Newton, Isaac (1642–1727)

4. Inferences from phenomena and rules of natural philosophy

The Propositions of Books I and II are powerful resources for establishing conclusions about forces from phenomena of motion. For example, according to Propositions 1 and 2, Kepler’s area rule holds if and only if the force acting on the moving body is centripetal. A corollary adds that the areal velocity is increasing when the force is off-centre in the direction of motion and decreasing when it is in the opposite direction. The variation of the areal velocity is thus a measure of the direction of the force. Similar systematic dependencies are involved in the inferences from Kepler’s 3:2 power rule and the absence of discernible orbital precession to the inverse-square variation of celestial centripetal forces (see Kepler, J.).

Rules of reasoning, which in the second and third editions are singled out at the beginning of Book III under the title Regulae philosophandi, strengthen the inferences that can be drawn from phenomena by licensing inductive generalizations (see Scientific method §2). The first two rules, for example, underlie the inference that the force holding the moon in orbit is terrestrial gravity – this, on the basis of the inverse-square relation between the centripetal acceleration of the moon and the acceleration of gravity at the earth’s surface. The third rule, appearing for the first time in the second edition, supports the inference that all bodies gravitate towards each planet with weights proportional to their masses – this, on the basis of pendulum experiments and the common acceleration of Jupiter and its satellites toward the sun.

The fourth rule authorizes the practice of treating propositions that are supported properly by reasoning from phenomena as ’either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions’. It was added in the third edition to justify treating universal gravity as an established scientific fact in the face of complaints that it was unintelligible without an explanation of how it results from mechanical action by contact. This rule, and the related discussion of hypotheses at the end of the General Scholium added in the second edition, distinguish Newton’s experimental philosophy most sharply from the mechanical philosophy of his critics.