Early Analytic Philosophy – New Perspectives on the Tradition THE WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE

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Early Analytic Philosophy – New Perspectives on the Tradition

123 Editor Sorin Costreie Faculty of Philosophy, Department of Theoretical Philosophy University of Bucharest Bucharest Romania

ISSN 1566-659X ISSN 2215-1974 (electronic) The Western Ontario Series in Philosophy of Science ISBN 978-3-319-24212-5 ISBN 978-3-319-24214-9 (eBook) DOI 10.1007/978-3-319-24214-9

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Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com) In memory of Jaakko Hintikka Preface and Acknowledgments

This collection originates from a series of three conferences under the auspices of the Bucharest Colloquium in Analytic Philosophy. The first took place in 2010, and it was called The Actuality of the Early Analytic Philosophy. It was followed in 2011 by Frege’s Philosophy of Mathematics and Language and in 2012 by Philosophy of Mathematics Today. Most of the papers in the volume were presented, in an earlier version, at one of these conferences; the remaining essays were specially commissioned. In putting together the present volume, I have kept the focus on the original idea of the first conference, namely the contemporary relevance of early analytic philosophy. Although the papers of this collection are mainly dedicated to a specialized public, familiar with the issues and methods of analytic philosophy, the volume is designed so that it can also serve as a useful companion for various introductory courses covering the origin and the evolution of the analytic tradition. All Bucharest Colloquiums took place at the University of Bucharest and were supported, at the institutional level, by the university’s Department of Theoretical Philosophy and its Center for Logic, History and Philosophy of Science, and by the Romanian Society for Analytic Philosophy. I am indebted to the Faculty of Philosophy of the University of Bucharest for making it possible for me to co-organize this series of colloquiums. At a more personal level, I am grateful to all of the Bucharest Colloquium’s participants, to my co-organizers—Mircea Dumitru and Gabriel Sandu—and to the many students who helped ensure that the con- ferences ran smoothly. I would like to thank first and foremost the authors for their willingness to contribute to this collection and for their understanding and forbearance in seeing this project through. Matthias Schirn deserves special thanks, for in addition to his essay, he contributed valuable ideas to the project and attracted several valuable contributors. I also thank Lucy Fleet, my editor at Springer, and William Demopoulos, the managing editor of The Western Ontario Series in Philosophy of Science, for their constant assistance and support. I am grateful to Bill for all the philosophical guidance he gave to me during my graduate years at The

vii viii Preface and Acknowledgments

University of Western Ontario. My interest in analytic philosophy began during my undergraduate studies at the University of Bucharest with the Frege course of Sorin Vieru; it was consolidated by Adrian Miroiu’s course on philosophical logic; and it was established as a constant direction in my academic life by Bill’s graduate courses on Frege, Russell, Carnap and Co. The appearance of this volume in a series edited by Bill was a happy coincidence, for Lucy’s suggestion that it be placed in the Series was given without prior knowledge of my acquaintance with its managing editor: The present has its roots deep in the past…

Bucharest Sorin Costreie July 2015 Contents

Part I Frege Frege on Mathematical Progress ...... 3 Patricia Blanchette Identity in Frege’s Shadow ...... 21 Jaakko Hintikka Frege and the Aristotelian Model of Science...... 31 Danielle Macbeth On the Nature, Status, and Proof of Hume’s Principle in Frege’s Logicist Project...... 49 Matthias Schirn

Part II Russell A Study in Deflated Acquaintance Knowledge: Sense-Datum Theory and Perceptual Constancy ...... 99 Derek H. Brown Whitehead Versus Russell ...... 127 Gregory Landini The Place of Vagueness in Russell’s Philosophical Development ...... 161 James Levine Propositional Logic from The Principles of Mathematics to Principia Mathematica ...... 213 Bernard Linsky

ix x Contents

Part III Wittgenstein Later Wittgenstein on the Logicist Definition of Number...... 233 Sorin Bangu Wittgenstein’s Color Exclusion and Johnson’s Determinable ...... 257 Sébastien Gandon The Concept of “Essential” General Validity in Wittgenstein’s Tractatus...... 283 Brice Halimi Reconstructing a Logic from Tractatus: Wittgenstein’s Variables and Formulae ...... 301 David Fisher and Charles McCarty Justifying Knowledge Claims After the Private Language Argument ...... 325 Gheorghe Ştefanov

Part IV Carnap Carnap, Logicism, and Ontological Commitment ...... 337 Otávio Bueno Frege the Carnapian and Carnap the Fregean ...... 353 Gregory Lavers On the Interconnections Between Carnap, Kuhn, and Structuralist Philosophy of Science ...... 375 Thomas Meier

Part V Various Echoes Abstraction and Epistemic Economy ...... 387 Marco Panza Torn by Reason: Łukasiewicz on the Principle of Contradiction ...... 429 Graham Priest Why Did Weyl Think that Dedekind’s Norm of Belief in Mathematics is Perverse? ...... 445 Iulian D. Toader

Index ...... 453 Contributors

Sorin Bangu University of Bergen, Bergen, Norway Patricia Blanchette University of Notre Dame, Notre Dame, USA Derek H. Brown Brandon University, Brandon, Canada Otávio Bueno University of Miami, Coral Gables, USA David Fisher Indiana University, Bloomington, USA Sébastien Gandon Blaise Pascal University, Clermont-Ferrand, France Brice Halimi Université Paris Ouest Nanterre La Défense (IREPH) & SPHERE, Paris, France Jaakko Hintikka Boston University, Boston, USA Gregory Landini University of Iowa, Iowa City, USA Gregory Lavers Concordia University, Montreal, Canada James Levine Trinity College Dublin, Dublin, Ireland Bernard Linsky Department of Philosophy, University of Alberta, Edmonton, Canada Danielle Macbeth Haverford College, Haverford, USA Charles McCarty Indiana University, Bloomington, USA Thomas Meier Ludwig Maximilians University Munich, Munich, Germany Marco Panza CNRS, IHPST, University of Paris 1, Panthéon-Sorbonne, Paris, France Graham Priest University of Melbourne, Melbourne, Australia; CUNY Graduate Center, New York, USA

xi xii Contributors

Matthias Schirn Ludwig Maximilians University Munich, Munich, Germany Gheorghe Ştefanov University of Bucharest, Bucharest, Romania Iulian D. Toader University of Bucharest, Bucharest, Romania Introduction

Early Analytic Philosophy (spanning the period from 1879 to the early 1930s) is now known and regarded as a distinct philosophical tradition. The growing interest in this not fully explored domain of study is not just historical. In the last decades, new connections, interpretations, and ideas discovered in relation to it have shed a different light on the origins of analytic philosophy. What we have inherited from the analytic tradition is similar to the inheritance Frege told his son Alfred was contained in the unpublished works he would be leaving him: “Even if they are not pure gold, there is gold in them.” The present volume is a collection of papers that focus on discussing (g)old ideas mainly originating in the works of some of the central figures who initiated the analytic tradition: Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, and Rudolf Carnap. The central point of the book is to show how these ideas remain present and influential in current philosophical debates. The collection is the pro- duct of the need to better understand these ideas by placing them in their original setting and to systematically examine how these ideas might illuminate debates that animate current philosophical discussion. The authors approach some crucial ideas of the founders of analytic philosophy with a keen interest in showing how much contemporary philosophy is indebted to its original setting; they also examine the extent to which current debates echo the “original” ones. The collection is designed to be a useful tool for those who rec- ognize the fruitfulness of (g)old thoughts and their significant influence in current philosophical disputes. The collection contains 19 new and original essays, written by junior and senior scholars in analytic philosophy who have been invited to write on what they take to be “old ideas in new clothes,” ideas which still shape current philosophical debates. As one might expect, a rich and diverse picture emerges. The present collection covers many kinds of topics belonging to early analytic philosophy, topics which continue to intrigue analytic philosophers today. The volume is organized into five parts. Each of the first four parts is dedicated to one of Frege, Russell, Wittgenstein, or Carnap. The last part gathers together several essays which discuss either the relation between two or more analytic

xiii xiv Introduction thinkers, or various important concepts such as the principles of abstraction and non-contradiction. Some information about each of the contributions completes this introduction. Patricia Blanchette explores the difficulties posed for Frege’s claim that math- ematical theories are collections of thoughts and that scientific continuity turns on thought-identity, by the conceptual development canonically involved in mathe- matical progress. Blanchette argues that the difficulties apparently posed to Frege’s central views stem from an overly simple view of Frege’s understanding of mathematical objects and of reference. The positive view recommended is one on which Frege’s view of mathematical theories is largely consistent with, and helps make sense of, the phenomenon of theoretical unity across conceptual development. Jaakko Hintikka draws attention to an important aspect of quantifiers, which was overlooked by Frege and others Fregean commentators like Kripke, namely their role of expressing, by their formal dependence on each other, the actual depen- dences between variables bound to them. The resulting flaw in Frege’s and other logicians’ logic began to be corrected only in IF logic. In any adequate logic, a fixed mode of identification is presupposed. The frameworks of identification can be perspectival or public. Hintikka claims that Kripke makes the same mistake about quantifiers as Frege and in addition assumes that only perspectival identification is needed in the last analysis. He also overlooks dependence relations between modal operators and quantifiers. Danielle Macbeth discusses the model of a science that is outlined in Aristotle’s Posterior Analytics. Frege is seen as one of the last great defenders of the model and a key figure in the very developments that have been taken to spell its demise. However, Macbeth claims that even though Frege remains true to the spirit of the model, he also modifies it in very fundamental ways. So modified, Macbeth sug- gests, the model continues to provide a viable and compelling image of scientific rationality by showing, in broad outline, how we achieve, and maintain, cognitive control in our mathematical investigations. Matthias Schirn analyzes both the status and the role of Hume’s Principle in Frege’s logicist project. Schirn carefully considers the options that Frege might have had to establish the analyticity of Hume’s Principle, bearing in mind that with its analytic or non-analytic status, the intended logical foundation of cardinal arithmetic stands or falls. Schirn reconstructs in modern notation essential parts of the formal proof of Hume’s Principle in Frege’s Grundgesetze. Schirn also scrutinizes Frege’s characterization of abstraction in Grundlagen, §64, and criti- cizes in this context the currently widespread use of the terms “recarving” and “reconceptualization” by Crispin Wright and other neo-logicists. Schirn concludes his essay with some interesting reflections on the introduction of the cardinals and the reals by abstraction in the context of Frege’s logicism. Derek Brown is interested in what remains of the early analytic approach to perception—sense-datum theory—when it is both (a) divorced from an overly ambitious commitment to the idea that perception delivers a wealth of certain knowledge about what is perceived and (b) updated to accommodate phenomena in contemporary perceptual theory such as the perceptual constancies. Brown argues Introduction xv that to achieve (a) one should “deflate” Russell’s notion of acquaintance and (b) one can utilize the space created by deflated acquaintance knowledge to allow perceptual representation to resolve the ambiguities inherent in perceptual con- stancies. Brown thus offers a two-factor (acquaintance-representation) sense-datum theory to meet these challenges. Gregory Landini points out some of the most striking intellectual differences between Whitehead and Russell that are relevant to Principia. Thus, Landini takes up the issues of typical ambiguity, the nature of classes, geometry, and the existence of mind and matter. It may seem surprising that there are such striking differences between Whitehead and Russell given their philosophical collaboration and very close personal relationship. Russell’s neutral monism took an eliminativistic stance with respect to life, mind, matter, motion, time, and change. On the other hand, Whitehead viewed nature as an organically integrated whole within which life, mind, and matter have a genuine reality. James Levine distinguishes three periods in Russell’s philosophical develop- ment: the Moorean period, following his break with Idealism around 1899 through his attending the Paris conference in August 1900 at which he saw Peano; the period following the Paris conference through his prison stay in 1918; and his post-prison period, in which he becomes concerned with the nature of language as such. Levine argues that while the topic of vagueness becomes an explicit theme in his post-1918 writings, his view that ordinary language is vague plays a central role in his post-Peano practice and characterization of analysis. Levine claims that the failure to recognize the character of Russell’s post-Peano conception of analysis reflects a broader misunderstanding of the character of Russell’s philosophy, and of his place in the history of analytic philosophy. Bernard Linsky understands the early chapters of Principia Mathematica as the result of a slow and laborious development out of Peano’s original ideas. Linsky illustrates this development by studying a theorem that is not proved in those early chapters of Principia: Peirce’s Law—[(p  q)  p]  p. Linsky distinguishes three Russellian systems of propositional logic: the first in Principles of Mathematics (1903), then the second in “The Theory of Implication” (1906), and the third in Principia Mathematica (1910). Linsky’s paper is designed as an investigation of the role of Peirce’s Law through those systems. Linsky shows that this valid formula is not even a theorem in the 1910 system although it is one of the axioms in 1903 and is proved as a theorem in 1906. The paper helps also to reconstruct some of the history of axiomatic systems of classical propositional logic. Sorin Bangu focuses on the lectures on the philosophy of mathematics delivered by Wittgenstein in Cambridge in 1939. He discusses several lectures, the emphasis falling on understanding Wittgenstein’s views on the most important element of the logicist legacy of Frege and Russell, the definition of number in terms of classes— and, more specifically, by employing the notion of one-to-one correspondence. Since it is clear that Wittgenstein was not satisfied with this definition (and with the overall logically oriented approach), the aim of Bangu’s essay is to propose a reading of the lectures able to clarify why that was the case. This reading draws xvi Introduction connections between Wittgenstein’s views on language and mind (expressed mainly in Philosophical Investigations) and his conception of mathematics. Sébastien Gandon compares Wittgenstein’s discussion of color exclusion in his “Some Remarks on Logical Form” to William E. Johnson’s doctrine of deter- minable and determinate expounded in his Logic. Gandon’s point in doing this comparison is not to uncover a hidden influence of Johnson on Wittgenstein. Gandon holds that instead of considering “Some Remarks on Logical Form” as a step in the journey from the Tractatus to the Investigations, we should see it as an integral part of a discussion, witnessed by Johnson (1921), which took place in Cambridge in the twenties. Gandon’s paper ends by putting Wittgenstein’s ideas in a broader historical context. Brice Halimi focuses on Wittgenstein’s characterization of logical truth in the Tractatus. Wittgenstein describes the general validity of logical truths as being “essential,” as opposed to merely “accidental” general truths. Few commentators have focused on this point, and most of them have construed it as the claim that generalized propositions cannot be but contingently true, if true. Halimi’s aim is to elucidate the crucial concept of essential general validity (a concept which brings into play the whole Tractarian conception of logic) and to explain that it has to do with a certain kind of generality, before any kind of necessity. Charles McCarty and David Fisher provide a mathematical demonstration that the assumption that the logical theory of Tractatus yields a foundation for (or is at least consistent with) the conventional logics represented in standard propositional, first-order predicate, and perhaps higher order formal systems is false according to a preferred account of argument validity. McCarty and Fisher show that the hierarchy of variables—and, hence, of propositions—defined at 5.501 has the expressive power of (at least) finitary classical propositional logic. Also, they prove that Wittgenstein’s hierarchy of iterated N-propositions, as specified in Remark 6, does not collapse: At any level k, one finds propositions at k+1 or above that are not logically equivalent to any proposition formed at k or below. Gheorghe Ştefanov focuses on Wittgenstein’s “Private Language Argument,” holding that no experience, conceived as an inner episode to which only the subject having it has direct access, can be semantically relevant. Stefanov sees that a direct consequence of this point is that no experience, thus conceived, can be epistemi- cally relevant, and thus then, the traditional empiricist project is in danger. However, on one hand, McDowell seems to offer a solution, and, on the other hand, Stefanov claims that a different solution to the same difficulties might have been suggested by Wittgenstein himself in On Certainty. Otávio Bueno discusses Carnap’s logicist stance and critically evaluates three moves made by Carnap to accommodate the abstract mathematical objects within his empiricist program: (i) the “weak logicism” in the Aufbau; (ii) the combination of formalism and logicism in the Logische Syntax; and (iii) the distinction between internal and external question characteristic of Carnap’s involvement with modality. The outcome of Bueno’s paper is an interesting picture of the clear interplay between Carnap’s philosophy of science and his work in the philosophy of math- ematics, and the developments of his ideas along these lines. Introduction xvii

Greg Lavers examines the fundamental views on the nature of logical and mathematical truth of both Frege and Carnap. Lavers argues that their positions are much closer than is standardly assumed. Lavers also argues against the common point that Frege was interested in analyzing our ordinary mathematical notions, while Carnap was interested in the construction of arbitrary systems, for, as Lavers claims, our ordinary notions play, in a sense, an even more important role in Carnap’s philosophy of mathematics than they do in Frege’s. Lavers’ paper ends by rejecting Tyler Burge’s interpretation of Frege which is in opposition to any rea- sonable Carnapian reading of Frege. Thomas Meier aims to provide a historical reconstruction of the interconnections between Carnap’s Aufbau, Kuhn’s model of theory change, and the structuralist view of scientific theories. Meier claims that scientific structuralism is rooted in Carnap’s early work, especially in the Aufbau. Meier claims that Carnap’s idea of purely structural definite descriptions exposed in the Aufbau can be seen to be analogous with the goal of the structuralist view of representing our knowledge about scientific theories structurally. He also discusses how the development of the structuralist view is strongly motivated by Kuhn’s conception of theory change. Marco Panza is concerned with the relation between analyticity and what he calls “epistemic economy.” This relation is analyzed in the context of questioning the analyticity of abstraction principles. Panza claims that one important virtue of these principles that is commonly overlooked is their epistemic economy. Thus, most of the paper is dedicated to a careful and interesting examination of this notion in the context of defining real numbers. Graham Priest provides an analysis and commentary on the second half of Jan Łukasiewicz’s book On the Principle of Contradiction in Aristotle (1910). The book contained a critique of the traditional attitude to the principle of non-contradiction and a re-evaluation of its significance in light of contemporary developments in logic. Priest shows that Łukasiewicz is seen to be badly torn, for even though he eventually endorses the principle, he does so, not in virtue of the evidence he considers, but despite it. In particular, he considers arguments against the principle, drawn from Hegel, Meinong, and the paradoxes of self-reference. Iulian Toader discusses Weyl’s criticism of Dedekind’s principle that there is no scientific provability without proof. This criticism, Toader claims, challenges not only a logicist norm of belief in mathematics, but also a realistic view about whether there is a fact of the matter as to which norms of belief are correct.

Sorin Costreie