The Debate between Whewell and Mill on the Nature of Scientific Induction

The very best examples of scientific induction were known in the time of William Whewell (1994–1866) and John Stuart Mill (1806–1873). It is puzzling, therefore, that there was such a deep disagreement between them about the nature of induction. It is perhaps astounding that the dispute is unresolved to this very day! What disagreement could there be about Newton’s discovery of universal gravitation? Prior to Newton, it was well known that gravity acts on objects near the Earth’s surface, and Copernicus even speculated that the planets have a spherical shape because they have their own gravity. But Newton was the first to understand that it’s the Earth’s gravity that keeps the Moon in orbit around the Earth, and that the Sun’s gravity keeps the Earth and the Moon in orbit around the Sun. At the root of this discovery was Newton’s explication of the kinematical concept of acceleration. To understand that the Moon (just like the fabled apple) is pulled by the Earth, one has to understand that the Moon is accelerating towards the Earth even if it is moving uniformly on the circular orbit around the Earth. Acceleration must not be defined as the time rate of change of speed, but as the time rate of change of velocity, where velocity has direction as well as magnitude. Thus, the Moon is accelerating towards the Earth because its velocity is changing its direction. Galileo, on the other hand, worked with a circular law of inertia, according to which uniform circular motion around the Earth was a “natural” motion that required no force. Further explication of the new conception of acceleration led Newton to discover that if the line from a point O to a body B sweeps out equal areas (Kepler’s second law), then B is accelerating towards O. If, in addition, the body follows an elliptical path with O at one focus (Kepler’s first law), then the acceleration towards O is inversely proportional to the square of the distance of B from O. In the case of the planets moving around the sun, if we assume that the constant of proportionality is the mass of the sun, then Kepler’s third law follows as well. Thus, Newton’s new conception of acceleration causes Kepler’s three laws to “jump together” in a way that tests the conceptions that Kepler had previously employed, involving ellipses,