Séminaire PhilMath

"Three dimensions of mathematical explanations"

 

Résumé : 

 

Recent literature on intra-mathematical explanation (mathematical explanation of a mathematical fact) has significantly expanded the range of case studies analysed from different areas of mathematical practice. Nevertheless, very few general accounts of mathematical explanation have been proposed since Steiner's [1978] and Kitcher's [1981], and none seems to attract a wide consensus. In this paper, I suggest that the case studies analysed so far show that intra-mathematical explanation varies along three main dimensions: (i) the goals of enquiry, (ii) the target audience, and (iii) the mathematical features of the explanans, and I argue that this framework can illuminate many aspects of the current disagreement about explanations in mathematical practice.