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Arguing for inconsistency: dialectical games in the academyIn Giuseppe Primiero (ed.), Acts of Knowledge: History, Philosophy and Logic, College Publications. 2009.
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1Wittgenstein's struggle with intuitionismIn Florian Franken Figueiredo (ed.), Wittgenstein's philosophy in 1929, Routledge. 2023.
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1Qu'est-ce que l'inférence? Une relecture du Tractatus logico-philosophicusArchives de Philosophie 64 (3): 545-567. 2001.En logique mathématique, on doit distinguer entre une conception « axiomatique »de la logique, qui fut celle de Frege, Russell et Hilbert, et une conception plus « pragmatique »en termes d’actes de preuves, que l’on retrouve dans les systèmes de déduction naturelle de Gentzen. Des parallèles sont esquissés entre la conception de l’inférence et de la logique dans le Tractatus Logico-philosophicus de Wittgenstein et celle de Gentzen. Ce cadre permet en outre de jeter un regard neuf sur l’argument …Read more
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64Aristotle on Universal Quantification: A Study from the Point of View of Game SemanticsHistory and Philosophy of Logic 37 (3): 201-229. 2016.In this paper we provide an interpretation of Aristotle's rule for the universal quantifier in Topics Θ 157a34–37 and 160b1–6 in terms of Paul Lorenzen's dialogical logic. This is meant as a contribution to the rehabilitation of the role of dialectic within the Organon. After a review of earlier views of Aristotle on quantification, we argue that this rule is related to the dictum de omni in Prior Analytics A 24b28–29. This would be an indication of the dictum’s origin in the context of dialecti…Read more
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20Friedrich Waismann - Causality and Logical PositivismSpringer. 2011.Friedrich Waismann (1896–1959) was one of the most gifted students and collaborators of Moritz Schlick. Accepted as a discussion partner by Wittgenstein from 1927 on, he functioned as spokesman for the latter’s ideas in the Schlick Circle, until Wittgenstein’s contact with this most faithful interpreter was broken off in 1935 and not renewed when exile took Waismann to Cambridge. Nonetheless, at Oxford, where he went in 1939, and eventually became Reader in Philosophy of Mathematics (changing la…Read more
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15International audience.
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Wilson, John Cook (1849-1915)In J. Mander & A. P. F. Sell (eds.), The Dictionary of Nineteenth-Century British Philosophers, Thoemmes Press. pp. 1253--1256. 2002.
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Wittgenstein, Finitism and the Founations of Mathematics, Clarendon PressRuch Filozoficzny 3 (3-4). 1999.
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19Was Royaumont merely a dialogue de sourds? An Introduction to the discussion généralePhilosophical Inquiries 6 (1): 197-214. 2018.
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17Waismann’s Lectures on Causality: An IntroductionVienna Circle Institute Yearbook 15 31-51. 2011.Waismann’s writings can be divided into three periods. The fi rst corresponds to his early work in Vienna under the aegis of Schlick, thus mainly to his collaboration with Wittgenstein on the fi rst drafts of Logik, Sprache, Philosophie, out of which came not only the book itself many years later but also transcriptions of conversations with Schlick and Wittgenstein and numerous dictations reworked by Waismann, now published under the title The Voice of Wittgenstein. The Vienna Circle. Waismann …Read more
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146Wittgenstein and BrouwerSynthese 137 (1-2). 2003.In this paper, I present a summary of the philosophical relationship betweenWittgenstein and Brouwer, taking as my point of departure Brouwer's lecture onMarch 10, 1928 in Vienna. I argue that Wittgenstein having at that stage not doneserious philosophical work for years, if one is to understand the impact of thatlecture on him, it is better to compare its content with the remarks on logics andmathematics in the Tractactus. I thus show that Wittgenstein's position, in theTractactus, was already …Read more
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6EditorialDois Pontos 6 (1). 2009.É fácil mostrar que, no Tractatus, atribuições de cor não podem ser proposiçõeselementares. Mas já não é tão fácil determinar que tipo de análise poderia ser feita dejuízos de percepção do tipo “a é vermelho”. Wittgenstein nos dá uma indicação vaga noaforismo 6.3751. Ele pede que o leitor tenha em mente o modo pelo qual lidamos com aexclusão das cores no campo da física. Mesmo assim, é difícil determinar o que exatamenteele estava tentando dizer ali. Ofereço uma interpretação do aforismo que ass…Read more
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Wittgenstein, Goodstein and the origin of the uniqueness rule for primitive recursive arithmeticIn David G. Stern (ed.), Wittgenstein in the 1930s: Between the Tractatus and the Investigations, Cambridge University Press. 2018.
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9Wittgenstein and AntirealismIn Hans-Johann Glock & John Hyman (eds.), A Companion to Wittgenstein, Wiley-blackwell. 2017.Mathematics is one of the many domains where the adoption of a form of realism has traditionally been challenged. Behaviorism and phenomenalism, opposed to realism about, respectively, mental entities and the existence of material objects, are other well‐known examples. The realism debate, as initiated by Dummett's challenge, appears to have run its course, at least on its original terms, and difficulties have been raised with respect to both antirealist and anti‐antirealist readings of Wittgens…Read more
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182Wittgenstein and finitismSynthese 105 (2). 1995.In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skole…Read more
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14Wittgenstein on Heidegger and cosmic emotionsIn Anne Reboul (ed.), Philosophical papers dedicated to Kevin Mulligan, . 2011.
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66Why Play Logical Games?In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy, Springer Verlag. pp. 3--26. 2009.
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16Wittgenstein et son œuvre posthume (review)Dialogue 35 (4): 777-790. 1996.Wittgenstein est mort en 1951 et on attend toujours une édition de ses œuvres complètes. Ce n'est qu'en 1994 que sont parus, accompagnés d'un volume d'introduction à l'ensemble du projet d'édition de la main du directeur de publication, Michael Nedo, les deux premiers d'une série de quinze volumes, les Wiener Ausgabe, qui reproduiront l'intégralité des écrits de Wittgenstein, de son retour à Cambridge en janvier 1929 à la première version du Big Typescript en 1933, avec index et concordances. D'…Read more
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13The Realism-Antirealism Debate in the Age of Alternative Logics (edited book)Springer. 2011.The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by …Read more
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37Wittgenstein et la preuve mathématique comme vérifacteurPhilosophiques 38 (1): 137-156. 2011.Dans ce texte, je pars de l’analyse intuitionniste de la vérité mathématique, « A est vrai si et seulement s’il existe une preuve de A » comme cas particulier de l’analyse de la vérité en termes de « vérifacteur », et je montre pourquoi Wittgenstein partageait celle-ci avec les intuitionnistes. Cependant, la notion de preuve à l’oeuvre dans cette analyse est, selon l’intuitionnisme, celle de la « preuve-comme-objet », et je montre par la suite, en interprétant son argument sur le caractère « syn…Read more
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31Wittgenstein, Ramsey and British PragmatismEuropean Journal of Pragmatism and American Philosophy 4 (2). 2012.In this paper, I examine the transmission of some ideas of the pragmatist tradition to Wittgenstein, in his ‘middle period,’ through the intermediary of F. P. Ramsey, with whom he had numerous fruitful discussions at Cambridge in 1929. I argue more specifically that one must first come to terms with Ramsey’s own views in 1929, and explain how they differ from views expressed in earlier papers from 1925-27, so a large part of this paper is devoted to this task. One is then in a better position to…Read more
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13Wittgenstein, l’intentionnalité et les règlesPhilosophiques 25 (1): 3-27. 1998.Après avoir présenté les grandes lignes de la réflexion phénoménologique de Wittgenstein en 1929 et son abandon de Vidée d'un langage phénoménologique, je montre qu'il fait face à un dilemme à propos de la notion de règle. Si on regarde l'expression symbolique d'une règle sous le mode physicaliste, on ne peut pas voir le lien entre celle-ci et ses applications. Comment peut-elle, de par elle-même, servir de guide à nos actions ? Il faut une intention, une interprétation, ce qui fait de la règle …Read more
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90Wittgenstein, finitism, and the foundations of mathematicsOxford University Press. 1998.This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus …Read more
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1Wittgenstein on Mathematics: Constructivism or Constructivity?In Annalisa Coliva & Eva Picardi (eds.), Wittgenstein Today, Il Poligrafo. pp. 201--222. 2004.
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28Wittgenstein on Equinumerosity and SurveyabilityGrazer Philosophische Studien 89 (1): 61-78. 2014.
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57Wittgenstein et le lien entre la signification d’un énoncé mathématique et sa preuvePhilosophiques 39 (1): 101-124. 2012.The thesis according to which the meaning of a mathematical sentence is given by its proof was held by both Wittgenstein and the intuitionists, following Heyting and Dummett. In this paper, we clarify the meaning of this thesis for Wittgenstein, showing how his position differs from that of the intuitionists. We show how the thesis originates in his thoughts, from the middle period, about proofs by induction, and we sketch his answers to a number of objections, including the idea that, given the…Read more
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4Philosophy of LogicIn Constantin V. Boundas (ed.), The Edinburgh Companion to Twentieth-Century Philosophies, Edinburgh University Press. pp. 252-269. 2007.
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