Horvat, Sebastian and Toader, Iulian Danut (2023) An Alleged Tension between Quantum Logic and Applied Classical Mathematics. [Preprint]

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Abstract

Timothy Williamson has argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the adoption, in non-mathematical domains, of a wide range of non-classical logics, including quantum logics (QL). We first reconstruct the argument and present its restriction to the case of QL. Then we show that there is no inconsistency whatsoever between the application of classical mathematics to quantum phenomena and the use of QL in reasoning about them. Once we identify the premise in Williamson's argument that turns out to be false when restricted to QL, we argue that the same premise breaks down for a wider variety of non-classical logics. In the end, we also suggest that the alleged tension between these non-classical logics and applied classical mathematics betrays a misunderstanding of the nature of mathematical representation in science.

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Item Type:	Preprint
Creators:	Creators Email ORCID Horvat, Sebastian sebastian.horvat@univie.ac.at Toader, Iulian Danut iulian.danut.toader@univie.ac.at
Keywords:	Deviant logics, quantum logic
Subjects:	Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics
Depositing User:	Unnamed user with email horvatsebastian96@gmail.com
Date Deposited:	18 Apr 2023 17:38
Last Modified:	18 Apr 2023 17:38
Item ID:	21992
Subjects:	Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics
Date:	2023
URI:	https://philsci-archive.pitt.edu/id/eprint/21992

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• An Alleged Tension between Quantum Logic and Applied Classical Mathematics. (deposited 18 Apr 2023 17:38) [Currently Displayed]
  • An Alleged Tension between Quantum Logic and Applied Classical Mathematics. (deposited 11 Aug 2023 16:47)

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