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MATHEMATICAL RIGOR AND PROOF

Part of: General and miscellaneous specific topics Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  04 October 2019

YACIN HAMAMI
YACIN HAMAMI*
Affiliation:
CENTRE FOR LOGIC AND PHILOSOPHY OF SCIENCE VRIJE UNIVERSITEIT BRUSSELBRUSSELSB-1050, BELGIUME-mail: [email protected]
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Abstract

Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowledge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary mathematicians, and is endorsed by many logicians and philosophers, but it has also been heavily criticized in the philosophy of mathematics literature. Progress on the debate between the proponents and opponents of the standard view is, however, currently blocked by a major obstacle, namely, the absence of a precise formulation of it. To remedy this deficiency, I undertake in this paper to provide a precise formulation and a thorough evaluation of the standard view of mathematical rigor. The upshot of this study is that the standard view is more robust to criticisms than it transpires from the various arguments advanced against it, but that it also requires a certain conception of how mathematical proofs are judged to be rigorous in mathematical practice, a conception that can be challenged on empirical grounds by exhibiting rigor judgments of mathematical proofs in mathematical practice conflicting with it.

Keywords

mathematical rigormathematical proofformal proofmathematical practice

MSC classification

Primary: 00A30: Philosophy of mathematics
Secondary: 00A35: Methodology of mathematics, didactics 03A05: Philosophical and critical
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 2 , June 2022 , pp. 409 - 449
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Copyright
© The Author(s), 2019. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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