Teaching philosophy with a PhD in math I am currently in a PhD program for math in the US studying mathematical logic, and I plan to pursue a teaching career at a university after I finish my degree. Philosophy has always been a side interest for me, and I am wondering how feasible it would be for me to teach some courses in it once I can land a position. Almost all my current knowledge comes from self-study. I took some undergrad courses, but no graduate work. Would I be considered qualified to teach an undergrad course in logic or philosophy of math if it is listed with a PHIL prefix? Personally, with my knowledge of mathematical logic, I feel that I am more qualified to teach these courses than many philosophers. However, I don't know that accreditation boards see it that way. Reaching further out, what about the philosophy of science, metaphysics, or epistemology?

I did think about taking some philosophy courses at my current institution, but it is a small department, and they seem to be interested in what I would call "soft" topics - nothing like what I normally read and am interested in. 

If I must take some graduate level philosophy, should I consider online courses? Are there even any decent places that will allow you to take courses without working toward a specific degree? Probably not, I fear.

Edit: I am particularly interested in the accreditation aspect here. Not what I think I am qualified for, but what I would be considered to be qualified for.
The basis for teaching university-level courses is publication, not so much the courses you may have taken. Therefore, in order to teach a PHY-xxx course, you should expect to be required to have published some research that is relevant for philosophy. That may be in the philosophy of logic, preferably in a philosophy journal.

How close your research has to be close to philosophy will be entirely dependent on the philosophy department and program as well as who their staff are. If they do not have a logic specialist they may be more open to consider you, but be assured that you have to give them reason to prefer you over one of their instructors (professor or lecturer). By allowing you to teach a PHI course the department clearly takes a risk (you are not "one of them"), a risk that is perceived to be higher than letting a philosophy professor teach a logic course, even if it is not that professor's main field.

Indeed, departments tend to take as granted that their professors are implicitly qualified to teach any of their courses (even though that may obviously not be the case), while being a priori suspicious of professors from other departments. 

It may therefore be easier for you to give a course on a topic you hage to learn from scratch in mathematics than a course for which you think you are perfectly qualified in philosophy.

In any case, you should not go to the PHI department and argue that you have taken PHI courses which supposedly qualify you to compete with their professors who, after all, have a PhD in Philosophy. Write a couple of articles, a book, that is the way to do it. Or, offer to teach the course jointly with a PHI professor and see how it goes from there. Who knows, the other prof may take a sabbatical and hand you the course!