A reader writes in:

How much math and also *what *math should one learn, in order to do well (maybe even stand out) in the philosophy of math? I'm a philosophy PhD student who knows roughly the first three semesters of calculus for an undergraduate science or engineering major. I also know that there are philosophers who make notable contributions to the philosophy of math without much mathematical training. So, to be careful with my question, what are the best math classes for philosophers of math---who enjoy taking math classes---to take?

I don't know the answers to these questions. Do any of you?

If you wanted to get a feel for math and professional mathematical practice, I would take the courses that mathematicians take: analysis, topology, and algebra. These are the "core" courses in any graduate math program and are typically offered at the undergraduate level, too.

If you're interested in what mathematicians themselves think about the nature of the natural/real/complex numbers, then analysis/topology/algebra are also good courses to take anyway. Nobody will be talking about Platonism vs Structuralism (or whatever), but you'll see the kind of constructions and axiomatizations mathematicians use to work with these numbers.

Beyond that I think it depends on what you're interested in and precisely which questions in phil math you want to work on.

There aren't many jobs in philosophy of math. I would caution that doing work in it, especially if it takes a lot of your time to catch up on the math side of things, isn't good for your career. Hopefully someone who does phil math as an AOS can chime in on what practitioners expect to see, although I suspect it varies by who you talk to. *Standing out* will be tough. The philosophers of math who do it without much connection to mathematical theory and practice probably won't care too much that you have the courses, and those engaging with the math itself won't be *impressed* by a few courses. If this is just a question of marketing yourself, simply try to mimic the CV/background of successful people you want to be like.

Posted by: A Philosopher | 07/01/2019 at 11:05 AM

I got an MS in math while doing my PhD in philosophy. As far as I can tell, no amount of coursework not leading to a degree will be terribly useful on its own. This is in part because nobody will, at any point in your post-PhD career, ever look at the list of courses you've taken. It's also partly because there are many ways to do philosophy of math, and different courses can be useful depending on the route you take.

But, having said that, it's probably crucial that you do *quite a bit* of math well beyond what you've done so far. Calculus is *not* representative of what most mathematics is like. And undergraduate mathematics (of any sort) is *not* representative of what graduate mathematics is like. And, finally, the sorts of mathematics one does in the classroom -- whether graduate or undergraduate -- is *not* representative of what the practice of mathematics is like. So if you want to do any sort of philosophy of mathematics that makes contact with practice, you should do a heavy amount of mathematics. But just do whatever interests you.

Having said all that, I want to make another point: I'm only still in academia at all because of my math degree. Fully half of my post-PhD employment has been in math departments, and I almost certainly would have had to leave academia had I not gotten those jobs. There are *loads* of VAP-ish positions available if you have some way of demonstrating you're a competent mathematician, and getting those can keep you afloat through thin years on the philosophy job market.

Finally, some personal anecdotes: my degree did seem to matter to some search committees. But it mattered just because it gave me a credible way to potentially build interdisciplinary connections. Also, in my experience, people who care about what kind of math you do care because either (a) they think you'll know about whatever math they also do (you probably won't, but meh) or (b) they've never heard of the kind of math you do (this will be true no matter how mainstream, mathematically speaking, you go).

Feel free to email me if you have further questions. I'll try to answer as best I can.

Posted by: Shay Allen Logan | 07/01/2019 at 04:43 PM

I agree with SAL that just taking a course or two won't really help you at all. Just taking a few undergraduate philosophy courses wouldn't give someone a feel for what real working philosophers do, and likewise the same in math.

And taking a 300-level undergraduate course in, e.g., topology would be on par with taking a 300-level undergraduate course on political philosophy (or some other philosophical area): you would get a small taste for the rudiments of the field, its methods, and its questions, but you would still be missing 98% of what there is to know, you wouldn't have any sense for the actual current research topics, and you would misunderstand and miscontextualize much of what you did learn.

This isn't to say it's hopeless to learn enough math, but just that if you're going to do it it's going to be a big investment and take a lot of time. The reader doesn't say if this is just a side interest of theirs or if they're planning on writing a dissertation on the topic. If the latter, then plunging into learning a new field (in this case, math) can just be par for the course. If the former, it's probably impractical and/or a bad use of time to try to learn math from scratch on the side to supplement what's already a side interest.

If you are trying to pursue phil math as an AOS or write a dissertation on it (despite the lack of jobs), then you should have an advisor who can answer this question about math coursework for you. It would help greatly to have a faculty advisor at your school who knows phil math well, knows math well, knows the details of your situation, the local opportunities, etc, and can help you devise a realistic plan.

Sorry for the pessimism of this post.

Posted by: A Philosopher | 07/01/2019 at 05:35 PM

I would highly advise against having your main area be philosophy of math. There just aren't jobs. Of course, if you don't want a philosophy job and are just doing it for some other end, then that is different. But I have several friends who got PhDs from the program ranked 1st in philosophy of math, and they left the discipline and became computer scientists.

Having it as an AOC is a different story. That might be helpful for certain jobs at tech schools.

Posted by: Amanda | 07/02/2019 at 03:20 AM