Toward a Synthetic Philosophy of Contemporary Mathematics


In the introduction and preceding chapters we saw that a contrasting (and often contradictory) multiplicity of points of view traverse the field of the philosophy of mathematics. Also, we have delineated (as a first approximation, which we will go on to refine throughout this work) at least five characteristics that separate modern mathematics from classical mathematics, and another five characteristics that distinguish contemporary mathematics from modern mathematics. In that attempt at a global conceptualization of certain mathematical tendencies of well-defined historical epochs, the immense variety of the technical spectrum that had to be traversed was evident. Nevertheless, various reductionisms have sought to limit both the philosophical multiplicity and mathematical variety at stake. Far from one kind of omnivorous philosophical wager, or one given reorganization of mathematics, which we would then try to bring into a univalent correlation, we seem to be fundamentally obliged to consider the necessity of constructing multivalent correspondences between philosophy and mathematics, or rather between philosophies and mathematics in the plural…