Identity Theory is committed to necessarily, P=Q. Dualism which contends that it's not necessary that P=Q, is committed to it not being possible that P=Q (after some modal logic). Standard Dualist arguments against Identity Theory start from the conceivability of the physical without qualia to the possibility of P & ~Q; if sound, then identity theory is false. Is there a route from conceivability to the possibility that P=Q and therefore also a counterexample to the denial of identity theory? I posted some brief comments on this here:
Notes on modality, mind, and conceivability
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