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Necessity Lost

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Necessity Lost Modality and Logic in Early Analytic Philosophy Volume I

Sanford Shieh

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Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford.

It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Sanford Shieh 2019 The moral rights of the author have been asserted First Edition published in 2019 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2018962715 ISBN 978–0–19–922864–5 Typeset by Sanford Shieh Printed and bound in Great Britain by Clays Ltd, Elcograf S.p.A. Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

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For Mihaela

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Contents Preface

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Abbreviations

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Introduction Necessity Lost: Frege Necessity Lost: Russell Looking Ahead: Necessity Regained Closing Remarks

1 2 6 10 12

Part I. Frege 1. The Modalities of Judgment 1.1 Frege against Traditional Logic 1.1.1 A Brief Sketch of Traditional Logic 1.1.2 Kant on Judgment and Logic 1.1.3 Problems of Traditional Logic 1.1.4 The Fregean Solution 1.2 Frege’s Early Conception of Judgment 1.3 Frege against Kant in Begriffsschrift 1.4 Modality in Frege’s Begriffsschrift

17 18 18 20 27 29 33 39 49

2. Amodalism 2.1 Two Interpretations of Frege on Modality 2.2 Truth is Absolute 2.2.1 Against Hilbert and Korselt 2.2.2 Thoughts are not Temporal or Spatial 2.3 Amodalism 2.4 Early Truth Absolutism and Amodalism 2.5 Inadequate Grounds for Amodalism

57 58 61 62 66 68 71 73

3. From Judgment to Amodalism 3.1 Judgment and Truth after the Sense/Reference Distinction 3.2 Redundancy against the Predication Analysis 3.2.1 More Varieties of Redundancy 3.2.2 Doubts about Redundancy 3.2.3 Summary

77 79 83 87 88 89

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contents 3.3 3.4 3.5

The Indefinability of Truth What is a Step to a Truth-Value?

The Recognitional Conception of Judgment 3.5.1 The Supervenience of Truth-Predicating Judgments 3.5.2 Judgment as Recognition 3.5.3 Recognition as Step to the Level of Referents 3.5.4 Thoughts (Gedanken) as Representations (Vorstellungen) 3.5.5 The Constitution of the Step to a Truth-Value 3.5.6 The Recognitional Conception and Redundancy 3.5.7 Nugatio ab Omnia Nævo Vindicatus 3.5.8 Two Worries 3.5.9 The Recognitional Conception and Object-Relation Interpretations 3.5.10 Recognition and Acknowledgment 3.6 Judgment, Judging, and Factivity 3.6.1 Against the Factivity of Fregean Judgment 3.6.2 For the Factivity of Fregean Judgment 3.6.3 Judging vs. Judgment; Holding True vs.

Acknowledgment of Truth 3.6.4 The Independence of Truth from Acknowledgment of Truth 3.6.5 A Letter to Jourdain 3.7 Apparent Thoughts 3.8 The Basic Argument for Truth Absolutism 3.9 The Basic Argument before the Sense/Reference Distinction?

3.10 A Concluding Remark 4. The Truth in Modalism 4.1 Parts of Thoughts 4.1.1 Between Begriffsschrift and the Sense/Reference Distinction 4.1.2 After the Sense/Reference Distinction 4.1.3 Multiple Analyses 4.2 Fregean Accounts of Temporalism 4.2.1 Senses expressed as a Function of Time 4.2.2 Another Argument against Temporalism 4.2.3 Senses presenting Times as Parts of Thoughts 4.2.4 Temporal Modal Discourse 4.3 Fregean Accounts of Circumstantialism 4.3.1 A Parallel to Temporalism

89 96 99 100 102 102 103 108 111 113 115 119 120 124 124 126 127 130 131 133 136 140 143 145 146 147 153 154 156 157 158 167 169 170 170

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4.4

4.3.2 Circumstances as Thoughts, I 4.3.3 Metaphysical Modal Discourse, I 4.3.4 Circumstances as Thoughts, II 4.3.5 Metaphysical Modal Discourse, II 4.3.6 Concluding Remark Analyticity, Apriority, and Modality

5. The Nature of Logic 5.1 Frege’s Main Characterizations of Logic 5.1.1 Universality or Generality (Allgemeinheit) 5.1.2 Logical Laws are Truths 5.1.3 The Justification of Logical Laws 5.1.4 Primitive and Dependent Truths 5.1.5 Logical and other Sources of Knowledge 5.1.6 Primitive Truths, Axioms and Justificational Independence 5.1.7 Self-Evidence and Self-Sufficiency 5.2 The Constitution of Justificational Self-Sufficiency 5.2.1 Semantics and Soundness Arguments 5.2.2 Soundness Arguments as Logicality Arguments 5.2.3 Is Frege giving Logicality Arguments?

5.2.4 A Problem for Logicality Arguments 5.2.5 An Alternative to the Logicality Interpretation?

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Part II. Russell and Moore 6. From Idealism to Logicism 6.1 Bradley’s Theory of Modality 6.1.1 Hypothetical Judgments 6.1.2 Judgments of Necessity and Possibility 6.2 Geometry, Logic, and Necessity 6.2.1 Kant on Geometry and the Problem of Non-Euclidean Geometries 6.2.2 Differences with Kant: Syntheticity, Apriority, and Necessity 6.2.3 The Transcendental Justification of Projective Geometry 6.3 The Ultimate Indemonstrability of Necessity 6.4 Necessity and Logicism 6.4.1 Main Features of Axioms 6.4.2 The Logical Calculus and Analysis of Manifolds

233 234 234 238 241 241 244 246 249 254 254 257

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The Main Problem of Russell’s Account of the Logical Calculus 6.5 Concluding Summary

266 267

7. The Rejection of Modality 7.1 The Path to the Rejection of Modality 7.2 Bradley’s Theory of Judgment 7.3 Moore’s Critique of Bradley’s Theory of Judgment 7.4 Moore’s Metaphysics of Judgment, Propositions, and Truth 7.5 Russell’s Metaphysics of Propositions 7.5.1 Terms, Being, and Existence 7.5.2 Things, Concepts, and Modes of Occurrence 7.5.3 The Unity of the Proposition 7.5.4 Denoting Concepts 7.6 Moore’s Critique of Kant’s View of Necessity 7.7 Russell’s Amodalism

270 271 276 279 287 295 295 296 297 299 300 305

8. Completing the Rejection of Idealism 8.1 Russell against Bradley in Principles 8.2 Bradley on Metaphysics and the Composition of Wholes 8.2.1 The Argument against Psychological Atomism 8.2.2 The Regress Argument against the Relations 8.3 Bradley’s Regresses, Sufficient Reason, and Modality 8.4 Parts and Wholes in Principles 8.4.1 Russell’s Doctrine 8.4.2 Aggregates 8.4.3 Unities

309 309 314 316 318 322 329 329 331 333

9. Logic and Implication 9.1 Inference and Formal Implication 9.2 The Generality of Logic 9.3 Problems of Formal Implication 9.3.1 The Composition of Propositions of Formal Implication 9.3.2 The Inferential Justification of Formal Implications 9.4 The Materiality and Indefinability of Implication 9.5 Whence Material Implication?

9.6 Implication in Principia

336 337 344 347

10. The Continuing Banishment of Modality 10.1 Moore on Necessity as Logical Priority 10.2 Russell on Necessity as Logical Priority 10.3 Our “Feelings” of Necessity

371 371 374 376

348 350 352 361 365

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contents 10.3.1 The Feeling from Apriority 10.3.2 The Feeling from Demonstrability 10.3.3 The Feeling from Analyticity 10.3.4 The Feeling from Generality 10.3.5 The Significance of the Feelings 10.3.6 The Significance of “Necessity and Possibility” 10.4 After “Necessity and Possibility” 10.4.1 “Some Explanations in Reply to Mr. Bradley” (1910) 10.4.2 The Problems of Philosophy (1912) 10.4.3 “On the Notion of Cause” (1912–13) 10.4.4 The Theory of Knowledge (1913) 10.4.5 Our Knowledge of the External World (1914) 10.4.6 “The Philosophy of Logical Atomism” (1918–19) 10.4.7 Introduction to Mathematical Philosophy (1919)

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Postscript

404

Bibliography

409

Index of Names

429

Subject Index

432

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Preface I have found that philosophy often calls on me to solve problems, but, almost equally often, also to figure out why what I’m trying to solve are problems and why what I’m doing are attempts at solutions. No doubt others find themselves facing different demands, but, for me these two aspects of philosophizing have always been inescapable, indeed, not altogether separable.

This book, ultimately, comes from the second of these demands.

Many of the problems and strategies of solution of recent philosophy in the analytic tradition live in a background constituted of the concepts of necessity, possibility, and contingency, often in the striking guise of Leibniz’s possible worlds.

My interest is to figure out how modal notions forms such a crucial framework for posing and answering philosophical questions. I approach this question by examining the philosophical history of modality in analytic philosophy.

This book is the first result of this examination.

Philosophical history is, of course, philosophy first and history second. The secondness of history in philosophical history does not, however, mean that it’s of secondary importance, especially for my purposes.

It is no secret that anachronism is a danger when one tries to understand texts from other philosophical traditions. It is equally a danger in reading texts that one thinks of as belonging to an earlier period of a philosophical tradition that one would like to call one’s own. This danger need not be fatal. Anachronism could be philosophically fruitful; many would point to P. F. Strawson’s The Bounds of Sense as a successful philosophical history in spite of the justice it fails to do to the Critique of Pure Reason.

However, anachronism in reading Gottlob Frege, Bertrand Russell, G. E. Moore, C. I. Lewis, or Ludwig Wittgenstein sometimes leads to less inspiring results: projecting onto them the philosophical concerns we have or turning them into the heroes and villains of a tale whose happy outcome is the way we do philosophy now, if not the philosophical positions we hold now. There is, of course, something to be said for making the writings of these philosophers simpler for us, now, to understand. One may also take such just-so stories of how contemporary philosophizing came to be as arguments for contemporary methods and positions, so that the interest of these stories lies, not in the accuracy of their historical representations, but in the cogency of the arguments that they embody.

It’s harder to see how one could really learn something from our philosophical predecessors by such procedures.

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preface

Perhaps, as it has been urged, we can never escape ourselves when we attempt to understand earlier philosophy. But that doesn’t preclude making the attempt to become conscious of how our assumptions may stand in the way of philosophical understanding. It is through such an attempt that we can come to learn something, from our fore-bearers, and about ourselves. The philosophical interest and fruitfulness that might result are what I hope for, for this book.

In one way, the beginnings of this project really go back to a Ph.D. dissertation that I did not write, with a supervisor I did not have.

Burton Dreben was to be that supervisor. I had been interested in Frege ever since I read Foundations of Arithmetic in a tutorial with Jonathan Barnes. However, the Frege I encountered in that tutorial seemed quite different from the one Burt urged on me in our long but somehow never conclusive conversations. Burt’s Frege, as elaborated in Warren Goldfarb’s classes on early analytic philosophy and the writings of Tom Ricketts and Joan Weiner, was the one inhabiting Emerson Hall. Warren, my actual Doktorvater, together with Tom, suggested that I think through the differences between the picture of Frege I found around me and the massive landmark interpretation of Frege propounded by Sir Michael Dummett. Ultimately, though, that plan for a dissertation came to naught.

One reason was that I had come to keep company with Riki Heck and Jason Stanley. I found them, and later, Ian Proops and Jamie Tappenden, expressing many of the reservations I had about Burt’s Frege. However, the effect of thinking more about these reservations was that it became harder and harder for me to pinpoint what exactly are the disagreements between the two styles of understanding Frege. Both left me dissatisfied in one way or the other, but I didn’t have much to say beyond these dis-satisfactions.

Another reason was that the time I had spent with Dummett’s writings on Frege led me to think about Dummett’s anti-realism and critique of classical logic. This brought the problem-solving side of my philosophical sensibilities to the fore, and I ended up devising ways of defending Sir Michael’s anti-realism and, at the same time, of turning aside the critique of classical logic he used it for.

I did not come back to Frege for over a decade, quite some time after the project of which this book is the first issue truly began. There were two proximate causes. One was Peter Momtchiloff’s asking me if I would be interested in writing something on the role of modality in analytic philosophy. I am sure he did not expect that nothing would come of that request for over ten years. I thank him for his patience over all this time and hope to make it up to him by giving him Volume II in short order. The other cause was Mike Beaney’s request for a contribution to his magisterial Handbook of the History of Analytic Philosophy. In the course and then the aftermath of writing that essay, I came gradually to see that, to do justice to the topic, much more was required than the book I had outlined to Peter. Some of what was required is the discussion of Frege in

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this book, and this material, I venture to say, might have formed part of that dissertation I did not write.

As I worked on this book, I was fortunate to have had the help, encouragement, and philosophical companionship of many friends, colleagues, and teachers.

A handful of these made a decisive difference in the writing of this book.

I have been philosophizing with Juliet Floyd ever since we shared an office.

We have long talked about the great thinkers at the inception of the analytic tradition—Frege, Russell, Wittgenstein, Harry Sheffer, and C. I. Lewis, and about the generation after them—Carnap and Quine. Our collaboration on Future Pasts shaped my conception of the history of analytic philosophy and the fruitful philosophical prosecution of it. But, more recently, she has been a tremendous influence on my thinking about the role of modality in early analytic philosophy; above all else, she was willing to confirm my sense of how to read Frege and Russell on modality, and to give me the courage to follow that sense to interpretations that seemed outlandish. She also gave me over and over, opportunities to talk about my views at the Boston Early Analytic Philosophy Workshop which she organized.

Robert May and I have been talking about Frege for almost as long as I have been working on this book. He suggested to me, shortly after we met, that for my project I should consider Frege’s criticisms of Hilbert. This was das erlösende Wort, pointing the way to my realizing just how deep in Frege’s philosophy lie the wellsprings of his opposition to modality. Since then I have regularly stolen Robert’s ideas about Frege; in particular, I got from him the idea of judgment as factive, that is, as implying truth, which plays a central role in Part I of this book. I hope that it will be worth Robert’s while repaying the favor.

I met Gary Ebbs when he was junior faculty at Harvard, and we have been discussing our common preoccupations—anti-realism, early analytic philosophy, and the dialogue between Quine and Carnap—ever since. I learn something from every one of our conversations; but, in the case of this book, there were several pivotal discussions. One was on Russell’s material implication, where his questions about how the idea made any sense prompted me to a much better understanding of Russell’s conception of logic. Another discussion sharpened my view of Russell’s rejection of British absolute idealism. Two others were on Frege: Gary got me to articulate much more fully why Frege resisted senses that presented referents relative to contextual factors, and to clarify for myself what of the conception of judgment I discern in Frege is truly essential.

Ian Proops has been a great friend since graduate school. I have learned a tremendous amount from his writings on Russell and on the Tractatus, especially where I disagree. More recently, he has given me expert advice on Kant. Ian is never doctrinaire in conversation, and his thorough command of the texts inevitably keeps me on the straight and narrow. If we’ve not had the chance to talk about Russell over the years, this book would certainly be the poorer.

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Arata Hamawaki is another friend and longstanding philosophical interlocutor from graduate school. We have spent countless hours meandering through all sorts of highways and byways of philosophy; that we never seem to arrive anywhere is part, indeed the main part, of the illumination, not to mention the fun, of Arata’s philosophical presence. I was extremely happy that I could have him as a colleague for a whole year, to indulge at length in this aimless philosophizing. Most recently, Arata, together with Keren Gorodeisky, got me over the final impediment to finishing this book, by providing me with a way out of a sticky point in my interpretation of Frege’s response to Kant’s table of judgments.

I wish to thank those who generously gave of their valuable time to read and comment on earlier versions of parts of this book. Max Weiss suffered through quite a few variations of my ideas about Frege’s conception of logic, and about modality in analytic philosophy. Mark Textor’s critical replies to my account of Frege’s conceptions of judgment, thought, and truth enabled me to sharpen my discussion immeasurably, even if I cannot fully allay all his worries. Jessica Leech patiently explained to me her view of Kant’s modalities of judgment, and her insightful questions about my view of Frege’s response to Kant led me to correct a critical mistake. Cheryl Misak not only helped with my discussion of Russell and Lewis, but she also shared with me the manuscript of her recent wonderful book, Cambridge Pragmatism.

I would like to thank two anonymous readers for Oxford University Press for their responses to the manuscript of this book. One of them certainly went way beyond the call of duty in furnishing me with extensive helpful comments.

These comments demanded some concentrated reworking and expansion of my arguments resulting in significant improvements.

I’m grateful for all the questions and criticisms I received at presentations of my views. In particular, I thank Roberta Ballarin, Paddy Blanchette, Jim Conant, Cora Diamond, David Hunter, Mike Kremer, Sandra Lapointe, Tom Stoneham, and Peter Sullivan.

Many others have, in one way or another, wittingly or otherwise, helped to make this book possible. Chief among these are my other Doktorvater, Charles Parsons, and my other former office-mate, Nancy Bauer. In addition, I thank Stewart Candlish, Emily Carson, Philip Ebert, Fan Zhao, Eli Friedlander, Michael Glanzberg, Michael Hallett, Jeremy Heis, Peter Hylton, Kelly Jolley, Greg Landini, Bernie Linsky, Tom Lockhart, David Macarthur, Eric Marcus, Jim O’Shea, Mark Richard, Marcus Rossberg, and Ian Rumfitt.

I have undoubtedly missed others; my apologies and my thanks.

It would be remiss of me not to mention Jean-Philippe Narboux, with whom I have not discussed the details of the present book, but only of the next volume.

Although I have known him since 2003, it wasn’t until we had occasion to talk at length in 2011 that I discovered how much he shares my philosophical sensibilities.

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I’m also grateful for his persistence in finding my conception of early analytic philosophy intelligible and useful.

I wish to recall two exemplary philosophers who are no longer with us.

Sir Michael Dummett was extremely kind in taking the time to discuss with me my ideas about what his anti-realism really is. I doubt he was ever fully convinced, but perhaps that is as much a reflection of his philosophical integrity as it is of my philosophical shortcomings. No doubt it has always been easier to place a label on some position one wishes, for some reason, to reject, than it is to do the work of understanding it. The lesson that I eventually came to learn from my discussions with Sir Michael is that this has been the fate of his ever-evolving conceptions of anti-realism. Anti-realism has been stuffed into a pigeonhole entitled “verificationism,” so that the subtlety of thinking and the courage to face philosophical difficulties that one would encounter in Sir Michael’s writings can be that much more easily avoided.

It was a privilege to have gotten to know Ruth Marcus and to have spent time with her thinking about her work and mine over the course of some three years.

She was, as anyone who knew her or knows her writings would expect, unstinting in her criticism of what she found wanting. But she was equally unstinting in her openness to the possibility of perspectives other than her own, so long as they are, as she puts it, serious about philosophy.

I have also benefited from the support of many institutions.

First among these to which I wish to express my gratitude is the Society for the Study of the History of Analytical Philosophy. Sandra Lapointe, its founder and president, has created a truly vibrant intellectual community. The regular annual conferences and sessions at the American Philosophical Association meetings have made it possible for all those interested in the philosophical history of the analytic tradition to present their ideas and receive helpful feedback. I would like also to thank the host institutions of the annual conferences I attended, and the philosophers there who provided support: Joan Weiner, Mark Kaplan, and Kirk Ludwig, in addition to Gary, at Indiana University, Mathieu Marion at Université de Quebec à Montréal, and Richard Zach at the University of Calgary.

The School of Sociology and Philosophy at Beijing Normal University, under the leadership of Professor Jiang Yi, has organized several conferences and workshops that have brought analytic philosophy and its history much more to the attention of Chinese scholars. Two especially fruitful ones that I attended were the Beijing International Conference on Wittgenstein and Contemporary Philosophy, and the workshop on the translation of Mike Beaney’s Handbook into Chinese. I would also like to thank Professor Jiang for inviting me to give a course of lectures on Wittgenstein’s Tractatus in 2016.

I thank the organizers of two conferences for affording me the occasion to present my views of on Russell’s conception of logic and C. I. Lewis’s criticism of it. These are Jean-Philippe, Steeves Demazeux, Quentin Kammer, Timur

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Uçan, and Henri Wagner for the Colloquium “La relativisation de l’a priori,” at Université Bordeaux Montaigne, and Eric Loomis, Ted Poston, and Richard Fumerton for the Orange Beach Epistemology Workshop. In addition, I thank the European Society for Analytic Philosophy for organizing its 2017 Congress of Analytic Philosophy, at which I participated in an especially stimulating panel with Robert May and Mark Textor.

I’m grateful to the National Endowment for the Humanities for awarding me a Fellowship Grant, #FB-58111-15, that made possible a year of concentrated work on this book.

I thank my colleagues, past and present, at Wesleyan University for the fine intellectual setting they’ve created. I have had interesting philosophical discussions with Lori Gruen, Steve Angle, Joe Rouse, Steve Horst, and Kent Bendall. I’m especially grateful to Lori for her steadfast encouragement of my work. Wesleyan University itself has also played a continuing role in supporting my research. In particular, I wish to single out two academic deans, Joyce Jacobsen and Andy Curran, for their timely help.

In preparing this book for publication, I used open-source software written by volunteers who generously committed their time and expertise without remuneration. I’m, in the first instance, grateful to Riki Heck, for writing the original OUP Royal LATEX document class, and for introducing me to the program LYX, of whose development team he is a member, and using which I wrote and typeset this book. I also thank Bennett Helm for making helpful changes to the OUP Royal class that made my own customizations that much easier to carry out.

In addition, I thank Ivan Valbusa, the author of the biblatex-philosophy LATEX package, and Alex Ball, the author of the biblatex-oxref package, for helping me with customizing their code. Finally, I’m grateful to members of the tex.stackexchange.org community who patiently answered my seemingly endless series of questions.

I’m sad that neither my parents nor my parents-in-law lived to hold a copy of this book in their hands. It is small consolation, but consolation nevertheless, to feel that they had been happy to know how much I appreciated their unflagging support throughout the years.

Finally, and most importantly, I could not have finished this book without my wife, Mihaela Fistioc. She has been vastly patient with my singular lack of progress over the years, and somehow saw her way to continue encouraging me to keep going. Although she claims to know little about the parts of philosophy to which much of this book belongs, the acuity of her questions prompted me to rethink and rewrite central arguments throughout the book. On Kant, about which she knows much more than I ever will, her questions and suggestions put me in possession of the key to my account of Frege’s reaction to the table of judgment. Her stern editorial advice has significantly improved the readability of this work, although, it is to be feared, not nearly enough to satisfy her high

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standards. But, important though these may be, they are, in the end, secondary.

The warmth of her love, and the humor and the fun with which she has invested our life, are what make it at all worthwhile.

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Abbreviations The following abbreviations are for frequently cited primary sources. Full details of these works are in the Bibliography.

In the following list, I provide English titles for Frege’s works, with the exception of German collections of his writings and correspondence.

Writings of Frege BLC

“Boole’s Logical Calculus and the Concept-Script,” 1880

BLI

Basic Laws of Arithmetic, Vol. I, 1893

BLII

Basic Laws of Arithmetic, Vol. II, 1903

BS

Begriffsschrift, a Formula Language of Pure Thought modelled on that of Arithmetic, 1879

CP

Collected Papers on Mathematics, Logic, and Philosophy, 1984

CSR

“Comments on Sense and Reference,” 1892–5

CT

“Compound Thoughts,” 1923–6

FA

The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, 1884

FGI

“On the Foundations of Geometry: First Series,” 1903

FGII

“On the Foundations of Geometry: Second Series,” 1906

IL

“Introduction to Logic,” 1906

L1

“Logic,” 1879–91

L2

“Logic,” 1897

LM

“Logic in Mathematics,” 1914

N

“Negation,” 1918–19

NS

Nachgelassene Schriften, 1969

PCN

“On Mr. Peano’s Conceptual Notation and My Own,” 1897

PMC

Philosophical and Mathematical Correspondence, 1980

PW

Posthumous Writings, 1979

SK

“Sources of Knowledge of Mathematics and the Mathematical Natural Sciences,” 1924–5

SR

“On Sense and Reference,” 1892

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abbreviations

T

“Thought,” 1918–19

WB

Wissenschaftlicher Briefwechsel, 1969

Writings of Moore Nec

“Necessity,” 1900

NJ

“The Nature of Judgment,” 1899

PE

Principia Ethica, 1903

RevFG

“Critical Notice of Russell, An Essay on the Foundations of Geometry,” 1899

TF

“Truth and Falsity,” 1901

Writings of Russell AEE

“Les axiomes propres a Euclide: Sont-ils empiriques?” 1898

AMR

“An Analysis of Mathematical Reasoning,” 1898

CR

“The Classification of Relations,” 1899

FG

An Essay on the Foundations of Geometry, 1897

FIAM

“The Fundamental Ideas and Axioms of Mathematics,” 1899

IMP

Introduction to Mathematical Philosophy, 1919

IO

“L’idée d’ordre et la position absolue dans l’espace et le temps,” 1901

IPST

“Is Position in Time and Space Absolute or Relative?” 1901

MTCA1

“Meinong’s Theory of Complexes and Assumptions (I),” 1904

MTCA3

“Meinong’s Theory of Complexes and Assumptions (III),” 1904

NP

“Necessity and Possibility,” 1905

NT1

“The Nature of Truth,” 1905

NT2

“The Nature of Truth,” 1906

NT3

“On the Nature of Truth,” 1906

NTF

“On the Nature of Truth and Falsehood,” 1910

OKEW

Our Knowledge of the External World, as a Field for Scientific Method in Philosophy, 1914

PLA3

“The Philosophy of Logical Atomism: Lectures V & VI,” 1919

PLA4

“The Philosophy of Logical Atomism: Lectures VII & VIII,” 1919

PM

Principia Mathematica, 1910

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PoL

A Critical Exposition of the Philosophy of Leibniz, with an Appendix of Leading Passages, 1900

PoM

The Principles of Mathematics, 1903

PoMD

“The Principles of Mathematics, Draft of 1899–1900,” 1899–1900

PoP

The Problems of Philosophy, 1912

RB

“Some Explanations in Reply to Mr. Bradley,” 1910

TI

“The Theory of Implication,” 1906

TK

“The Theory of Knowledge,” 1913

Other Primary Sources PLI

Bradley, F. H., The Principles of Logic, 1883

PLII

Bradley, F. H., The Principles of Logic, with Commentary and Terminal Essays, 1922

SAT

Bradley, F. H., “On Some Aspects of Truth,” 1911

AR

Bradley, F. H., Appearance and Reality: a Metaphysical Essay, 1893

ETR

Bradley, F. H., Essays on Truth and Reality, 1914

JL

Kant, I., “The Jäsche Logic,” 2004

CPR

Kant, I., Critique of Pure Reason, 1998

KrV

Kant, I., Kritik der reinen Vernunft, 1956

SSL

Lewis, C. I., A Survey of Symbolic Logic, 1918

SL

Lewis, C. I. and Langford, C. H., Symbolic Logic, 1932

NL

Wittgenstein, L., “Notes on Logic,” 1913

NB

Wittgenstein, L., Notebooks, 1914–1916, 1979

WC

Wittgenstein, L., Wittgenstein in Cambridge: Letters and Documents 1911–1951, 2008

A Note on Citation and Translations In citing texts of Frege and of Wittgenstein, I mostly use standard translations, with which I do not much disagree. However, I do differ frequently from them on a number of small points pertaining to the interpretive arguments I’m making and so I have (mostly slightly) modified the translations. Rather than indicate all these modifications, I always provide the original texts in footnotes.

Frege’s published works are cited in the text with the published pagination, which is given in all of the standardly used translations; I give no page reference

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for the German text in footnotes. Frege’s unpublished writings and correspondence are cited in the text with the pagination of, respectively, Posthumous Writings (PW ) and Philosophical and Mathematical Correspondence (PMC ); the German text in footnotes are cited with the pagination of, respectively, Nachgelassene Schriften (NS ) and Briefwechsel (WB).

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Introduction Logic, as many philosophers would agree, consists of the standards of correctness governing all deductive reasoning. A long tradition, going back to Aristotle, conceives of these standards in terms of the concepts of necessity and possibility: a line of reasoning is correct if the truth of its conclusion follows necessarily from the truth of its premises or, put differently, if it is not possible for the conclusion to be false when the premises are true.1 While a range of conceptions of necessity and possibility—the concepts of modality—are of central importance in contemporary analytic philosophy, and while the philosophy of logic is an active area of research, there is at present relatively little work on the question of whether modality is indeed intrinsic to the standards of correctness that constitute logic.

However, this question of the relationship between modality and logic is the crux of a controversy which dates back to the beginnings of analytic philosophy, in the late nineteenth and early twentieth centuries. The founders of analytic philosophy, Gottlob Frege and Bertrand Russell, form one side of this controversy.

They were committed to rejecting modal notions. Thus, while they of course accept that the correctness of deductive reasoning involves truth and falsity, they also insist that logic has fundamentally nothing to do with modality. It is logic, rather than modality, that lies at the foundation of their philosophies, and so they explained away modal concepts in terms of logical ones. The other side of the controversy consists of replies to Frege and Russell by two of their immediate successors, C. I. Lewis and Ludwig Wittgenstein. They argue, against Frege and Russell, that reason, truth, and logic are not conceivable independently of modality. So for them modality is philosophically prior, and the nature of logic is explained in terms of necessity and possibility.

The present book is the first of two volumes in which I offer a detailed account of this controversy over the relative philosophical priority of modality and logic.

The first volume focuses on Frege and Russell’s side of the controversy. The second volume focuses on Lewis’s and Wittgenstein’s responses to Frege and Russell. In the next two sections of this Introduction, I will outline my main interpretive arguments concerning Frege and Russell. I will then briefly sketch the interpretations of Lewis and Wittgenstein to be presented in Volume II. I will conclude with a remark on the relevance of this theme in early analytic philosophy to contemporary analytic philosophy.

1

Aristotle himself puts it thus: “συλλογισμὸς δέ ἐστι λόγος ἐν ὧι τεθέντων τινῶν ἕτερόν τι τῶν κειμένων ἐξ ἀνάγκης συμβαίνει τῶι ταῦτα εἶναι” (Prior Analytics: 24b18–20), that is to say, a valid argument (συλλογισμὸς) is a discourse in which, certain things having been supposed, something else results out of necessity (ἐξ ἀνάγκης).

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introduction

Necessity Lost: Frege My discussion of Frege begins by showing how his rejection of modality follows from central philosophical commitments, and ends with an account of his conception of the nature of logic.

In Chapter 1, I give the philosophical background of Frege’s view of modality in his first book, Begriffsschrift (1879). The background is Kant’s theory of judgment.

Kant held that in making a judgment a judger forms a representation. Frege rejects this view, and claims that judgment has nothing to do with the formation of representations, but consists of taking a representation, however formed, to be true. A number of commentators have noted this difference between Frege and Kant, without, however, giving any account of why they differ.2 I show that Frege’s grounds for this disagreement lie in one of Frege’s great achievements in Begriffsschrift: the formulation of modern quantificational logic. Frege’s logic resolves a number of difficulties with the traditional logic of Kant’s time, and Frege rejects those aspects of Kant’s conception of judgment which depend on features of traditional logic superseded by Frege’s logic. This disagreement does not extend to Kant’s view that modality is not a feature of the representations involved in judgments. In Begriffsschrift, Frege also holds that necessity and possibility are not aspects of the representation involved in a judgment—the “content” of a judgment in Frege’s terminology. For Frege, then, the judgment that necessarily 2 + 2 = 4 has the same content as the non-modal judgment that 2 + 2 = 4. As he puts it, ascribing necessity “has no meaning for us” (BS : §4, 5, emphasis in original).3 It is widely acknowledged that Frege’s adoption of the distinction between sense and reference, roughly a decade after Begriffsschrift, is of central importance in his philosophical development. Indeed, it is reasonable to divide Frege’s philosophy into an early phase, before this distinction, and a later, post-sense/reference phase.

After the early Begriffsschrift, Frege never discusses modality. However, I show that Frege’s later philosophy commits him to rejecting a conception of necessity and possibility prominent in the history of philosophy, down to the present day.

There are two parts to this conception. First, necessity and possibility are modes of truth and falsity, that is to say, different ways of being true or false. Some thoughts or propositions are in fact true, but might have been false. Others are not only actually true, but could not have been false. Others are in fact false, but might have been true. Yet others are not only false, but could not have been true. Second, what it means to say that a thought might be true or might be false is explained in terms of alternatives to the circumstances that actually obtain: a thought might be true if it is true in alternative, non-actual circumstances, and might be false if it is false in alternative circumstances. This notion of 2 3

See, for instance, Longuenesse (1993; 2006) and Wolff (1995). “so hat die Form des apodiktischen Urtheils für uns keine Bedeutung.”

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alternative circumstances is expressed vividly by G. W. Leibniz’s possible worlds.

In Leibnizian terms, a thought is necessarily true if it is true in all possible worlds, and possibly true if it is true in some world. Thus, the concepts of necessity and possibility require the relativization of truth and falsity: a proposition isn’t simply true or false; rather, it is true or false relative to a set of circumstances or a possible world. This two-part conception I call modalism. In Chapter 2, I argue that Frege is committed to rejecting modalism, because he insists that there is no relativization of truth and falsity. Truth is absolute, and there is no such thing as truth in certain circumstances, as opposed to truth simpliciter. Hence there are no modes of truth, and no classification of truths into actual, possible, or necessary. Frege’s position I call amodalism.

In Chapter 3, I take up the question of why Frege insists on the absoluteness of truth. The answer lies in the conceptions of judgment, truth, and thought that underlie some puzzling and controversial positions of his later philosophy. First, Frege claims that truth and falsity are two objects, the “truth-values” named “the True” and “the False.” Frege holds that thoughts in general refer to one of the truth-values, and that judgment consists in “stepping forth from a thought to a truth-value” (SR: 35).4 Second, Frege holds that some thoughts don’t refer at all, and are “apparent thoughts” (Scheingedanke). Third, Frege holds that ascribing truth to a thought is in some way redundant; for example, a sentence such as ‘the thought that 5 is a prime number is true’ says no more than does the simple sentence ‘5 is a prime number’ (SR: 34–5).5 Finally, Frege argues that truth is not definable.

These views appear to be in some tension with one another. If truth is an object referred to by thoughts, then isn’t it the sentence ‘the thought that Saturn is a planet is true’ about this object, while the sentence ‘Saturn is a planet’ is not? So how can these sentences express the same thought? Moreover, can one not define the truth of thoughts as the property of referring to the True?

Commentators have tended to resolve these tensions by arguing that Frege either didn’t really or shouldn’t have held one or the other of these positions.6 But I show that, properly understood, these positions reflect a single coherent conception of judgment, truth, and thought.

The conception is this. For Frege, a thought represents something to be the case. For example, the thought that Saturn is a planet represents an object, Saturn, as falling under the concept of being a planet. A judgment is fundamentally the recognition of the obtaining of what a thought represents. To make 4

“Urteilen kann als Fortschreiten von einem Gedanken zu seinem Wahrheitswerte gefaßt werden.”

“Man kann ja geradezu sagen: ‘der Gedanke, daß 5 eine Primzahl ist, ist wahr’. Wenn man aber genauer zusieht, so bemerkt man, daß damit eigentlich nichts mehr gesagt ist als in dem einfachen Satze ‘5 ist eine Primzahl’.”

6 For example, Heck (2007) holds that Frege should not have accepted the redundancy of truth ascriptions, while Greimann (2007) questions whether Frege really took truth and falsity to be objects.

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the judgment that Saturn is a planet is to recognize that the object Saturn does indeed fall under the concept of being a planet. Judgment is primarily knowing what is the case, and truth is involved in judgment only secondarily: recognizing the truth of a thought supervenes on recognizing the obtaining of what that thought represents. By recognizing that Saturn falls under the concept of being a planet, one thereby also recognizes the truth of the thought that Saturn is a planet; alternatively, recognizing that this thought has the property of truth is at bottom just recognizing that Saturn falls under the concept of being a planet.

Thus, truth is not a fundamental property of thoughts, but rather that property of thoughts which one recognizes in virtue of recognizing the obtaining of what thoughts represent. Finally, one of the fundamental functions of a thought is to enable the acquisition of knowledge, which is to say, judgment. This is the meaning of Frege’s claim that judgment is taking a step from a thought to a truth-value: making a judgment is going beyond a mere representation of what is the case to recognizing that what is represented actually obtains.

This conception is incompatible with the view that truth and falsity are relative to time, space, or circumstance. If truth and falsity were relative, then a thought would not be determined as true or false except with respect to a time, a place, or a circumstance. From Frege’s perspective, what this purported thought represents, by itself, without a time, place or circumstance, is not something that one can recognize to obtain, or recognize not to obtain. Hence this purported thought fails to provide what is required for judgment; it fails to fulfill the primary function of thoughts and so is, at best, a defective thought, if it is a thought at all.

It is an apparent thought. The truth and falsity of genuine thoughts, in contrast, are absolute.

In Chapter 4, I indicate how Frege explains away certain intuitions that seem to support the relativity of truth. Intuitively it seems that a sentence like ‘France is a monarchy’ is false in 2018 but true in 1788. Frege’s opponent would explain this intuition by holding that this sentence expresses a thought that is false in 2018 and true in 1788. The opponent’s claim, then, is that only given a time is this supposed thought true or false. Thus, only given a time is there such a thing as recognizing what is represented as obtaining, or as not obtaining. From Frege’s perspective, the only way to make sense of this idea is to take what is represented to be something about 1788. The sentence ‘France is a monarchy’ is true in 1788, not because it expresses a thought that is true relative to this time, but rather because it expresses a thought about this time, and that thought is absolutely true. An analogous account provides a Fregean explanation of sentences that appear to be true or false relative to alternative circumstances. For Frege, the reality underlying the purported relativization of truth to time and circumstance is the embedding of time and circumstance in thought. On the basis of these accounts, which explain away the appearance of truth-relativization, I show how Frege would explain sentences that appear to ascribe necessity or possibility to

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thoughts. The illusion that such sentences describe modal properties is dispelled using the logical notions of generalization and conditionalization.

What Frege is committed to rejecting is clearly only one conception of modality. What of other conceptions? What, for example, of historically important accounts of necessity as analyticity or as apriority? In Chapter 4, I show that neither analyticity nor apriority is philosophically fundamental for Frege. In The Foundations of Arithmetic (1884), Frege explicitly formulates his own versions of Kant’s analytic/synthetic and a priori/a posteriori distinctions, explaining them in logical terms. Thus, analyses of modality as analyticity or as apriority are also at bottom explanations of modality in terms of logical notions. Incidentally, Frege’s account of the Kantian distinctions allows not only for synthetic a priori truths, but also for necessary a posteriori and contingent a priori truths.

Now, there are still other analyses of modality, not in terms of truth in alternative circumstances, or analyticity, or apriority. There is, indeed, also the view that necessity and possibility are primitive, unanalyzable concepts. Frege’s writings give us no basis for deciding whether he would have accepted or rejected these conceptions of modality. However, the idea that modality is primitive takes center stage in Volume II: neither Lewis nor Wittgenstein reject the absoluteness of truth, but take primitive notions of possibility and necessity to lie at the foundations of logic.

In Chapter 5, I discuss what logic is for Frege. Apart from displaying the nonmodal nature of Frege’s conception of logic, this account prepares the ground for understanding Wittgenstein’s criticisms of Frege, to be presented in Volume II. For Frege, logic consists of standards of correctness governing all reasoning, and is a system of truths, some of which are primitive and the remainder of which are justified on the basis of the primitive truths. Frege conceives of logic as determining the correctness of the justification of judgments by inference from other judgments. In order to avoid an infinite regress, inferential justification must rest on judgments that are not themselves inferentially justified.

These endpoints of justification divide into three kinds of judgments: those justified by sense-perception, those justified by pure intuition of space, and those justified by what Frege calls “the logical source of knowledge.”7 This last kind of judgments are the primitive truths of logic. Frege suggests that primitive logical truths are non-inferentially justified in that, in some sense, they provide their own justifications—they are self-justifying. The central questions about Frege’s conception of logic are: what is it for a thought to be self-justifying, and how do we know which thoughts are self-justifying? On my reading, Frege entertains the view that a thought is self-justifying just in case it is true in virtue of its logical structure. However, he also has reasons for holding that there are no non-circular arguments for demonstrating that a thought is self-justifying. Thus, 7 Frege’s phrase is “logischen . . . Erkenntnisquelle,” and it occurs in a letter to Hilbert written in 1899 (WB: 63).

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