... of Arithmetic . Trans. J. L. Austin. New York: Blackwell. (Translation of Frege 1884) Gamut, L. T. F. 1991 . Logic, Language, and Meaning , vol. 2 . Chicago: University of Chicago Press. Hale, Bob. 2001a . Singular Terms (1) . In Hale and Wright 2001. Hale, Bob. 2001b . Singular Terms (2...

...Agustín Rayo This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters...

...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...

.... The Philosophical Review, Vol. 111, No. 3 (July 2002) Michael Potter, Reason’s Nearest Kin. New York: Oxford University Press, 2000. Pp. x+305. This book is a study of the philosophy of arithmetic in one of the most signifi- cant periods of its history—from Frege to Carnap—prefaced by an account...

... -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, 1983...

... . “The Consistency of Frege's Foundations of Arithmetic.” In On Being and Saying: Essays in Honor of Richard Cartwright , ed. Judith Jarvis Thomson, 3 -20. Cambridge: MIT Press. Reprinted in Boolos 1998, 183-201. Citation is to reprint. ____. 1997 . “Is Hume's Principle Analytic?” In Language, Thought...

.... This book is a study of the philosophy of arithmetic in one of the most signifi- cant periods of its history—from Frege to Carnap—prefaced by an account of Kant. Potter aims at a philosophical history, a story told from an explicit inter- pretative perspective. These theories of arithmetic are seen...

... theories about the nature of mathematics that cannot underpin standard arithmetic, we should look askance at philo- sophical theories about what fi xes the semantics of language that cannot underpin best theory in empirical linguistics, whatever this is.9 Interpretationist approaches take...

... . Cantini Andrea . 1990 . “ A Theory of Formal Truth Arithmetically Equivalent to ID 1 .” Journal of Symbolic Logic 55 , no. 1 : 244 – 59 . Conee Earl , and Feldman Richard . 2004 . Evidentialism: Essays in Epistemology . Oxford : Clarendon Press . Dickie...

...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...

..., prefabricated to stand all at once before the mind. Geometrical, arithmetical, and infinitesimal notions of magnitude proliferated, as hopes for a unitary idea of mathematical quantity waned. Efforts were made to corral the aggregate numbers of Heine, Dedekind, and Cantor into a single arithmetic continuum, set...

... of these other notions. The best way to frame this discussion is to assume a theory rich enough to talk about its own syntax and generate self-referential sentences (in this case arithmetic) that also contains vocabulary with which one can talk about truth and vocabulary with which one can diagnose...

... tradition of possible worlds semantics. The resulting modal structure has several interesting properties. Most notably, truth in the modal structure is equivalent to truth in second-order arithmetic, and indeed there is a fairly natural way to formalize second-order arithmetic within the modal theory...

... of numbers presented in the Tractatus. This is the subject of chapter 2, where the notion of “operation”in the Tractatus is seen as pivotal to the theory of truth-functions and to a non-extensional theory of arithmetic (where numbers are conceived of as the “exponent of an opera- tionThe...

... between “metaphysical platonism,” which is the view that the meaning of state- ments of arithmetic and their objective truth values are explained by there being a model of arithmetic “out there,” existing independently of us, and “contextual platonism,” which reverses the order of explanation...

... are specially prominent in the cases of 0, 1 and 2. (1959, 14-17). Note that Frege does not base his rejection of nondeductive reasoning in arithmetic on a dogmatic identification of mathematical truth with prova- bility, but on an internal property of the natural numbers themselves. I find...

... understood as only one with “no glimmering of a suspicion of the existence of indefinitely extensible concepts” would seek to under- stand it; he demonstrates, by pointing to the now well-known consistency of “Frege Arithmetic” (the same higher-order framework, minus Axiom V, plus Hume’s principle...

.... Such views set an implausibly high standard, Casullo charges, in effect obliging the rationalist to withhold attributions of a priori knowledge of basic arithmetic from those who “are not conversant with the metaphysical distinction between necessary and contingent propositions” (15), or, worse, from...

.... Such views set an implausibly high standard, Casullo charges, in effect obliging the rationalist to withhold attributions of a priori knowledge of basic arithmetic from those who “are not conversant with the metaphysical distinction between necessary and contingent propositions” (15), or, worse, from...

.... Such views set an implausibly high standard, Casullo charges, in effect obliging the rationalist to withhold attributions of a priori knowledge of basic arithmetic from those who “are not conversant with the metaphysical distinction between necessary and contingent propositions” (15), or, worse, from...