On the Architectonic Idea of Mathematics

The architectonic is key for situating Kant’s understanding of science in the coming century. For Kant the faculty of reason turns to ideas to form a complete system. The coherence of the system rests on these ideas. In contrast to technical unity which can be abstracted a posteriori, architectonic ideas are the source of a priori unity for the system of reason because they connect our reasonable pursuit to essential human ends. Given Kant’s focus on mathematics, in the architectonic and his critical philosophy more generally, we must have some sense of the architectonic idea of mathematics. In this paper, I argue for the key principles of the architectonic idea of mathematics: ۱) because mathematics is grounded in a priori intuition, it is a peculiarly human activity; ۲) the method of mathematics is one of a priori construction, a method only mathematics can employ and: ۳) the objects of mathematics are extensive magnitudes. Given these principles, we can use the architectonic idea to have some clarity about how mathematics has dealt with historical development.

Keywords:

architectonic , geometry , Mathematics , Arithmetic , Construction