Another matter-of-detail post. At the end of chapter 4, F/M rebut the Weatherson argument that all the pragmatic encroachment in the theory can be explained by pragmatic encroachment on belief itself, yielding a story on which pragmatic encroachment is of no epistemological significance at all. What I expected to see from F/M was the following: Here’s what we defend in terms of pragmatic encroachment on belief, here’s what we defend in terms of pragmatic encroachment on justification and knowledge, and you can’t get the latter from the former. They do just this, and the argument is interesting and persuasive. But they also do something before doing this, and what they do before the key argument puzzles me immensely.

The passage is on p. 158, and F/M use the account of “rational to prefer as if p” to explain what it is to prefer as if p. Recall that the skeletal outline of the the account of the former looks like this (a full explanation of the details can be found here):

RP*sp iff

For all A,B(RP(A to B) iff RP(A&p to B&p)).

F/M want to use this principle to get the conclusion that preferring as if p is a partially normative notion. They give an example in the footnote on that page, one where you believe John is away from home and (irrationally) prefer robbing his home given that he’s away to not robbing given he’s away (and, I assume, irrationally prefer robbing to not robbing). F/M want to insist that you don’t prefer as if John is away, however. They say, “No! To prefer as if p would be to prefer not robbing his home to robbing it, because *given that he isn’t at home* it is rational to prefer not robbing the home to robbing it.”

I find this passage a head-scratcher. So it is worth seeing how one is supposed to get here.

In the passage in question, F/M are trying to show that the following is a lousy theory of belief:

S believes that p iff S prefers as if p.

Well, I don’t quite know what it is to prefer as if, but on any reasonable guess, this biconditional is hopeless. But F/M don’t settle for some of the obvious things one might be tempted to say here (I believe some things that I prefer are false, I believe some things but my preference orderings can easily fail to conform to my beliefs, etc.), preferring instead to try to argue for a particular construal of preference-as-if, and then using that construal to argue against the above proposal. Sounds fine, except I can’t make sense of the argument.

The argument goes like this: start with the account of “rational to prefer as if”, given above. They then say,

If we subtract ‘rational to’ from ‘prefer as if p’, what do we get? This: for all A and B one prefers A to B iff it is

rationalto prefer A&p to B&p. That’s what preferring as if p is. It is a partially normative state.

But that’s not right. They dropped not only the ‘rational to’ from ‘prefer as if p’, they also dropped one of the rationality operators on preferences inside the right side of the formula. That is, the original formula has three rationality operators, and when simplified, has this structure:

R(X) iff for all A,B(R(Y) iff R(Z)).

Only the first R operator governs the phrase ‘prefer as if p’, so if that’s all we drop, we get:

(X) iff for all A,B(R(Y) iff R(Z))

not:

(X) iff for all A,B((Y) iff R(Z))

Moreover, if we are going to drop rationality operators from both sides, why are we being selective about which one to drop from the right side? Why drop one rather than two? Why drop the left one rather than the right one? If we drop both, we get:

(X) iff for all A,B((Y) iff (Z))

In English, you prefer as if p iff (for all A and B, you prefer A to B iff you prefer A&p to B&p). But that’s not a partially normative notion, and doesn’t help explain the footnote example about thieving from John.

If the original proposal were an ‘iff’ claim with clauses on each side governed by a rationality operator, it might make sense to propose dropping the governing operator from each side to move from a characterization of ‘rational to prefer as if’ to a characterization of ‘prefer as if’ (though it would still be highly questionable, since it is not a good rule of inference to go from R(X) iff R(Y) to X iff Y, for reasons F/M themselves make clear in the chapter). But the form of the original proposal doesn’t have rationality operators governing both right and left sides, and once you start dropping operators inside the quantifiers from the right side of the account, I can’t figure out what is motivating the choice.

I also think that, if this is what it is to prefer as if p, nearly everyone never prefers as if p, for any p whatsoever (read this slightly hyperbolically!). Here’s why.

The first reason is the Irrational Preferences Problem. Suppose I irrationally prefer some B to some A, when it is rational to prefer A to B. I do, take my word for it! In the usual case, for a given p, there will be irrational preferences that are completely disconnected from p, so that it will also be rational to prefer A&p to B&p. Moreover, for most any value for p, and people with some irrational preferences, we’ll be able to find examples that fit this schema. It is a schema where the definiendum for “S prefers as if p” to have a falsehood on one side if the biconditional and a truth on the other side. All we need is one irrational preference of the sort described for each claim p.

The second reason is more general. It is the Problem of Incomplete Preferences. Every ordinary rational agent has gappy preferences: values for A and B such that the person has no preference orderings at all for those values. Take such a case. Then the right side of the definiendum is false. It is also typically true of such gappy preferrers, however, that the scope of rational preferences outdistances the scope of actual preferences. So for some of these preference gaps, it will be rational to prefer one of the things to the other. Now, all we need is to find one such case for each p where the rational preference order is completely unrelated to p itself, so that it is rational to prefer A&p to B&p when it is rational to prefer A to B. How likely is it that we’ll be able to find such, for any given value for p? It looks exceedingly easy for any ordinary agent with incomplete preferences who lacks full rationality. The result, then, is that we ordinary creatures with such intellectual foibles rarely prefer as if.

So maybe the result of the notion of ‘prefer as if’ endorsed here is that the most plausible theory of belief is this:

S believes that p iff S doesn’t prefer as if p,

at least if we restrict the class of persons to those with ordinary foibles.

(OK, the last proposal is clearly hyperbole, but, I say, much closer to the truth than the original proposal.)

Just quickly,

Yeah, I agree that the wholly non-normative construal of preferring as if p is problematic as a theory of belief. Our discussion would have been improved by considering it as a possibility as well.

In the 2002 article, as you correctly note, we don’t proceed by first defining preferring as if p and then claiming that if you’re justified in believing p, you’re rational in doing that (i.e., preferring as if p). We define “rational to prefer as if p” as follows:

for any states of affairs A, B, you are rational to prefer A to B iff you are rational to prefer A to B given p. (The ‘given p’ business gets further explained via p-involving conjunctions, but let’s leave that aside.) Now, what is preferring as if p, if this is what rationally preferring as if p is?

Think about acting as if p, for starters. Suppose you know p. We say you’re rational to act as if p. We take that to mean you’re rational to do a certain thing. Which thing? The thing which it is rational to do given p. If you do that action, then you acted as if p. That’s how we were thinking. Applied to preferences, the idea would be you’re rational to have certain preferences. Which? The ones that it are rational to have given p. This gives us the “partially normative” account of preferring as if p.

Take the high stakes bank case. Is Hannah (or Keith or whoever it is!) rational to act as if the bank is open tomorrow? Well, that’s asking whether Hannah is rational to do a certain act. Which act? The one it’s rational to do given it is open tomorrow, which is just waiting till tomorrow to deposit the check.

Finally, let me add just a couple remarks on the notion of preferring as if p. Again, that’s not an important notion for the book. It was a key notion for the 2002 article. In thinking about the notion, I think it helps to start with the most intuitive formulation: you’re rational to prefer as if p just if the chance that p is false doesn’t make a difference to your rational preferability ordering. That is: you can ignore the chance that p is false in your preferences. (Subject to some important restrictions!) Then to spell out just what this means we turning to the idea comparing what it is rational to prefer with what it is rational to prefer given p. Then this in turn is spelled out in terms of one’s being rational to prefer A to B iff one is rational to prefer A&p to B&p. If you consider the “finished” principle by itself it might look rather techy and unintuitive. But I think the original idea is pretty intuitive.