A lot of philosophy seems to be "philosophy of x" -- philosophy of science, philosophy of language, philosophy of mathematics, etc. Given this, should philosophy, institutionally speaking, be treated as a separate discipline at all? I mean, why couldn't the various philosophies of x be absorbed into the various types of x?

What you are offering is a philosophy of philosophy. From your principle that "philosophy of x" should be absorbed into the department of x, institutionally speaking, doesn't it follow that philosophy of philosophy should be absorbed into the department of philosophy? But it must be treated as "a separate discipline" for this to happen. Where else would you teach the philosophy of philosophy, metaphilosophy? In the department of physics perhaps?

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