On several occasions I have heard that Philosophy of Mind is "the first philosophy" of our time. But if this is true, I think thoeries about Philosophy of Mind should be able to be applied to other branches of Philosophy to help us gain a better and more in-depth understanding of original problems.
So my question is: is Philosophy of Mind really the first Philosophy of our time? If so, is there any work of the sort I described above that has been done?
PS: When I say "other branches of Philosophy" , what I have in mind is mainly Epistemology, Philosophy of Language, Philosophy of Logic and Philosophy of Mathematics, for these are the branches of Philosophy that I had most interest in.