Comparative Epistemology and Sheafification


We have described the (quasi-)objects of contemporary mathematics as webs of structured information and as (in Leibniz’s sense) ‘compossible’ deformations within those webs, open to relative and asymptotic composition in variable contexts. The dynamism of those webs and deformations straddles the eidal and the quiddital, in an iterated weaving of conceptual and material approaches. These are bimodal objects in Petitot’s sense, situated in both physical and morphological-structural space, acting and reacting along spectra of formal and structural correlations with the many mobile environments where their partial transit takes place. In this way, the ontological ‘what’ and ‘where’ are blurred, and their frontiers become murky…