Fans of pragmatic encroachment need a way to resist the arguments of Weatherson and Nagel and Bach, arguments that show that in many of the motivating cases, an explanation in terms of pragmatic encroachment into belief itself can replace pragmatic encroachment into knowledge or justification. One way to push this response to the motivating cases is to defend a functionalist account of belief, and this is Weatherson’s tack. He endorses this account:

$$BEL(p) \leftrightarrow \forall A \forall B \forall q(A \ge_q B \leftrightarrow A \ge_{q \& p} B)$$

A and B are actions, and q is a proposition. The $$\ge$$ symbol stands for preference, so the account says that you believe a claim just in case the ordering of your conditional preferences isn’t affected by adding that claim to the condition. Later in the article, Brian notes that this formulation needs to require that p and q are consistent, but I think that restriction doesn’t go far enough. If p and q are probabilistically or evidentially in tension, the account is subject to counterexample.

Consider this case. Given that it seems to me that I’m not married, I prefer leaving my wedding ring in the drawer to wearing it. But given that it seems to me that not I’m married but actually married, my preferences reverse. But I do in fact believe that I’m married.

The fix strikes me as simple, however: Just restrict q to propositions independent of p. Would love to hear, though, if that can’t work. (For Weatherson aficianados, I should note that the quantifiers above are restricted, but that the restrictions in question don’t rule out counterexamples of this sort. I’ll leave it to the reader to verify that I’m right about this.)

[UPDATE: I fixed the original garbled example, sorry for any confusion! And a bit more below the fold.]

We can generalize as well. Identify q as something that is evidence against something p you believe. For example, let q= the objective chance of p is nearly zero, or let q=the evidence against p is (nearly) conclusive. So, if p is that today is 4/13/2012, something I believe, my preferences for driving to DFW early in the morning over sleeping in favor the latter, given q. But given both p and q I prefer to drive, since I want to get to Gonzaga for the conference on that day.