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Nonreductive Physicalism and Strict Implication

Do physicalists have to be reductionists? I have argued that a strong kind of physicalism based on the ‘Strict Implication thesis’ can consistently reject both eliminativism and reductionism (in any non-trivialising sense: see II below) [8, 9, 10]. Andrew Melnyk disagrees. He faces me with this dilemma: either my formulation doesn’t actually entail physicalism, or it must be interpreted in such a way that the mental is after all reducible to the physical [12]. His alternatives depend on two interesting assumptions, each worth discussing for its own sake. One is about the metaphysical implications of my formulation of physicalism, the other concerns what it takes to establish the strict implication thesis. Each assumption turns out to be mistaken. The outcome, I think, is that this kind of nonreductive physicalism becomes both clearer and more clearly defensible.