Suppose P is the conjunction of all truths statable in the austere vocabulary of an ideal physics. Then phsicalists are likely to accept that any truths not included in P are different ways of talking about the reality specified by P. This ‘redescription thesis’ can be made clearer by means of the ‘strict implication thesis’, according to which inconsistency or incoherence are involved in denying the implication from P to interesting truths not included in it, such as truths about phenomenal consciousness. Commitment to the strict implication thesis cannot be escaped by appeal to a posteriori necessary identities or entailments. A minimal physicalism formulated in terms of strict implication is preferable to one based on a priori entailment.