Thanks to Dylan for his doughty defense of Lewis against Williams' criticism of the Rule of Attention. On reflection, though, I'm still inclined to side with Williams. Once we enforce the distinction between de facto ignoring and normative properly ignoring, I think it would beg the question to reiterate the original infallibilist argument in favor of the Rule. Here's the dialectic as I now see it:
DKL: [Rule of Attention]
MW: "Purged of confusion, the Rule of Attention stipulates that no consciously recognized possibility may properly be ignored. But why should anyone accept this?" [p. 16]
DKL (via WDS): You've forgotten my original infallibilist argument. To know, the subject has to have ruled out every (contextual) possibility of error. Once she is in fact attending to an evil-demon possibility and her evidence does not rule it out, she cannot rule out every possibility of error. So her belief is not infallible (and, we may add though it is not directly pertinent, she knows that); she does not know.
MW (via WGL): That begs the question. My claim is that although the subject is de facto aware of the evil-demon possibility and even aware that her evidence does not rule it out, she may still properly ignore it. So she still can and does rule out every possibility of error (Psst!--except for those possibilities that we are properly ignoring).
DKL: "If you are still a contented fallibilist,...we have reached a standoff. I started with a puzzle.... We just disagree about the explanandum phenomenon." [p. 232]
MW/WGL:
First, I am not a fallibilist at all, much less a contented one.
I fully agree that a knower's evidence must rule out every possibility
of error (Psst!--...). Second, I grant that I must relinquish your
own explanation of the attraction of skepticism, but I don't find it at
all plausible anyway; you make knowledge much too elusive and elusive in
a somewhat silly manner. But I am free to come up with my own explanation.
I (MW) offered one in my book. WGL may put forward another.
There are plenty of options.