Avigad, Jeremy (2019) Reliability of mathematical inference. [Preprint]
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Abstract
Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification.
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| Item Type: | Preprint | ||||||
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| Keywords: | mathematical proof, formalization, reliability | ||||||
| Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics > Values |
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| Depositing User: | Prof. Jeremy Avigad | ||||||
| Date Deposited: | 17 Dec 2019 15:30 | ||||||
| Last Modified: | 17 Dec 2019 15:30 | ||||||
| Item ID: | 16725 | ||||||
| Subjects: | Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics > Values |
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| Date: | 15 December 2019 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/16725 |
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Reliability of mathematical inference. (deposited 02 Aug 2019 23:26)
- Reliability of mathematical inference. (deposited 17 Dec 2019 15:30) [Currently Displayed]
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