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Unificatory Understanding and Explanatory Proofs.
- Source :
-
Foundations of Science . Dec2021, Vol. 26 Issue 4, p1105-1127. 23p. 1 Black and White Photograph. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATHEMATICAL proofs
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 12331821
- Volume :
- 26
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Foundations of Science
- Publication Type :
- Academic Journal
- Accession number :
- 153370205
- Full Text :
- https://doi.org/10.1007/s10699-020-09654-4