Quote from The Web of Belief
“Rather, believing is a disposition that can linger latent and unobserved. It is a disposition to respond in certain ways when the appropriate issue arises. To believe that Hannibal crossed the Alps is to be disposed, among other things, to say “Yes” when asked. To believe that frozen foods will thaw on the table is to be disposed, among other things, to leave such foods on the table only when one wants them thawed.” (p. 6 in the online version.1)
One dispositional account of belief may seem to imply that we have an infinite number of beliefs. The reasoning goes like this: Suppose that if (if one is asked “Do you believe that P?”, then one is disposed to answer “Yes.”), then one holds a belief that P. So the disposition to answer “Yes” to such questions materially implies belief. If that’s true, then it could seem that such a dispositional account of belief implies an infinite number of beliefs in persons. It seems that regardless of what number n is, one will always answer in the affirmative to the question “n is a number”.
Some numbers are so large that it will take more than a life time to pronounce them therefore no question will ever be asked. This does not however disprove the material implication; it actually proves it. Recall that if the antecedent is false, then the implication is true.
The liar objection
One objection to m. implication is that one’s answering “Yes” to such a question does not imply belief in P because it is sometimes the case that one lies, and therefore there are cases where one answers “Yes” to believing something but does in fact not. It is easy to amend the implication to avoid this objection. Simply add a clause about sincerity: If one is disposed to answer sincerely “Yes” to the question “Do you believe P?”, then one believes P.
The brain objection
Beliefs are stored in the brain and they take up space. Moreover the brain is finite in size. Thus, an infinite number of beliefs would take up an infinite amount of space. Since there is not an infinite amount of space in the mind, then there is not an infinite number of beliefs stored in the brain. This holds for all humans, thus, no human holds an infinite number of beliefs.
This objection may seem forceful, but it is begging the question against the dispositional account. Basically it says that if this other brain-physical account of belief is true, then the dispositional account is false. That of course proves nothing since it would need the premise that the brain-physical account is true and that would be question begging.