Mathematical explanations are explanations in which mathematics plays a fundamental role. The expression ‘mathematical explanation’ (ME) has two distinct, although connected, meanings: in relation to pure mathematics ME denotes proofs that are able not only to demonstrate the truth of a given mathematical statement, but also to explain why the statement is true, whereas in connection with empirical sciences ME refers to explanations of non-mathematical facts (physical, biological, social, psychological) justified by recourse to mathematics.
Although the concept of ME has been the subject of analysis at least since Aristotle’s distinction between apodeixis tou oti and apodeixis tou dioti (Post. An. I.13), and has been dealt with a few times over the course of the development of Western thought (e.g. Descartes, Newton, and Bolzano), it is only since the 1970s that an intense philosophical debate has sprung up regarding the nature of ME. This debate, linked to the gradual diffusion of Quinean epistemology (Steiner 1978) and the development of the anti-foundationalist philosophy of mathematics (the so-called ‘maverick’ tradition, Cellucci 2008), centers on the following questions: Do mathematical explanations exist? If mathematical explanations exist, can they be reduced to a single model or are they heterogeneous among themselves? What implications does the comprehension of the concept of mathematical explanation have for some of the most important problems of the contemporary philosophy of science (e.g. indispensability arguments, inference to the best explanation, and the theory of scientific explanation)?
The key works about mathematical explanation within mathematics are Steiner 1978 (for criticisms of the model proposed by Steiner see Resnik & Kushner 1987, Weber & Verhoeven 2002, and Mancosu & JØrgensen 2006), Kitcher 1983, and Kitcher 1989 (a careful analysis of the limitations of the model proposed by Kitcher can be found in Mancosu & Hafner 2008). Regarding the notion of mathematical explanation in natural sciences, see Batterman 2002, Baker 2005, Pincock 2007, and Baker 2009.
|Introductions||For general overviews on the subject, see Mancosu 2011, Pincock & Mancosu 2012, and Molinini 2014.|
- Functional Explanation (25)
- Mechanistic Explanation (88)
- Narrative Explanation (13)
- Statistical Explanation (31)
- Varieties of Explanation, Misc (15)
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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