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Title: Explanation, Understanding, and Definitions in Mathematics
Author(s): COUMANS, Vincent , FRANS, Joachim , DE REGT, Henk W.
Journal: Logique et Analyse
Volume: 257    Date: 2022   
Pages: 79-99
DOI: 10.2143/LEA.257.0.3291072

Abstract :
Following trends in the study of explanation in mathematics, we look at explanatory definitions. In particular, we build on the work of Lehet, who describes explanatory definitions as those definitions that generate understanding. From this starting point, we investigate what types of understanding are associated with definitions, in order to develop a conception of explanatory definitions. Using the work of Baumberger, we show that definitions can be explanatory in two ways: symbolically or factually. Furthermore, we zoom in on the impact of contextual factors on the explanatory value of definitions.

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