Horvat, Sebastian and Toader, Iulian D. (2023) An Alleged Tension Between non-Classical Logics and Applied Classical Mathematics. [Preprint]
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Abstract
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first reconstruct his argument and present its restriction to the case of quantum logic (QL). Then we show that there is no problematic tension between the applicability of classical mathematical models to quantum phenomena and the endorsement of QL in the reasoning about the latter. 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 fails for a wider variety of non-classical logics. In the end, we use our discussion to draw some general lessons concerning the relationship between applied logic and applied mathematics.
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| Item Type: | Preprint | |||||||||
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| Keywords: | Non-classical logics, quantum logic, applicability of mathematics | |||||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics |
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| Depositing User: | Unnamed user with email horvatsebastian96@gmail.com | |||||||||
| Date Deposited: | 06 Jul 2024 18:21 | |||||||||
| Last Modified: | 06 Jul 2024 18:21 | |||||||||
| Item ID: | 23672 | |||||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics |
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| Date: | 2023 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/23672 |
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