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432000-2001 Spring Meeting of the Association for Symbolic LogicBulletin of Symbolic Logic 7 (3): 413-419. 2001.
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Book reviews (review)History and Philosophy of Logic 15 (1): 127-147. 1994.Hide Ishiguro, Leibniz’s philosophy of logic and language. 2nd ed. Cambridge:Cambridge University Press, 1990. x + 246pp. £27.50/$49.50 ; £10.95/$16.95 Massimo Mugnai, Leibniz’ theory of relations. Stuttgart:Franz Steiner Verlag, 1992. 291 pp. 96 DM W. A. Wallace, Galileo’s logic of discovery and proof The background, content, and use of his appropriated treatises on Aristotle’s posterior analytics. Dordrecht, Boston, and London:Kluwer, 1992. xxiii + 323 pp. £84, $139, DF1240 W. A. Wallace, Gali…Read more
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2Proof and Knowledge in Mathematics (edited book)Routledge. 1992.This volume of essays addresses the main problem confronting an epistemology for mathematics; namely, the nature and sources of mathematical justification. Attending to both particular and general issues, the essays, by leading philosophers of mathematics, raise important issues for our current understanding of mathematics. Is mathematical justification a priori or a posteriori? What role, if any, does logic play in mathematical reasoning or inference? And of what epistemological importance is t…Read more
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24Formalism and Hilbert’s understanding of consistency problemsArchive for Mathematical Logic 60 (5): 529-546. 2021.Formalism in the philosophy of mathematics has taken a variety of forms and has been advocated for widely divergent reasons. In Sects. 1 and 2, I briefly introduce the major formalist doctrines of the late nineteenth and early twentieth centuries. These are what I call empirico-semantic formalism, game formalism and instrumental formalism. After describing these views, I note some basic points of similarity and difference between them. In the remainder of the paper, I turn my attention to Hilber…Read more
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Critical essay on W. P. Newton-Smith's The Rationality of Science (review)Revue Internationale de Philosophie 37 (146): 364-371. 1983.
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Proof: Its Nature and SignificanceIn Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy, Maa. pp. 3-32. 2009.
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Rigor, Reproof and Bolzano's Critical ProgramIn Pierre Edouard Bour, Manuel Rebuschi & Laurent Rollet (eds.), Construction: A Festschrift for Gerhard Heinzmann, King's College Publications. pp. 171-184. 2010.
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Sensing objectivity: A comment on Mary Leng's "Creation and Discovery in Mathematics"In John Polkinghorne (ed.), Mathematics and its Significance, Oxford University Press. pp. 70-71. 2011.
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Discovery, Invention and Realism: Gödel and others on the Reality of ConceptsIn John Polkinghorne (ed.), Mathematics and its Significance, Oxford University Press. pp. 73-96. 2011.The general question considered is whether and to what extent there are features of our mathematical knowledge that support a realist attitude towards mathematics. I consider, in particular, reasoning from claims such as that mathematicians believe their reasoning to be part of a process of discovery (and not of mere invention), to the view that mathematical entities exist in some mind-independent way although our minds have epistemic access to them.
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Dedekind against Intuition: Rigor, Scope and the Motives of his LogicismIn Carlo Cellucci, Emily Grosholz & Emiliano Ippoliti (eds.), Logic and Knowledge, Cambridge Scholars Publications. pp. 205-221. 2011.
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Freedom and ConsistencyIn Emily Goldblatt, B. Kim & R. Downey (eds.), Proceedings of the 12th Asian Logic Conference, World Scientific. pp. 89-111. 2013.
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1Completeness and the Ends of AxiomatizationIn Juliette Cara Kennedy (ed.), Interpreting Gödel, Cambridge University Press. pp. 59-77. 2014.The type of completeness Whitehead and Russell aimed for in their Principia Mathematica was what I call descriptive completeness. This is completeness with respect to the propositions that have been proved in traditional mathematics. The notion of completeness addressed by Gödel in his famous work of 1930 and 1931 was completeness with respect to the truths expressible in a given language. What are the relative significances of these different conceptions of completeness for traditional mathemat…Read more
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On the motives for proof theoryIn Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning, Springer. 2015.
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Gentzen's anti-formalist ideasIn Reinhard Kahle & Michael Rathjen (eds.), Gentzen's Centenary: The Quest for Consistency, Springer. pp. 25-44. 2015.
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Abstraction, Axiomatization and Rigor: Pasch and HilbertIn Roy Cook & Geoffrey Hellman (eds.), Hilary Putnam on Logic and Mathematics, Springer Verlag. 2018.
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64Ian Hacking. Why Is There Philosophy of Mathematics At All?Philosophia Mathematica 25 (3): 407-412. 2017.© The Author [2017]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] author makes clear that he does not see this book as a contribution to the philosophy of mathematics as traditionally understood. He takes it instead to be an essay about the philosophy of mathematics, one whose purpose is to explain its existence and to make clear the limited extent to which its current and past forms are properly regarded as philosophi…Read more
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116Proof, Logic and Formalization (edited book)Routledge. 1992.The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.
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190On an alleged refutation of Hilbert's program using gödel's first incompleteness theoremJournal of Philosophical Logic 19 (4). 1990.It is argued that an instrumentalist notion of proof such as that represented in Hilbert's viewpoint is not obligated to satisfy the conservation condition that is generally regarded as a constraint on Hilbert's Program. A more reasonable soundness condition is then considered and shown not to be counter-exemplified by Godel's First Theorem. Finally, attention is given to the question of what a theory is; whether it should be seen as a "list" or corpus of beliefs, or as a method for selecting be…Read more
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71FormalismIn Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press. pp. 236--317. 2005.A comprehensive historical overview of formalist ideas in the philosophy of mathematics.
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460Brouwerian intuitionismMind 99 (396): 501-534. 1990.The aims of this paper are twofold: firstly, to say something about that philosophy of mathematics known as 'intuitionism' and, secondly, to fit these remarks into a more general message for the philosophy of mathematics as a whole. What I have to say on the first score can, without too much inaccuracy, be compressed into two theses. The first is that the intuitionistic critique of classical mathematics can be seen as based primarily on epistemological rather than on meaning-theoretic considerat…Read more
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88Wright on the non-mechanizability of intuitionist reasoningPhilosophia Mathematica 3 (1): 103-119. 1995.Crispin Wright joins the ranks of those who have sought to refute mechanist theories of mind by invoking Gödel's Incompleteness Theorems. His predecessors include Gödel himself, J. R. Lucas and, most recently, Roger Penrose. The aim of this essay is to show that, like his predecessors, Wright, too, fails to make his case, and that, indeed, he fails to do so even when judged by standards of success which he himself lays down.
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1Proof and Knowledge in MathematicsRevue Philosophique de la France Et de l'Etranger 185 (1): 133-134. 1992.
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3Introduction to the Fiftieth Anniversary IssuesNotre Dame Journal of Formal Logic 51 (1): 1-2. 2010.
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14Introduction to Special Issue on George S. BoolosNotre Dame Journal of Formal Logic 40 (1): 1-2. 1999.
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66Constructive existence claimsIn Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993, Clarendon Press. pp. 1998--307. 1998.It is a commonplace of constructivist thought that a claim that an object of a certain kind exists is to be backed by an explicit display or exhibition of an object that is manifestly of that kind. Let us refer to this requirement as the exhibition condition. The main objective of this essay is to examine this requirement and to arrive at a better understanding of its epistemic character and the role that it plays in the two main constructivist philosophies of this century---the intuitionist pro…Read more
Michael Detlefsen
(1948 - 2019)
Notre Dame, Indiana, United States of America
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |