Minimal physicalism: All mental facts are necessitated by physical facts. (Or: mental facts supervene on physical facts.)
Generic knowledge argument against physicalism
M: a mental fact (i.e. a fact about mental states of some sort)
P: the sum total of all the physical facts
2. I could know P without knowing (or being able to figure out) M.
3. If you can know X without knowing Y, then X does not necessitate Y.
4. M, and P does not necessitate M.
5. Physicalism is false.
How plausible this argument is may depend on what sort of mental fact we plug in for M. If M is something like "I am processing a visual representation" or "I believe that bats have wings," then (I think) it seems pretty likely that 2 is false.
Nagel's version of the argument takes M to be the facts about what it is like to be a bat. (In general, we could M to be a fact about conscious experience, i.e. about qualia.)
Is there anything wrong with this argument?
Most physicalists (the "reductionists" in Nagel's rather broad sense of the term) will deny either 2 or 3. They may insist that if you really did know and properly appreciate all the physical facts, you would be able to figure out what it's like to be a bat. (That's the denial of 2.) Or they may insist that the limitations of our knowledge and reasoning don't show anything about possibility, i.e. that P may necessitate M even if we couldn't figure out on the basis of P that M is true. That's the denial of 3.
Dennett's response is quite different: Dennett denies 1! This makes him an eliminative materialist. (At least about qualia; he seems to be some sort of functionalist about most other mental states.)
In a nutshell:
If there are such things as qualia, then there is a fact about whether you
have OK memories and inverted qualia, or OK qualia and inverted memories. Such a
fact could never be empirically determined. But if you can't empirically
determine something, there can't be a fact about it. Since assuming the
existence of qualia leads to a contradiction, there must be no qualia after all.