On Mathematical Explanation

Abstract

In the present paper I would like to present some reflections which occurred to me upon reading Grosholz's paper ``The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge.'' However, I should warn the reader that although Grosholz's paper provided the original stimulus for mine, in the end I pursue a number of issues which were perhaps not the central ones Grosholz was addressing. Grosholz begins by claiming that, Relations among distinct areas of mathematical activity are most commonly discussed in terms of the reduction of axiomatized theories, where reduction is defined to be the deductive derivation of the axioms of the reduced theory as theorems of the reducing theory (Grosholz 1999, 81).