Abstract

This dissertation is a detailed study of the manner in which ratio and proportion are utilized by Aristotle in his description of animal differences. I argue that Aristotle's method for collecting and comparing animal traits has been drawn from and geometric practices, in particular the theories of ratio and proportion produced by Theaetetus and Eudoxus. I begin the dissertation with a survey of some of the current literature on the overall goal of division and difference in degree in Aristotle's biological works. I then reconstruct the technical importance of ratio and proportion in numerous disciplines, thus establishing that mathematics itself is a constructive practice. Based on this review I show in detail two methods for establishing ratios and proportions, i.e., the gnomic method and the anthyphairetic method. ;The gnomic method illustrates how to construct and classify quantitative relationships between numbers. It serves as a "rule book" for identifying differences and building similarities between quantities. The anthyphairetic method allows one to establish and compare ratios between phenomena susceptible to differences in degree, i.e., anything magnitude-like, via a process of reciprocal subtraction. ;Using these mathematical/geometric foundations I explain how thew methods also established ratio and proportion between the "one and the many" in Plato's Philebus. In order to understand the complex philosophical issues, e.g., the relationship between the limited and unlimited, in this dialogue one must have at hand a grasp of the mathematics of this time period. ;Next I present a study of James Lennox's and David Depew's accounts of resemblance, difference, division, and the more and less in Aristotle's descriptions of animal traits. Lennox applies quantitative difference in degree to differences in morphological traits, and by extension to differences in animals belonging to the some kind. Depew adds to Lennox's work by making a preliminary sketch of Aristotle's use of difference in degree to establish variations in behavioral traits. ;I close with an extended account of the manner in which ratio and proportion we utilized by Aristotle to organize variations and distributions in animal traits belonging to the same kind, i.e., courage or intelligence. I argue that ratio and proportion lay the groundwork for comparing variations in animal bio-practices and eco-niches