Mathematical Principles of Natural Philosophy

Newton's Principia (1687) established the mathematical framework for classical mechanics and remained the standard of scientific achievement for two centuries. It is organized as a deductive system on the model of Euclidean geometry: definitions, axioms (the three laws of motion), and theorems derived from them.

Book I develops the mathematics of motion under central forces. Book II treats motion in resistant media. Book III, "The System of the World," applies the machinery to the solar system, deriving Kepler's laws of planetary motion from the inverse-square law of universal gravitation and calculating the trajectories of comets, the behavior of the tides, and the precession of the equinoxes. The same force that governs falling bodies on earth governs the orbit of the moon.

The philosophical significance is as large as the scientific. Newton refuses to speculate about the cause of gravity: Hypotheses non fingo, I frame no hypotheses. The task of natural philosophy is to derive mathematical laws from phenomena; the question of why gravity operates at a distance Newton sets aside as beyond his method. This broke with the Cartesian requirement that physical explanation proceed from intelligible mechanical contact between bodies.

Hume took Newtonian method as the model for a science of human nature. Kant took the Principia as the paradigm case of synthetic a priori knowledge and made the entire Critique of Pure Reason an account of how such knowledge is possible. When Einstein's general relativity superseded Newtonian mechanics, the philosophical problem shifted: what had seemed a priori necessary turned out to be approximately true.