Landsman, Klaas (2025) Rigour from rules: Deduction and definition in mathematical physics. [Preprint]
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Abstract
We ask how and why mathematical physics may be seen as a rigorous discipline. Starting with Newton but drawing on a philosophical tradition ranging from Aristotle to (late) Wittgenstein, we argue that, as in mathematics, rigour ultimately comes from rules. These include logical rules of inference as well as definitions that give a precise meaning to physical concepts such as space and time by providing rules governing their use in models of the theories in which they are defined. In particular, so-called implicit definitions characterize "indefinables" whose traditionally assumed familiarity through "intuition" or "acquaintance" from Aristotle down to Russell blasts any hope of both rigour and innovation. Given the basic physical concepts, one may subsequently define derived concepts (like black holes or determinism). Definitions are seen as a priori meaning-constitutive conventions that are neither necessary à la Kant nor arbitrary à la Carnap, as they originate in empirical science as well as in the autonomous development of mathematics and physics. As such definitions are best seen as hypothetical.
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| Item Type: | Preprint | ||||||
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| Additional Information: | Invited contribution to The Philosophy of Rigour, eds. Dean Rickles and Karim Thébault (Routledge, to appear) | ||||||
| Keywords: | Rigour; definition; inference; mathematical physics | ||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Practice General Issues > Logical Positivism/Logical Empiricism |
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| Depositing User: | Nicolaas P. Landsman | ||||||
| Date Deposited: | 25 Jul 2025 13:16 | ||||||
| Last Modified: | 28 Jul 2025 20:13 | ||||||
| Item ID: | 26010 | ||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Practice General Issues > Logical Positivism/Logical Empiricism |
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| Date: | 24 July 2025 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/26010 |
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