The paradigmatic philosophical debate concerns whether there is such a thing as philosophy at all. And if so, what it is.
At Rationally Speaking, Massimo Pigliucci has an excellent post responding to the oh-so-common, Wittgenstein-inspired claim that philosophy is just a matter of confusion about language. (One species of this argument is that dualism is a "category mistake" -- and so doesn't even rise to the level of a theory that doesn't work for interesting reasons). [Update: I'm not precisely attributing this view to Wittgenstein himself -- see Duncan Richter's description of Wittgenstein's position here). It shouldn't need saying that there's a difference between linguistic and conceptual definitions, or that every system of knowledge rests on unproven axioms or assumptions -- mathematics, logic, and science as much as philosophy. That's why philosophical "meta discussions" about these fields -- and knowledge in general -- become genuinely interesting and problematic (rather than merely a matter of linguistic confusion or semantics), even while we know that that these problems don't bear on their practical application:
In the same way, we are not going to throw out math, logic, or ethics just because meta discussions of those topics seem to constantly get us into trouble. Hume would have approved retaining science, math, logic and ethics regardless of their respective foundational problems. But he would have simply smiled if someone rushed to him with a dictionary in hand to tell him that the problem of induction is all just a matter of definitions.
By: Wes Alwan