The indispensability argument and multiple foundations for mathematics

Philosophical Quarterly 53 (210):49–67 (2003)
Abstract
One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects
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    References found in this work BETA
    Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
    O. Bueno (2000). Empiricism, Scientific Change and Mathematical Change. Studies in History and Philosophy of Science Part A 31 (2):269-296.
    Penelope Maddy (1992). Indispensability and Practice. Journal of Philosophy 89 (6):275-289.
    Colin McLarty (1990). The Uses and Abuses of the History of Topos Theory. British Journal for the Philosophy of Science 41 (3):351-375.

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    Citations of this work BETA
    Russell Marcus (2013). Intrinsic Explanation and Field's Dispensabilist Strategy. International Journal of Philosophical Studies 21 (2):163 - 183.
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