Landsman, Klaas (2025) Philosophy of Mathematical Physics. [Preprint]

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Abstract

A philosophy of mathematical physics ought to balance a philosophy of physics with a philosophy of mathematics, such that the early modern `mathematization of the world picture' as well as the theory-laden and ambiguous character of the targets of mathematical models of modern physics fall into place. Wigner's `unreasonable effectiveness of mathematics in the natural sciences' also falls within its scope. Guided by a historical survey, we propose that theories of mathematical physics (such as general relativity, quantum mechanics, and statistical mechanics) should be seen as meaning-constitutive a priori constructions, hypothetical but far from arbitrary, whose models mediate between theory and nature, that is, between the a priori and the a posteriori. Models do so by playing the role of Wittgensteinian yardsticks or objects of comparison to be held against data models, where the comparison is done via surrogative inference. This balancing act involves a loss of realism on both sides.

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Item Type:	Preprint
Creators:	Creators Email ORCID Landsman, Klaas landsman@math.ru.nl 0000-0003-2651-2613
Keywords:	philosophy of mathematics, models, conventionalism, inferentialism, Wittgenstein
Subjects:	Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > History of Philosophy
Depositing User:	Nicolaas P. Landsman
Date Deposited:	07 Jul 2025 13:40
Last Modified:	07 Jul 2025 13:40
Item ID:	25843
Subjects:	Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > History of Philosophy
Date:	28 June 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/25843

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