Ancient greek philosophy and mathematics

Seminars: 2 sessions / week, 1 hour / session

There are no prerequisites for this course.

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.

There is a substantial amount of readings for this course. You may want to purchase the following texts:

Plato. Theaetetus. CreateSpace Independent Publishing Platform, 2014. ISBN: 9781505227550.

Aristotle. The Nichomachean Ethics. Penguin Classics, 2004. ISBN: 9780140449495.

Euclid. Euclid's Elements. Green Lion Press, 2002. ISBN: 9781888009194.

See Readings section.

Each week you will be expected to hand in the answers to a set of study questions.

There are three required papers, each approximately 7 pages long. For the first paper, a draft or substantive outline must first be turned in to the TA, 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.

The second paper will be comprised of your responses to questions I have posted to you on your study questions.

After each of the three papers, I will offer the opportunity for individual paper conferences, to discuss the substance of your paper. For the first paper this is mandatory, for the second and third its optional.

Each student will be expected to spend one class in the "hot seat." This mean that you will come to that class especially prepared, having given very careful attention to the reading and the study questions. The other students and I will address questions to the hot seater throughout the class.

Regular participation in class discussion is expected (if you have trouble speaking up in class, please talk to me and we will develop a strategy together.) In additional students will be called on throughout the semester to guide the class through selected mathematical proofs.

For more information about the assignments, visit the Assignments section.

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