I once attended a talk by Alan Sokal, where he said something like “I do physics on mondays to fridays, and then think about philosophy on sundays”.
The idea he was trying to put forward was that his ideas of philosophy of science, although he is a science practitioner, has little background into the philosophy of science insofar as it works as an afterthought to his real work (physics and statistical mathematics).
I have recently been reading some scholarship on Kant (no surprise) which presupposes knowledge of mathematics up to about an undergraduate mathematics standard, and a knowledge of theoretical physics up to about an Einstein standard! The understated response was that I raised an eyebrow, mainly of surprise, but also of fear (that is the understated response…the real response involved a few expletives and loss of hair).
So it led me to think; what makes a philosopher of science? a philosopher of mathematics? a Kant scholar? a logician? Where there are interplays of a subject; how important is the subject discourse rather than the discourse subject?
Can I for instance, be a philosopher and think about mathematics (then I’ll end up talking about mathematical platonism and semantics of mathematical utterances; fictionalism for instance…)
Can I be a philosopher and think about science? (then I’ll end up talking about issues that have been borrowed from Hume, and is a very crude “rationalism vs. empiricism” debate, or general epistemology discussion
Can I be a physicist and a philosopher? (then talk about the nature of theoretical entities, or what implications the physicist’s work has, or how to understand theories…I think the most important thing a physicist can do for a philosopher)
Can I be a mathematician (solely) and attempt philosophical thinking? (Interesting question; I know more than a view mathematician/philosophers over history, and they have had pretty good ancestors: Leibniz, Russell, for instance; but they are independently philosophers from their work in mathematics…although the converse may not hold for Russell’s work on foundations) I think the most poignant instance of a mathematician who tried to be philosophical is Poincare; who came under heavy criticism, and became infamous for his defence of Kantianism about mathematics…Poincare is perhaps the most assuring person to take the side of Kant on the issue of mathematics…but sadly, the other side is far stronger…