Abstract
One of the central aims of the philosophical analysis of mathematical explanation is to determine how one can distinguish explanatory proofs from non-explanatory proofs. In this paper, I take a closer look at the current status of the debate, and what the challenges for the philosophical analysis of explanatory proofs are. In order to provide an answer to these challenges, I suggest we start from analysing the concept understanding. More precisely, I will defend four claims: (1) understanding is a condition for explanation, (2) unificatory understanding is a type of explanatory understanding, (3) unificatory understanding is valuable in mathematics, and (4) mathematical proofs can contribute to unificatory understanding. As a result, in a context where the epistemic aim is to unify mathematical results, I argue it is fruitful to make a distinction between proofs based on their explanatory value.
| Original language | English |
|---|---|
| Pages (from-to) | 1105-1127 |
| Number of pages | 23 |
| Journal | Foundations of Science |
| Volume | 26 |
| Early online date | 28 Feb 2020 |
| DOIs | |
| Publication status | Published - 2 Nov 2021 |
Keywords
- Mathematical explanation
- Understanding
- Unification
- Mathematical proof