The Examining Life

Episode 9: Mathematics in Plato's Republic

Welcome to "The Examining Life," a podcast of the Arts of Liberty Project. Hosted by Drs. Jeffrey Lehman and Andrew Seeley, the podcast covers both works from the Western tradition and contemporary events of interest. Lively, personal, and timely, "The Examining Life" contributes to the renewal of liberal education.

What role should mathematics play in a liberal education? Is it merely practical, or is it more fundamental to the formation of the human person? Join Drs. Andrew Seeley and Jeffrey S. Lehman this week as they discuss mathematics--and the quadrivium more generally--through the lens of Plato's Republic.

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Podcast Colloquy Excerpt

Plato's Republic, Book 7, 525b-526

"Then it would be fitting, Glaucon, to set this study down in law and to persuade those who are going to participate in the greatest things in the city to go to calculation and to take it up, not after the fashion of private men, but to stay with it until they come to the contemplation of the nature of numbers with intellection itself, not practicing it for the sake of buying and selling like merchants or tradesmen, but for war and for ease of turning the soul itself around from becoming to truth and being....

"And further," I said," now that the study of calculation has been mentioned, I recognize how subtle it is and how in many ways it is useful to us for what we want, if a man practices it for the sake of coming to know and not for trade."

"In what way?" he said.

"In the very way we were just now saying. It leads the soul powerfully upward and compels it to discuss numbers themselves. It won't at all permit anyone to propose for discussion numbers that are attached to visible or tangible bodies. For surely, you know the way of men who are clever in these things. If in the argument someone attempts to cut the one itself, they laugh and won't permit it. If you try to break it up into small coin, they multiply, taking good care against the one's ever looking like it were not one but many pieces."

"What you say is very true," he said.

"What, Glaucon, do you suppose, would happen if someone were to ask them, 'you surprising men, what sort of numbers are you discussing, in which the one is as your axiom claims it to be--each one equal to every other one, without the slightest difference between them, and containing no parts with itself?' What do you suppose they would answer?"

"I suppose they would answer that they are talking about those numbers that admit only of being thought and can be grasped in no other way."

"Do you see then, my friend," I said, "that it's likely that this study is really compulsory for us, since it evidently compels the soul to use the intellect itself on the truth itself?"

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Michael Augros’ Geometry Course

Available through the Arts of Liberty, Michael Augros' introductory geometry curriculum is available to download for free here.

A Mathematician’s Lament

This week, the Doctors mentioned Paul Lockhart's book on the contemporary state of mathematics education, A Mathematician's Lament. You can find it here.

Galileo's Dialogues Concerning Two New Sciences

Explore and download Galileo's dialogue, Dialogues Concerning Two New Sciences, on this website.