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Question A friend of a friend of mine posed a really odd problem regarding our beliefs that I’ve not really been able to answer to my own satisfaction. If we believe that X is the case, then it seems to go without saying that we also believe that we believe X is the case. It would be odd to say that we believe X but don’t believe we believe it. But then if that has to be so, it also seems that we must also believe that we believe that we believe that X is the case. And if that’s so then it seems we must believe that we believe… You get the picture. What’s going on here? We’re finite beings so we can’t have an infinite number of beliefs, can we? I’d put forward some of the thoughts I had about it, but I’m not entirely sure that I think I had them.

Accepted:
October 21, 2006

Comments

Here are just a two brief reactions to your good question. First of all, maybe we do have an infinite number of beliefs. I believe a have fewer than three arms, and that I have fewer than four arms, and just maybe I believe that I have fewer than x arms, where x is any integer greater than two. But that is an infinite number of beliefs. Second of all, there can be belief that p without a belief that there is a belief that p. Dogs are good examples. Fido believes that there is food in his bowl, but he doesn't believe that he believes that he has food in his bowl, because he cannot entertain a thought like that. Dogs have beliefs, but they don't have the concept of belief. Perhaps people are like that two. Sure we, unlike Fido, can entertain the thought that there is a belief that there is food in the bowl, but maybe when you iterate the belief operator beyond a certain number of times, we lose conceptual grip.

The standard way to resolve this problem is to distinguish explicit from implicit beliefs. Suppose, just for illustration, that believing that p, in the explicit sense, is having a sentence that means that p written on a blackboard in your head. So believing that snow is white, for example, is having a sentence that means that snow is white written on a blackboard in your head. (You can think of this as meaning, roughly, that this information is explicitly stored in memory somehow.) Now, suppose I have the sentence "I have two arms" written on my mental blackboard and that I also have the sentence "two is less than three" written on my internal blackboard. Suppose, further, that I am capable of simple reasoning. Then, if the question were to arise, it seems reasonable to suppose I would conclude, from those explicit beliefs, that I have fewer than three arms. So we might say, in this case, that I implicitly believe that I have fewer than three arms. And so on.

It is not an easy matter to make all of this precise. But my own view, for what it's worth, is that this doesn't matter very much. As far as psychology is concerned, the notion of explicit belief is the one that is central. To be sure, our ordinary use of the verb "to believe" seems not to correspond to the notion of explicit belief but rather to the notion of implicit belief. But I don't know of any reason to suppose that our ordinary notion of belief should admit of precise analysis.

And, by the way, most of what I've just said is stolen from Jerry Fodor.