The logic of Kant’s temporal continuum

In this thesis I provide an account of the philosophical foundations and mathematical structure of Kant's temporal continuum. I mainly focus on the development of a formalization of Kant's temporal continuum as it appears in the Critique of Pure Reason and in other works from Kant's critical period, employing tools from discrete and point free topology, order theory and category theory. The formal apparatus of the thesis is also applied to the elucidation of the elusive distinction, at B161n of the Critique of Pure Reason, between space and time as "forms of intuition" and as "formal intuitions". While the bulk of the work concerns Kant's continuum, most of my results are generally relevant for the problem of developing mathematically rigorous foundations for a phenomenological concept of the continuum. I this respect, I show that my analysis of Kant's continuum subsumes and extends Russell's and Walker's constructions of instants from events and that it is closely related to point-free topology in the predicative and constructive tradition of formal topology. This paves the way for a constructive and predicative treatment of bitopological spaces in formal topology and for reviving the Russell-Walker-Whitehead project of constructing relativistic spacetimes from events.