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Reliability of mathematical inference

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
Creators:
CreatorsEmailORCID
Avigad, Jeremyavigad@cmu.edu0000-0003-1275-315X
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
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
Date: 15 December 2019
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16725

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