Mathematical Method and Proof

Synthese 153 (1):105-159 (2006)

Authors
Jeremy Avigad
Carnegie Mellon University
Abstract
On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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Reprint years 2006
DOI 10.1007/s11229-005-4064-5
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References found in this work BETA

Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Cambridge University Press.
Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Studia Logica 81 (2):285-289.
Mathematical Explanation.Mark Steiner - 1978 - Philosophical Studies 34 (2):135 - 151.

View all 22 references / Add more references

Citations of this work BETA

Modularity in Mathematics.Jeremy Avigad - 2020 - Review of Symbolic Logic 13 (1):47-79.
Mathematical Inference and Logical Inference.Yacin Hamami - 2018 - Review of Symbolic Logic 11 (4):665-704.
Against Mathematical Explanation.Mark Zelcer - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):173-192.

View all 14 citations / Add more citations

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