Frege, Indispensability, and the Compatibilist Heresy

Philosophia Mathematica 23 (1):11-30 (2015)
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In Grundgesetze, Vol. II, §91, Frege argues that ‘it is applicability alone which elevates arithmetic from a game to the rank of a science’. Many view this as an in nuce statement of the indispensability argument later championed by Quine. Garavaso has questioned this attribution. I argue that even though Frege's applicability argument is not a version of ia, it facilitates acceptance of suitable formulations of ia. The prospects for making the empiricist ia compatible with a rationalist Fregean framework appear thus much less dim than expected. Nonetheless, those arguing for such compatibility eventually face an hardly surmountable dilemma



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Andrea Sereni
Scuola Universitaria Superiore IUSS Pavia

Citations of this work

On the Philosophical Significance of Frege’s Constraint.Andrea Sereni - 2019 - Philosophia Mathematica 27 (2):244–275.
Mathematical platonism meets ontological pluralism?Matteo Plebani - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):655-673.

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References found in this work

The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Frege.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.

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