Platonism, De Re, and (Philosophy of) Mathematical Practice

Marco Panza ()
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Marco Panza: CNRS, IHPST (CNRS and University of Paris 1, Panthéon Sorbonne)

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 2307-2335 from Springer

Abstract: Abstract The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called “Plato’s problem,” in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded as individual contents that we have (or can have) a de re epistemic access to. The question of the existence of mathematical objects is then replaced by that of the modalities of our de re epistemic access to individual mathematical contents.

Keywords: Platonism; Nominalism; Mathematical objects; Plato’s problem; De re vs de dictum epistemic access (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_56

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DOI: 10.1007/978-3-031-40846-5_56

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