Here’s a toy functionalist definition of belief.
bq. To believe that P is to be disposed to act in ways that would tend to satisfy ones desires, whatever they are, in a world in which P (together with ones other beliefs) were true. (Stalnaker, _Inquiry_, p. 15)
Stalnaker says that this is much too simple, so my criticisms of this definition aren’t criticisms of Stalnaker. I’m just interested here in working out just how this is too simple. I’m interested in this in part because of how it relates to this claim that Stalnaker makes, one he doesn’t qualify.
bq. If a person is, in general, disposed to act in ways that would tend to be successful if P (together with his other beliefs) were true, and is also disposed to act in ways that would be successful if Q (together with his other beliefs) were true, then he is disposed to act in ways that would be successful if P & Q (together with his other beliefs) were true. (82)
It seems to me that this isn’t true, unless we accept the toy definition, which we should not. The following example should illustrate this. (By the way, I have no idea whether I’m just reinventing the wheel with this example. I suspect all the points in this post have been made elsewhere – I’m a little out of my expertise here.) [UPDATE: As Matt Weiner points out in comments, the case I describe is very similar to one he describes “here”:http://mattweiner.net/blog/archives/000508.html, without appealing to beliefs. So I’m _certainly_ not original!]
Lauren is a manager at a large industrial plant. She normally works until 7, when she leaves responsibility to the two nightwatchmen who come in, one for the north factory and one for the south factory. In some ways, Lauren acts as if she supposes the nightwatchmen will each turn up. For instance, she spent some time this afternoon writing out instructions. It is now 6:30, and Lauren has done all that she has to do for the day. If she leaves now, she’ll be able to get home by 7 to watch baseball. But part of her job is finding an emergency security guard if one of the nightwatchmen doesn’t turn up for any reason. If one of them doesn’t turn up, and she isn’t there to arrange emergency security, she’ll be fired. (Since she has done all her work she could safely leave work if the nightwatchmen are going to show. She isn’t on a time clock.) But it’s not worth losing her job over a baseball game, and there is a risk they won’t both show. So she stays to see whether the nightwatchmen will arrive, and leaves at 7 when they both show up.
Let N be the proposition that the nightwatchman for the north factory will show up for work. And let S be the proposition that the nightwatchman for the south factory will show up for work. At 6:30, does Lauren believe N? Does she believe S? Does she believe N & S?
The first two questions are, I think, underdetermined by the data. But let’s add one stipulation – Lauren has _exactly_ the same attitudes towards each of the propositions. They play perfectly symmetric roles in her dispositions. (Symmetric rather than identical because it’s her attitude towards N not S that causes her to leave notes for the north factory nightwatchman.)
It seems clear that on the toy functionalist story, she does not believe N & S. Her desires are to not get fired and watch the baseball game. If N & S is true, then the action that satisfies those desires is leaving work early. But she doesn’t leave work early. (And not because of irrationality, other causes etc.) So she doesn’t believe N & S.
Assume, for reductio, that she believes N. Then if S were true, along with her other beliefs, N & S would be true, and the action that satisfies her desire would be leaving work. Since she stays, she does not believe S. So if she believes N, she doesn’t believe S. By similar reasoning, if she believes S, she doesn’t believe N.
Assume, again for reductio, that she doesn’t believe N. Then believing S is not sufficient for believing N & S. Now all the actions she performs (leaving notes for the nightwatchmen, waiting to see whether the nightwatchmen turn up) are ones that maximise expected utility in a world in which S and her other beliefs are true. So on the toy story, if she doesn’t believe N, she does believe S. And if she doesn’t believe S, she believes N.
Now we have a problem. We have good reason to say that she believes N iff she believes S. But the toy functionalist story is committed to saying she believes N iff she doesn’t believe S. Contradiction! Well, we said it was a toy story. How should we get out of it.
I think the best way out is to revise the toy theory in the following way. Rather than making dispositions to act be the basic concept in the theory, we make conditional dispositions to act the basic unit. So we end up with the following theory (still a little simple, but closer to the truth).
bq. To believe that P is to be such that for any relevant Q, the agent is conditionally disposed given Q to act in ways that would tend to satisfy their desires, whatever they are, in a world in which P & Q (together with their other beliefs) were true.
I think it can be proven that as long as the class of relevant propositions is closed under conjunction, the class of beliefs is also closed under conjunction. (Compartmentalisation might threaten both premise and conclusion in this argument.)
I also think it can be proven that on this definition, Lauren believes _neither_ N nor S, at least not if her conditional dispositions to act are also symmetric and she is coherent. So we don’t have an argument against closure under conjunction from the pragmatic theory of belief. But we do have an argument against one of Stalnaker’s claims I quoted above.
bq. If a person is, in general, disposed to act in ways that would tend to be successful if P (together with his other beliefs) were true, and is also disposed to act in ways that would be successful if Q (together with his other beliefs) were true, then he is disposed to act in ways that would be successful if P & Q (together with his other beliefs) were true.
Lauren is disposed to act in ways that would tend to be successful if N (together with her other beliefs) were true. And she’s disposed to act in ways that would tend to be succesful if S (together with her other beliefs) were true. But she’s not disposed to act in ways that would be successful if N & S (together with her other beliefs) were true.