Abstract

EVEN in Aristotle’s day, there were some problems about the status of the "mixed sciences," mechanics, optics, astronomy, harmonics. They were mathematical in form, and depended on generalizations drawn from repeated and careful observation. In both respects they differed from "physics," as Aristotle saw it; he made them "the most physical part of mathematics," and thus inaugurated a long two-thousand year history of separation between two ways of approach to nature, the philosophical, and the mathematical. Galileo’s central achievement, perhaps, was to end this split; he showed that a single account was possible. Though he claimed the titles both of "Philosopher" and of "Mathematician" to the Grand Duke of Tuscany, the "new science" he proposed in 1638 would not need two separate talents. Mechanics for a while to come would still be classified as "natural philosophy," but it would rapidly become evident that philosophers could no longer claim the competence to intervene in it on their own account. True, some of the first great exponents of the new physics, Descartes, Newton, Leibniz, were also philosophers. But it was abundantly clear that the new science of nature was mathematical-experimental in form, not "philosophical" as that narrowed term had come to be understood.