A Method for Mathematical Physics

The Baconian method had few followers at first. The attention of philosophers was soon riveted on Galileo Galilei, who had trained the telescope on the heavens and discovered many surprising things there. He championed the Copernican system of the planets, describing the earth as a moving planet. He also proposed a new conception of geometry, which underlies modern metaphysics, describing a mathematical universe through and through that undercut the ancient conception of a qualitative and finite cosmos. Together with these innovations, he proposed a new method of gaining knowledge, according to which we can know some mathematical principles as certainly as God knows them. However, our intensive knowledge is limited to a few Principles, whereas God’s is extensive and complete. In this chapter, we see how the problem of knowledge that Aristotle raised in his Posterior Analytics can be solved by a foundational method proposed by Galileo Galilei, using thought experiments and a reductio ad absurdum technique. Although Galileo Galilei’s remarks were suggestive and not systematically developed, they immensely influenced later natural philosophers, thus overshadowing Francis Bacon’s method for some time.