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2023
- handle: 10670/1.1diotm
- hal: hal-04303153
- doi: 10.1093/philmat/nkad023
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info:eu-repo/semantics/altIdentifier/doi/10.1093/philmat/nkad023
info:eu-repo/semantics/OpenAccess
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Mathematical explanation proof complexityCiter ce document
Francesca Poggiolesi, « Mathematical explanations: an analysis via formal proofs and conceptual complexity », HAL-SHS : philosophie, ID : 10.1093/philmat/nkad023
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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.