Jean De Groot

In the introduction to An Approach to Aristotle’s Physics, David Bolotin presents an exceptionally clear account of the difficulties of making a claim for Aristotle’s natural philosophy as a contemporary teacher about nature. Modern science has repudiated the chief elements of the Aristotelian cosmos—the geocentric universe, the account of projectile motion—and so the contemporary interpreter treats Aristotle as a brilliant expositor of the world “as it appears.” Alternatively, the interpreter may say there is no final truth in the matter of nature, so Aristotle’s cosmos within its own perspective was as compelling as our modern science is within its own perspective. Neither of these interpretations suits Aristotle, Bolotin says, since the philosopher’s conception of science included its being a true account of nature itself.

This paper traces the significance of first principles in Greek philosophy to cognitive developments in colonial Greek Italy in the late fifth century BC. Conviction concerning principles comes from the power to make something true by action. Pairing and opposition, the forerunners of metonymy, are shown to structure disparate cultural phenomena—the making of figured numbers, the sundial, and the production, with the aid of device, of fear or panic in the spectators of Greek tragedy. From these starting points, the function of the gnômôn in knowledge is explored.

Examples are presented of Aristotle’s use of non-idealized mathematics. Distinctions Husserl makes in Crisis help to delineate the features of this empiricalmathematics, which include the non-persistence of mathematical aspects of things and the selective application of mathematical traits and proper accidents. In antiquity, non-abstracted mathematics was involved with practical sciences that treat motion. The suggestion is made that these sciences were incorporated by Aristotle into natural philosophy without first being abstracted as pure mathematics—a state of affairs not envisioned by Husserl, for whom science recast natural ontology by means of the idealization of pure mathematics. The relation of empirical mathematics to life-world ontology is considered