Abstract
Benacerraf’s “Mathematical Truth” (Benacerraf 1973) takes on the form of a well-known dilemma. Either a referential semantics for ordinary language is extended to mathematical language, but then one lapses into platonism, or a reasonable account of mathematical knowledge as a proof activity is put forward, but then no account of mathematical truth as truth is given.
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Benacerraf, P. (1965). What numbers could not be. The Philosophical Review, 74(1), 47–73.
Benacerraf, P. (1973). Mathematical truth. The Journal of Philosophy, 70(19), 661–679.
Benacerraf, P. (1981) Frege: The last logicist. Midwest Studies in Philosophy, 6(1), 17–36.
Brentano, F. C. (1874). Psychologie vom empirischen Standpunkt. Leipzig: Verlag von Duncker & Humblot.
Frege, G. [1892] (1952). On sense and reference. Translations from the philosophical writings of Gottlob Frege (P. Geach & M. Black, Eds., M. Black, Trans., pp. 56–78). Oxford: Basil Blackwell.
Kant, I. [1787] (1998). Critique of pure reason (P. Guyer & A. W. Good, Eds., Trans.). [from the second edition of Kritik der reinen Vernunft, Johann Friedrich Hartknoch, Riga, 1787]. Cambridge: Cambridge UP.
Keränen, J. (2006). The identity problem for realist structuralism II. A reply to Shapiro (Chapter 6). In F. MacBride (Ed.), Identity and modality. New essays in metaphysics (pp. 146–163). Oxford: Oxford UP.
Russell, B. (1903). The principles of mathematics. Cambridge: Cambridge UP.
Shapiro, S. (2006). Structure and identity (Chapter 5). In F. MacBride (Ed.), Identity and modality. New essays in metaphysics (pp. 109–145). Oxford: Oxford UP.
Stanley, J., & Williamson, T. (2001). Knowing how. The Journal of Philosophy, 98(8), 411–444.
von Dyck, W. F. (1882). Gruppentheoretische Studien. Mathematische Annalen, 20(1), 1–44.
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Halimi, B. (2016). Benacerraf’s Mathematical Antinomy. In: Pataut, F. (eds) Truth, Objects, Infinity. Logic, Epistemology, and the Unity of Science, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-45980-6_3
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