Modern physicalists frequently offer the generous concession that although dualism is false, it is not a metaphysical impossibility. And it appears that the proper formulation of physicalism allows for this concessionary position. It would be expected that dualists also could accept that while physicalism is false, it too is a metaphysical possibility. I will argue that a careful analysis of physicalism and dualism shows that in fact these concessionary positions cannot be maintained. In particular, the nature of the metaphysical determination relation which holds between matter and mind on both physicalist and dualist views precludes either from allowing that the other is a metaphysical possibility.
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