34I0156

What is the nature of mathematical knowledge, as compared to knowledge of the natural world? What, if any, is the connection between the two? What role does mathematics play in empirical sciences such as physics? What role does philosophy play in clarifying the foundations of mathematics? Do abstract objects, such as numbers, exist? Is mathematics somehow true of our world, or is it merely an ingenious language devised by humans to address all sorts of problems?

In this class, we will address these questions and study how leading philosophers and mathematicians have attempted to answer them, giving special attention to the influential schools of logicism, formalism, and intuitionism.

No prior university-level mathematics or philosophy is presupposed, although both will be helpful. Since it offers a focal point for many issues raised in the class, I will give a self-contained introduction to set theory. I will presuppose the notation of first-order logic with quantifiers. If you ever took a logic class, you've seen this; if you haven't, don't worry: you'll quickly pick it up.

This course will be conducted entirely in English. I plan to be giving lectures throughout, even though there will be the possibility of giving presentations in case someone needs them to obtain credit.

Recommended Texts

Mandatory readings:

  • Stewart Shapiro. Thinking about Mathematics: The Philosophy of Mathematics. Oxford University Press (2000).
  • All (mandatory) reading materials are available through Moodle.

Other excellent textbooks on the philosophy of mathematics include the following:

  • Mark Colyvan. An Introduction to the Philosophy of Mathematics. Cambridge University Press (2012).
  • Joel David Hamkins. Lectures on the Philosophy of Mathematics. MIT Press (2020).

Course Requirements

If this seminar is taken for credit, please let me know. For credit in philosophy you will have to fulfill requirements, depending on the module for which you are taking this course:

BA7, module 7:
- Evaluation: petit mémoire en philosophie dactylographié (30 à 40 pages, 60'000 à 80'000 signes, espaces non-compris) sur un sujet en relation avec un CR ou SE ou sur un sujet soumis et approuvé par un enseignant du Département de philosophie qui supervise le travail, et soutenance orale d’environ 30 minutes.
MA2, demi-module 2b:
- Attestation: travail écrit de 12 pages d'environ 24'000 signes; ou présentation orale et complément écrit.
- Evaluation: examen oral (env. 45 min.) portant sur le contenu du CR ou du SE et sur le travail du séminaire.
MA5, demi-module 5b:
- Attestation: travail écrit de 12 pages d'environ 24'000 signes; ou présentation orale et complément écrit.
- Evaluation: examen oral (env. 45 min.) portant sur le contenu du CR ou du SE et sur le travail du séminaire.

Contact me if you need credit in another programme.

Course Materials

Course materials such as lecture notes, handouts, etc will be made available as they will be used in class.

Schedule (Spring 2023)

This is the schedule for the seminar. It is subject to adjustment.

Date Topic Readings
23.02. Introduction Shapiro, Ch 1 and Ch 2
02.03. Set theory 1 Handout Set Theory
09.03. Set theory 2 *Bagaria (2019)
16.03. Set theory 3 *Irvine and Deutsch (2020)
23.03. Transfinite Mathematics Moore, Ch 10
30.03. Logicism Shapiro, Ch 5
06.04. Formalism Shapiro, Ch 6
13.04. No seminar (semaine de lecture)
20.04. Intuitionism Shapiro, Ch 7
27.04. Numbers exist Shapiro, Ch 8
04.05. Numbers don't exist Shapiro, Ch 9
11.05. Structuralism Shapiro, Ch 10
18.05 No seminar (Ascension Day)
25.05. Rapporteur session