Date of Award

Spring 1959

Document Type




First Advisor

Rev. Achilles Edelenyi


In this paper we are concerned with the foundations of mathematics. We are discussing the basis of the "Queen of the Sciences," for mathematics is the foundation of the modern age of science and the tool upon which all the applied or theoretical physical sciences rely for their work. Philosophers have also used mathematics in their studies.

For centuries mathematics has enjoyed a privileged place in science and thought in general. Among the Greeks it had such importance that the Pythagoreans based their whole philosophy upon mathematics, placing "number behind phenomena as their basal principle and ground." Plato is reported to have studied under the Pythagoreans in Italy, and there is undoubtedly evidence of their influence in his interest in mathematics and number.

Aristotle was Plato's pupil, but he doesn't seem to have acquired the mathematical outlook of his master. As a matter of fact, mathematics "is the one science where Aristotle shows himself least at home." In establishing his philosophy, Aristotle paid more attention to the facts of reality as presented to him through the senses than to any mathematical reasonings (or imaginings). This, perhaps, explains why mathematics from the time of Aristotle was on the decline, although we do see such important figures as Euclid, Menelaus, Ptolemy and Pappus continuing on until the third century A.D.