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

eyond unification 173E I (K) comes out as the best systematization of K on Kitcher’s model, aspointed out above, contrary to how it is considered from the perspective ofactual mathematical practice. This reveals a serious defect of Kitcher’s model.Against this result one may object as follows. The account of Kitcher’smodel on which our ranking of E I (K) is based leaves out completely thestringency criterion. Yet, the argument pattern TSP has exactly the same flawas the trivial argument patterns considered—and rejected—above. It allowsany vocabulary whatever (from the language of ordered fields) to appear inthe place of ‘ϕ’ and‘ψ’. Hence it, too, should be rejected as non-stringent.In other words, taking into account the stringency criterion not only blocksE I (K) from being ranked higher than E II (K) and E III (K) but it even excludesE I (K) altogether from the ‘competition’ as an inadmissible, spurious unification.Hence it poses no threat to Kitcher’s model after all.To see how much weight this objection indeed carries we have to evaluateit not at the level of our intuitive concept of stringency but in light of theexplicit requirement Kitcher formulates to screen out spurious unifications.If the filling instructions associated with a pattern P could be replaced by differentfilling instructions, allowing for the substitution of a class of expressions of thesame syntactic category, to yield a pattern P ′ and if P ′ would allow the derivationof any sentence, then the unification achieved by P is spurious. (Kitcher, 1981,p. 527f)This requirement in fact identifies as spurious the previously consideredtrivial argument patterns since the filling instruction ‘α’ istobereplacedby any sentence we accept’ can be generalized to ‘α’ istobereplacedbyany sentence’ thus allowing the derivation of any sentence. Kitcher furtherillustrates and motivates his new requirement with respect to the followingargument pattern which might be used by ‘a group of religious fanatics’ toexplain and unify their beliefs about the world (cf. Kitcher, 1981, p.528).(1) God wants it to be the case that α.(2) What God wants to be the case is the case.(3) αFilling instruction: ‘α’ is to be replaced by any sentence describing thephysical world.This pattern is also identified by the new requirement as spurious since itcan be trivialized by changing the filling instruction to ‘α’ istobereplacedbyany sentence’. And Kitcher continues:Why should patterns whose filling instructions can be modified to accommodateany sentence be suspect? The answer is that, in such patterns, the nonlogical