Education
Henry Mendell (California State) gives a talk for the Power Structualism in Ancient Ontologies series Abstract: Historians in the twentieth century argued about whether Aristotle presents a general theory of dynamics in Physics VII 5 or merely presents examples from ordinary experience, which he then applies abstractly to arguments about the unmoved mover and general issues about the balance of elements in the sublunary realm. Recently the pendulum of opinion has swayed towards taking Aristotle's account more robustly as a general theory of dynamics, but more can be said. I shall argue that one reason why the debate arose was because both sides have seen the examples in the context of Greek style mathematics, where we expect generalized principles and theorems, often couched in a modern, anachronistic representation. I suggest that the dynamics come from an older mathematical tradition, which we associate with Babylon and Egypt and which, I believe, was ordinary Greek mathematical practice even in the fourth century BCE. Mathematicians present their work as problems, given such and such, here is how to calculate such and such. It is also characteristic of a problem and the procedure for its solution that actual numbers are used. We find both in Aristotle's presentation. Aristotle's rules are stated in the form of conditionals with actual numbers. So the rules have the form: if mover A moves moved B in time D over distance G, then one may vary A, B, D, and G in the following ways, e.g. 1/2 B over 2 D. The initial conditions in the antecedent, in effect, implicitly set the parameters for the variations in the consequent, as given by example. In this way, the procedures are general over all dynamic problems set up conditionally. Aristotle proceeds to set boundaries on the consequent. However, the text that we have at this point, regardless of variations in the textual tradition, is mathematically bizarre. Whether this is Aristotle's error or an early error in the transmission of the text, the anomaly contributes to the evidence that Aristotle is actually borrowing his examples from an earlier work on dynamics that was written in the problem tradition.