Most of you know I’m applying to grad schools right now, because I finally decided that what I want to do with my life is to learn and teach philosophical logic. This has been taking up most of my time. The final list of schools:

• Massachusetts Institute of Technology
• Columbia University
• University of California, Berkeley
• Carnegie Mellon University
• City University of New York, Graduate Center

I’m applying directly to doctoral programs at the four that are not CMU (many of them don’t even have master’s-level programs), and a M.S. program at CMU as a backup. A professor suggested that I do that in case I do not gain admission to anywhere, since I do not have a peer-reviewed publication on my CV. In that case, I’ll work with him over the next year and publish a paper while I work on the M.S., and have a stronger application for Ph.D. programs in the following year.

What I intend to study is going to be a part of philosophical logic, as noted. I’m most interested in modal logic, nonmonotonic logic, and belief revision. (All of these topics also have excellent introductory articles at the Stanford Encyclopedia of Philosophy, but I linked to Wikipedia since its articles assume less prior knowledge.)

I’m mostly done with the applications, I mostly need to finish my writing sample, which I intend to do over the weekend. I’m not completely certain about what it’s going to be on. Primarily, though, it’ll be about the Levi identity (which essentially says that any change in an agent’s beliefs can be thought of as a series of additions of new beliefs and losses of old beliefs) and Levi contractions (a particular method of losing old beliefs). I might also cover coherentist theories of belief (in which beliefs may justify each other).

I’m looking forward to next semester, too. Unfortunately, the seminar in philosophy of mathematics I was going to take was apparently cancelled since I was the only person who registered for it. This leaves me with a course schedule of:

• 15312 Foundations of Programming Languages
• 21805 Lambda Calculus
• 80511 Thesis Seminar
• 80818 Seminar on Epistemology

So I’ll be designing programming languages, higher-order functions, and learning about knowledge. Also, writing a thesis. Currently I am thinking that I want to find an axiomatization for a class of belief revision operators which does not have one (though this might be hard…), but a professor has been doing interesting work on what happens if you permit the relation that generates a Levi contraction operator to be a partial order (as opposed to a total order).

Hopefully this is enough of a window into what I’m doing. I’ll try to write more (and actually about topics other than myself) in the future. I thought about writing a short primer to logic in this space for my friends who don’t know it, though I’m doubting I’ll ever actually do it. Maybe over summer.

I entered college thinking I was going to study to become a computer scientist. When I was growing up, I always thought that I loved working with computers—and I thought I was good at it. And I was relatively good at understanding what was going on, but I never, in retrospect, actually sat down and wrote code, and this should’ve been a sign to me. About a year and a half into college, I finally decided that even with the great CS instructors here, any time I sat down and did a programming assignment I was annoyed, and any time I sat down and did a theoretical CS assignment I was bored. Why should I care how fast various algorithms run?

So, I thought, I was actually a mathematician. The problem with computer science was that it wasn’t abstract and “perfect” enough for me. I only cared about existence of concepts, not implementation. I liked doing some of my math assignments, and I already was actually a math major, it seemed natural. But in a lot of my math classes, still, I didn’t care about the material. Why should I care about epsilon-delta definitions of limits in analysis? In my mathematical logic courses, though, I was interested. The subject matter there was (and is) attractive because it is the foundation for other mathematics, and the arguments seemed considerably purer. I thought about being a mathematical logician.

And then, a year and a half ago, because of a particularly good professor I had and the advice of a friend, I added a double major in the logic program within the philosophy department. I originally didn’t think there was going to be much of a difference with regard to the math program I was already in, but saw that I liked the faculty in the department (the math faculty and I have never really gotten along, perhaps they could see my dissatisfaction with math before I could) and decided to try it.

So for the last three semesters I have been pretending to be just a “logician,” not specifically a mathematician or a philosopher. I’ve been taking logic courses in both departments about both subjects with applications to both disciplines, and I’ve been confused. Because right about now I have to start applying to grad schools, and therefore I have to pick what field I want to study. I didn’t think I knew.

I’d been becoming aware of the distinction between mathematical and philosophical logic, but this wasn’t the only choice. I also had to choose between the various ways of studying mathematical logic. This semester, I am taking one course each in introductory model theory and introductory proof theory, the two main approaches. It’s become very clear to me that I want little more to do with model theory. I think that this is because it’s too mathematical, in that it is only related to mathematics. I realized recently that I will not be upset if I never hear about another application of logic to, for example, Galois theory. And this, I think speaks not only to a dislike of model theory but a dislike of mathematical logic in general.

I think I was attracted to mathematics because of my attraction to certainty. Friends and family know that I place great importance on specificity and structure of arguments and thought. Mathematics is often held to be the very embodiment of specific, structured argument, and I think this is why it attracted me. I wanted to be in an area where I could be sure I wasn’t wrong when I expressed ideas, so long as I expressed them properly, and where I could interact with people who shared this approach to thinking.

Moreover, I think this is why I did not initially consider studying philosophy. The popular conception of philosophy is a field where anything goes, where old men argue endlessly without purpose or structure. The popular conception is that to be a philosopher one only needs to be persistent, annoying, and interested in minutiae. This is obviously wrong, and I knew that, but I didn’t know one could study philosophy in the way one studies mathematics.

My problem was that I confused method with subject matter. I was exactly correct in my realization that I wanted to use mathematical methods, the problem is that I don’t actually want to use them to study mathematics itself. I’m interested in knowledge and in belief, in thought. That is, I’m interested in philosophy, particularly in epistemology. I was just unattracted to the popular conception of the discipline.

But I now know that there is an entire discipline, formal epistemology, devoted to what I find interesting. There are people, philosophers, logicians who are studying traditional problems like “What is belief?” using formal logical methods. I’ve tried to convince myself, I think, that this area is only one of many areas I am interested in. When I actually think about it, though, I realize that when I excitedly talk to my disinterested friends and family about my work, though, it’s always about philosophical logic. I’m always trying to tell them about how to axiomatize knowledge or maybe about the philosophical implications of a more mathematical topic like the incompleteness theorems or undecidability of predicate logic. I’m never excitedly trying to tell uncaring people about Lie groups. I’m not attempting to convince people that graph theory or topology is interesting.

Perhaps, then, I’ve really, finally figured out what actually interests me. I don’t want to do traditional philosophy, and I don’t want to do traditional mathematics. I want to use mathematical techniques to study philosophical problems.

Edit, 4pm, same day: Interestingly, in my Logic & Artificial Intelligence class today (basically a class on belief revision, and consequently my favorite class at the moment), the professor mentioned that learning can be thought of as the process of deciding what is not possible. This mirrors my opening comments…