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mathematics

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Journal Article
The Philosophical Review (2000) 109 (1): 115–118.
Published: 01 January 2000
...Mark Steiner MATHEMATICS AS A SCIENCE OF PATTERNS. By Michael Resnik. New York: Oxford University Press, Clarendon Press, 1997. Pp. xiii, 285. Cornell University 2000 Frege, Gottlob. 1959 . The Foundations of Arithmetic. Trans. J. L. Austin. Oxford: Blackwell. Kitcher, Philip...
Journal Article
The Philosophical Review (2001) 110 (1): 79–82.
Published: 01 January 2001
...John P. Burgess PLATONISM AND ANTI-PLATONISM IN MATHEMATICS. By Mark Balaguer. New York, Oxford: Oxford University Press, 1998. Pp. xii, 217. Cornell University 2001 BOOK REWEWS without careful and difficult argument. The Humean principle has become...
Journal Article
The Philosophical Review (2001) 110 (2): 286–289.
Published: 01 April 2001
...Paolo Mancosu WITTGENSTEIN, FINITISM, AND THE FOUNDATIONS OF MATHEMATICS. Oxford Philosophical Monographs. By Mathieu Marion. New York: Oxford University Press, Clarendon Press, 1998. Pp. xx, 260. Cornell University 2001 Nedo, Michael, ed. 1993 . Ludwig Wittgenstein. Wiener...
Journal Article
The Philosophical Review (2003) 112 (3): 425–427.
Published: 01 July 2003
...Adam Rieger Penelope Maddy, Naturalism in Mathematics. Oxford: Oxford University Press, Clarendon Press, 1998. Pp. viii, 254. Cornell University 2003 BOOK REVIEWS The Philosophical Review, Vol. 112, No. 3 (July 2003) Penelope Maddy...
Journal Article
The Philosophical Review (2004) 113 (2): 157–201.
Published: 01 April 2004
..., Calif.: Wadsworth. ____. 1972 . Kantian Intuitions. Inquiry 15 : 341 -45. ____. 1974a . Kant's `New Method of Thought' and His Theory of Mathematics. In his Knowledge and the Known . Dordrecht: D. Reidel. ____. 1974b . Kant on the Mathematical Method. In his Knowledge and the Known...
Journal Article
The Philosophical Review (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...
Journal Article
The Philosophical Review (2018) 127 (3): 422–426.
Published: 01 July 2018
... the picking, not the dividing, caused the pile's size. Likewise, suppose some population of cicadas doesn't have a prime life-cycle period and we want to know why. Here's a putative, distinctively mathematical explanation: because that population doesn't tend to suffer less from predation by predators...
Journal Article
The Philosophical Review (2020) 129 (4): 670–674.
Published: 01 October 2020
...Mark Wilson Bueno Otávio French Steven Applying Mathematics Oxford: Oxford University Press 2018 xvii + 257 pp. © 2020 by Cornell University 2020 The authors address the following question: “Why is it that mathematics is so useful in empirical science?” They first...
Journal Article
The Philosophical Review (2021) 130 (3): 471–474.
Published: 01 July 2021
...Ethan Brauer eebauer@gmail.com Horsten Leon , The Metaphysics and Mathematics of Arbitrary Objects . Cambridge : Cambridge University Press , 2019 viii + 232 © 2021 by Cornell University 2021 Consider the arbitrary triangle. It is a closed planar figure with three...
Journal Article
The Philosophical Review (2014) 123 (4): 485–531.
Published: 01 October 2014
...Marc Lange Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations (as well as canonical examples of nonexplanations, such as “the flagpole,” “the eclipse...
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Journal Article
The Philosophical Review (2015) 124 (3): 393–406.
Published: 01 July 2015
Journal Article
The Philosophical Review (2014) 123 (1): 1–41.
Published: 01 January 2014
... mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full...
Journal Article
The Philosophical Review (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 (2016) 125 (3): 397–430.
Published: 01 July 2016
... and 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...
Journal Article
The Philosophical Review (2017) 126 (1): 81–122.
Published: 01 January 2017
... suspect in requiring nonstandard assumptions about mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle...
Journal Article
The Philosophical Review (2022) 131 (1): 1–49.
Published: 01 January 2022
... worlds and the presence of several other accompanying features. Under certain assumptions, such vagueness prevents the fundamental physical theory from being completely expressible in the mathematical language. Moreover, I suggest that such vagueness can be regarded as vagueness in the world . For a case...
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Journal Article
The Philosophical Review (2011) 120 (2): 247–283.
Published: 01 April 2011
... employ in logic, mathematics, and the sciences can be fully captured in English, there is also reason to think that the threat can be averted. © 2011 by Cornell University 2011 Earlier versions of the article were presented at a Rutgers Semantics Workshop, at Arché in St. Andrews...
Journal Article
The Philosophical Review (2014) 123 (3): 342–354.
Published: 01 July 2014
... Foundations …is to explain how the application of pure mathematics to the empirical concepts of mathematical physics becomes possible” (88). Kant's goal is to explain, concept by concept, how the fundamental concepts of Newtonian physics—for example, duration , mass , velocity , and force— come...
Journal Article
The Philosophical Review (2002) 111 (4): 579–582.
Published: 01 October 2002
... and of then reconciling Poincaré s various theses about the foundations of mathematics and the natu- ral sciences (1), it might give the reader hope that all of these theses might be shown to be part of one unified position. In fact, though, Poincaré s philoso- phy of physics and his philosophy of mathematics turn out...
Journal Article
The Philosophical Review (2000) 109 (3): 456–459.
Published: 01 July 2000
...Mark Eli Kalderon REALISTIC RATIONALISM. By Jerrold Katz. Cambridge: MIT Press, Bradford Books, 1998. Pp. xxxiv, 226. Cornell University 2000 Benacerraf, P. 1973 /1989. “Mathematical truth.” In Philosophy of Mathematics: Selected Readings , ed. P. Benacerraf and H. Putnam, 403...