The Object and Nature of Mathematical Science in Aristotle and St. Thomas Aquinas: A Comparison
Date of Award
Dissertation - Restricted
Doctor of Philosophy (PhD)
Francis J. Collingwood
Michael V. Murray
The following dissertation attempts to set forth the nature and object of the science of mathematics according to Aristotle and St. Thomas Aquinas, and to compare the doctrines of these two men.
At the present there are very few works which compare the teaching of the two philosophers in the area of mathematics, and none of them are extensive. Many authors do make reference to one or other pints of similarity and/or difference between the doctrine of the two men, but I know of no comprehensive treatment of this topic. One reason for this seems to be that it is often taken for granted that the two men have identical teachings. Indeed, as we shall show throughout this paper, many contemporary historians of philosophy very clearly but apparently unknowingly attribute positions in the philosophy of mathematics of Thomas Aquinas to his Greek predecessor. In a sense the purpose of this paper is to see if such attribution is justified, or, to put it another way, to determine whether or not there is an essential difference between the ancient philosopher and his medieval disciple in the philosophy of mathematics.
One thing should be made very clear from the beginning. When we speak of the philosophy of mathematics of either of these thinkers we mean by mathematics the area of knowledge which was so named in their respective times. In general, for both men the mathematics which existed at their time and of which they were aware comprised what we would call today arithmetic and plane and solid Euclidean geometry, as well as the various sciences which apply these to physical phenomena. (In Thomas's time the algebra was also known. The question of how much awareness of it St. Thomas had will be discussed below.) This limitation must always be kept in mind in a discussion the their mathematical doctrines. No attempt will be made in this dissertation to relate their teachings to kinds of mathematics of which they were totally unaware, such as the calculus or modern set theory. I will leave to others, with more knowledge of the mathematics of our day than I, the very important task of determining the relevancy of the teaching of these two men to our modern science (or Sciences) of the same name. It is hoped that the first step in such a determination has been taken in the following pages.