1st Semester 2014/15: Philosophy of Mathematics

Instructors

Luca Incurvati
If you are interested in this project, please contact the instructor by email.

ECTS

6

Description

The project will revolve around three selected themes from the philosophy of mathematics, with a special focus on the philosophy of set theory.

• The iterative conception of set. The iterative conception maintains that every set occurs at one level or another of the cumulative hierarchy, and is widely thought to lie behind standard set theory ZFC. We will discuss various accounts of the conception and the conception's capacity to justify the ZFC axioms.
• The question of realism. Mathematical realists typically hold that every mathematical statement, and hence every set-theoretic statement, has a determinate truth-value. Others have argued that set-theoretic statements such as the Continuum Hypothesis do not have a determinate truth-value. We will discuss some of the arguments that have been advanced in this debate, paying special attention to the significance of categoricity arguments.
• Mathematical naturalism. Quinean naturalism holds that we have to look at science to decide what we ought to believe. Penelope Maddy has advanced a form of naturalism which aims to be more faithful to mathematical practice and judges mathematics by its own standards. We will explore Maddy’s naturalism, especially as applied to set theory, paying special attention to her argument that proper set-theoretic methods demand that the Axiom of Constructibility should be rejected.

Organisation

There will be three introductory lectures by the instructor, one on each of the selected themes. The rest of the project will have a seminar structure, during which each student will have to present an article. A list of articles will be made available, but suggestions from students are welcome. Each student will also have a meeting with the instructor to discuss the preparation of their essay.

Prerequisites

Familiarity with set theory will be an advantage.

Assessment

The project will be assessed on the basis of a presentation and a short essay. Participation will also be taken into account.

References

Website: Further information is available at the project website.