2nd Semester 2018/19: Computational Approaches to the History and Philosophy of Mathematics.
This Master of Logic (ILLC) coordinated project aims to discuss computational and quantitative approaches to the study of the history and philosophy of mathematics. We have two main aims: (i) to discuss influential philosophical interpretations of the nature and methodology of mathematics in the 18th and 19th century. (ii) To methodologically reflect on the benefits and limitations of computational and quantitative approaches to the study of the history and philosophy of mathematics, and possibly to implement some of these approaches.
Ad (i). We will discuss the philosophy of mathematics of Immanuel Kant (1724-1804) and Bernard Bolzano (1781-1848). With respect to Kant, we will deal with Kant’s general philosophy of science, the analytic/synthetic distinction in Kant, Kant’s philosophy of geometry, and Kant’s philosophy of arithmetic in light of traditional logic. With respect to Bolzano, we will discuss Bolzano’s general philosophy of science, the analytic/synthetic distinction in Bolzano, and Bolzano’s ideal of proof: both the theory and the application of this ideal in his mathematical practice.
Ad (ii). We will let the students methodologically reflect on historical studies that use conceptual models, on quantitative methods used in history of ideas, on computational approaches based on formal models in the history of ideas, and on the use of formalization in philosophy. Students may apply some of these novel methodologies to the study of the history and philosophy of mathematics in the research report that they will write for this project.
We will start reading material on the first meeting (students will be mailed the reading schedule and reading materials if they sign up). In the first week, we will have two meetings on Kant. In the second week, we will have two meetings on Bolzano. In the third week, we will have two meetings on computational and quantitative approaches to the history and philosophy of mathematics. In the fourth week, students will present their research. In the fifth week, students will hand in their research report.
None, but familiarity with philosophy (especially philosophy of mathematics) and interest in novel methodologies to study philosophy is helpful.
(i) Oral presentation on research report in week 4. To pass, students must also attend the other students’ presentations. (ii) A written research report in the style of a short conference paper.
The entire project will be graded with a pass/fail.