This course focuses on the question: how is the reasoning in Greek mathematical texts to be understood? This question is a philosophical one, because it is a particular case of the question how reasoning, as expressed in natural language, is to be understood. We will focus on the language of Euclid's Elements. How does it convey the logical structure of proof? There is a complex network of similarities to, and differences fcontemporary mathematical practice. For instance, (most) Greek mathematical texts avoid all explicit discussion of themselves (expressions such as, "In theorem XYZ, . . ."). This makes the question of how to interpret the inferences in the Greek texts both interesting and tricky. One prominent problem, which we will discuss, is how to understand the generality of the proofs. Most interpreters understand Greek mathematical proofs as first establishing something about a particular item and then inferring that it is true for all items of a certain sort. (E.g., this triangle has angles equal to two right angles. Therefore all triangles have angles equal to two right angles.) Do the Greek mathematicians really make such inferences from particular to general? If so, how are they to be understood? If not, how is the language that appears to draw such inferences to be understood?
Our main mathematical text will be Euclid's Elements. We will also compare it with less familiar mathematical works (e.g., Heron). We will also draw on a range of ancient and contemporary philosophical texts, such as Stoic logic, Wittgenstein, and Kit Fine.
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.)