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

eyond unification 175(3) F(ϕ) = 0 →¬ϕ(4) F(ϕ) = 1 → ϕ(5) ψHere ‘ϕ’, ‘ψ’ ,and‘x’ are dummy letters.Filling instructions:Replace ‘ϕ’ by a sentence in the language of RCF.Replace ‘ψ’ by a sentence in the language of RCF.Replace ‘x’ by ‘0’ or ‘1’.Classification:Sentence (1) isapremise.Sentence (2) follows from (1) by metatheory, i.e. by using facts about thefunctioning of F.Sentences (3) and(4) also follow from (1) using facts about the functioningof F.Sentence (5) follows from (2) together with either (3) or(4) by ModusPonens.In this reformulation the filling instructions only specify the syntactic categoriesof the expressions to be substituted for the dummy letters without making anyreference to semantic, logical, or epistemic features of these expressions. Therehas to be a rigorous separation between, on the one hand, filling instructionsqua purely syntactical constraints on substitutions for dummy letters and theclassification, on the other hand, which specifies inferential characteristicsof the schematic argument, i.e. puts in effect further constraints on thosesubstitutions based on (deductive or inductive) logical relationships betweensentences in the argument and/or theories in the background. Maintainingthis separation sets TSP ′ apart from argument patterns which achieve onlyspurious unifications. The filling instructions of, e.g. the pattern of selfderivation(‘from α infer α’) or the theological pattern involve the notionof the acceptance of sentences. Thus all (or almost all) of the work is doneby these kind of filling instructions, which ensure that a particular type ofconclusion (for instance, accepted sentences describing the physical world) isgenerated by such patterns. Neither the structure of the schematic argumentnor the classification really contribute anything to this ‘unification’. As Kitcherput it, the remaining nonlogical vocabulary in such patterns is idling. Thereal work of unifying beliefs is only mimicked by the filling instructions, i.e.by appropriate restrictions on the sentences to be substituted for the dummyletters (cf. Kitcher, 1981, p.527). And that’s precisely why such patterns can