How important is studying higher mathematics for graduate study in philosophy?

Question

I am planning to apply to phd programs in philosophy. I am majoring in philosophy but I also have the opportunity to complete a second major in math (I have a few more classes to go).

I'd like to finish my math major, but I'm concerned that my math classes are taking too much time (they take me 3x as much time as the philosophy classes to get an equivalent grade e.g. A or B) and detracting from my ability to focus on philosophy classes. I want to spend a lot of time on philosophy classes so I can earn strong letters of recommendation from philosophy professors since I understand this is one of the most important parts of the phd application.

To make myself competitive for admission to philosophy phd programs, would I be better off sticking with the double major or just focusing on philosophy at the expense of math. (I also asked this question on academia stack exchange but I was concerned that that site is a bit too general so I'm asking here to get expertise of people who know philosophy)

Answer 1

A second major in Mathematics could definitely be an asset for applying to graduate school in Philosophy, but whether it is, or how much it could be, depends a great deal on what specialization you suggest you are likely to pursue in your application statements. If you anticipate specializing in (a) an area where mathematical methods are used (e.g. logic, formal epistemology, or decision theory), or (b) a "philosophy of x" area where the subject analyzed involves math (e.g. philosophy of math, philosophy of physics and a number of other scientific fields, philosophy of computing), it could have significant value. If you plan to pursue areas where neither of these apply (e.g. virtue ethics, wittgensteinian philosophy of language), the second major would serve only to support your academic seriousness. Meanwhile, there are other ways of demonstrating academic seriousness. In any case, it is certainly not essential.

The question then is a matter of relative benefit, in comparison with what else you could be doing with that time. Your first priority, in terms of applying to graduate school, should be doing very well in Philosophy courses, helping (to the extent you can) philosophers who may write letters for you get to know you intellectually, and producing an excellent, well-revised writing-sample essay. Think about whether the Math major interferes significantly with any of that. If it interferes mainly with the last, consider whether you can continue to work seriously on your writing-sample and get feedback on it, after graduation. To the extent that your college or university does not have a high academic reputation or your recommenders do not have reputations as philosophers, it becomes increasingly important to spend time in addition to coursework revising your sample essay.

However, you might also consider, in light of the possibility that you come to be in the majority of students starting a PhD in Philosophy who don't end up in an academic position in Philosophy, whether the Math major might have significant value (along with your work in Philosophy) in your application to another career. Given your interest in Math, I suspect that it might. Indeed, I know cases like that—of Philosophy PhDs pursuing non-academic careers—where an undergraduate major in Math has been a career-asset, at least at the beginning of their careers.

Answer 2

I have a strong background in mathematics and philosophy minor. Consider this answer biased.

Mathematics teaches a lot about deductive precise reasoning (by the way of practice). It also teaches you how to read and compose complicated arguments. All of this supports the practice of philosophy, though mostly indirectly.

If major means the equivalent of a master's degree, then you should certainly complete it, since an effective master's degree at mathematics with top grades makes you a possible PhD student and is quite an accomplishment in and of itself. If it is the equivalent of a bachelor's degree, then the situation is more murky.

Answer 3

The question of a double major always comes down to whether you can personally do both majors well. If you don't feel you can handle majoring in math on top of philosophy, then drop the second major --it doesn't mean you can't still take math courses. The benefits of a second major can be considerable, but they'll never outweigh the disadvantages of doing poorly as a result.

Answer 4

The answer turns on what you shall study in philosophy! I quote merely one paragraph from Peter Boghossian and James Lindsay's 29 May 2016 article Want to Be Good at Philosophy? Study Maths and Science.

Of course, mathematics is most clearly applicable to philosophy where it intersects with the mathematically hard sciences, like physics. Much in physics, for example, depends upon clearly understanding the scope, power, and impact of Noether's (first) theorem, named for Emmy Noether. Her theorem, proved a century ago and published in 1918, was truly revolutionary for physics because it completely changed how we understand conservation laws, revealing that conservation laws follow automatically from certain assumptions of invariance of physical laws (for example, if the laws of physics do not vary with locations in space, conservation of momentum automatically follows). Whether Noether's theorem is best classified as a result in abstract mathematics or theoretical physics isn't important, but that philosophers need to understand it is, at least if they want to work competently on ideas related to that which it pertains. Fully understanding and appreciating Noether's theorem, however, requires a solid grasp of abstract algebra, at the least at an advanced undergraduate level. Cosmological metaphysicians don't have much choice, then, but to learn enough mathematics to understand such ideas.