Courses:

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Legend has it that over the gate to Plato's Academy were the words "Let no one enter who has not studied geometry." Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course we will read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. We will examine how the discovery of the incommensurability of magnitudes upset the Pythagorean faith that 'everything is number', and how early philosophy responded to this challenge to the Greek presumption that the kosmos is fundamentally understandable. Finally, we investigate Greek attempts to circumvent the resistance of human ethics to precise (i.e. quantitative) expression.

Plato. Meno. 2nd ed. Indianapolis, IN: Hackett Pub. Co., 1976. ISBN: 9780915144242.

———. Protagoras. Translated by Stanley Lombardo and Karen Bell. Indianapolis, IN: Hackett Pub. Co., 1992. ISBN: 9780872200944.

———. Theatetus. Translated by Robin H. Waterfield. New York, NY: Penguin Classics, 1987. ISBN: 9780140444506.

———. Republic. Translated by R. E. Allen. New Haven, CT: Yale University Press, 2006. ISBN: 9780300114515.

Aristotle. Nicomachean Ethics. Translated by Christopher Rowe. New York, NY: Oxford University Press, 2002. ISBN: 9780198752714.

Euclid. Elements. Translated by Thomas L. Heath. Santa Fe, NM: Green Lion Press, 2002. ISBN: 9781888009194.

Nicomachus. Introduction to Arithmetic. Translated by Martin Luther D'Ooge. New York, NY: The Macmillan Co., 1926.

There is a substantial amount of reading for this course. Each week you will be expected to hand in the answers to a set of study questions. Three papers will be required, each approximately 7 pages long. For the first paper, a draft or substantive outline must first be turned in to the teaching assistant, and a meeting scheduled to discuss the draft. After the paper has been returned to you with comments, you will re-write the paper, in a way that addresses my challenges and objections. After each of the four papers, I will offer the opportunity for individual paper conferences, to discuss the substance of your paper. These are not mandatory. Papers are due at the end of the fifth, ninth, and thirteenth week of the semester.

Each student is expected to do one oral presentation during the semester. The oral presentation will concern the reading of that week, and will be either a response to one of the study questions for that week, or on a subject cleared with me. Regular participation in class discussion is expected. In addition, students will be called on throughout the semester to guide the class through selected mathematical proofs.