Matteo Plebani
University of Turin
I will contrast two conceptions of the nature of mathematical objects: the conception of mathematical objects as preconceived objects, and heavy duty platonism. I will argue that friends of the indispensability argument are committed to some metaphysical theses and that one promising way to motivate such theses is to adopt heavy duty platonism. On the other hand, combining the indispensability argument with the conception of mathematical objects as preconceived objects yields an unstable position. The conclusion is that the metaphysical commitments of the indispensability argument should be carefully scrutinized.
Keywords indispensability argument   heavy duty platonism   metaphysical grounding
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DOI 10.1387/theoria.17613
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Essence and Modality.Kit Fine - 1994 - Philosophical Perspectives 8 (Logic and Language):1-16.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.

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