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philosophy of mathematics

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Journal Article
The Philosophical Review (1 April 2016) 125 (2): 298–302.
Published: 01 April 2016
...Charles McCarty Parsons Charles , Philosophy of Mathematics in the Twentieth Century: Selected Essays . Cambridge, MA : Harvard University Press , 2014 . xii +350 pp. © 2016 by Cornell University 2016 The phrase ‘ontology of mathematics’ is ambiguous: it can refer either to...
Journal Article
The Philosophical Review (1 April 2004) 113 (2): 157–201.
Published: 01 April 2004
... 7 : 1 -6. ____. 1981 . Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Cambridge: MIT Press. Parsons, Charles. 1969 . Kant's Philosophy of Arithmetic. Page references are to the version reprinted in Mathematics in Philosophy (Ithaca: Cornell University Press...
Journal Article
The Philosophical Review (1 April 2017) 126 (2): 147–190.
Published: 01 April 2017
...Daniel Sutherland Despite the importance of Kant's claims about mathematical cognition for his philosophy as a whole and for subsequent philosophy of mathematics, there is still no consensus on his philosophy of arithmetic, and in particular the role he assigns intuition in it. This inquiry sets...
Journal Article
The Philosophical Review (1 July 2016) 125 (3): 397–430.
Published: 01 July 2016
... Jonathan Bennett in effect interprets the result to mean that PSR entails that there are no contingent truths. But reflection on parallels in philosophy of mathematics shows it can equally be interpreted either as a proof that there are “too many” contingent truths to combine in a single conjunction or as...
Journal Article
The Philosophical Review (1 April 2001) 110 (2): 286–289.
Published: 01 April 2001
... himself principally with questions about the foun- dations of mathematics” (Nedo 1993, 57). However, an understanding of his philosophy of mathematics has long been a desideratum. This was the case, in particular, for the period stretching from the Tractatus Logico-Philosophicus to the so-called...
Journal Article
The Philosophical Review (1 January 2000) 109 (1): 115–118.
Published: 01 January 2000
..., since mathematics is “essentially” about structures, not objects. In fact, structuralism has not been a very popular philosophy of mathematics, probably because of the hostility of Frege and other influential logicists, and quasi-logicists like Quine. Recently, however, structuralism has finally...
Journal Article
The Philosophical Review (1 July 2015) 124 (3): 393–406.
Published: 01 July 2015
... Stanford Encyclopedia of Philosophy (Winter 2011 Edition) , ed. Zalta E. N. plato.stanford.edu/archives/win2011/entries/epistemic-utility . © 2015 by Cornell University 2015 probabilism rational requirements self-reference accuracy Dutch book scoring rule dependence...
Journal Article
The Philosophical Review (1 July 2018) 127 (3): 422–426.
Published: 01 July 2018
...Mark Povich; Carl F. Craver Lange Marc , Because without Cause: Non-Causal Explanations in Science and Mathematics . New York: Oxford University Press , 2016 . 489 pp. . © 2018 by Cornell University 2018 The consensus in the philosophy of science, at least since the 1980s, has...
Journal Article
The Philosophical Review (1 July 2003) 112 (3): 425–427.
Published: 01 July 2003
.... In short, the methodologies of both 425 BOOK REVIEWS mathematics and science conflict with the philosophical view engendered by the indispensability arguments; Maddy’s naturalistic inclinations are that it is the philosophy that...
Journal Article
The Philosophical Review (1 January 2001) 110 (1): 79–82.
Published: 01 January 2001
... Philosophical Review, Vol. 110, No. 1 (January 2001) PLATONISM AND ANTI-PLATONISM IN MATEEMATICS. By MARK BALAGUER. New York, Oxford: Oxford University Press, 1998. Pp. xii, 217. Mathematics tells us there exist infinitely many prime numbers. Nominalist philosophy, introduced by Goodman and...
Journal Article
The Philosophical Review (1 October 2014) 123 (4): 485–531.
Published: 01 October 2014
... philosophy of science has been seriously engaged for at least six decades, explanation in mathematics has been little explored by philosophers. 1 Its neglect is remarkable. Mathematical proofs that explain why some theorem holds were distinguished by ancient Greek mathematicians from proofs that...
Journal Article
The Philosophical Review (1 April 2018) 127 (2): 240–247.
Published: 01 April 2018
... 2002. Hilary Putnam (1926–2016) has left many lasting marks. The editors of this volume have done an admirable job of providing a broad and well-balanced coverage of important strands of Putnam's work in logic, philosophy of mathematics, philosophy of science, epistemology, philosophy of language...
Journal Article
The Philosophical Review (1 October 2013) 122 (4): 667–670.
Published: 01 October 2013
...C. C. W. Taylor Cooper John M. , Pursuits of Wisdom: Six Ways of Life in Ancient Philosophy from Socrates to Plotinus . Princeton, NJ : Princeton University Press , 2012 . xiv+442. © 2013 by Cornell University 2013 The project of this impressive work is the exploration in...
Journal Article
The Philosophical Review (1 July 2008) 117 (3): 465–468.
Published: 01 July 2008
...Wayne Proudfoot Andrew Dole and Andrew Chignell, eds., God and the Ethics of Belief: New Essays in the Philosophy of Religion . Cambridge: Cambridge University Press, 2005. xii + 282 pp. Cornell University 2008 xxx pr08-004 June 10, 2008 10:56...
Journal Article
The Philosophical Review (1 April 2015) 124 (2): 269–272.
Published: 01 April 2015
...Mark Wilson Sklar Lawrence , Philosophy and the Foundations of Dynamics . Cambridge : Cambridge University Press , 2013 . ix + 272 pp . © 2015 by Cornell University 2015 In philosophy classes, we hear of the fabled struggles between theory T and T  ′, armored in their...
Journal Article
The Philosophical Review (1 January 2014) 123 (1): 1–41.
Published: 01 January 2014
... mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for...
Journal Article
The Philosophical Review (1 July 2007) 116 (3): 482–485.
Published: 01 July 2007
... Consequence: A Case for Nominalism. New York: Oxford University Press, 2004. viii + 241 pp. Jody Azzouni’s book covers a variety of topics in metaphysics, the philosophy of science, and the philosophy of mathematics. At its core, however, is a radical and original proposal about ontology and how to...
Journal Article
The Philosophical Review (1 October 2001) 110 (4): 626–629.
Published: 01 October 2001
... Heidegger’s philosophy of science can make a substan- tial contribution to contemporary theory of science. Glazebrook, unfortunately, skims over the mathematical projection and turns instead to the question of the institutional setting of scientific practice. This has been a fascinating field of...
Journal Article
The Philosophical Review (1 January 2002) 111 (1): 101–105.
Published: 01 January 2002
... between philosophy and the specific scientific disciplines of mathematics, astronomy, and medicine. Sedley points out (368) that Lucretius’s argument (1.370–84) that a fish could not move through water in the absence of void proves too much, since it would rule out the possibility of a solid wheel...
Journal Article
The Philosophical Review (1 January 2007) 116 (1): 131–135.
Published: 01 January 2007
...Fred Rush Brian O'Connor, Adorno's Negative Dialectic: Philosophy and the Possibility of Critical Rationality . Cambridge, MA: MIT Press, 2004. xviii + 199 pp. Cornell University 2007 BOOK REVIEWS Gary Iseminger, The Aesthetic Function of Art. Ithaca, NY...