## Marius Stan

Affiliation:

Boston College

## Kantian Foundations for Exact Science : Beyond Euclid and Newton

The dominant readings of Kant’s doctrine of exact science commonly see it as a philosophical analysis of key presuppositions in the science of his time (see, e.g., the influential Friedman 1992 and 2013.) Specifically, on this construal Kant tried to give a philosophical grounding of metric structure for Euclidean geometry and inertial-kinematic structure for Newtonian particle dynamics. This account commits Kant to specific theories, and it has him engage particular 17th century figures.

## Kant’s Natural Philosophy and Generalized Mechanics

In this paper, I uncover in Kant’s Metaphysical Foundations of Natural Science a deep conflict: between his Dynamics and Mechanics. Specifically, his theory of matter entails continuous bodies, but his laws of mechanics can handle only discrete particles not continua. Kant’s laws of motion are too weak to be fully general, namely to yield equations of motion for all possible bodies, including continuous bodies. To remedy this defect, Kant would need an additional principle: the Torque Law, also called the Balance Law of Angular Momentum: viz.