The Science of Conjecture: Evidence and Probability Before Pascal

by James Franklin

It has been common to see, in consequence of the (true) ellipse theory and the (false) Platonic solids theory, two Keplers, or at least two opposing aspects of Kepler’s thought—one, rationalist and looking forward to modern scientific method, with its curve fitting and hypothesis testing; the other backward looking and “mystical,” misled by all manner of unlikely Pythagorean speculations. Kepler’s works reveal no such split. The difference between the two theories is simply that the ellipse theory turned out to be right, the solids theory wrong. Kepler’s manner of thinking, and of argument, is the same in both cases and is the one that lies at the bottom of the success of modern mathematical science. It involves finding the harmonies of the world, to use Kepler’s words, or in the language of a more pedestrian century, argument from concomitant variation.