Advising & Teaching

Advising

Very broadly, I am available to advise PhD projects in logic and philosophy of mathematics. Some (relatively) broad philosophical questions include: 

• What is a foundation for mathematics? 

• Should we make our theories stronger to compensate for incompleteness?

• Or should we search for more conservative foundations that are more amenable to justification?

• Are disputes over foundations substantive or merely instances of people arguing past each other?

More specifically, I am interested in advising projects that apply logical and mathematical techniques to the philosophy and foundations of mathematics. For example, I am thinking a lot about the ways that different theories can interpret each other via translation. I am also interested in work that aims to critically investigate the viability of using formal tools for philosophical purposes. While most of my expertise is in set theory, I am very also interested in other foundational systems and how they might be compared.

I should probabaly also note that I'm generally antithetical to projects in the metaphyics and (traditional) epistemology of mathematics. I think most metaphysics is a waste of time (although I realize that, in itself, is a metaphysical postion) that distracts philosophers from more tractable questions where philosophical methodologies can provide genuine assistance.

If you are interested in working with me, I would first suggest having a look over the LPS website to get a feel for things. If the program appeals to you, please feel free to contact me via email and we can talk about logic, mathematics and philosophy.

My previous students include: Andreas Fjellstad and Tom Colclough. 

My current students include: Jason Chen, Ainsley May and Antoine Mercier.

Teaching

Each year, I teach a course in introductory logic and another coure on incompleteness.  I also assist my colleague, Kai Wehmeier, in convening the UCI, Logic Seminar. 

I then teach two further courses that vary from year to year and cover more advanced logic topics or problems in analytic philosophy and philsophy of mathematics. In recent years, I've taught courses on: Pen Maddy's Defending the Axioms; Effective Descriptive Set Theory; Kripke's Naming & Necessity (with Kai); Category Theory; Set Theoretic Geology; and Large Cardinals and Determinacy. 

In addition to this, I frequently convene independent studies on topics in logic. This year, we've worked done a session one forcing and another on Gentzen's proof of the consistency of arithmetic.

In 2024/24, in addition to intro logic and incompleteness, I'll be teaching a courses on:

• Large cardinals; and

• Homotopy Type Theory (with Jim Weatherall).