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

176 johannes hafner and paolo mancosube trivialized by varying (i.e. generalizing) their filling instructions. In sharpcontrast, the nonlogical vocabulary in TSP ′ , the name ‘F’ of the decisionalgorithm for RCF ,isnot idling, the presence of it does pose constraints on the(combination of) the expressions we can substitute for ‘ϕ’, ‘ψ’, and ‘x’. HenceTSP ′ cannot be turned into a pattern that yields any sentence whatsoever bymodifying the filling instructions. Its classification does not allow that. In fact,the filling instructions, due to their purely syntactic character, are already statedin the utmost generality and cannot be generalized any further (as could easilybe done in case of the spurious unifications).To sum up, in Kitcher’s framework E I (K) cannot be dismissed as spuriousbecause of non-stringency; it clearly passes the test based on the newrequirement. The problem posed by this systematization for Kitcher’s modelof mathematical explanation won’t thus go away.Acknowledgments. We would like to thank Jeremy Avigad, ChristianFermüller, Philip Kitcher, Dana Scott, Jamie Tappenden, and Mark Wilsonfor many useful comments which improved the final version of this chapter.