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6Wittgenstein's Diagonal Argument: A Variation on Cantor and TuringDisputatio 8 (9). 2019.Turing was a philosopher of logic and mathematics, as well as a mathematician. His work throughout his life owed much to the Cambridge milieu in which he was educated and to which he returned throughout his life. A rich and distinctive tradition discussing how the notion of “common sense” relates to the foundations of logic was being developed during Turing’s undergraduate days, most intensively by Wittgenstein, whose exchanges with Russell, Ramsey, Sraffa, Hardy, Littlewood and others formed pa…Read more
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12Frege-Wittgenstein CorrespondenceIn Enzo De Pellegrin (ed.), Interactive Wittgenstein, Springer. pp. 15--73. 2011.
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6Nudging Choices Through Media: Ethical and Philosophical Implications for Humanity (edited book)Palgrave Macmillan. 2023.This book addresses the growing use of computerized systems to influence people’s decisions without their awareness, a significant but underappreciated sea-change in the way the world works. To assess these systems, this volume’s contributors explore the philosophical and ethical dimensions of algorithms that guide people’s behavior by nudging them toward choices preferred by systems architects. Particularly in an era of heightened awareness of bias and discrimination, these systems raise profou…Read more
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6CodaIn J. E. Katz & J. Floyd (eds.), Philosophy of Emerging Media: Understanding, Appreciation and Application, Oxford University Press. 2015.A revisiting and distillation of themes, questions, and results of the book’s chapters, with a description of possible alternative pathways through the volume. Open problems and suggestions for further research are also offered, laying out a vision of the field as a whole, and calling for future research, especially into topics relating to qualitative vs. quantitative uses of big data, the concept of “media”, issues in the history of philosophy and digital humanities, normative questions concern…Read more
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5IntroductionIn J. E. Katz & J. Floyd (eds.), Philosophy of Emerging Media: Understanding, Appreciation and Application, Oxford University Press. 2015.A survey of open questions in the field; definitions of “emergence” and “media” are given, as well as their relationship to big data. Rationale for the volume is given, and c. 100 word descriptions and analyses of each essay in the volume are put forward. The volume is differentiated from other books and approaches, and open problems and questions set forth.
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23Modal Moments: Transpositions of the Tractatus in Wittgenstein’s Later WorkRevue Internationale de Philosophie 300 (2): 125-146. 2022.L'idée de « progrès » en philosophie, ancrée dans la devise des Recherches Philosophiques, est à la fois grammaticale et autobiographique. Où se trouvait le progrès de Wittgenstein dans les années qui avaient suivi le Tractatus? Quelles leçons tirer de son parcours? Pour répondre à la question, il faut repenser la manière dont la grammaire du « progrès » doit être pesée et mesurée en philosophie. Nous nous appuyons sur l'essai de Jacques Bouveresse « Les ténèbres de notre temps (1991)» et l'idée…Read more
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8Steiner’s WittgensteinIn Carl Posy & Yemima Ben-Menahem (eds.), Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner, Springer. pp. 345-376. 2023.Throughout his philosophy of mathematics, Steiner’s views bear affinities and contrasts with those of Wittgenstein. From his early insistence on an intelligible notion of mathematical “explanation”, to his remarks on the necessity of certain extensions of mathematical concepts, to his analysis of the ideas of logicism, “surveyability” and “applicability” in mathematics and his reading of Kripke on rule-following, Steiner probed fundamental issues in contemporary philosophy of mathematics. This e…Read more
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14Heautonomy: Kant on Reflective Judgment and SystematicityIn Herman Parret (ed.), Kants Ästhetik · Kant's Aesthetics · L'esthétique de Kant, De Gruyter. pp. 192-218. 1998.
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20Truth in Russell, Early Wittgenstein and GödelIn Friedrich Stadler (ed.), Wittgenstein and the Vienna Circle: 100 Years After the Tractatus Logico-Philosophicus, Springer Verlag. pp. 179-208. 2023.This Tractatus’s engagement with the issue of the nature of truth and falsity emerged from engagement with Russell. This engagement reverberated through the Vienna Circle and in particular affected Gödel. The Tractatus’s “elementary sentences” must be seen against the backdrop of Russell’s “multiple relation theory of judgment”, his theory of truth in Principia Mathematica, which Wittgenstein discussed at length with Russell in 1912–1913 and Gödel studied in 1929–1932. Russell’s approach was dir…Read more
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31“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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Ch. 35. The varieties of rigorous experienceIn Michael Beaney (ed.), The Oxford Handbook of The History of Analytic Philosophy, Oxford University Press. 2013.
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10Philosophical Explorations of the Legacy of Alan Turing: Turing 100 (edited book)Imprint: Springer. 2017.This volume presents an historical and philosophical revisiting of the foundational character of Turing's conceptual contributions and assesses the impact of the work of Alan Turing on the history and philosophy of science. Written by experts from a variety of disciplines, the book draws out the continuing significance of Turing's work. The centennial of Turing's birth in 2012 led to the highly celebrated "Alan Turing Year", which stimulated a world-wide cooperative, interdisciplinary revisiting…Read more
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Sheffer, Lewis, and the 'logocentric predicament'In Quentin Kammer, Jean-Philippe Narboux & Henri Wagner (eds.), C.I. Lewis: the a priori and the given, Routledge. 2021.
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Number and Ascriptions of Number in Wittgenstein's TractatusIn Edited by Erich H. Reck (ed.), From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy, Oup Usa. 2002.Wittgenstein's treatment of number words and arithmetic in the Tractatus reflects central features of his early conception of philosophy. In rejecting Frege's and Russell's analyses of number, Wittgenstein rejects their respective conceptions of function, object, logical form, generality, sentence, and thought. He, thereby, surrenders their shared ideal of the clarity a Begriffsschrift could bring to philosophy. The development of early analytic philosophy thus evinces far less continuity than s…Read more
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26IntroductionJournal for the History of Analytical Philosophy 9 (11). 2021.In this introduction we present the principal themes of the special issue and highlight the main interpretive theses of the contributions.
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22Cavell's 'Must We Mean What We Say' at 50 (edited book)Cambridge University Press. 2022.In 1969 Stanley Cavell's Must We Mean What We Say? revolutionized philosophy of ordinary language, aesthetics, ethics, tragedy, literature, music, art criticism, and modernism. This volume of new essays offers a multi-faceted exploration of Cavell's first and most important book, fifty years after its publication. The key subjects which animate Cavell's book are explored in detail: ordinary language, aesthetics, modernism, skepticism, forms of life, philosophy and literature, tragedy and the sel…Read more
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20Wittgenstein's Philosophy of MathematicsCambridge University Press. 2021.For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics grew from his Early and Middle philosophies, a dialectical path reconstruct…Read more
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33Aspects 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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47Wittgenstein 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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61Wittgenstein 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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33Teaching 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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34‘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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IntroductionIn Alisa Bokulich & Juliet Floyd (eds.), Philosophical Explorations of the Legacy of Alan Turing, Springer Verlag. 2017.
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Turing on “Common Sense”: Cambridge ResonancesIn Alisa Bokulich & Juliet Floyd (eds.), Philosophical Explorations of the Legacy of Alan Turing, Springer Verlag. 2017.
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44Lebensformen: 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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Wittgenstein on Philosophy of Logic and MathematicsIn Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press. 2005.This article is a survey of Wittgenstein’s writings on logic and mathematics; an analytical bibliography of contemporary articles on rule-following, social constructivism, Wittgenstein, Gödel, and constructivism is appended. Various historical accounts of the nature of mathematical knowledge have 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 …Read more
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130A 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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22Mathieu Marion. Wittgenstein, Finitism, and the Foundations of MathematicsPhilosophia Mathematica 10 (1): 67-88. 2002.
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