This course focuses on the deductive machinery of a Greek mathematical proposition. How do the deductions work? One important question is: do the deduction introduce a particular object, prove something about it, and generalize to other objects? Special emphasis will be put on the role of geometrical constructions, which we shall investigate in a new perspective. We shall also clarify the function of denotative letters and of diagrams, with particular attention paid to the phenomenon of “overspecification” of the latter. We shall extensively discuss the crucial part of a Greek mathematical proposition called “setting-out”.
The study of the deductive structures at work in the proof—such as relations and atomic inferential patterns—will allow us to see parallels between mathematical practice and ancient grammatical and logical doctrines (both Stoic and Peripatetic).
This course is the sequel to a course taught in the fall, but participation in the previous course is not required. We will not presuppose knowledge of Greek, nor of Greek mathematics. Participants are required to have completed a course in logic. Some previous exposure to ancient philosophy and/or some general knowledge of mathematics will be useful. Language of instruction: English. (Hausarbeiten may be written in German.) |
