relation to the discontinuity of the occurrence (in the example, the incision of the white on the blackboard). Discontinuity, Secondness, is once again not to be understood abstractly in itself. Peirce states this clearly: if you imagine points or dimensions that originate isolated in themselves–he observes– “nothing could then unite them”; they have to be thought as in a relation (the only correct way to think them), that is involved in some kind of “existence” (of occurrence, precisely). Hence, the original potentiality is not a thing but precisely a “limit”: the latter receives through difference the continuous and the discontinuous. And, moreover, they are not on the same level even though they occur “existentially” at the same time. The discontinuous shows itself as repetition, that is as original quality in its own way (for instance, whiteness), which emerges persisting through difference from a potential blackness. The latter, indeed, becomes what it is only by retroflexion from the white: from its “continuing” to be, that is to put itself forward by repeating and interpreting itself as white. This is exactly habit or generality in movement: Thirdness, that is “realized”, or “conceived” or “thought”, continuity; in other words made gradually more and more “real” in the succession of its discriminating “existences” (discriminating the only potential continuity of the origin). All of this is the reason why–to use Peirce’s own words–every sign, in order to be such, presupposes having already interpreted, that is, not the simple “white” (which, taken in itself, is equal to nothing) but its “acknowledgement” (“here it is again”). However, acknowledgement presupposes in turn the discontinuity of the occurrence, that is the realization “in points” (or “dimensions”) of an all-reaching and eternal possibility of which the white is only the transient incorporation into Thirdness of a habit in movement. Furthermore, it is to be pointed out that, as in various ways Peirce shows he has understood, all this is said in a precise universe of experience, that is to say ours; in other words it starts from that determinate existence and difference that is the human habit of perception and of thought and, in fact, from the difference of this actual present human habit, determinate in this and in that way. It is through difference and retroflexion from this universe of experience that emerges the picture of a universe of pure dimensional possibilities which are manifested in a 4

See in this regard Carlo Sini, Figure dell'enciclopedia filosofica. vol. V, Raccontare il mondo. Filosofia e cosmologia (Milano: Jaca Book, 2005), 107-110.

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movement of generalizations and “rational” habits. It is our difference that speaks here, saying about the universe what it must say and cannot not say, adding nonetheless that the universe of which it speaks is not in itself either perceptible or “rationalizable”, nor is it not perceptible or not “rationalizable” or neither of the two or both. Only when we take this into account, will we do justice to Peirce’s ideas (it remains, moreover, a mere “conjecture” on our part whether he would have liked and accepted such an interpretation or not). That all of this has any significant connection with Spencer today is perhaps difficult to imagine. With regard to Aristotelian potentiality, to which in truth Peirce refers more effectively, it is in contrast a different matter. We could for instance say the following (and these brief remarks will also serve as a conclusion). In the immense, infinite black night of the universe, divine fires and divine flashes continually light up and go out. They are the worlds and innumerable beings whose material potentiality is realized in form and substance by the infinite cause of God’s thought. This thought has always held within itself the actuality of all possible thought; it is through this actuality that it draws every thing into existence and to the final realization of its essence. Together with this always fully realized actuality, however, coexists the incalculable and inexhaustible immensity of its own realizable pure power since that which is always one in God is two in entities and three in the image of thought. Thought of thought and act always in act, Aristotle’s God is properly neither one, nor two, nor three, nor some of them, nor none of them, nor all of them.5 But saying this is not extraneous to him; where indeed could it occur if not in him? Just as, according to Peirce, happens to us; whether we understand it or not we occur in thought: the only really indispensable and in its own way necessary condition for thought to occur in us.

REFERENCES Maddalena, Giovanni. “Introduzione” to Ch.S. Peirce, Scritti scelti, Torino: UTET, 2005. Peirce, Charles Sanders. The Logic of Continuity. CP 6.185-213. Sini, Carlo. Teoria e pratica del foglio-mondo. La scrittura filosofica. Roma-Bari: Laterza, 1997.

5 For this example I refer to vol. II of my Figure dell'enciclopedia filosofica (La mente e il corpo. Filosofia e psicologia), 43 and ff. For the notion of support and its relation to the concepts of "universe" and "sheet-universe" see my Teoria e pratica del foglio-mondo. La scrittura filosofica (Roma-Bari: Laterza, 1997), Part Two.

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__. Figure dell'enciclopedia filosofica. Vol. 2, La mente e il corpo. Filosofia e psicologia; vol. 5, Raccontare il mondo. Filosofia e cosmologia. Milano: Jaca Book, 2004-2005.

CHAPTER 3 PEIRCE, PROPER NAMES, AND NICKNAMES Giovanni Maddalena The topic of proper names is very important to understand reference, namely the relationship between names and objects. It is the easiest way to start exploring the more general relationship between words and world or reality. The two main reference theories of the twentieth century are the “descriptivist theory” of the so-called dominant paradigm and the theory of direct reference proposed by the American philosopher Saul Kripke. Since many authors attempted to develop this view in a realistic sense, the theory has been called “causalist theory”. According to the descriptivists, proper names, like every other kind of names, have both a sense and a meaning, while for Kripke proper names and certain common names (at least those of natural species) have only meaning. According to the first model briefly summed up, proper names can be understood as short-cuts for one or more descriptions clustered together. In other terms, the meaning of a proper name is reachable through its sense, the denotation through the connotation. According to the second theory, proper names are “rigid designators”: they merely denote. They are labels put on objects through an operation Kripke calls “baptism”; from that point on, objects retain that label whatever sense they assume during their history. Peirce never wrote a paper or conceived a definite theory on this topic but his writings clearly show the importance he attached to the problem. The literature about Peirce and proper names, though not abundant, is significant. Different authors have tried to understand Peirce’s thought by comparing it to the two main theories just referred to. Both of these theories appear to apply to some extent to Peirce’s few notes on this topic. Among this literature I will just mention two papers that defend opposite interpretations: “C.S. Peirce’s Theory of Proper Names” by J.R. Di Leo in Studies in the Logic of Charles S. Peirce, and “Peirce on Names and Reference” by D. Boersema in Transactions of the Charles S. Peirce Society (vol. 38, 3 (2002): 351-362). The difference between these two thorough approaches to Peirce’s view is relevant. Di Leo stresses Peirce’s definition of proper name as an index and tries to show the perfect harmony between Peirce’s and Kripke’s theories. Proper names do not have any “sense”, denote without

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connoting, and they follow a chain of causal transmission that starts with a “baptism”. Boersema, on the other hand, maintains that Peirce’s theory cannot support Kripke’s approach because of its triadic concept of sign in which both object and interpretant play integral parts in the ongoing process of semiosis. If the object lies within the sign there is no room for “semantic proof”, namely for the difference between the reality of the object and the “sense” included in our knowledge that is so important to Kripke’s strategy. Besides, if we need an interpretant in order to identify the object of our reference, object and interpretant must stay within a sphere of sense through which we recognize the name as a sign. Both analyses show a kind of reasonableness that deserves further inquiry. Accordingly, this paper tries to frame a new analysis of Peirce’s statements on proper names and to see which interpretation is more faithful to the textual evidence. We will see that we must understand Peirce’s view in all its semiotic depth and that if the descriptivist and causalist approaches have any validity, it is due to their semiotic foundation. The paper ends by proposing both a reference theory based on Peirce’s suggestions and a way to justify this different view.

I. Peirce on Proper Names According to Peirce, the overwhelming majority of languages comprise only class names and proper names. A Term is simply a class-name or proper-name. I do not regard the common noun as an essentially necessary part of speech. Indeed, it is only fully developed as a separate part of speech in the Aryan languages and in the Basque–possibly in some other out of the way tongues (CP 8. 337).

But class names have always verbs, at least the copula, wrapped up in them. The present author leaves the is as an inseparable part of the class-name; because this gives the simplest and most satisfactory account of the proposition. It happens to be true that in the overwhelming majority of languages there are no general classnames and adjectives that are not conceived as parts of some verb (even when there really is no such verb) and consequently nothing like a copula is required in forming sentences in such languages (EP2: 285).

This implies that, notwithstanding the desire of logicians, knowledge does not need to be founded on common nouns. Language and reality can be understood by using only the absolute determination typical of proper names and the generality expressed by the implication of verbs in class-terms.

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This binary linguistic condition is well expressed in this passage by Peirce: Every language must have proper names; and there is no verb wrapped up in a proper name. Therefore, there would seem to be a direct suggestion there of a true common noun or adjective. But, notwithstanding that suggestion, almost every family of man thinks of general words as parts of verbs (EP2: 285).

Proper names, on this view, are the only way to identify an individual to which we want to refer. Moreover, proper names are the only linguistic means we can use to identify an individual within a general class. This particular fact will become even more important when Peirce realizes that the nature of the relationship between individual and generality is the essential question to investigate for a true understanding of continuity, the crucial nexus of his whole philosophy (Maddalena 2004). Peirce explains that proper names fulfill the same function as the letters (or “selectives”) that he uses to simplify his existential graphs. In such a case, and indeed in any case in which the lines of identity become too intricate to be perspicuous, it is advantageous to replace some of them by signs of a sort that in this system are called selectives. A selective is very much of the same nature as a proper name; for it denotes an individual and its outermost occurrence denotes a wholly indesignate individual of a certain category (generally a thing) existing in the universe, just as a proper name, on the first occasion of hearing it, conveys no more (CP 4.460).

Starting with this function of individuation within a generality, I will develop in this section two semiotic features of proper names: (1) proper names are words to some extent and as such they share a certain form of generality; (2) their function is to identify an object: in semiotic terms, they are indices. (1) Peirce uses “the George Washington example” to explain what he means by the generality of proper names. What do you make to be the meaning of “George Washington”? […] it must be admitted that pragmaticism fails to furnish any translation or meaning of a proper name, or other designation of an individual object. […] you will perceive that the pragmaticist grants that a proper name (although it is not customary to say that it has a meaning) has a certain denotative function peculiar, in each case, to that name and its equivalents; and that he grants that every assertion contains such a denotative or pointing-out function […]. Whatever exists, ex-sists, that is, really acts upon existents, so obtains a self-identity, and is definitely individual. As to the general, it will be a help to thought to notice that there are two ways of being general. A statue of a soldier on some village monument, in his overcoat and with his musket, is for each of a hundred families the image of its

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uncle, its sacrifice to the union. That statue, then, though it is itself single, represents any one man of whom a certain predicate may be true. It is objectively general. The word “soldier”, whether spoken or written, is general in the same way; while the name “George Washington” is not so. But each of these two terms remains one and the same noun, whether it be spoken or written, and whenever and wherever it be spoken or written. This noun is not an existent thing: it is a type, or form, to which objects, both those that are externally existent and those which are imagined, may conform, but which none of them can exactly be. This is subjective generality (EP2: 341-342).

It follows that proper names are subjectively general signs. This subjectivity forbids them to be entirely substituted by definite descriptions. A definite description–i.e. “to die for the cause of the union”–can substitute for the common image of the statue and hence for the common noun “soldier” represented by the statue. “Objective generality” consists in this peculiar feature. But the same cannot be said of a proper name. The proper name can only boast the subjective generality that belongs to every name: it can never coincide with the individual referent. But the proper name does not have any kind of objective generality, namely there is no definite description nor number of individuals nor predicate that can substitute for or satisfy the sense of the name. However, it retains a certain “denotative or pointing-out function”. How can we define more precisely this kind of generality capable to point an individual? In his letter to Lady Welby of 12 October 1904, Peirce classifies proper names as Rhematic Indexical Legisigns (CP 8.341). The three terms express the classification of signs according to the relationship the sign has with itself, with the dynamical object and with the interpretant. From the standpoint of the sign’s relation to its interpretant, Peirce’s reconstruction considers a proper name a “rheme”. Peirce defines a “rheme” as “any sign that is not true nor false” (CP 8.337). The interpretant reads the rhematical sign “as if it were a character or mark (or as being so)” (CP 8.337). In the “if it were” lies the specificity of any rheme, and thus it applies to proper names as well. Proper names bring a mark that we can interpret. Peirce says that “the Interpretant of a Rhematic Indexical Legisign represents it as an Iconic Legisign”. This mark is not a predicate that a certain amount of objects, finite or numerically infinite, can saturate; it is a kind of reference that is neither individual nor general in the sense of a law. Rhemes are fragmentary signs that must be embedded in “completer signs” (propositions or arguments); they express a possibility that may become actual or general. In Peirce’s words, they are “a sign of essence” (EP2: 294). Before examining the indexical dimension of proper names, let us turn to the “legisignic” one. By classifying proper names as legisigns, Peirce is claiming that

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what makes them signs as such, or allows them to operate qua signs, is their own generality or law-like character. As it is in itself, a sign is either of the nature of an appearance, when I call it a qualisign; or, secondly, it is an individual object or event, when I call it a sinsign […]; or thirdly, it is of the nature of a general type, when I call it a legisign (CP 8.334).

In the case of legisigns, generality is internal to the sign and does not depend upon, or is not received from, its interpretant. As generals, proper names cannot be pure sinsigns (something that is a sign by virtue of its singularity) but at the most the special kind of sinsigns that are actual replicas of legisigns. But what is the difference between legisign and qualisign? As Peirce explains, The difference between a legisign and a qualisign, neither of which is an individual thing, is that a legisign has a definite identity, though usually admitting a great variety of appearances (CP 8.334).

To be a legisign allows the proper name to conserve its identity in different occurrences, and in this sense every proper name shares an aspect of law like governing power. So far, then, generality seems to prevail, but things change when we consider that proper names serve to indicate a single object or event. In the relationship with its object, the proper name is definitely an index. Once again, as it is the case with continuity and with reasoning, Peirce in his later years focuses his research on the problem of knowing the general through or in the individual. (2) What does it mean to say that proper names are indices? The triad Icon, Index, Symbol classifies the three types of connection between object and representamen. Icons represent an object by similarity and Symbols represent their objects “independently alike of any resemblance or real connection, because dispositions or factitious habits of their interpreters insure their being so understood” (EP2: 461). Indices, on which we are focusing our attention, represent a comparison, a real connection, a clash, that we can associate with what happens in acts of volition or, more generally, of existence. Index has a force but neither sense nor character (CP 3.434). An Index, or Seme (VKҋPD), is a Representamen whose Representative character consists in its being an individual Second. If the Secondness is an existential relation, the Index is genuine. If the Secondness is a reference, the Index is degenerate […]. Examples of Indices are the hand of a clock, and the veering of a weathercock. Subindices or hyposemes are signs which are rendered such principally by an actual connection with their objects. Thus, a proper name, [a] personal,

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demonstrative, or relative pronoun, or a letter attached to a diagram, denotes what it does owing to a real connection with its object, but none of these is an Index, since it is not an individual (EP2: 274).

As for their relationship to the object, proper names semiotically speaking are indices. Peirce’s metaphysical studies confirm this view: when he talks about relationships among existent individuals he maintains that we must consider an individual as an undetachable ultimate unity (as Duns Scotus’ haecceitas) that we can call by a proper name. […] every correlate of an existential relation is a single object which may be indefinite, or may be distributed; that is, may be chosen from a class by the interpreter of the assertion of which the relation or relationship is the predicate, or may be designated by a proper name, but in itself, though in some guise or under some mask, it can always be perceived, yet never can it be unmistakably identified by any sign whatever, without collateral observation. Far less can it be defined. It is existent, in that its being does not consist in any qualities, but in its effects–in its actually acting and being acted on, so long as this action and suffering endures. Those who experience its effects perceive and know it in that action; and just that constitutes its very being. It is not in perceiving its qualities that they know it, but in hefting its insistency then and there, which Duns called its haecceitas […] (CP 6.318).

Keeping in mind the general (but subjective) character capable of identifying an individual and the indexical one, even though a name can never be an individual, Peirce’s conclusion is that a proper name is a conventional index “which denotes a single individual well known to exist by the utterer and interpreter” (EP2: 307). “Well known” refers both to the “collateral knowledge”—acquired by observation—that utterer and interpreter must share the first time they use a proper name in conversation, and to the non-collateral knowledge that refers to one’s competence with using a general system of signs. All that part of the understanding of the Sign which the Interpreting Mind has needed collateral observation for is outside the Interpretant. I do not mean by “collateral observation” acquaintance with the system of signs. What is so gathered is not COLLATERAL. It is on the contrary the prerequisite for getting any idea signified by the Sign. But by collateral observation, I mean previous acquaintance with what the Sign denotes (EP2: 494).

Proper names involve a peculiar mixture of generality and individuality that needs further exploration.

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Peirce himself tried to refine his theory of indexicality in order to explain the entanglement between generality and singularity in proper names. In an article written in 1903, he wrote: A proper name, when one meets with it for the first time, is existentially connected with some percept or other equivalent individual knowledge of the individual it names. It is then, and then only, a genuine Index. The next time one meets with it, one regards it as an Icon of that Index. The habitual acquaintance with it having been acquired, it becomes a Symbol whose Interpretant represents it as an Icon of an Index of the Individual named (EP2: 286).

To understand how a proper name can be a genuine Index the first time we meet with it and a degenerate one or an Icon of an Index the second time, we need to look at two more quotations from the same year of 1903: It is desirable that you should understand clearly the distinction between the Genuine and the Degenerate Index. The Genuine Index represents the duality between the representamen and its object. As a whole it stands for the object; but a part or element of it represents [it] as being the Representamen, by being an Icon or analogue of the object in some way; and by virtue of that duality, it conveys information about the object. The simplest example of a genuine index would be, say, a telescopic image of a double star. This is not an icon simply, because an icon is a representamen which represents its object solely by virtue of its similarity to it, as a drawing of a triangle represents a mathematical triangle. But the mere appearance of the telescopic image of a double star does not proclaim itself to be similar to the star itself. It is because we have set the circles of the equatorial so that the field must by physical compulsion contain the image of that star that it represents that star, and by that means we know that the image must be an icon of the star, and information is conveyed. Such is the genuine or informational index (EP2: 171-172). A genuine Index and its Object must be existent individuals (whether things or facts), and its immediate Interpretant must be of the same character. But since every individual must have characters, it follows that a genuine Index may contain a Firstness, and so an Icon, as a constituent part of it. Any individual is a degenerate Index of its own characters (EP2: 274).

The first time we meet with it, a proper name is an Index that contains an Icon so that it is capable of conveying information. Afterward it becomes degenerate because it merely conveys reference without any information. But since it is similar to the first one, it is an Icon of an Index. A Degenerate Index is a representamen which represents a single object because it is factually connected with it, but which conveys no information whatever. Such for

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example, are the letters attached to a geometrical or other diagram. A proper name is substantially the same thing; for although in this case the connection of the sign with its object happens to be a purely mental association, yet that circumstance is of no importance in the functioning of the representamen […]. A degenerate index may be called a Monstrative Index, in contradistinction to an Informational or Genuine Index (EP2: 172).

To conclude this analysis we can say that the function of a proper name, as an index that contains an icon, thus as a genuine index existentially connected with the object that it represents, is operative only in its first occurrence when it conveys new information. The second time only the reference remains. Moreover, from the third time on, a symbolic habit sets in. Now, which of the two most popular theories of reference can we associate Peirce’s view of proper names with? Subjective generality and indexical character of the representamen “proper name” bring his theory on the tracks of direct reference theory. As a matter of fact, there is always a difference between a proper name and a definite description, and the proper name itself expresses a rigid connection that, once set, changes itself first into an icon of index and then in a symbol interpreted as an icon of an index. That symbol then may be used without the real or existential presence of the object itself. […] meaning is the association of a word with images, its dream exciting power. An index has nothing to do with meanings; it has to bring the hearer to share the experience of the speaker by showing what he is talking about (CP 4.56).

Di Leo appears to be right when he says that there are “affinities between Peirce’s and Kripke’s views” (Di Leo, 593). However, Boersema’s impression that Peirce sometimes intends a name to signify certain characters remains. Indeed the definition of a genuine Index as Informative makes one think about such a possible sense. Intuitively, Semitic or native American proper names, or, more generally, the etymology of proper names, suggest that the claim that proper names have meaning is sensible. The problem is that, according to Peirce’s theory, we cannot use a descriptivist approach because subjective generality and indexicality exclude it. Although we cannot say that there is a definite description wrapped up in a proper name, we do need to explain how its representative power makes us recognize it as a proper name and often leads us to identify correctly the object to which it refers. Since we cannot make use of the generality of the interpretant because it is subjective and we cannot substitute a definite description for it, we must focus our research on the role played by iconicity inside the genuine index. Peirce himself seems to have followed this path or at least to have broached these questions in a manuscript of 1905:

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Yet it does not follow and could only very rarely be true that the name signifies certain defining marks, so as to be applicable to anything that should possess those marks, and to nothing else. For not to speak of the fact that the interpreter only uses the marks as aids in guessing at his acquaintance’s identity, and may possibly be mistaken, however extraordinary they may be, there will be no one definite set of marks which the name signifies rather than another set of equally conclusive marks. If there were any mark which a proper name could be said essentially to signify, it would be the continuity of the history of its object (MS 283: 317-318).

Peirce’s conclusion appears therefore to be really close to Kripke’s, but it leaves open a perspective that I would like to follow. If there was an essential mark in the object, it would be found in the history of the object. Now, taking it for granted that the name is an index, which expresses a direct reference, we can find whether there are marks of its latent meaning or sense. This investigation should explain why we recognize the identity of an object. In Peircean terms: can we provide a satisfactory account of the iconic aspect implied in the genuine index, namely in a proper name at its first occurrence? I suggest that we can, if there are proper names that make us see their origin. Once we find them, we will verify whether such proper names carry with them the essential marks of the history of their object.

II. Nickname Theory Nicknames are the kind of proper names we are looking for because they allow us to see the prehistory of the name, and this suggests a different “image” of the “baptism” proposed by Kripke. First, I would like to stress the asymmetry existing between nicknames and proper names from an epistemological point of view. Let us consider a statement likely to have been pronounced in Rome in 1605 on the occasion of introducing a certain person: “This is Michelangelo Merisi, called Caravaggio”. There is no doubt that the reference works. Both “Michelangelo Merisi” and “Caravaggio” are rigid designators. A hearer with some level of linguistic (or geographical) competence, however, could conceivably ask “why” because to such a person the statement could sound like “This is Mont Blanc”, or, rather, “xy is z” where “xy” and “z” are different individuals possibly belonging to different species. Of nicknames, as in this case, we can often ask “why?” because to a person with linguistic competence they show a heterogeneity of references. To establish the identity of the two terms, an explanation then becomes necessary. A proper

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name, on the other hand, does not create the same ambiguity and does not call for explanation, except in the case when it is used as a nickname. Are we facing here the very same problem encountered in the classical statement “Hesperus is Phosphorus”? I think so. But this case makes it fully clear why “Hesperus is Phosphorus” does not imply the existence of a “sense” through which the reference gets set. It is only empirically that we can find out that “Michelangelo Merisi is Caravaggio”. It does not on its own express unambiguously two equivalent ways of referring to the same object–a confusion that “Hesperus is Phosphorus” avoids because here we have two different referents that are said to point to the same object. How, then is the identification taking place? What are the elements upon which we can base our knowledge of meaning or reference? Kripke says that there are “contingent marks by which we identify a certain planet and give it a name” (Kripke, 105). The two referents establish an identity by providing an explanation that, instead of focusing on the object’s qualities (such as are not a priori wrapped up in the sense of the proper name itself) or the circumstances of its naming, looks rather at historical relationships between particulars or individuals. From the interpreter’s point of view, these properties assume an iconic appearance, which is recognizable in our knowledge. It is worth noticing at this point that for those who do not have the adequate linguistic competence the nickname “Caravaggio” works exactly as any other proper name without requiring any explication. In other words, nicknames are also proper names to the extent that without linguistic competence their peculiarity cannot be acknowledged. Let us go back to the “characteristic marks” that the interpreter recognizes or rather to the properties of the object they come from. Kripke came to call them the “essential properties”, and made the metaphysical claim that we use them in order to refer to an object “in every possible world”. Kripke’s example is the following: Richard Nixon remains Richard Nixon even in the possible world where he does not win the 1968 presidential elections. The object of the reference remains the same. What are the “essential properties” we cannot change if we do not want to change the reference itself? Here Kripke and his epigones took different paths, taking sometimes hyper-realistic attitudes not easily defendable (Devitt, 1987). In “Naming and Necessity” essential properties seem to coincide with the Aristotelian synolos but there is no compelling reason to prefer this thesis over some other one. Nicknames show that the object of reference has essential properties that coincide both with certain properties belonging to the historical evolution of the object and with what we have acknowledged and known about it. Such properties don’t refer to “qualities” implied in the sense of a name, but to “criteria of identity of particulars in terms of other particulars, not qualities” (Kripke, 52). To be born in Caravaggio is an accidental and particular property. However, at a certain point

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in history, someone selected that property as essential and decisive for identifying the painter-object that we call “Caravaggio”. What is at stake here is a quality or a property–understood in relationship to other particular qualities or properties or objects–that some historical “baptist” found, erroneously or not, to be essential at a certain historical moment. In point of fact, “Caravaggio” was not born in Caravaggio but in Milan. The possibility of error does not work against the possibility of exploiting the fact that there are historical relationships that make some properties essential. These historical relationships are also the only way we have to identify an object in a different possible world that we stipulate. When we do that, we assume a world with all these historical relationships in the same place, except those we want to modify. These historical relationships are also the only characters we may use to recognizably identify an object in a different possible world that we stipulate. All we need to do is to assume a world in which all these historical relationships still hold except for the few that we modify. For example, we may stipulate a world in which all the conditions found in 1605 remain the same, except that we introduce a person nicknamed “Caravaggio” who is not a painter. Larger-scale modifications would turn the conditional situation we want to explore into utter nonsense (we could envision a situation in which “Caravaggio” is a pig in an Orwellian tale set in 1756; but then all the world would be “a tale/ Told by an idiot, full of sound and fury,/ Signifying nothing” [Macbeth, act V, scene V]). It is the act of stipulation itself that requires this acceptance of our actual world up to the point or up to the property we want to change in order to develop a given reasoning. To stipulate the world in which Richard Nixon loses the 1968 presidential elections, we need to take for granted all the other properties that bring him up to that precise moment. If he had had a broken nose through boxing, had not been married, had been a democrat, and had always lived in Indianapolis, would he have still been Richard Nixon? May be so—and this is Kripke’s answer—but not the one in the possible world that stipulates that Richard Nixon does not win the presidential elections of 1968. In this sense I think Kripke is wrong to claim that we do not need these essential “properties of an object” to identify it “in another possible world, for such an identification is not needed. Nor need the essential properties of an object be the properties used to identify it in the actual world, if indeed it is identified in the actual world by means of properties” (Kripke, 53). Precisely because we need to start from objects and not from worlds, such objects need to be defined by certain historical relationships that make them such as we want them to be up to the moment (or to the moments or to the properties) that we decide to modify. If our representation of these essential or historical properties, as also suggested by Peirce’s analysis, is correct, then we need to change the image of “baptism”.

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Nickname creation supposes a “baptist” who underlines some historical marks that belong or should belong to the object. Therefore, the meaning is neither reached through the sense nor rooted in an isolated object: it is rooted in the meeting between essential or historical properties and the baptist’s ability to recognize them. Nicknaming as a kind of “baptism” stems from recognizing as icons the historical properties belonging to the object itself. This done, the rest of the causal chain that Kripke describes remains functionally valid. I think that this conclusion is independent from both descriptivist and causalist frameworks. Here we obtain meaning without identifying reference through sense, while also avoiding identifying the object with an implausible and unrecognizable existence completely detached from experience. Iconic marks belong to the object and its history but their acknowledgment depends on human understanding.

III. Suggestions Two suggestions arise from what we have seen, one metaphysical and one historiographical. The metaphysical one deals with the a posteriori necessity Kripke insists on. Our nickname theory wholly supports that kind of necessity. The “historical connotation” we give to the essential properties makes it necessary to look at accidental particulars. One problem is that there is a gap between the essentiality of particulars when we recognize and use them in the baptism and their necessity. This distinction between “essential” and “necessary” requires further study. The second suggestion stems from the fact that our nickname theory is supported by Peirce’s analysis of the genuine index and its involved icons. This shows that in the debate on reference Peirce helps solve the prejudice common to both descriptivists and causalists that every kind of representation is subjective and that, therefore, knowledge can work in an objective way only if it talks about facts or signs that objectively “stand for” facts. In this sense, Frege’s example of a telescope remains the common root of both theories (Frege, 60). However, if we consider representation as a possible object of study, namely, if we look at representation as potentially objective knowledge, we can better understand what is going on in the debate between descriptivists and causalists and justify our nickname theory. Descriptivists use only one kind of sign: symbols. Symbols represent facts without any real connection either of similarity or of existential compulsion. It is because symbols imply no genetic relationship with their objects that they can be devised and formalized. This explains why many descriptivists are always longing for a perfectly formalized language.

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Kripke’s critique of descriptivism uses another kind of signs: indices. It is through indices that he appeals to the physical and direct relationship between object and name (proper name in our case) and that he stresses the importance of the singularity of reference. Kripke’s strength is that he achieves this result by appealing to a semantical and epistemological reasoning that is perfectly understandable from a symbolic point of view. His weakness lies in not realizing that he is using a different kind of signs and that there are even more kinds that can help solve the problems of identification his theory poses. Using Peirce’s analyses we have tried to show that there is a kind of sign that we often use unconsciously and that represents the connection between proper names and “essential relationships” (Peirce) or “essential properties” (Kripke) of an object. In Peirce’s terms, that kind of sign is an icon. Its advantage is that it neither fixes an objective representation in a positivistic sense nor does it allow for an arbitrary or conventionalist view of reference. The semiotic analysis thus makes much sense, but it does not preclude the fact that the other two theories—the descriptivist and the causalist—each have validity within a certain field and that, though they are not fully viable alternatives, they are complementary within a multi-level semiotic view of reference whose basic level is iconic. In other words, the method of inquiry stems from the fact that there is an object “out there” endowed with essential properties, but it can work only because there is a semiotically intelligent subject. REFERENCES Boersema, Dan. “Peirce on Names and Reference”. Transactions of the Charles S. Peirce Society, vol. XXXVIII, 3 (2002): 351-362. Devitt, Michael and Sterelny, Kim. Language and Reality: An Introduction to the Philosophy of Language. Cambridge (Mass.): MIT Press, 1987 (1999, 2nd ed.) Di Leo, Jeffrey R. “C.S. Peirce’s Theory of Proper Names”. In Studies in the Logic of Charles S. Peirce. Edited by N. Houser, D. Roberts, and J. Van Evra. Indianapolis and Bloomington: Indiana University Press, 1997. Frege, Gottlob. Philosophical Writings of Gottlob Frege. Ed. by P. Geach and M. Black. London: Basil Blackwell, 1980 (3rd edition). Kripke, Saul. Naming and Necessity. Oxford: B. Blackwell, 1980. Maddalena, Giovanni. “Peirce and Cantor on Metaphisical Realism”. Semiotiche 2 (2004): 137-149.

CHAPTER 4 PSYCHOLOGY AND ANTI-PSYCHOLOGISM IN PEIRCE Rosa M. Calcaterra Peirce’s logic is, to use a current definition, “anti-psychologist”, that is, founded on the paradigmatic formula offered by Kant when he states that the philosopher’s task consists of demonstrating “how we ought to think”, instead of showing “how we do think”.1 According to Kant, as well as to all those have accepted the methodological injunction which underlines his approach, the “how we do think” is the realm of psychology, which is ancillary to clarify the factual conditions to which our thinking is subjected, whereas logic must define the essential rules for rational knowledge. In Kant’s view, such necessary rules must be identified by the transcendental logic that he outlines in a quite definite way. On the contrary, Peirce adopts an extremely open and complex type of inquiry, which outflows into a final project calling for a “scientific metaphysics”. However, his “anti-psychologist” approach– as he reminds us, for instance, in the exordium of the third of his 1898 Cambridge Lectures–concerns with logic considered both in its narrower and wider sense. In the first instance, logic is “that science which concerns itself primarily with distinguishing probable reasonings into good and bad reasonings, and with distinguishing probable reasonings into strong and weak reasonings”,2 while in its wider meaning it “concerns itself with all that it must study in order to draw those distinctions about reasoning”,3 that is, the nature and functioning of signs as means and objects of thought. From this perspective, the founder of Pragmatism also develops his own methodology, in which the issue of logic being entirely independent of psychology acquires implications, eventually different from Kant’s anti-psychologist conceptions.

1 Immanuel Kant. Logik, Kant’s Werke Band IX (Berlin und Leipzig: Walter de Gruyter & Co, 1923), 14. 2 RLT: 143. 3 RLT: 143.

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The idea of logic and psychology being independent the one from the other results in the methodological criterion of externalism, namely in Peirce’s assertion that logic must be based on the analysis of the “external signs” of thinking rather than of the “internal” functioning of the mind. The externalist methodology is preferable rightly because it presents the greatest degree of epistemological reliability we are able to achieve. The following passage concisely expresses this point of view: There are many general truths with regard to signs, which hold good for all signs whatever of necessity, being involved in the essential nature of signs. The origin of these principles is undoubtedly the nature of the mind. But they are involved in so much of what is true of the mind as is implied in our capability of reasoning at all and which may therefore be said to be implicitly taken for granted by all men [...], and which is thus taken out of the special domain of psychology and made the common property of science. These principles might be evolved from a study of the mind and of thought, but they can also be reached by the simple consideration of any signs we please. Now the latter mode of studying them is much the easiest, because the examination of external signs is one of the most simple researches which we can undertake, and least susceptible to error, while the study of the mind is one of the most difficult and doubtful.4

The methodological criterion of externalism is one of the most recurring aspect of Peirce’s philosophy, but its implications are different in relation to the various contexts he applies to. In particular, externalism constitutes both an alternative option to psychology as an analysis of the mind based on introspective criterion, and an approval of experimental psychology á la Wundt. In addition, it may represent a methodological and theoretical perspective calling for an approach to the normative level of rationality that is quite different from Kant’s definition as it is envisaged in his own formula of “anti-psychologism”. In the following, I will try to bring together these aspects without pretending to provide an unequivocal interpretation to such a relevant feature of Peirce’s thought. As a matter of fact, a number of multifaceted issues, which sometimes are even incongruous, emerge in his writings. However, Peirce’s peculiarity rests exactly on the varied range of theoretical hints, which constitute food for our thoughts. The externalist option had already been articulated in the so-called anticartesian essays of 1868, where Peirce began elaborating his “logic socialism”. As it is known, the first of these essays, Questions Concerning Certain Faculties Claimed for Man, is devoted to the critique of the epistemic value of immediate intuition that Peirce rejects, too, in reference with the question of the origin of self4

W3: 83.

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consciousness and the philosophical investigation of the structure of sensations and emotions. In both instances, the aim is to expound the inferential nature of all our notions using the principle of the “external criteria”, within a perspective similar to that adopted by Wittgenstein in his Philosophical Investigations,5 and, later on, in the Remarks on the Philosophy of Psychology, where he develops his own version of the so-called “third-person approach” to mental events. As for Wittgenstein, it is not to deny the reality of mental facts, their real occurrence, but to provide an alternative to the opposition internal/external, which entails the theoretical difficulties of the mentalist approach.6 Moreover, Peirce’s essay contains an approach to psychological phenomena that recalls Brentano’s principle of intentional consciousness. On the basis of this principle, Brentano denies the traditional hypothesis according to which the self consciousness would be a primary and all-inclusive datum (as also in Kant’s doctrine of transcendental “apperception”), to rather contend that the self consciousness is always the awareness of being in a certain way and not a generic awareness of our own being.7 Likewise, Peirce explains the source of self consciousness by connecting it to the experience of the error which appears at a crucial stage of human individual psychological development, namely, at the stage of apprehending a language. Learning a language, in fact, implies the possibility that individual judgements may not be confirmed by the “testimony by others”, nor by empirical verifications that this latter solicits. By the time these contradictions first occur, Peirce says, the distinction between “facts” and “appearances” involved in our cognitive dynamics takes place. More importantly, we tend to store the original psychological structure of this distinction, namely the tendency to associate the “facts” with the testimony and the “appearances” with a “self” which is fallible. Specifically, a strong attitude to consider this testimony as a “stronger mark of facts than the facts themselves” will remain “through life”.8

5

Ludwig Wittgenstein. Philosophical Investigation. Ed. by G.E. Ascombe, R. Rhees (Oxford: Blackwell, 1953), § 580. 6 This analogy has been more extensively examined in Rosa M. Calcaterra, Pragmatismo: i valori dell’esperienza. Letture di Peirce, James e Mead (Roma: Carocci, 2003), 43-57. 7 See Giovanni Jervis, “Significati e malintesi del concetto di ‘sé’”, in La nascita del sé. Ed. by M. Ammaniti (Roma-Bari: Laterza, 1989). 8 Notwithstanding its epistemic value and its fundamental role in the process of understanding, the testimony of others cannot guarantee any absolute certainty. Rather, Peirce puts an emphasis on its limitation in regard with the rising of self-consciousness. Although it represents the condition which gives the first dawning to self-consciousness, being “the very best evidence of fact”, that testimony is nevertheless questionable: “Testimony will convince a man that he himself is mad” (CP 5.233).

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The language is also called into action to oppose the mentalist approach to sensations and emotions, according to which they exclusively belong to the socalled “inner world”. On the contrary, Peirce claims that both sensations and emotions imply a relation with something that is external to the mind; indeed, sensations and emotions are “predicates of something external”. In particular, as far as the emotions are concerned, to simply express them-I’m angry, I’m happy, I’m confused, I’m satisfied etc.,–means a “return to reason”, or overcoming a stalled subjective condition that, at first sight, would appear inherently senseless and reasonless. According to Peirce, the “return to reason” basically makes our emotions interconnected with the social cognitive and value-related criteria shaping the “external” frame of individual life.9 By all means, the “inner” aspect of sensations and emotions refers to the “constitution of the mind”, namely–as Peirce argues in his second essay of 1868, Some Consequences of Four Incapacities–it is an “arbitrary” datum, or something that lies outside the realm of reason.10 Accordingly, forgoing the immediate introspection power of knowing also entails dismissing the attempt to meet–as Wittgenstein maintained–the most “profound” and “essential” aspects of our inner world. The relevancy of the social factor in Peirce’s externalism is endorsed in his last essay of the anti-Cartesian series, Grounds of Validity of the Laws of Logic. I deem this essay worth mentioning particularly because it throws new light on the deep connection between the esthetical/emotional and the logical/rational levels. I refer to that sentiment of “infinite hope”, which turns to be the core of an idea of rationality based upon the identification between logic and cognitive semeiotic, and, therefore, upon the principle of the infinite development of the meanings urged by the cognitive processes of human society. In fact, it is just because we must deal with signs, with their framing of facts and the complexity of the interpretation activities they set in motion, that it is not possible to identify both the ultimate foundation and the final end of such cognitive processes. As Peirce will put it in How to Make our Ideas Clear, the semeiotic character of logic gives the way to a distinctive awareness that we do not hold a certain criterion of rationality exactly “because there is no royal road to logic”. We can only rely upon the chance that the human community’s future experiences and ways of reasoning would confirm our logical inferences, and above all upon the “infinite hope” that human community will never stop its pursuit of truth. In sum, this is the overall meaning of the fundamental “social” principle of logic, whose justification cannot be attained, according to Peirce, without resorting to that sentiment of “infinite hope”, which is, by definition, transcendental to the very 9

CP 5.245-247. CP 5.291.

10

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means of logic and still–to use his own words–“rigidly demanded by logic”.11 Does perhaps all that allude to a normative value of certain emotional instances, thus entailing an indication towards putting aside the traditional dichotomy, á la Hume, between the domains of “feeling” and “understanding”, which is usually a byproduct of the opposition between psychology and logic? I will go back to this question later on. For now, I deem useful to remind that in 1883 Peirce taught at Johns Hopkins University a course on the psychology of “great men”, a subject he had found intriguing since his youth, as Nathan Houser reminds us. The topic, in fact, was discussed on at least two occasions at the meetings of the Metaphysical Club, with reference to the work of Francis Galton on the same subject and to the publication of William James’s essay Great Man, Great Thoughts, and the Environment.12 Peirce’s course outline was focused on applying statistics to comparative biography, for which nonetheless he depended largely on impressionistic data. Indeed, from an historical point of view, his next year experiment (1884) is by far more interesting. He conducted such an attempt with Joseph Jastrow, one of his advanced logic students, who would have later become a professional psychologist. This was one of the earliest studies in experimental psychology in America, and its goal was to test Gustav Fechner’s tentative definition of the minimum perceptible difference of human sensations, below which it is impossible to discern differences of intensity. The result of Peirce’s and Jastrow’s work was not consistent with Fechner’s thesis; yet, their methodology was very much appreciated, mostly because their study was the first to employ a new criterion of inquiry, the randomisation, which, since then, would have been more and more applied in psychological investigations. This is, perhaps, only one of the numerous episodes attesting Peirce’s passion to work in scientific laboratories. However, such incursion into the domain of the “new” psychology, the physio-psychology, which, in those years, was just starting to replace the philosophical investigation based on self-reflection, suggests his appreciation for a methodology focused on the observation of the physiological aspects of psychic phenomena, namely for the psychology externalism á la Wundt. In one of his latest works, An Essay toward Improving our Reasoning in Security and Uberty, 1913, Peirce declares a “great admiration” of both Fechner and Wundt for their “experimental researches concerning the relations and reactions of the material and mental worlds”. Immediately thereafter, however, we read that such a “modern psychology” “can afford no aid whatever in laying the foundation of a sane philosophy of reasoning, albeit it has been and can still be of the most precious service in planning and executing the observations on which the 11 12

CP 5.355-57. See N. Houser, in W5: XXIII.

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reasonings depend and from which they spring”.13 Should we intend, thus, that physio-psychology is viewed as preliminary to a “sound philosophy of reasoning”? And if this is the case, what does it mean that it cannot provide the “foundation” of this philosophy of reasoning? I would like to outline that this writing mainly concerns the complex issue of rational instinct, bringing us to a sort of metaphysics of the mind, which tends to justify that “mysterious” ability to guess the right solution for objective issues. In the famous classification of sciences, presented in 1902, Peirce places the “Psychical Sciences” in the “Idioscopy” class, together with the “Physical Sciences”, so that, according to Comte’s principle informing such classification, the former depend upon the latter, that is, they receive the contents of the latter. As known, the term “Idioscopy” is borrowed from Jeremy Bentham to indicate the “special sciences depending upon special observations”. Even though these sciences are classified as “theoretical sciences of discovery”,14 they are by all means submitted to Philosophy, which is, in turn, preceded by Mathematics. This scheme, therefore, ratifies the independency of the philosophical knowledge from any other particular knowledge, especially from physio-psychology, the science that in those years aimed at becoming more and more a kind of self-sufficient discipline, or even an alternative to philosophy, rightly because its new experimental status was considered more reliable. As a result, it is worth trying to understand the relation between “Idioscopy” and philosophy. First of all, it is important to put an emphasis on the relevancy of the normative sciences–aesthetics, logic and ethics–as placed in between Phenomenology and Idioscopy. Concomitantly, it is also relevant to consider Peirce’s idea of phenomenology as prior to any other philosophical perspective.15 As it has been observed, such claim constitutes, together with the issue of normative sciences, what, in the 1902 classification, mostly supports “the systemoriented and speculative sides of Peirce’s project”.16 Let us now return to Peirce’s externalism in order to tentatively deal with the semantic ambiguity of the very term “observation”. This term, by itself rather equivocal in the ordinary language, is indeed used by Peirce in a particularly wide range of different meanings, according to the different levels of his speculation. As a first approximation, it could be noticed that the use of this term rests in between a meaning roughly attaining to the physical reality perceptions level, and another one, referring to the merely logical rational level. Furthermore, these two levels 13

EP2: 470-471. CP 1.242. 15 See Carlo Sini, Semiotica e filosofia (Bologna: Il Mulino, 1990), 9-122. 16 Rossella Fabbrichesi, Introduzione a Peirce (Roma-Bari: Laterza, 1993), 61. 14

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sometimes appear in a sequel (similarly to a “prior” and a “subsequent” in the cognitive processes), at times merged in the complex figure of the “real Generals”, upon which Peirce bases his effort to overcome the opposition between realism and idealism. Finally, and perhaps, this constitutes the most sensitive aspect of the issue, the term “observation” refers to Phenomenology or Phaneroscopy, as a science investigating the direct objects of consciousness, the pure presence of its constitutive phenomena. In the 1872 manuscript Of Reality, where the fundamental outlines of Peirce’s pragmatist logic are set forth, observation is indicated as a fundamental aspect of scientific investigation, although by itself inadequate to the settlement of beliefs which could correctly be qualified as “objective”. According to Peirce, observation produces “wholly new ideas” springing up in the mind in the process of investigation, that is, those ideas “which are not produced by previous ideas” but are caused by “something out of the mind”. Observation must, therefore, be distinguished from “thinking par excellence”, this latter elaborating previous ideas. More precisely, observations are “those parts of investigation which consist chiefly in supplying such materials for thoughts to work over, combine and analyse”. Accordingly, the ultimate achievements of investigation “depend entirely upon observations”.17 However, observations are “wholly peculiar and private”, that is, they are in no instance exactly reproducible. Not only can no man make another man’s observations; he cannot even make at one time those observations that he himself made at another time. We can only say that there are alike observations, but this can only mean that we are making a comparison. Since “comparison is not observation”, it follows that “there is a some mental process besides observation”.18 Clearly enough, we are dealing with the close relation among the categories of “quality”, “relation” and “representation”, as Peirce defines them in A New List of Categories. As a part of scientific investigation, observation must be considered a linking point between knowledge, objectivity and truth, and therefore it is fundamental for the model Peirce is elaborating over these years, that is his contentious conception of the investigation final end as “fated opinion”,19 namely, as “public”, or depending upon both the inter-subjective nature of reasoning and the concept of reality supporting its genuine “scientific” expressions. On the other side, observing something external to the mind, yet constitutes one of the fundamental operations in the process of reasoning, so that it cannot be distinguished from this latter except for purely analytical goals. This idea is, since 17

W3: 40. W3: 42-43. 19 W3: 273. 18

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the very beginning, at variance with Kant’s philosophy and constitutes, among other issues, the core of Peirce’s preliminary manuscript for a review–remained unfinished–of the English edition of Kant’s Introduction to logic (1885). In this manuscript, Peirce criticises Kant’s sharp distinction between “the intuitive and the discursive processes of the mind”, or–as Peirce himself specifies–between “the operations of observation and of ratiocination”. In his opinion, it was such a discrimination to have allowed the German philosopher “to think that the latter only begins after the former is complete; and wholly fails to see that even the simplest syllogistic conclusion can only be drawn by observing the relations of the terms in the premises and conclusions”.20 As I previously mentioned, perhaps the most problematic aspect concerning observations refers to Phenomenology or Phaneroscopy. Among Peirce’s various attempts to define his method of logic over those years, I deem worth quoting the following note: For in my opinion, excepting Metaphysics, there is no science that is more in need of the science of Logic than Psychology proper is. On the other hand, I found Logic largely on a study which I call Phaneroscopy, which is the keen observation of and generalization from the direct Perception of what we are immediately aware of.21

In order to clarify the distinction among logic, psychology and phenomenology, I will rely upon the analysis suggested by Giovanni Maddalena in his book on the latest Peirce.22 Maddalena–on the basis provided by a number of contemporary manuscripts–identifies three criteria of distinction: 1) goals; 2) methodologies; 3) contents. Considering the first aspect, the Phenomenology tends to identify the power of consciousness; psychology tends to clarify “which facts are hidden within the mind”, and logic attempts to grasp the functioning of the scientific hypotheses. From a methodological perspective, however, there seem to be a close similarity between Psychology and Phenomenology, since both require plenty of observations and a small amount of reasoning. On the contrary, Logic requires much reasoning and small observations (MS 645: 6). Eventually, these subjects differ also in their contents: Phenomenology deals with the immediate objects of consciousness (namely it deals with “the keen observation and generalization from the direct Perception of what we are immediately aware of”); Psychology deals with the functioning of mind, whereas Logic deals with “any process by which knowledge that is already possessed by a mind is made to yield further 20

W5: 258-259. EP2: 501. 22 Giovanni Maddalena, Istinto razionale. Studi sulla semiotica dell’ultimo Peirce (Torino: Trauben, 2003). 21

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knowledge”.23 Maddalena concludes that “to dismiss the Feeling as a source of reasoning means to validate both the distinction between Phenomenology and Logic, and the difference between the pure logical meaning of the semeiotic relation and any psychology-like approach”. Yet, immediately thereafter, Maddalena adds that “the source of knowledge is thereby determined by those mental functions which prompt the ‘signs’ relations, among which sensations, sensitive impressions and perceptions are included”. This claim seems to support Peirce’s externalist option: the function of reasoning might be studied only by considering the external signs instead of the mental signs.24 I admit to nurture some doubts about the concept of “pure logical meaning of the semeiotic relation”, rightly indicated by Maddalena as the reference point of latest Peirce’s externalism. And this is simply because it appears to me that if externalism represents the marking point between logic and psychology, then we must assume that we are dealing with formal logic as Peirce meant it.25 As a consequence, it is not immediately clear how this latter may succeed in representing the sensorial/perceptive side of knowledge. At the same time, I am wondering whether the idea of a phenomenological science risks to appear too much similar to the introspective psychology. In this respect, I have already noted that in his first essay of the 1868 series, Peirce denied that the faculty of introspection may have immediate access to the mental world. Furthermore, on the basis of Peirce’s logical-ontological reformulation of the three categories, which he was elaborating in those years, the objects of Phenomenology correspond to the Firstness, namely, the category denoting the pure possibility of phenomenal appearances. With regard to the Firstness, Peirce refers to a “tonality” of perceptions, the so-called Prebits, while underlining their impossibility to be grasped as well as their insignificance in the matter of logic. To put it in few words, the category of Firstness is by itself inexpressible, that is, it might be grasped only through the different interpretations we can provide, which in turn inevitably deprive it from its self-sufficiency. This prompts the questions: isn’t perhaps a mere assumption of principle to state the priority of a phenomenological science? Or: upon which basis may phenomenology be able to observe and generalise perceptions without applying to that immediate intuition Peirce, since the beginning, rejected and replaced by adopting totally innovative argumentations? Could ever be persuading Potter’s comment to Peirce’s conception of Phenomenology, according to which “Phenomenology takes inventory of what appears without passing any judgement 23

MS 667: 2. Maddalena, 92-93. 25 Maddalena, 1. 24

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upon what it observes”, by refraining from defining the observed phenomena in terms of “false”, or “true”, or “good”, or “bad”?26 These questions seem to me even more pressing than those the hermeneutical side of contemporary philosophy addressed to Husserl’s phenomenology, especially if one considers the relevant contribution of the founder of pragmatism to overcoming the dichotomies facts/values, sentiment/rationality, ethic/logic. This is more convincing if we take into account Peirce’s “synechism”, the ontological and logical law of continuity in the various spheres of existing world and human experience.27 The concept of synechism is by far more technically sophisticated than I can say here. Still, I hope to at least succeed in indicating its relevancy in order to allow an understanding of the so-called Peirce’s “anti-psychologism”. This latter, as I have already mentioned at the beginning of this paper, presents different implications, which differ from Kant’s classical formula of the discrepancy between logic and psychology. In the light of the principle of continuity, the “antipsychologist” label appears even inadequate, if, by such definition, we assume an ontological dualism between thinking and nature, between rational and psychological domains, and, finally, between the normative and factual spheres. Synechism does not certainly imply a denial of such distinctions; it rather suggests to look upon these distinctions as functional aspects of human existence, namely as different and yet “substantially” contiguous features of an evolving reality, or as signs of its own factual complexity. On the other hand, there is no sign which cannot be included in the process of reasoning, thus acquiring an “objective” meaning which also entails a self-controlled selection of the “pragmatic” and intellectual implications as connected with whatsoever acknowledgement of objectivity. From this point of view, the psychological-natural elements of our being does not exactly represent, as Kant was inclined to hold, a domain of human reality which is not determined by reason, but rather the departing point for its specific normative function. In other words, the psychological-natural level is the ground where the typically human ability to identify and follow the logical rules may be rooted and developed. To sum up, we can hold that the normative pattern 26

See Vincent Potter, Charles S. Peirce on Norms and Ideals (Amherst: The University of Massachussetts Press, 1967), 8. 27 The concept of Synechism constitutes the framework of the 1903 discourse on normative sciences. Although it can be considered the most refined anti-dichotomic piece of Peirce’s writings, it also constitutes one of the most problematic works, because of the idea of a “fatal” increasing of rationality implied therein. I have already discussed this idea taking into account Kant’s emphasis on the limits of human reasoning and on the relevance of subjective responsibility with respect to the accomplishment of both rational thinking and acting. See Rosa M. Calcaterra, “Spazi e forme di responsabilità. Postille alla logica normativa di Peirce”, Semiotiche 2 (2004): 103-115.

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of logic pertains to our capacity to reflect on the “natural” mechanisms inherent to our very existence as human beings, and, consequently, to distil all factors that can provide a positive value in order both to attain a correct reasoning, and to get rid of what might, on the contrary, jeopardise the “security” and the “uberty” of our reasoning. It is not by chance that I use those two words, “security” and “uberty”: they, in fact, appear on the very title of one of the 1913 Peirce’s essays, An Essay toward Improving our Reasoning in Security and Uberty, which I have already referred to. This essay helps us to clarify the difference between the speculative “naturalistic” reading of Peirce’s view of the normative character of logic, and the more usual patterns of scientists naturalism. For the time being, it is worth mentioning Training in Reasoning, one of the 1898 Cambridge Lectures, which purports to underline the importance of an assiduous training of the “different mental operations that enter into the business of inquire”.28 These psychological operations–described by a sequel of meticulous distinctions endorsing Peirce’s penchant for describing things in terms of trichotomies–consist of Observation, Experimentation and Habituation. In addition, he stresses the relation between these three psychological operations and the categories of Firstness, Secondness and Thirdness, specifying that they are “all-pervasive categories and appear in psychology with great clearness”.29 We do not need, here, to follow in details the analysis contained in this writing. Rather, I would like to shortly return to the issue of observation. Strictly speaking, as Peirce maintains in this essay, observation refers to “the relations of real objects and parts of objects external to us”. This is the “easiest” kind of observation and it surely requires professional training.30 Nevertheless, what ought to be carefully trained is “the power of observing the objects of our own creative fancy”, that is, the mental images in the wider sense of such definition: from the most obvious and transient to the most stable and complex ones: “systems, forms, and ideas”. These latter pertain to “the highest kind of observation”. As it is well-known, the Cambridge Lectures are predominantly concerned with the definition of the structure of rational reasoning in terms of logicalmathematical continuity, and therefore it is by no means surprising that Peirce suggests the study of both pure mathematical theories and Hegel’s Phaenomenologie des Geistes31 in order to strengthening such a “highest” kind of our power of observation. On the contrary, it might appear quite odd that “the 28

RLT: 182. RLT: 190. 30 RLT: 185. 31 RLT: 187. 29

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observation of system, forms, and ideas” is categorised as a psychological operation, namely as something belonging to the “natural” constitution of our mind. The world of systems, forms, ideas corresponds, in fact, by definition, to the world of rationality, that is, a tier of the mental world, which, by itself goes beyond the natural mechanisms of thinking. However, such transcendence–according to the principle of continuity–derives from the “essential condition” inherent to our psychological attitude to observation, that is, the “passivity”, through which we tend to uphold the “dicta of Nature”, while avoiding to “conjecturally emend them”.32 According to the already mentioned essay of 1913, even the most sophisticated logical conjectures, specifically those leading to new scientific achievements, largely deals with our natural constitution, or with the “reasoning-power” which is related to human nature “very much as the wonderful instincts of ants, wasps, etc., are related to their several natures”.33 There is a continuity between nature and rationality; but this is a continuity-in-difference, since “the just authority of instinct”, mentioned by Peirce in reference with the scientific discoveries, must eventually be verified through a sequel of “self-controlled” logical and empirical procedures.34 Among such procedures, the externalism is by large the theoretical core, the criterion which allows us to distinguish between the mere natural attitude to the settlement of beliefs, and the typically rational attempt to prepare and organise sufficiently guaranteed “objective” knowledge. As a matter of fact, externalism comes out once again as a landmark: Here is but fair to the Reader, lest he should be seduced unawares into assent to a disputable doctrine, that I should at once avow that in my endeavour to meet the exigency of verifiable thought in science, I have long ago come to be guided by this maxim: that as long as it is practically certain that we cannot directly, nor with much accuracy even indirectly, observe what passes in the consciousness of any other person, while it is far from certain that we can do so ( and accurately record what [we] can even links at best but very glibberly) even in the case of what should through our own mind, it is much safer to define all mental characters as far as possible in terms of their outward manifestations. In the case of any consciousness of the nature of our thought, I shall show that their appears to be an even more imperative reason for following the maxim then that methodological, or prudential, one just given, though this ought to be sufficient to determine us.35

32

RLT: 187. EP2: 464. 34 EP2: 472-473. 35 EP2: 465. 33

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Current achievements of neurosciences probably compels us to conclude that such “impossibility” is nowadays significantly reduced; nonetheless, we might reply, with Peirce, that “our knowledge of how we think is no mere description of it, as a knowledge of how the brain, or any other physical machine, works would be, so far as it is correct, amounts positively to a translation of it, or in some cases to a ‘grammatical’, ‘synctactical’, analysis of thought”.36 Above all, the new scientific findings on our mental process do not diminish what is, in my opinion, the most significant aspect of the “externalist” option, upon which Peirce’s analysis of the relation between logic and psychology is founded. I refer to the “social” character informing his doctrine of logic, which is called into action as well by his advice to not devoting much time to observations of oneself, a suggestion which can be found in the pages of the Cambridge Lectures. In fact, it is crucial, Peirce writes, “to become emancipated from oneself” in order to achieve a correct reasoning. Clearly enough, Peirce’s remark refers to the Socratic statement “make you own acquaintance”, which, in his opinion, does not mean “introspect your soul”; rather, it means “see yourself as others would see you if they were intimate enough with you”.37 I would like to conclude my considerations returning to the question I had previously left aside: is it possible to detect, in the “logical socialism”, a spur to identify the normative character of certain sentiments? I may attempt to give an answer by drawing attention to Peirce’s famous contribution to the classic philosophical enquiry about the most “rational” method for “the fixation of beliefs”, as the title of his famous 1878 paper bears it. Although Peirce later endeavoured to oppose any interpretation of this essay in terms of psychology, I am inclined to believe that it is just in this writing that the founder of Pragmatism puts to work the particular normative pattern, which I have introduced with respect to synechism. It would be sufficient to recall that Peirce indicates the scientific method as the most correct road to the fixation of beliefs, precisely because its peculiarity consists of conceiving the truth as “something public”, together with striving to allow beliefs to coincide with “real things”. These words, in Peirce’s ordinary language, indicate the ability of those theoretical meanings to last in the long run of the “social” experience of thought, that is, in the “infinite” process of the community quest for truth. However, this is not a sort of “idealism of sociality”. The strict connection, here and elsewhere, between the “public” conception of truth and the realistic hypothesis, on which the empirical scientific investigation is based, may even 36 37

MS 678: 42. RLT: 186.

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constitute a disincentive to the rhetorical account of the human being as a “social animal”. Rather, Peirce’s analysis of the four methods suggests that the social “impulse” or “sentiment”, which humans generally demonstrate, is constantly subject to the risk of being a wrong answer to human need “to shape our actions” according to sufficiently reliable beliefs. At the same time, the positive effectiveness of such a sentiment may derive only by our deliberate choice to transform it in a normative criterion of reasoning. In this frame, sentiments of approval or disapproval, pleasantness or unpleasantness, coming up in the course of our relations with others, are not relevant, since what really matters is the ability to discern whether or not our, or others’, way of reasoning is correct. This must be done bearing in mind the “resistance” that factual experience may at times oppose to our most immediate impulses, including our natural attitude to agree with those who neighbour us. In terms of semeiotic categories, we may affirm that sociality is a Firstness, a pure and simple “possibility” of human nature, which could and should evolve into a Thirdness, namely into a logical and practical habit, which, by definition, acquires a normative value. According to this view, the normative value of sociality is, therefore, typically pragmatic: its justification must be sought on the side of praxis, or in the functioning of the “sociality” category within an approach to the problem of the “fixation of beliefs” implying the emancipation from personal and group idiosyncrasies, the awareness of the possibility of error that ensues from the acceptance of a lack of definite foundations of our knowledge, and, hence, calls for an anti-dogmatic attitude. In few words, the epistemic relevance of sociality corresponds to a theoretical and practical outlook in which the Cartesian quest for static certainties gives way to the dynamism of both reasoning and feeling, to a continuous openness to new perspectives of meaning and action that, according to Peirce, corresponds to the evolution of the very tools of scientific investigation. Upholding such a pragmatic justification, eventually means that the notion of sociality goes beyond the ontological opposition between “facts” and “values”, translating itself into a logic-linguistic entity which can be treated–to use Wittgenstein’s words–“one time as a proposition to be checked against experience and another time as a rule for checking it”.38 As Wittgenstein taught us, the acknowledgment of the functional duality of our notions may be used to remove the very idea of certainty from the empirical scientific procedures in order to make room for the so-called community view of rules, according to which even the normative character of mathematical laws derives from the consolidation of a certain community practice. This does not mean surrendering oneself to mere contingency or denying the logical necessity value of rules, but, rather, it means 38

Ludwig Wittgenstein, On Certainty (Oxford: Blackwell, 1969), § 98.

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recognizing that praxis is an inescapable point of reference for understanding their functioning. I believe that Peirce’s ‘logic socialism” may at least suggest a reflection on this issue, which eventually means to wonder about to what extent we would be ready to follow a philosophical perspective rejecting absolute criteria of truth, although by no means ceasing to search for points of reference to be considered sufficiently justified inasmuch as they are made up in the course of the cooperation among individuals.

REFERENCES Brentano, Franz. Psychologie vom empirischen Standpunkt. Ed. by O. Kraus. Leipzig: Felix Meiner, 1924-25. Calcaterra, Rosa M. Introduzione al pragmatismo americano. Bari: Laterza, 1997. __. Pragmatismo: i valori dell’esperienza. Letture di Peirce, James e Mead. Roma: Carocci, 2003. __. “Spazi e forme di responsabilità. Postille alla logica normativa di Peirce”. Semiotiche 2 (2004). Colapietro, Vincent. “The Space of Signs: C.S. Peirce’s Critique of Psychologism”. In Philosophy, Psychology & Psychologism. Ed. by D. Jaquette. Dordrecht-Boston-London: Kluwer Academic Publishers, 2003. Fabbrichesi Leo, Rossella. Sulle tracce del segno. Semiotica, faneroscopia e cosmologia nel pensiero di Ch. S. Peirce. Firenze: La Nuova Italia, 1986. __. Introduzione a Peirce. Roma-Bari: Laterza, 1993. Jervis, Giovanni. “Significati e malintesi del concetto di ‘sé’”. In La nascita del sé. Ed. by M. Ammaniti. Roma-Bari: Laterza, 1989. Kant, Immanuel. Logik, Kant’s Werke. Band IX. Berlin und Leipzig: Walter de Gruyter and Co, 1923. Kasser, Jeffrey. “Peirce’s Supposed Psychologism”. Transactions of the Charles Peirce’s Society 3 (1999). Kripke, Saul. Wittgenstein on Rules and Private Language. Oxford: Blackwell, 1982. Maddalena, Giovanni. Istinto razionale. Studi sulla semiotica dell’ultimo Peirce. Torino: Trauben, 2003. Potter, Vincent. Charles S. Peirce on Norms and Ideals. Amherst: The University of Massachussetts Press, 1967. __. Peirce’s Philosophical Perspectives. New York: Fordham University Press, 1996. Rosenthal, Sandra B. Speculative Pragmatism. Amherst: University of Massachusetts Press, 1986.

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Sini, Carlo. Semiotica e filosofia. Bologna: Il Mulino, 1990. Wittgenstein, Ludwig. Philosophical Investigation. Ed. by G.E. Ascombe and R. Rhees. Oxford: Blackwell, 1953. __. On Certainty. Ed. by G.E. Ascombe and G.H. von Wright. Oxford: Blackwell, 1969.

CHAPTER 5 THE ANALYTIC/SYNTHETIC DISTINCTION AND PEIRCE’S CONCEPTION OF MATHEMATICS Michael Otte I We have shown elsewhere1 that the analytic-synthetic distinction has relevance and makes sense only if one shares the Kantian theses that true knowledge refers to some object as well as that all knowledge must be the knowledge of someone, some human subject. We claim that Peirce shares these Kantian views although his conception of the epistemic subject as well as of the objectivity of mathematics are very different from Kant’s and that it is therefore fruitful to consider his notion of mathematics from the point of view of this distinction between the synthetic and analytic. If somebody has to solve a problem, he/she might fumble around and experiment with the data trying to find a solution; or one might begin and analyze the type and relations of the problem, trying to understand it as a whole, because a problem absolutely unlike and unrelated to any formerly solved problems “would be insoluble”, as Polya has so aptly observed.2 The purpose is working on the problem, rather than on the problem solution, and this in turn means not to simply get the right answer, but to analyze and compare different ways of thinking about the problem. Today’s positivism and nominalism would in general prefer synthetic methods to analytic ones and would search to directly solve a problem, rather than trying to generalize it. But even in a case like the search for the terrorist bombers in London’s City the British Police, although satisfied with definite facts and distinct data only, certainly would concentrate their investigations primarily on certain 1

Michael Otte, Marco Panza, “Mathematics as an Activity and the Analytic-Synthetic Distinction”, in Analysis and Synthesis in Mathematics. Ed. by M. Otte, M. Panza (Dordrecht: Kluwer, 1997), 261-272. 2 George Polya, How to Solve It (Princeton: Princeton Univeristy Press, 1971), 98.

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cultural and ethnic groups. In pure mathematics the analytical aspects are still more prominent as mathematics is concerned with possibilities or with ideal states of affairs, rather than concrete facts. Mathematical analysis becomes especially important when data are missing. A great help in cases of incomplete knowledge is the formation of fertile hypotheses and then try and draw out their testable consequences. Mathematics is, as Peirce defines it, “the science which draws necessary conclusions”.3 The formulation of mathematical hypotheses is certainly constrained by previous knowledge and experience, and is not free, in the manner Cantor wanted it to be; and the constraints are not merely logical, in the narrow sense of mathematical logic. Mathematical analysis does, however, not proceed by empathizing into the meanings of concepts; it is no hermeneutic science, based on interpretations of the vague and constantly oscillating meanings of words. If mathematics is, as Peirce has defined it “the science which draws necessary conclusions” and if its whole business consists in deducing the consequences of hypothetical assumptions, it is the one science to which a science of logic is not pertinent. For nothing can be more evident than its own unaided reasonings. But there is a part of the business of the mathematician where a science of logic is required. Namely, the mathematician is called in to consider a state of facts which are presented in a confused mass. Out of this state of things he has at the outset to build his hypothesis. Thus, the question of topical geometry is suggested by ordinary observations. In order definitely to state its hypothesis, the mathematician, before he comes to his proper business, must define what continuity, for the purpose of topics, consists in; and this requires logical analysis of the utmost subtlety.4

It is in fact the problem of infinity as well as the processes of generalization, meant by it, which require a new logic and this new mathematical logic started from the actual presence of the infinite in the context of the mathematics of the continuum, for example, in relation to the methods of indivisibles or of projective (or topical) geometry.5 This were two manners in which infinity entered mathematical discourse and both required a logic of relational thinking to escape the paradoxes of the continuity, or the “labyrinth of the continuum”, as was said. The related problems have transformed the “principle of continuity” into a powerful means of mathematical investigation and experimentation (Descartes, 3

CP 3.558. CP 7.525. 5 See Amir R. Alexander, “Exploration Mathematics: The Rethoric of Discovery and the Rise of Infinitesimal Methods”, Configurations 9, 1 (2001): 1-36, Ladislav Kvasz, “History of Geometry and the Form of its Language”, Synthese 116 (1998): 141-186. 4

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Leibniz, Poncelet, and Peirce). The continuity principle is first of all a means of idealization and generalization, that is, a means of the creation of ideal or idealized objects in terms of invariants as well as a new way of reasoning, namely “diagrammatic reasoning”.6 For instance, if all external influences on a moving body are eliminated, it will move infinitely and uniformly or remain at rest. Galileo discovered this property. Galileo’s achievement impressed Kant very much,7 who emphasized its constructive aspects. Kant did not think very highly of the continuity principle, however, because there is no continuity in real things,8 thus that this principle appears only as a subjective principle of reason. With Peirce or Poncelet the continuity principle becomes an instrument of analysis of relational structures and their possible transformations, rather than being conceived of as principle of order among given phenomena or a mere principle of reason. For instance, mathematicians “use a generalized perspective”,9 when compared with painters, in so far as they understand it in terms of a relation between two representations, while the painter formulates the problem of perspective as a relation between a picture and some concrete reality. There have been, however, two different trends in the foundational debate of mathematics during the 19th century, for which the contrasting conceptions of the continuity principle of Cauchy and Poncelet respectively, mark a significant expression.10 Rather than conceiving of this principle in terms of structure and variation or invariance, Cauchy thought of continuity in terms of approximation and limit, as part of a kind of inductive or bottom-up strategy. The program of rigorization by arithmetization searched to solve the foundational problems in a reductionistic manner, by defining all mathematical concepts in terms of some basic entities, ultimately the natural numbers. Complex numbers, for example, were for Cauchy nothing but pairs of real numbers. The axiomatic movement, in contrast, as anticipated in the work of Poncelet or Grassmann, tried to employ, so to say, a top-down strategy, solving the foundational problems of mathematics by extending and generalizing its relational structures and its rules of inference. Grassmann’s dropping of the commutativity of 6

CP 4.418. Immanuel Kant, Kritik der Reinen Vernunft (Frankfurt: Suhrkamp, 1956), B XII. 8 Kant, B 689. 9 CP 6.26. 10 Bruno Belhoste, Augustin-Louis Cauch: a Biography (New York: Springer, 1991), Giorgio Israel, “‘Rigor’ and ‘Axiomatics’ in Modern Mathematics”, Fundamenta Scientiae 2, 2 (1981): 205-219, Michael Otte, “The Ideas of Hermann Grassmann in the Context of the Mathematical and Philosophical Tradition since Leibniz”, Historia Mathematica 16 (1989): 1-35. 7

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a general product and his definition of the anti-commutative vector product provide a pertinent example here. Axiomatic thinking is thinking about form and form must be constructed and idealized. Whereas the rigor movement tries to synthesize from pre-given primary elements, according to narrowly fixed methods, the top down strategy observes the indications emerging from the overall structure and its behavior under possible variation. Now Peirce’s definition of mathematics as “the science which draws necessary conclusions” and his affirmation that mathematics busies itself exclusively with ideal states of things are a consequence of his semiotic conception of cognition and knowledge and are associated with his affirmation that mathematical reasoning is essentially “diagrammatic reasoning”, as well as that iconicity represents the dominant character of mathematical diagrams. Peirce rejecting the view, held by Descartes as well as Kant, that the edifice of knowledge is to be erected on individual self-consciousness and, affirming that “there is no need at all of considering what passes in one’s mind”,11 transforms their mental representationalism into a theory of semiotic activity. Every symbol or representation is an instrument as well as a reality in its own right, rather than being merely a mirror of reality. A sign, although being objectively constrained, is like a tool representing crystallized experience and knowledge and at the same time making it available for further application and use (in mathematics, for deductive reasoning, for example). This is just an expression of the pragmatic conception of semiosis. Intuition and discovery are therefore directed towards the realm of signs and towards the creation of form, rather than related to the concrete world of existence. We already mentioned this with respect to perspective painting. In a diagram, like in a theory or a work of art, synthesis of representation is realized in the construction and transformation of the representation, that is, in the process of generalization. To generalize in this way one must “see” something and to see means to construct a representation and to show it, in a way similar to the way the very essence of Monet’s garden at Giverny has been realized in his paintings. What may be termed “poetic imagination” is as important to the aesthetic world view as its is essential to Peirce’s logic of science and mathematics. Peirce writes: The work of the poet or novelist is not so utterly different from that of the scientific man. The artist introduces a fiction; but it is not an arbitrary one; it exhibits affinities to which the mind accords a certain approval in pronouncing them beautiful, which if it is not exactly the same as saying that the synthesis is true, is something of the same general kind. The geometer draws a diagram, which if not exactly a fiction, is 11

NEM 1: 122.

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at least a creation, and by means of observation of that diagram he is able to synthesize and show relations between elements which before seemed to have no necessary connection. The realities compel us to put some things into very close relation and others less so, in a highly complicated, and in the [to?] sense itself unintelligible manner; but it is the genius of the mind, that takes up all these hints of sense, adds immensely to them, makes them precise, and shows them in intelligible form in the intuitions of space and time.12

The objectivity of a piece of art or of a theory which “compels us to put some things into very close relation and others less so” is due to the fact that works of art or theories, being signs, must have a style or coherence in order to convey any meaning at all. “Consistency”, says Peirce, “belongs to every sign as far as it is a sign; and therefore every sign, since it signifies primarily that it is a sign, signifies its own consistency”.13 The axiomatic method has sometimes interpreted this consistency in terms of logical consistency and might feel justified in this as long as it does not derive existence claims in the ordinary sense therefrom. Theories as well as works of art are intensional entities in the first place. It is not the what, but the how of representation that imports. The rigor movement in contrast sees science and mathematics as more or less accurate and precise descriptions of the actual world. But the more technical and instrumental mathematical language becomes the more truth and explanation become identified with rigorous or mechanical proof, the more analytical mathematics seems to get. Gödel’s incompleteness theorem throws, however, doubts on this conclusion, resp. on such a possibility. And with the advent of the computer things have become worse or more extreme in various respects. Computer proofs, for example, are rigorous, but are regarded as meaningless and are therefore considered as unsatisfactory by many. We encountered a fact, but not its meaning. Furthermore, rigorous mathematics had been accustomed to consider the incompleteness phenomenon as something on the fringes of real mathematical practice, something irrelevant and happening in very unusual pathological circumstances only. With the advent of the computer things have changed, however. A real number, for example, as a rule is not computable, because the computable numbers form a countable subset only (presupposing Turing’s Thesis about computability). Randomness becomes a central notion in foundational

12 13

CP 1.383. CP 5.313.

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considerations14 and frequently now mathematical facts are discovered, which are random and have no proof at all and thus “are true for no reason. They are true by accident!”.15 Kolmogorov-Chaitin complexity theory throws completely new light on the incompleteness phenomenon. It seems an interesting twist of fate indeed, that now as computational universality seems to succeed, the analytical notion of mathematics, as the Vienna circle positivists had favored it, conceiving of mathematics as a great tautology, has to be abandoned and quasi-empirical or contingent elements must be admitted. Let us add one more observation. Philosophers and mathematicians have sometimes tried to avail themselves of Gödel’s incompleteness results, in order to claim that human mathematical reasoning must be intuitive to a large degree, in contrast to the “blind” and mechanical proceedings of logic and computers. The common tendency to regard incompleteness as vindicating those who, like Dreyfus and Lucas,16 have emphasized the primacy of intuition, as opposed to those who emphasize with Hilbert, Gödel or Kolmogorov the importance of formalism, proves rather superficial, because it ignores the fact that things must be made explicit and definite to become distinguishable. Gödel already did avail himself of an extreme formalization of mathematics as codified in the Principia by Russell and Whitehead. The incompleteness theorem shows that as soon as we have finished any specification of a formalism for arithmetic we can, by reflecting on that formalism (Hilbert’s ‘Wechselspiel’), discover a new truth of arithmetic which not only could not have been discovered working in that formalism, but–and this is the point that is usually overlooked–which presumably could not have been discovered independently of working with that formalism. The very meaning of the incompleteness of formalism is that it can be effectively used to discover new truths inaccessible to its proof-mechanism, but these new truths were presumably undiscoverable by any other method. How else would one discover the ‘truth’ of a Gödel sentence other than by using a formalism meta-mathematically? We have here not only the discovery of a new way of using a formalism, but a proof of the

14

David Mumford, “The Dawning of the Age of Stochasticity”, in Mathematics: Frontiers and Perspectives. Ed. by V. Arnold, M. Atiyah, P. Lax, B. Mazur (Providence: American Mathematical Society, 2000), 197-218. 15 Gregory J. Chaitin, The Limits of Mathematics (New York: Springer, 1998), 54. 16 Hubert L. Dreyfus, What Computers cannot do (New York: Harper and Row, 1979) and John R. Lucas, “Minds, Machines and Gödel”, in Minds and Machines. Ed. by A.R. Anderson (Englewood-Cliffs: Prentice-Hall, 1964), 43-59.

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eternal indispensability of the formalism for the discovery of new mathematical truths.17

These experiences resemble those made when it was realized that Viete’s algebraic notation and Descartes algebraization of geometry, or the invention of the printing press,18 enabled people to experience the yet unknown by reifying it symbolically and relating it to the known and identified. To be able to “reflect” on the form of some thought a new representation and a change of perspective is required. One might even claim that the “new” mathematics has been brought about to a large degree by the opportunities offered by the writing system and, even more, by the printing press.19 Writing evolved, it is stated, “from the coming together of two independent semiotic systems, (oral) language on the one hand and visual imagery on the other”.20 Peirce’s semiotic conception of mathematical epistemology realizes these fundamental premises to an extraordinary degree. The continuity principle is also to be seen within this semiotic context and it was so important to Peirce that he decided to call the doctrine based on this princple “Synechism”.21 Tychism, in contrast, means the breaking of continuity. The realm of particular existents, or absolutely distinct entities, is governed by contingency and chance. Thus law and chance are two components which Peirce understands as belonging together. Peirce is known for his “evolutionary realism”, conceived of in semiotic terms. The main error of analytical philosophy consists in its direct representationalism, which is devoted to the achievement of literal truths. It is to be seen in the endeavor to directly relate knowledge structures to the structures of the objective world and thus to conceive of knowledge as resting on basic propositions to whose truth we have indubitable access,22 rather than conceiving of knowledge as part of semiotic activity. A proposition or judgment, according to the positivistic tradition is a sign or “image” of a fact,23 and the world is “the totality of all facts”, as Wittgenstein says in the opening statements of his famous Tractatus. Now, for 17 Judson C. Webb, Mechanism, Mentalism and Metamathematics (Dordrecht: Reidel, 1980), 126-127. 18 Elisabeth L. Eisenstein, The Printing Press as an Agent of Change (Cambridge: Cambridge University Press, 1979). 19 Eisenstein. 20 Michael A.K. Halliday, Spoken and written language (Oxford: Oxford University Press, 1989), 14. 21 CP 6.103. 22 Quine Willard v.O., “Two Dogmas of Empiricism”, in From a Logical Point of View (New York: Harper Torchbooks, 1961), 20-21. 23 Moritz Schlick, Allgemeine Erkenntnislehre (Berlin: Julius Springer, 1925), 58.

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Peirce a proposition is a rule or law, or, stated in semiotic terms, it is a symbol and a symbol is a Third, and Thirdness is but meaning or intelligibility.24 The symbol mediates between an object, which itself might be a sign, and an idea, to bring about an interpretation, or rather a disposition or a habit. Representation, in the sense of Peirce, thus is triadic, rather than dyadic: it involves an object, a sign (idea) and an interpreter;25 or stated in semiotic terms, an index, an icon and a symbol (which is a law or habit).26 Thus a sign is not only a structure, but is also a process. The symbol is the process of the circular interaction between indexical and iconic elements, realized as an endless process of interpretation. This is the pragmatic view. Peirce, in fact, defines semiosis as the action or process of a sign. He writes: By ‘semiosis’ I mean an action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs.27

Evolutionary realism therefore means the co-evolution of reality and knowledge, that is, the evolution of symbolism. It is the symbol in movement. A symbol consists in a habit or law and the human species is apt at assuming and changing habits. Habits, like rules or natural laws, considered from the point of view of evolutionary realism, are objective and relative at the same time, they represent conditions of cognition and action which however change in the course of accumulated action. In view of the principle of continuity, the supreme guide in framing philosophical hypotheses, we must […] regard matter as mind whose habits have become fixed so as to lose the powers of forming them and losing them, while mind is to be regarded as a chemical genus of extreme complexity and instability. It has acquired in a remarkable degree a habit of taking and laying aside habits.28

Pure mathematics, being concerned with general ideas alone, would have to be called analytic. Peirce, however, has always emphasized that the general can be effective and real only when closely interconnected with the concrete and particular. This comes out already in his triadic conception of symbol, that is, in the affirmation, just quoted, that triadic relations are not “in any way resolvable 24

CP 5.105. CP 8.361. 26 CP 4.464. 27 CP 5.484. 28 CP 6.101. 25

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into actions between pairs”. A symbol, being a habit or a convention, might thus be considered as arbitrary by nominalist philosophies. But one would have to explain then how objectivity comes from arbitrariness, or, as Peirce formulated it, how “law ought to be explained as a result of spontaneity”.29 Let us give an illustration and assume a mouse wishes to cross a meadow, and it finds before its eyes a meadow where all the blades of grass are aligned even more regularly than on the best-trimmed English lawns. The mouse will have to select his own path spontaneously and without a reason for there is no indicator within the lawn’s continuity, which would help in selecting this course or that. Perception reposes, as we well know, not on light, but rather on differences. At the beginning, there are no differences at all to be found, in this lawn. It is totally homogeneous. As soon as the mouse has once run across, some of its small blades will have been dislocated, however light-footed the mouse may be. And it may be assumed that while the mouse will not necessarily select precisely the same path for a second run across the meadow, it will nevertheless select a similar one. In the course of time, the mouse’s traces will become more and more visible, until a wellestablished mouse-path cuts through the meadow at last. The lawn’s continuity has been broken, and the mouse now can determine its course at a glance. The mouse, however, does no longer determine its course at all, but quite to the contrary, it is the established path, which now determines the mouse’s behavior. From the mouse’s view, it is a habit to follow this established path. From the path’s view, this is a case of a law, i.e. of determining the mouse’s movement. “Chance is indeterminacy, is freedom. But the action of freedom issues in the strictest rule of law”.30

II So far we have sketched some basic ideas. Let us now turn to the historical evolution of these ideas and to the related problems of mathematical development. The distinction between intuitive and discursive knowledge respectively, which is reproduced in the systems of writing itself, has a long tradition, although classical Rationalism kind of blurred it. For Descartes the problem was to find a proposition that leads directly to its own validity; hence his reliance on intuition. In intuition perceiving some fact and seeing that it is true, amount to the same. But intuitive insight is nothing but a very compressed logical argument: it is the flash

29 30

MS 954. W4: 551-552; see also CP 1.175.

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of the idea which shortens a long discursive path, as if forming a perceptual judgment. The very same belief that thinking deals with reality itself or that understanding is determined by its object could therefore stimulate Leibniz to create the idea of a completely formal proof to enforce communication and to base truth on proof.31 During the age of classical Rationalism the term “analysis” is used in two applications: 1. Empirical theories are analytical, as far as they claim to speak about the essence of reality as such, as far as they perceive more or less directly and a priori what is essential about a thing, what is its core. Substances or essences are real and are the real subjects of predication. Leibniz’ conception of truth consists in a relation of containment between concepts, rather than in a relation between propositions and states of affairs. Every true statement is thus analytic. 2. Logical theories are analytical, as far as they deal with the way something which has been said can be said in another way as well, and this is how the law of contradiction, that is, the rule that one cannot simultaneously affirm two opposite statements p and non-p about something, obtains its significance. The world of existence must have a consistent meaning. Analysis during the 17th and 18th centuries was meant to help and establish order in the world and in the knowledge about the world and did by no means signify a dominance of mathematics or mathematization, but signified a dominant interest in the idea of representation. The fundamental element of the Classical Episteme, says Foucault in his “The Order of Things”, “is neither the success or failure of mechanism, nor the right to mathematize or the impossibility to mathematize nature, but rather a link with the mathesis”.32 Mathesis means here two things essentially, first the dominance of the search for order, so that the relationship of all knowledge to the mathesis is posited as the possibility of establishing an ordered succession among things […]. In this sense, analysis was very quickly to acquire the value of a universal method; and the Leibnizean project of establishing a mathematics of qualitative orders is situated in the very heart of Classical thought.33

31 Ian Hacking, “Leibniz and Descartes: Proof and Eternal Truths”, in Philosophy Through its Past. Ed. by T. Honderich (Harmondsworth: Penguin, 1984), 207-224. 32 Michel Foucault, The Order of Things (New York: Vintage, 1973), 57. 33 Foucault, 57.

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This analysis presupposes the continuity principle, because without it analysis would have to stop somewhere34 and therefore would not be able to provide proofs of the contingent truths. Everything has an explanation and the general and ideal therefore rules over the existing. The sign is more important than the thing. Leibniz conceived of mathematics and mathematical proof as a means of philosophy. But classical mathematics itself remained, in fact, essentially synthetical and confined to a working within seemingly arbitrary and pre-established frameworks, even though the notions of “variable” and “function” did indicate possible further developments.35 Desargues projective geometry was not recognized at the time and turned into a mathematical discipline during the 19th century only. Peirce claims that even during his own time the “whole of topical geometry remains in an exceedingly backward state and destitute of any method of proof simply because true continuity has not been mathematically defined”.36 Leibniz, by seeking to subordinate algebra to combinatorics, that is, to possible order, on the one hand realized that relations expressible by algebraic notations were not necessarily metrical. On the other hand, Leibniz’ geometric thinking was still static and limited focussing on questions related to individual geometric figures, just as it had been the case since the time of Euclid. The failure of Leibniz’ project of a geometric characteristics, that was supposed to allow to calculate directly with the things themselves and thus to reproduce the “order of things”, is due exactly to this unresolved contradictions of classical ontologism.37 Mathematics consisted mainly in problem solving, rather than theory construction or investigating about the possibility or impossibility of certain solutions. When at the beginning of the 19th century, Bolzano and others, in contrast, characterized mathematics as the science of the possibility of things, they were promoting an analytical ideal of mathematical knowledge. Rather than trying to construct a mathematical relationship, one first asks, “whether such a relation is indeed possible”, as Abel stated in his memoir On the Algebraic Resolution of Equations of 1826, in which he presented one of the famous impossibility proofs of modern mathematics. Abel’s theorem is not only paradigmatic for quite a number of impossibility proofs (doubling of the cube, trisecting of the angle, etc. etc), which culminate in the work of Gödel, but also expresses a general feature of modern mathematics, its becoming meta-mathematics. The second characteristic of classical Mathesis, as Foucault defines it, is that “we perceive the appearance of a certain number of empirical fields now being 34

Leibniz, letter to DeVolder 1699. Pierre Boutroux, L’Ideal Scientifique des Mathematiciens dans l’Antiquité et dans les Temps Modernes (Paris: Alcan, 1920). 36 MS 75. 37 Otte 1989. 35

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formed and defined for the very first time”.38 During the 18th century in particular the empirical sciences grew enormously. Increasing breadth, complexity and unclearness of human experience brought an end to the Classical age and its traditional forms of classification and representation. More than ever before, the sciences are faced with the inevitability of experience in the 18th century. Even though quantitative extensions of knowledge had always led to changes in scientific methods, techniques and theories, this increase in knowledge accelerated to such a degree that the capacity of the traditional information processing technologies, based on the spatial organisation of the stock of knowledge, seemed exhausted.39

Therefore evolutionary conceptions of epistemology, being concerned with the circular connection between conditions and conditioned and its development in time gained ground during the 19th century. We may read off some of these developments from Kant`s own philosophical development. In his “Untersuchung über die Deutlichkeit der Grundsätze der natürlichen Theologie und der Moral” of 1764, which was written as a reply to the question – posed by the Royal Academy at Berlin – whether metaphysical truth could be equated with mathematical truth, Kant draws his well-known distinction between analytic and synthetic truths. He classifies mathematics as based on arbitrary definitions and thus as synthetic and affirms that it is, in contrast to mathematics, much too early for metaphysics and natural philosophy to proceed according to the synthetic method. “Only after Analysis has provided us with clearly and extensively understood concepts, synthesis will be able, like in mathematics, to subsume involved knowledge under its simplest elements” (Second Consideration). Similar statements are known from Leibniz.40 The empirical method should be nothing but a variant of the analytical one, simply confined to those characteristics, which sound and secure experience detects about things. Its principles are not given, but have to be inferred by analysis of given experiences. This means thus that philosophy finds itself jointly with natural science in one camp and both stand in opposition to mathematics, which is synthetical knowledge. Kant writes (Second Consideration): The genuine method of metaphysics is basically identical with that which Newton introduced into natural science and which was there of such useful consequences. One should, it is said there, seek the rules according to which given appearances of 38

Foucault, 57. Wolf Lepenies, Das Ende der Naturgeschichte (Frankfurt: Suhrkamp, 1978), 16-17. 40 Gottfried W. Leibniz, Fragmente zur Logik (Berlin: Akademie Verlag, 1960), 84-85. 39

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nature proceed through secure experience, at best (allenfalls) with the help of geometry […]. Equally so in metaphysics: seek through secure inner experience […] those characteristics that certainly lie in the concept of some general property; and although you do not know the entire essence of the thing, you can still make secure use of it and derive much about the thing from it.

This sounds very much like scientific positivism, as it became so productive at about that time in Lavoisier`s chemical revolution. And it expresses a certain continuity between science and everyday thinking, which does no more exist nowadays. Mathematics, being considered as too abstract at that time, was not held in unanimous esteem among natural philosophers. Kant’s expression “at best some geometry” indicates this just as well as the remark of a professor of physics in Germany saying that, “it is absurd to treat the same subject as applied mathematics and as physics”.41 Only after having understood from Hume that even causal relations are not analytical, in fact, that all relations must be considered external, Kant changed his conceptions of philosophy, natural science and of mathematics. In 1764 he adhered to a very formal conception of mathematics – mathematics being a science from arbitrary definitions and operating with signs “according to simple and secure rules” (First Consideration, §2). In 1764 Kant held a view of arithmetic, for example, which came much nearer to modern axiomatic views–because of its letting aside all questions with respect to the nature of number–than what he presented in his Critique of Pure Reason. In the latter geometry and geometrical construction become paradigmatic for his notion of mathematics and mathematical method. But even his conception of geometry was more operative and formal in his earlier publication. He criticizes Wolff, for example, for not having seen that geometrical concepts, like “similarity” have nothing to do with the general meanings of words, but must be defined in such a manner as to be operatively useful (First Consideration, §1). To Kant, Christian Wolff (1679-1754) was “playing with reason like an artist (‘Vernunftkünstler’), making use of it but not searching for its sources”. In the Critique mathematics is no more a merely formal science but is objective and the nature of its objects is responsible for the fact that mathematics was able to develop its particular synthetic method, which enabled it to make real cognitive progress, differently from logics.

41

John L. Heilbron, “Experimental Natural Philosophy”, in The Ferment of Knowledge. Studies in the Historiography of Eighteenth-Century Science. Ed. by G.S. Rousseau, R. Porter (Cambridge: Cambridge University Press, 1980), 364.

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Mathematics affords us a brilliant example, how far, independently of all experience, we may carry our a priori knowledge. It is true that mathematics occupies itself with objects and cognitions only in so far as they can be represented in intuition. But this circumstance is easily overlooked, because the said intuition can itself be given a priori and therefore is hardly to be distinguished from a mere pure conception.42

Mathematics, being concerned with functions or relations, cannot be based on concepts alone, but must exhibit the possibility of its constructions in the intuition of space and time. To distinguish mathematics from empirical experience, which by 1781 Kant also considered being essentially synthetic, he called mathematics synthetical a priori. Everything that appears as a precondition of intuition and experience, rather than being a product of it, is classified as synthetical a priori by Kant. For Kant, the law of causality, for example, is a discursive judgment that is synthetic and a priori, because causality is the precondition for any experience to be at all possible. Contrary to Hume, he believed in the objective character of the synthesis and the resulting knowledge because the subject’s activity is framed by conditions that are a priori, and are as such objective, namely based on our human constitution itself, that is, on the way humans can achieve objective knowledge. The reality thus becomes the real as it is reflected in real knowledge. As Peirce comments: “It was the essence of his philosophy to regard […] the reality as the normal product of mental action, and not as the incognizable cause of it”.43 Kant`s project of understanding how synthetic knowledge a priori is possible and his asking, “how is pure mathematics possible?”, might have been an important step towards the notion of mathematics as a science of possibility, had Kant not believed that what belongs among the conditions of knowledge can never be its object. Peirce now claims that his new philosophy of Synechism (Synechism is a regulative principle of logic based on the idea of continuity) allows these general conditions or the A priori of cognition to be understood as being both subjective and objective by relating them to an evolutionary process which is at the same time constrained and productive. The resulting relativity of the distinction between the subjective and the objective leads to a relativization of the analytic/synthetic distinction, because the framing of productive hypotheses is not completely arbitrary or subjective. We have tried to illustrate this in part I of this paper already.

42 43

Kant, B 8. CP 8.15.

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III The evolution of Kant’s views foreshadows the transformations to come in the 19th century and certainly will help to better understand Peirce’s philosophy of mathematics. The essential transformation that occurred in Post-Kantian philosophy concerns Kant`s notion of intuition, which Schelling called a kind of empiricist relict. The distinction between the inner and outer worlds of the human being became more accentuated, intuition should be freed from the bounds of experience and notions, like volition, decision, construction or activity in general got more prominence. These changes amounted to a stronger accentuation of the subjective aspects of knowledge. Nevertheless these developments followed directions indicated by Kant already. Kant took great pains to distinguish analytic and synthetic propositions, because his view of the analytic-synthetic distinction depends on the invalidation of the ontological proof of God’s existence and represents his own Copernican step. Kant’s essential concern was first of all to make clear that only knowledge of a subjective kind may be called real knowledge. Secondly he emphasized that there is no direct way from language to objective reality. Classical rationalism rested in the idea of God, as providing the means of a preestablished harmony between discursive knowledge and the objective world. Platonic idealism could thus be combined with the idea that knowledge is directly determined by the domain of its objects. The proof of the existence of God warrants Leibniz’ foundation of truth on proof as well as the Cartesian cogito ergo sum, this final truth which constitutes the foundations of the entire structure of Cartesian rationality. Accordingly a schism was caused in the heritage of the classical age, hence also in the foundations of modern mathematics and science, by the invalidation of the proofs of God’s existence, for God guaranteed a strict correspondence between clear and distinct thought on the one hand and external reality on the other. Kant claims that God exists, can never be analytic, as Leibniz believes, because “being is not a real predicate; that is, it is not a concept of something which could be added to the concept of a thing […]. Logically, it is merely the copula of a judgment”.44 Thus the proposition “God exists” is not real knowledge. Kant realized “that no general description of existence is possible, which is perhaps the most valuable proposition that the Critic contains”, says Peirce. But he adds that Kant’s greatest merit was at the same time his greatest fault, because “he drew too hard a line between the operations of observation and

44

Kant, B 626.

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ratiocination”.45 This sharp discrimination motivated him, to assume that all relations are external and are, according to the nominalist conviction, the product of a priori constructions. Kant had learnt from Hume that relations represent nothing of the essence of relates, that they are arbitrary. What in the nature of Paul should cause his being taller than Peter? Or, to cite another example, the laws of nature do not by themselves cause the book on the table to fall down. Classical Rationalism, in contrast, believed that the laws must be based on the natures of things. All subjects are active but are isolated like Leibnizean monads. Continuity we find, according to Leibniz as to Kant, only in the realm of phenomena as they are synthesized by the human mind (or by God). Space, says Kant, is subjective; it is a mere subjective form of our representations. Peirce accepts that there are relative conditions of knowledge as well as that there is a limit to rational explanation at any moment in time, but he endorses the continuity principle, like Leibniz did. For Peirce, like for Leibniz, the idea of continuity is a presupposition of the idea of explanation, as we have seen already. The general motive for this is to avoid the hypothesis that this or that subject matter remains completely inexplicable, because such an assumption would amount to forbidding the framing of any further hypotheses and would thus end scientific or mathematical inquiry. According to Leibniz, God only could accomplish the infinite proofs to establish contingent truths of fact. Peirce thinks about this matter in terms of infinite evolution; nothing is absolutely determined. For Kant’s critical philosophy the insight is essential that mathematics, although necessary and a priori, produces real discoveries and gains new knowledge. Kant’s intention in introducing the analytic/synthetic distinction was to say that we can never gain any knowledge by means of analytical reasoning from concepts and that therefore even an a priori knowledge, like mathematics must be based on intuition. Subjective consciousness discovers only afterwards what had been constructed by the subject itself. It is, thus, important to observe the reflexivity of (mathematical) knowledge considered as an evolutionary process. Mathematics is always at the same time meta-mathematics, or is discourse on discourse. Now, in his Critique Kant gives two different descriptions of the analytic/synthetic distinction: In all judgments wherein the relation of the subject to the predicate is thought this relation is possible in two different ways. Either the predicate B belongs to the subject A, as something, which is contained (covertly) in this concept A; or B lies

45

CP 1.35.

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completely outside of the concept A, although it stands in connection with it. In the first instance, I term the judgment analytical, in the second synthetical.46 If the judgment is analytical […] its truth must always be recognizable by means of the principle of contradiction. We therefore hold the principle of contradiction to be the universal and fully sufficient principle of all analytical cognition.47

In his Prolegomena of 1783 Kant provides still another description in terms of a distinction between amplifying (erweiternd) and illustrative (erläuternd) arguments (4.266, §2). These definitions seem to rephrase the two understandings of “analytic” indicated above and they have different meaning, at least, if we do not identify concepts and objects. A judgment is, however, not a linguistic entity (assertion or statement) for Kant, but is rather a mental representation (Vorstellung),48 which may not yet be explicit knowledge. Thus our judgments conceived of as mental dispositions are inseparably linked with our faculty to judge and the latter encompasses more than mere linguistic or logical powers. It includes perceptions of complex realities and includes even emotional components. Kant’s definition of analytical judgments becomes thus understandable as a direct reaction to Leibniz and is a kind of mentalist version of Peirce’s notion of a judgment, as it has been described above. In addition one might observe that the first definition of analycity is an expression of traditional subject-predicate thinking, whereas the second also applies to a relational thinking, as it is exhibited in modern axiomatics or in formal systems, like logic or algebra. In a subject predicate expression an existential claim is always included, which, as a rule, remains implicit but was in fact essential for Kant. The proposition that a triangle necessarily has three angles does not say, Kant states, “that three angles are absolutely necessary, but that, under the condition that there is a triangle, three angles will necessarily be found in it”.49 Kant, contrary to Cantor or Leibniz, did not consider conceptual consistency sufficient for existence even in mathematics. Only from such a point of view Kant’s two characterizations of the analytic/synthetic distinction may be considered as equivalent. Peirce does not believe that pure mathematics is concerned at all with existing things. Axiomatic characterizations define concepts or indefinite general entities, not particular objects and therefore there are no existence claims involved here. Peano’s axioms, for example, do not answer the question; what a number really is, as Russell already objected, nor do they affirm that numbers exist. A categorical 46

Kant, B 11. Kant, B 190. 48 Andreas Kamlah, Der Griff der Sprache nach der Natur (Paderborn: Mentis, 2002), 112. 49 Kant, B 622. 47

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statement like “5 is an odd number” must now be rephrased as “If x=5 then x is odd”. In this way we get rid of the existence claim and come to a mere conditional, if-then statement, reducing questions of existence to those about truth. We will say in addition to this that if an odd number is divided by 2, then there will, by definition, be left a remainder of one. Subjects and predicates of statements are transformed into conditional statements themselves. In this way mathematics becomes transformed into a deductive science. For Peirce this elimination of the existence claim was important, because he believed that mathematics contains no knowledge of particular existents, as only hypothetical truths could be necessary. “x” functions then as an index, which is of a rather degenerate form as it does not indicate a definite existing object. “Whatever is determinate in every respect must be banished from the logic of mathematics”, says Peirce.50 Mathematics is concerned, as Peirce writes, with the substance of hypotheses. “Mathematics is purely hypothetical: it produces nothing but conditional propositions”.51 Still we must be able to decide questions of identity, to see whether A=B, or not, or, stated differently, mathematics being an activity and practice, rather than a mental reflection, operates on “objects”. Therefore indices are absolutely indispensable in pure mathematics also. One might think, Peirce himself says, that there would be no use for indices in pure mathematics, dealing, as it does, with ideal creations, without regard to whether they are anywhere realized or not. But the imaginary constructions of the mathematician, and even dreams, so far approximate to reality as to have a certain degree of fixity, in consequence of which they can be recognized and identified as individuals. In short, there is a degenerate form of observation which is directed to the creations of our own minds–using the word observation in its full sense as implying some degree of fixity and quasi-reality in the object to which it endeavors to conform. Accordingly, we find that indices are absolutely indispensable in mathematics.52

The indices occurring in pure mathematics refer to entities or objects that belong to a model, rather than to “the real world”, that is, they indicate objects in constructed semantic universes. They may thus be considered as some sort of degenerate indices. That mathematics, on the one hand, does not make existential claims only outlining possibilities and, on the other hand, makes essential use of indices, in order to represent statements of fact, is fundamental for Peirce’s conception of mathematics as “diagrammatic reasoning”. Indexicality is what in 50

NEM 4: XIII. CP 4.240. 52 CP 2.305. 51

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particular makes the semiotic approach unavoidable, because it shows that mathematical reasoning is contextual like all other reasoning. The relevant contexts are semiotical contexts. And it is, in fact, sometimes claimed that it is with his notion of index “that Peirce is at once novel and fruitful”.53 Peirce saw, Seboek continues, “as no one before him had, that indication (pointing, ostension, deixis) is a mode of signification as indispensable as it is irreducible”. A proposition like Kant’s famous example of a synthetical statement from arithmetic, “7+5=12”54, is certainly analytical according to Peano or Peirce, in terms of the second definition of Kant. “It is not even necessary to take account of the general definition of an integer number”.55 Kant clearly would object to this, as for him the indexical character of the number signs already implies that the arithmetical functions, like addition etc., cannot be part of the number concepts themselves. Kant certainly would not have accepted Peano’s or similar axiomatic characterizations of the notion of number and he would have shared company in this with scholars like Cantor, Frege or Russell, who wanted the number concept to be based on the notion of cardinality. As soon as one formulates the concept of arithmetical sum, for instance, in terms of the cardinality of sets (intuitively assuming the existence of the latter), the concept is obtained as a law, and the arithmetical theorems in question thus become synthetical.56 As soon as the whole numbers, however, are constructed completely from the concept of ordinal numbers, introducing the concept of sum axiomatically and recursively on the basis of the successor operation of ordinal numbers, arithmetical theorems like Kant’s become analytical. But Kant would not even accept that arithmetic has axioms at all57 and his arguments reappear more than a hundred years later in Hölder’s review of Grassmann’s axiomatization of arithmetic of 1861. Hölder objected to Grassmann’s presentation by unintentionally repeating Kant in saying that, “if one wants to accept these formulas as arithmetical axioms, one would be let to introducing similar axioms for countless notions of number theory and analysis and the number of arithmetical axioms becomes infinite”.58 And so what, the reader might be inclined to say. Cassirer has described in some detail how a “representational” (abbildliche) view of mathematics struggled with a “functionalist” one. One party wanted to 53 Thomas A. Seboek, “Indexicality”, in Peirce and Contemporary Thought. Ed. by K.L. Ketner (New York: Fordham University Press, 1995), 223. 54 Kant, B 15. 55 NEM 4: 59. 56 Ernst Cassirer, “Kant und die moderne Mathematik”, Kant-Studien 12 (1907): 1-49. 57 Kant, B 206. 58 Otto Hölder, “R. Grassmann, Die Zahlenlehre oder Arithmetik”, Göttingische gelehrte Anzeigen 15 (1892): 592.

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fundamentally answer the question, “what numbers really are”, while the other searched for generative methods to develop number systems and arithmetical representations of things. What makes this controversy interesting from an epistemological point of view is the general motivation underlying it. We have here before us two opposing fundamental attitudes, which transcend the sphere of mathematics by far, because it is the general question at issue here, how our knowledge acquires objective meaning at all, rather than merely the notion of mathematical objects.59

Mathematical thought, as Aristotle already says, begins with the Pythagoreans, with “theoremata” like: “The product of two odd numbers is odd”. Or: “If an odd number divides an even number without rest, it also divides half that number without rest”. These are theorems, which, as one says, go beyond what can be experienced concretely, because they state something about infinitely many objects. Actually, they do not state anything at all about objects (e.g. about numbers), but they are analytic sentences, which unfold the meaning of certain concepts or hypostatic abstractions. This kind of conceptual inference finds its most exalted expression in the modern axiomatics, a method not at all confined to mathematics and to logic. How precisely do we prove, however, those analytic propositions, like the already quoted “the product of two odd numbers is odd”? We intuitively represent certain activities and the concept’s meaning will be represented as a hypotheticdeductive statement or operation, as indicated above already. By reflecting on the process of division, for example, we infer that there is for each odd number X another number N such as that X = (2N + 1) holds. If we now have two odd numbers represented in this way before us, and if we multiply these, the said theorem will result quasi automatically by applying the distributive and commutative laws. This seems to show that the proposition in question is in fact analytic, contrary to what Kant believes. The distinction between analytical and synthetical reasoning therefore is not to be derived from the use or not use of diagrams as such and from the related intuitions, as Kant had assumed, although such diagrams simply serve to make mathematics an activity, but results from the fact that activity itself is creative and is, in general, not rule-determined. The essential fact, responsible for mathematics not being simply and straightforward analytical knowledge, refers to the necessity of idealization and generalization. Peirce stresses the importance of what he called theorematic reasoning, in contrast to corollarial reasoning, which relies only on that which is enunciated in the premises. If, however, a proof is possible only by reference to 59

Cassirer 1973, 68.

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other things not mentioned in the original statement and to be introduced by intuition and abductive reasoning, if we need, for example, auxiliary constructions, which were not mentioned in the premises of the theorem, in order to be able to carry out a geometrical argument, such a proof is theorematic. Peirce claims that theorematic reasoning is necessary to gain new insight in the more involved cases and that it depends on experimental activity, including random elements. Deduction thus becomes “really a matter of perception and of experimentation, just as induction and hypothetical inference are; only, the perception and experimentation are concerned with imaginary objects instead of with real ones”.60 The distinctive character of mathematics, according to Peirce, then is to be seen in the fact that it “busies itself with hypotheses”,61 or with ideal objects and this fact makes it a part of evolutionary realism. “Hypothesis substitutes, for a complicated tangle of predicates attached to one subject, a single conception”.62 This must be so in order to reduce the complexity of the procedure and to enlarge the range of formal methods. The creation of new hypotheses and new idealizations enters the very process of deductive reasoning itself, as the incompleteness phenomenon has indicated. In theorematic reasoning the mathematician must handle an abductive strategy capable of integrating the missing information The mathematician constructs and manipulates or modifies a diagrammatic representation of the premises in order to find out that foreign idea — to use Peirce’s expression — which must be added to the set of explicit premises already available. Theorematic reasoning implies generalization that is the introduction of new ideal objects, which are a result of a process called “hypostatic abstraction” by Peirce.63 In order to get an inkling–though a very slight one–of the importance of this operation in mathematics, it will suffice to remember that a collection is an hypostatic abstraction, or ens rationis, that multitude is the hypostatic abstraction derived from a predicate of a collection, and that a cardinal number is an abstraction attached to a multitude.64

Hypostatic abstraction, that is, idealization and compressed reification, is by its nature a kind of observation with respect to one’s own mathematical activity and it transforms mathematics into meta-mathematics. An important example is provided 60

CP 6.595. CP 3.558. 62 W3: 337. 63 With respect to the fundamentally important notion of hypostatic abstraction see also: CP 4.234, 4.235, 4.463, 4.549, 5.447, 5.534 and NEM 4: 49. 64 CP 5.534. 61

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by modern axiomatics. Geometrical axioms are nothing but hypostatization of constructions or perceived invariants, and Peano’s axioms of number are nothing but crystallized operations. Hypostatic abstraction proceeds by synthesis. One must bring things together that seem to have little to do with each other and perceive them as a unity. This process of abstraction or idealization is exactly opposed to the transformation of mathematical concepts into hypothetic-conditional statements, as it was described above. Peirce considers Kant’s example “7+5=12”, as a case of corollarial reasoning and writes: Kant was quite unaware that there was such a thing as theorematic reasoning, because he had not studied the logic of relatives. Consequently not being able to account for the richness of mathematics and the mysterious or occult character of its principal theorems by corollarial reasoning, he was led to believe that all mathematical propositions are synthetic.65

Arithmetic does not have axioms, according to Kant, and his claim that it be synthetic thus rests on his conviction that some inference steps in an arithmetical proof are synthetic. Peirce disagrees, considering arithmetic to be analytic. Why would geometry be different? Because the ideas of continuity and infinity are at issue here, causing questions of meaning to become something very complex and quite indeterminate.66 The challenges of the continuum require relational ways of thinking and concepts cannot be understood in the traditional way, as “names” of things. The mathematical development of the notions of space and of function were of special importance to Peirce logic and his whole philosophy. No conception of mathematical generalization is possible without regard for the questions of continuity and infinity. It is well-known that many theorems of discrete mathematics, of number theory, for example, can be proved only when reformulated in generalized continuous terms.

IV Mathematics is sometimes considered to be the art of assigning predicates or relations to substances. This art is, to the main part of it, constructive, that means synthetic, says Kant, because quite a number of predicates cannot be linked to a concept without employing the concept as a rule of construction within the intuition of space and time and observing the general circumstances of this 65 66

NEM 4: 59. See part I.

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construction. For instance, the concept of a triangle does not analytically contain the fact that the sum of its angles amount to two right angles. The philosopher would try, Kant writes, to analyze the concept of triangle, but: He may analyze the conception of a straight line, of an angle, or of the number three as long as he pleases, but he will not discover any properties not contained in these conceptions. But, if this question is proposed to a geometrician, he at once begins by constructing a triangle. He knows that two right angles are equal to the sum of all the contiguous angles, which proceed from one point in a straight line; and he goes on to produce one side of his triangle, thus forming two adjacent angles, which are together equal to two right angles. He then divides the exterior of these angles, by drawing a line parallel with the opposite side of the triangle, and immediately perceives that he has thus got an exterior adjacent angle, which is equal to the interior. Proceeding in this way, through a chain of inferences, and always on the ground of intuition, he arrives at a clear and universally valid solution of the question.67

Mathematics makes progress and, differently from logics, produces new truths, according to Kant. Therefore it cannot be based on arbitrary definitions (as Kant himself had affirmed in 1764), nor can it proceed by logical measures and conceptual reasoning alone, but mathematics requires objects of its own. The principle of contradiction itself, according to Kant, only applies if there is an object given, as was mentioned in the last part already. Mathematical demonstration has to rely on particular instantiations of its concepts, that is, on particular objects. Even in a deductive proof one might argue, for example, that line A is parallel to line B, or intersects with it at point C, etc. One has to draw on relationships that had not been enunciated in the theorem. Classical synthetic geometry had always had this disadvantage of requiring a fair amount of ingenuity in dealing with the intricacies of a particular situation. Analytical geometry, in the sense of Descartes, was designed to exactly eliminate these difficulties and to provide a uniform method. This uniform method, however, did no more deal with the geometrical meanings at all. It eliminated all imagination from the business of doing geometry and all relations to geometrical facts, as mathematicians from Leibniz to Grassmann were to complain. Kant took great pains to draw our attention to the objective and synthetical aspects of geometrical proofs. As Hintikka comments: Kant’s characterization of mathematics as based on the use of constructions has to be taken to mean merely that, in mathematics, one is all the time introducing particular representatives of general concepts and carrying out arguments in terms of 67

Kant, A 716/B744.

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Michael Otte such particular representatives, arguments which cannot be carried out by the sole means of general concepts.68

Hintikka’s interpretation of Kantian intuition touches an important aspect of Kant’s view. Kant’s diagrams could be seen as models of mathematical method in the first place. They are intended to avail ourselves of the truth of propositional functions. We should not forget that a mathematical concept is for a Kant a kind of rule or function69 and the statement “mathematical cognition is cognition by means of the construction of conceptions”70 is to be taken quite literally and is conceived, as Lachterman (1989) has argued, in analogy to the method of constructing the roots of algebraic equations as geometrical segments, which was meant to demonstrate the intuitive existence of a quantity, corresponding to the analytical determination in algebraic terms.71 Far into the 18th century algebra and analytical geometry were not supposed to furnish objective knowledge by themselves. Algebra was, until the end of the 18th century, considered a mere language, that could not ensure the relevant claims to objectivity. But, rather than concentrating on the verificationalist aspects of geometrical diagrams, which will always remain a rather futile enterprise (for this reason geometrical intuition was excluded from mathematical method by analytical philosophy of science), on might interpret them in terms of relational thinking that is, as means of generalization as well as an instrument to decide upon questions of meaning. Even Kant’s notion of space as a form of intuition and experience represents the general conditions of mathematical knowledge, rather than merely illustrating the mathematical procedure. It means this exactly the introduction of the question of continuity into geometrical theory. It could be said, for instance, in the vein of the analytical-formal conception of mathematics, that drawing a parallel straight line cannot show anything about the existence of the latter with respect to mathematics. The entire process then provides more of an insight into the character of mathematical proofs as “if-then”connections: If Euclid’s parallel postulate is valid, then we can draw a parallel line to one of the sides of the triangle and passing through the opposite vertex and by this measures we perceive then, more or less directly, that the sum of angles in the 68 Jaakko Hintikka, “Kant on the Mathematical Method”, in Kant’s Philosophy of Mathematics. Ed. by C. Posy (Dordrecht: Kluwer, 1992), 24. 69 Kant, B 181; Peter Schulthess, Relation und Funktion. Eine systematische und entwicklungsgeschichtliche Untersuchung zur theoretischen Philosophie Kants (Berlin: de Gruyter, 1981). 70 Kant, B 740. 71 See also Henk Bos, “Arguments on Motivation in the Rise and Decline of a Mathematical Theory”, Archive for History of Exact Sciences 30 (1984): 331-380.

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triangle is 180 degrees, etc. Neither Peirce nor modern analytical philosophy of mathematics is concerned with absolute existence claims at all. For Kant a judgment is synthetic, as was said already, if it has some objective content and thus depends on its subjective realization. Analytical truths in contrast are truths, which do not depend on a subjective perspective or activity. To a certain degree these consierations correspond to Peirce’s views, because it is essential for Peirce, like it was for Kant, that there is no knowledge without a subject having that knowledge, although Peirce does not conceive of that subject in mentalist terms or in terms of subjective consciousness, but conceives of it semiotically: “Man is a sign” (Peirce). Differently from the analytic conception of mathematics, as pushed to the extreme firstly by the Vienna Circle philosophers, who rejected mathematical intuition as a means of proving altogether and believed axioms the result of completely arbitrary choice, Peirce considers the subject matter of mathematics as real and as representing the reality of the possible. The possible is that which is not fully specified and determined, such that questions of its determination are open to creative decision. Here enters the idea of theorematic reasoning. Proofs have to generalize in order to become real mathematical explanations. And in contrast to modern analytical philosophy of science, which replaced Kant’s reference to the epistemic subject by the functioning of logical and linguistic frameworks, Peirce’s pragmatism retains the subjective relation of knowledge, conceiving of it, however, in semiotic terms, that is, with reference to the evolving sign processes. Peirce’s epistemology has sometimes been called a semiotic transformation of Kant’s Transcendental Philosophy.72 And like in Hilbertian axiomatics, by which the Aristotelian conception of theory as episteme was overthrown, the foundational basis of a theory, according to Peirce’s famous Pragmatic Maxim lies in the future applications of a theory. This new idea of the objectivity of a theory is another feature by which Peirce distinguishes himself from the analytical philosophy of science.73 There is a problem, however, involved here, which Peirce himself points at, conceding, that the pragmatic maxim might easily be misapplied, so as to sweep away the whole doctrine of incommensurables […]. The doctrine appears to assume that the end of man is action […]. If it be admitted, on the contrary, that action wants an end, and that that end must be something of a general description, then the spirit of the maxim itself, which is that we must look to the upshot of our concepts in order rightly to 72

Karl-Otto Apel, Transformation der Philosophie (Frankfurt: Suhrkamp, 1993), 164. See also C.B. Christensen, “Peirce’s Transformation of Kant”, The Review of Metaphysics 48, 1 (1994): 92. 73

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Michael Otte apprehend them, would direct us towards something different from practical facts, namely, to general ideas, as the true interpreters of our thought.74

The “doctrine of incommensurables” represents here the contradiction between the definite determinations of the everyday world, on the one hand, and the world of theory and development, on the other hand, between direct action and general intelligibility and reasonableness. Laws do not apply themselves. I maintain, says Peirce “the existence of law as something real and general. But I hold there is no reason to think that there are general formulae to which the phenomena of nature always conform, or to which they precisely conform”.75 Therefore Peirce does not deny that geometry contains propositions which may be understood to be synthetical propositions a priori […]. But the difficulty is that considered as applicable to the real world they are false. Possibly the three angles of every triangle make exactly 180 degree; but nothing more unlikely can be conceived.76

Therefore the true character of geometry and its real importance do not appear in the examples of traditional Euclidean geometry, given by Kant. Only projective, or, as Peirce called it, topical geometry, “which branch of geometry really embraces the whole of geometry”,77 expresses the real potential of mathematical generalization and analysis. Classical geometry consists in its entirety of axioms and theorems, which represent nothing but the description of constructions. It is the very same procedure that leads to the axiomatical view of arithmetic. How the translation of figures and constructions into propositions and the subsequent use of these propositions to form geometrical theories could take place, has been shown, among others, by the famous Göttingen topologist Kurt Reidemeister some time ago in his book “Raum und Zahl”.78 Reidemeister selects as an example the configuration of Desargues’ so-called small theorem. This configuration consists of two triangles ABC, A’B’C’, in which, firstly, the corresponding sides are parallel, and in which, secondly, the three straight lines connecting two respectively corresponding vertices are parallel to one another. This figure can also be conceived of as an image of a three-sided spatial prism. We now assign steps of construction to this figure, for instance in the following way: the corners A, B, C, and the corner A’ 74

CP 5.3. CP 6.588. 76 NEM 4: 82. 77 MS 75. 78 Kurt Reidemeister, Space and Number (Springer Heidelberg, 1957). 75

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shall be given. We draw the four straight lines AB, BC, AC, AA’. Then we construct B’ as the point of intersection of the line parallel to AB through A’ and the parallel to AA’ through B. And in an analogous fashion we construct C’ as point of intersection of the parallels to AC through A’, and to AA’ through C. Now all points and lines of the configuration have been constructed, except for the one straight line B’C’. We can construct this line B’C’, however, in three different ways.

In other words, the point C’ is over determined, constructive mathematics begins by operating with intensional objects, and then obtains its theorems in the form of “X = Y”. Classical geometry did not have any idea of global space; its figures were situated, as Salomon Bochner once said, in a kind of metaphysical “nowhere-land”. Starting from the notion of space and employing the principle of continuity one might, however, begin with the observation of an invariant of the form “X = Y” and then search for the theorem or axiom to be distilled or hypothetically assumed from this observation.79 Poncelet’s or Peirce’s use of the continuity principle in the service of axiomatics represents a top down strategy, rather than being synthetic and constructive, like in Kant or Euclid’s Elements. We shall come back to these two versions of mathematical axiomatics in part VI. Thus the essential specificity of pure mathematics lies in its being concerned with the continuity of general ideas. Mathematics is about “ideal states of things”, that is about generals, as Peirce says, and it contains no categorical affirmations at all. The true difference between philosophy and mathematics is related to the type of knowledge provided. Mathematics studies nothing but pure hypotheses, and is the only science which never inquires what the actual facts are; while philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all; so that its principal reasoning are not mathematically necessary at all, but are only necessary in the sense that all the world knows beyond all doubt those truths of experience upon which philosophy is founded.80

V Kant’s two definitions of analyticity, as well as his qualification of the term “being” in his refutation of rationalism as “the copula of a judgment”, take on new 79 80

See Otte 2003, 206-209. CP 3.560.

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meanings from a relational and model theoretical perspective, conceiving of propositions as relations between ideal or concrete objects, rather than as subjectpredicate expressions. Let us look more at this! Analytical philosophy considers the existential quantifier as a second-order predicate and does interpret Kant as someone asking for concepts that are “not empty”. McGinn illustrates this view as follows: When you think that tigers exist you do not think of certain feline objects that each has the property of existence, rather you think of the property of tigerhood, that it have instances […]. The concept of an object existing simply is the concept of a property having instances.81

Or stated in Russell’s terms: To say that tigers exist is to say, that ‘x is a tiger’ is sometimes true. In this manner mathematics gets rid of the problem of existence. Hyothetico-deductive mathematical reasoning is primarily concerned with truth of consequences, rather then with existence of objects. And truth means truth with respect to a model. Models need not and in general are not specified in linguistic terms. Russell’s propositional attitude in contrast implies that we may speak of existents only if we have a description of them. This contradicts Kant’s rejection of Leibniz conceptualism and his requirement of intuitive representation, as well as, Peirce’s affirmation, that even pure mathematics uses indices as an essential part of its diagrammatical representations.82 Thus the question is, is mathematical knowledge itself contextual. Kant’s famous statement, “Thoughts without content are empty”83 could certainly be understood in the sense described in the last chapter. But there is a different or complementary interpretation possible, according to which there does not exist any thought at all without intuition and experience. When Kant claimed that we have to establish the objectivity of our definitions by means of intuition, he might have had in mind the fact that in general we do not recognize something as something–the face of a person known to us, for example–by means of definitions or their verification.84 To recognize Mrs.Y as Mrs.Y implies the establishing of a perceptual judgment and thus implies a generalization, because it involves a general idea, which comes about by, what Peirce calls, “abductive inference”. But 81

Colin McGinn, Logical Properties: Identity, Existence, Predication, Necessity, Truth (Oxford: Clarendon Press, 2000), 18. 82 CP 2.305. 83 Kant, B 75. 84 See also John McDowell, Mind and World (Cambridge: Harvard University Press, 1998); by the way: only the “Man who mistook his Wife for a Hat” (O. Sacks) needed specific details to recognize even the face of his own wife.

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what we intuit or perceive thereby is not the result of a verification or predication, but is a general conceived of in terms of continuity. Let me give an example. A cook was dismissed from the staff of a restaurant because another person, a guest perhaps, had seen him smoking a cigarette, while cooking. Later it became known by pure chance that these affirmations were false. The person had in fact seen the cook smoking as well as cooking, but not doing both together and at the same time. This person had in his mind synthesized an “idea” or “essence” of that cook, as a “subjective general” (Peirce), by conceiving of him as a sort of “continuum”. The abductive suggestion comes to us like a flash. It is an act of insight, although of extremely fallible insight. It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together, which flashes the new suggestion before our contemplation. On its side, the perceptive judgment is the result of a process, although of a process not sufficiently conscious to be controlled, or, to state it more truly, not controllable and therefore not fully conscious. If we were to subject this subconscious process to logical analysis, […] this analysis would be precisely analogous to that which the sophism of Achilles and the Tortoise applies to the chase of the Tortoise by Achilles.85

From these remarks therefore results the idea that the general occurs in two forms, namely predicative generality on the one hand, and perceptive continuity on the other. Both were present in Aristotelian thought already. Peirce, calling himself “an Aristotelian of the scholastic wing”, describes them thus: The old definition of a general is Generale est quod natum aptum est dici de multis. This recognizes that the general is essentially predicative and therefore of the nature of a representamen […]. In another respect, however, the definition represents a very degenerate sort of generality. None of the scholastic logics fails to explain that sol is a general term; because although there happens to be but one sun yet the term sol aptum natum est dici de multis. But that is most inadequately expressed […]. Take any two possible objects that might be called suns and, however much alike they may be, any multitude whatsoever of intermediate suns are alternatively possible, and therefore as before these intermediate possible suns transcend all multitude. In short, the idea of a general involves the idea of possible variations”, or continuity.86

The general as continuity is objective and is interrupted or punctuated by our decisions about what it means for something to belong to the range of a concept or 85 86

CP 5.181 CP 5.102-103.

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predicate, the concept of “sun”, for example, or, much more important, the concept of “I”. The question of personal identity represents the key point in Peirce’s dynamization of Kant`s epistemology. Even if you might be inclined to attribute the recognition of Mrs. X as Mrs. X to processes of definition and verification, you would certainly not believe that your own personal identity, as the person who performs this recognition of Mrs. X, be also established in such a manner. Now, these differences have direct bearings on the notion of analyticity, because the distinction between analytic and synthetic statements depend in the end on notions, like (cognitive) synonymy,87 sameness, identity or equivalence, that is, on the meaning of statements of the type A=B. Every perceptual judgment and any act of creative imagination consists in particular in the seeing of an A as a B: A=B. Now statements like, A=B could be classified in two ways, depending on whether A and B are conceived as indices or icons, respectively. On one account A=B is synthetic, on the other analytic. As Peirce says: “Analytical reasoning depends upon associations of similarity, synthetical reasoning upon associations of contiguity”.88 This sounds very simple, but remains very abstract. Let us have a closer look. The so called “direct reference theory” understands A and B as two different names of the same thing. John Stuart Mill believed that “proper names” are not “connotative” i.e. they do not have any discursive meaning that can be explained. “They denote the individuals who are called by them; but they do not indicate or imply any attributes as belonging to those individuals”. The meaning of a name, according to this theory, is just the entity to which it refers. A=A, on this account, has the same meaning as A=B. Science or mathematics would than be just sets of contingent facts of various kinds. Mill therefore postulated a law of “uniformity of nature” to explain mathematical or scientific theories. Frege had pointed out that the same individual might have various names, whose meanings are somewhat different. His own classic example was that “Hesperus” is the name of the “Evening Star”, while “Phosphorus” (or “Lucifer”) is the name of the “Morning Star”; but it turns out that the Evening Star and the Morning Star are the same thing, the planet Venus. The identity of the object, however, does not make it correct to call Venus in the evening “Phosphorus”. But why not? Would it not be more informative to use a name like “Phosphorus” also referentially? Frege, in order to explain why A=B should be less trivial than A=A, introduced the distinction between sense or meaning and reference and assumed that descriptions function like referring expressions. Frege postulated a fixed 87 88

Quine. CP 6.595.

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universe with objects and functions making up its only inventory. These considerations demonstrating some complexities of the analytic/synthetic distinction indicate also the failure of a rigid separation of the subjective and objective. Axiomatical theories are intensional theories in the first place and describe general objects or types only, rather than existing objects.89 They have therefore to be completed by sets of intended applications or models, in order to treat questions of equality and difference in a sensible manner. In order to establish equality in the context of an axiomatic theory, we would have to single out those functions and predicates that make up the substitution axioms which distinguish equality from other equivalence relations, those n-ary functions f or predicates p for which it holds that, if xi=yi, for i = 1...n, then f(x1...xn) = f(y1...yn) and p(x1...xn) = p(y1...yn). The technical aspects of the matter do not interest here, what concerns us at the moment is the fact that the meanings of key notions of an axiomatic theory have to be related by axioms and meaning postulates. But although these axioms and postulates serving to decide whether A and B mean the same or not, are stipulated largely as a matter of decision, rather then resulting from logical analysis and objective impact, they are not completely arbitrary and random. Peirce would even say that such things as complete randomness or completely isolated particulars do not exist at all. He was interested in mathematics because of its potential to generalize beyond all bounds and he therefore adhered to his theory of the continuum as a superior form of infinity and considered the principle of continuity as the supreme means of analysis. Still we claim that Peirce’s conception of mathematics was fundamentally formed by the axiomatic method in the modern Hilbertian sense. What matters to him is the ontological status of mathematical axioms, which he conceives, as was said, analogous to natural laws.

VI Why did Peirce not accept Kant’s belief that one might be able to distinguish between mathematics and philosophy or logics in terms of method? Because the method of mathematics became since the early 19th century a universal prerequisite of all knowledge. The rationality of mathematics and science was considered to be a function of its method, which consists of hypothesis, deduction and experimentation. Pragmatism became the first really methodical philosophy.

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I believe, said Hilbert, “that everything that can be a subject matter of scientific cognition at all, becomes subject to the axiomatic method, as soon it is ripe, such that a theory can be formulated about it”.90 And the Norwegian philosopher Foellesdal advocated the thesis “that the so-called hermeneutic method is actually the same as the hypothetic-deductive method applied to materials that are meaningful (e.g. the systems of beliefs and values of human beings in action)”.91 Now there is a paradox here, “Bernal’s Paradox”,92 at the time during the 19th century, when mathematization became an essential tool of science, society and technology, it arose the idea of pure mathematics. Pure mathematics wanted to be rigorous and wanted to free itself from intuitions, which it had inherited from its fields of application. At the same time these applications were, as Hilbert himself has emphasized in 1900 at the International Congress in Paris, of the outmost importance for the growth of pure mathematics itself. Or stated somewhat differently, when mathematical method became universal, the problem of application of mathematics was obscured and escaped definite determination, because very new creative analyses and idealizations were required. Cantor’s set theory is a good example. It had been invented to generalize the mathematical approach and to make mathematical methods universally applicable. The whole arithmetization program of mathematics, including Frege’s or Russell’s conception of the notion of number is evidence for that. Set theory itself had in the end to be conceived of in axiomatic terms because of the paradoxes. An axiomatic theory does not apply directly to some area and it is not a theory of its own application either. From the point of view of application such an axiomatized theory is just a sign or a representation or a perspective on some objective situation. An axiomatic system provides just a particular perspective on some object field. And every theory may be axiomatized in a variety of ways. An axiomatized theory on such an account is not supposed to provide complete identifications or descriptions of its intended applications. But modern axiomatics came in two different forms.93 A logical and abstractive version of axiomatics dates back from Moritz Pasch`s “Vorlesungen über neuere Geometrie” of 1882. Pasch’s notion of a theory follows the traditional Aristotelian understanding. Axioms were still conceived as fundamental truths, which had been established by empirical abstraction and logical analysis and on which the whole edifice of knowledge had to be erected (L). The objects about the theory intends to 90

David Hilbert, “Axiomatisches Denken”, Mathematische Annalen 78 (1918): 415. Dagfinn Foellesdal, “Hermeneutics and the hypothetico-deductive method”. Dialectica 33 (1979): 319-336. 92 After John D. Bernal (1901-1971). 93 See Johannes Lenhard, Michael Otte, “Analyse und Synthese. Von Leibniz und Kant zum Axiomatischen Denken”, Philosophia Naturalis 39 (2002): 277ff. 91

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speak are thought to be given in experience and intuition, completely independently from the theory, like in traditional Euclidean geometry. A second, quite different model theoretical version of axiomatics appeared some years later when David Hilbert published his “Grundlagen der Geometrie” in 1899. Axioms according to this understanding were hypotheses, which are to be evaluated according to their usefulness and theoretical fertility. The foundations of a theory now seem to lie in its future applications. The intended applications or models of a theory become a second constitutive element of theoretical development. Truth means true in a model. “The development of the notion of model and the emergence of the idea of truth have gone largely hand in hand in our century”, writes Hintikka94 (M). This distinction in the notion of axiomatics corresponds to a distinction in the conception of logic, to which van Heijenoort (1967) has drawn attention and which has been vastly developed and applied by Hintikka (1997): logic as a lingua universalis vs. as a calculus ratiocinator. Van Heijenoort writes: Answering Schröder’s criticism of his Begriffsschrift, Frege states that, unlike Boole’s, his logic is not a calculus ratiocinator, or not merely a calculus ratiocinator, but a lingua characteristica. If we come to understand what Frege means by this opposition, we shall gain useful insight into the history of logic.95

We see here again the very same opponents we have met in the debate on the foundations of arithmetic and the conception of number. Frege considered logic as universal and as a language, rather than as a part of an algebraic calculus in the sense of Boole, Grassmann, or Peano. Frege’s universal conception “of logic expresses itself in an important feature of Frege’s system. As is well known, according to Frege, the ontological furniture of the universe, divides into objects and functions”.96 The other conception of logic does not know of the notion of a fixedly given universal ontology. Rather, the ontology can be changed. The universe of discourse comprehends only what we agree to consider at a certain time, in a certain context. For Frege it cannot be a question of changing universes. One could not even say that he restricts himself to one universe. Not necessarily the physical universe, of course, because for Frege some objects are not physical. Frege’s universe consists of all that there is, and it is fixed.97 94

Hintikka 1997, 29. Jan van Heijenoort, “Logic as Calculus and Logic as Language”, Synthese 17 (1967): 233. 96 Van Heijenoort, 234. 97 Van Heijenoort, 234. 95

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Peirce belongs to the model-theoretical camp, as Hintikka has argued extensively on various occasions and the conceptions of logics Peirce has in mind here are those developed by De Morgan, Boole, Grassmann and Schröder, and by himself. Now this logic has evolved from an observation of the development of mathematical thought and of mathematical practice during the 19th century, rather then being meant as a normative answer to the question, how mathematicians should develop their business.

Conclusion In his excellent and influential book on the development of Peirce’s philosophy, M.G. Murphey claims that mathematics is, according to Peirce, analytic,98 as well as that in spirit “Peirce has more in common with the logicist school than with intuitionism”.99 Murphey argues on basis of the necessary character of mathematical arguments or proofs. What makes mathematics effective in communication is the compelling character of its deductions. This is however a rational compulsion. Mathematical proof does not characterize an interaction between reactive systems, but rather one between cognitive systems. Every compulsion, says Peirce, is something which takes place hic et nunc, that is, on a particular occasion, and affects an individual person. It is essentially anti-general. But the compulsion of rational assent is not merely an individual compulsion; it is one, which it is perceived, must be felt by every rational being […]. Such a general compulsion supposes a law.100

And a law or a habit, being the meaning of some sign, is conceived by Peirce according to how it causes us to act upon certain circumstances. A sign represents something in some respects and for somebody. Therefore Peirce, differently from the analytic philosophy of science, believes that knowledge is knowledge of somebody in respect to some intention or purpose. Analytic philosophy is sometimes characterized as an effort to rewrite all philosophy hitherto existing. This re-writing consists in the fact that where traditional philosophy saw problems and advanced statements concerning the 98

Murray G. Murphey, The Development of Peirce’s Philosophy (UCambridge: Harvard University Press, 196), 232-233. 99 Murphey, 288. 100 MS 787 (1897).

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world, analytical philosophy invites us to see merely linguistic conventions or their logical consequences, briefly: analytical sentences. Mathematics, having given birth to the method of hypothetic-deductive reasoning, set some ideal for these philosophical efforts to follow. Now Peirce belongs among the fathers of these new philosophical interests, although his conception of semiosis was much wider, including, for instance, explorations into the evolution of these “linguistic conventions”. Given these reservations mathematical reasoning is, in fact, a measure to find out what follows necessarily, given certain assumptions or premises. It is true, as Murphey argues that Peirce is concerned with the immense complexity and intricacy of deductive reasoning. […] neither Kant nor the scholastics provide for the fact that an indefinitely complicated proposition, very far from obvious, may often be deduced by mathematical reasoning, or necessary deduction, by the logic of relatives, from a definition of the utmost simplicity, without assuming any hypothesis whatever (indeed, such assumption could only render the proposition deduced simpler); and this may contain many notions not explicit in the definition.101

This instrument of mathematical analysis is, so powerful indeed, that “a Phenomenology which does not reckon with pure mathematics […] will be the same pitiful club-footed affair that Hegel produced”, as Peirce stated it in his Lectures on Pragmatism of 1903. By the employing of mathematical analysis knowledge systems should become less immune to internal contradictions and more sensitive to recognize surprising new facts. Peirce was quite aware of the fact that this special “instrument of analysis”, that mathematics seems to be, must itself be modified and further developed by means of its applications. Murphey ignores Peirce’s evolutionism, which embraces everything, the laws of nature and of logic as well as the phenomena, because “the postulate that things shall be explicable extends itself to laws as well as to states of things”.102 From this results the importance of notions like, experimentation, perception, hypothesis, abduction and continuity, even for the understanding of pure mathematics. Peirce certainly did not hold that pure mathematics is analytic in toto, expressing mere tautologies. Mathematics might, with Kant, be called synthetic a priori in some parts, but the essential thing, which distinguishes it even from philosophy or logic, is that it operates with “ideal states of things”, which have to be abstracted from continuous reality. Mathematics proceeds by hypothetic-deductive reasoning, and “hypothesis 101 102

CP 2.361. W4: 548.

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substitutes, for a complicated tangle of predicates attached to one subject, a single conception”,103 that is, introduces an ideal object. Peirce’s notion of mathematics could thus be called axiomatic mathematics, if we take into account the introduction of new hypotheses or axioms, as well as, the mathematical capacity to produce objective knowledge by means of successful applications. Mathematical deduction represents Thirdness, after all, and thus presupposes abduction (First) and verification (Second). Peirce’s interest in mathematics was philosophical, rather then mathematical or technical.

REFERENCES Alexander, Amir R. “Exploration Mathematics: The Rethoric of Discovery and the Rise of Infinitesimal Methods”. Configurations 9, 1 (2001): 1-36. Apel, Karl-Otto. Transformation der Philosophie. Frankfurt: Suhrkamp, 1993. Belhoste, Bruno. Augustin-Louis Cauch: a Biography. New York: Springer, 1991. Bos, Henk. “Arguments on Motivation in the Rise and Decline of a Mathematical Theory”. Archive for History of Exact Sciences 30 (1984): 331-380. Boutroux, Pierre. L’Ideal Scientifique des Mathematiciens dans l’Antiquité et dans les Temps Modernes, Paris: Alcan, 1920. Cantor, Georg. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Berlin-Heidelberg-New York: Springer Verlag, 1932-80. Cassirer, Ernst. “Kant und die moderne Mathematik”. Kant-Studien 12 (1907): 149. —. Substanzbegriff und Funktionsbegriff. Untersuchungen über die Grundfragen der Erkenntniskritik. Berlin: Bruno Cassirer, 1910. —. Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit, vol. 4. Darmstadt: Wissenschaftliche Buchgesellschaft, 1973. Chaitin, Gregory J. The Limits of Mathematics. New York: Springer, 1998. Christensen, C.B. “Peirce’s Transformation of Kant”. The Review of Metaphysics 48, 1 (1994): 91-120. Dreyfus, Hubert L. What Computers cannot do. New York: Harper and Row, 1979. Eisenstein, Elisabeth L. The Printing Press as an Agent of Change. Cambridge: Cambridge University Press, 1979. Foellesdal, Dagfinn. “Hermeneutics and the hypothetico-deductive method”. Dialectica 33 (1979): 319-336. Foucault, Michel. The Order of Things. New York: Vintage, 1973. Frege, Gottlob. Die Grundlagen der Arithmetik. Breslau: Wilhelm Koebner, 1884.

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W3: 337.

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Grice, H. Paul, Peter F Strawson. “In Defense of a Dogma”. In The AnalyticSynthetic Distinction. Ed. by S. Munsat, Belmont: Wadsworth, 1971: 111-127. Haack, Susan. “Peirce and Logicism: Notes Towards an Exposition”. Transactions of the Charles S. Peirce Society 29, 1 (1993): 33-56. Hacking, Ian. “Leibniz and Descartes: Proof and Eternal Truths”. In Philosophy Through its Past. Ed. by T. Honderich, Harmondsworth: Penguin, 1984: 207224. Halliday, Michael A.K. Spoken and written language. Oxford: Oxford University Press, 1989. Heilbron, John L. “Experimental Natural Philosophy”. In The Ferment of Knowledge. Studies in the Historiography of Eighteenth-Century Science. Ed. by G.S. Rousseau, R. Porter, Cambridge: Cambridge University Press, 1980: 366-383. Hilbert, David. “Axiomatisches Denken”. Mathematische Annalen 78 (1918): 405415. Hintikka, Jaakko. “Kant on the Mathematical Method”. In Kant’s Philosophy of Mathematics. Ed. by C. Posy, Dordrecht: Kluwer, 1992: 21-42. Hintikka, Jaakko. Lingua universalis vs. Calculus Ratiocinator: An Ultimate presupposition in Twentieth-Century Philosophy. Selected Papers, vol. 2. Dordrecht: Kluwer, 1997. Hölder, Otto. “R. Grassmann, Die Zahlenlehre oder Arithmetik”. Göttingische gelehrte Anzeigen 15 (1892): 585-595. Houser, Nathan. “On ‘Peirce and Logicism’: A Response to Haack”. Transactions of the Charles S. Peirce Society 29, 1 (1993): 57-67. Israel, Giorgio. “‘Rigor’ and ‘Axiomatics’ in Modern Mathematics”. Fundamenta Scientiae 2, 2 (1981): 205-219. Kamlah, Andreas. Der Griff der Sprache nach der Natur. Paderborn: Mentis, 2002. Kant, Immanuel. Kritik der Reinen Vernunft. Frankfurt: Suhrkamp, 1956. Kvasz, Ladislav. “History of Geometry and the Form of its Language”. Synthese 116 (1998): 141-186. Lachterman, David R. The Ethics of Geometry. London: Routledge, 1989. Leibniz, Gottfried W. Fragmente zur Logik. Berlin: Akademie Verlag, 1960. Lenhard, Johannes, Michael Otte. “Analyse und Synthese. Von Leibniz und Kant zum Axiomatischen Denken”. Philosophia Naturalis 39 (2002): 259-292. Lepenies, Wolf. Das Ende der Naturgeschichte. Frankfurt: Suhrkamp, 1978. Lucas, John R. “Minds, Machines and Gödel”. In Minds and Machines. Ed. by A.R. Anderson, Englewood-Cliffs: Prentice-Hall, 1964: 43-59. McDowell, John. Mind and World. Cambridge: Harvard University Press, 1998. McGinn, Colin. Logical Properties: Identity, Existence, Predication, Necessity, Truth. Oxford: Clarendon Press, 2000.

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Mumford, David. (2000), “The Dawning of the Age of Stochasticity”. In Mathematics: Frontiers and Perspectives. Ed. by V. Arnold, M. Atiyah, P. Lax, B. Mazur, Providence: American Mathematical Society, 2000: 197-218. Murphey, Murray G. The Development of Peirce’s Philosophy. Cambridge: Harvard University Press, 1961. Otte, Michael. “The Ideas of Hermann Grassmann in the Context of the Mathematical and Philosophical Tradition since Leibniz”. Historia Mathematica 16 (1989): 1-35. —. “Arithmetic and Geometry: Some Remarks on the the Concept of Complementary”. Studies in Philosophy and Education 10 (1990): 37-62. —. “Does Mathematics have Objects? In what Sense?”. Synthese 134 (2003): 181216. —. “Mathematics, Sign and Activity”. In Activity and Sign: Grounding Mathematics Education. Ed. by M.H.G. Hoffmann, J. Lenhard, F. Seeger, New York: Springer, 2005: 9-22. Otte, Michael, Marco Panza, editors. Analysis and Synthesis in Mathematics. Dordrecht: Kluwer, 1997. —. “Mathematics as an Activity and the Analytic-Synthetic Distinction”. In Analysis and Synthesis in Mathematics. Ed. by M. Otte, M. Panza, Dordrecht: Kluwer, 1997: 261-272. Polya George. How to Solve It. Princeton: Princeton Univeristy Press, 1971. Quine, Willard v.O. “Two Dogmas of Empiricism”. In From a Logical Point of View. New York: Harper Torchbooks, 1961: 20-21. Reidemeister, Kurt. Space and Number. Springer Heidelberg, 1957. Russell, Bertrand. “Recent Work on the Philosophy of Leibniz”. Mind 13 (1903): 177-201. Sacks, Oliver. The Man who mistook his Wife for a Hat. New York: Touchstone, 1970. Schlick, Moritz. Allgemeine Erkenntnislehre. Berlin: Julius Springer, 1925. Schulthess, Peter. Relation und Funktion. Eine systematische und entwicklungsgeschichtliche Untersuchung zur theoretischen Philosophie Kants. Berlin: de Gruyter, 1981. Sebeok, Thomas A. “Indexicality”. In Peirce and Contemporary Thought. Ed. by K.L. Ketner, New York: Fordham University Press, 1995: 222-242. Van Heijenoort, Jan. “Logic as Calculus and Logic as Language”. Synthese 17 (1967): 324-330. Webb, Judson C. Mechanism, Mentalism and Metamathematics. Dordrecht: Reidel, 1980. Weyl, Hermann. Das Kontinuum. Berlin: Teubner, 1918.

CHAPTER 6 THE HEURISTIC EXCLUSIVITY OF ABDUCTION IN PEIRCE’S PHILOSOPHY Ivo Assad Ibri I In 1868 Peirce stated: According to Kant, the central question of philosophy is ‘How are synthetical judgments a priori possible?’ But antecedently to this comes the question how synthetical judgments in general, and still more generally, how synthetical reasoning is possible at all. When the answer to the general problem has been obtained, the particular one will be comparatively simple. This is the lock upon the door of philosophy.1

Here, the author, still in his philosophical youth, questions the possibility of synthesis in general beyond an a priori synthesis. Peirce was driven, very early on, in quest of a solution to this question, probably because it was implied in his rebuttal of transcendentalism and in all his critique of an underlying nominalism in Kant’s work. In fact, Peirce moves toward a gradual and increasingly vigorous adoption of ontological realism, which is deeply grounded, one can say, on the condition of possibility for all mediative thought, in the extent that it has syntax and sense and is structured on positive concepts that are full of phenomenological content. Such realism appears, essentially, as a continuum of real relations that give shape to the object. This shape is ultimately a spatio-temporal order of the

1

CP 5.348. This refers to a section of the essay Grounds of Validity of The Laws of Logic: Further Consequences of Four Incapacities published in the Journal of Speculative Philosophy, vol.2, pp. 193-208. Although it is an early article, it was reviewed and corrected in 1893. See also, CP 2.690 (1878). In various passages of his mature work, however, the author actually refuses the division of judgments between analytical and synthetical, in view of his logic of the relatives. On this point, see CP 3.560 (1898) and CP 4.85 (1893).

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world that ideally has permanence as a condition for the possibility of any grammar and, thus, for any positive knowledge. Indeed, in our view, the realism of the universals is a basic hypothesis in Peirce’s philosophy. A shapeless world would require the human mind to assume itself in the face of the absolutely chaotic, and substantiate its cognitive impotence admitting, through a negative bias, the necessity of realism. The necessary character of permanence implied by the realism of generals, does not solely refer to the substance, as, incidentally, is adopted by Kant. This permanence, in fact, is much more than what could be materialized in particulars objects enabling the term in language, but to the order of general real relations between these objects, enabling the enunciates the possibility of enunciation. Indeed, the adoption of realism as starting point is basic to enable all and every general representation and operation of semiosis. Realism, in short, makes thought2 possible. In categorial terms, we may say, real thirdness makes possible the thirdness of human reason. It is also necessary to bring to the fore the Peircean evolutionism, which considers the issues of genesis within space-time. Thus, while realism provides the conditions for mediative thought to be, evolutionism can propose an answer to its origin. In this way, one may presume, with a high degree of plausibility that all our cognitive faculties stem from natural processes. Given their obviously mental and live character, consequent upon an evolutionary process, we favor an ancestry of an equal nature, incurring in a mind-matter monism in which the former is, necessarily, primordial, originating Peirce’s doctrine of Objective Idealism, very strongly inspired by Schelling’s Absolute Idealism, although this is not the space to substantiate this relation. For our purposes, it will just suffice to consider that this idealism, indifferentiating the natures of subject and object, produces a synthetic substratum, derived from an originary unity between the internal and external worlds. In such unity, incidentally, on the phenomenological plane, the category of firstness is defined. By one hand, Peirce’s adoption of synechism, in fact his realism of continua instead of a mere realism of genders or classes of objects,3 and by other hand, his claim of objective idealism, seems to easily explain the fact that 2 In Ivo A. Ibri, Kósmos Noétos. A Arquitetura Metafísica de Charles S. Peirce (São Paulo: Perspectiva/Hólon, 1992), 104, we commented on this point, that Peirce, possibly, would not refuse a modification of the Cartesian cogito “I think, therefore the universals are real”, concluding that the phenomenon of mediative thought revealed the order of the world. More radically, in fact, and prior to language itself, the man (subject) as an organism must be possible. 3 The formulation of the logic of the relatives made the author, in our view, radicalize his realism.

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everything that is cognoscible is of the nature of the human mind as, incidentally, Kant claimed. However, under the prism of realism, it is necessary to consider the object of knowledge fundamentally a second for the mind, without it meaning a genetic relation of strangeness between subject and object. It must be stressed that Peirce’s entire philosophy, to our mind, distinguishes itself by the search for a logical symmetry between subject and object, which, in fact, is already born in his Phenomenology through the categorial indifferentiation between the external and internal worlds of experience. This genetic symmetry founded in Peirce’s Phenomenology, is, in fact, the roots for considering logical alternative paths to the assumptions founded in the transcendental epistemology, allowing the substantial conaturality between representation and object not to require a constitutive subjectivity. We maintain that other ontological doctrines complement the support provided by realism and evolutionism, smoothing the logical rough edges of an investigation of the origin of the human capacity of conjecturing, creating theories, in Kantian terms, of effecting syntheses or, finally, reflecting on a Logic of Discovery or Heuristic Logic within the Peircean philosophy. These doctrines appear in two famous and virtually contemporary texts, i.e., The Law of Mind4 (1892) and Evolutionary Love5 (1893), where the former considers the tendency to generalization as the fundamental law of the mind, in its widest sense, and the latter proposes the evolutionary mode of Agapism, which appears as a cosmic agglutinating force, particularly of ideas, under the wide-ranging spectrum of realism and idealism.6 The achievement of understanding a logic of discovery in Peirce requires presupposing that the ideas that intertwine a heuristic concept associate themselves in an ambiance of freedom, typical of firstness. No rule as principle intervenes as a conditioning factor in the formation of a new idea. It is also interesting observe that in another famous text, A Neglected Argument for the Reality of God,7 Peirce develops this Idea of musement as that state of mind subtracted from time, creating a hiatus in the consciousness between past and

4

CP 6.102-163. CP 6.272-317. 6 We can find a brilliant approach of Peirce’s evolutionary metaphysics in Carl R. Hausman, Charles S. Peirce's Evolutionary Philosophy (Cambridge: Cambridge University Press, 1993), mainly his consideration of the importance of realism, in the same way as this doctrine is highlighted here. 7 CP 6.452-493 (1908). 5

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future, where the three universes of experience,8 parade before the eyes, subsuming the three categories. The first shows mere qualities in its diversity; the second, the existence of things in their particularity; and the third, that aspect of ordering, permanence and regularity of the qualities in things, through the relation between the two universes. The lack of purpose of this mind enables the contemplation and the free flow of other ideas to occur unconditionally, where a purely aesthetic quality is initially distinguished. Totally absorbed by that Schellingean spirit of valuing an immediate feeling that provides the most primary experience, that in which the spirit divests itself of mediation before the spectacle of nature and becomes, in its genetic unity, a stage for play, which is free of sentiments and ideas, opening itself to a continuum of possibilities. On this, Peirce founds his hypothesis of the reality of God. However, he does not refer, solely, to an argument for the Absolute, but also to the way in which that initial musement can, slowly, become heuristic: The dawn and the gloaming most invite one to Musement; but I have found no watch of the nychthemeron that has not its own advantages for the pursuit. It begins passively enough with drinking in the impression of some nook in one of the three Universes. But impression soon passes into attentive observation, observation into musing, musing into a lively give and take of communion between self and self. If one's observations and reflections are allowed to specialize themselves too much, the Play will be converted into scientific study; and that cannot be pursued in odd half 9 hours.

The heuristic valorization of this play will mean, in other words, that there are no rules to govern synthesis. However, this principle of freedom will not suffice for an assimilation of new ideas. It is on this point that an agglutinating principle provided by the doctrine of Agapism ensures the association of ideas in a continuum. We are aware that we have invoked, within the limited space of this essay, Peircean doctrines that, by themselves, are worth profound investigation. However, our aim is to draw from them some basic guidelines that may, in an original way, 8

CP 6.455. Thomas A. Sebeok, The Play of Musement (Bloomington: Indiana University Press, 1991), starting from the concept of play of musement, semiotically analyses verbal and non-verbal systems of communication. 9 CP 6.459. The reflexive aspect of musement also appears in another passage where Peirce demonstrates having absorbed the spirit of the beautiful images or romanticism: “Enter your skiff of Musement, push off into the lake of thought, and leave the breath of heaven to swell your sail. With your eyes open, awake to what is about or within you, and open conversation with yourself; for such is all meditation” (CP 6.461).

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provide support to the synthesis as viewed by Peirce and, further, demonstrate, within its system, the interaction between ontology and epistemology.

II After all, however, what is a logic of investigation within Peirce’s philosophy? And, more specifically, how does the development of a hypothesis occur? The author will provide the answer, establishing three types of reasoning: These three kinds of reasoning are Abduction, Induction, and Deduction. Deduction is the only necessary reasoning. It is the reasoning of mathematics. It starts from a hypothesis, the truth or falsity of which has nothing to do with the reasoning; and of course its conclusions are equally ideal. The ordinary use of the doctrine of chances is necessary reasoning, although it is reasoning concerning probabilities. Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. The only thing that induction accomplishes is to determine the value of a quantity. It sets out with a theory and it measures the degree of concordance of that theory with fact. It never can originate any idea whatever. No more can deduction. All the ideas of science 10 come to it by the way of Abduction.

In order to ascribe heuristic power originating solely from abduction, in various passages of his mature work Peirce engages in a criticism of his ideas of abduction as a form of induction.11 The heuristic exclusivity of abduction also appears in Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea; for induction does nothing but determine a value, and deduction merely evolves the necessary consequences of a pure hypothesis.12

10

CP 5.145 (1903). See, also, CP 5.161 (1903), Charles S. Peirce, Historical Perspectives on Peirce's Logic of Science. Ed. by Carolyn Eisele (Berlin-New York-Amsterdam: Mouton, 1985), vol. 2, 895-896 (1901). 11 The essay where this point is subjected to self-criticism is A Theory of Probable Inference of 1873, in Studies in Logic by Members of Johns Hopkins University. Ed. by Charles S. Peirce (Amsterdam-Philadelphia: John Benjamins Publishing, 1983), 126-181, and in CP 2.694-754. The correction made by the author is in Historical Perspectives on Peirce's Logic of Science, vol. 2, 1031-1032 and RLT: 141. 12 CP 5.171 (1903).

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Let us first take induction. The self-correction of possible errors in the inductive process implies that, in the long run, there will be established a genuine representative relation between sample and sampled universe. According to the doctrine of fallibilism we know that Peirce banned the unjustifiable pretense of exactness and final truths in science,13 notably when one considers his ontologically based indeterminism. Thus, this correction of errors is never effectively complete within what, in Peirce, can be termed a vector of approximation of truth, manifest in an evolutionary process of theories, and associated with his conception of final interpretant.14 Within the thematic spectrum of this paper, we shall limit ourselves to that evolutionary dimension at the level of mere referral, proceeding with the understanding of induction in the sense of experimental substantiation of theories. Inductive experimentation, in general, can lead to three situations: “the hypothesis is sensibly correct, or requires some inessential modification, or must be entirely rejected”.15 As a third stage of investigation, the one that precisely confronts theory with experience, induction16 is decisive for acceptance, parametric correction or rejection of the system of signs that constitutes a model of predictive representation of phenomena. Let us now go to abduction,17 which, we already know, is the logical argument originating from a new mediative idea. It is important to stress that its formulation as inference should occur after some state of mind wherein that idea should be in a condition of vagueness. To explain what is the content of this idea and its experimental consequences will be the role of deduction and induction:

13

In a letter addressed to J.H. Kehler, dated June 22, 1911 (L231), Peirce appears to have become aware that the then recent theory of relativity had forced the Newtonian mechanics to review its reach: “All scientific reasoning, outside of mathematics and the Arabian Nights, is provisional. Every scientific man knows it. It was only the other day that the second law of motion was exploded. The same force that would accelerate a slowly moving body very much, will have hardly any effect if the body affected is moving nearly as fast as light”. (NEM 3/1: 197). 14 See, for example, CP 4.536, CP 4.572 (1906). 15 CP 6.472 (1906). 16 Outside the scope of interest of this paper, Peirce classifies induction in three parts. The reader may examine this classification of the author continuing on the last and subsequent paragraph referred to (CP 6.473), and further, in NEM 3/1: 189-210 (1911). 17 The author often uses the equivalent term retroduction, from which invention is attributed, see NEM 3/1: 178 (1911).

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Observe that neither Deduction nor Induction contributes the smallest positive item to the final conclusion of the inquiry. They render the indefinite definite; Deduction explicates; Induction evaluates: that is all.18

The author’s emphasis is, once more, evident as to the exclusive heuristic power of abduction, since he adds that the conclusion was already contained in that indefinite condition of the idea. In our view, there is nothing to contest as regards the genetic indefinition of abduction prior to its argumentative form. We must keep in mind the freedom of the play of musement, under which ideas are associated within a new synthesis.19 In order that such a state of mind be formed, Peirce suggests to the investigator to sit down and listen to the voice of nature until you catch the tune…The invention of the right hypothesis requires genius–an inward garden of ideas that will furnish the true pollen for observation’s flowers.20

To catch the tune can also mean “that man's mind must have been attuned to the truth of things in order to discover what he has discovered. It is the very bedrock of logical truth”.21 Evidently, to say that the human mind is “tuned to the voice” of nature and ascribe to it the grounds for the possibility of logical truth seems, again, to take away from the necessitarist feet the safe terrain of deductive certainty. But, Peirce does not need any magical internal power of an unknowable, psychology-driven mind;22 his evolutionary philosophy will allow him to resort to a genetic theory of subjective faculties: […] if the universe conforms, with any approach to accuracy, to certain highly pervasive laws, and if man's mind has been developed under the influence of those laws, it is to be expected that he should have a natural light, or light of nature, or instinctive insight, or genius, tending to make him guess those laws aright, or nearly

18

CP 6.475 (1906). See, also, Peirce, Historical Perspectives on Peirce's Logic of Science, vol. 2, 899-900 (1901). 19 In CP 5.171 (1903), Peirce clearly excludes logical necessity from abduction: “Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be”. 20 CN 2: 222 (1899). 21 CP 6.476 (1903). 22 Psychology is, to the author, a special science and, as such, must be based on logic. See, for example, CP 2.51 (1902). According to Peirce, some logicians “continually confound psychical truths with psychological truths”, CP 5.485 (1907).

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Ivo Assad Ibri aright. This conclusion is confirmed when we find that every species of animal is endowed with a similar genius.23

Peirce, in this passage, mentions the ideas of “insight”, “instinct” and “guessing”. In fact, these terms are almost ubiquitous in his work when abduction is referred to. The ascription of an instinctive aptitude for guessing truths, apparently an exotic line of argument, is nothing more than referring to an evolutionary consequence of a kind of tuning of the human mind with nature that enabled man, amid an infinity of possible conjectures, to select a given few, among which one has been proven as true: How is it that man ever came by any correct theories about nature? We know by Induction that man has correct theories; for they produce predictions that are fulfilled. But by what process of thought were they ever brought to his mind? A chemist notices a surprising phenomenon. Now if he has a high admiration of Mill's Logic, as many chemists have, he will remember that Mill tells him that he must work on the principle that, under precisely the same circumstances, like phenomena are produced. Why does he then not note that this phenomenon was produced on such a day of the week, the planets presenting a certain configuration, his daughter having on a blue dress, he having dreamed of a white horse the night before, the milkman having been late that morning, and so on? The answer will be that in early days chemists did use to attend to some such circumstances, but that they have learned better. How have they learned this? By an induction. Very well, that induction must have been based upon a theory which the induction verified. How was it that man was ever led to entertain that true theory? You cannot say that it happened by chance, because the possible theories, if not strictly innumerable, at any rate exceed a trillion–or the third power of a million; and therefore the chances are too overwhelmingly against the single true theory in the twenty or thirty thousand years during which man has been a thinking animal, ever having come into any man's head. Besides, you cannot seriously think that every little chicken, that is hatched, has to rummage through all possible theories until it lights upon the good idea of picking up something and eating it. On the contrary, you think the chicken has an innate idea of doing this; that is to say, that it can think of this, but has no faculty of thinking anything else. The chicken you say pecks by instinct. But if you are going to think every poor chicken endowed with an innate tendency toward a positive truth, why should you think that to man alone this gift is denied?24 23

CP 5.604 (1898); italics are from the original text; see, also, CP 1.81 (1896), CP 5.47 (1903), CP 6.417 (1878), CP 7.39 (1884) and RLT: 110-111 (1898). The mention of the “natural light” is an explicit reference to Galileo’s “lume naturale” as shall be seen later. 24 CP 5.591 (1898). In 1883, another passage expounds on this probability of choice of a correct hypothesis: “Nature is a far vaster and less clearly arranged repertory of facts than a census report; and if men had not come to it with special aptitudes for guessing right, it may

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Another passage, along this line of argument, is: “Our faculty of guessing corresponds to a bird's musical and aeronautic powers; that is, it is to us, as those are to them, the loftiest of our merely instinctive powers”.25 This primary element deriving from evolution becomes a central point, within Peirce’s logic of investigation, the “sheet-anchor of science”.26 Coached as we have been by experience, we have a tendency to have faith in what we believe because this fact contains the revelation that our behavioral habits serve our purposes and have the general nature of successful predictive concepts. Thus, whenever this tendency towards belief manifests itself in any way as regards the choice of a path, among the many that appear for a hypothesis, there is an instinctive indicator that must be considered: .

It is a rule of the logic of hypothesis that whatever one finds an impulse to believe one should develop into so definite a form that experiment and observation may have a fair opportunity to refute it, if it be not true. The proposition so developed should thereupon be adopted provisionally and students should at once go hard to work to develop its consequences and compare them with the facts.27

There is clearly here an enhancement of logica utens for the development of a logica docens; such enhancement being, incidentally, an indicator of the force of Nature28 over the mind of man, reflecting on his behavioral adjustment to life. For well be doubted whether in the ten or twenty thousand years that they may have existed their greatest mind would have attained the amount of knowledge which is actually possessed by the lowest idiot” (CP 2.753). 25 CP 7.48 (1907). 26 CP 7.220 (1901). 27 NEM 3/2: 892 (1908). 28 To which, incidentally, Hume himself surrenders: “Most fortunately it happens, that since reason is incapable of dispelling these clouds, nature herself suffices to that purpose, and cures me of this philosophical melancholy and delirium, either by relaxing this bent of mind, or by some avocation, and lively impression of my senses, which obliterate all these chimeras. I dine, I play a game of back-gammon, I converse, and am merry with my friends; and when after there or four hour’s amusement, I would return to these speculations, they appear so cold, and ridiculous, that I cannot find in my heart to enter into them any farther”, David Hume, A Treatise of Human Nature. Ed. by L.A. Selby Bigge (Oxford: Clarendon Press, 1978): book I, part IV, section II, 269. On Hume’s skepticism, Schelling has an interesting opinion: “Hume (faithful to his principles) […] has to assume that the succession of appearances takes place only in our ideas; but that we take just this particular succession as necessary he declares to be pure illustration. But what one can justly demand of Hume is that he at least explain the source of the illusion”, Friedrich W.J. Schelling, Ideas for a Philosophy of Nature (Cambridge: Cambridge University Press, 1988), 26.

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no other reason, Peirce advocates that the start of a philosophy should occur from an analysis of our set of beliefs that translate into our behavioral habits, and not from theoretical doubts incapable of deterring them, rupturing a correspondence between the worlds of reflection and conduct.29 The “impulse to believe” and act accordingly is an indicator of the action of our instinctive faculty that, according to the author, is a powerful rudder that guides toward the correct path, noting that those animals we regard as “inferior” hardly ever err in their actions.30 This is how the author stresses the force of this faculty among the major discoveries of modern science: In examining the reasonings of those physicists who gave to modern science the initial propulsion which has insured its healthful life ever since, we are struck with the great, though not absolutely decisive, weight they allowed to instinctive judgments. Galileo appeals to il lume naturale at the most critical stages of his reasoning. Kepler, Gilbert, and Harvey–not to speak of Copernicus–substantially rely upon an inward power, not sufficient to reach the truth by itself, but yet supplying an essential factor to the influences carrying their minds to the truth.31

Apart from the support to his thesis of “instinctive insight” in the genesis of abductive argument, which Peirce finds in Galileo’s “lume naturale”,32 the author displays his great admiration for Kepler, notably as to the way in which he conjectures on the observations he had received from Tycho Brahe on the orbit of Mars:33 The business of a man of science is to guess, and disprove guess after guess, being guided by the particular way the last guess failed in forming the next one. A scientific genius has seldom had to guess as many times as Kepler did.34

The formulation of a hypotheses, as we have said before, does not depend on some rule over which we may have some control, i.e., our deductive rationality 29

In Ibri, 99-101 we analyze the belief-doubt duality in light of Peirce’s pragmatism. See, for example, RLT: 110 (1898). 31 CP 1.80 (1896). 32 On Galileo’s influence on the author, see the excellent essay by Carolyn Eisele, Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce (The Hague: Mouton, 1979), 169-176. 33 Norwood R. Hanson, Patterns of Discovery. An Inquiry into the Conceptual Foundations of Science (Cambridge: Cambridge University Press, 1977) makes an id-depth analysis of this Peircean reflection on Kepler’s works. 34 NEM 3/2: 893 (1908); see also NEM 3/1: 169-171, where Peirce analyzes Kepler’s discoveries. 30

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contributes nothing whatsoever to that instinctive insight: “However man may have acquired his faculty of divining the ways of Nature, it has certainly not been by a self-controlled and critical logic”35 and further, “Concerning that quite uncontrolled part of the mind, logical maxims have as little to do as with the growth of hair and nails”.36 While abductive inference37 is not under the control of a critical logic, Peirce proposes its formula as an argument that, incidentally, explains how a hypothesis restores the possibly thinkable character of the coarse fact without, however, becoming a rule for the formulation of abduction itself. Such formula, according to the author, is: The surprising fact, C, is observed; But if A were true, C would be a matter of course, Hence, there is reason to suspect that A is true.38

Vis-à-vis what has been so far analyzed, we now delve into the issue of the limits between a critical logic and that heuristically spontaneous behavior of the mind: Where then in the process of cognition does the possibility of controlling it begin? Certainly not before the percept is formed. Even after the percept is formed there is an operation which seems to me to be quite uncontrollable. It is that of judging what it is that the person perceives. A judgment is an act of formation of a mental proposition combined with an adoption of it or act of assent to it. A percept on the other hand is an image or moving picture or other exhibition.39

35

CP 5.173 (1903). CP 5.212 (1903). In CP 5.109 (1903), Peirce reinforces this position: “To criticize as logically sound or unsound an operation of thought that cannot be controlled is not less ridiculous than it would be to pronounce the growth of your hair to be morally good or bad. The ridiculousness in both cases consists in the fact that such a critical judgment may be pretended but cannot really be performed in clear thought, for on analysis it will be found absurd”. 37 Peirce does not hesitate in classifying abduction as a legitimate inference: “Any novice in logic may well be surprised at my calling a guess an inference. It is equally easy to define inference so as to exclude or include abduction. But all the objects of logical study have to be classified; and it is found that there is no other good class in which to put abduction but that of inferences”, Historical Perspectives on Peirce's Logic of Science, vol. 2, 899 (1901). 38 CP 5.189 (1903). 39 CP 5.115 (1903). 36

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Thus, it seems that there is a perceptive moment, a relationship between the cognoscenti mind and the object investigated that occurs in a time space wherein no self-control exists. Peirce now sets the stage for his theory of judicative perception, introducing The perceptual judgment, that is, the first judgment of a person as to what is before his senses […] I do not see that it is possible to exercise any control over that operation or to subject it to criticism. If we can criticize it at all, as far as I can see, that criticism would be limited to performing it again and seeing whether, with closer attention, we get the same result. But when we so perform it again, paying now closer attention, the percept is presumably not such as it was before. I do not see what other means we have of knowing whether it is the same as it was before or not, except by comparing the former perceptual judgment and the later one. I should utterly distrust any other method of ascertaining what the character of the percept was. Consequently, until I am better advised, I shall consider the perceptual judgment to be utterly beyond control. Should I be wrong in this, the Percept, at all events, would seem to be so.40

According to Peirce, “our perceptual judgments are the first premisses of all our reasonings and that they cannot be called in question”,41 since they are totally beyond self-control. Thus, it follows that the initial assumptions of our positive arguments are not subject to criticism, provided they derive from perception. Nevertheless, this perception may contain hallucinatory elements; but, in this case, what would be the criterion to distill a sane perception from one that could easily be an illusion, if no critical logic is possible, per se? Peirce answers this question,42 stating that it would not be difficult to distinguish a perception that more than one person could similarly have, from another full of idiosyncrasies. According to Peirce, there is no reason to doubt the veracity of the senses, affirming that future physics will discover that they are more real than the current state of knowledge permits verifying.43 Notable among the conferences given by him in Harvard (1903) on pragmatism is Pragmatism and Abduction,44 where he presents his theory of judicative perception associated with abduction. In it, Peirce submits what he calls the three cotary propositions, with which he intends honing45 the 40

CP 5.115 (1903). CP 5.116 (1903). 42 CP 5.117-118 (1903). 43 CP 5.118 (1903). In CP 5.402, n. 2, Peirce comments: “It is not ‘my’ experience, but ‘our’ experience that has to be thought of; and this ‘us’ has indefinite possibilities”. 44 CP 5.180-212. 45 According to the author, the term cotary derives from cós, cotis, or a honing stone (CP 5.180). 41

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maxim of pragmatism. The first is “nihil est in intellectus quod non prius fuerit in sensu”, meaning, by intelectus, “the meaning of any representation in any kind of cognition, virtual, symbolic, or whatever it may be” and, by in sensu, as being “in a perceptual judgment, the starting point or first premiss of all critical and controlled thinking”.46 His second proposition is The second is that perceptual judgments contain general elements, so that universal propositions are deducible from them in the manner in which the logic of relations shows that particular propositions usually, not to say invariably, allow universal propositions to be necessarily inferred from them.47

The third proposition, in turn, enunciates that The third cotary proposition is that abductive inference shades into perceptual judgment without any sharp line of demarcation between them; or, in other words, our first premisses, the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from which they differ in being absolutely beyond criticism.48

Evidently, Peirce asserts here a bold theory, mainly as regards perceptive judgment containing general elements. On the other hand, that question of a limit between controlled inference and the instance of the percept or set of percepts associated with judgments seems to lead to a continuity between perception and abduction. Although we are in the field of indeterminacy for a critical logic, Peirce is careful not to turn the theme into an object of psychology: In saying that perceptual judgments involve general elements I certainly never intended to be understood as enunciating any proposition in psychology. For my principles absolutely debar me from making the least use of psychology in logic. I am confined entirely to the unquestionable facts of everyday experience, together with what can be deduced from them. All that I can mean by a perceptual judgment is a judgment absolutely forced upon my acceptance, and that by a process which I am utterly unable to control and consequently am unable to criticize. Nor can I pretend to absolute certainty about any matter of fact. If with the closest scrutiny I am able to give, a judgment appears to have the characters I have described, I must reckon it among perceptual judgments until I am better advised.49

46

CP 5.181. CP 5.181. See, also, CP 5.186. 48 CP 5.186. 49 CP 5.157 (1903). 47

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In light of the realism of the continuum in Peircean philosophy, it seems incongruous to suppose that perceptive experience can, on its own, acquire a semblance of generality in the human mind. Let us consider the necessity of a unity of consciousness in the face of the object that, in time, gathers all percepts in a continuum and that also brings past ideas to presentness for a heuristic suggestion in the form of a hypothesis. Obviously, in this case, let us recall, we are simulating a state of things different from a mere habitual recognition. If, to the spatiotemporal order of percepts, a possible and correlated order of sensed objects does not correspond, we will be committed to nominalism, which, as we know, is not Peirce’s position. So, perceptive judgment should effectively contain general elements, in that undefined border between the descriptive and the interpretative, which, alternatively, transfers itself to the relations between perception and abduction, not precluding saying that “perception is interpretative”.50 In this way, the doctrines of synechism51 and the theory of judicative perception are associated, provided a continuum is required between the instances of experience, in the sense of a system of percepts, and the critical and controlled preparation of a theory. This genetic indeterminacy of heuristic insights is also one of the essential sources of fallibilism. The world’s eidetic fabric is insinuated into the approaching mind: The abductive suggestion comes to us like a flash. It is an act of insight, although of extremely fallible insight. It is true that the different elements of the hypothesis were in our minds before; but it is the idea of putting together what we had never before dreamed of putting together which flashes the new suggestion before our contemplation.52

It should be observed, in this passage, the author’s statement that “the different elements of the hypothesis were in our minds before”; indeed, there is no doubt that the subject should possess a repertoire of signs capable of being associated with the system of percepts for a judgment, as it is a fact that “ we perceive what we are adjusted for interpreting”.53 Under a categorial point of view, as thirdness has an ontological statute characterized by the system of relations between the 50

CP 5.184 (1903). In CP 2.148-149 (1902) Peirce states emphatically that actual laws govern percepts, otherwise theories would be arbitrary. 51 Christopher Hookway, Peirce (London-New York: Routledge and Kegan, 1992) devotes the chapter “Perception and the Outward Clash” to this theme, observing correctly, in our view, that “unless the generality expressed in the perceptual judgment is also present in the percept, there seems to be an unbridgeable epistemological gap between them” (Hookway, 163). 52 CP 5.181. 53 CP 5.185.

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phenomena that have spatio-temporal continuity, generality perceptively grasped is, in fact, an insight of that system. In a passage of his work, Peirce confirms this viewpoint also manifesting his admiration for the human faculty of guessing: […] man has a certain Insight, not strong enough to be oftener right than wrong, but strong enough not to be overwhelmingly more often wrong than right, into the Thirdnesses, the general elements, of Nature. An Insight, I call it, because it is to be referred to the same general class of operations to which Perceptive Judgments belong. This Faculty is at the same time of the general nature of Instinct, resembling the instincts of the animals in its so far surpassing the general powers of our reason and for its directing us as if we were in possession of facts that are entirely beyond the reach of our senses. It resembles instinct too in its small liability to error; for though it goes wrong oftener than right, yet the relative frequency with which it is right is on the whole the most wonderful thing in our constitution.54

There is no longer that division between reason and senses that inaugurated so many nominalistic systems; by splitting interiority, we separate our rationality from the world, since the gateway to the latter would be more like a contingency and accidentality. Nevertheless, […] there is a Thirdness in experience, an element of Reasonableness to which we can train our own reason to conform more and more. If this were not the case, there could be no such thing as logical goodness or badness; and therefore we need not wait until it is proved that there is a reason operative in experience to which our own can approximate. We should at once hope that it is so, since in that hope lies the only possibility of any knowledge.55

Recognizing that our knowledge of the world occurs evolutionarily, it may also be said that such gateway of experience is considerably wider, impregnated with the “undefined possibilities” of the continuum formed by the common ideality of Nature and the human mind. The terms ideality and mind here imply, again, a unity, since “Thirdness pours in upon us through every avenue of sense”.56 54

CP 5.173 (1903). The generality contained in the level of sensitivity is, according to KarlOtto Apel, Charles S. Peirce. From Pragmatism to Pragmaticism (Amherst: University of Massachusetts Press, 1981), 117, the “ final bracket of Peirce’s conception of his system”, seeing, in the theory of perceptual judgments of the author, a sort of “immediacy of meditation” or a “firstness of thirdness”. Murray G. Murphey, The Development of Peirce's Philosophy (Indianapolis-Cambridge: Hackett Publishing Co., 1993), 376-377, lucidly analyses the necessary presence of thirdness in perception, based on the homology of orders in the object and in the senses. 55 CP 5.160 (1903). 56 CP 5.157 (1903).

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III We still have to expound on deductive argument in light of the Peirce’s logic of investigation. We already know that the heuristic content of a theory is contained in the abductive instance. We must emphasize that in the light of Peirce’s realism this heuristic content is necessarily judicative and general; otherwise, it would disrupts the continuum of generality between world and consciousness. In the abductive process, there is that indefinability typical of a fabric of possibilities that results from the lack of a constrictive rule57 for the formation of a hypothesis that, leads to a propositional form. Peirce, as we already know, claims that deduction is a reasoning of a mathematical nature that draws the necessary consequences from the state of things contained in the hypothesis, without questioning whether it is linked or not with reality.58 According to Peirce, the deductive phase of the logic of investigation is developed through diagrams. A diagram is a representamen which is predominantly an icon of relations and is aided to be so by conventions […]. It should be carried out upon a perfectly consistent system of representation, founded upon a simple and easily intelligible basic idea.59

Still according to the author, geometry and algebra corroborate this diagrammatic character,60 where a system of relations is “helped” by conventions, such as, operating signs, letters, etc. In this sense, a geographic map is also a diagram, an icon of spatio relations, which, to be comprehended, requires verbal symbols, geometric scale and other necessary referential signs.61 Peirce also 57

Reinforcing this point which we had already defined as such, we can resort to the following passage of the author’s work: “What are to be the logical rules to which we are to conform in taking this step (the abduction)? There would be no logic in imposing rules, and saying that they ought to be followed, until it is made out that the purpose of hypothesis requires them”, CP 7.202 (1901). 58 “Deduction, of course, relates exclusively to an ideal state of things”, CP 7.205 (1901). 59 CP 4.418 (1903). The definition of icon can be found in CP 2.276 (1902). We can understand it as a sign that has with its object a relation of similitude or similarity, not requiring the actual reality of such object for its possible meaning. 60 “Of all the sciences–at least of those whose reality no one disputes–mathematics is the one which deals with relations in the abstractest form; and it never deals with them except as embodied in a diagram or construction, geometrical or algebraical”, CN 1: 73 (1895). See also CP 2.279 (1902) and CP 5.148 (1903). 61 CP 3.419 (1892).

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considers verbal language a type of algebra and, as such, diagrammatic.62 Indeed, Chomsky’s recent generative grammar shows that the deep syntactic structure of language is, in this sense, an icon of relations or a diagram. Such diagram, of course, must be available in the human mind as a linguistic capability.63 There are, nevertheless, serious differences between the verbal spoken or written language, and mathematical language as regards their respective heuristic capabilities. On this point we shall expound later. The primary quality of a diagram, in Peirce’s view, is to allow those relations to be observed: “All necessary reasoning without exception is diagrammatic. That is, we construct an icon of our hypothetical state of things and proceed to observe it”;64 and further: “A diagram has the advantage of appealing to the eye”.65 This “appeal to the eye” is confirmed in the exemplary case of mathematics, whose truth “is derived from observation of creations of our own visual imagination, which we may set down on paper in form of diagrams”.66 But, what effectively provides this observation, and what is its importance? Let us recall very simple examples, such as auxiliary constructions in geometry that allow the visualization of relations and properties that lead to the demonstration of a theorem, or, even, in algebraic systems with more than one variable, where relations of similarity determine their solution. Evidently these, as well as those unrelated with mathematical language, are trivial cases that were illustratively experienced. Under a conceptual viewpoint, it seems to us that the author says exactly the same thing regarding the method that: consists in studying constructions, or diagrams. That such is its method is unquestionably correct; for, even in algebra, the great purpose which the symbolism subserves is to bring a skeleton representation of the relations concerned in the problem before the mind's eye in a schematic shape, which can be studied much as a geometrical figure is studied.67

What power of our vision is this that enables the solution of a problem, whether in the imagination, through the “eyes of the mind”, or in the contemplation of the diagram graphically materialized on a sheet of paper? This question is the heuristic core of deduction; however, on placing it there is an apparent contradiction: was not the entire content of discovery contained in the abductive inference? How, 62

CP 3.419 (1892). Noam Chomsky, Sintatic Structures (The Hague: Mouton, 1969), chapters 3 and 4. 64 CP 5.162 (1903). 65 NEM 3/2: 1120 (1903). 66 CP 2.77 (1902). 67 CP 3.556 (1898). 63

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then, can we conciliate what we already know with this heuristic facet of the necessary argument? That it effectively exists, the author’s words leave no doubt whatsoever: The act of interference consists psychologically in constructing in the imagination a sort of diagram or skeleton image of the essentials of the state of things represented in the premises, in which, by mental manipulation and contemplation, relations which had not been noticed in constructing it are discovered.68

In order to seek the solution of this question, let us start by pointing out that the use of the term construction refers to the Kantian constructivism present in the Transcendental Doctrine of Method.69 Indeed, Peirce makes countless references70 to the theme, of which we quote: Kant is entirely right in saying that, in drawing those consequences, the mathematician uses what, in geometry, is called a ‘construction’, or in general a diagram, or visual array of characters or lines. Such a construction is formed according to a precept furnished by the hypothesis. Being formed, the construction is submitted to the scrutiny of observation, and new relations are discovered among its parts, not stated in the precept by which it was formed […].71

However, in Transcendental Analytics, Kant proposes the concept of transcendental scheme, which performs a mediating role between categories and phenomena, with simultaneously intellectual and sensible characteristics. He defines it, also, as the “product of the capacity of imagination” and a “rule of synthesis” for such capacity,72 in such a way that schemata are nothing but a priori determinations of time in accordance with rules. These rules relate in the order of the categories to the time-series, the time-content, the timeorder, and lastly to the scope of time in respect of all possible objects.73

68

CN 1: 149 (1892). Immanuel Kant, Critique of Pure Reason (New York: Macmillan Press, 1978), A713738/B741-766. 70 See, for example, CP 4.2 (1898), CP 4.86 (1893) and CP 5.178 (1893). 71 CP 3.560 (1898). 72 Kant, A138-141/B177-180. Herbert J. Paton, Kant's Metaphysic of Experience (New York: The Humanities Press, 1965), 2, 39-40, accuses Kant of “obscurity” on this point, given the difficulty of conciliating the ideas of product and rule of synthesis of imagination, as concepts of scheme. 73 Kant, A145/B184. 69

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Ascribing a predicate of generality to schemata, Kant distinguishes it from image: Indeed it is the schemata, not images of objects, which underlie our pure sensible concepts. No image could ever be adequate to the concept of a triangle in general […]. The schema of the triangle can exist nowhere but in thought.74

In the Transcendental Doctrine of Method,75 Kant distinguishes philosophical and mathematical knowledge, the first for being discursive through concepts and the other for the construction of concepts.76 Comparing these two forms of knowledge, Kant simulates a situation in which a philosopher and a geometrician confront the development of a demonstration that the sum of the internal angles of a given triangle is two straight lines. The former, conceptually reflecting on angles, straight lines or the number three “will produce nothing new”. The geometrician, in turn, “starts building a triangle” and, through other auxiliary constructions, “sees” the solution.77 To which Kant adds: […] thus in algebra by means of symbolic construction, just as in geometry by means of an ostensive construction (the geometrical construction of the objects themselves), we succeed in arriving at results which discursive knowledge could never have reached by means of mere concepts.78

It is thus that the constructive method of mathematics “together with its heuristic advantages, protects all inferences against error by placing each one of them before our eyes”.79 Notwithstanding the differences of principle between the philosophies of Peirce and Kant, the latter, as is known, had a great influence on the formation of the former’s thought.80 It is true that Peirce had full knowledge of the “constructions” of ancient Greek geometry, used in theorematic demonstrations, and one cannot say that he drew this concept from Kant. However, in our view, Kant seems to have been the first to differentiate, in the context of 74

Kant, A141/B180. Kant, A705-728/B733-756. 76 Kant, A713/B741; A719/B747. 77 Kant, A716/B744. Here, Kant proposes that, exemplarily in an ABC triangle, the geometrician would extend the BC side of the triangle and draw a parallel line to AC by vertices B. The external angles thus formed would be, respectively, equal to D and E, which, with J, would add to two straight angles. 78 Kant, A717/B745. 79 Kant, A734/B762. 80 In a letter to his friend William James (April 1897), Peirce says: “The Critique of Pure Reason, as you know, was my wet nurse in philosophy”. 75

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epistemology, verbal and mathematical discourses. Nevertheless, Peirce generalizes the idea of diagram to an extreme that results in its correlation with the logic of relatives and theory of logical graphs.81 This deepening of the notion of diagram made him interpret transcendental logic as an uncalled for pretense of Kant to reduce all necessary reasoning to the syllogism in Barbara;82 Peirce sees, for example, diagrammatic deductivity in the operations of predictive thought, in a kind or internal dialogue in which the mind draws a plan of conduct for a presumed course of future experience.83 According to Peirce, even in the simplest syllogism, a diagrammatic structure is present,84 and he says, also, that ancient syllogistic logic, reviewed under the logic of the relatives, leads arguments to a multiplicity of possible conclusions.85 We now propose to reflect, firstly, on that heuristic power of our human vision that, as shown, whether in Peirce or Kant, appears as an effective resource of discovery of relations and systemic understanding of a state of things contained in a diagram. Let us take the Kantian concept of rule of synthesis for the whole of time, as valid for his idea of a schema.86 If we consider a diagram as an icon of relations evident to vision, there shall be before it the presentness of all those relational predicates. We believe that this is the idea of time contained in the Kantian concept of schemata, in which time is, in fact, abolished from intuition. Those qualities are absolutely simultaneous to the mind, being already a first 81

This theory is, intrinsically, a radical display of the possible universe of logical relations in the form of diagrams. Don D. Roberts, The existential graphs of C.S. Peirce (The HagueParis: Mouton, 1973) is a profound “classical” interpreter of Peirce’s theory of graphs. 82 See the paragraphs mentioned in note 70. In CP 4.37 (1893), Peirce extends his critique to Kant’s supposition that logic had reached a definitive point, with no space for further advances. 83 See, exemplarily, CP 2.169 (1902). 84 CP 1.35 (1903). 85 See an explicit pertinent passage in Peirce, Historical Perspectives on Peirce's Logic of Science, vol. 2, 1123 (1899). In RLT: 156 (1898), Peirce, apart from the technical details of the logic of relatives, explains it conceptually: “where ordinary logic considers only a single, special kind of relation, that of similarity,–a relation, too, of a particularly featureless and insignificant kind the logic of relatives images a relation in general to be placed. Consequently, in place of the class,–which is composed of a number of their relation of similarity, the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever”. In our view, this replacement of class by system, provided by the logic of the relatives is, under an ontological prism, a radicalization of his realism. 86 According to Peirce: “Kant holds that all the general metaphysical conceptions applicable to experience are capable of being represented as in a diagram, by means of the image of time. Such diagrams he calls ‘schemata’”, CP 2.385 (1902).

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synthesis and perceptively facilitating the association of others to correlate ideas. The synthesis of time would, in these terms, imply its own exclusion from consciousness; the importance of time87 in a diagram is, in fact, its vital absence, by gathering, simultaneously, all predicates of relations in a single system. Let us recall that this presentness of ideas for the mind is the fundamentally heuristic condition, despite the diagram, as an icon, shows the object in a structurally analogous form. For this observing mind there is no recurrent need for mnemonic operations; the diagram’s presentness enables a contemplation free of any constraints: this is the state of creative ideality that will discover new relations, in which the eye for the diagram’s exteriority and the eye for the interiority of the imaginary join in the unity of a heuristically perceptive consciousness. This is the way that a deductive diagram causes “surprises”. It is in this sense that Peirce criticizes those who are “utterly overlooking the construction of a diagram, the mental experimentation, and the surprising novelty of many deductive discoveries”.88 In light of this approach, verbal language does not have the visual resource that avails itself of a kind of “time paralysis” in ostensive predicates, which require in spoken or written expressions, the temporality for the intellection of the whole of conceptual relations. Add to this line of argument the fact that the verbal sign, in its atomicity or even, in its expressive system, depends exclusively on conventional rules, unable to resort to that relation of formal similarity between the iconic structures and their objects. Not without reason, the scientific revolution that occurred in the Renaissance also coincides with a revolution in the sciences of Nature, to the detriment of medieval verbalism, through the systematic and heuristically advantageous use of geometry and mathematics, in the preparation of its theoretical body.89

87 We believe this to be the reading of this issue that makes Findlay’s mistaken when he affirms not to understand why Kant gives such privilege to time in the schematism. See John N. Findlay, Kant and the Transcendental Object. A Hermeneutic Study (Oxford: Clarendon Press, 1981), 159. 88 CP 4.91 (1893); a similar content can be found in CP 3.363 (1892). Murphey, 231 comments on this “surprising” aspect of the diagrams, pointing out that “in constructing the icon, we do not construct one particular case under the hypothesis, we rather construct any particular case under the hypothesis” (Murphey, 234). 89 Contemporarily, there is an interesting example of the heuristic power of diagrams in the work of Paul Dirac, Directions in Physics (New York: John Wiley and Sons, 1978), 11-20. Conjecturing on Einstein’s quadratic equation referring to the energy of atomic particles, it was asked whether the negative root of this equation could have a physical meaning. Shortly after, this conjecture led to the discovery of the positron.

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It is opportune to return to the question of the heuristic possibility of deduction, in view of having ascribed to abduction the exclusive power of discovery of new theories or truths in science. We presume this is a solvable question, if we recall that deduction draws necessary consequences from hypothesis. This operation is, in Peirce’s words, one of the stages of the definition of that typically conjecturable indetermination of abduction.90 If we restrict ourselves to a positive science, i.e., one that has as object some cut from reality, we must conceptually distinguish creation and discovery.91 The latter, within a realistic philosophy, should acknowledge that reality investigated is a system of relations endowed with absolute alterity in relation to the mind, and, thus, is not an arbitrary creation of a nominalism that can, only, save appearances. In this sense, to call a theory discovery is to explicitly confess that it did not constitute or construct its object. Thus, deduction, within the realm of an ideal state of things,92 requires a creative act of the mind over its diagrams as a way of revealing what of the world was already genetically contained in abduction.93 If we may use a metaphor, the deductive stage of the logic of investigation has the lapidary function of a rough stone covered by the impurities of reason; the surprises of the diagrams are nothing more than the luster of reality on the faces of that original prism that gradually reflects the light of the world when revealing itself as a precious discovery, through the creation of man over the diagrams. Such diagrams, if inductively true, would suggest a continuity between Peirce’s cosmic intelligence and Schelling’s poetic soul: Visible mind of visible Nature. 94

90 See again note 17. Regarding the linking of the three arguments to Peirce’s three categories, not discussed in this paper, please consult Wim Staat’s interesting essay “On Abduction, Deduction, Induction and the Categories”, Transactions of Charles S. Peirce Society 29, 2 (1993): 225-238. It should be noted that Peirce himself admits hesitating on the solution to this question. See CP 5.146 (1903). 91 Mathematics, as such, is always a science of the imaginary, and its hypotheses, under the terms of the analysis that follows are uncommitted with an empiric reality. See, for example, CP 2.240 (1902) and CP 4.176 (1897). 92 In 1911 (NEM 3/1: 177) Peirce states: “Deduction, or necessary reasoning, is only one, and certainly not the highest one, of three absolutely disparate ways of reasoning. I believe I was the first to prove this, perhaps the first even to assert it”. 93 In our view, the necessary distinction between creation and discovery in the realm of Peirce’s philosophy is required by its realism. Concerning the abductive argument, our point of view is that we must consider Peirce’s complex theoretical and markedly ontological framework, which certainly hampers nominalistic approaches. 94 See Schelling, 42: “Nature should be Mind made visible, Mind the invisible Nature”.

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REFERENCES Apel, Karl-Otto. Charles S. Peirce. From Pragmatism to Pragmaticism. Amherst: University of Massachusetts Press, 1981. Chomsky, Noam. Sintatic Structures. The Hague: Mouton, 1969. Dirac, Paul. Directions in Physics. New York: John Wiley and Sons, 1978. Eisele, Carolyn. Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce. The Hague: Mouton, 1979. Findlay John N. Kant and the Transcendental Object. A Hermeneutic Study. Oxford: Clarendon Press, 1981. Hanson, Norwood R. Patterns of Discovery. An Inquiry into the Conceptual Foundations of Science. Cambridge: Cambridge University Press, 1977. Hausman, Carl R. Charles S. Peirce's Evolutionary Philosophy. Cambridge: Cambridge University Press, 1993. Hookway, Christopher. Peirce. London-New York: Routledge and Kegan, 1992. Hume, David. A Treatise of Human Nature. Ed. by L.A. Selby Bigge, Oxford: Clarendon Press, 1978. Ibri, Ivo A. Kósmos Noétos. A Arquitetura Metafísica de Charles S. Peirce. São Paulo: Perspectiva/Hólon, 1992. Kant, Immanuel. Critique of Pure Reason. New York: Macmillan Press, 1978. Murphey, Murray G. The Development of Peirce's Philosophy. IndianapolisCambridge: Hackett Publishing Co., 1993. Paton, Herbert J. Kant's Metaphysic of Experience. New York: The Humanities Press, 1965. Peirce, Charles S., editor. Studies in Logic by Members of Johns Hopkins University. Amsterdam-Philadelphia: John Benjamins Publishing, 1983. Peirce, Charles S. Historical Perspectives on Peirce's Logic of Science. Ed. by Carolyn Eisele, Berlin-New York-Amsterdam: Mouton, 1985. Roberts, Don D. The existential graphs of C.S. Peirce. The Hague-Paris: Mouton, 1973.

Schelling, Friedrich W.J. Ideas for a Philosophy of Nature. Cambridge: Cambridge University Press, 1988. Sebeok, Thomas A. The Play of Musement. Bloomington: Indiana University Press, 1991. Staat, Wim. “On Abduction, Deduction, Induction and the Categories”. Transactions of Charles S. Peirce Society 29, 2 (1993): 225-238.

CHAPTER 7 SEMIOTICS AND DEDUCTION: PERCEPTUAL REPRESENTATIONS OF MATHEMATICAL PROCESSES Susanna Marietti It is well known that Peirce conceived mathematics as a semiotic activity using particular kinds of signs, which he called “diagrams”. In his view, the work of a mathematician consists entirely in observing and manipulating these diagrammatic signs. To think mathematically means to construct diagrammatic representations of the relations between the objects under consideration, in some cases to modify these representations on the basis of a rule that allows us to do so, and to observe the new relations that result. But what is a diagrammatic representation? I believe that Peirce would agree that a representation can be said to be diagrammatic if and only if it represents the relations between the objects of the state of things represented through corresponding perceptual relations between the elements constituting the representation. Perceptual, and hence spatio-temporal, relations that are generally–but not inevitably–spatial relations (Peirce sometimes mentioned auditory representations, which are developed along the time dimension). Diagrams, these particular signs used in mathematics, are able to function as such, namely as signs specific to deductive inference, only because they possess a series of semiotic features both when taken in themselves statically and when they are being used. I would like to begin with some important quotations from two different moments in Peirce’s work that lie far apart: A Diagram, in my sense, is in the first place a Token, or singular Object used as a Sign; for it is essential that it should be capable of being perceived and observed. It is, however, what is called a General sign; that is, it denotes a general Object […]. The Diagram represents a definite Form of Relation.1 [A] Diagram is an Icon of a set of rationally related objects […]. [T]he Diagramicon having been constructed with an Intention, involving a Symbol of which it is the Interpretant (as Euclid, for example, first enounces in general terms the

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proposition he intends to prove, and then proceeds to draw a diagram, usually a figure, to exhibit the antecedent condition thereof) which Intention, like every other, is General as to its Object, in the light of this Intention determines an Initial Symbolic Interpretant. Meantime, the Diagram remains in the field of perception or imagination.2 Demonstration of the sort called mathematical is founded on suppositions of particular cases. The geometrician draws a figure; the algebraist assumes a letter to signify a single quantity fulfilling the required conditions.3

These statements might at first sight appear to conflict with one another. To begin with, Peirce says that the diagram is a singular sign and that it is singular in two different senses. First, it is so in respect of the sign in itself (it is “a Token, or singular Object used as a Sign”). Using another term from Peirce’s classification, it is a sinsign. The diagram must be a singular object that stands before us, not the general form of a sign. It must, Peirce says, be “capable of being perceived”. Elsewhere, speaking of deductive inference, he asserts that “[e]very addition or improvement to our knowledge, of whatsoever kind, comes from an exercise of our powers of perception”.4 The important thing is the singular writing by means of which the mathematician carries out a demonstration. Second, the diagram is singular with regard to its object. It represents an individual object. “Demonstration of the sort called mathematical is founded on suppositions of particular cases”, says Peirce in one of the quotations above. When a mathematician begins a demonstration, he supposes a particular case and a diagram is drawn to represent this particular case. The diagram is therefore singular in this dual sense, both subjective and objective, as Peirce himself also at times put it. Nevertheless, in this regard I do not think that Peirce is always clear about the difference between propositions belonging to different branches of mathematics. He equates the propositions of Euclidean geometry and those of algebra with respect to a series of characteristics (for example, the capacity for informative content) and then tends to apply this equation universally. Between the two branches, however, there are some differences that cannot be neglected. Indeed, taking the supposition of particular examples as a basis differs according to whether a geometric or an algebraic demonstration is being carried out. In algebra, being particular means being usable as a variable; in geometry, on the other hand, it means being truly singular: a single triangle, a single circle and so on. By

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representing space by means of space, geometry imposes on us such determinacy. When we draw, for instance, the cathetus of a triangle, we can only draw it a given length. In this sense, we can say that geometry has privileged tokens, more transparent than those in algebra. Now, all of Peirce’s descriptions of various aspects of mathematical processes are always most suited to Euclidean geometry, while it is sometimes difficult to extend them to algebra. Also, Peirce himself very often, though not always, refers explicitly to Euclidean geometry in the examples he chooses. I do not want to go into such problems here, which would require thorough investigation of a quite different kind. I would like at least, however, to point out that a very first consideration reveals a big difference between algebra and geometry. Whereas algebraic diagrams stand on their own, geometric diagrams do not function independently. For Peirce, the diagrams in algebra are the algebraic formulae, which reproduce between the letters as such, in a material sense, the relations they intend to represent, thus making them spatial and perceptible. Now, an algebraic passage, the transformation of one formula into another, of a diagram into another diagram, is, so to speak, self-contained. It needs nothing else in order to get its meaning across and be accepted. It shows its own validity. It is enough to write out the two formulae–that is to say the diagrammatic device–for the inferential passage to impose itself. Clearly, one needs to be familiar with the practice of algebra and so know what Peirce calls the general formulae of algebra, which are “patterns which we have the right to imitate in our procedure”.5 But if we assume such familiarity, the algebraic passage shows itself in the written diagrams. This never happens in a geometric passage, however familiar one is with the practice of geometry. The diagram, which is here a spatial figure, is never selfcontained. The figure cannot function on its own: it is always accompanied by a text. Taking this consideration as a starting point, let us now go back to the quotations from Peirce at the beginning. We will confine ourselves to the case of Euclidean geometry, which is that to which Peirce also refers explicitly here and which, as has already been said, is often the only case he seems to have in mind. In these quotations, Peirce not only makes the above-mentioned assertion relative to the individuality of the diagram in its dual subjective and objective sense. He also adds a further consideration that could appear to be inconsistent with it; he says that the diagram is a general Sign in the sense that it denotes a general Object, namely a Form of Relation. In truth, the two statements are not at all contradictory. What Peirce is in fact saying is that the geometric figure taken in itself–the diagrammatic sign as such– 5

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represents an individual object but, nonetheless, he also says that this individual moment is preceded and followed by two symbolic moments. It is then these three moments, taken together, which ensure that the diagram is able to denote a general object. The figure–Peirce says in one of the quotation above–is constructed according to a general Intention (which, so to speak, stands behind it) and then determines a Symbolic Interpretant. The figure constitutes a passage through the individuality that exists between two symbolic moments (this between is obviously logical-semiotic and not temporal however much it also has a temporal correspondence in the actual carrying out of the demonstration). The figure is preceded and followed by two symbolic moments and it is solely this interplay between different semiotic stages that allows it to function, that is to become the essential instrument of geometric inference. Let us try, then, to see concretely what these two moments preceding and following the figure are. What, first of all, is the symbolic moment that comes before the figure? As I said, the figure is accompanied by a text and is inseparable from it. It cannot function without the text. This is what Peirce says in the initial quotations when he maintains that Euclid draws the figure on the basis on the proposition expressed in general terms. We cannot work on the figure without taking into consideration that behind it lies this proposition expressed in general terms. The inferences we make in the course of the demonstration are based on information drawn from both the figure in its spatial quality and the text. There is some information that the figure does not store in its own individual objects. Nevertheless, in order to proceed with the argument, it is necessary for these individual objects to be perceived, though always in the light of the information coming from the symbolic moment of the text. The two things go together. Note that, here, I am not presenting a foundational but, rather, a very concrete discourse. I am not in fact saying that there is information that is essentially spatial and other information that is essentially linguistic but that, in effect, the kind of practice that consists in reasoning on the figure works in this way. And it has done so since the time of the Greek geometricians. When making a geometric inference, we all put together diagrammatic and symbolic information, hints that we get from the figure as such and those we get from the text. Here is an example: a type of information that the figure does not contain is that two lines are parallel. Theorem I.32 in Euclid’s Elements presents the following construction:

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Fig. 1 The theorem states that: In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles […].6

The key point is to see that the angle BAC is equal to the angle ACE and that the angle ECD is equal to the angle ABC. This is so on the basis of a previously demonstrated theorem, because AB and CE are parallels and AC and BD are both secants of these parallels. Nonetheless, the figure on its own is unable to produce statements of the kind “AB and CE are parallels”. None of us would ever use the figure in this way, that is trusting the metrical features that are seen in it. It would never occur to anyone to measure the distance between AB and CE at various different points so as to check that they are parallel. The figure might even be badly drawn, but nobody would deem it significant. It is the text which guarantees that AB and CE are parallels because it says that we constructed them so. On the other hand, it is from the figure and not the text that we see that AC and BD intersect the parallels. This is not written anywhere: once we draw CE, the information emerges by itself from the figure; it comes into being and is not an

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Taken from Thomas L. Heath, Euclid. The Thirteen Books of The Elements (New York: Dover Publications, 1956).

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explicit object of construction. To make the inference, we base ourselves both on information that the figure gives us and on information we know we have codified in it. We take all these hints and use them simultaneously. At this point, the information is all available in the diagram at the same time, part of it because it has emerged from the figure and part of it because we have explicitly inserted it in the figure. This is the fundamental point: the diagram is synoptic. Once we have deposited in it the information through a previous symbolic level, the diagram gives it back to us all together. It is a highly relevant feature of diagrams in general, which symbolic-linguistic representations do not have. As we have seen, the general and symbolic moment not only comes before the construction of the figure but also after it, at the moment of its interpretation. “[I]n the light of this Intention”, says Peirce in the quotations at the beginning, the Diagram-icon “determines an Initial Symbolic Interpretant”. Thus, the individual and truly iconic moment lies between two symbolic moments. We have, so to speak, in both the input and output an instance of generality, which is not there in the central semiotic stage when the figure is a true unicum. In order to explain in what sense the iconic diagram determines a symbolic interpretant, we could express it differently by saying that the geometric figure is reconceptualized symbolically. It does not remain at the level of individual infinity; it is no longer an individual figure made up of infinite points. The relevant points are not infinite but are, in the interpretation, only those points to which we give a name (in general the intersecting and the end points), the ones we indicate by letters, which in Peirce’s classification play the role of indices. What remains in the interpretative reconceptualization are the relations between these relevant points. This concept becomes quite clear if we consider the idea, present in Euclid and which plays a very important role, of the repeatability of demonstrations. In general, Greek geometry uses the idea of the repeatability of demonstrations and not that of the extensibility of their results.7 It is curious that the word “generally” (katholou) is almost never used in the corpus of Greek geometry. In the whole of Euclid’s Elements, it appears only twice and both times in particular contexts. The key word is not katholou but homoiǀs, “similarly”; the Greeks do not say that by means of a certain demonstration a result is demonstrated generally or in general but, rather, that “similarly it will be proved that…”. The single demonstration is, in other words, valid for a single result and does not automatically demonstrate another. Nonetheless, it can be repeated.

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I refer here to the most complete study available on the use of the diagram in ancient Greek geometry, namely Reviel Netz, The Shaping of Deduction in Greek Mathematics (Cambridge: Cambridge University Press, 1999).

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The following is a simple example: proposition I.15 states that “[i]f two straight lines cut one another, they make the vertical angles equal to one another”.

Fig. 2 The demonstration is carried out on one of the two pairs of angles and ends by asserting that similarly it can be demonstrated for the other pair. Therefore, the demonstration made does not constitute in itself a demonstration for the other pair; nevertheless it can be repeated. Now in this case, it is evident that repetition is problem-free. However–and this is the point connected with the reconceptualization of the diagram–there are cases in which the situation is more problematical. Let us consider, for example, proposition III.1, which presents the following construction:

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Fig. 3 What we have here is a problem, not a theorem, that is in which you need to do something: in this case, to find the center of a given circle. On the basis of previous knowledge, Euclid comes up with this construction and states that the center is F. He then goes on to demonstrate ab absurdo that the center can only be F. Hence, he supposes that the center is G and arrives at a contradiction. At this point he says: similarly we can demonstrate that the center cannot be any other point than F. This statement is formally like the one in the preceding case, but clearly there is a substantial difference. In the other case, we had only two demonstrations to carry out, whereas here they are infinite since we have an infinite number of points we could choose instead of G. Euclid’s move is an extremely risky logical move: he promises to provide an infinite number of demonstrations. And yet he makes this move (there are other similar ones in the Elements) with complete self-assurance. Why so? The reason is–as I said above–that the figure is reconceptualized symbolically at the “outgoing” stage, that is at the level of Peirce’s interpretant (the Symbolic Interpretant in the quotation at the beginning). The idea is that in reality we do not have to make infinite demonstrations but a limited number of them according to the various areas in which we can choose point G (and at most some limit cases such as that in which G is chosen on the circumference, though the

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Greeks tended not to consider such cases). All the demonstrations in which G is in the same area are the same demonstration. The general picture that emerges from all of this is that the diagram can function only due to this semiotic interplay in which all three types of signs take part. Each single geometric passage starts from a symbolic moment, passes through the writing of a concrete iconic individuality, which is then newly reconceptualized at a symbolic level (where this symbolic reconceptualization has been undertaken using indices). It is a cyclical process: within the demonstration the process that sees the succession of symbolic moment, iconic moment and again symbolic moment is repeated. In this context, a more specific question that I am now going to address concerns to some extent the non-eliminable presence itself of the individual iconic moment lying between the two symbolic moments. Why is it necessary for there to be this individual moment when it is evident that geometry aims to demonstrate general results? Peirce repeats again and again that the concrete quality of the diagram is absolutely essential in any deductive reasoning. I think that the importance of this concrete quality is well understood if we look at the distinction made by Peirce within mathematical propositions between theorems and corollaries. It is a distinction to which he attributed the maximum importance. As is well known, the theorems are the main propositions in mathematics while the corollaries are minor ones. Peirce’s thesis is that there exist two essentially different models of deduction that lead, precisely, one to the theorems and the other to the corollaries. By extension, Peirce calls these two models “theorematic deduction” and “corollarial deduction”. The first constitutes the truly fertile model for mathematical thought, that which leads to genuinely new information. The classic description given by Peirce of the two types of deduction is this: A Corollarial Deduction is one which represents the conditions of the conclusion in a diagram and finds from the observation of this diagram, as it is, the truth of the conclusion. A Theorematic Deduction is one which, having represented the conditions of the conclusion in a diagram, performs an ingenious experiment upon the diagram, and by the observation of the diagram, so modified, ascertains the truth of the conclusion.8 What I call the theorematic reasoning of mathematics consists in so introducing a foreign idea, using it, and finally deducing a conclusion from which it is eliminated.9

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Hence, both models of deductive reasoning have an observational, perceptual basis and so the importance of the single token, of the individual sign to be observed, is understandable. It is even more understandable, however, in the case of the most fertile type of deduction, theorematic deduction, in which it is not only a question of observing the relations that emerge but also to carry out some operations on this single model, on the individual token. What is to be done is to manipulate this sign, to implement a series of ingenious experiments–hence creative and not mechanical–aimed at finding the correct modification so as to cause to emerge the new relations that we then observe. Such concrete work presupposes the concrete quality of a material sign. The foreign idea of which Peirce speaks, which characterizes the informative demonstrations, is, he says, introduced in the course of the demonstration and then eliminated before reaching the conclusion. In other words, it is not present either in the premises or in the conclusion and so is not suggested by them. Peirce calls the introduction of this idea, the ingenious experiment, a theoric step. The theoric step therefore constitutes the core of the informative mathematical demonstration. A brilliant reconstruction has been made by Jaakko Hintikka of what these theoric steps are, of what that passage consists of that makes a demonstration informative (theorematic in Peirce’s terminology or we can also say synthetic, as Hintikka himself puts it).10 Without here going into the technical details of his distributive normal forms of first-order logic, it is sufficient for us to say that in his reconstruction a mathematical demonstration, represented in first-order predicate calculus, is synthetic when it is compelled to consider in its intermediate stages a greater number of individuals in their reciprocal relations than that considered by the premises and conclusion. In the logical representation, this means that at some intermediary stage the demonstration has to increase the number of layers of quantifiers in the formulae used (their depth, in Hintikka’s terminology). In an article of 1980,11 Hintikka maintains that Peirce’s distinction between theorematic and corollarial should be viewed as an informal anticipation of his own distinction between informative and non-informative demonstrations. Therefore, Hintikka holds that every theoric step in Peirce’s sense consists in an increase in the individuals considered simultaneously during the demonstration. In the case of Euclidean demonstrations, the individuals to be introduced in the course of the demonstration evidently consist of individual geometric objects (segments, triangles, circles, etc); those that are introduced in the so-called auxiliary 10

See Jaakko Hintikka, Logic, Language-games and Information: Kantian Themes in the Philosophy of Logic (Oxford: Clarendon Press, 1973). 11 Jaakko Hintikka, “Peirce’s ‘first real discovery’ and its contemporary relevance”, The Monist 63 (1980): 304-315.

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construction, namely in those changes that Euclid makes to the initial figure during the demonstration. Hintikka thus invariably identifies the auxiliary construction with a set of additions, with new geometric objects that enter the figure. In my view, though very brilliant from a formal standpoint, this reconstruction runs the risk of missing the sense of Peirce’s idea, the importance of that passage through individuality which, as we saw above, lies between the two symbolic moments but is still indispensable for Peirce’s conception. By reducing the question to a problem of individual entities considered, the importance of the demonstration’s perceptual aspect is lost. In Hintikka, it is not important for the individuals to be visualized; it is enough for them to be mentioned in the demonstration. In Peirce’s terminology referred to above, the sign used in Hintikka’s demonstrations is objectively individual precisely because it denotes individuals; but it is not individual subjectively; namely, that it is a token, a single writing on which to work spatially, is not relevant whereas for Peirce it is fundamental. Returning to geometric demonstrations, I in fact believe that Peirce had in mind types of auxiliary construction that do not match Hintikka’s reconstruction; in other words, they do not consist in the introduction of individuals. The passages in which Peirce states this explicitly are few. Here is one: the exposition, as it is termed, having been obtained, certain changes are made in the figure, consisting either in moving certain parts of it, or in adding new lines, or both.12

So Peirce has in mind the possibility that experimenting on the diagram involves merely moving some parts of it that are already given without adding anything new. Peirce’s idea does in fact have any application in geometry. In Euclid’s Elements can be found demonstrations in which nothing new is added to the set of objects mentioned in the premises and conclusion and, yet, the diagram is not left unaltered. I hold that Peirce would have classified these demonstrations under the theorematic ones in spite of their not being covered by Hintikka’s description. Here is a very elementary example. The first proposition in the second book of the Elements states: If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments.

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Fig. 4 Up to this point, all we can draw in the figure are these two unconnected segments, the observation of which tells us nothing. The premises, that is the condition of the theorem or antecedent of the implication, do not help us do anything else. It is true, on the other hand, that the conclusion mentions a certain number of rectangles, but they are entirely separate from one another and suggest nothing about their reciprocal relation. It is here that the theoric step comes in. The figure accompanying the demonstration is this:

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What had to happen to get to this diagram? It was necessary to put line A (now BG) at right angles to BC, construct rectangle A,BC, and lastly draw A perpendicular to BC at each dividing point. In other words, those rectangles that were only mentioned in the conclusion have now been organized into a very particular spatial configuration, highly suitable for our aim of demonstrating the theorem. So if the rectangles in themselves were already suggested in the initial proposition, their reciprocal position is a foreign idea introduced by a theoric step. It is only at this point that by observing the thus constructed diagram, we can see that the conclusion holds. And yet no new object has been introduced: all the geometric objects identifiable in the figure (rectangles, initial lines and segments) had already been mentioned either in the theorem’s premises or conclusion. In Hintikka’s reconstruction this would be a corollarial demonstration, which I do not think Peirce would have agreed with. I do not in fact believe that for Peirce the introduction of new individuals is the parameter for the synthetic. Instead, I hold that this parameter is something much more associated with the diagram’s concrete spatial quality (as is also the case in the previous example). In my view, it is possible to identify an operation in thought–it takes place essentially above the diagram and involves precisely the perceptual relations organized by it–which forms the core of the abductive inference that makes the demonstration synthetic, theorematic, creative. This is the point: there has to be an abductive inference in every informative demonstration given that a connecting thread running through Peirce’s thoughts on the logic of science is that “[a]ll the ideas of science come to it by the way of Abduction”.13 In a theorematic demonstration–that is in a demonstration introducing new knowledge into our mathematical system–it is necessary to carry out an abductive passage. Together with all the required preparation, which makes up its real core, this abduction constitutes the ingenious experiment that introduces the new idea, the theoric step. Also, I hold that the theoric steps in the Euclidean demonstrations can be interpreted as deriving from a common structure, as the same operation repeated within the demonstrations. Essentially connected with the diagram’s perceptual materiality, this operation can be described as that of seeing something as something else.14 In my opinion, Peirce would have agreed with considering this seeing as a good way to convey his idea of a theorematic passage in the 13

CP 5.145. This perspective was suggested to me by Orna Harari, “The concept of existence and the role of constructions in Euclid’s Elements”, Archives for History of Exact Sciences 57 (2003): 1-23. 14

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demonstration, of a passage on which the creative moment of the demonstration hinges. Returning to our example, we see that it is an operation of this kind that paves the way for the abductive inference made during the argument. Once the construction is finished, Euclid’s true demonstration consists in taking note of the fact that the first rectangle (BGKD) can be considered as the rectangle lying between A and BD (since BG is equal to A)–that is, it can be seen as this rectangle–that the second rectangle can be seen as the rectangle lying between A and DE (since DK is equal to A) and so on. The relevant objects have to be reidentified in the new figure. This line of argument is based on an implicit abduction. In one of its forms, abduction is described by Peirce as the inference of the minor premise in a syllogism from the major premise and the conclusion. In this case, the syllogism has as its inexplicit major premise the fourth of what in the first book of the Elements Euclid calls “common notions”: “[t]hings which coincide with one another are equal to one another”. Or, better, to make it clear we can say that the major premise consists in specifying this common notion in the particular case we are interested in, namely that of the rectangles: “rectangles which coincide with one another are equal to one another”. The syllogism then has this form: rectangles which coincide are equal; A, BC and A, BD + A, DE + A, EC are rectangles which coincide; therefore: A, BC and A, BD + A, DE + A, EC are equal.

The conclusion is obviously the theorem to be demonstrated, which is something we already have since the proposition itself gives it to us from the very start. The major premise is also something we already have in our initial set of axioms, as a common notion. The minor premise is the truly new piece of information that the diagram gives us and which is here the conclusion of the abductive inference. The diagram is able to give us this minor premise because we are implicitly establishing all those conditions we met with above (that the rectangle BGKD can be seen as the rectangle between A and BD, etc.). At this point, the relevant coincidence of the rectangles is shown perceptually. The material diagram helps us to make this identification, which, though in this case it is quite immediate, in other circumstances may not be at all self-evident. Take for instance the following case, which is a classic construction in the Elements:

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Fig. 6 What we have is the construction of Pythagoras’ Theorem. Here, in the demonstration, we need to identify a series of geometric objects, constructing them on the basis of knowledge previously acquired as solved constructional problems. Look for example at triangle ABD. In order to connect our initial construction to the auxiliary construction, the diagram must, among other things, enable us to see AB, which at first is only a side of the initial triangle, as a side of triangle ABD. The diagram must allow us to effect this change in meaning, and the same goes for the other geometric objects to be identified. We could say, at bottom, that a good part of mathematical reasoning can be viewed as tied to the ability to see something as something else, to see a X as a Y. I believe that this view can be applied also to elucidating the idea of “theorematicity” in Peirce, of the creativity of mathematical thought. Algorithmic thinking, that which is based on mere sequence-matching or–as Peirce says–on definitions (on automatically replacing definitions with definitions, superimposing and embedding the right side and the left side) has no need for this change in

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meaning, this seeing as. It is enough for it to see a thing as that which it is, identical to itself, to see its syntactic codification without even touching on the meaning, let alone a change in meaning. In conclusion, I hold that the above considerations allow us to broaden our perspective to encompass Peirce’s general approach to mathematics as an activity carried out on diagrams. Against the backdrop of the distinction between theorems and corollaries, we can understand in greater depth the importance attributed by Peirce to the spatial configuration of the signs used in mathematics. Indeed, signs must allow us to effect acts of perception in which a certain configuration is identified as something or as something else. In my view, this possibility of change in geometric meaning, of reinterpreting the spatial relations that, in its concrete material quality, the diagram gives us can be extended to other branches of mathematics and constitutes the core of Peirce’s idea of this science as a diagrammatic science.

REFERENCES Harari, Orna. “The concept of existence and the role of constructions in Euclid’s Elements”. Archives for History of Exact Sciences 57 (2003): 123. Heath, Thomas L. Euclid. The Thirteen Books of The Elements. New York: Dover Publications, 1956. Hintikka, Jaakko. Logic, Language-games and Information: Kantian Themes in the Philosophy of Logic. Oxford: Clarendon Press, 1973. —. “Peirce’s ‘first real discovery’ and its contemporary relevance”. The Monist 63 (1980): 304-315. Marietti, Susanna. Icona e diagramma. Il segno matematico in Charles Sanders Peirce. Milano: LED, 2001. —. “Mathematical individuality in Charles Sanders Peirce”. Cognitio 6, 2 (2005): 201-207. Netz, Reviel. The Shaping of Deduction in Greek Mathematics. Cambridge: Cambridge University Press, 1999.

CHAPTER 8 REFLECTIVE ACKNOWLEDGEMENT AND PRACTICAL IDENTITY: KANT AND PEIRCE ON THE REFLEXIVE STANCE Vincent Colapietro I. Introduction Charles Peirce emphatically acknowledged his indebtedness to Immanuel Kant1 and, in turn, expositors of Peirce have appropriately stressed both his youthful enthusiasm for this German predecessor and the enduring imprint of this early influence. Even so, Peirce’s relationship to Kant is more complex than most interpreters of this pragmatist seem to appreciate,2 not least of all because the most 1

In an autobiographical remark, Peirce claimed: “The first strictly philosophical books that I read were of the classical German school; and I became so deeply imbued with their ways of thinking that I have never been able to disabuse myself of them”. As a youth (after first studying Schiller’s Aesthetic Letters), he “devoted two hours a day to the study of Kant’s Critic of the Pure Reason for more than three years”. As a result of such focused, sustained study Peirce boasted: “I almost knew the whole book by heart, and had critically examined every section of it” (CP 1.4). Tracing the ancestry of the pragmatic position to the meetings of the Metaphysical Club, Peirce, Peirce recalled: “Wright, James, and I were men of science. […] The type of our thought was decidedly British. I, alone of our number, had come upon the threshing floor of philosophy through the doorway of Kant, and even my ideas were acquiring [in the context of these interlocutors] the English accent” (CP 5.12). 2 Christopher Hookway also stresses “Peirce’s complex relations to Kant”. He rightly notes that Peirce “saw himself as a broadly Kantian philosopher, who wanted to correct Kant’s logic and improve on his system of categories. This makes it unsurprising that he would be interested in hunting down the presuppositions of logic. […] In spite of this, however, he wanted to reject the transcendental method: showing that something was a presupposition of logic was no guarantee of its truth”. Peirce also rejected the idea of an a priori derivation of philosophical or any other concepts; against Kant, he insisted that philosophy had to be experiential and, thus, “scientific” in a broad sense; Christopher Hookway, Truth, Rationality, and Pragmatism (Oxford: Clarendon Press, 2000), 37. Finally, he repudiated the

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important respects in which Peirce appropriates Kant’s critical philosophy are not fully identified by Peirce.3 The aim of my paper is to identify and explore a crucial central Kantian notion of a thing-in-itself: “The Ding an sich […] can neither be indicated nor found”, (CP 5.525); “The Kantist has only to abjure from the bottom of his heart the proposition that a thing-in-itself can, however indirectly, be conceived; and then correct the details of Kant’s doctrine accordingly, and he will find himself to have become a Critical Common-sensist”–and a less confused pragmatist! “Kant (whom I more than admire) is nothing but a confused pragmatist” (CP 5.525). Cf. Manley Thompson, “Things in Themselves”, Proceedings and Addresses of the American Philosophical Association 57, 1 (1982): 33-48. 3 Closely connected to this is the way in which Peirce came to Kant. Before turning to Kant’s first Kritik, he studied intensely with a youthful companion Friedrich Schiller’s Aesthetische Briefe, cf. Joseph Brent, Charles Sanders Peirce: A Life (Bloomington: Indiana University Press, 1998); Joseph L. Esposito, Evolutionary Metaphysics: The Development of Peirce’s Theory of Categories (Athens: Ohio University Press, 1980), 11-13. In turning to Kant’s work, he was guided by his father Benjamin Peirce’s imposing example of uncompromising critic. “In the Aesthetische Briefe […] Schiller was writing”, Joseph Esposito notes, “in response to the predicament of philosophy produced by Kant’s Critique. And in spite of his claim to that it was upon Kant’s principles that his position in the letters was based, Schiller was in fact involved in an effort to undermine completely the subjective approach of the Critique. By postulating two coexisting tendencies–the sensuous drive toward the finite, particular, and temporal, and the formal drive toward the infinite, universal, and eternal–and by offering a historical/genetic analysis of the relation of philosophic thought to culture, he was undercutting the privileged position of Sensibility and denying the very possibility of a truly transcendental philosophy. Critical philosophy, he argued, was one-sidedly analytic and [thus] incapable of accounting for the ultimate harmony of goodness, truth, and beauty, or for the irreducible reality of the human personality. Thus reason and analysis had to be tempered with esthetic sensibility as the only means of harmonizing the two conflicting drives of feeling and law, and this elevated, dynamic sensibility largely involved the ideal of beauty as the unity of contingency and law” (Esposito, 12). Peirce’s mature philosophy might be read as a return to the animating impulses of Schiller’s aesthetic philosophy. Just as his initial encounter with Kant was mediated by his intense study of Schiller, so his eventual return to something akin to Schiller’s philosophical project. Moreover, Peirce’s reading of Kant’s first Kritik was mediated by his father’s example of how to subject even the most carefully constructed arguments to uncompromising criticism: “When in my teens I was first reading the masterpieces of Kant, Hobbes, and other great thinkers, my father, who as a mathematician, and who, if not an analyst of thought [i.e., not a logician in Charles’ sense], at least never failed to draw the correct conclusion from given premises, unless by a mere slip, would induce me to repeat to him the demonstrations of the philosophers, and in a very few words would usually rip them up and show them empty. In that way, the bad habits of thinking that would otherwise have been indelibly impressed upon me by those mighty powers, were, I hope, in some measure, overcome. Certainly, I believe the best thing for a fledgling

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respect in which Peirce’s mature pragmatism carries forward, though in a more consistently experimental manner, the central impulse of Kant’s critical project. The respect in which Peircean pragmatism carries forward the Kantian project is, however, also the means by which we can mark the eventually unbridgeable gulf between Peirce’s experimental approach and Kant’s transcendental procedure. In any event, this respect concerns nothing less than the reflexive stance at the heart of the Kantian project, most obviously in Kant’s “practical” (or moral) philosophy but no less fundamentally in other parts of his critical philosophy. Kant’s philosophy merits the adjective critical by virtue of the thoroughgoing and systematic manner in which he takes a reflexive stance toward our epistemic, ethical, and aesthetic judgments.4 In brief, his critical philosophy is critical mainly by virtue of this stance. A contemporary philosopher deeply influenced by Kant forcefully argues for the reflexive (or critical) stance as the least problematic source of our most truly authoritative norms. In The Sources of Normativity, Christine Korsgaard makes a painstaking case for what she calls “reflective endorsement”, presenting such endorsement as the most effective way in which rational agents can resolve normative conflicts of various kinds. She sharply contrasts this position with normative (or axiological) realism. Moreover, she takes the position of “reflective endorsement” in its most viable form to be broadly Kantian. It involves granting an “authority to reflection”, especially vis-à-vis our passions, emotions, sentiments, dispositions, and temperaments.5 The arguments formulated in defense of such philosopher is a close companionship with a stalwart practical reasoner” (CP 3.405). Peirce does not seem aware of the possibility that the disposition to rip arguments up “in a very few words” might itself be a bad habit, one his own youthful self was in the abstract at least disposed to condemn. Reflecting on the traditional maxim Errare est hominis, Peirce in 1860 (i.e., at the age of twenty-one) wrote: “This reflection should teach us the inhumanity of a polemic spirit and should teach us still to revere a great man notwithstanding his mistakes” (W1: 5). In any event, Peirce’s early encounter with Kant’s critical philosophy was complexly mediated and, in addition, the enduring imprint of, and eventual deviations from, this early influence bears the marks of this complex mediation. Peirce’s relationship to his own thoughts was, as a result of his relationship with his father and indeed countless others, mediated by a critical stance having the concrete form of a set of deeply ingrained habits to interrogate and criticize along the lines exemplified by these others and modified by the course of experience. 4 See John E. Smith America’s Philosophical Vision (Chicago: University of Chicago Press, 1992), chapter 5. 5 The effective capacity to take and maintain such a reflective stance is, from a Peircean perspective, a passionate affair in which the irreducibly personal investment in, and thus identification with, a deliberately cultivated sensibility is the communal achievement of embodied agents bound together by shared commitments and mutual affections. Such a

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reflection are extremely helpful in enabling us to grasp Peirce’s unique approach to the inescapable entanglement of rational agents in normative conflicts. That is, Korsgaard presents a version of Kant that is very useful for any interpreter of Peirce who is desirous to identify what, a bottom, the mature Peirce owes to the Kantian project. I will, accordingly, use her depiction of Kant as an aid in crafting my own portrait of Peirce. While my proximate goal is to attain a better understanding of Peircean pragmatism, especially in connection with the intertwined themes of rational agency and normative conflicts, my ultimate goal is to sketch (however quickly and thus roughly) a compelling account of rational agency. Such an account must, following the lead of Peirce, make more central than does Kant, even on Korsgaard’s interpretation, the insights of realism and sentimentalism. Above all else, anyone articulating such an account must highlight the constitutive role of certain human sentiments (the “logical sentiments” of faith, hope, and love being dramatic examples of this) in such cognitive endeavors as experimental investigation, moral deliberation, and political debate. The reason for characterizing these sentiments as constitutive is because (as Peirce insists) they make up the substance of the self. In other words, we are constituted as recognizably human selves (or subjects) above all through the operations of legisigns of such sentiments and emotions.6 Put yet otherwise, certain affective stance is, hence, decidedly not the merely formal exercise of a purely reflective power, especially when what Charles Taylor calls the “punctual self” is presumed to be a sufficiently robust agent to exercise this power. A more robust conception of the human self, thus of human agency, than the transcendental subject of Kant’s critical philosophy is required for the exercise of the capacity in question. We need to acknowledge nothing less, but also nothing more, than the human animal markedly transformed by its thorough immersion in the social life of other human animals. 6 David Savan, “Peirce’s Semiotic Theory of Emotion”, in Proceedings of the Charles S. Peirce Bicentennial International Congress. Ed. by K.L. Ketner (Lubbock: Texas Tech Press, 1981), 323. In his illuminating exposition of Peirce’s semiotic account of human emotions, David Savan suggests, “every emotion has certain lawlike features, and these cannot be represented by a sinsigh. First, an emotion has a pattern unrolling over a period of time. Joy [for example] rises and falls, becomes more intense and fades. […] Second, an emotion is general, and exists only through its instances. […] Third is Peirce’s repeated thesis that what can be fitted into a system of explanation must have at least some of the characteristics of a law. But emotions do enter into the systematic explanation of behavior. Further, emotions can be justified, shown to be inappropriate, disproportionately strong or weak, and so on. It is clear, I think, that [on basis of such considerations] an emotion is a legisign. Like any legisign, it exists through its instances or replicas. Each such replica is an iconic sinsign” (Savan, 323). Later in this essay, Savan draws a crucial distinction: “Beyond the natural and moral emotions [fear being an example of the former and remorse an

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dispositions are constitutive of rational agency: apart from such dispositions, such agency is unintelligible.7 This is so even if the manner in which the Kantian endorses or acknowledges the authority of reflection precludes the recognition (the re-cognition) of such constitutive sentiments. Indeed, Peirce diverges from Kant and his more orthodox followers precisely at this point. Reflective agents are for him not trans-empirical selves but practically identifiable, thus historically implicated, actors. That is, practical identity in a substantive sense is a matter from which such agents cannot abstract.

II In On Certainty and elsewhere, Ludwig Wittgenstein contends: “Knowledge is based in the end on acknowledgment” (§378). In different yet overlapping ways, Peirce and Wittgenstein address the normative conflicts inevitably confronting rational agents by acknowledging that to which we as rational human agents are always already committed, because these factors are the ones in and through which we as human agents are formed and transformed.8 In contrast to the transcendental subject endorsed by Kantian philosophy, however, the rational human agent acknowledged by Peirce and Wittgenstein is a historical actor–a somatic, social, and semiotic subject only identifiable in reference to an extended family of human practices and, as a consequence of involvement in such practices, a being equipped with recognizable human responses. Knowing how to act, or what to believe, or even what to forebear requires such agents to acknowledge not only who they are but also the concrete historical circumstances (thus, the specific normative conflicts) in which action, belief (or knowledge), forbearance, and much else become deeply problematic. Agents committed to such acknowledgment resist the temptation of taking a transcendental turn; they also fight against the impulse to secure indubitable foundations.9 The drive toward acknowledgment bids us to go back to the “rough ground” of human history where normative conflicts are instance of the latter] there is a third class, not of emotions but of sentiments. Our twentieth century has almost lost the sense of the distinction between the emotions and the sentiments. The sentiments are enduring and ordered systems of emotions, attached either to a person, an institution, or, in Peirce’s case [and that of countless other disciplined inquirers], a method. Love is the prime example of a sentiment” in the sense intended here (Savan, 331). 7 Cf. Hookway, chapter 9. 8 Cf. Hans Joas, The Genesis of Values (Chicago: University of Chicago Press, 2001), chapters 7 and 8. 9 Cf. Christine Korsgaard, The Sources of Normativity (Cambridge: Cambridge University Press 1996).

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inevitable but resolvable (to the extent that they are) in the only manner practically important (i.e., humanly significant) for human agents.10 The manner in which such conflicts are resolved is, more often than not, one encompassing a redescription of the terms by which such conflicts are identified and characterized, also a renarration of various aspects of these normative conflicts. The Kantian form of reflective endorsement is, thus, radically transformed by Peirce into a pragmatist form of reflective acknowledgement (one manifesting at least a distant kinship with the Wittgensteinian form of reflective acknowledgement). Such acknowledgment is one with the ongoing, self-consciously historical task of owning up to the enabling constraints of human rationality. The authority of reflection, as it actually operates in the context of inquiry and other human practices, enforces a reflection on the guises of authority, not least of all the historically influential guise of transcendental reason. From Peirce’s perspective, this is in truth a disguise, so thoroughly a disguise that experimental intelligence fails in this instance to recognize itself in its actual character. Peircean pragmatism is, hence, nothing less than the philosophical acknowledgement of experimental intelligence in its most radical implications. At the center of this acknowledgement, we encounter “an experimenter of flesh and blood”–that is, an embodied agent exemplifying experimental intelligence.11 This pragmatism is, at once, an attempt to carry forward the central impulse Kant’s critical project and a radical modification of that project. Unless interpreters of Peirce acknowledge this, they miss the significance of his pragmatism. In appreciating this significance, however, we are in the position to attain not only a deeper understanding of Peirce and his relationship to Kant but also a fuller comprehension of our rational agency.

III In The Sources of Normativity, Christine Korsgaard suggests: Normative concepts exist because human beings have normative problems. And we have normative problems because we are self-conscious rational animals, capable of reflection about what we ought to believe or to do.12 10

Ludwig Wittgenstein, Philosophical Investigations (NY: Macmillan Co., 1953), §107. 11 “What Pragmatism Is” (1905), CP 5.424. 12 Korsgaard, 46. She notes, “normativity is a problem for human beings because of our reflective nature. Even if we are inclined to believe that an action is right and even if we are motivated by that fact, it is always possible for us to call our beliefs and motives into question. This is why, after all, we seek a philosophical foundation for ethics in the first place” (Korsgaard, 49; emphasis added). But the quest for such a foundation is what drives

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In the end, she identifies the resource for offering a compelling account of the reflective stance with the source of such problems themselves (the source of the ineluctable normative conflicts with which human agents, especially in the modern epoch, are confronted), this (re)source being nothing other than our reflective nature. Korsgaard appropriately stresses, “the normative question is one that arises in the heat of action. It is as agents that we must do what we are obligated to do, and it is [also] as agents that we demand to know why”.13 This stress aligns her with not only Kant but also Peirce. Her very next step however signals her fundamental allegiance with Kant and her crucial difference from Peirce: “So it is not [as Hume and others argue it is] just our dispositions, but rather the particular motives and impulses that spring from them, that must seem to us to be normative”.14 In fact, it turns out not to be our dispositions at all but a purely formal test devised and used by the rational will that provides (on Korsgaard’s account) the ultimate source of our most truly authoritative norms. She argues that the practical identity of human agents who are identifiable with the formal exercise of nothing other than their rational will is, in one sense, empty and, in another sense, not at all empty. Such identity is formal (insofar as it abstracts from the contingent and determinate impulses, inclinations, and emotions of the agents in question) and, being formal, it is “in one sense empty”.15 “The reflective structure of human consciousness requires”, she quickly adds, “that you identify yourself with some law or principle which will govern your choices. It requires you to be a law to yourself”.16 This self-imposed requirement is, for her,

us outside of our bodies and histories. Peirce’s “conservative sentimentalism” (see, e.g. CP 1.661) might be taken as a deliberately endorsed alternative to Kant’s transcendental turn, a turn animated as much as anything else by the desperate search for an apodictically certain foundation of human judgments in the various spheres of its proper exercise. Such a sentimentalism bids us to acknowledge our own moral, mutable bodies (and thus our animality), also our intersecting, internalized histories. These bodies and histories provide a stable enough basis for our self-corrective procedures and practices. Accordingly, the demand for self-warranting or self-certifying cognitions or judgments to serve as a foundation is exposed as unnecessary and, indeed, even worse than unhelpful, since it is one of the main roots from which the transcendentalist illusion grows. 13 Korsgaard, 91; emphasis added. 14 Korsgaard, 91. 15 Korsgaard, 103. 16 Korsgaard, 103-104.

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“the source of normativity”.17 Moreover, the identity secured by means of this identification18 is somehow not an utterly empty conception of practical identity. In his critique of The Sources of Normativity Raymond Geuss argues that the Kantian position being defended by Korsgaard requires a more robust conception of practical identity than either Kant or Korsgaard offer, or possibly could offer, within the limits of their project able to provide.19 In particular, he contends: “Korsgaard’s project of recentering Kant around notions of identity seems to me to push him [Kant] toward a position in which it will be difficult for the Kantian to reply” to a line of criticism put forth by Friedrich Schlegel in the 1790s.20 “Who I am” is not exhausted by my capacity to identify with a universal law; indeed, the identification with this capacity tends to engender an impulse toward dissociation, so strong an impulse that it prompts me to keep the law distant from me, “treating it ironically” and “precisely not identifying with it”. My identity is, upon this account, more the result of my capacity for dissociation than the outcome of my power to identify with the law: it is one with “my continuing ability to distance myself in thought and action from any general [or universal] law”,21 also presumably any other prior identification. The particulars of this criticism do not so much concern us as its general point regarding the systematic need to address the critical question of the practical 17

Korsgaard, 104. One might quibble with Korsgaard here. The reflective structure of human consciousness does not require one to identify ultimately with some law or principle but rather with our very capacity to identify with a law or principle of a certain character (this character being nothing other than that of being self-imposed or self-espoused). This makes the identity of the agent intrinsically reflexive, for it involves identifying with a our capacity for identifying itself with the universalized demands of truly legislative authority. 19 Geuss acknowledges his debt to Martin Heidegger in developing this specific criticism: “In his Kritik der reinen Vernunft he [Kant] claims that the interest of reason is exhausted when one has given answers to the three questions: ‘What can I know? What ought I to do? What may I hope?’ As Heidegger pointed out […] Kant adds to these three the fourth question: ‘What is the human being?’ The question: ‘Who am I?’ doesn’t appear [in Kant], as if it were obvious that the correct answer is: ‘A human being’; that is, as if the questions ‘Who am I?’ and ‘What am I?’ were philosophically not properly distinct”, Raymond Geuss, “Morality and Identity”, in The Sources of Normativity. Ed. by O. O’Neill (Cambridge: Cambridge University Press, 1996), 191. The question of the practical identity of any human agent, in its immediately existential form, is not answered by identifying the biological species to which the being belongs. Self-identity, thus both self-identification as a humanly grounded capacity and self-identifications as densely sedimented habits, possess particular salience to this pressing but neglected question. 20 Geuss, 192. 21 Geuss, 192. 18

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identity of human agents. Peirce’s pragmatic and thus naturalistic alternative to Kant’s transcendental and (as I will suggest near the conclusion of this paper) Cartesian position involves acknowledging our practical identity in a more direct manner and also more robust form than anything found in either Kant or Korsgaard.22

IV There are passages in Peirce where he appears to be utterly at odds with the reflexive stance at the heart of Kant’s critical philosophy. Perhaps the most famous of these, one bearing directly upon the distinctive employment of human reason wherein the reflexive turn is most dramatically present (“practical” or ethical reason), is a text in which Peirce appears to identify moral conduct with unreflective conformity to traditional morality. To be a moral man is to obey the traditional maxims of your community without hesitation or discussion. Hence, ethics, which is reasoning out an explanation of morality is–I will not say immoral, [for] that would be going too far–composed of the very substance of immorality.23

This text is to be found in the first lecture (“Philosophy and the Conduct of Life”) in a series entitled “Detached Ideas on Vitally Important Topics”. The background to this series is helpful in appreciating the degree to which Peirce is being hyperbolic and ironic at pivotal points in this lecture series, especially in the inaugural lecture. In an attempt to advise Peirce about what would be most appropriate for the series James was trying to arrange for his friend, James wrote: I am sorry you are sticking so to formal logic. I know our graduate school here, and so does Royce, and we both agree that there are only three men who could possibly follow your graphs and [logic of] relatives. Are not such highly abstract and mathematically conceived things to be read rather than heard; and ought you not, at the cost of originality, remembering that a lecture must succeed as such, to give a very minimum of formal logic and get on to metaphysics, psychology and cosmogony almost immediately?24

22

In fairness to Korsgaard, she attempts to answer objection posed by Geuss. Suffice it to say here that I find her response as unconvincing as I find the position itself cogent. 23 CP 1.666; emphasis added. 24 Ralph B. Perry, The Thought and Character of William James (Boston: Little, Brown and Co., 1935), 2, 418.

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He went on to advise his slightly older friend: Now be a good boy and think a more popular plan out. I don’t want the audience to dwindle to three or four, and I don’t see how one can help that on the program you propose. I don’t insist on an audience of more than fifteen or sixteen, but you ought certainly to aim at that, and that does n’t condemn you to be wishy-washy.

So James proposed to Peirce: You are teeming with ideas, and the lectures need not by any means form a continuous whole. Separate topics of a vitally important character would do perfectly well.25

In his private response, Peirce informed James: My philosophy […] is not an ‘idea’ with which I ‘brim over’; it is serious research to which there is no royal road; and the part of it which is most closely connected with formal logic is by far the easiest and least intricate.26

Even so, he begrudgingly accepted the counsel of his friend: I will begin again, and will endeavor to write out some of the ‘ideas’ with which I am supposed to be ‘teeming’ on ‘separate topics of vital importance.’ I feel I shall not do well, because in spite of myself I shall betray my sentiments about such ‘ideas’; but being paid to do it, I will do it as well as I possibly can.27

In the public discourse, one of the places where Peirce betrayed just such sentiments, is near the end of the first lecture: Among vitally important truths there is one which I verily believe–and which men of infinitely deeper insight than mine have believed–to be solely supremely important. It is that vitally important facts are of all truths the veriest trifles. For the only vitally important matter is my concern, business, and duty–or yours. Now you and I–what are we? Mere cells of the social organism. Our deepest sentiment pronounces the verdict of our own insignificance. Psychological analysis shows that there is nothing which distinguishes my personal identity except my faults and my

25

Perry, 2, 419. Perry, 2, 419. 27 Perry, 2, 419-420. 26

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One of the most illuminating texts in Peirce’s corpus for understanding how the annihilation of this will (the merely idiosyncratic will of the supposedly separate self) is to be accomplished is found in his review of Ernst Mach’s The Science of Mechanics: A Critical and Historical Exposition of Its Principles (a review appearing in The Nation in 1893). Here he notes: Having once surrendered to the power of nature, and having allowed the futile ego in some measure to dissolve [or be annihilated], man at once finds himself in synectic union with the circumambient non-ego, and partakes in its triumphs. On the simple condition of obedience to the laws of nature, he can satisfy many of his selfish desires; a further surrender will bring him the higher delight of realizing to some extent his ideas; and a still further surrender confers on him the function of cooperating with nature and the course of things to grow [or, at least, to assist in the growth of] new ideas and institutions. Almost anybody will admit there is truth in this; the question is [only] how fundamental that truth may be.29 28

CP 1.673. This point can be stated positively. Peirce himself does so when he asserts: “we know that man is not whole as long as he is single, that he is essentially a possible member of society. Especially, one man’s experience is nothing, if it stands alone. If he sees what others [in principle] cannot, we call it hallucination. It is not ‘my’ experience, but ‘our’ experience that has to be thought of; and this ‘us’ has indefinite possibilities” (CP 5.402, n. 2). 29 CN 1: 188-189. This important text invites to be coordinated with other important ones. First, the “synectic union with the circumambient non-ego” calls to mind Peirce’s definition of religion: “In each individual it is a sort of sentiment, or obscure perception, a deep recognition of a something in the circumambient All, which, if he strives to express it, will clothe itself in forms more or less extravagant, more or less accidental, but ever acknowledging the first and the last, the $ and : as well as a relation to that Absolute of the individual’s self, as a relative being” (CP 6.429). The emphasis on the growth of ideas and institutions calls to mind a passage from Evolutionary Love: “Suppose, for example, that I have an idea that interests me. It is my creation. It is my creature; for […] it is a little person. I love it; and I will sink myself in perfecting it. It is not by dealing out cold justice to the circle of my ideas that I can make them grow, but by cherishing and tending them as I would the flowers in my garden” (CP 6.289). Somewhat paradoxically, this series of ever more radical self-surrenders makes possible the acquisition of ever more effective self-control. The progressive annihilation of the blind will of aggressive and possessive individuality is the negative side of the progressive realization of rational agency. Peirce highlights an important facet of the positive side of this progressive realization when he suggests: “it is by the indefinite replication of self-control upon self-control that [to borrow a term from Henry James, Sr.] the vir is begotten, and by action, through thought, he [this vir] grows an esthetic ideal, not for the behoof of his own poor noodle merely, but as the share which God permits

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From the Peircean perspective, then, the moral person is the deliberative agent, one who conscientiously engages in discussion and deliberation not about the foundations of morality but about the ethical dimensions inherent in actual circumstances. In turn, a deliberative agent is one guided and goaded by various ideals having a decisive hold on the actual character of the agent in question. “Every man has”, Peirce insists, “certain ideals of the general description of conduct that befits a rational animal in his particular station in life, what most accords with his total nature and relations” (CP 1.591). To abstract from this station and nature, these relations and entanglements, transforms our moral identity into a formal and, arguably, empty one. To dissociate our selves in some respect, for some purpose, from one or more facets of any of these is, however, not only legitimate but also (on occasion) imperative.

V The hold of such ideals is the result of the way ideals ordinarily and properly establish their authority over the deliberations of agents. The way they do so involves nothing less than the constitution of agency: the incorporation of ideals, primarily in the form of more or less integrated habits, makes of the human organism a human agent. Peirce identifies three “ways in which ideals usually recommend themselves and justly do so”. First, “certain kinds of conduct, when the man contemplates them, have an esthetic quality. He thinks that conduct fine”. Second, persons endeavor to make their ideals consistent with one another, inconsistency being odious to human beings since it is an impediment to the exercise of their agency. Third, individuals imagine what the consequences of fully

him to have in the work of creation” (CP 5.402, n. 3). “This [esthetic] ideal, by modifying the rules of self-control modifies action, and so experience too–both the man’s own and that of others, and this centrifugal movement thus rebounds in a new centripetal movement”, without limit (CP 5.402, n. 3). “The great principle of logic is self-surrender, which does not mean that the self is to lay low for the sake of an ultimate triumph. It may turn out so; but that must not be the governing purpose” (CP 5.402, n. 2). The governing purpose must rather be ever more thoroughgoing devotion to (or espousal of) a trans-personal cause or ideal. Cf. Walter P. Krolikowski, “The Peircean Vir”, in Studies in the Philosophy of Charles Sanders Peirce, Second Series. Ed. by E.C. Moore, R.S. Robin (Amherst: University of Massachusetts Press, 1964); also Richard J. Bernstein, “The Lure of the Ideal”, in Peirce and Law. Ed. by R. Kevelson (New York: Peter Lang, 1991), 29-43.

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carrying out what their ideals would be–and then question the esthetic quality of these imagined consequences.30 The ideals actually animating agents have their roots in ones largely imbibed in the childhood of these agents. Even so, these ideals are gradually shaped to the personal nature and the reigning ideas in the social spheres of individual agents; this is accomplished more “by a continuous process of growth than by any distinct acts of thought”. “Reflecting upon these ideals, he [the agent] is led”, Peirce suggests, “to intend to make his own conduct conform at least to part of them–to that part in which he thoroughly believes”.31 But just as agents shape their conduct to accord with their ideals, they shape their ideals themselves to accord with their aesthetic susceptibility to the inherently admirable (or fine). In sum, the moral person is the truly deliberative agent and, in turn, deliberative agency encompasses a conscientiously cultivated sensibility: If conduct is to be thoroughly deliberative, the ideal must be a habit of feeling which has grown up under the influence of [ordinarily] a [long] course of self-criticisms and of hetero-criticisms.

The deliberate formation of such affective habits–these habits being the shape in which ideals are maximally effective in deliberation–is an integral part of deliberative agency.32 In the ongoing formation of such habits and the everyday exercise of our agency, the reflexive stance of human beings toward various dimensions of their actual lives is clearly in evidence. This stance depends not so much on universalizability as on generalizability and, moreover, on generalizability in the service of continuity.33 Or so Peirce proclaims near the conclusion of the lecture in which he in a hyperbolic and ironic manner says, “To be a moral man is to obey the traditional maxims of your community without hesitation or discussion”.34 One’s highest business is to recognize a higher business than one’s own. The practical realization of this higher vocation generates “a generalized conception of duty which completes your personality by melting it into the neighboring parts of the universal cosmos” (emphasis added). Here we are at any rate confronted with “the supreme commandment of the Buddhisto-christian religion”–the 30

CP 1.591. CP 1.592. 32 CP 1.574. 33 The relationship between generality and continuity needs to be explored more fully than I have done. In Peirce’s thought, the intimacy of the relationship between the two, however, cannot be gainsaid (see CP 1.82-84; also CP 6.185ff.). 34 CP 1.666. 31

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commandment “to generalize, to complete the whole system even until continuity results and the distinct individuals weld together”.35 The reflexive stance at the heart of this deliberative process is, however, not primarily a cognitive accomplishment: “the very supreme commandment of sentiment is that man should generalize” and the work of such generalization manifests “what true reasoning consists in”.36 But this commandment does not thereby “reinstate reasoning” or cognition as paramount. The reason is that the form of generalization in question “should come about, not merely in man’s cognitions, which are but the superficial film of his being, but objectively in the deepest emotional springs of his life”.37 An accurate understanding of this supreme commandment marks “duty at its proper finite figure”.38 The accent on finitude is as critical as the emphasis on generalizability. A word specifically about pragmatism is in order here. According to Peirce’s articulation of this doctrine, 35

CP 1.673. CP 1.673. 37 CP 1.673. “Reason […] appeals to sentiment in the last resort. Sentiment on its side feels itself to be the man. That is my simply apology for philosophical sentimentalism” (CP 1.632). “It is the instincts, the sentiments, that make the substance of the soul [or psyche]. Cognition is only its surface, its locus of contact with what is external to it” (CP 1.628). “Instinct [or innate disposition] is capable of development and growth–though by a movement which is slow in proportion in which bit is vital. […] And just as reasoning springs from experience, so the development of sentiment [and the growth of ‘instinct’] arises from the soul’s Inward and Outward Experience. Not only is it of the same nature as the development of cognition [that nature being the growth of complex signs]; but it chiefly takes place through the instrumentality of cognition. The soul’s deeper parts can only be reached through its surface. In this way the eternal forms […] will by slow percolation gradually reach the very core of one’s being; and will come to influence our lives […]” (CP 1.648). 38 CP 1.675. “Here we are in this workaday world, little creatures, mere cells in a social organism itself a poor and little thing enough, and we must look to see what little and definite task our circumstances have set before our little strength to do. The performance of that task [at least, if conscientiously undertaken] will require us to draw upon all our powers, reason included. And in the doing of it we should chiefly depend not upon that department of the soul which is most superficial and fallible–I mean our reason–but upon that department that is deep and sure–which is instinct” or sentiment (CP 1.647). “The dry light of intelligence is manifestly not sufficient to determine a great purpose; the whole man goes into it” (CP 7.186; cf. 7.595). The distinctively religious cast which Peirce gives to marking “duty as its proper finite figure” is evident when he claims: “All communion from mind to mind is through continuity of being. A man is capable of having assigned to him a role in the drama of creation, and so far as he loses himself in that role,–no matter how humble it may be–so far as he identifies himself with its Author” (CP 7.772). 36

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the true meaning of any product of the intellect lies in whatever unitary determination it would impart to practical conduct under any and every conceivable circumstance, supposing such conduct to be guided by reflexion carried to an ultimate limit.39

In a letter to F.C.S. Schiller (September 10, 1906), Peirce explained: “By ‘practical’ I mean apt to affect conduct; and by conduct, voluntary action that is self-controlled, i.e., controlled by adequate deliberation”.40 The meaning of practical in this context is whatever bears upon conduct (perhaps most of all, upon our comportment as participants in some identifiable human practice), insofar as conduct through deliberation is alterable.

VI What could be more Kantian than in one’s effort to vindicate reason,41 to establish the authority of reflection, one stresses the limits of reason, indeed, the rather narrow bounds within which human rationality can operate effectively? What also could be more Kantian than to underscore the link between rationality and reflexivity, in particular, the capacity of reason to restrain itself, to control its operations by appeal to norms and ideals themselves having won reflective endorsement? But what could be more Hegelian than to rescue such reflective endorsement from being an empty formalism by appealing to the actual, ongoing history in which the norms, ideals, and indeed motives for such endorsement have taken authoritative shape? Closely allied to this, what could be more Hegelian than to accord passion an eliminable and indeed central role in the constitution of reason itself? Also what could be more Hegelian than to acknowledge reflectively the paradox of autonomy, the extent to which mastery over the self involves a series of surrenders to what is other than the self? Since these surrenders to what is other than the self involve acts of identification with what is other, the achievement of autonomy involves, both at the outset and at every step along the way, the incorporation of others and thereby the transformation of the self. I am able to give laws to myself only to the extent that I give myself to others (even more radically, only to the extent that I am always already given over to others and, as a consequence of this, given to myself not only by others but also in 39

CP 6.490, emphasis added; cf. Hookway, 302). CP 8.322. 41 Cf. Onora O’Neill, “Vindicating Reason”, in The Cambridge Companion to Kant. Ed. by P. Guyer (Cambridge: Cambridge University Press, 1992), 280-308. 40

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terms inherited and authorized by these others). This is, at least, partly what I mean by the paradox of autonomy. The roots of autonomy are to be traced to heteronomy.42 Moreover, the dramatic crises in the lives and engagements of autonomous agents (including crises in engagements such as the historical life of an experimental community, i.e., an open-ended community of self-critical inquirers) are bound up with the fateful necessity of disowning parts of oneself and incorporating others in oneself. Elsewhere I have gestured toward these crises as integral to dramas of self-correction.43 The fateful character of these decisive dramas (decisive above all because the actions and decisions of agents so significantly, so profoundly, define these agents and their engagements) is brought to light by recalling one of Hegel’s guiding concerns. In the Preface to The Phenomenology of Spirit, Hegel asserts: We learn by experience that we meant something other than we meant to mean; and this correction of our meaning compels our knowing to go back to the proposition [our formulation of what we meant to mean], and [to] understand it [this proposition] in some other way.44

In brief, experience compels to go back to confront what we meant to mean in order that we can go forward. Such compulsion, felt as (to use one of Peirce’s favored expressions in this regard) force majeure,45 is exerted upon agents as a result of their exertions and conceptions.46 Existence “is not a form to be conceived, but a compulsive force to be experienced”.47 Hegel offers pivotal insights into, and a vivid sketch, of the communal processes by which autonomous individuals come into self-possession, to the 42 Judith Butler, The Psychic Life of Power (Stanford: Stanford University Press, 1997), chapter 1. 43 Vincent Colapietro, “Portrait of an historicist: an alternative reading of Peircean semiotic”, Semiotiche 2 (2004): 49-68. 44 Friedrich G. W. Hegel, The Phenomenology of Spirit (Oxford: Oxford University Press, 1981), 39. 45 See, e.g., CP 5.581. 46 “We experience vicissitudes, especially. We cannot experience the vicissitude without experiencing the perception which undergoes the change; but the concept of experience is broader than that of perception, and includes much that is not, strictly speaking, an object of perception. It is the compulsion, the absolute constraint upon us to think otherwise than we have been thinking that constitutes experience. Now constraint and compulsion cannot exist without resistance, and resistance is effort opposing change. Therefore there must be an element of effort in experience; and it is this which gives it [experience] its peculiar character” (CP 1.336). 47 CN 3: 37.

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degree they ever do. Central in this sketch is his emphasis on to the extent that in giving myself to what is other than me I am willing to be made other than myself. The “I” emerges out of the “We”. At critical junctures in its precarious development, the human self secures and solidifies its effective (or practical) identity by affective identifications with others in their otherness, who thereby become incorporated (principally in the form of habits) in the very constitution of the “I”. The “I” as “I”, i.e., as a form of agency distinguished by the degree to which its exercise involves reflexivity, is a social being whose reflexivity is inseparable from its sociality, moreover, one whose autonomy is intertwined with heteronomy. The self as a divided being is one who, in its status as self, confronts itself as other.48 In addition, the self precisely as an autonomous being is who, in the very exercise of its autonomy, confronts the directives, challenges, and criticisms of others as though they provisionally have an authority comparable to anything issuing from the self.49 The ideal of self-control is inseparably linked to that of self-criticism. “Now control”, Peirce stresses, “may itself be controlled, criticism itself subjected to criticism; and ideally there is no obvious limit to the sequence”.50 In an unpublished manuscript, he suggests: “if any criticism is beyond criticism (which may be doubted) it is the criticism of criticism itself”.51 In its most embryonic (or nuclear) sense (that sense wherein the nucleolus or nucleus of rationality is identified), rationality as concretely felt in any process of genuine reasoning is at the very least “a sense of taking a habit, or disposition to respond to a given stimulus in a given kind of way”.52 “But the secret of rational consciousness is not so much to be sought in the study of this one peculiar nucleolus, as [it is to be 48

Two things are “all-important” for understanding self-control. “The first is that a person is not absolutely an individual. His thoughts are what he is ‘saying to himself,’ that is, saying to that other self that is just coming into life in the flow of time. When one reasons it is that critical self [that internalized other] that one is trying to persuade; and all thought whatsoever is a sign, and is mostly of the nature of language” (CP 5.421; emphasis added). In other words, the self as self is inclusive of the other as other: the reflexivity constitutive of selfhood embodies the apparent paradox of identity being secured and solidified by ongoing processes of identification with what continuously confronts the self, even in its deepest interiority, as other. The “I” is not the being who stands absolutely over against the other but rather the being who enacts its individuality by means of its engagement with alterity. 49 See, e.g., CP 5.378. 50 CP 5.442. 51 MS 598: 5. 52 CP 5.440.

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sought] in the review of the process of self-control in its entirety”.53 The consideration of this process in its entirety extends to the deliberate cultivation of affective dispositions: when fully conceived, the ideal of self-control (an ideal evident in the conscientious adoption of a critical stance toward our epistemic, ethical, and aesthetic judgments) needs to be traced to its actual governance of human conduct. When traced to its operation in this context, what we discover is that the ultimate source of human normativity is (at least, for Peirce) the esthetically motivated cultivation of esthetically governing affections. This is no doubt a far distance from Kant’s more austere rendering of the critical stance, on Korsgaard or anyone else’s interpretation. What however could be more Kantian than to offer an architectonic critique of experimental reason in which the limits of reason are stressed as much as the efficacy and dignity of reason? To be sure, Peirce interprets the finite character of human rationality in explicitly Darwinian (at least, evolutionary) terms, not in formally transcendental terms. In a manuscript on pragmaticism, he reveals: I hold […] that man is so completely hemmed in by the bounds of his possible practical experience, his mind is so restricted to being the instrument of his needs, that he cannot, in the least, mean anything that transcends those limits.54

Peirce’s stress on finitude here is, at once, a sign of his kinship with Kant and (given the naturalistic motive for emphasizing this particular point in this particular manner) his distance from the figure whom he dubbed “the King of modern thought”.55 Peirce’s characterization of human agents being completely inscribed within the bounds of practical experience does not limit human rationality to being nothing but an instrument of human needs, least of all given needs (those we just happen to feel an urgency to satisfy). Historically emergent desires come to attain the status of needs and, in addition, historically evolved and evolving practices such as the experimental investigations of those devoted to theoretical truth come to define purposes transcending given biological needs or even regnant human desires. But the achievement or approximation of these transcendent purposes (purposes transcending any given biological or cultural inheritance) relies utterly on a reason incapable of transcending the somewhat narrow bounds of “possible practical experience”. A practically bounded intelligence can evolve to the point where its commitment to what might be called transcendent purposes becomes a defining trait of such intelligence. 53

CP 5.440; emphasis added. CP 5.536. 55 CP 1.369. 54

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Hence, precisely the place at which Peirce so clearly joins Kant is the place where he so decisively moves away from the critical perspective allegedly provided only by Kant’s innovative conjunction of empirical realism and transcendental idealism. For Peirce no less than for Kant, the limits of our understanding are defined by the limits of our experience. Peirce insists, however, “a proposition which has no relation whatever to experience is devoid of all meaning”.56 In his hands, this claim is not wielded as a weapon of positivism by which to slay the champions of metaphysics, ethics, aesthetics, and religion. Either the thing-in-itself is related to experience in a different sense than that permitted by Kant’s transcendental idealism (in a more intimate and direct sense than Kant would allow) or it is “devoid of all meaning”. Insofar as the thing-in-itself is defined as transcending the possibility of experience, it is, for Peirce, meaningless: to be unknowable in this way is to be inconceivable. Insofar as it is defined as part of a practically instituted and maintained distinction between how things happen to appear to us and how they are apart from the idiosyncratic structure of one or another species of cognitive agents, this dangerously misleading expression might be given a pragmatic meaning. A sense of finitude is here conjoined to an acknowledgment of our capacity for self-transcendence and self-transformation. To repeat, what could be more Kantian than offering a Critic57 of reason in which defining the limits of reason is of paramount concern? Also what could be more Kantian that defining these limits in terms of experience? But what could be more Hegelian than bringing into sharp focus the historical character of human experience and, as a salient feature of such experience in its historicity, the selftranscending and self-transformative momentum inherent in our experientially rooted practices and indeed in the course of our lives? Much keeps us stuck; much thwarts and arrests the inherent drive of human experience toward selftranscendence and self-transformation. Perhaps Peirce is too sanguine when he asserts experience will in time break down even the most pigheaded and passionate person who has sworn to hold to a proposition that the force of experience is destined to discredit (his example is the spherical shape of our planetary abode).58 56

CP 7.566. “I do not see why”, Peirce wrote, “we should not retain Kant’s term, critic, especially as he borrowed it from the English [cf. CP 6.205]; for in our language this word has been used since Hobbes and earlier, for the science of criticism, and was admitted by Johnson [in this sense] into his dictionary. The peculiar turn of meaning given to it by Kant, which makes it the critic of knowledge, or, as he would have said, the critic of the cognitive faculties, is quite admissible. Besides, the immense importance of Kant’s work upon this problem imposes upon us [given the ethics of terminology] the duty of accepting his word, as long as it is so far from being a bad one” (CP 2.62; cf. CN 3: 94-95). 58 Cf. CP 7.78; 7.281. 57

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For Peirce, then, reason operates within the bounds of “possible practical experience”. The experiential sense of these bounds is defined–and re-defined–in reference to our actual historical experience. Our actual experience (at least) intimates the possibility of experiential transformations and (quite often) compels us to confront that what we mean to mean cannot be advanced by tenaciously espousing what we meant to mean. Our practical identity, even insofar as it encompasses a defining commitment to reflective endorsement, is at once a historical inheritance and a historical attainment. The authority of reflection is nothing other than the authority of historically situated, and hence practically implicated, agents who respond to the experiential compulsions inherent in their own practical involvements (though theoretical inquiry might be here counted as one such “practical” involvement).59 This takes the authority of reflection to be the authority of history, though the possibilities of misunderstanding this assertion are numerous and ubiquitous. Such authority is first and foremost a task, the task of owning up more fully to the complex inheritances in which the practical identity of any human agent is inevitably rooted. Above all else, this task demands of agents the necessity of acknowledging, in the first instance, their indebtedness to these inheritances and, in decisive moments thereafter, their ongoing need to incorporate in their habits, methods, and self-understanding their ineradicable ambivalence toward the fateful developments giving authoritative shape to these historical practices. We learn by experience that “we meant something other than we meant to mean”. That is, you and I, as practically identified by our involvement in some actual historical (or intergenerational) community, come by experience to learn this. Wittgenstein’s insights into the connection between knowledge and acknowledgment might accordingly be adapted to our purpose. In the first instance, we (you and I and potentially countless others who are ineluctably defined in and through their involvement in certain practices) are compelled by experience to acknowledge our indebtedness to one or another of our inheritances, for our practical identity is bound up with this historical inheritance. In decisive moments thereafter, we are also compelled by the momentum of experience to incorporate

59

“For him [Francis Bacon] man is nature’s interpreter; and in spite of the crudity of some anticipations, the idea of science is, in his mind, inseparably bound up with that of a life devoted to single-minded inquiry. That is also the way in which every scientific man thinks of science. […] Science is to mean for us a mode of life whose single animating purpose is to find out the real truth, which pursues this purpose by a well considered method, founded on thorough acquaintance with such scientific results already ascertained by others as may be available, and which seeks cooperation in the hope that the truth may be found, if not by any of the actual inquirers, yet ultimately by those who come after them and who shall make use of their results” (CP 7.54).

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the lessons of experience into the habits of our being.60 We can do so begrudgingly or otherwise (e.g., graciously or gratefully). The authority of reflective endorsement carries force and possesses substance as the result of practical identification with the experientially sanctioned beliefs of various historical communities. Practical identity itself only results from such practical identification. The practical identity of autonomous agent, in the very exercise of their reflexive commitments (their commitments to self-consciousness, self-criticism, and self-control), is at bottom the historical achievement of fissured individuals who are continuously struggling, consciously or otherwise, to bear effective witness to the fateful crises of their defining histories. In his later years, Peirce became increasingly appreciative of just how eloquent and insightful was Hegel’s project, precisely as an attempt to bear self-conscious witness to our self-transformative histories. (The role of such a witness becomes, partly because of the impact of Hegel’s work, integral to the dynamics of selftransformation.) Unquestionably, Peirce’s early philosophy took memorable form as an immanent critique of the Kantian project. But his mature philosophy assumed equally memorable form by transforming Kant’s project along some of the lines already articulated in Hegel’s writings. One of these lines was a thoroughly historicist rendering of human experience. Another was a resolute refusal to sever thought and being61 (and, closely allied to this refusal, an equally resolute refusal to disjoin appearance and reality, self and other, autonomy and heteronomy). The appeal to experience is an experientially and, thus, a historically motivated and sanctioned appeal in which the self-imposed limitations constitutive of human rationality62 alone hold out hope of the self-transformative possibilities intimated by human experience. The identity of thought and being is, in Peirce’s own thought, not so much the grounding claim of speculative philosophy (the task of reflection insofar as it merits the name philosophy) as one of the defining commitments of his experimental approach. Over against any cognition, there is an unknown but knowable reality; but over against all possible cognition, there is only the self60

Vincent Colapietro, “Human Agency: The Habits of Our Being”, Southern Journal of Philosophy 26, 2 (1988): 153-68. 61 Peirce insists, “the human mind and the human heart have a filiation to God” (CP 8.262). One of the ways in which he tries to illuminate this relationship is by proposing: “It is somehow more than a mere figure of speech to say that nature fecundates the mind of man with ideas which, when those ideas grow up, will resemble their father, Nature” (CP 5.591). The link or affinity between thought and being is here given a naturalistic twist, in several distinct senses of naturalism. 62 Peirce asserts, “‘rational’ means essentially self-criticizing, self-controlling and selfcontrolled, and therefore open to incessant question” (CP 7.77).

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contradictory. In short, cognizability (in its widest sense) and being are not merely metaphysically the same, but are synonymous terms.63 However limited and deformed is the actual shape of human rationality– however much it is forced to acknowledge as a consequence of its own exercise its inherent limitations and inherited disfigurements–such rationality is compelled by its own defining commitment to the fateful crises generated by our historical experience (e.g., the unavoidable drama of self-correction) to acknowledge its kinship to being (in addition, its kinship to nature). To postmodern ears, the affirmation of such kinship cannot help but sound like the fantastic utterance of a speculative mind operating apart from the guidance of experience.64 But, to some of us who have devoted our selves to the study of Peirce, especially those who have undertaken this study in light of those historical figures in reference to whom Peirce characterized his philosophical project, we hear an inspiring acknowledgment of an ancient “truth”. This ancient claim is inflected in such a way as to express clearly the experimental temper of our historical moment. But the acknowledgment of this kinship carries with it the invitation to acknowledge a degree of kinship between contemporary theory and ancient theoria. To some extent, we can say with Aristotle that the phenomena relevant to any inquiry include the logoi of our predecessors and contemporaries, our modes of discourse and forms of articulation. Not only is being said in many ways, but the various ways in which it has been articulated are potentially manifestations of nothing less than being itself.65 Our modes of speech might be more than simply a 63

CP 5.257. However, see Umberto Eco, Kant and the Platypus: Essays on Language and Cognition (London: Vintage, 2000). 65 “We must not begin”, Peirce asserts, “by talking of pure ideas,–vagabond thoughts that tramp the road without any human habitation,–but must begin with men and their conversation. We are familiar with the phenomenon of a man expressing an opinion, sometimes decidedly, otherwise not. Perhaps it will be a mere suggestion, a mere question. Any such suggestion that may be expressed and understood relates to some common experience of the interlocutors, or, if there is a misunderstanding, they may think they refer to some common experience when, in fact, they refer to quite different experiences. A man reasoning with himself is liable to just such a misunderstanding” (CP. 8.112; emphasis added). Elsewhere he suggests: “Different systems of expression are often of the greatest advantage” (EP2: 264). This is perhaps nowhere more advantageous than in philosophy. In general, what will count as “ideal terminology will differ somewhat for different sciences. The case of philosophy is [however] very peculiar in that it has positive need of popular words in popular senses,–not as its own language (as it has too usually used those words), but as objects of its study” (EP2: 264-265; emphasis added). In making such words and expressions objects of its study, philosophy is in effect treating them as phenomena, manifestations of what is other than themselves. 64

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patchwork of conventions indicative of local contingencies and arbitrary associations. The contingent features of various natural languages certainly need to be identified, but the arguably universal–at least, the indefinitely generalizable– facets of any human language, such as indexical signs and even iconic features, equally need to be acknowledged.66 We must therefore attend to how things manifest themselves not only in our perceptual experience but also in various forms of human articulation, not least of all poetic and philosophic utterance.67 Our utterances are, in however attenuated and disguised a form, interpretants of dynamical objects complexly mediated by intersecting histories of various human practices. The realization of this has prompted some thinkers to dream of the possibility of transcending mediation entirely. It has disposed other thinkers (most notably, Immanuel Kant) to acknowledge the inescapability of mediation, but then in effect to deny the refractive power of semiotic mediation in particular (i.e., the power of signs to exhibit what is radically other than them). It is as though the rainbow is taken to be solely indicative of the properties of water, not in the least those of light.68 But the realization under consideration has inclined yet other thinkers (ones such as Hegel, Peirce, Heidegger, Gadamer, and Eco) to conceive the historicity of semiosis neither as a prison to be escaped or a definitively bounded perspective. We are caught up in histories not of our own initiation, ones over which we can exert at most very limited control. But the exercise and enhancement of selfcontrol, such control being for Peirce the very center of rationality, depend upon acknowledging our indebtedness to and locus in these histories. The open-ended task of self-critical interpreters is, accordingly, one with acknowledging the finite, fallible, and implicated character of human endeavor, while at the same time being animated by the hope of carrying forward the precarious work of an intergenerational community. The formalist dreams so captivating to the philosophical imagination are transcendental illusions (and, in this regard, transcendental idealism is itself to be counted among these transcendental illusions). The human hopes born of–and indeed borne by–the human histories in and through which our practical identities have been formed and transformed are not necessarily such illusions, at least when tempered by contrite fallibilism. 66

Winfried Nöth, “Peircean semiotics in the study of the iconicity of language”, Transactions of Charles S. Peirce Society 35, 3 (1999): 613-619. 67 Vincent Colapietro, “The Routes of Significance: Reflections on Peirce’s Theory of Interpretants”, Cognitio 5, 1 (2004): 11-27; also “Striving to Speak in a Human Voice: A Peircean Contribution to Metaphysical Discourse”, The Review of Metaphysics 58 (2004): 367-398. 68 Thompson.

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VII. Conclusion In “Philosophical Conceptions and Practical Results”, the lecture in which William James so effectively accomplished what Peirce two decades before failed to do–launch pragmatism as a movement–he suggests: “The true line of philosophical pragmatism lies […] not so much through Kant as round him to the point where now we stand”.69 But where James stood at that moment was a place prepared by Peirce (and James is explicit in acknowledging his indebtedness to Peirce in this regard).70 That place was however one reached by Peirce by going originally through and ultimately beyond Kant. One dimension of the trajectory of Peirce’s thought is his movement through the tangled intricacies of the first Kritik. In addition to the creative appropriation of distinctively Kantian doctrines such as the priority of logic to metaphysics71 and the ineliminable role of conceptual mediation even in our most rudimentary perceptual experience, Peirce appears to have taken from Kant the ideal of a deliberately reflexive and thus interrogative stance toward one’s given desires, emotions, and beliefs. In The Sources of Normativity, Christine Korsgaard offers a painstaking account of the sort of reflective endorsement required for a rational resolution of normative conflicts. Such conflicts are inevitably generated by the exercise of reflexivity. They can be most satisfactorily resolved, she contends, only by making the source of the conflicts itself a resource for their resolution. But the identity of the agent effectively (i.e., practically) resolved to take a reflexive, critical stance toward its desires, emotions, and beliefs cannot be secured by the purely formal identification of an essentially “punctual self”72 with an utterly abstract law. The identity of agents is secured, strengthened, and altered by means of the complex identifications by which somatic actors incorporate within themselves, principally through the process of habituation, the rules, norms, and ideals constitutive of this or that historical practice. Our practical identities are forged in the crucible of our practical involvements, involvements ineluctably insuring (in however tenuous and conflicted a form) identifications. The deliberately reflexive stance definitive of human agency is, accordingly, the historical achievement of embodied beings. This 69 William James, The Writings of William James: A Comprehensive Edition. Ed. by J.J. McDermott (Chicago: University of Chicago Press, 1977), 361-362. 70 See James, 347-349. 71 Cf. Murray G. Murphey, The Development of Peirce’s Philosophy (Indianapolis: Hackett, 1993). 72 Charles Taylor, The Sources of the Self (Cambridge: Harvard University Press, 1989).

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is not a contingent fact about human rationality. It is an inescapable condition for acquiring any distinctively human capacity.73 The acknowledgment of this condition is required for the fuller possession of rationality or any other capacity. Such acknowledgment however prompts our awareness that the self-legislative agent is anything but a self-generated being. The traditions in which we were reared and, as a result of this, the sentiments making up the substance of our psyches are so much a part of our practical identity that whatever reflective distance we can attain regarding these traditions and sentiments inevitably–and deeply–draws upon what we are striving, if only reflectively, to distance our selves from. Insofar as the critical stance is conceived by Kant and Korsgaard as resulting from the formal exercise of a purely punctual self (one defined in radical opposition to its actual habits and hence habitual attachments and affections, entanglements and identifications), rather than resulting from (at bottom) the affective dispositions of the human animal, the reflexive stance is the inexplicable accomplishment of an all too familiar and all too ethereal subject–the Cartesian cogito. But, insofar as this stance is the dramatic accomplishment of a historical actor prompted by, and addressed to, the fateful contingencies of an ongoing history,74 we have decisively broken with the illusory aspirations of both Descartes’ foundationalist project and Kant’s transcendental turn.75 Fully acknowledging our animality and historicity does not render inexplicable this reflexive stance; rather such acknowledgment alone renders this stance intelligible

73

John McDowell, Mind and World (Cambridge: Harvard University Press, 1994). This is but a way of talking about deliberation in its distinctively pragmatist sense. In Human Nature and Conduct, John Dewey illuminates this process when he states: “deliberation is a dramatic rehearsal (in imagination) of various competing possible lines of action. It starts from the blocking of efficient overt action, due to that conflict of prior habit and newly released impulse. […] Then each habit, each impulse, involved in the temporary suspense of overt action takes its turn in being tried out. Deliberation is [hence] an experiment in finding out what the various lines of possible action are really like”, John Dewey, Human Nature and Conduct [Volume 14 of The Middle Works of John Dewey] (Carbondale: SIU Press, 1988), 132; cf. CP 5.533. 75 The break with these conceptions of selfhood and agency opens the possibility of a return to what in some passages Peirce depicts as a Christian (or traditionally religious) portrait of self and agency. In MS 659, e.g., he insists: “a man’s Real Self consists in his Actual Existing Feelings, and not in the view he would take if his nature accomplished its proper development. The orthodox [Christian] view according to my and most other churches is, I believe, though perhaps I am in error, that an infant is Regenerate when his sponsors at the [baptismal] font have promised that his mind shall receive that Christian nurture which will insure his ultimately having the Feelings, at least, and the valuations of Feelings that are about all that is common to all Christians”. 74

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and practical.76 For this acknowledgment brings into focus the extent to which the relationship of the self to itself is complexly related to its attachments to, and identifications with, others; also the extent to which “thoroughly deliberate” conduct depends on a deliberately cultivated sensibility,77 a sensibility thereby rendered ever more finely and fully attuned to the attractions of what would show itself to be intrinsically admirable.78 The intrinsically admirable would most reliably, least deceptively, show itself to be so only to “reflexion carried to an ultimate limit”.79 76

The utterly straightforward and immediately plausible account of this capacity is clearly implied in Peirce’s mature remarks on self-control: “there are inhibitions and coordinations that entirely escape consciousness [though these are the most rudimentary forms of selfcontrol–somewhat paradoxically, forms of self-control operating in absence of selfconsciousness]. There are, in the next place, modes of self-control which seem quite instinctive. Next, there is a kind of self-control which results from training. Next, a man can be his own training-master and thus control his self-control [though the manner and efficacy of the assumption of this role will depend much on how others reared and educated–i.e., ‘trained’–the individual]. When this point is reached much or all the training may be conducted in imagination. When a man trains himself, thus controlling control, he must have some moral rule in view, however special and irrational it may be. But next he may undertake to improve this rule; that is, to exercise a control over his control of control. To do this he must have in view something higher than an irrational rule. He must have some sort of moral principle. This, in turn, must be controlled by reference to an esthetic ideal of what is fine [or beautiful or admirable or adorable]. There are certainly more grades than I have enumerated. Perhaps their number is indefinite. The brutes are certainly capable of more than one grade of control; and it seems to me that our superiority to them is more due to our greater number of modes of self-control than it is to our versatility” (CP 5.533; emphasis added). 77 CP 1.574. 78 In a letter to William James (July 23, 1905), Peirce identifies the admirable with the adorable in its original sense and thereby connects the esthetic ideal with traditional theism: “anthropomorphism [a doctrine he endorses] implies for me above all that the true Ideal is a living power, which is a variation of the ontological proof. […] That is, the esthetic ideal, that which we all love and adore, the altogether admirable, has, as ideal, necessarily a mode of being to be called living. Because our ideas of the infinite are necessarily extremely vague and become contradictory the moment we attempt to make them precise. But still they are not utterly unmeaning [or nonsensical], though they can only be interpreted in our religious adoration and the consequent effects upon conduct. This I think is good sound solid strong pragmatism. Now the Ideal is not a finite existent. Moreover, the human mind and the human heart have a filiation to God. That to me is a most comfortable [comforting?] doctrine. At least I find it most wonderfully so every day in contemplating my misdeeds and shortcomings” (CP 8.262). 79 CP 6.490.

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Peirce suggests, “the good is the attractive,–not to everybody, but to the sufficiently matured agent; and the evil is the repulsive to the same”.80 The sufficiently mature person is one who is especially acute in discerning the beauty of character because that person has taken such pains in becoming responsive to the character of beauty. Indeed, herein lies the deepest root of such maturity, also what is, at bottom, the governing impulse of whatever reflective stance we ever manage to achieve.

REFERENCES Allison, Henry E. Kant’s Theory of Freedom. Cambridge: Cambridge University Press, 1990. Anderson, Douglas R. “The esthetic attitude of abduction”. Semiotica 153, 3/4 (2005): 9-22. Beiser, Frederick C., editor. The Cambridge Companion to Hegel. Cambridge: Cambridge University Press, 1993. Bernstein, Richard J. “Toward a More Rational Community”. In Proceedings of the Charles S. Peirce Bicentennial International Congress. Ed. by K.L. Ketner. Lubbock: Texas Tech Press, 1981: 115-120. —. “The Lure of the Ideal”. In Peirce and Law. Ed. by R. Kevelson. New York: Peter Lang, 1991: 29-43. Brent, Joseph. Charles Sanders Peirce: A Life. Bloomington: Indiana University Press, 1998. Butler, Judith. The Psychic Life of Power. Stanford: Stanford University Press, 1997. Cavell, Stanley. This New Yet Unapproachable America: Lectures after Emerson after Wittgenstein. Albuquerque: Living Batch Press, 1989. —. Conditions Handsome and Unhandsome: The Constitution of Emersonian Perfectionism. Chicago: University of Chicago Press, 1990. Christensen, C.B. “Peirce’s Transformation of Kant”. The Review of Metaphysics 48, 1 (1994): 91-120. Colapietro, Vincent. “Human Agency: The Habits of Our Being”. Southern Journal of Philosophy 26, 2 (1988): 153-168. —. “The Dynamical Object and the Deliberative Subject”. In The Rule of Reason: The Philosophy of Charles Sanders Peirce. Ed. by J. Brunning, P. Forster, Toronto: University of Toronto Press, 1997: 262-288

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—. “The Space of Signs: C.S. Peirce’s Critique of Psychologism”. In Philosophy, Psychology, and Psychologism. Ed. by D. Jacquette, Netherlands: Kluwer Academic Publishers, 2003: 157-179. —. “The Routes of Significance: Reflections on Peirce’s Theory of Interpretants”. Cognitio 5, 1 (2004): 11-27. —. “Portrait of an historicist: an alternative reading of Peircean semiotic”. Semiotiche 2 (2004): 49-68. —. “Striving to Speak in a Human Voice: A Peircean Contribution to Metaphysical Discourse”. The Review of Metaphysics 58 (2004): 367-398. Deleuze, Gilles. Kant’s Critical Philosophy. Minneapolis: University of Minnesota Press, 1999. Dewey, John. Human Nature and Conduct [Volume 14 of The Middle Works of John Dewey]. Carbondale: SIU Press, 1988. Eco, Umberto. Kant and the Platypus: Essays on Language and Cognition. London: Vintage, 2000. Esposito, Joseph L. Evolutionary Metaphysics: The Development of Peirce’s Theory of Categories. Athens: Ohio University Press, 1980. Fisch, Max H. Peirce, Semeiotic, and Pragmatism. Ed. by K.L. Ketner, C.J.W. Kloesel, Bloomington: Indiana University Press, 1986. Geuss, Raymond. “Morality and Identity”. In The Sources of Normativity. Ed. by O. O’Neill, Cambridge: Cambridge University Press, 1996: 189-199. Guyer, Paul. “Thought and being: Hegel’s critique of Kant’s critical philosophy”. In The Cambridge Companion to Hegel. Ed. by F.C. Beiser, Cambridge: Cambridge University Press, 1993: 171-210. —, editor. The Cambridge Companion to Kant. Cambridge: Cambridge University Press, 1992. Hegel, Friedrich G.W. Logic: Part One of the Encyclopaedia of the Philosophical Sciences (1830). Clarendon: Oxford University Press, 1973. —. The Phenomenology of Spirit. Oxford: Oxford University Press, 1981. Hookway, Christopher. Truth, Rationality, and Pragmatism. Oxford: Clarendon Press, 2000. James, William. The Writings of William James: A Comprehensive Edition. Ed. by J.J. McDermott, Chicago: University of Chicago Press, 1977. Joas, Hans. The Genesis of Values. Chicago: University of Chicago Press, 2001. Kant, Immanuel. The Critique of Pure Reason. New York: St. Martin’s Press, 1965. Korsgaard, Christine. The Sources of Normativity. Ed. by O. O’Neill, Cambridge: Cambridge University Press, 1996.

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Krolikowski, Walter P. “The Peircean Vir”. In Studies in the Philosophy of Charles Sanders Peirce, Second Series. Ed. by E.C. Moore, R.S. Robin, Amherst: University of Massachusetts Press, 1964: 257-270. McDowell, John. Mind and World. Cambridge: Harvard University Press, 1994. Midtgarden, Torjus. “Peirce’s Epistemology and Its Kantian Legacy: Exegesis and Systematic Considerations”. Journal of the History of Philosophy. Forthcoming, 2006. Misak, Cheryl. “Pragmatism and the Transcendental Turn in Truth and Ethics”. Transactions of the Charles S. Peirce Society 30, 4 (1994): 739-775. Murphey, Murray G. “Kant’s Children: The Cambridge Pragmatists”. Transactions of the Charles S. Peirce Society 4, 1 (1968): 3-33. —. The Development of Peirce’s Philosophy. Indianapolis: Hackett, 1993. Nöth, Winfried. “Opposition at the root of semiosis”, in Origins of Semiosis. Ed. by W. Nöth, Berlin: Mouton de Gruyter, 1994: 37-60. —. “Peircean semiotics in the study of the iconicity of language”. Transactions of Charles S. Peirce Society 35, 3 (1999): 613-619. O’Neill, Onora. “Vindicating Reason”. In The Cambridge Companion to Kant. Ed. by P. Guyer, Cambridge: Cambridge University Press, 1992: 280-308. Perry, Ralph B. The Thought and Character of William James. Boston: Little, Brown and Co., 1935. Rorty, Richard. Consequences of Pragmatism. Minneapolis: University of Minnesota Press, 1982. Savan, David. “Peirce’s Semiotic Theory of Emotion”. In Proceedings of the Charles S. Peirce Bicentennial International Congress. Ed. by K.L. Ketner, Lubbock: Texas Tech Press, 1981: 319-333. —. An Introduction to C.S. Peirce’s Full System of Semeiotic. Toronto: Monograph series of Toronto Semiotic Circle, no. 1, 1987-88. Schiller, Friedrich. On the Aesthetic Education of Man in a Series of Letters. New York: Frederick Ungar Publishing Co., 1965. Schneewind, J. B. “Autonomy, obligation, and virtue: An overview of Kant’s moral philosophy”. In The Cambridge Companion to Kant. Ed. by P. Guyer, Cambridge: Cambridge University Press, 1992: 309ff. Short, Thomas L. “The Development of Peirce’s Theory of Signs”. In The Cambridge Companion to Peirce. Ed. by C. Misak, Cambridge: Cambridge University Press, 2004. Smith, John E. “Being, Immediacy, and Articulation”. The Review of Metaphysics 24, 4 (1971): 593-613. —. “Hegel’s Critique of Kant”. The Review of Metaphysics 23, 2 (1973): 438460.

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—. America’s Philosophical Vision. Chicago: University of Chicago Press, 1992. Taylor, Charles. The Sources of the Self. Cambridge: Harvard University Press, 1989. Thompson, Manley. “Things in Themselves”. Proceedings and Addresses of the American Philosophical Association 57, 1 (1982): 33-48. Wittgenstein, Ludwig. Philosophical Investigations. New York: Macmillan Co., 1953. —. On Certainty. New York: Harper and Row, 1972.

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CHAPTER 9 THE IMPORTANCE OF THE MEDIEVALS IN THE CONSTITUTION OF PEIRCE’S SEMEIOTIC AND THOUGHT-SIGN THEORY Claudine Tiercelin Peirce called himself “an Aristotelian of the scholastic wing, approaching Scotism, but going much further in the direction of scholastic realism” (CP 5.77 n.) or “a scholastic realist of a somewhat extreme stripe” (CP 5.470). Indeed, “there is a mix of criticism and praise in Peirce’s attitude towards medieval thinkers”1 who showed “a beastlike superficiality and lack of generalizing thought” in their writings on logic (CP 1.560), “a dunsical opposition to the new learning”, “a dreadful corruption of the university” (CP 7.666), were very insufficient in mathematics (CP 3.554), and “set up their idle logical distinctions as precluding all physical inquiry”(CP 6.361). However, as Boler notes, “Peirce’s put down of the humanists’ reaction to the scholastics is, if possible, even more rude”(Boler 2004, 58-59). And most of all, even if the scholastics “can tell us nothing concerning methods of reasoning since their own reasoning was puerile”, Peirce praises “the minute thoroughness with which they examined every problem that came within their ken”(CP 1.560), and the fact that “their logic, relatively to the general condition of thought, was marvelously exact and critical”. Indeed, “their analyses of thought and their discussions of all those questions of logic that almost trench upon metaphysics are very instructive as well as very good discipline in that subtle kind of thinking that is required in logic”(CP 1.15, 1905; my emphasis). In what follows, I would like to make some suggestions about the reasons why the medievals should have retained Peirce’s attention, and the respects in which his reading of them might have not so much “influenced”2 as “stimulated” him in his 1

Boler 2004, 60. I agree with Boler that “it is not an easy task to distinguish cases where Peirce finds something he agrees with in a medieval text from cases where his own position was influenced by such a text” (Boler 2005, 21), even if I think that he sometimes understates the case.

2

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early (Kantian) inquiry “into the logical support of the fundamental concepts called categories”(CP 1.560),3 and in the constitution of his early Semeiotic and thought sign theory.

1. Peirce’s reading of the medievals For quite some time now, the influence exerted on Peirce by the medievals, and in particular by Duns Scotus, has been studied and recognized.4 It is Duns Scotus’s analysis of the Consequentia simplex de inesse and of modalities which provides Peirce with the framework he is looking for in his accounts of logical consequence and possibility.5 But most of all, Peirce chose the Scotistic solution to the problem

3

Peirce is very severe with Kant’s “most astounding ignorance of the traditional logic, even of the very Summulae Logicales, the elementary schoolbook of the Plantagenet era” and holds that “the debonnaire and degagé fashion” he treated logic, was very much responsible for his “most hasty, superficial, trivial, and even trifling” examination of the relation of his categories to his “functions of judgment” (CP 1.560; CP 2.31). 4 Boler 1963 and 2004 and 2005. But, as we shall see, Ockham also played an important role in Peirce’s early metaphysical project (see Boler 1980, Wolter 1978, Tiercelin 1993a) as well, of course, as Kant, Boole, Locke, Aristotle, or Abbot (Tiercelin 1985, 1993a, 2004). See what Peirce says himself of his intellectual itinerary, how he was led from Kant who had greatly impressed him, but in whose reasoning his father the mathematician Benjamin Peirce pointed out to him lacunae, “to an admiring study of Locke, Berkeley, and Hume, and to that of Aristotle’s Organon, Metaphysics, and psychological treatises, and somewhat later drived the greatest advantage from a deeply pondering perusal of some of the works of medieval thinkers, St. Augustine, Abailard and John of Salisbury, with related fragments from St. Thomas Aquinas, most especially from John of Duns, the Scot […] and from William of Ockham” (CP 1.560; NEM 3/1: 161). 5 Peirce wished to modify the too narrow framework of Aristotelian syllogistic (Tiercelin 2004b), so as to inscribe logic within a normative science of good and bad reasonings, which might be applied to dialectic and rhetoric as much as to scientific discourse (CP 2.169-173; cf. Paul of Venice, Logica Parva, 167 ff.). Peirce not only keeps the medieval distinction between deduction and inference, deemed more fundamental than the former, but he distinguishes formal and material illatio, according to the “leading principles” guiding inference, conceived less as mechanical rules than as flexible habits (CP 3.154-166, 3.168; CP 2.588-589). See Perreiah, 45-46. Peirce also sees the fruitfulness of Scotus’s treatment of modalities, thanks to which on can leave the statistic and determinist Aristotelian model by taking account, through the Consequentia simplex de inesse, of the factor of time (hic et nunc) in modality. See Tiercelin 1985, 244, note 90, 1999 and 2004b. The originality on these topics of Duns Scotus who breaks with the principle of plenitude and introduces a new definition of possibility and contingence, has been noted by Hintikka 1981 and examined in

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of universals and conceived his realist scientific metaphysics as an adaptation of the Subtle Doctor’s ideas to the modern times.6 In fact, without a rigourous analysis of Duns Scotus (and his Avicennian background), the nature of Peirce’s realism, which is the key-stone of his philosophy, remains perfectly opaque.7 But the importance of the medievals cannot be restricted to that of the Subtle Doctor. Very early (in the mid 1860s),8 in search of a better logical basis for his metaphysical enterprise, convinced that “one should adopt our logic as our metaphysics” (W1: 690; 1866) and dissatisfied with the logic texts of his time, Peirce reads closely such authors as Roger Bacon, Peter of Spain, Peter Abailard, or William Ockham, to whom he devotes several lectures in November and December (W2: 310-336). When one takes a look at the list of books by medieval logicians which are available in Harvard in 1880, one is impressed by the amount of rare books belonging to Peirce himself (295 volumes), books which he had acquired during his various stays in Europe and which were donated by his wife to the Johns Hopkins Library after his death: among the listed works and authors, one can find such names as: Boethius, Berangarius, Gilbert of Poitiers, John of Salisbury, Averroes, Peter of Spain, Alexander of Hales, Thomas Aquinas (7 books), Roger Bacon, Duns Scotus (five books), Ockham (5 books), Paul of Venice, etc.9 Hence, Peirce’s erudition is not only from secondary sources (as in CP 2.797, where he quotes Sherwood from Prantl, Geschichte der Logik (Leipzig, 1860, vol. 3): he also goes directly to the texts themselves10 (and even takes the liberty to have reservations about the attribution to Thomas of Erfurt (and not to Duns Scotus) of the Grammatica Speculativa.11 The legacy of the scholastics takes various forms: an admiration for the precision of the scholastic method, as may be shown by his ethics of terminology. “To use the scholastic terms in their anglicized forms for philosophical detail by Knuuttila 1993 (who, however, does not mention Peirce’s early interpretation of Scotus along these lines). 6 Boler 1963, Tiercelin 1999. 7 To get a clear picture of this, see in particular the classical book by Boler 1963 and Bastian 1953, MacKeon 1952, Moore 1952 and 1964, Tiercelin 1992 and 1999. 8 For the details about the datations see Michael 1976, 48. 9 For more details see Fisch and Cope 1952, and on the authors and sources which may have been available to Peirce, see Michael 1976, Michael and Michael 1979 and also Boler 2004, 62-64. 10 As in the Memoranda from November 1866 in which he quotes Peter of Spain from the text, or in the review of the Fraser’s Berkeley where, as Boler notes (2004, 63), he clearly has in front of him Scotus’s treatment of universals from Book VII, q. 18 of the Questions on the Metaphysics (Duns Scotus, II, 337-356). 11 Although he was wrong, as the work is now generally attributed to be by Thomas of Erfurt. See Bursill-Hall, 34 n. 9.

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conceptions, so far as they are strictly applicable; and never to use them in other than their proper senses”(CP 2.226). But also, the adoption of the mould constituted by the trivium: Grammar, Logic and Rhetoric.12 First named Symbolistic, Semiotic was divided into Universal Grammar, Logic and Universal Rhetoric (spring 1865; W1: 174), then into General Grammar, General Rhetoric, General Logic (May 1865; W1: 303-304) before becoming Formal Grammar, Logic and Formal Rhetoric in 1867 and, in 1903, Speculative Grammar, Critic and Methodeutic. From the start, as Allan Perreiah has noted, Peirce had a certain view of Grammar such as it had developed among such writers as Roger Bacon, then among the modists in the XIIIth century: a grammar which tried to free itself from the framework of the traditional grammar inherited from Donatus and Priscian still tied to the various species of the languages and their linguistic accidents, and which aimed at universality—and the congruitas of expressions—in exhibiting the general (nominal, verbal or adverbial) characteristics of language.13 From 1867 until the end,14 Peirce kept considering that the different analyses of Semiotic should take account of three levels (terms, propositions, arguments), each level being itself decomposed, for terms, into icons, indices and symbols, for propositions, into true, false and doubtful, for arguments, into deductions, inductions and abductions. On that issue again, Peirce was true to the teachings of the scholastic manuals which would divide logic into terms, propositions and arguments,15 but also of the manuals of rhetoric which, from the Middle Ages to the Renaissance, observed the basic three-fold division of rational discourse.16 However, in keeping with the diversity of interpretations allowed by the scholastic 12

Cf. Michael 1976 and 1977, Perreiah, 46. “In the Roman schools, grammar, logic, and rhetoric were felt to be akin and to make up a rounded whole called the trivium. This feeling was just; for the three essential branches of Semeiotic, of which the first, called grammatica speculativa by Duns Scotus, studies the ways in which an object can be a sign; the second, the leading part of logic, best termed speculative critic, studies the ways in which a sign can be related to the object independent of it that it represents; while the third is the speculative rhetoric just mentioned" (“Ideas, Stray or Stolen, about Scientific Writing”, EP2: 326-327, 1904). 13 See Perreiah, 43 who quotes Roger Bacon: “Grammatica una et eadem est secundum substantiam in omnibus linguis, licet accidentaliter varietur” (Gram. Graec. Oxford Ms, ed. Charles, 278), quoted by Bursill-Hall, 12. See also: 26 ff. 14 Cf. Fisch 1978, in Fisch, 323-324. 15 Peter of Spain, Summulae Logicales, William of Sherwood, Introduction to Logic, Paul of Venise. Perreiah, 43. 16 Perreiah, 43, who observes that a difference should be noted here between the grammarians who mainly insisted on the first two domains (partes orationis and compositiones) and the rhetoricians (like Lorenzo Valla) who discussed about spoken discourse under the three headings.

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consequence,17 Peirce also claims that “the relation between subject and predicate, or antecedent and consequent, is essentially the same as that between premises and conclusion” (CP 4.3). Which amounts to admitting that, finally, the distinction between terms, propositions and arguments is less false than useless (CP 2.407 n. 1; CP 3.175) since the basic relation is the illative relation (CP 3.175; CP 2.44 n. 1).18 However, it is undoubtedly at the level, both of Peirce’s interpretation of Logic, concerning, in particular the relationships between grammar and logic, and of his ambitious project of a new model of the mind, a model which should no longer owe anything to psychologism, and yet should account for some facts of psychology, by a formally regulated use of signs and meaning, that one can see how deep and subtle the medieval stimulation may have been. In what follows, we shall try to understand how Peirce’s reading of the medievals may have been an incentive both for his elaborate conception of Logic or (Semiotic) and his theory of thought-sign, and consequently, for the constitution of pragmatism itself, if one recalls that, according to his founder, pragmatism was nothing but the development of the following two key-ideas: 1. Pragmatism entirely grew out from formal logic (CP 5.469). 2. It is the view that “every thought is a sign” (CP 5.470).

17 Indeed, for the medievals, “a consequentia may be a conditional proposition or the relationship between the antecedent and the consequent in a conditional proposition. It may be an argument or the relationship between the premises and conclusion of an argument, which may be called, confusingly, ‘a rational proposition’. A consequentia may be an immediate inference—e.g. “No S is P; therefore no P is S”—or an enthymeme—e.g., “Socrates is a man; therefore Socrates is an animal”—or a fully expressed syllogism in the object language—e.g., “If every M is P and every S is M, then every S is P”—or, finally, as a disconnected series of propositions arranged as premises and conclusion expressed in the meta-language—e.g., “A, B; therefore C”. (Boh, 300-301). Like Duns Scotus, Peirce does not draw a distinction between “if p, then q”, and “p entails q”. 18 “We may say that the purpose of signs—which is the purpose of thought—is to bring truth to expression. The law under which a sign must be true is the law of inference; and the signs of a scientific intelligence must, above all conditions, be such as to lend themselves to inference. Hence the illative relation is the primary and paramount semiotic relation. It might be objected that to say that the purpose of thought is to bring the truth to expression is to say that the production of propositions rather than that of inferences, is the primary object. But the production of propositions is of the general nature of inference, so that inference is the essential function of the cognitive mind” (CP 2.444 n.).

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2. A new definition of logic and of its tools: second intentions and suppositio Peirce quickly realized what a revolution19 the medievals had accomplished in the domain of the reflexions between thought and language, and that it was in their works (more, finally, than in Locke’s representationism)20 that he was most likely to find the rhetorical means he needed to work out the general “semantization” of thought he had in mind,21 in the form of what he had himself called, following beside the medievals, the inspiration of both Kant and Boole,22 a “logical analysis of the products of thought”.23 In them, he finds “the habit of thinking in signs”, which he was soon to take as the definition of pragmatism, namely “a philosophy which should regard thinking as manipulating signs so as to consider questions” (NEM 3/1: 191). Now, for a scholastic, to claim that thought is a sign, simply means that thought “is of the same general nature” as a sign. As Peirce wrote in 1871 in the Fraser’s review of the Works of Berkeley: Ockham always thinks of a mental conception as a local term, which, instead of existing on paper, or in the voice, is in the mind, but is of the same general nature namely, a sign. The conception and the word differ in two respects: first, a word is arbitrarily imposed, while a conception is a natural sign; second, a word signifies whatever it signifies only indirectly, through the conception which signifies the same thing directly (W2: 472).24

Now this should first permit an extension of the sphere of logic. Despite his “devotion” to him, Peirce holds that Kant limits logic to a much too narrow theory of concept: indeed, if all symbols “are in one sense relative to the understanding”, “on this account, the relation to the understanding need not be expressed in the 19

This should not come as a surprise, as more than anyone else before, the scholastics devoted a very close examination to the various uses of signs and to the relationships between language, thought and reality. See de Rijk, 161. 20 See W1: 172-174 (1865). Short, 216. 21 “Sémantisation” is the term used by Panaccio, 71, who analyzes the constitution of the problematic of mental language (oratio mentalis) in the Middle Ages, and shows in what respect it is close to some contemporary debates (such as J. Fodor’s concept of mental language). 22 On the importance, then, of Boole who, like him, “plainly thought in algebraic symbols” and regarded “thinking as consisting not necessarily in talking to oneself”, see Tiercelin 1993a, 42-46. See NEM 3/1: 161; 191; 227; 298; 313-314 (1865); W1: 404 (1866). 23 For more details on the nature and aims of this project, see Tiercelin 1993a, in particular 27-57. 24 See Ockham, Summa Logicae I, 1, 50.

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definition of the sphere of logic, since it determines no limitation of that sphere” (W2: 56). Thanks to symbols, one can extend logical analysis to what is virtualiter or habitualiter—a distinction borrowed, according to Peirce, from Duns Scotus (CP 5.504 n. 1) and which will be fundamental in the completely elaborate pragmatism. Secondly, as the emphasis is now laid on the symbolizing process itself, independently of the fact of thinking itself, it becomes possible to avoid any intrusion of the psychological in the logical, which is highly desirable, since “we ought to adopt a throroughly unpsychological view of logic”(W1: 164).25 Logic is now “said to treat of second intentions as applied to first”, the second intentions being “the objects of the understanding considered as representations” and the first intentions to which they apply being “the objects of those representations”. This is the view formulated as early as 1867 in On a New List of Categories which states that: The objects of the understanding, considered as representations, are symbols, that is, signs which are at least potentially general. But the rules of logic hold good of any symbols, of those which are written or spoken as well as of those which are thought (W2: 56).

Why does this enable a logical (and non psychological) analysis of the products of thought? Because symbols can now be treated as signs or logical terms, and the analysis be centered no longer on the kind of entities they are, that 25 One should be aware of Peirce’s very complexe position on that issue (see Tiercelin 1993a, 29-41: briefly 1) He was absolutely against psychologism in logic if it meant that logic should be based on or derived from any psychology (in the mainly Anglo-Scottish or German) sense of introspection, association, intuition, sense data, consciousness, Gefühl, faculties, etc.): on this, see W1: 63; W1: 164-167; CN 1: 23-37; CP 1.310; CP 2.40-43; CP 2.47; CP 5.85; CP 5.157; CP 5.244-249; CP 5.265; CP 7.376; CP 7.419-425; CP 8.144; MS 633; MS 645. 2) He had nothing against experimental psychology (in the sense of Wundt or Fechner) of which he was himself (even before W. James) an actor (see Cadwallader, 173), and which he never gave up (see Fisch and Cope, 292): see also the 1868 papers, “How to make our ideas clear” and “The Fixation of Belief”; and CP 8.196; CP 7.597; MS 891; MS 919-930; W3: 111-137; W3: 382-493. 3) He always found it necessary, both not to use the “untrustworthy” psychology of introspection and to verify, for instance, that the deduction of categories was in keeping with “empirical psychology”. 4) He had a conception (partly inherited from his interpretation of the theories of evolution) of normativity and of the relations between norms and nature which allowed him to see logical laws and norms more as emerging from nature than as radically distinct from it, in the sense of a kind of natural logic (see Tiercelin 1997). 5) He thought that, for Kant and the writers of the classical age, it was not so decisive to separate logic from psychology, insofar as, for them, logic, viewed as the science of the forms of thought in general was, despite its ambiguities, hardly different from a logical analysis of the products of thought (W1: 306; MS 726).

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is, “may be sounds, marks, or mental states or images (‘intentions of the soul’)” but on “the use made of them in forming statements about things which they are not” (Moody, 18). In defining the domain of logic as that of second intentions, Peirce takes for his own count the advances accomplished by the via moderna: the adoption of “what might be called a ‘metalanguage’ or ‘syntax language’ in relation to the ‘object-language’”, since “such terms of second intention abstract wholly from the meaning or ‘material content’, of the terms of first intention for which they stand, characterizing the latter only by their formal properties as constituents of statement” (Moody, 27).26 Peirce is convinced that by adopting such a view of second intentions as applied to the first intentions, “thoughts of thoughts”, we do not study the properties of thought themselves: we merely study the properties of the object as an object of thought, or the ways in which an object can be a sign. Very rightly, Peirce took Ockham to be the one who, although he did not invent it, yet rendered more precise and elaborate the logical instrument of supposition, “one of the useful technical terms of the middle ages which was condemned by the purists of the renaissance as incorrect” (W2: 243, n. 1), which enabled to treat the sign merely in its capacity to stand for something in virtue of its being combined with another language sign in a proposition (cf. Ockham, Summa Logicae I, 63, 188-189), thus leaving aside the significatio of the sign. But suppositio presents another advantage which often tends to be underestimated when one stresses—as Moody does—the formal (or syntactical) character of the new logic: indeed it functions as a semantic tool. This is why, in particular, Ockham’s mostly focuses on suppositio personalis, in a word, on reference. Thus, formalizing the sign does not mean (for Ockham nor for Peirce) any reduction of semantics to syntax: it only means—and for Peirce this is even provisional27—that the signification of the sign, that is, of what the sign would 26

As is well known, for the medievals, second intentions are those terms which, in their significative usage or in personal supposition—i.e., such as in their normal interpretation, they serve as signs to the things which they have been instituted to signify, contrary to the suppositio materialis, in which terms are interpreted autononymously as a name for itself— stand for language signs: thus, such words as “term”, “proposition”, and (at least in the 14th century) “universal”, “genus”, “species”, “property”, etc. are words whose domain of significance is that of language signs. On the contrary “those terms which, in their normal or significative usage in personal supposition, cannot stand for things which are language signs (i.e., as signs, though they may stand for them as instances of physical objects or mental states), were called terms of first intentions; such terms are those like ‘stone’, ‘tree’,’blue’, etc.” (Moody, 26). 27 Provisional indeed, for, as we shall see, Peirce will develop a whole theory of the pure meaning or signification of the sign—Speculative Grammar being defined as “the general theory of the nature and meanings of signs” (CP 1.191)—which, incidentally, closely

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pretend to say about itself or about the world, independently of its simply functioning as a sign, is left aside. Now logic is supposed to deal with the relationships of signs to their objects: in that respect, what counts is to see how a sign is supposed to “represent” or “stand for” an object in a proposition.28 Therefore, in analyzing the sign and the sign-relation in terms of supposition, Peirce emphasizes its formal and semantic characteristics and provides a systematic analysis of the sign-relation within the framework of a radical “semiotization” of the mental, but also, in turn, of an irreductible “mentalization” of the sign.

3. The role of the scholastic model within Peirce’s analysis of the sign-relation or the impossible identity between thought and sign “We have no power of thinking without signs” (W2: 213) is presented in the second of the three 1868 papers as the third consequence of the criticism of intuition and, more generally, of “the spirit of cartesianism”,29 which reveals a number of crucial points concerning, for example, the genesis of selfconsciousness or the importance of language in the constitution of the self. The self is not at all the place of a priviledged monologue between us and the external world. The self, which is supposed to be the manifestation by excellence of privacy, gets constituted as a dialogue with it. Refuting in advance Fodor’s thesis of methodological solipsism—which identifies contents to particular internal states of information processing—Peirce strongly rejects any conception of the mental which would be represented, in Putnamian terms, as “meanings in the head”30 and

resembles the central concept of significatio in Speculative Grammar, such as the Modists were to use it, who distinguished the various ways in which the mind signifies (modi significandi) when it knows particular objects (see Perreiah, 44). 28 Although there are many ways in which a term may have supposition, there are three basic forms, that is: 1. when it stands for itself or its equiform as a language sign (materialis suppositio); 2. when it stands for its signification (suppositio simplex). 3. when it stands for some individual or complex of individuals (suppositio personalis). As Perreiah notes (45), this is very close to Peirce’s discussion of the various ways in which a thought sign is supposed to stand: “A sign has, as such, three references : 1st, it is a sign to some thought which interprets it; 2nd, it is a sign for some object to which in that thought it is equivalent; 3rd, it is a sign, in some respect or quality, which brings it into connection with its object” (W2: 223). 29 W2: 193-272. I have analyzed these papers in detail in Tiercelin 1993a, 56-118. 30 See for example Putnam 1988. Generally speaking, Putnam is to Peirce what Fodor is to Ockham: contrary to both, and for reasons which are often strangely close to those of

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comes close to the famous thesis invoked by Plato in the Theetaetus according to which thought proceeds as a dialogue and a necessary communication (189e190a). Even where language might be thought not to be necessary in the exercice of thought, one does in fact always think in language, not at all because language would be a conveying form of thought, but because on the contrary it is its “matter”, “in the sense in which a game of chess has the chessmen for its matter”: Not that the particular signs employed are themselves the thought! Oh, no; no whit more than the skins of an onion are the onion (About as much so, however). One selfsame thought may be carried upon the vehicle of English, German, Greek or Gaelic; in diagrams, or in equations, or in graphs: all these are but so many skins of the onion, its inessential accidents. Yet that the thought should have some possible expression for some possible interpreter, is the very being of its being […] (CP 4.6).

In other words, just as if the chessmen disappeared, one could not even go on playing; just the same, if there were no signs, there would be no thought. This is why “just as we say that a body is in motion, and not that motion is in body we ought to say that we are in thought and not that thoughts are in us” (W2: 227, n. 4, cf. CP 2.26). As early as 1868, such a conception of thought as pure semiotic expression and as a dialogue introduces to the social principle of logic as a theory of information and communication which Peirce’s Speculative Grammar will elaborate in the form of an original theory of assertion.31 The second major consequence of the criticism of intuition is the claim of the necessarily continuous character of knowledge. From the fact that every cognition is necessarily determined by a previous cognition, ideas follow one another in a continuous process. “If we seek the light of external facts, the only cases of thought which we can find are of thought in signs. But […] only by external facts can thought be known at all. The only thought, then, which can possibly be cognized is thought in signs. But thought which cannot be cognized does not exist. All thought, therefore, must necessarily be in signs” (W2: 207). Strictly speaking, Peirce does not claim that thought is a sign, nor does he claim a straightforward (idealistic) identity between thought and sign. He most of the times says that “thought must be in signs”. However he happens to write that thought is a sign— even if he often qualifies this or uses analogies as that of the onion (CP 4.6)—, or even views man as a sign (W2: 240-241). Indeed “thought and expression are really one” (CP 1.349) so that, finally “the man and the external sign are identical, in the same sense in which the words homo and man are identical. Thus my Peirce, Putnam finally refuses to go too far in the direction of a naturalist (as well as internalist or functionalist) semantization of the mental. See Tiercelin 2002a, 75-84. 31 See Brock 1975; Tiercelin 1993a, 258-334.

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language is the sum total of mysef; for the man is thought” (W2: 241). “The wool and warp of all thought and research is symbols, and the life of thought and science is the life inherent in symbols; so that it is wrong to say that a good language is important to good thought, merely; for it is of the essence of it” (CP 2.220). However, even if he admitted in 1892, that he gave a “too nominalistic” sounding to his analysis (CP 6.103) and, in 1905, that he went a little too far towards idealism, when he claimed “that a person is nothing but a symbol involving a general idea” (CP 6.270)—he never really changed his mind about the deep meaning of the theory. So how should we interpret it? It is here that the scholastic inspiration may have been decisive in that it allows, through the sign-relation, a new possible reading of the relationships between thought and language. Indeed a complete remelting of the traditional subjectpredicate relation32 is operated in the New List, through a renewed deduction of the categories. The subject is now taken as “a sign of the predicate”. But what does it mean? First, that, as for the medievals, the sign relation does not introduce a relation of signification from a term to an object or to a psychological designatum. There is no identity, mimesis, causality or inherence between subject and predicate: it is rather a term to term relation, which, moreover, as is the case with Ockham, is not realized between absolute terms, but between absolute and connotative terms, that is, terms such as they “signify one thing primarily and another one secondarily” (Ockham, I, 5-9, 57-69), and such that they have a “nominal definition”.33 As a consequence, such terms do refer to individual objects, but they do it in an indirect or “oblique” way, by referring to a signification. Thus it may be said that they signify primarily the individual objects and secondarily those objects on the basis of that signification. To assert that the same thing is said by “the stove is black” and “there is blackness in the stove” (W2: 50), is to say that black refers to the 32 Boler draws argument from this (2004, 64), and from the fact the Modists stuck to the traditional subject-predicate form, to suggest that the commentators (Michael 1976 and Kloesel 1981) are exaggerating the influence of the Modistic model (Scotus/Erfurt) of Speculative Grammar on Peirce whose interest in the topic lay mostly in his identifying Speculative Grammar with “Erkenntnisslehre”, an idea he more likely got from Kant than from Scotus/Erfurt. While this is indeed partly true, I think Boler underestimates the contribution of the Scotistic model as when he says that “while Peirce refers to the medieval work frequently, he never quotes from it or even gives exact citations”. There is at least one passage from the lectures on the British Logicians (1869) where the Grammatica Speculativa is translated extensively (the first six chapters) (W2: 321-327), and followed by a comparison between the Modists’s and Ockham’s models. 33 See Peirce’s praise of the distinction in CP 2.393: “The whole deserves to be read”. Michael 1974 has shown the importance of Peirce’s early reading of Ockham’s analysis of connotative and relative terms for his own account of relatives and relations.

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stove on the ground that it embodies a quality, blackness, or again, that black may be viewed as directly referring to the stove, or referring obliquely to blackness (Michael 1976, 50). Second, such a process allows us to say that “embodying blackness is the equivalent of black”.34 But why? Precisely for reasons which have to do with Peirce’s interpretation of abstraction and which were already emphasized by the medievals.

4. The medievals on hypostatic and precisive abstraction Indeed, there. are two current ways of abstracting, which Peirce rejects from the start: on the one hand, dissociation, or “that separation which, in the absence of a constant association, is permitted by the law of association of images. It is the consciousness of one thing, without the necessary simultaneous consciousness of the other”. (W2: 50). But it is to be proscribed, for it is to much related to imagination and psychologism and leaves many phenomena unexplained. It is because they remained submitted to it that the nominalists (such as Berkeley and Locke) confounded together “thinking a triangle without thinking that it is either equilateral, isosceles, or scalene, and thinking a triangle without thinking whether it is either equilateral, isosceles, or scalene” (W2: 235).On the other hand, abstraction may be viewed as a mere “mental separation” or discrimination, as when we discriminate red from blue, space from color and color from space. But then, we only realize a logical operation which has to do merely with “the essence of terms” or “distinctions in meaning” (W2: 50; CP 2.428) and teaches us nothing about what terms refer to. However, there are two other forms of abstraction, on which the medievals drew attention: namely, hypostatic or “subjectal” abstraction and prescisive abstraction. The former allows to change a transient object of thought into a substantive: what we formely thought of now becomes an object of thought, as when we pass from “the library building is large” to “the library building has largeness” (CP 4. 332). It thus becomes possible to study the relations of these new objects of thought in applying them new predicates. For example, we can say of the largeness of the library that it is impressive (CP 4.332; CP 4.235). Once

34

Peirce notes that “this agrees with the author of de Generibus et Speciebus”, and quotes the V. Cousin edition Ouvrages Inédits d’Abélard, 528 (W2: 52, n. 1). This is perfectly true. See in particular Abailard, Logica Ingredientibus, part I in McKeon, 246-250. For a more detailed comparison between both, see Tiercelin 1994, 106.

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abstraction is thus understood, i.e. neither as a mere verbal transformation, nor as a kind of universal, it becomes one of the most useful tools of human intelligence.35 The second useful form which abstraction can take is called by Peirce prescision or precisive abstraction, a term which is borrowed, in his own words, from the medieval (and in particular Scotistic) notion of praecisio.36 Compared

35 Not only in mathematics where it enables, by susbstitution, to make the operations the very subjects of the operations (CP 4.235; CP 3.462; NEM 4: 11-12, 49, 161-162), but everywhere in science (biology, chemistry; CP 1.383; CP 3.509; CP 6.382; CP 4.171; CP 5.161; CP 5.447 n.). Abstraction may neither be reduced to mere verbal transformation—as when one explains why opium makes people sleep because it has a dormitive virtue (NEM 4: 11)—nor compared with some hypostasis—it would amount to believing that you could “load a pistol with dormitive virtue and shoot it into a breakfast roll”. For “though it is in opium as wholly and completely and entirely in every piece of opium in Smyrna, as well as in every joint in the Chinatown of San Francisco”, ”it has not that kind of existence which makes things hic et nunc. Why, it consists in something being true of something else that has a more primary mode of substantiality” (NEM 4: 162). Against the nominalists, the medieval realists were right in finding some reality (realistas) to that kind of abstraction. Not only can one treat the statement that opium puts people to sleep as “an induction from many cases in which we have tried the experiment of exhibiting this drug, and have found, that if the patient is not subjected to any cerebral excitement, a moderate dose is generally followed by drowsiness, and a heavy dose by a dangerous stupor”, which is “simply a generalization of experience and nothing more”, but one can even go further, for indeed, one is convinced that “there must be an explanation of the fact”, and “to fix our ideas”, tries, for example, to find “some relation between a part of the molecule of morphine or other constituent of nerve-protoplasm as to make a compound not so subject to metabole as natural protoplasm”. One can also envisage another type of explanation. At any rate, somehow or other, one takes things as if there were some secularity in opium which, were it understood, “would explain our invariably observing that the exhibition of this drug is followed by sleep” (NEM 4: 161.) It is then to science to establish the practical or sensible consequences which would render the statement true. So, by “reality” of an abstraction, nothing else is meant “except the truth of statements in which the real thing is asserted” (NEM 4: 164; cf. CP 4.463), in other words, “the truth of an ordinary predication” (CP 3.642). And this is why the determination of the reality of abstraction lies, in the end, upon the truth or falsity of pragmatism itself. Peirce insists a lot on the heuristic value of abstraction in that sense: one does not claim that all abstractions are real, but only that some of them are. So when one posits an abstraction, one merely tries to consider that there is “some explanation behind the fact” (NEM 4: 11). In that manner, it is possible to make reasoning progress, thanks to the generalizations which are then permitted (NEM 4: 210). 36 See the note from the article “Precision” from the Baldwin Dictionary note 1 of CP 1.549. It is taken in that sense in Boethius, and constitutes, incidentally, one way of solving the problem of universals (see for ex. In Isagogen Porphyrii Commenta, in Corpus Scriptorum Ecclesiasticorum latinorum, vol. 48, 135-139, in McKeon, vol. 1, 96-97). And of course, it

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with discrimination, precision implies more: I can indeed, by an act of discrimination, “separate color from extension; but I cannot do so by precision, since I cannot suppose that in any possible universe color (not color-sensation, but color as a quality of an object) exists without extension. So with triangularity and trilaterality” (CP 1.549 n.). But it implies “much less than dissociation, which, indeed, is not a term of logic, but of psychology”. There is something more in precision, which takes us away both from the domain of psychology and from mere logical or verbal distinctions and which directs us, so to speak, toward the real. It is “the act of supposing (whether with consciousness of fiction or not) something about one element of a percept, upon which the though dwells, without paying any regard to other elements” (CP 1.549 n.). Now this is something which had been particularly stressed by the medievals, who had made considerable advances in the theory of abstraction (and, as a consequence, in the solution of the problem of universals), when they insisted that abstraction is not merely an operation consisting in drawing one’s attention away from an object, or in simply drawing one element of thought–form–away from the other element–matter–which last is then neglected, in other words, in “the contemplation of a form apart from matter, as when we think of whiteness”, but rather an operation consisting in “thinking a nature indifferenter or without considering its individuals, as when we think of a white thing in general” (CP 2.428). On this Abailard had many fruitful suggestions and had noted that though being “alone, naked and pure”, abstraction understood in that way was not “empty”. For as was noted by him after Boethius, the mind could thus “both compound that which was disjoined and resolve that which is composite, departing nevertheless in neither from the nature of the thing, but only perceiving that which is in the nature of the thing. Otherwise it would not be reason, but opinion, that is, if the understanding should deviate from the state of the thing” (Abailard, 247-248). In that respect precision is mid-way between the logical and the psychological and signifies the real. Indeed it comes from the “attending to a part of an idea and neglecting the remainder” (CP 2.428) but it involves also mental operations which are more “complicated” than mere attention (CP 1.313 n.; CP 2.428). Now we can see why “embodying blackness is equivalent to black”, without implying any hypostasis of a universal (as is shown by the references to texts by John of Salisbury or Abailard (W2: 52; CP 2.415): to think that “there is blackness in the stove”, is to think about a nature, indifferenter, without regard to the differences of its individuals, as when we think of a black thing generally. One simply substitutes a substantive here to an adjective by creating indeed an ens rationis, but without committing oneself to its realitas. Such a procedure merely is found in Abailard who also develops an interesting conception of the image in the process of abstraction. See Logica Ingredientibus, part I.

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furnishes us “the means of turning predicates from being signs that we think or think through, into being subjects thought of. We thus think of the thought sign itself by making it the object of another thought-sign. Thereupon, we can repeat the operation of hypostatic abstraction, and from these second intentions derive third intentions” (CP 4.549). Subjects and predicates, therefore, are not, strictly speaking, concepts, but rather, hypotheses (W2: 52). But we now have a better grasp of the way in which the sign relation 1) can find itself mid-way between logic and psychology, 2) continue to work as a sign towards things (hence in a realist and not merely nominalistic way) 3) and yet remain formal.

5. The semiotization of the mental and the mentalization of signs All this tends to show that Peirce’s interpretation of the subject-predicate relation as a sign relation as such is in no way original.37 What makes it so, of course, is the richness of his analysis and the implications which he thinks may be drawn from this, on which we can only be very brief. 1) As soon as we form a proposition and assign qualities to things, we do not merely “read” some given reality, as from a wide open book, so to speak, we already interpret.38 I look at a black stove. There is a direct sensation of blackness. But if I judge the stove to be black, I am comparing this experience with previous experiences. I am comparing the sensation with a familiar idea derived from familiar black objects. When I say to myself that the stove is black, I am making a little theory to account for the look of it (MS 403: 92).

So a sign never denotes its object directly or dyadically39 but only in virtue of another sign—which is not necessarily a mind—interpreting it as doing so. As

37

One can also find in Boethius of Dacia interesting developments along such lines. See Stump, 285. 38 I cannot go into more detail on Peirce’s theory of perception and abduction here. Briefly, Peirce views perception as something in which there is no strict demarcation between the percept itself, the percipuum and the perceptive judgement: “If the percept or perceptual judgement were of a nature entirely unrelated to abduction, one would expect that the percept would be entirely free from any characters that are proper to interpretations” (CP 5.184). But, as a matter of fact, “the perceptive judgement and the percept itself seems to keep shifting from one general aspect to the other and back again” (CP 5.183) so that “abductive inference shades into perceptual judgment without any sharp line of demarcation between them” (CP. 5.181). See Tiercelin 2005b.

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early as 1867, Peirce defines the sign-relation in terms of such a ternary relation: the reference to an object is made possible by a representation (its “interpretant”) which interprets it, with respect to such and such aspect which has been prescinded or abstracted (its “ground”) (W2: 553; CP 2.228). Any genuine synthesis involves a sign-relation for which three categories are indispensable, the functions of which the method of suppositio has rendered plainly manifest: the reference to the object (Quality), the reference to the ground (Relation) and the reference to the interpretant (Representation). In other words, “when we think, we, ourselves, as we are at that moment appear as a sign” (W2: 223). 2) One does not have to adopt an external stance in appealing, for example, to some consciousness, mind or even God, to “inject” meaning from the outside, to “animate” so to speak the signs, in order to endow them with life (CP 2.222). If the sign as such is not indeed meaning, the sign-relation, on the contrary, is sufficient, as such, for meaning to take place. What really counts is not so much the sign (nor the various classes of signs, nor even “Semiotic” as a separate domain), but sign in action.40 3) Thought being a sign, one can understand the semiotization of the mental in the following way: thought is a sign which refers not to an object, but to another thought which is its interpretant sign, this one referring in turn to another thought sign which interprets it in an endless continuous process. “Each former thought suggests something to the thought which follows it, i.e. is the sign of something to this latter” (W2: 223-224). 4) The semiotic process is a three terms relation: a sign is a thing related in some respect to a second sign, its object, so as to relate a third thing, its interpretant, to this very object, and thus indefinitely. But, as can be seen from the New List, such a triadicity has been made obvious by the logico-categorial analysis itself, through the process of supposition, which has identified three irreducible and distinct categories.41 5) Such an ontological and realistic conception of the sign-relation implies that if thought and expression are one, it is not only because thought would be, so to speak, explained and absorbed by the semiotic process (it would amount to nominalism).The analysis is also true the other way round: namely, what the logico-categorial analysis highlights is the fundamentally intelligible (because irreducibly triadic, and mediating) dimension of the sign relation, correctly 39 This is one of the central objections he makes to Berkeley’s otherwise quite successful theory of signs. See Tiercelin 1987, 48. 40 Or “Semiosis”. See Fisch, 330; Tiercelin 1993b, 43 ff. 41 Which means that it is perfectly impossible to dissociate Peirce’s semiotics from his ontology, and, in particular, from his very specific ontological realism of vagueness. See Tiercelin 1991, 1992, 1993b, chap. 2.

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understood.42 “If you take any triadic relation, you will always find a mental element in it. Brute action is secondness. Any mentality involves thirdness” (CP 8.331). Therefore, just as Peirce’s model of the mind is semeiotic, semeiotic cannot be viewed except as an irreducibly mental and intelligent process (Tiercelin 1993a, 197 ff).

6. Terminists or Modists? An impossible choice One of the difficulties raised by the evaluation of the importance the scholastics had on Peirce’s early thought is the following: there is an obvious mixture of Terminist and Modistic (if not Scotistic) elements in Peirce’s first approaches to semiotic and mind, although this does not seem to be a problem for him. Now, as is well known, not only did such authors defend opposite positions as far as the realist-nominalist solution towards the problem of universals is concerned, but they clearly did not have a common attitude with respect to semantic issues or to the nature of the relations between language, thought and reality. One can hardly forget that during the XIIIth and XIVth centuries, there were lively debates on the question of meaning and signification between Terminists (Ockham) and Modists (Boethius and Martin of Dacia, Radulphus Brito, Siger of Courtrai, Thomas of Erfurt, etc.), and that one consequence of Terminism was to “shave” such superfluous entities as the modi significandi (a fundamental principle for the construction of the Modistic grammar).43 From what we have said above, it is rather easy to understand why Peirce may have felt close to Ockham, as can be seen from his 1869 Harvard lecture: as has been often noted, Ockham was indeed one of those who, through the development of terminist logic, and of the powerful metalinguistic instruments of the “supposition” made it possible “to analyze the formal structure of language rather than to hypostatize this structure into a science of Reality or of Mind” (Moody, 6).44 However, if Peirce is so interested by the Venerabilis Inceptor, it may also be because he has seen that Ockham’s logic is not a mere scientia sermocinalis—as it is too with Duns Scotus—but a scientia rationalis, and that what is characteristic of such a logic is not only to be a logic merely interested, among signs, on terms, or emphazising, among the various signifying functions of signs, that of supposition (Ockham, I, 33); but also to be a logic based on the view of a natural 42

Lack of space forbids me to study this in more details. See Tiercelin 1993a, 194-223. Rosier, 239 ff. 44 Contrary, for ex. of what will be the case with the Port Royal Logic, in which what remains essential is to study the ways men use signs to signify their thoughts and judgments. 43.

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and prior mental language. Peirce saw that part of the Ockhamist revolution lay in the systematic elaboration of the oratio mentalis view: in other words, in that moment when language is no longer taken–as was the case in Antiquity–as pure logos, a mere vehicle of thought which, through words and prior to them, goes directly to things; a moment also when one no longer simply refers, as did Augustine, to a verbum mentis, affected in the end by the immaterial divine light, more a vision than speech, and also “prior to all signs”. With Ockham, as Panaccio notes, thought (or concept) “becomes the priviledged depositary of meaning”, no longer identified with what is signified by signs, but what actually signifies (Panaccio, 73). While with such authors as Abailard, it was still the word (the name) that signified—intellections could not be signs—“Ockham puts language into the mind”,45 and it is the concept, not the word, which becomes the first bearer of meaning. As a consequence, thought itself is viewed as a language, to which one can directly apply the apparatus of Terminist logic, with its notions of signification, connotation, supposition, etc. (Panaccio, 71). Today it is easier to appreciate the advantages of such an attitude. First the hypothesis of a mental language allows Ockham to avoid such abstract entities as propositions, in Frege’s sense, or properties. One can merely view intentional states, beliefs, for example, as “relations between the individual mind and some concrete and individual psychological entities (the mental symbols) rather than as relationships to extramundane, immutable and disembodied objects”. Ockham thinks he can use this for a direct analysis of cognitive activity: since concepts are bearers of a natural meaning, they can combine so as to form, according to a precise syntax, mental propositions which are structurally similar to sentences. Second, one can also apply to them, in the very rich language of suppositio, the notions of truth and falsity, on the model of spoken or written propositions (whose truth value, incidentally, is derived, compared with that of the mental proposition). Ockham thus comes to a genuine logical analysis of inner thought, to a “formal theory of pure thought”, built onto a logically ideal language endowed with a simple syntaxic structure, devoid of any equivocity or synonymy, which opens the way to a precise characterization of the structure of knowledge. As Panaccio notes: “The new approach possessed, in the field of medieval knowledge, an impressive unifying power: it harmonized in a very natural way the verbum mentis of the theologians to the oratio mentalis of the old logicians, and it articulated together at the same time logic, theory of knowledge and theory of meaning”(Panaccio, 7078). For someone who, like Peirce, was looking for an analysis of thought that would not indulge in psychologism and remained both formal and true to the framework of scientia rationalis, such a program could only be attractive. 45

Jolivet, 167.

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However, as we saw, at the time when he acknowledges his preferences for Ockham, and follows him both in his deduction of categories—directly led by means of the suppositio—and in his analysis of relative terms, Peirce also recalls that his aim is that of a Speculative (also named: Formal) Grammar, and it is also Duns Scotus46 whom he follows both in his interpretation of the argument as a consequentia simplex de inesse and in the identification between categorical and hypothetical propositions.47 He even goes so far as to write that, although Ockham’s view is “much more simple and lucid”, it is “much more certain Scotus’s complex theory is to take into account all the facts than Ockham’s simple one” (W2: 327), hence to become a genuine Philosophy of Grammar. Let us recall that the doctrine of the Modists turned around the five following basic principles: 1) The signified of a word (significatum) is distinct from its mode of signifying: before, for example, signifying in the singular or in the plural, the sound (vox) must first signify, (this is at the foundation of the distinction between dictio and pars orationis). 2) The mode of signifying, modus significandi, is principle of the construction, of the grammatically correct conjunction of the words within the sentence or congruitas. 3) Intervening at both semantical and syntaxical levels, the modus significandi belongs to the pars orationis composed by “the sound, the signified and the mode of signifying”(John of Dacia), but can also be “a property of the thing signified” (Thomas Erfurt). 4) For the Modists—who agree with the Aristotelian inspiration—there is a ternary correspondence between the modes of being (modi essendi), the modes of knowing (modi intelligendi) and the modes of signifying (modi significandi), which allows, by an interplay of formal distinctiosn and real identities, the articulation of being, thought, and language. 5) Finally, as there is such a parallelism between the three modes, there must exist a general grammar, constituted by the essentialia grammaticae. Whence it follows that Boethius of Dacia considers that there is but one grammar, just as there is but one logic.48 46

It should be clear that, in following the Grammatica Speculativa, strictly speaking, Peirce follows Erfurt and the Modists and not Scotus (who may not even be characterized as a Modist, even if he had some views close to them and developed himself, if not a theory, interesting personal reflexions on the philosophy of language and on semantic issues). See Perler 2003. 47 See in particular CP 3.175; NEM 4: 171; NEM 4: 365. Our reluctance to do so comes from our tendency to think that the logical structure of the categorical proposition corresponds to a grammatical structure, and to think that logic is but a “reformulation” of ordinary language. Now, like the Modists, Peirce thinks logic and grammar should be distinguished, since “appeals to language can serve no other purpose than as most inadequate and deceptive evidence of psychological necessities or tendencies; and these psychological necessities and tendencies, after they are ascertained, are utterly useless for the investigation of logical questions” (CP 2.70). 48 Jolivet, 164-165.

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We may have here some of the reasons why Peirce might have found both approaches attractive and not totally incompatible for him. Indeed Terminists often blame Modists for favoring grammar instead of logic, and for multiplying entities praeter necessitatem. Now, although Peirce also stresses the necessary distinction between the logical and the grammatical levels, he does not see why, provided it is not confined to a study of the empirical (rhetorical, poetic) accidents of the languages, but extends to a general grammar, such a grammar might not be a priori as rigorous or “exact” as logic (see CP 3.430). Now, such was the aim of the grammar of the Modists: it had a scientific, demonstrative and universal, and we should add, normative49 ambition: it did not aim at the study of meaning but at the analysis of the conditions which had to be satisfied in order for meaning to be produced, which involved a study of the constructibles and of the rules of construction (Rosier, 44). One could indeed object that the greater importance given by the Modists to language than to thought might be a problem for someone like Peirce, engaged as he was, in the wake of Kant, in the elaboration of the logical forms of judgment. But if such is not the case, in the end, it is probably because, for him, the Modists less advocated the view of some consistency proper to language than they explained its universality out of the intimate connection relating thought and being. For someone who wanted not only to account for the links between language and thought, but also to insist on the narrow relations between logic and metaphysics, and moreover, to realize such a project from a realistic point of view, the nominalist ontology of the Terminists could not be the last word on this. In the end, such waverings—or should we rather say, joint borrowings from both—between Ockham and Duns Scotus are revealing of the nature and ambition of Peirce’s early project. What is the ambition? To build a Philosophy of Grammar, both formal and wide enough so as to account for all the links between language, thought and reality. Formal enough? Then the models are rather to be looked for on the side of George Boole and Ockham. Wide enough? Then it is rather from Kant and Scotus that one should draw one’s inspiration. Yet unable to master the meaning of his own process, the young Peirce is training himself, listening to those various influences, which may explain why we get an impression of tuggings or tensions in the writings of the years 1864-1870. Should one follow Ockham? No doubt. But then, by staying too close to him, one runs the risk of falling into some kind of nominalistic reductionism. Such is the temptation which 49

Rosier, 24 ff. This is a point which had been underlined by Heidegger, who notes that the meaning of the modi significandi was to be understood from its syntaxical value, the meaning of the modi intelligendi from the truth value so that the theory of meaning is closely linked with logic, even more, is nothing else than a part of it.

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Peirce does not always resist, going so far as writing in the 1868 papers, that thought is not only a sign, but a sign developing according to the laws of valid inference. Now, at the same time, such texts are intended to denounce all possible forms of nominalistic reductionism. Besides, is Ockham the best defence against psychologism? Peirce is perfectly aware that the formal theory of pure thought is not free from ambiguities and that Ockham’s mentalism (as his theories of the fictum or of the act of intellection testify) does not allow him to avoid certain commitments (on dualism, the immateriality of the soul), which, Peirce holds, any genuine theory of the mind should manage to do without.50 An important consequence follows: no more than he would be ready to accept Ockham’s theory of the fictum51 he would not, or so it seems, be willing to adopt the mental act theory, later introduced by Ockham to avoid the realist risks present in the fictum and implying a causal instead of a mimetic relation between thought and meaning, at least if such a “naturalization” of meaning, implied indeed in Ockham’s approach to the oratio mentalis, were to be taken in such a reductionist way as to be unable to really account for the mechanisms of thought, and, in the end, of meaning.52 50

On this, see Adams, vol. 1, chap. 3 and Panaccio, 62, 111ff. Such a mimetic or picture view of mind is totally opposed to Peirce’s view defended in 1868 that we do not have images in the mind (not even in actual perception) (W2: 235) although, as he will insist later, we do think in images, that is, use icons as well as indices and symbols, whenever we think or reason. 52 Indeed this needs to be qualified because, to a certain extent, Peirce’s semiotic enterprise (even from the start), cannot be taken as radically opposed to some kind of semantic naturalism. It all depends how one understands such an enterprise, and in particular, on the options one takes as to the relations between language, causation, nature and perception. In brief, I think there are many common points between Peirce and such projects as Condillac’s or Th. Reid’s, who, in their respective ways, had a naturalistic, semiotic approach to language, based on narrow links between language, perception and action (see Tiercelin 2002b). Again, there is a close connection, in my view (contrary to what is often argued), between Peirce and Morris (if one does not merely reads his views as being irreducibly psychologistic and behavioristic), and, more recently, with such naturalists as R. Millikan or F. Dretske (a point also noted by Short, 233), not merely in terms of teleosemantics (purposive action is also essential in Peirce’s view of the semiotic process). Indeed, Peirce would (rightly) object to the major drawbacks of such projects: their insufficient attention to the ‘symbolic’ and “interpretative” dimension of the process, as well as a reduction of causality to mere efficient causality, when final causation is what counts. However, such qualifications would not imply, for him, the adoption of a non naturalistic stance: if being triadic and purposeful is indeed the condition of a right intentional semiotic relation–whence the dyadic action of a thermometer does not belong to semiosis itself but to a mere “automatic regulation”–what it first means is that the genuine form of a sign cannot limit itself to human thought but may be extended to the sunflower 51

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Should one follow Duns Scotus? Indeed and it is not surprising that Peirce, after comparing Scotus and Ockham, notes that he wishes “to lean a little towards the side of Scotus”(W2: 327): for the aim is to build a Formal Grammar. Even if Peirce prefers that term to “Speculative”, the purpose is clear: to choose Duns Scotus as a model, means that one can analyze the structure of the modi significandi independently of the structure of the modi essendi, as was required by the program worked out by the Pseudo-Scotus at the beginning of the Grammar,53 but also that it is impossible to reduce the essendi to the modi significandi, in other words, that the logical universal and the metaphysical universal should be distinguished and that the latter is irreducible to the former. So, if logic can become a generalized semiotic, on the model of a formal Grammar, it is because it is not merely concerned with arguments, but with “signs of any kind” (CP 2.206). Thus it is easier to understand why such a Formal Grammar to which Peirce aspires which “treats of the formal conditions of symbols having meaning” (W2: 57), that “Pure Grammar” whose task wil be to “ascertain what must be true of the representamen used by every scientific intelligence inorder that they may embody any meaning” (CP 2.229) can be assimilated to Kant’s Transcendentale Elementarlehre, to an Erkenntnisstheorie or even to epistemology” (CP 2.206): it has no more to do with a psychologist theory of knowledge than logic itself is concerned with the psychological processes of thought. But, at the same time, the models which inspire or stimulate him, the very definition Peirce gives to logic, and the mission he assigns to it both impose and allow its widening. If its essential task is a “logical analysis of the products of thought”, one of the functions of logic will be the establishment of an “art of judging”. In that sense, if Peirce’s obsession, during all these years, is to get rid of the ambiguities of Kant’s critique of the faculties, and of the psychology of introspection and association, psychology, in its experimental sense but also in Kant’s sense of a possible science of the forms of thought in general, is part and parcel of logic, and, therefore of the metaphysical project as a whole, in so far as the metaphysical categories are the mirror of the categories of formal logic. Which means that Peirce’s antipsychologism will never be so strong as Frege’s or Wittgenstein’s: at any rate, it does not imply that the theory of knowledge should be discredited because of its shady deals with psychology. If Peirce abandons the issues about the foundations or origins of knowledge, it is to concentrate on the (CP 2.274). For him, there is an identity of structure between mind and matter (CP 6.158; 6.268), and this entails that we should not establish a radical break between them, neither limit mind to the human mind (but extend it to bees and crystals), nor give up the regulative idea that the empire of meaning is, if not a part (or reducible to), at least, a prolongation of the empire of nature (Tiercelin 1998). 53 See Peirce’s translation and comments of the first chapters of the book, W2: 321-327.

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problem of its justification.54 How is synthetical judgment in general possible? On what is grounded the validity of the laws of logic? In leaving to a Formal Grammar the task to analyze the relation between thought and meaning, Peirce follows the Modistic inspiration, and announces, in a way, Husserl. But, contrary to Husserl, if such a Grammar is to study what must be true of all the representamen in order that they may embody meaning (CP 2.229), those must not concern the mind as consciousness (were it transcendental), but thought in general.55 For Peirce, who remains true, in that sense, to the formal and semantic requirements of the scholastics, there is only one way to realize such a task and, in particular, to avoid the traps not so much of mentalism as of psychologim (and of such notions as consciousness, intuition, evidence, priviledged first person access) as well as the traps presented by the grammar of ordinary language: it is to start from a sufficiently formal and precise analysis of sign ond of its functions. Since “thought and expression are really one” (CP 1.349) and the meaning of a term is the conception it conveys, meaning can no longer take refuge in some mysterious, inner, glassy thought: it will have to be expressed though external facts and tangible effets. Therein lies Peirce’s pragmatism, which helps to understand why the logician of Milford may have been so concerned, stimulated, inspired, or even influenced by such outstanding technicians of the sign as the scholastics were: So it appears that every species of actual cognition is of the nature of a sign. It will be found highly advantageous to consider the subject from this point of view, because many general properties of signs can be discovered by a set of words and the like which are free from the intricacies which perplex us in the direct study of thought (CP 7.355).

REFERENCES Abailard, Peter. “Logica Ingredientibus”, part I. In Selections from Medieval Philosophers. Ed. by R. McKeon. New York: Charles Scribner’s sons, vol. 1, 1957: 208-258. Adams, Marilyn. William Ockham, 2 vols. Notre Dame: Notre Dame University Press, 1987.

54 Such an attitude is, in my view, typical of the pragmatist attitude towards knowledge and, as a corrolary, towards scepticism, as I have shown in Tiercelin 2005a. 55 This explains why, in particular, Peirce took very seriously the hypothesis of thinking machines. On all these points and on the possible links between Peirce’s semiotic model of the mind and contemporary approaches in artificial intelligence and cognitive science, see Tiercelin 1984, 1993a, 223-257, and 1995. More recently, Skagestad 2004.

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Bastian, Robert J. “The Scholastic Realism of C.S. Peirce”. Philosophy and Phenomenological Research 14 (1953): 246-249. Boh, Ivan. “Consequences”. In The Cambridge History of Later Medieval History. Ed. by N. Kretzmann et al. Cambridge: Cambridge University Press, 1982: 300-314. Boler, John. C.S. Peirce and Scholastic Realism. Seattle: University of Washington Press, 1963. —. “Peirce, Ockham, and Scholastic Realism”. The Monist 63 (1980): 290-303. —. “Peirce and Medieval Thought”. In The Cambridge Companion to Charles Sanders Peirce. Ed. by C. Misak. Cambridge: Cambridge University Press, 2004: 58-86. —. “Peirce on the Medievals: Realism, Power and Form”. Cognitio 6, 1 (2005): 13-24. Brock, Jarrett. “Peirce’s conception of Semiotic”. Semiotica 14, 2 (1975): 124-141. Bursill-Hall, Geoffrey L. Speculative Grammars of the Middles Ages. The doctrine of partes orationis of the Modistae. The Hague-Paris: Mouton, 1971. Cadwallader, Thomas C. “Peirce as an experimental psychologist”. Transactions of the Charles S. Peirce Society 11 (1975): 166-186. de Rijk, Lambertus M. “The Origins of the Theory of the Properties of Terms”. In The Cambridge History of Later Medieval History, 1982: 161-173. Duns Scotus, John. Quaestiones Super Libros Metaphysicorum Aristotelis. St. Bonaventure: The Franciscan Institute, 1997. Fisch, Max. “Peirce’s General Theory of Signs”. In Sight, Sound and Sense. Ed. by T. Sebeok. Bloomington: Indiana University Press, 1978: 31-70; reprinted in Peirce, Semeiotic and Pragmatism, Essays by Max Fisch. Ed. by K.L. Ketner, C.J.W. Kloesel, Bloomington: Indiana University Press, 1986: 321-355. Fisch, Max., Jackson Cope. “Peirce at the Johns Hopkins University”. In Studies in the Philosophy of C.S. Peirce. Ed. by P. Wiener, P. Young, Cambridge: Harvard University Press, 1952: 277-311, reprinted in Max Fisch 1986: 35-78. Heidegger, Martin. Die Kategorien-und Bedeutungslehre des Duns Scotus. Ed. by P. Siebeck (Hab.-Schr., Freiburg i. Br.) Tübingen: J. C. B. Mohr, 1916. Hintikka, Jaakko. “Gaps in the Great Chain of Being: an Exercise in the Methodology of Being”, and “Aristote on the realization of Possibilities in Time”. In Reforging the Great Chain of Being, Studies of the History of Modal Theories. Ed. by S. Knuuttila. Dordrecht: D. Reidel, 1981: 1-17 and 55-72. Kloesel, Christian. “Speculative Grammar: From Duns Scotus to Charles Peirce”. In Proceedings of the C.S. Peirce Bicentennial International Congress. Ed. by K.L. Ketner. Lubbock: Texas Tech University, 1981: 127-34. Knuuttila, Simo. Modalities in Medieval Philosophy. London-New York: Routledge, 1993.

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Jolivet, Jean. “Comparaison des théories du langage chez Abélard et chez les nominalistes du XIVe siècle”. In Peter Abailard. Ed. by E. Buytaert, Louvain, 1974: 163-178. MacKeon, Richard. “Peirce’s Scotistic Realism”. In Studies in the Philosophy of C.S. Peirce. Ed. by P. Wiener, F. Young, Cambridge: Harvard University Press, 1952: 238-50. Michael, Emily. “Peirce’s Early Study of the Logic of Relations, 1865-1867”. Transactions of the Charles S. Peirce Society 10 (1974): 63-75. —. “Peirce’s Earliest Contact with Scholastic Logic”. Transactions of the Charles S. Peirce Society 12 (1976): 46-55. —. “A note on the Roots of Peirce’s Division of Logic into Three Branches”. Notre Dame of Formal Logic 18 (1977): 639-640. Michael, Emily, Fred Michael. “Peirce on the Nature of Logic”. Notre Dame of Formal Logic 20 (1979): 84-88. Moody, Ernst. Truth and Consequence in Medieval Logic. Amsterdam: North Holland, 1953. Moore, Edward C. “The Scholastic Realism of C.S. Peirce”. Philosophy and Phenomenological Research 12 (1952): 238-250. —. “The Influence of Duns Scotus on Peirce”. In Studies in the Philosophy of C.S. Peirce, Second series. Ed. by E.C. Moore, R. Robin, Amherst: University of Massachusetts Press, 1964: 401-413. Panaccio, Claude. Les mots, les concepts et les choses: la sémantique de Guillaume d’Occam et le nominalisme aujourd’hui. Paris: Bellarmin-Vrin, 1992. Paul of Venice. Logica Parva. Munich: Philosophia Verlag, 1984. Perler, Dominik. “Duns Scotus’s Philosophy of Language”. In The Cambridge Companion to John Duns Scotus. Ed. by T. Williams, Cambridge: Cambridge University Press, 2003: 161-192. Perreiah, Allan R. “Peirce’s Semeiotic and Scholastic Logic”. Transactions of the Charles S. Peirce Society 25 (1989): 41-50. Peter of Spain. Summulae Logicales. Edited and translated by J.P. Mullally (Publications in Mediaeval Studies, 8), Notre Dame: Notre Dame University Press, 1945. Putnam, Hilary. Representation and Reality. Cambridge: The MIT Press, 1988. Rosier, Irène. La grammaire des Modistes. Villeneuve d’Ascq: Presses universitaires de Lille, 1989. Short, Thomas L. “The Development of Peirce’s Theory of Signs”. In The Cambridge Companion to Charles Sanders Peirce. Ed. by C. Misak. Cambridge: Cambridge University Press, 2004: 214-240.

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Skagestad, Peter. “Peirce’s Semeiotic Model of the Mind”. In the Cambridge Companion to Charles Sanders Peirce. Ed. by C. Misak. Cambridge: Cambridge University Press, 2004: 241-256. Stump, Eleonor. “Topics: Their Development into Consequences”. In The Cambridge History of Later Medieval Philosophy, 1982: 273-285. Tiercelin, Claudine. “Peirce on machines, self-control and intentionality”. In The Mind and The Machine: Philosophical Aspects of Artificial Intelligence. Ed. by S. Torrance, Chichester, Sussex, 1984: 99-113. —. “Logique, psychologie et métaphysique: les fondements du pragmatisme selon C.S. Peirce”. Zeitschrift für allgemeine Wissentschaftstheorie 16, 2 (1985): 229-250. —. “Peirce et Berkeley : l’esprit et les signes”. Cahiers du Groupe de Recherches sur la philosophie et le langage. Vol. 8. Paris: Vrin, 1987: 23-48. —. “C.S. Peirce ou la sémiotique peut-elle être une science?”. Cruzeiro Semiotico (1991): 27-47. —. “Vagueness and the Unity of Peirce’s Realism”. Transactions of the Charles S. Peirce Society 28 (1992): 51-82. —. La Pensée-Signe: Etudes sur Peirce. Nîmes: Jacqueline Chambon, 1993a. —. Peirce et le pragmatisme. Paris: Presses Universitaires de France, 1993b. —. “Entre grammaire spéculative et logique terministe: la recherche peircienne d'un nouveau modèle de la signification et du mental”. Histoire, Epistémologie, Langage 16 (1994): 89-121. —. “Peirce’s relevance for contemporary issues in Cognitive Science”. Acta Philosophica Fennica 58 (1995): 37-74. —. “Peirce on norms, evolution and knowledge”. Transactions of the Charles S. Peirce Society 33, 1 (1997): 35-58. —. “L’empire du sens fait-il partie de l’empire de la nature?”. Critique 612 (1998): 246-267. —. “L’influence scotiste dans le projet peircien d’une métaphysique comme science”. Revue des Sciences Philosophiques et Théologiques 83 (1999): 117134. —. Hilary Putnam, l’héritage pragmatiste. Paris: Presses Universitaires de France, 2002a. —. “Dans quelle mesure le langage peut-il être naturel (Condillac, Reid)?”. In Condillac, l’origine du langag, Ed. by A. Bertrand, Paris: Presses Universitaires de France, 2002b: 19-56. —. “Le problème des universaux: aspects historiques, perspectives contemporaines”. In La structure du monde : objets, propriétés, états de choses; le renouveau de la métaphysique australienne. Ed. by J.-M. Monnoyer, Paris: Vrin, 2004: 339-353.

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—. “Peirce, lecteur d’Aristote”. In Aristote au XIXe siècle. Ed. by D. Thouard, Villeneuve d’Asc: Presses Universitaires de Lille, 2004b: 353-376. —. Le Doute en question: parades pragmatistes au défi sceptique. Paris: Editions de l’éclat, 2005a. —. “Abduction and the Semiotics of Perception”. Semiotica, special issue on Abduction edited by F. Merrell, J. Queiroz (2005b): 389-412. William of Ockham. Philosophical Writings. Ed. by P. Boehner, Indianapolis: The Bobbs-Merrill Company, 1964. —. The Theory of Terms (Part I of the Summa Logicae). Translated and edited by M.J. Loux, Notre Dame: University of Notre Dame Press, 1974. Wolter, Allan B. “An Oxford Dialogue on Language and Metaphysics”. Review of Metaphysics 31 (1978): 615-648; Review of Metaphysics 32, 323-348. William of Sherwood. Introduction to Logic. Translated with introduction and notes by N. Kretzmann, Minneapolis: University of Minnesota Press, 1966.

CHAPTER 10 PEIRCE AND PLATO Rossella Fabbrichesi “Symbol” and “unlimited” are two key terms in Peirce’s thought, which he adopted with full theoretical awareness in the 1860s and never discarded. It can be said that this American philosopher’s entire conception of semiotics hinges on these terms, which are not lacking in theoretical weight and important historical roots. In this paper, I shall examine what their presuppositions and reference points are with a view to clarifying the links between Peirce’s thought and ancient philosophy and suggesting that the choice of these terms is anything but an artless or unpremeditated step in his philosophical career. It is in fact my intention to trace these notions back to their Greek origin, in particular to Plato, by means of a specific hermeneutical operation. I do not think that such an operation is farfetched since this is exactly what that great interpreter of Peirce’s thought, Max Fisch, had hoped would be done. Fisch often recalled the close connection between Peirce and the Greeks and how much his deep appreciation of their culture had marked the most promising results of his philosophical work.1 In particular, Fisch tells us that in the 1880s Peirce felt attracted by classical culture, by his revered Aristotle of course, but also in a new and irresistible way by Plato as well, “who had hitherto bored him”. The very name Arisbe, which he had given to his last abode, came from one of the settlements belonging to Miletus in Asia Minor. This was the Miletus of Thales, Anaximenes and Anaximander, where Western philosophy originated and found sanctuary. I cannot, of course, nor do I wish to make an historical analysis of this aspect of Peirce’s work, which would require very thorough research and the essential lines of which have already been adequately carried out by Fisch.2 Instead, I have 1

I am referring especially to the article “Peirce’s Arisbe. The Greek Influence in His Later Philosophy”, in Peirce, Semeiotic, and Pragmatism. Essays by M.A. Fisch. Ed. by K.L. Ketner, C.J.W. Kloesel (Bloomington: Indiana University Press, 1986), 227-248. 2 In Peirce’s writings can be found references not only to Plato and Aristotle but, as Fisch points out, also to Epicurean physics, “a garden of beautiful and fruitful suggestions” (CP 1.364), and to the treatise on signs, written in the same school of thought by Philodemus of

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chosen just two words–symbolon and apeiron–around which I will weave the threads of my argument in an attempt to explain the reasons for which semiotics is, at bottom, philosophical knowledge and philosophy has always crossed paths with the sign. Taking Peirce as my starting point, I want to try and interpret the words in the contexts where they first have a noticeable philosophical connotation: Plato’s Symposium for the first term and his Philebus for the second, the concept of unlimited. A concept that in this case Plato inherited from an extensive tradition of studies running from Anaximander to Pythagoras. Let us begin with symbolon. The word “symbol” is perhaps the one which best characterizes both modern and contemporary semiotics. I believe it can be asserted that in the early stages of Peirce’s work “symbol” is preferred to sign; this seems to transpire, for example, from his first Harvard Lecture of 1865: “Every thought is a symbol and the laws of logic are true of all symbols” (W1: 166). As we well know, the same formulation is repeated in On a New List of Categories in a fundamental treatment of the subject where, in a cogent sequence of arguments, Peirce maintains that “the objects of the understanding, considered as representations, are symbols, that is, signs which are at least potentially general” (W2: 56-57).3 Furthermore, given that the rules of logic apply to every symbol it can be said that what logic investigates are all symbols, and not only concepts, and that, therefore, logic deals with the reference of symbols to their objects; in other words, it coincides tout court with semiotics. On a New List of Categories is a fundamental work because, as will be demonstrated, in it are introduced the reference points of a Gadara, entitled Peri semeion kai semeioseon, which Peirce studied with his pupil Allan Marquand. All that remains from their study of this treatise is the text written by Marquand alone, “The Logic of the Epicureans”, published in Studies in Logic by Members of the Johns Hopkins University, Boston 1883. In MS 1604, Peirce says that he dedicated a lot of time to studying this piece of Epicurean writing and that he fought to have this and other Herculaneum papyri published. “This philosophy is my particular pet”, he records in the manuscript. His curiosity concerning the pre-Socratics is also well known–and note that in his time the Diels collection was not available. In particular, he worked on a biography of Pythagoras and in his honor called the categories “cenopythagorean” (see CP 1.351). This is how Fisch, 242 concludes: “the revisions of his philosophy during his Arisbe period, and his approaches toward completion of it, were prompted and aided by the study of Aristotle, Epicurus and Philodemus, Plato and the earlier cosmologists, in that order of importance”. Neither must we forget that the most important gains of Peirce’s logic owe very much to his study of the Megarians and Stoics. In his Formale Logik (Freiburg-München: Verlag Karl Alber GmbH, 1956), Bochenski states that Peirce was the first to understand that theirs was a propositional logic. His own semiotics is greatly indebted to the Stoic approach to the discipline of philosophy. 3 In this work, Peirce prefers to attribute the term “signs” to the indices and speak of the general signs as symbols.

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semiotics based on the use of symbols and governed by an original and powerful categorial device, which arises out of the need to mediate between the sphere of the unlimited throng of sense impressions and three ordered limit-concepts. But let us proceed systematically. From this moment on, symbols are identified with the third kind of general signs, those that are significant only by convention due to a general law, and like every sign, a symbol “is something which stands to somebody for something” (CP 2.228). It is a Medium that establishes a relation between the Object that determines it and the Interpretant that it itself determines. Above all, however, it is a relation that refers to something that remains unavoidably at a distance even though it is, as object of reference, intertwined with the process of inferential and interpretative mediation determined by the sign that aims for the object, but never takes hold of it. Having gone through these general considerations by Peirce, which mark the birth of his semiotics, let us look at Plato’s text. The word symbolon appears for the first time4 in our philosophical literature in the Symposium. So we find it not in the dialectic dialogues–where we might reasonably have expected it to be–or in the Cratylus, which is the first full reflection in Greece on the theme of language, but in the most famous text in antiquity dedicated to the pangs of love and to praising Eros. Not only, for in the Symposium Plato captures and immobilizes a term that, until then, belonged almost exclusively to the language of trade and he delivers it to the philosophical tradition transformed internally and so already molded for a possible semiotic use. It may be that we have not adequately assessed the significance of this transfer of meaning and its connection with the aspects of love, to which the Symposium is dedicated. I would like to try and do this concisely here, keeping in mind that in classical Greece symbolon was a sign of recognition that an exchange had taken place between two parties. It was an object in various materials which, broken in half, indicated some kind of contract to be honored. The first “symbol” was the so-called tessera hospitalis, a widespread practice also in Roman culture in which a tessera divided between two families represented their everlasting duty of reciprocal hospitality. The two halves were receipts indicating a contracted debt, the sign–precisely–of a relationship that remained valid even after a long period without any contact. The term was closely linked to the verb symballo: I throw or put together, match or join different things. Hence, the Two in the One. Peirce himself talks about this in MS 404 “What is a Sign” (EP2: 9), which in itself is enough to demonstrate his immense linguistic and philosophical ability. 4

To tell the truth, there does exist a passage by Democritus (fragment 135) in which the word “symbol” is used precisely in the sense of a linguistic sign exchanged for a thing. But it is the only occurrence in the Presocratics of this type and Plato never uses the word in this sense. For this and other references see Franco Lo Piparo, Aristotele e il linguaggio (RomaBari: Laterza, 2003), 54.

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Here he maintains that the proper use of the term “symbol” coincides perfectly with the ancient meaning of “throw together”. In the Symposium the term appears about half way through–and its use is rare in Plato–in the famous speech by Aristophanes where the poet speaks about what he calls “ancient human nature”. This is represented by androgynes, ridiculous beings that combine male and female features (or those of two individuals of the same gender) within a spherical circularity that makes them perfect and needing nothing. Their omnipotence renders them so arrogant as to try and scale Mount Olympus. Zeus punishes them for this wild and arrogant act by dividing them into two: thus primordial man does not disappear but is halved, given over to sex (the word deriving from the verb secare, “to cut”) and, above all, enslaved by the weaknesses arising out of desire. Desire that comes from love, which did not exist before: It was their very essence that had been split in two, so each half missed its other half and tried to be with it; they threw their arms around each other in an embrace and longed to be grafted together. As a result, because they refused to do anything without their other halves, they died of starvation and general apathy (191a-b).5

There is no more wonderful account of love in all of literature, in my opinion, nor a more perfect description of erotic desire, which in its intensity discovers that it is not directed towards something totally external but towards part of itself. But this part of itself is elusive and its pursuit gives rise to that continual alternation of attacks and defeats that characterize the adventure of each poor half of man. Now we come to the part in which we are interested: So that’s how, all that time ago, our innate sexual drive arose. Love draws our original nature back together; he tries to reintegrate us and heal the split in our nature. Turbot-like, each of us has been cut in half, and so we are human tallies, constantly searching for our counterparts (symbolon) (191d).

Every man, therefore, is a symbol and Peirce will remember this (W2: 241); but also, more broadly, it is human nature that reveals an intentional and sign characteristic which is translated into the reference to its own meaning, acquirement of which is deferred and for the most part suspended. As Aristophanes says, it is in the end eros that rejoins the two divided halves: “he will restore us to our original nature, healed and blessed with perfect happiness” (193d). This, then, is what the myth says. Looking closely, we can see that it works not with two but three terms: the perfect One of the androgyne, “which enjoys the 5

Plato, Symposium, translated by R. Waterfield (Oxford-New York: Oxford University Press, 1994).

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solitude that envelops everything” as Empedocles had already said;6 the Two, the divided half, and the Three, the return to the One through reunification brought about by love. The scar from the laceration will always be visible (the navel) but the pain is sublimated in the pleasure of erotic union, which shackles every man to the urgent needs of his own body and makes him forget that he can match the Gods. So the severing is that which actually allows the mediation of the Three: the break it causes is what sets off the movement of knowledge and, likewise, the movement that generates love, these movements being nothing other than the search for and tension towards completion of the part. When man was a whole, he did not go in search of anything; now that he is forever set apart from his other self, he makes it his goal, desires and pre-figures it through his own broken forms. The entire Symposium binds human knowledge to this erotic act of desire: there is no path to knowledge other than the passionate, “maniacal” one, seduced by the symmetry of its own object. The call for truth, the tension towards the desired object is at the same time an erotic and symbolic tension.7 The Two is not, however, recomposed in the One by simply adding itself to another Two as if it were a mere fraction. In fact, at the third stage of recomposition effectuated by Eros, the part recognizes itself as that full unity it used to be: it glimpses its own possible completion, a vestige of what once existed, and at the same time its own irremediable incompleteness; “the Two in the One”, as Plato puts it. Hence, Eros is a form of mediation–called a mediating daemon later on in the dialogue–an example of “thirdness”, Peirce would say, as is tmesis, the cut, the void that divides the two lovers. For man, love is not peace in perfection but tension, anxiousness, continual deferment. And the other half remains, though endlessly prefigured, taken away for ever and enjoyed precisely in as much as it is taken away. Human nature is thus sym-ballica, a sign nature. This is what Plato tells us, which is like saying that anthropology can only be semiotics and semiotics lies at the heart of philosophy as invented and handed down by Plato: a philosophy understood as an activity of a “philiac” and erotic kind, totally predisposed towards searching for and interpreting what is true, good, beautiful. The “manya” of love therefore has very close links with the hermeneutics of signs, and in his use of the word symbolon, Plato seems to give us more than just a mere suggestion.8 He 6

According to Diels’ ordering, 31 B 28. I have dealt more fully with these themes in La freccia di Apollo. Semiotica ed erotica nel pensiero antico, ETS, Pisa, 2006. 8 See the important passages in the Symposium (202-203) in which Eros is determinate like a daemon, and one that stands in the middle (metaxy) between human and divine. His power is that of conveying (ermeneuon) to the Gods the affairs of men and to men the commands from the Gods. It is through the daemonic, writes Plato, that all divination and every magical 7

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provides us with an invaluable way to explain significant referral and does so bringing into play desire, distance, love, and human nature. He tells us that a symbol is given when a break occurs in a whole, when the whole shows itself to be an absence that cannot be filled and equally unbridgeable is the space of continual referral with which the sign alludes to the whole. The Two in the One, the One broken into the Two, the Symbol and its Object constantly refer to one another for an interpretant Three that restores the union, that is the recognition connected with an act of love. From now on, this will be the movement of the sign in our tradition: something that is present addressing something else that is absent for an interpretant third thing, as Peirce says.9 He clearly sees that the true nature of semiotics is triadic and not purely dyadic like the union of signifier and signified à la De Saussure. In the Symposium this triadicity has an anything but ordinary origin: it emerges as a point of opening for the “two in one” that inspired the myth of love. What would be forgotten in the passage of the new knowledge centered on signs to the developments in logic during the centuries of Hellenism and Scholasticism was precisely the erotic urge that constitutes its driving force and is alone able to explain the tension of the Two towards the original One, regained in the hermeneutical and desiring dispersion of the Three. Having said this, namely that in the Symposium Plato reproduces a scheme of “symbolic” movement that would become the model of signification up until our time, let us go back to Peirce and his semiotic paradigm. As is well known, one of his first principles is that “the idea of representation involves infinity, since a representation is not really such unless it be interpreted in another representation” (CP 8.268), that is to say semiosis can only exist as an unlimited process. Omne symbolum de symbolo, we go on to read (CP 2.302), and if the series of these references is interrupted the sign loses its internal signifying character. Where there is a sign, there will be an interpretation in another sign: “the essence of the relation is in the conditional futurity” (CP 8.225 n. 10), that is in the exercise of a habit as a “disposition of behavior”. It “does consist in what would happen under certain and prophetic power proceeds. Eros keeps together, sym-ballei, and does so through the language of semata: it is through the daemonic that divination, prophecy and mystagogy can act, all that which in the ancient world has to do with signs, with the signs of the divine. Thus Plato holds in the circle of the erotic the scattered parts of archaic semiotics, reading the one in the light of the other many terms that appeared to be without explicit links: eros, daimon, metaxy, semeion, mantiké, and lastly philo-sophia, which will become the most sublime among the erotic and daemonic activities. 9 See, for example, CP 2.92: “A Sign is anything which is related to a Second thing, its Object, in respect to a Quality, in such a way as to bring a Third thing, its Interpretant, into relation to the same Object […]”.

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circumstances if it should remain unchanged throughout an endless series of actual occurrences” (CP 8.225). The extent to which this principle of unlimitedness and possible, vague and general, conditionality of signification was of overriding importance for Peirce is demonstrated by the very definition of the principle of pragmatism. His maxim is tied to this infinite and purely potential chain of acknowledgements: the meaning of a concept is read in the entire possible and conditional series of resolutions to act that I am willing to implement in order to demonstrate my understanding of that concept. Also, he says, it is something that no agglomeration of actual events could ever exhaust (EP2: 402). Semiotics and pragmatism–the two pillars of Peirce’s reflection–are invigorated by the reference to a limitless series. Let us move on, then, to analyzing a crucial piece of writing on the subject entitled New Elements and contained in the collection The Essential Peirce (EP2, chap. 22). Significantly given a subtitle in Greek (kainà stoicheia), it was considered by Fisch to be the best thing that Peirce wrote on the sign. This is the argument it puts forward: it is of the essential nature of a symbol that it determines an interpretant, which is itself a symbol. A symbol, therefore, produces an endless series of interpretants. The symbol is something that has the capacity to reproduce itself and to do so in an essential way since it is the property of a symbol to be interpreted. But this leads to a new symbol being produced; so given a symbol, an infinite series of new symbols is also given, that is of interpretants, within a continual oscillation between the totally vague passage from one sign to the other and the determinate actual interpretation. “But every endless series must logically have a limit” (EP2: 323), concludes Peirce. In this case he is thinking of limit in the mathematical sense: “the series of whole numbers is an increasing endless series. Its limit is the denumerable multitude” (CP 4.213), as he says elsewhere.10 But he also considers limit in the semiotic sense: when he talks of the Final Logical Interpretant, he mentions a limit to the semiotic series that coincides with “that which would finally be decided to be the true interpretation if consideration of the matter were carried so far that an ultimate opinion were reached” (CP 8.184). Reality, for example–he goes on to say in New Elements–“can only be regarded as the limit of the endless series of symbols” (EP2: 323). But does this not contradict what was said earlier about the unlimitedness of the hermeneutic semiotic process? Because, either the nature of the symbol is to be perpetually open to interpretation or there is a limit to the series of interpretations–a subsiding into a determinate, 10 The passage is mentioned by the editors of the Essential Peirce in the note to 2: 323. They go on to add the following explanation of the notion of limit, taken from another passage in Peirce’s work: “an object which comes after all the objects of that series, but so that every other object which comes after all those objects comes after the limit also” (CP 6.185).

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stable habit–in which case the symbol is no longer such and there remains no trace of unlimited reference. In order to address this difficult problem, I propose going back to Plato and this time to the Philebus. This is the dialogue chosen to discuss limit and unlimitedness, in which he deals with a very old, predominantly Pythagorean, tradition that had already posed and discussed this theme in various ways. What he does, however, is to bring the tradition to a close by going beyond its rigid dichotomies. This time, the choice of dialogue is not an audacious hermeneutic move on my part. It is Peirce himself who copies out word for word a long passage from the Greek (18b-c) without making any significant annotations. He does this in one of the later manuscripts (MS 990) as far as we can tell since it is not dated. It is well known that Peirce became fully competent as regards the problem of dating and ordering Plato’s dialogues, basing himself on the studies made by Lutoslawski. Also, Robin’s manuscript list bears witness to Peirce’s keen interest in certain dialogues in particular, which he translated–at least in part–annotated and commented on.11 His interest in Plato came late, Fisch tells us, but it is essential for reconstructing Peirce’s later philosophy, in particular, the idea of summum bonum, and his investigation of ethics and the normative sciences as a whole can surely be put down to an increasingly enthusiastic reading of Plato’s writings. The Philebus is one of the great dialogues of the late Plato, in which important ontological themes–those relating to the limit and the unlimited and the mixture that must derive from them–are interwoven with those of good and pleasure, undoubtedly not by accident. Let us dwell on the passage written out by Peirce where Plato explains the power of the dialectic order, that “gift of the gods” which helps us to understand that “all things that are ever said to be consist of a one and a many, and have in their nature a conjunction of Limit and Unlimitedness” (16c)12. This, then, is the way to proceed, says Plato. Between the unlimited multiplicity of 11

These dialogues are found in particular in manuscripts 973 to 990, where besides discussing chronological and biographical aspects, he comments briefly on the Cratylus, Phaedo, Gorgias, Protagoras, Republic and Laws. In his above-mentioned article, Fisch (Fisch, 239) also recalls that Peirce added his own notes and altered noticeably some of Lutoslawski’s conclusions, formulating his own hypothesis on the chronology of the dialogues based on a mathematical approach. He also translated all or parts of some of the dialogues himself from the Greek (which he read fluently) and came to consider the Theaetetus and the Parmenides as the great Greek philosopher’s most important works. Furthermore, in CP 6.349-352 we find attempts to write dialogues after the manner of Plato and in the draft of Minute Logic of 1902 over 200 pages on Plato and ethical themes. 12 I quote from Plato, Philebus, translated with an introduction and commentary by R. Hackforth (Cambridge: Cambridge University Press, 1972).

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things and the unity of the idea, we have to grade what he calls oi mesoi, the intermediates, the numerically determined many. But we are not to apply the character of unlimitedness to our plurality until we have discerned the total number of forms the thing in question has intermediate between its One and its unlimited number. It is only then, when we have done that, that we may let each one of all those intermediate forms pass away into the unlimited (apeiron) and cease bothering about them (16e).

In other words, the many constitute a quantitatively determinate dimension intermediate between unity and unlimitedness; it is this dimension alone that allows a definite and dialectically distinct knowledge. Referring to grammar, the example copied out by Peirce (18b-c) lends substance to this powerful theoretical hypothesis: the letters make the unlimitedness of the voice’s continuum discrete by composing numerically limited elements that are bound together, combined and connected to one another to determine all the words in a language. Like dialectics, grammar is the art of forming relations and combinations, seeing intermediate links (ta mesa), and making that balanced mixture that can reflect both the One and the Unlimited. Without doubt, in choosing precisely this passage from the Philebus, Peirce shows here his interest as a linguist and semiologist, but anyone who knows his thought well cannot but hear the echo from the first sections of On a New List of Categories (W2: 49-58). And it is indeed a theme of categorial propaedeutics, so to speak, that Plato is posing here, the theme of what Peirce would define in his piece on categories as the conceptual mediation between the unity of being and the manifold of sensuous impressions, through the graded and numerically determinate series of being, quality, relation, representation and substance. “This passage from the many to the one is numerical”, says Peirce (W2: 55), surprisingly echoing the Philebus. Peirce’s categorial theory is too well-known to dwell any further on it here. But there is another direction–a more productive one, as I see it–which makes it possible to associate Plato’s apeiron and the unlimited of Peirce. It cannot in fact have escaped him, above all in the period he was transcribing the dialogue, that it dealt mainly with ethical themes. Or, better, ethical themes that trace the need to moderate that unlimited, that apeiron which is excessive unbridled pleasure, through the measure of limit and of proportion, through the mixture between knowledge and pleasure. “For the qualities of measure and proportion invariably, I imagine, constitute beauty and excellence” (64e). This is the final thesis in the Philebus, which refers to the third thing that is mixed life, as a good way to live lying between pure pleasure and pure knowledge, able to balance the tension between the extremes. But the true protagonist of the

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dialogue is in reality what is without measure and proportion: the asymmetrical, incommensurable, boundless apeiron whose unlimited oscillation characterizes realities as, in the famous example, “hotter” that “never stops where it is but is always going a point further; whereas definite quantity is something that has stopped going on and is fixed” (24d). In the dialogue’s opening exchanges, Plato bows to this imposing apeiron diffused in all reality: hotter and colder, greater and smaller, quicker and slower, high and low in pitch, swift and slow, and lastly, and significantly, “very” (sphodra, 24d), are all examples of a purely qualitative, fluctuating and uncertain range that can only be indicated by the crude, hardly scientific stuttering of the “more-and-less”.13 What we have are realities that appear internally split, that diverge and go in opposite directions after germinating from the same root: the One that is never at rest and so divides into the Many; the Many which in their magmatic continuous generation appear as an undifferentiated Unity. I have a specific reason for emphasizing the word “continuous”. When Peirce subscribed to synechism, he presented it more or less consciously as a revival of Plato’s apeiron: “There is a famous saying of Parmenides, ‘being is, and not-being is nothing’. This sounds plausibile; yet synechism flatly denies it, declaring that being is a matter of more or less, so as to emerge insensibly into nothing” (EP2: 2). Peirce’s continuum, very soon linked with the notion of vagueness, revives the apeiron that preoccupied the Greek philosophers.14 The more-and-less, therefore, impedes the formation of a limit, which would mark its end. For Plato, apeiron is infinite and advancing excess and the languishing of an unlimited defect. It is a place, a chora (24d), where the order of measure, its punctuality cannot be allowed because each point, every discrete element, that is every clear boundary, fades away and gels into another. But when measure, quantity, poson–as Plato writes–intervenes, then we are in the area of the 13

Very many comments have been made on the way in which Plato’s discourse is formulated. See, among others, for the clarity with which the critical positions are summarized and examined, Maurizio Migliori, L’uomo tra piacere, intelligenza e bene. Commentario storico-filosofico al Filebo di Platone (Milano: Vita e pensiero, 1993). Migliori notes that in the Philebus “more-and-less” appears almost always as a single term and in fact Plato always uses one definite article to refer to it. Apeiron is always in the singular while peras is often found in the plural. “It’s not the great-and-small of the dyad but it’s certainly very close to it”, is Migliori’s comment (Migliori, 149). The indeterminateness of the process governed by apeiron lies in the fact that “hotter” can be interpreted as “less cold” and the oscillation between these two opposites prevents their exclusive distinction. But once a relation is fixed between the two–that hot is 12 times greater than that cold–pure hot, incommensurable vis-a-vis pure cold, ceases to be and we reach a precise definition of “this hot here”. 14 I have gone into synechism, or Peirce’s doctrine of continuity, in more detail in Rossella Fabbrichesi Leo, Federico Leoni, Continuità e variazione (Milano: Mimesis, 2005), part I.

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determinate and limited–of “equal, double, and any term expressing a ratio of one number to another, or one unit of measurement to another” (25b). Not “today is too (excessively) hot” but “Today is hot to this extent”. The limit “puts an end to the conflict of opposites with one another, making them well-proportioned (summetra) and harmonious (sumphona) by the introduction of number” (25d-e). From the imbalance of excess we come to the symmetry of limit, which makes science and knowledge possible. Better still, we come to proportion, analogy, the “symphony” among entities, that is the possibility to establish a structured relation between magnitudes.15 Indeed, Plato’s intuition is that to introduce the limit does not mean to cancel the apeiron. Quite the reverse: it means staying in that chora where the more and the less stand face to face without being able to cancel one another in turn. It means referring immediately–simultaneously–to the unlimited that the limit incises and indicates (what would the limit be a limit of if this background, this indistinct chora, did not exist which it incises)? Thus the limit is to be considered a relation. A relation that exists between three terms: the Unlimited, the Limit, and “the mixture of the unlimited with that which has limit” (26b). The examples Plato gives of this wonderful mixture are paradigmatic examples: the seasons, health, beauty, strength, “and all other beautiful things” (ibid.) that are produced in this interweaving. But, within this interweaving, limit and the unlimited do not stand distinct and form a sum–like the categories, in Peirce they never exist unrelated from one another–and the third thing is not simply their result. Once again, an example from Peirce will, I think, help us to understand this. In a manuscript on cosmology (CP 6.203-208) he says that the chalk line drawn on a blackboard is a discontinuous act because it interrupts the continuity of the black but, at the same time, it retains continuity by showing that it is itself nothing other than blackboard. Even more, the continuity of the blackboard–its black background, a kind of potential material, of apeiron or Aristotelian hyle–would not even be noticed if it were not broken by the “brute act” of incising the white line. It is the line, says Peirce, that by breaking the continuity indicates it, and the boundary between black and white is neither black nor white but simply the pairedness between the two in that third element which is the sign of the blackboard. Here, too, limit is thought of as a relation, that is as a triadic and not a dyadic event.16 15

As Migliori, 445, notes, drawing on Toeplitz, for the Greeks number should not be thought of as integer, that is as a full magnitude, but as a relation between magnitudes, between logoi and analoghiai. On the relation between ethics and geometry, see the fundamental passage in Gorgias, 508a. 16 It is true that in CP 6.205 Peirce writes that “the limit is essentially discontinuous”, that is it is an event of Secondness; but if we consider it on the basis of the acknowledgement and habit that it establishes, it can be thought of in terms of a triad (as, precisely, a sign of the

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So, for Plato, we can only grasp the unlimited in a limited reality, that is in the mixture, as its possible background.17 The unlimited can be seen in the, so to speak, freeze-frame of the determinate quantity that blocks the infinite process and declines it by measures. Thus the two exist together in the third genos,18 that is in the mixture, the medium that preserves them both, which is the point of equilibrium, kairòs, the limit-point at which opposites, excesses, disproportions converge. The limit (which then coincides with the Good and the One) which Plato speaks to us of is a sort of contraction of the unlimited into a point of crasis, of blending; it is the apeiron limited and completed in the measure, in the form expressed by beauty, proportion and truth. This is in fact the conclusion to the dialogue: Then, if we cannot hunt down the Good under a single form, let us secure it by the conjunction of three, Beauty, Proportion, and Truth (kallei kai simmetria kai aletheia); and then, regarding these three as one, let us assert that that may most properly be held to determine the qualities of the mixture, and that because that is good the mixture itself has become so (65a).

That is late Plato. Let us now turn out attention to late Peirce. First of all, one cannot help noticing that the reference to beauty, proportion and truth re-echoes when he deals with the three normative sciences–esthetics, ethics and logic. But this is not what I wish to dwell on now. What we are considering are apeiron and peras, that indefinite oscillation that is balanced by a way of life based on mixture, which is found in every form of a good life. We might even go so far as to say that this reference to the form of life, to an idea of the Good that can only be seen blackboard). For this example and its interpretation, see the paper by Carlo Sini included in this volume. 17 Gadamer writes (Platos dialektische Etik: Phänomenologische Interpretationen zum Philebos. Hamburg: Felix Meiner Verlag, 1983, translated in Italian as “Interpretazione del Filebo”, in H.G. Gadamer, Studi platonici, Vol. 1, Genova: Marietti, 1983, 112) that it is not a question of uniting indeterminate and determinate and adding one to the other. What we have is a mixture in which indeterminateness should be viewed together with determinateness as, for example, health should be viewed together with the indeterminate sphere of possible illnesses that could undermine it. As Migliori adds (Migliori, 441), apeiron is negated in the mixture as unlimited, but continues to exist as a privative moment without which limitation could not act as such. Evidently, Aristotle’s form-matter dialectic is already implied in these passages. 18 Third that is also defined as genesin eis ousian, coming into being (26d). I will not go here into the difficulty of interpreting this notion, followed by, as fourth kind, the “cause of mixture and of generation”. For the continuation of the dialogue and its explanation, see the work by Migliori.

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translated into an adequate way of life, the bios miktos, gives these late Platonic considerations an ethical-pragmatic tone.19 Of course, we Peirceans cannot but think of Peirce’s habits, of the deliberate and controlled forms of action, the general modes of rational conduct that he assumes to lie at the basis of pragmatism. In addition, however, we have seen that Peirce speaks of the unlimited reference of semiosis as a process that should be able to reach a final end, understood as limit. Is it not perhaps the case that the solution to the apparent limit-unlimited antinomy has to be formulated in the same mode as Plato’s Philebus? Let us see. Peirce says that the Final Logical Interpretant, that is the apparent conclusion to the semiotic process, is the habit alone, which though it may be a sign in some other way, is not a sign in that way in which that sign of which it is the logical interpretant is the sign [...]. The deliberately formed, self-analyzing habit–self-analyzing because formed by the aid of analysis of the exercises that nourished it–is the living definition, the veritable and final logical interpretant. Consequently, the most perfect account of a concept that words can convey will consist in a description of the habit which that concept is calculated to produce (EP2: 418).

So Peirce is very clear on this point: a Logical Interpretant can be a concept, an argument, a proposition. But its most perfect description, its ultimate expression will have to be translated into a habit of response, a habit that, in turn, will be described by appealing to the singular concrete action to which it gives rise, that concentrates and silences with a few gestures the intense work of interpretation. “It is just like directly taking hold of something, as I take hold of my towel without having doubts”, wrote Wittgenstein, describing an analogous process.20 Habit is, then, precisely the idea (the general, writes Peirce) which unfolds in a given form of life, as Plato thought. It is the limit that interrupts the limitless chain of reasoning (“final […] self-analyzing habit”), by becoming a definite stable practice, but also the privileged sign of an unlimited and conditional series of “dispositions to act” and hence the possibility for them to be hermeneutically revived at any time. Let us now go back to the impasse mentioned above. In New Elements (EP2: 323), Peirce says that reality can be considered as the limit to an unlimited series of 19

Ethical-pragmatic in the sense, of course, of Peirce’s pragmaticism. Also Gadamer (Gadamer, 143) seems to go in this direction when he notes that the definitions of good in this work remain “elastic” and its essence inexpressible. 20 Ludwig Wittgenstein, On Certainty. Ed. by G.E. Anscombe, G.H. von Wright (Oxford: Basil Blackwell, 1979), § 510. See on these themes my “Peirce and Wittgenstein on Common Sense”, Cognitio 5, 2 (2004): 180-193.

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symbols. But if this is so, can the series still be considered as unlimited? Only if one understands the limit not exactly as the final end but, as we said before, in the sense of the denumerable multitude, that is of the actual infinite set which is embodied in each moment of the series as the internal potential tension of its components. Only if we think, for example, of each habitual practice as a limit that actualizes the unlimited oscillation of “more and less” in the interpretative processes that determine it. Thus, as Peirce points out, in the sum of any convergent infinite series one moves towards a limit that, nonetheless, does not belong to the indefinite sequence of the partial sums tending towards this same limit, which is not an end to the sequence but a point of reference, present in as much as referred to, but never as actually attained.21 Peirce thus learnt very well from Plato how to move between limit and unlimited and produce that third which is the good mixed life of the measured selfcontrolled habit. I believe that reaching this solution at the end of his life made him skeptical about his early boldness with regard to the unlimitedness of the semiotic process, the conditionality and futurity of pragmatic meaning, and the sociality of logic (all theories constructed on the predominant idea of apeiron). In support of this, my last quote comes from very late Peirce. It is perhaps too rhapsodic to build a firm interpretation on but very effective, I think, for making the situation I have presented clearer. In An Essay toward Improving our Reasoning in Security and in 21 Just as the infinite (and denumerable) set of all integers (which increase limitlessly) can be taken as the actual infinite limit of this infinite (potential, one by one) increasing. Or, again, as in the attempts to square the circle we can say that the circumference is a limit that comprises the limitless succession of polygons, although it does not form an actual limit that is reached. On this point see Paolo Zellini, Breve storia dell’infinito (Milano: Adelphi, 2001), 34, who says as well: “This means it is possible for the final end to an unlimited process to emerge, though without abandoning the latter’s potential character […] though without ever leaving the finite, which is, rather, nothing other than an unending repetition. The unlimited can indicate something that transcends it, set out this transcendence as the characteristic sign of an actual and infinite completeness and, as a consequence, evoke or reflect its intimate nature by analogic transposition”. Zellini refers to Antiphontes for the Greek period (and consider also, though still confined within a merely potential dimension of the infinite, the method of exhaustion put forward by Eudoxus) and to Cusanus and the methods for straightening a curve, for that crucial period in the development of the idea of actual infinity that was the 15th century. “In the straight line all ‘curvedness’ disappears, the ‘more and less’ of that which can be more or less curved ceases to exist […]. In the ‘more and less’ is in fact implicit a criterion of measure that postulates the existence of an invisible entity about which one can say ‘more’ or ‘less’ and which is itself neither more nor less than something else” (Zellini, 113). What I want to say here is that in Peirce habit designates a place similar to Cusanus’s straight line. I would like to thank Giuseppe Longo for having discussed this part of the text with me.

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Uberty–possibly the last work he finished–there is this bewildering statement: “Yet, the maxim of Pragmatism does not bestow a single smile upon beauty, upon moral virtue, or upon abstract truth: the three things that alone raise Humanity above Animality” (EP2: 465). It is impossible not to hear the echo of “kallei kai simmetria kai aletheia” in the Philebus; impossible to accept that pragmatism has nothing to do with all of this, also because the three principles appear to delineate the development of the normative sciences which Peirce had elevated to the foundation of pragmatism ten years earlier.22 However, these conclusions are in line with what has been said above about the limit-unlimited, habit-semiosis relation in late Peirce. Perhaps, having abandoned his slightly positivist and slightly theological faith in the limitless increase in knowledge as a guarantee for the table of values, Peirce at the end of his life may have hypothesized the foundation of a different and deeper ethics: an ethos founded on harmonious conduct, the perfect symmetry of a truth proportional to “the logic of events” (CP 6.218),23 that is on a way of inhabiting the universe that would find unexpected delight in the measure of limit.

22

The passage needs of course to be put in context. It belongs to a series of unfinished pieces on the theme of reasoning written a few months before the author’s death. Deductive reasoning, he maintains, proceeds in practically total security with almost complete reliability but is not always productive (uberous, precisely). Only abduction is particularly fecund and original but, unfortunately, often unreliable. Pragmatism, or at least the rational maxim that guides it, seems to be classified in this piece as a secure, but unproductive, form of reasoning: “It certainly aids our approximation to the security of reasoning. But it does not contribute to the uberty of reasoning, which far more calls for solicitous care” (EP2: 465). This piece, which has not been commented on very much, seems to me to be written in a purely Platonic spirit. It renews the interweaving between eros and logos, between reason and passion or, in the terms used here, between the security of logical-inferential definitions and the uberty of desire’s urges towards “beauty, virtue and truth”, which we have seen underlie the will to have knowledge. 23 “It appears then that the intellectual significance of all thought ultimately lies in its effect upon our actions. Now in what does the intellectual character of conduct consist? Clearly in its harmony to the eye of reason; that is in the fact that the mind in contemplating it shall find a harmony of purposes in it” (CP 7.361). Recalling the quotation of Plato from 64e: “the Good has taken refuge in the character of the Beautiful”, since measure and proportion constitute beauty and excellence we could then also say that, platonically speaking, ethics, interwoven into Peirce’s logic, has essentially an aesthetic virtue.

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REFERENCES Fisch, Max. “Peirce’s Arisbe. The Greek Influence in His Later Philosophy”. In Peirce, Semeiotic, and Pragmatism. Essays by M.A. Fisch. Ed. by K.L. Ketner, C.J.W. Kloesel, Bloomington: Indiana University Press, 1986: 227-248. Fabbrichesi Leo, Rossella. La freccia di Apollo. Semiotica ed erotica nel pensiero antico. Pisa: ETS, 2006. Fabbrichesi Leo, Rossella, Leoni, Federico. Continuità e variazione. Leibniz, Goethe, Peirce, Wittgenstein Con un’incursione kantiana. Milano: Mimesis, 2005. Gadamer, Hans-George. Platos dialektische Etik: Phänomenologische Interpretationen zum Philebos. Hamburg: Felix Meiner Verlag, 1983. Migliori, Maurizio. L’uomo tra piacere, intelligenza e bene. Commentario storico-filosofico al Filebo di Platone. Milano: Vita e pensiero, 1993. Plato. Philebus, translated with an introduction and commentary by R. Hackforth. Cambridge: Cambridge University Press, 1972. —. Symposium, translated by R. Waterfield. Oxford-New York: Oxford University Press, 1994. Zellini, Paolo. Breve storia dell’infinito. Milano: Adelphi, 2001.

LIST OF CONTRIBUTORS Rosa M. Calcaterra is Professor of Philosophy of Knowledge at Università Roma Tre (Italy). Her areas of specialization are Modern and Contemporary Philosophy, American and European Pragmatism, Analytic Philosophy, Topics and Competences, Theories of Knowledge, Hermeneutics, Social Philosophy, Ethics, and Philosophy of Psycology. Her publications include: Ideologia e razionalità. Saggio su Jürgen Habermas (1984); Interpretare l’esperienza. Scienza etica e metafisica nel pensiero di Ch. S. Peirce (1989); Introduzione al pragmatismo americano (1997); Pragmatismo: i valori dell’esperienza. Letture di Peirce, James e Mead (2003). Vincent Colapietro is a Professor of Philosophy at Pennsylvania State University whose books include Peirce's Approach to the Self: A Semiotic Perspective on Human Subjectivity (1989), A Glossary of Semiotics (1993), and Fateful Shapes of Human Freedom (2003). In The Monist, The Review of Metaphysics, Semiotica, and other important journals, he has also published numerous articles on Peirce, pragmatism, and semiotics as well as a wide range of other topics (including contemporary French philosophers, psychoanalysis, cinema, and jazz). His essays include comparative studies of James and Derrida, of Dewey and Foucault, also of Peirce and Derrida. In addition to the interests already indicated, metaphysics, aesthetics, and philosophy of literature are among his areas of systematic research, while the reception of Darwin in the United States, the traditions of naturalism in Western philosophy, and the intersection of various contemporary movements number among his areas of historical research. One of the main threads running throughout this array of concerns is a sustained, systematic preoccupation with questions of normativity, agency, and critique. He is presently completing a book on pragmatism and psychoanalysis in which these questions are of central consideration. In recent years he has served as President of The Metaphysical Society of America and the Semiotic Society of America. He is presently President of the C.S. Peirce Society. Rossella Fabbrichesi is Professor of Hermeneutics at the State University of Milan, Italy. She has been studied Peirce since her Ph.D. in Philosophy, publishing La polemica sull’iconismo (1983); Sulle tracce del segno (1986); Il concetto di relazione in Peirce (1992); Introduzione a Peirce (1993). She edited two anthologies of Peirce’s writings: La logica degli eventi (1989); Categorie (1992).

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She also worked on the link between Peirce and Wittgenstein (Cosa significa dirsi pragmatisti: Peirce e Wittgenstein a confronto, 2002; Peirce and Wittgenstein on Common Sense, 2004) and the connexions between both authors and the Leibnizian tradition (I corpi del significato. Lingua, scrittura e conoscenza in Leibniz e Wittgenstein, 2000; and, with F. Leoni, Continuità e variazione. Leibniz, Goethe, Peirce, Wittgenstein. Con un’incursione kantiana, 2005). Recently, she turned to the topic of a genealogy of sign in Greek thought (La freccia di Apollo. Semiotica ed erotica nel pensiero antico, 2006). She edits the first Italian web-site entirely devoted to Peirce (www.unimi.it/peirce/). Nathan Houser is Professor of Philosophy at Indiana University in Indianapolis (IUPUI). He is Director of the Peirce Edition Project and Director of IUPUI’s Institute for American Thought. He has served as President of the Charles S. Peirce Society and is President Elect of the Semiotic Society of America. His research focuses on Peirce studies, pragmatism, semiotics, philosophy of text, and philosophy of mind. Since 1993, he has been the General Editor for the Indianapolis critical edition of Peirce’s writings and he has co-edited the twovolume Essential Peirce and Studies in the Logic of Charles Sanders Peirce. Other publications include the historical introductions to vols. 4, 5, 6, and 8 of the Writings of Charles S. Peirce, “Peirce’ s General Taxonomy of Consciousness” (1983; revised and expanded 2000); “Toward a Peircean Semiotic Theory of Learning” (1987); “La Structure formelle de l’expérience selon Peirce” (1989); “Peirce and the Law of Distribution” (1991); "A Peircean Classification of Models" (1991); “The Fortunes and Misfortunes of the Peirce Papers” (1992); “The Scope of Peirce’s Semiotics” (1992); “On Peirce’s Theory of Propositions” (1992); “On ‘Peirce and Logicism’” (1993); “Algebraic Logic from Boole to Schröder, 1840–1900” (1994); “The Semiotics of Critical Editing: Is There a Future for Critical Editions?” (1997); “Peirce as Logician” (1997); “Peirce’s Pragmatism and Analytic Philosophy; Some Continuities” (2002); “Pragmatism and the Loss of Innocence” (2003); “The Scent of Truth” (2005); and “Peirce in the 21st Century” (2005). Ivo A. Ibri is Full Professor of Philosophy at the Pontifical Catholic University of São Paulo (PUCSP), Brazil. He got his PhD in philosophy from the University of São Paulo in 1994 and made a post-doctoral research, in 2004, at the Indiana University–USA, under a fellowship given by the Institute for Advanced Study of that university. He is the founder and director of the Center for Pragmatism Studies of PUCSP and is the editor of “Cognitio”–journal of philosophy. He is also the general coordinator of the International Meetings on Pragmatism, which annually takes place in São Paulo. His main research interest is American pragmatism, especially the work of Charles Peirce, as well as the theoretical connections

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between Peircean thought and German idealism, mainly Schelling. He published several papers on pragmatism and the book Kósmos Noétos–A Arquitetura Metafísica de Charles S. Peirce (1992). Giovanni Maddalena is Assistant Professor at the University of Molise (Italy). He works on American thought especially focusing on Charles S. Peirce and classic pragmatism. His earlier studies are on the theoretical problems connected to MacIntyre’s ethical proposals (La lotta delle tradizioni. A. MacIntyre e la filosofia in America, 2000). Then, he inquired the roots of American thought through the late work of the founder of pragmatism C.S. Peirce. On this topic he wrote the monograph Istinto razionale. Studi sulla semiotica dell’ultimo Peirce (2003). In this monograph as in his many articles on International journals, he tries to apply the philological reconstruction of Peirce’s work to actual philosophical problems especially concerning theory of reference, normative sciences, theory of reasoning and abduction, and the passage from logic to metaphysics. He recently edited, translated and introduced a large Italian anthology of Peirce's work: C.S. Peirce, Scritti scelti (2005, 750 pp). Susanna Marietti is a Post-Doctoral Researcher and Assistant Professor in the Department of Philosophy at the University of Milan. After her earlier studies in formal logic, she became interested in the foundation of logic and mathematics, a topic she treats by making use of Peirce’s semiotics. Besides various essays on this subject, she authored a volume on Peirce’s philosophy of mathematics (Icona e diagramma. Il segno matematico in Charles Sanders Peirce, 2001), edited an Italian anthology of Peirce’s manuscripts (Pragmatismo e grafi esistenziali, 2003) and collaborated on the creation of the first Italian website dealing entirely with Peirce. She has also been conducting research on Kant’s and Wittgenstein’s philosophy. Susanna Marietti is the editor of various volumes on human rights and penal issues and belongs to the editorial board of Antigone, an Italian periodical on related subjects. Michael Otte was born in Riga in 1938. He studied Mathematics and German literature at the universities of Muenchen and Goettingen. In 1973 he founded an interdisciplinary research group on mathematical epistemology, history and cognition at the University of Bielefeld (Germany). Over the years quite a number of projects have been elaborated by this group and many studies, on such themes as Grassmann and Romantic Naturphilosophie; The Theory of Integration from Cauchy to Lebesgue; Peirce` Conception of Mathematical Generalization and his Evolutionary Realism; Cassirer’s Philosophy of Science, among others, have been published.

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Carlo Sini is Professor of Theoretical Philosophy at the University of Milan, member of the Institut International de Philosophie of Paris, and “Accademico dei Lincei”, in Italy. He is author of a number of books, including studies on phenomenology, semiotics, American pragmatism (Il pragmatismo americano, 1972), and the genealogy of scripture from a philosophical point of view (Etica della scrittura, 1992; Filosofia e scrittura, 1994). Recently, he has devoted his thought to a “philosophy of practices” (Teoria e pratica del foglio-mondo, 1998; Gli abiti, le pratiche, i saperi 1996, Idoli della conoscenza, 2000). Sini’s early work was in classical philosophy and the phenomenology of Hegel and Husserl. His later work has been on Peirce’s philosophy, particularly his semiotics, which Sini, together with Umberto Eco, was responsible for bringing to the fore in Italy. He has been trying to link the Peircean notion of interpretation and unlimited semiosis with Nietzsche’s and Heidegger’s hermeneutic circle and the event of meaning (Semiotica e filosofia, 1978; Passare il segno, 1981; Immagini di verità 1985; I segni dell’anima, 1989). Most recently, he wrote an extended Encylopedia of Philosophical Figures, in six volumes, which intends to survey the circle of Western knowledges (metaphysics, psychology, ethology, anthropology, cosmology, and pedagogy) (Figure dell’enciclopedia filosofica, 2004-5). Claudine Tiercelin is Professor of Philosophy at the University of Paris XII (Créteil) and a researcher at the Institut Jean Nicod. She has mainly worked and written on C.S. Peirce and pragmatism (Putnam, Ramsey) and is currently working on issues in contemporary analytic metaphysics. Her main published books are: La pensée-signe, études sur Peirce (1993); Peirce et le pragmatisme (1993); Hilary Putnam, l’héritage pragmatiste (2002); Le doute en question: parades pragmatistes au défi sceptique (2005). And among her articles related to metaphysics: “La métaphysique et l’analyse conceptuelle” (2002); “Sur la réalité des propriétés dispositionnelles” (2002); “Le problème des universaux: aspects historiques et perspectives contemporaines” (2004).

INDEX OF NAMES AND KEY TOPICS abduction xii, 9-13, 70-71, 79, 85-86, 93-110, 124-125, 154, 161, 172, 184, 199. Abailard, Peter 159, 160, 169-171, 175. abstraction 70-72, 83, 169-171. agent 86, 130-154. Alexander of Hales 160. analysis/synthesis 52-54, 60-62, 64, 69, 71, 76, 79, 81, 83, 85, 89, 92, 106, 108-109. anti-Cartesianism 11, 13, 36, 38. Antiphontes 198. anti-psychologism 35-36, 44. apeiron 186, 193-196, 198. Aquinas, Thomas 159, 160. Aristophanes 188. Aristotle 15, 20, 70, 149, 159, 185, 186, 196. auxiliary construction 70, 105, 107, 121-122, 126. Avicenna 160. axiomatics 53-55, 63, 67, 69-71, 75-77, 81-83, 86. Bacon, Francis 147. Bacon, Roger 160-161. belief 3, 5, 8, 11, 41, 46-48, 82, 97, 98, 132, 148, 151, 164, 175. Bentham, James 40. Berkeley, George 159, 160, 163, 169, 172, 182. Bochenski, Joseph 186. Boersema, David 22, 23, 29, 34. Boole, Gorge 83-84, 159, 163, 177. Brentano, Franz 37, 49. Brito, Radulphus 174. Butler, Judith 143, 154.

calculus ratiocinator 83, 87. Caravaggio (Michelangelo Merisi) 30-32. categories x, xii, 15, 16, 41, 43, 45, 48, 90, 92, 106, 110-111, 128129, 155, 159, 164, 168, 172173, 175, 179, 186, 193, 195. Colapietro, Vincent 49. common sense 8, 13, 197. Comte, Adam 40. Condillac, Etienne, Bonnot de 178, 183, consciousness 37, 41-42, 46, 54, 66, 75, 89, 92, 102, 104, 109, 134135, 144, 148, 153, 164, 166, 169, 171, 173, 180. continuum/continuity xii, 4-6, 15-20, 24, 26, 30, 44-46, 52-53, 57-59, 61, 64, 66, 72, 74, 77, 79, 80-81, 85-86, 101-104, 110, 140-141, 167, 193-195. corollarial reasoning 70, 72, 120-121, 124. corollary 120, 127. cosmology xii, 12, 15-17, 195. Courtrai, Siger of 174. Cusanus (Nicola of Kues) 198. Dacia, John of 176. Dacia, Martin of 174. Dacias, Boethius of 172, 176. De Saussure, Ferdinand 190. deduction 11, 54, 68, 70-71, 73, 78, 81-82, 84-86, 93-95, 104-105, 110, 112-113, 120-121, 159, 161, 164, 168, 175. Democritus 187. descriptivism 34.

206

Devitt, Michel 31, 34. Dewey, John 4, 152, 155. diagram xii-xiii, 9, 27, 29, 53-55, 68, 70-71, 74, 74, 78, 104-110, 112-127, 167. Di Leo Jeffrey R. 22, 29, 34. Donatus 161. Dretske, Fred 178. Duns Scotus, John 159, 164, 174175, 177, 178, 181-183. Eco, Umberto vii, 10, 149. Empedocles 189. Epicurus 186. epistemology xi, 12, 57, 62, 75, 80, 91, 93, 108, 133, 156, 179. Euclid 61, 74, 76-77, 83, 112-115, 117, 119, 121-122, 124-125, 127. externalism 36, 38-41, 43, 46. Erfurt, Thomas of 160, 168, 174176. eros 187-190, 199. ethics x, 40, 136, 146, 192, 196, 199. evolutionism 4, 15, 85, 90, 91. Fabbrichesi, Rossella 8, 13, 17, 40. fallibilism 1-14, 94, 102, 150. Fechner, Georg 39. Firstness 17, 19, 28, 43, 45, 48, 90, 91, 103. Fisch, Max 155, 185-186, 192, 200. Fodor, Jerry 163, 166. Frege, Gottlob 33, 34, 69, 80, 82, 83, 175, 179. Frost, Robert 9. Gadamer, Hans-Georg 196-197, 200. Galton, Francis 39. Geuss, Raymond 135-136. Grammatica speculativa 160, 161, 168, 175.

Index

Haack, Susan 7, 12, 86, 87. habit xii, 7-8, 16-20, 26, 29, 48, 5859, 84, 97-98, 139-140, 144, 147-148, 152, 159, 163, 190, 192, 195, 197-199. Hegel, Georg W.F. 15, 45, 85, 142143, 146, 148, 150. Heidegger, Martin 135, 150, 177. heuristics 89, 91-93, 95, 99, 102, 104110, 170. Hilbert, David 56, 75, 81-83. Hintikka, Jaakko 73-74, 83-84, 121-122, 124, 159. history xii, 22, 30-33, 129, 132134, 142-143, 145-152. Hobbes, Thomas 129, 146. Hookway, Christopher 102, 128. Houser, Nathan 34, 39, 87. Hume, David 39, 63-64, 66, 97, 134, 159. Husserl, Edmund 44, 180. hypostatic abstraction 70-71, 169, 171. hypothesis, mathematical 52, 68, 71, 77, 79, 82-83, 85-86, 93, 104, 106, 109, 110. iconicity 25-26, 27-31, 33-34, 54, 58, 80, 104-105, 108-109, 112, 117, 120, 150, 161, 178. idealism 41, 48, 65, 90-91, 146, 150, 167-168. il lume naturale 7, 96, 98. indexicality 22, 25-30, 33, 58, 6869, 150. inference 94, 99, 101, 105, 107, 112113, 115, 117, 124-125, 159, 162, 172, 177. inquiry 1-8, 13, 34, 35, 39, 66, 95, 133, 147, 149, 158. insight 7, 11, 59, 71, 79, 95-96, 9899, 102-103.

Index

instinct 7-9, 11, 13, 40, 46, 95-99, 103, 141, 153. Interpretant x, 5, 8-9, 11-12, 23, 25-29, 58, 94, 112-113, 115, 117, 119, 150, 172-173, 187, 190-191, 197. James, William x, 39, 107, 136137, 151, 164. Jastrow, Joseph 39. Joas, Hans 132. Kant, Immanuel xi, 35-37, 42, 44, 51, 53-54, 62-67, 69-70, 7278, 80-81, 85, 89-91, 106-109, 128-136, 142, 145-146, 148, 150-152, 158, 159, 163, 164, 168, 177, 179. Knuuttila, Simo 159. Korsgaard, Christine 130-131, 133136, 145, 151-152. Kripke, Saul 22-23, 29-34, 49. Leibniz, Gottfried W. ix, 53, 60-62, 65-67, 73, 78. Lo Piparo, Franco 187. Locke, John 159, 163, 169. logic ix-xiii, 4-5, 15-17, 35-49, 52, 54, 56, 60, 63-64, 67-68, 70, 72-73, 79, 81-85, 89-91, 9397, 99-101, 104, 108, 110, 121, 124, 128, 136-137, 139, 151, 158-180, 186, 190, 196, 198-199. Lutoslawski, Witold 192. Maddalena, Giovanni 15, 17, 20, 42-43. Margolis, Joseph 2-7, 11-12. Marquand, Allan 186. McDowell, John 10, 78, 152. medium 187, 196. mentalism 37-38, 57, 74, 57, 178, 180. Migliori, Maurizio 194-196.

207

Millikan, Ruth 178. Modists 161, 165, 168, 174, 176177, 180. Morris, Charles 178. nicknames 22, 30-33. Nixon, Richard 31-32. normative conflict 131-134, 151. number 53, 55, 63, 67-73, 82-83, 107, 191, 195. observation 17, 27, 39-42, 45-46, 52, 55, 65, 68, 71, 77, 92, 9798, 105-106, 120-121, 123. Ockham, William of 159-160, 163, 165-166, 168, 174-179. ontology 44, 81, 83, 91, 93, 173, 177, 192. Paul of Venice 160. Peirce, Benjamin 129, 159. perception 7, 9-11, 19, 41-43, 59, 67, 71, 85, 100-103, 109, 112114, 121-122, 124-125, 127, 143, 150-151, 172, 178. perceptual judgment 9-10, 13, 60, 7980, 100-103, 172. Peter of Spain 160. phaneroscopy 17, 41-42. Philebus 186, 192-194, 197, 199. Philodemus of Gadara 185-186. Plato 19, 65, 167, 185-199. Port Royal, Logic of 174. positivism 34, 51, 56-57, 63, 146, 199. potentiality 15-16, 19-20, 195, 198. Potter, Vincent 44. practical identity 128, 132, 134136, 144, 147-148, 151-152. pragmatism ix, xiv, 3-4, 10, 24, 35, 44, 47, 75, 82, 98, 100-101, 130-131, 133, 141, 145, 151153, 162-164, 170, 180, 191, 197-199.

208

Index

Prantl, Carl 160. Priscian 161. proper names 22-31, 34, 80. psychology 35-37, 39-40, 42-47, 95, 101, 106, 136-137, 162, 164, 171-172, 175-176, 178179. Putnam, Hilary 12, 166. Pythagoras 126, 186. rationality 36, 38, 44, 46, 65, 81, 98, 103, 133, 142, 144-145, 148-150, 152-153. realism 1-4, 12, 41, 57, 59, 71, 89-91, 102, 104, 108, 110, 130-131, 146, 158, 160, 173. reflection, authority of 130, 132133, 142, 147. reflective endorsement 130, 133, 142, 147-148, 151. Reid, Thomas 178. Rescher, Nicholas 1-2, 12-13. Russell, Bertrand 56, 67, 69, 78, 82. Salisbury, John of 159-160, 171. Savan, David 131-132. Schelling, Friedrich W.J. 65, 90, 92, 97, 110. Schiller, Friedrich 128-129, 142. scholastic method 160. scientia rationalis 174-175. scientia sermocinalis 174. Sellars, Wilfrid 10. semiosis 8, 12, 23, 54, 58, 85, 91, 151, 173, 178, 190, 197, 199. semiotics ix-xii, xiv, 15-17, 23-24, 27, 34, 38, 43, 48, 54, 57-58, 68, 75, 112, 115, 117, 120, 158-159, 161-162, 173, 178180, 185-187, 189-191, 197198.

sentiment 38, 44, 47-48, 92, 130132, 137, 138, 141, 152. Sherwood, William of 160, 184. sign x-xiii, 5, 15, 17-19, 23-27, 29, 33-34, 35-36, 38, 43-44, 5455, 57-58, 61, 63, 69, 75, 82, 84, 94, 102, 104, 109, 112114, 120-122, 127, 131, 141, 144, 150, 158-159, 161-168, 171-175, 177-180, 185-191, 195, 197. Sini, Carlo x, 40, 50, 196. skepticism 12-13. socialism, logic 36, 47, 49. spatial relation 112, 114, 121, 124, 127. Speculative Grammar 161, 165, 167-168, 181. Spencer, Herbert 15, 20. Sterelny, Kim 34. symbol x, 26, 28-29, 33, 54, 58-59, 104, 112-113, 115, 117, 119120, 161, 163-164, 168, 175, 178-179, 185-192, 198. symmetry 16, 91, 189, 194-195, 199. Symposium 186-190. synechism xii, 6, 11, 44, 47, 57, 64, 90, 102, 194. Taylor, Charles 131, 151. Terminists 174-175, 177, 183. theorematic reasoning 70-72, 75, 107, 120-122, 124, 126. theorem 55-56, 61, 69-70, 72-73, 76-77, 105, 107, 115-116, 119120, 123-127. theoric step 121-124. Thirdness 3, 17-19,45, 48, 58, 86, 90, 102-103, 174, 189. truth 2, 5-7, 9, 12, 14, 38, 41, 47-49, 56-57, 60-62, 65-68, 73-75, 77-

Index

78, 82-83, 94-96, 98, 105, 110, 120, 128-129, 137, 145, 147, 155, 156, 170, 175, 177, 182, 189, 196, 199. universals 90, 160, 170-171, 174. unlimited x, 185-187, 190-199. vagueness 8, 11, 15, 17, 52, 94, 153, 173, 183, 191, 194.

209

values 36-39, 44, 48-49, 82, 132, 155, 199. Washington, George 24-25. Welby, Lady Victoria 25. Wittgenstein, Ludwig 8, 37-38, 48, 49, 57, 132-133, 147, 154, 179, 197, 202-203. Wundt, Wilhelm 36, 39, 164. Zellini, Paolo 198.