We get inferences to reduction even when we're not certain that our reductionist model accounts for every pre-reduction fact. For example, there are some complex systems of water that have not been simulated in terms of H2O molecules because the computational task is beyond our abilities. So it is possible that, say, some kinds of whirlpools cannot be accounted for in terms of H2O. Perhaps such whirlpools require some sort of irreducible water spirit? Yet, we don't doubt that water reduces to H2O. Why?
The argument is roughly like this: irreducible water spirits don't place constraints on experimental tests (while still being relevant to them), whereas physical reductionism does. Experimental results are consistent with the constraints when they needn't have been. Therefore, it is probable that water reduces to H2O.
Suppose there are fair coins and two-headed coins, and I take one of the coins at random and flip it in front of you. It lands heads. What are the odds that the coin is fair? Clearly, it is more likely that the coin is the two-headed coin. Now take this to the Nth power, and you'll see why we don't regard water as consisting of water spirits (fair coins), even if we have not formally reduced every instance of water behavior we have ever observed.
Similarly, there are a great many ways that minds are consistent with physics in ways they needn't have been if minds were not reducible to physics. Hence, it is rational to believe that minds are likely to be physical systems (they might be irreducible, but it is terrifically unlikely because we would be supposing that very special, fine-tuned form of irreducibility that looks just like reducibility wherever we look).
As for the zombie argument, I personally think there's some very subtle question-begging going on. In order for qualia to escape the aforementioned reductionist inference, it has to be claimed that qualia are wholly irrelevant and disconnected with physics. By making this claim, it is also implicitly claimed that qualia cannot have a physical explanation. If this assumption is sustained, then qualia don't have any implementation, so physical minds don't place any more constraints on experiment than do irreducible ones, and the inference to reduction to physical minds fails.
However, if we deny from the start that qualia can have a physical explanation, that's begging the question. There are also multiple arguments to the effect that physically irrelevant qualia don't exist at all.
(Originally a comment on Philosophy Etc.)