Themes from Wittgenstein and Quine PDF
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THEMES FROM WITTGENSTEIN AND QUINE Grazer Philosophische Studien INTERNATIONAL JOURNAL FOR ANALYTIC PHILOSOPHY FOUNDED BY Rudolf Haller EDITED BY Johannes L. Brandl Marian David Maria E. Reicher Leopold Stubenberg VOL 89 - 2014 Amsterdam - New York, NY 2014 THEMES FROM WITTGENSTEIN AND QUINE Edited by KAI BÜTTNER, FLORIAN DEMONT, DAVID DOLBY, ANNE-KATRIN SCHLEGEL (Special Topic I: Wittgenstein) and DIRK GREIMANN (Special Topic II: Quine) Die Herausgabe der GPS erfolgt mit Unterstützung des Instituts für Philosophie der Universität Graz, der Forschungsstelle für Österreichische Philosophie, Graz, und wird von folgenden Institutionen gefördert: Bundesministerium für Bildung, Wissenschaft und Kultur, Wien Abteilung für Wissenschaft und Forschung des Amtes der Steiermärkischen Landesregierung, Graz Kulturreferat der Stadt Graz The paper on which this book is printed meets the requirements of “ISO 9706:1994, Information and documentation - Paper for documents - Requirements for permanence”. Lay out: Thomas Binder, Graz ISBN: 978-90-420-3912-4 E-book ISBN: 978-94-012-1194-9 ISSN: 0165-9227 E-ISSN: 1875-6735 © Editions Rodopi B.V., Amsterdam - New York, NY 2014 Printed in The Netherlands TABLE OF CONTENTS Special Topic I WITTGENSTEIN Guest Editors Kai BÜTTNER, Florian DEMONT, David DOLBY, Anne-Katrin SCHLEGEL Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Pasquale FRASCOLLA: Realism, Anti-Realism, Quietism: Wittgen- stein’s Stance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Severin SCHROEDER: Mathematical Propositions as Rules of Grammar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Felix MÜHLHÖLZER: How Arithmetic is about Numbers. A Witt- gensteinian Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Mathieu MARION & Mitsuhiro OKADA: Wittgenstein on Equinu- merosity and Surveyability . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Esther RAMHARTER: Wittgenstein on Formulae . . . . . . . . . . . . . . 79 Ian RUMFITT: Brouwer versus Wittgenstein on the Infi nite and the Law of Excluded Middle . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Special Topic II QUINE Guest Editor Dirk GREIMANN Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Peter HYLTON: Signifi cance in Quine . . . . . . . . . . . . . . . . . . . . . . 113 Rogério Passos SEVERO: Are there Empirical Cases of Indetermi- nacy of Translation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Oswaldo CHATEAUBRIAND: Some Critical Remarks on Quine’s Th ought Experiment of Radical Translation . . . . . . . . . . . . . . . . 153 Dirk GREIMANN: A Tension in Quine’s Naturalistic Ontology of Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Guido IMAGUIRE: In Defense of Quine’s Ostrich Nominalism . . . . 185 Pedro SANTOS: Quinean Worlds: Possibilist Ontology in an Exten- sionalist Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Special Topic WITTGENSTEIN Grazer Philosophische Studien 89 (2014), 3–10. INTRODUCTION Kai BÜTTNER, Florian DEMONT, David DOLBY, Anne-Katrin SCHLEGEL University of Zurich Mathematics occupied a central place in Wittgenstein’s work. He was led to philosophy by an interest in disputes about the foundations of mathematics. His refl ections resulted in the Tractatus’ short but insightful critique of the logicism of Frege and Russell. Moreover, it is reported that he decided to return to philosophy in 1929 after having attended a talk given by the intuitionist mathematician Brouwer. In the 1930s and early 1940s Wittgenstein wrote extensively on the philosophy of mathematics, covering a large variety of themes, including the notions of number and infi nity, the method of proof by induction, the role of contradictions and consistency proofs in mathematics, the application of mathematics, and the nature of mathematical proof and mathematical necessity. In 1944 he stated that his most signifi cant contribution had been in the philosophy of mathematics (Monk 1990, 466). However, the initial reception of Wittgenstein’s philosophy of math- ematics was predominantly negative (Dummett 1959, Kreisel 1958, Ber- nays 1959). Many of his remarks about mathematics were dismissed as either wrong or irrelevant; and some were alleged to contain technical errors. To a certain extent, this reaction can be explained by the radical nature of Wittgenstein’s ideas, which often challenge traditional assump- tions about mathematics. Another cause has been misunderstanding: the interpretation of Wittgenstein’s writings has proven diffi cult due to his unconventional style of writing, the fact that the material from his Nachlass is partly unfi nished and was not intended for publication, and the delayed publication of many relevant manuscripts from his middle period. Fortunately, the exegesis of Wittgenstein’s writings on mathematics has progressed considerably in recent years, with the appearance of such excellent monographs as Shanker 1987, Frascolla 1994, Marion 1998 and Mühlhölzer 2010. Th ese books clarify Wittgenstein’s claims and show how the accusations of technical incompetence were often the result of misinterpretation. Th is has led to a greater appreciation of Wittgenstein’s unorthodox views, which promise fresh perspectives on debates that had appeared to have reached deadlock. Th e essays in this volume are recent contributions to the newly invigorated debate about Wittgenstein’s phi- losophy of mathematics by leading scholars and specialists. According to the later Wittgenstein, many philosophical misconcep- tions and mythologies can be traced back to the assumption that any declarative sentence describes a corresponding portion of reality. Th us, he famously argues that self-ascriptions of mental predicates have an expres- sive function and do not describe an inner world of private experiences. And, similarly, mathematical propositions have a normative rather than a descriptive function. Instead of describing a realm of abstract objects, they are rules for the transformation of empirical descriptions. In his paper Pasquale Frascolla discusses a potential diffi culty for Wittgenstein’s conception, which arises from the intuitive assumption that for a sen- tence to have a descriptive function is equivalent with its being truth-apt. According to Frascolla, Wittgenstein did not mean to deny this principle in order to make room for sentences which are both non-descriptive and truth-apt. Instead he considered neither mathematical propositions nor self-ascriptions of mental predicates to be truth-apt. Mathematical proposi- tions, in particular, correspond to reality at best in the way in which rules correspond to social practices. And the proof of a mathematical proposition determines the latter’s sense rather than establishing its truth. In his contribution Severin Schroeder investigates how we should understand Wittgenstein’s claim that mathematical propositions are rules of grammar for non-mathematical language. In particular he explores how to resolve the tension between Wittgenstein’s claim that mathe- matical propositions are rules and his emphasis on the practical useful- ness of mathematics. As Wittgenstein himself asks: “How can the mere transformation of an expression be of practical consequence?” (RFM 357) According to Schroeder, Wittgenstein’s answer is that mathematical propositions are not merely stipulative defi nitional rules: they forge con- nections between independently comprehensible concepts. A proposition expressing an empirical correlation may be fi xed as a rule. It is in this way that mathematical propositions are “dependent on experience but made independent of it” (LFM 55). A problem for Wittgenstein’s view nevertheless remains: what violates a grammatical rule is nonsense and yet non-mathematical statements that are not in conformity with mathemati- 4
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