Affiliation:
1. CNRS, IHPST , UMR 8590, Université Paris 1 Panthéon-Sorbonne , 75006 Paris, France
Abstract
Abstract
This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in 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; secondly we will show that those mathematical proofs that are regarded as having explanatory power all display an increase of conceptual complexity from the assumptions to the conclusion.
Publisher
Oxford University Press (OUP)
Subject
Philosophy,General Mathematics
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