An argument for the irreducible naturalism thesis is advanced in the next chapter, and Wedgwood’s intention is to show that irreducibility is compatible with naturalism, such that he is not arguing for naturalism, just for this compatibility thesis, and so assumes a strong version of naturalism, as by extension, if irreducibility is compatible with a strong version of naturalism it will also be compatible with weaker versions. The version of naturalism that Wedgwood assumes is the thesis that it is necessary that all contingent normative and mental facts are realized in physical facts.
The tension that emerges, upon inspection, is that, because the moral realist owes us an explanation for why normative properties supervene on non-normative properties — what Horgan and Timmons have called “specific supervenience facts” — this project seems to contradict the irreducibility thesis that Wedgwood argued for, as while it seems an appropriate account of supervenience would explain these facts as being logically derived from fundamental truths about the essences of things, such an account would entail the reducibility of normative properties. Wedgwood did make a good case for why normative properties are irreducible to non-normative properties, so we must take an inventory to see where we went wrong. This leads Wedgwood to conclude that we should dismiss the assumption that specific supervenience facts must be explained directly by the fundamental truths of the essences of things, and rather that these facts be explained indirectly by fundamental truths, “that is, [they] must be explained by some fundamental essential truths, together with some other wholly non-modal truths” (207).
The wholly non-modal truths that Wedgwood has in mind are metaphysically contingent rather than metaphysically necessary. These metaphysically contingent truths would be cases where a physical property is regularly co-instantiated with a normative or mental property, such that it is a non-accidental regularity that whenever a creature has physical property B it has the relevant mental property, i.e. pain. Against the objection that regular co-instantiation is a thinly veiled appeal to psycho-physical laws, and psycho-physical laws are only plausible if reduction is possible, such that psycho-physical laws cannot be used to argue for irreducibility, Wedgwood argues that such regularities do not entail that mental property is necessarily equivalent to a physical property, so it does not entail that reductionism is true.
From the notion that we can offer physical descriptions of properties that regularly instantiate certain mental properties, it seems possible, says Wedgwood, that we could note that in worlds physically similar to our own, those same physical properties will be regularly co-instantiated with those certain mental properties. This specific physicalist description would in turn provide an explanation for the general supervenience fact that a certain mental property, say pain, supervenes on physical properties. As such, contingent metaphysical facts explain modal facts on this account, and offer a theory of supervenience relations that depend on these contingent facts, not metaphysically necessary facts that would entail reductionism.