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I am a math major and I currently am preparing for admissions in a masters program.

Though late, but I realised that I have interest in philosophy as well and I think I want to pursue it professionally.

I would like to pursue philosophy of mathematics.

Is a change of stream necessary/possible? How can I go about this as I get into a masters program in mathematics?

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I know this may seem like an obvious question, but what can you do with a philosophy degree? I am a computer science student focusing on network security and would like to do security research professionally. I am currently also working towards a philosophy minor. I have an enormous interest in it, which is almost exclusively why I'm pursuing it, but what can I do with a philosophy masters degree? Thanks. – Goodies Feb 14 at 22:15
    
Some related threads: Switching to philosophy after a PhD in mathematics academia.stackexchange.com/questions/49020/… How important is studying higher mathematics for graduate study in philosophy? philosophy.stackexchange.com/questions/31395/… Does undergraduate math major make an applicant for philosophy phd more competitive? academia.stackexchange.com/questions/61340/… – Conifold Feb 15 at 3:39
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@goodies I would like to do research that's why – Non-Being Feb 15 at 5:58
up vote 4 down vote accepted

I would like to add some issues, which possibly complement virmaior's answer.

Anybody who works in philosophy of mathematics should have his own experience in a broad field of mathematics. He needs an overview over different fields of mathematics. And he should have done own research, e.g., on the level of a PhD in pure mathematics.

Why not continuing with mathematics and in addition taking some courses in philosophy, in order to base a later decision on a broader experience with both disciplines, mathematics and philosophy?

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I am aware of very few places where you could simultaneously pursue a masters in math and the "professional pursuit of philosophy." You would need to research programs specifically.

But most of these are not going to be targeted at the MS/MA level. Instead, what I would suggest is to do your masters in math and take a course or two in philosophy -- outside of the philosophy of math during your MA. Then apply to PhD programs for the philosophy of math (The Philosophical Gourmet -- formerly under Brian Leiter's management would be a good place to find the list of good programs).

Without a PhD, there's not much you can do professionally in philosophy. And diversifying at the MA level is not going to help you much. Instead, it will mostly hurt your chances. The key to getting into a good philosophy of math PhD would be strong math skills (demonstrated by coursework and a recommendation letter from someone on the math faculty) and competent philosophical writing (demonstrated by your writing sample).

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+1. Lots of good advice here OP. – shane Feb 14 at 23:54

There is an area of specialization within many mathematics programs focussed on 'Foundations', or 'Symbolic Logic', (although that latter is often 'Symbolic Logic and Combinatorics', and may lie closer to hard-core computer science than philosophy in some programs.)

If you find a relatively 'old school' advisor, courses in the history and philosophy of mathematics (and/or science) are still part of this 'Logic' concentration, and will be sometimes cross-listed with philosophy and also with computer science, as some old, deep ideas still influence 'Cognitive Science' and AI. Interdisciplinary studies at that 'triple-point' are sometimes encouraged.

Taking this path as broadly as possible does not prepare one to 'pursue philosophy professionally', just to have a more meaningful, humanistic basis behind your mathematics. At the same time, a terminal Master's in Mathematics is also not generally adequate to constitute 'pursuing mathematics professionally'. Instead, it provides a more abstract and more thoroughly grounded basis for some kind of computing, scientific, or engineering career, or for teaching those who will pursue such careers.

There is also no shame in multiple Bachelor's degrees instead of a Master's or multiple Master's degrees instead of a Doctorate. All forms of thinking reinforce one another. And given the ubiquity of education and the way jobs have changed, breadth and flexibility may trump dedication in a market where people don't work "in their field" most of the time.

And if it is a real issue, you might want to work this out at the MS level. From personal experience, I do not suggest attempting a Doctorate in math if your loyalties are in any way divided. The level of focus necessary to even 'qualify as a candidate' much less find an advisor and a problem, in a good program does not leave room for indecision.

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Yes. Foundations of mathematics/set theory is an area which I look forward to – Non-Being Feb 15 at 5:59

The answer really depends on what type of philosophy you are interested in. If you are interested solely in the philosophy of mathematics, you might not need to make a change at all --there's a reason a PhD is a "Doctorate of Philosophy." Upper level coursework in any field tends to touch on the philosophy of the field, and mathematics is no exception.

When I was working towards a grad degree in philosophy, I took some upper level mathematics courses, and they were very abstract and philosophical, quite similar to the upper-level logic courses I was taking at the same time. I was actually shocked how little computation they actually involved, as opposed to conceptual work. You'll probably find them very different from your undergraduate courses.

Depending on your program, you may be able to take a limited number of courses outside your department, assuming they're related. Philosophy of mathematics courses would almost certainly be considered on topic --you might even be mandated to take some of those. So the only real reason to switch would be if you have strong philosophical interests OUTSIDE of philosophy of mathematics.

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Given that the other answers have given very good advice on the means towards philosophy, I'll concentrate, here, on the ends.

Given the heavy representation of foundations in the philosophy of mathematics, it might be worth looking more broadly to at least find where you are situated in this philosophical landscape.

For example, this article on the philosophy of Lautmon begins by saying:

Albert Lautmon, is a rare example of a philosopher whose engagement with contemporary mathematics goes beyond the 'foundational areas' of mathematical logic and Set Theory.

and

he insists that the new areas of topology, abstract algebra, analytic number theory and class field theory have a philosophical significance that distinguishes them from earlier eras.

As Lautmon was writing in the first half of the 20th C, one should add computer science, and category theory.

Lautman classification goes dialectic ally, by:

  • continuous/discontinuous

  • infinite/finite

  • symmetric/anti-symmetric

From this post by Gowers one could add

  • abstraction/concretisation

Zalamea from what I've read about his work moves on from here. Badiou takes a very different tack, taking perhaps a cue from Heidegger:

Our epoch, can be said to have been stamped and signed by the return of the question of being.

But whereas H appeals to poesis; B posits ontology itself to be mathematical.

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