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

eyond unification 153initially appeared to be different situations. Here the switch in conceptionfrom premise–conclusion pairs to derivations proves vital. Science advances ourunderstanding of nature by showing us how to derive descriptions of manyphenomena, using the same patterns of derivation again and again, and, indemonstrating this, it teaches us how to reduce the number of types of facts thatwe have to accept as ultimate (or brute). So the criterion of unification I shall try toarticulate will be based on the idea that E(K) is a set of derivations that makes thebest tradeoff between minimizing the number of patterns of derivation employedand maximizing the number of conclusions generated. (Kitcher, 1989, p.432)We will come back to the distinction between arguments and derivationsand to a clarification of what E(K) is below.Local vs. global notions of explanation. In many accounts of explanation,including the Hempelian one, explanations are arguments. Arguments areidentified with pairs of premises and conclusions and can be assessed individuallywith respect to explanatoriness. Following Friedman, we would like to saythat whether an argument is an explanation is a local property, i.e. it does notdepend on more global constraints. Kitcher rejects both the identification ofexplanations as arguments conceived as above and the local characterizationof explanation. The informal idea is that explanations qualify as such becausethey belong to the best systematization of our beliefs. Moreover, explanationsare not pairs of premises–conclusions, as in Hempel, but rather derivations:On the systematization account, an argument is considered as a derivation, as asequence of statements whose status (as a premise or as following from previousmembers in accordance with some specified rule) is clearly specified. An idealexplanation does not simply list the premises but shows how the premises yieldthe conclusion. (Kitcher, 1989, p.431)6.1.2 The formal details of the modelLet us make this more formal. Let us start with a set K of beliefs assumedconsistent and deductively closed (informally one can think of this as a set ofstatements endorsed by an ideal scientific community at a specific moment intime (Kitcher, 1989, p.431)). A systematization of K is any set of argumentswhich derive some sentences in K from other sentences in K. Theexplanatorystore over K, E(K), is the best systematization of K (Kitcher here makesan idealization by claiming that E(K) is unique). Corresponding to differentsystematizations we have different degrees of unification. The highest degreeof unification is that given by E(K). But according to what criteria can asystematization be judged to be the best?Kitcher’s criteria for systematizations. Kitcher lists three criteria for judging thequality of a systematization , although as it turns out only two of them