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Article Dans Une Revue Philosophia Mathematica Année : 2023

Mathematical explanations: an analysis via formal proofs and conceptual complexity

Résumé

This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. In particular, the goal of the paper is to attempt to provide a rigorous analysis of these explanations. This will be done into two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof-trees together with a decomposition of their elements into assumptions, conclusion and rules; secondly we will show that those mathematical proofs that are regarded as having an explanatory power all have the same formal presentation: they display an increase of conceptual complexity from the assumptions to the conclusion.

Domaines

Philosophie
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Dates et versions

hal-04303153 , version 1 (23-11-2023)

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Citer

Francesca Poggiolesi. Mathematical explanations: an analysis via formal proofs and conceptual complexity. Philosophia Mathematica, In press, ⟨10.1093/philmat/nkad023⟩. ⟨hal-04303153⟩
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