Instructor: István Bodnár, Nenad Miscevic
No. of Credits: 2
Status: PhD elective
Time: (Will be set later)
Description:
The course concerns ancient and contemporary approaches to mathematical knowledge and to intuitive insight, from two related perspectives. One will be an assessment of contemporary Aristotelianism in the philosophy of mathematics, the other an evaluation of the different claims about the source of mathematical knowledge. Here the contrast to the contemporary positions will be the different modern interpretative traditions about the emergence of Greek mathematics: the claim that what we have in
Euclid is algebra (of Babylonian origin) in geometrical garb, the opposing view that ancient geometry is the result of the Parmenidean philosophical impasse, and is dependent on the procedures of argumentation and proof of the Eleatics, and the two more recent proposals, according to which what we have in Euclid is a tool-box of setting up constructions and theorems, or the other, according to which the key cognitive development responsible for the emergence of Greek mathematics was the introduction of lettered diagrams, which gave rise to a new way of grasping truths about geometrical
(and arithmetical) structures.
Course goal:
The primary goal of the course is to help students to tackle topical issues in the interpretation of philosophy of mathematics, and the way these are relevant in the history of mathematics and to metaphysics and epistemology, and to appreciate the discussions about these issues in the modern literature. For this latter aim, important texts of the secondary literature will be introduced and discussed on a regular basis.
Learning outcomes:
By the end of the course students will be expected to be able to assess, in their own context, and also in a comparative perspective, different theories, with special emphasis on their use of, and commitment to mathematical objects, and the way we have access to these entities, from a contemporary perspective and from the way these entities feature in ancient mathematics and in the philosophical reflection on the ancient mathematical practice. Students will also be expected to be able to assess the implications of alternative modern interpretations of these theories, and to formulate their own interpretation in the context of these options.
Weekly schedule:
Week Theme
Week 1 Contemporary Aristotelianism: structure in rebus
Week 2 Aristotle on the ontological status of mathematical objects
Week 3
The closest relative: Shapiro’s structuralism
Week 4 Recognizing spatial structure
Week 5 Spatial structure vs. geometrical algebra
Week 6 Recognizing spatial structure, cont.
Week 7 Axiomatic structures in early arithmetics and Eleaticism
Week 8 Is geometrical intuition empirical?
Week 9 The introduction of lettered diagrams and the emergence of
Greek geometry
Week 10 Is geometrical intuition empirical?, cont.
Week 11 Is arithmetical intuition empirical?
Week 12 Euclid as a toolbox
Reading
James Franklin:
Aristotelian Realism
Aristotle, Physics II.2
Shapiro, Parsons
Resnick, Mancosu
Klein, selections from
Euclid
Szabó, Euclid selections
Giaquinto
Netz, Euclid selections
Maddy
Ito

Requirements:
• regular attendance
• regular preparation
• active participation in discussions
• Presentation of papers from the secondary literature throughout the term
• 2000–2500-word term paper
Assessment:
• 20% class participation (discussions); 20% presentations; 60% term paper