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.