have proven and characterized a devastating logical truth, (IN), centered on these arguments: namely, that their soundness entails the inconceivability of reductive physicalism. In this paper, I demonstrate that (IN) is only a logical truth when reductive physicalism is interpreted in its stronger, intrinsic sense (e.g., as an identity theory), as opposed to its weaker-yet considerably more popular-extrinsic sense (e.g., as a supervenience theory). The basic idea generalizes: perhaps surprisingly, stronger (intrinsic) forms of reduction are uniquely resistant to the conceivability arguments opposing them. So far as the modal epistemology of reduction is concerned, therefore, it pays to go intrinsic.

Phenomenal facts are facts about the ways things feel or 'what it is like' to feel them (Nagel 1974)-facts witnessed by instances of phenomenal properties or states, like searing pain or tingling orgasm or unendurable boredom. It is hoped by some philosophers-perhaps fewer and fewer, these days-that phenomenal facts are somehow reducible to or reductively explainable in terms of physical facts, or, by way of some realization relation, the functional facts they make true (or both). This position is oftentimes called reductive physicalism.The 'two-dimensional conceivability argument' (Chalmers 2010) purports to refute reductive physicalism, on the basis of both a priori reflection and the two-dimensional semantic content of our concepts or expressions for physical and phenomenal states of affairs. In its simplest form, the argument is as follows. Where P is the sum of actual, fundamental physical facts (and, if you'd like, indexical facts, and a closure clause specifying that nothing further is involved-'that's all'), and Q is any phenomenal fact (e.g., 'I am in pain'):