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 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, 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 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: | 11 Aug 2023 16:47 | |||||||||
| Last Modified: | 11 Aug 2023 16:47 | |||||||||
| Item ID: | 22396 | |||||||||
| 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/22396 |
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An Alleged Tension between Quantum Logic and Applied Classical Mathematics. (deposited 18 Apr 2023 17:38)
- An Alleged Tension between Quantum Logic and Applied Classical Mathematics. (deposited 11 Aug 2023 16:47) [Currently Displayed]
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