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

152 johannes hafner and paolo mancosuunification. Then we will look at a particular case of mathematical explanationcoming from real algebraic geometry. Finally, we will check Kitcher’s accountof explanation against our case study. By doing this we will heed Kitcher’sadvice in his paper ‘Explanatory unification’:Quite evidently, I have only sketched an account of explanation. To provide preciseanalyses of the notions I have introduced, the basic approach to explanation offeredhere must be refined against concrete examples of scientific practice. What needsto be done is to look closely at the argument patterns favored by scientists andattempt to understand what characteristics they share. (Kitcher, 1981, p.530)6.1.1 Kitcher’s account of explanation as unificationWe will follow here the account of explanation given by Kitcher in his paper‘Explanatory unification and the causal structure of the world’ (1989). Kitcherclaims that behind the account of explanation given by Hempel’s coveringlaw model—the official model of explanation for logical positivism—therewas an unofficial model which saw explanation as unification. What shouldone expect from an account of explanation? Kitcher in 1981 points out twothings. First, a theory of explanation should account for how science advancesour understanding of the world. Secondly, it should help us in evaluating orarbitrating disputes in science. He claims that the covering law model fails onboth counts and he proposes that his unification account fares much better.The basic intuition. Kitcher found inspiration in Friedman’s article of 1974,‘Explanation and scientific understanding’ where Friedman put forward theidea that understanding of the world is achieved by science by reducing thenumber of facts we take as brute:this is the essence of scientific explanation—science increases our understandingof the world by reducing the total number of independent phenomena that wehave to accept as ultimate or given. A world with fewer independent phenomenais, other things equal, more comprehensible than one with more. (Friedman,1974, p.15)Already Friedman had tried to make this intuition more precise by substitutingfor the notions of phenomena and laws linguistic descriptionsof such. Kitcher disagrees with the specific details of Friedman’s proposalbut thinks that the general intuition is correct. He modifies Friedman’sproposal by emphasizing that what lies behind unification is the reduction ofthe number of argument patterns used in providing explanations while beingas comprehensive as possible in the number of phenomena explained:Understanding the phenomena is not simply a matter of reducing the ‘fundamentalincomprehensibilities’ but of seeing connections, common patterns, in what