The case for a mathematics of structural transformation and genesis: Whitehead against Badiou?

From a mathematical perspective, this paper will compare the 'Speculative' Realist Philosophy of Alain Badiou with the Process Philosophy of Alfred North Whitehead. To this end, each philosophy will be examined in terms of how it departs from the strictures of Kantian Critical Philosophy, specifically, in terms of how it articulates the structural relationship between subjects, objects, and relata. Moreover, each philosophy will also be judged both in terms of how it addresses the mereological distinction between internal and external relations, and how it conceives of the relationship holding between philosophy and its others: the four Althusserian 'generics' of science, politics, art, and love.