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457Putnam's 'the meaning of meaning': Externalism in historical contextIn Yemima Ben-Menahem (ed.), Hilary Putnam (Contemporary Philosophy in Focus), Cambridge University Press. 2005.
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429Prose versus proof: Wittgenstein on gödel, Tarski and TruthPhilosophia Mathematica 9 (3): 280-307. 2001.A survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937–1939, and later testimony of Goodstein and Kreisel; 2) Discussion of the philosophical and historical importance of Wittgenstein's attitude toward Gödel's and other theorems in mathematical logic, contrasting this attitude with that of, e.g., Penrose; 3) Replies to an instructive criticism of my …Read more
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368A Note on Wittgenstein’s “Notorious Paragraph” About the Gödel TheoremJournal of Philosophy 97 (11): 624-632. 2000.
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199Recent themes in the history of early analytic philosophyJournal of the History of Philosophy 47 (2). 2009.A survey of the emergence of early analytic philosophy as a subfield of the history of philosophy. The importance of recent literature on Frege, Russell, and Wittgenstein is stressed, as is the widening interest in understanding the nineteenth-century scientific and Kantian backgrounds. In contrast to recent histories of early analytic philosophy by P.M.S. Hacker and Scott Soames, the importance of historical and philosophical work on the significance of formalization is highlighted, as are the …Read more
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185Wittgenstein on Philosophy of Logic and MathematicsGraduate Faculty Philosophy Journal 25 (2): 227-287. 2004.A survey of Wittgenstein's writings on logic and mathematics; an analytical bibliography of contemporary articles on rule-following, social constructivism, Wittgenstein, Godel, and constructivism is appended. Various historical accounts of the nature of mathematical knowledge glossed over the effects of linguistic expression on our understanding of its status and content. Initially Wittgenstein rejected Frege's and Russell's logicism, aiming to operationalize the notions of logical consequence, …Read more
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146A Note on Wittgenstein’s “Notorious Paragraph” About the Gödel TheoremJournal of Philosophy 97 (11): 624-632. 2000.A look at Wittgenstein's comments on the incompleteness theorem with an inter-pretation that is consistent with what Gödel proved.
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126Chains of Life: Turing, Lebensform, and the Emergence of Wittgenstein’s Later StyleNordic Wittgenstein Review 5 (2): 7-89. 2016.This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his la…Read more
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1143 Wittgenstein and the InexpressibleIn Alice Crary (ed.), Wittgenstein and the Moral Life: Essays in Honor of Cora Diamond, Mit Press. pp. 177-234. 2007.
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113Bays, Steiner, and Wittgenstein’s “Notorious” Paragraph about the Gödel TheoremJournal of Philosophy 103 (2): 101-110. 2006.
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99Future pasts: the analytic tradition in twentieth-century philosophy (edited book)Oxford University Press. 2001.This collection of previously unpublished essays presents a new approach to the history of analytic philosophy--one that does not assume at the outset a general characterization of the distinguishing elements of the analytic tradition. Drawing together a venerable group of contributors, including John Rawls and Hilary Putnam, this volume explores the historical contexts in which analytic philosophers have worked, revealing multiple discontinuities and misunderstandings as well as a complex inter…Read more
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81The Frege-Wittgenstein Correspondence: Interpretive ThemesIn Enzo De Pellegrin (ed.), Interactive Wittgenstein, Springer. pp. 75--107. 2011.
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60Response to Michael FriedmanIn Schneewind J. (ed.), Teaching New Histories of Philosophy, . pp. 225-234. 2004.
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58Prose versus Proof: Wittgenstein on Gödel, Tarski and Truth†: ArticlesPhilosophia Mathematica 9 (3): 280-307. 2001.1) A survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937–1939, and later testimony of Goodstein and Kreisel; 2) Discussion of the philosophical and historical importance of Wittgenstein's attitude toward Gödel's and other theorems in mathematical logic, contrasting this attitude with that of, e.g. , Penrose; 3) Replies to an instructive criticism of…Read more
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57Wittgenstein on ethics: Working through LebensformenPhilosophy and Social Criticism 46 (2): 115-130. 2020.In his Tractatus Logico-Philosophicus, Wittgenstein conveyed the idea that ethics cannot be located in an object or self-standing subject matter of propositional discourse, true or false. At the same time, he took his work to have an eminently ethical purpose, and his attitude was not that of the emotivist. The trajectory of this conception of the normativity of philosophy as it developed in his subsequent thought is traced. It is explained that and how the notion of a ‘form of life’ (Lebensform…Read more
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54Depth and Clarity * Felix Muhlholzer. Braucht die Mathematik eine Grundlegung? Eine Kommentar des Teils III von Wittgensteins Bemerkungen uber die Grundlagen der Mathematik [Does Mathematics need a Foundation? A Commentary on Part III of Wittgenstein's Remarks on the Foundations of Mathematics]. Frankfurt: Vittorio Klostermann, 2010. ISBN: 978-3-465-03667-8. Pp. xiv + 602 (review)Philosophia Mathematica 23 (2): 255-276. 2015.
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43Lebensformen: Living LogicIn Christian Georg Martin (ed.), Language, Form(s) of Life, and Logic: Investigations After Wittgenstein, De Gruyter. pp. 59-92. 2018.
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42Wittgenstein and TuringIn Gabriele Mras, Paul Weingartner & Bernhard Ritter (eds.), Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium, De Gruyter. pp. 263-296. 2019.
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35Prosa versus Demonstração: Wittgenstein sobre Gödel, Tarski e a VerdadeRevista Portuguesa de Filosofia 58 (3). 2002.O presente artigo procede, em primeiro lugar, a um exame das evidências disponíveis referentes à atitude de Wittgenstein em relação ao, bem como conhecimento do, primeiro teorema da incompletude de Gödel, incluindo as suas discussões com Turing, Watson e outros em 1937-1939, e o testemunho posterior de Goodstein e Kreisel Em segundo lugar, o artigo discute a importância filosófica e histórica da atitude de Wittgenstein em relação ao teorema de Gödel e outros teoremas da lógica matemática, contra…Read more
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32Teaching and Learning with Wittgenstein and Turing: Sailing the Seas of Social MediaJournal of Philosophy of Education 53 (4): 715-733. 2019.
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30Aspects of the Real Numbers: Putnam, Wittgenstein, and NonextensionalismThe Monist 103 (4): 427-441. 2020.I defend Putnam’s modal structuralist view of mathematics but reject his claims that Wittgenstein’s remarks on Dedekind, Cantor, and set theory are verificationist. Putnam’s “realistic realism” showcases the plasticity of our “fitting” words to the world. The applications of this—in philosophy of language, mind, logic, and philosophy of computation—are robust. I defend Wittgenstein’s nonextensionalist understanding of the real numbers, showing how it fits Putnam’s view. Nonextensionalism and ext…Read more
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30‘Ultimate’ Facts? Zalabardo on the Metaphysics of TruthAustralasian Philosophical Review 2 (3): 299-314. 2018.ABSTRACTZalabardo argues that the Tractatus account of picturing is a direct and successful refutation of Russell’s ‘multiple relation’ theory of judgment, its role being ontological: Wittgenstein...
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29“Surveyability” in Hilbert, Wittgenstein and TuringPhilosophies 8 (1): 6. 2023.An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability” of symbols, sequences, and structures of proof in all these thinkers. Hilbert initiated the idea within his metamathematics, Wittgenstein took up a kind of game formalism in the 1920s and early 1930s in response. Turing carried Hilbert’s conception of the “surveyability…Read more
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28Review of James C. Klagge ed., Wittgenstein: Biography and Philosophy (review)Notre Dame Philosophical Reviews 2002 (6). 2002.Wittgenstein Biography and Philosophy
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25Frege, semantics, and the double definition strokeIn Anat Biletzki & Anat Matar (eds.), The Story of Analytic Philosophy: Plot and Heroes, Routledge. pp. 141-166. 1998.
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