Sophia Stone, Lynn University Hegeman 204A 12:00 pm – 1:00 pm EST/GMT-5 Plato reserved high esteem for mathematics, even saying in the
Laws that learning mathematics was a necessity, that without the use or knowledge of mathematics, ‘a man cannot become a God to the world, nor a spirit, nor yet a hero, nor able earnestly to think and care for man.’ Bertrand Russell remarks on this passage in
The Study of Mathematics, “Such was Plato’s judgment of mathematics; but the mathematicians do not read Plato, while those who read him know no mathematics, and regard his opinion upon this question as merely a curious aberration,” (Russell 1963, p. 85).
Reflecting on Bertrand Russell’s ruminations about Plato, it is well known, though we no longer have direct evidence, that before the entrance to Plato’s Academy was the inscription, “no one should enter here unless he is a geometer.” Sprinkled throughout Plato’s dialogues are geometry problems (
Meno), statements about the Odd and the Even (
Phaedo, Euthyphro, Parmenides), and of course, that well known claim in his
Republic VII, 526g-527c that while there are two kinds of numbers, those used in practical endeavors like star gazing and military soldier formation on the one hand, and those that can only be grasped in the mind on the other, that even those who are slow at calculation or reasoning, if they are educated in it, even if they gain nothing else, improve and generally become sharper in thinking than they were. So if mathematics, and especially the study of geometry, improves the quality of the soul and makes it easier to see the form of the Good (526e-527b6-8), then could Plato’s treatment of mathematics in his dialogues tell us something about his theory of forms?
In this talk, I’ll lay out some of the problems of understanding Plato’s theory of forms and why we have yet to solve these problems. While Plato saw the form-sensible relation as essentially a non-expressible mathematical relation, contemporary scholars commonly think of the form-sensible relation in terms of sets and its members. My own view is that we are unable to solve the problems of understanding Plato’s theory of forms because of our own advances in mathematics.