Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

6Beyond UnificationJOHANNES HAFNER AND PAOLO MANCOSUAs pointed out in the introduction there are at the moment two theoriesof mathematical explanation on offer. The first is due to Steiner (1978) andhas been extensively discussed in Resnik and Kushner (1987), Weber andVerhoeven (2002), and Hafner and Mancosu (2005). The second theory is dueto Philip Kitcher, who is a well-known defender of an account of scientificexplanation as theoretical unification. Kitcher sees as one of the virtues of hisaccount that it can also be applied to explanation in mathematics, unlike othertheories of scientific explanation whose central concepts, say, causality or lawsof nature, do not seem relevant to mathematics. In this paper we are going todiscuss Kitcher’s account of explanation in the context of a test case from realalgebraic geometry.6.1 Kitcher’s theory of explanationKitcher has not devoted any single article exclusively to mathematical explanationand thus his position can only be gathered from what he says aboutmathematics in his major articles on scientific explanation. In his later work,such as Kitcher (1989), he uses unification as the overarching model forexplanation both in science and mathematics:The fact that the unification approach provides an account of explanation, andexplanatory asymmetries, in mathematics stands to its credit. (Kitcher, 1989,p. 437)Unlike Steiner’s model of mathematical explanation, Kitcher’s accountof mathematical explanation has not been extensively discussed. A generaldiscussion is found in Tappenden (2005) but not a detailed analysis. Our aimhere is threefold. We will present in outline Kitcher’s theory of explanation as