-
17Michael Detlefsen, Hilbert's program. An essay on mathematical instrumentalism. Synthese library, vol. 182, D. Reidel Publishing Company, Dordrecht etc. 1986, xiv + 186 pp (review)Journal of Symbolic Logic 54 (2): 620-622. 1989.
-
31Proof and knowledge in mathematics, edited by Michael Detlefsen, Routledge, London and New York1992, x + 256 ppJournal of Symbolic Logic 59 (3): 1105-1107. 1994.
-
23Hilbert's Program. An Essay on Mathematical InstrumentalismJournal of Symbolic Logic 54 (2): 620-622. 1989.
-
17Gödel's theorem in focus, edited by Shanker S. G., Philosophers in focus series, Croom Helm, London, New York, and Sydney, 1988, and Routledge, London and New York 1989, ix + 261 pp (review)Journal of Symbolic Logic 58 (1): 365-366. 1993.
-
18Review: Michael Detlefsen, Hilbert's Program. An Essay on Mathematical Instrumentalism (review)Journal of Symbolic Logic 54 (2): 620-622. 1989.
-
10Review: S. G. Shanker, Godel's Theorem in Focus (review)Journal of Symbolic Logic 58 (1): 365-366. 1993.
-
645Intensionality and the gödel theoremsPhilosophical Studies 48 (3): 337--51. 1985.Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative …Read more
-
230Saying It With NumeralsNotre Dame Journal of Formal Logic 35 (1): 130-146. 1994.This article discusses the nature of numerals and the plausibility of their special semantic and epistemological status as proper names of numbers. Evidence is presented that minimizes the difference between numerals and other devices of direct reference. The availability of intensional contexts within formalised metamathematics is exploited to shed light on the relation between formal numerals and numerals
-
717How to Say Things with FormalismsIn Michael Detlefsen (ed.), Proof, Logic and Formalization, Routledge. pp. 77--93. 1992.Recent attention to "self-consistent" (Rosser-style) systems raises anew the question of the proper interpretation of the Gödel Second Incompleteness Theorem and its effect on Hilbert's Program. The traditional rendering and consequence is defended with new arguments justifying the intensional correctness of the derivability conditions.
Raleigh, North Carolina, United States of America
Areas of Specialization
Science, Logic, and Mathematics |
Logic and Philosophy of Logic |
Philosophy of Mathematics |