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On the unreasonable reliability of mathematical inference

Larvor, Brendan (2022) On the unreasonable reliability of mathematical inference. [Preprint]

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Abstract

In (Avigad, 2020), Jeremy Avigad makes a novel and insightful argument, which he presents as part of a defence of the ‘Standard View’ about the relationship between informal mathematical proofs and formal derivations. He considers the various strategies by means of which mathematicians can write informal proofs that meet mathematical standards of rigour, in spite of the prodigious length, complexity and conceptual difficulty that some proofs exhibit.

In this paper, I will first argue that the observational core of Avigad’s argument is no threat to critics of the Standard View. On the contrary, it looks very like the paper that they have been waiting for one of their number to write. I will then argue that Avigad’s project of accounting for the relation between formal and informal proofs raises a prior question: what sort of thing is an informal proof? His paper vacillates between two answers, which we can call ‘syntactic’ and ‘semantic’. Since the ‘syntactic’ reading of informal proofs reduces the Standard View to triviality, makes a mystery of the valuable observational core of his paper, and underestimates the value of the achievements of mathematical logic, he should choose some version of the ‘semantic’ option.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Larvor, Brendanb.p.larvor@herts.ac.uk0000-0003-0921-1659
Keywords: Proof; rigour; semantic; syntactic
Subjects: Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Depositing User: Dr Brendan Larvor
Date Deposited: 13 Jul 2022 15:10
Last Modified: 13 Jul 2022 15:10
Item ID: 20887
Subjects: Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Date: 13 July 2022
URI: http://philsci-archive.pitt.edu/id/eprint/20887

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