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

eyond unification 171unification in Kitcher’s sense, a more fine-grained analysis of different types ofunification seems to be needed.6.5 Stringency and spurious unificationLet’s now return to E I (K), the systematization of K whose basis contains only asingle argument pattern and which is thus ranked best by Kitcher’s model. Wewant to discuss (and dispel) a worry one might have concerning this rankingand the resulting criticism of Kitcher’s model. In fact, this kind of worry orobjection which invokes the notion of stringency has been voiced on severaloccasions when this paper was presented.So far in our exposition and discussion of Kitcher’s theory the stringencycriterion has played no role. What does it consist in? Kitcher proposes ‘thatscientists are interested in stringent patterns of argument, patterns which containsome non-logical expressions and which are fairly similar in terms of logicalstructure’ (Kitcher, 1981, p.518). The stringency of an argument pattern isdetermined by two different constraints concerning two respects in whichargument patterns may be similar.Derivations may be similar either in terms of their logical structure or in termsof the nonlogical vocabulary they employ at corresponding places. The notionof a general argument pattern allows us to express the idea that derivationssimilar in either of these ways have a common pattern. [...] To capture thenotion that one pair of arguments is more similar than another pair, we needto recognize the fact that general argument patterns can demand more or lessof their instantiations. If a pattern sets conditions on instantiations that are moredifficult to satisfy than those set by another pattern, then I shall say that the formerpattern is more stringent than the latter. The stringency of an argument pattern isdetermined in part by the classification, which identifies a logical structure thatinstantiations must exhibit, and in part by the nature of the schematic sentencesand the filling instructions, which jointly demand that instantiations should havecommon nonlogical vocabulary at certain places. (Kitcher, 1989, p.433)Apart from these rather general remarks Kitcher does not give us much togo on. He just sketches the main idea ‘without trying to provide an exactanalysis of the notion of stringency’ (Kitcher, 1981, p.518; cf.alsoKitcher,1989, p.433). In spite of this vagueness stringency is supposed to be one ofthe factors which determine the unifying power of a basis, since that unifyingpower is supposed to vary directly with the stringency of the patterns inthe basis (cf. Kitcher, 1981, p.520; Kitcher,1989, p.435). However, in theabsence of an exact definition of stringency and a precise, workable account of