Reconciling Rigor and Intuition

Erkenntnis 86 (6):1783-1802 (2021)
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Abstract

Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses.

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Silvia De Toffoli
Linkoping University

Citations of this work

What Are Mathematical Diagrams?Silvia De Toffoli - 2022 - Synthese 200 (2):1-29.
Philosophy of Mathematics.Leon Horsten - 2008 - Stanford Encyclopedia of Philosophy.
The Philosophy of Logical Practice.Ben Martin - 2022 - Metaphilosophy 53 (2-3):267-283.
Intersubjective Propositional Justification.Silvia De Toffoli - forthcoming - In Luis R. G. Oliveira & Paul Silva Jr (eds.), Propositional and Doxastic Justification. Routledge.

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References found in this work

Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
Proofs and Refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
Reliability of Mathematical Inference.Jeremy Avigad - 2020 - Synthese 198 (8):7377-7399.
Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.

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