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Do we only believe statements like "2+2=4" when we think of them? That is what I believe(at least at this moment!). I am not saying we believe it is false, either, but most of the time we are just not thinking of it, hence not believing it. I would be open to any counterarguments.

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Yep. Just like running, speaking, throwing, climbing, ambling etc., beliefs are not something you have (vis. container/storage metaphors) it’s something you do. The same presumably goes for all cognitive attitudes: knowing, conjecturing, considering, remembering, inferring, suspecting, alluding, etc. See Eric Shwitzgebel for dispositional accounts of belief: http://www.faculty.ucr.edu/~eschwitz/SchwitzAbs/AccountBel.htm Also a good paper by Daniel Casasanto (at the top of the list) “All Concepts are Ad Hoc,…” http://www.casasanto.com/

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As in so many matters, a clarifying answer to precisely this question is given by Wittgenstein. Belief, like so many psychological attitudes, does not have genuine duration. It is more akin to an ability or a disposition than a state.

For example, you car has 300 Horse Power. It has this regardless of whether it is moving or not. Its power is not a state but an ability. Understanding, belief and knowledge are similar.

I want to talk about a "state of consciousness", and to use this expression to refer to the seeing of a certain picture, the hearing of a tone, a sensation of pain or of taste, etc. I want to say that believing, understanding, knowing, intending, and others, are not states of consciousness. If for the moment I call these latter "dispositions", then an important difference between dispositions and states of consciousness consists in the fact that a disposition is not interrupted by a break in consciousness or a shift in attention. (And that is of course not a causal remark.) Really one hardly ever says that one has believed or understood something "uninterruptedly" since yesterday. An interruption of belief would be a period of unbelief, not, e.g. the withdrawal of attention from what one believes, or, e.g. sleep.

Remarks of the Philosophy of Psychology, vol II, sec. 45.

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  • I believe, at this moment, that beliefs are thought-dependent. But in a couple of minutes, I will no longer believe it. I will not believe the negation either. I will just focus on other things.
    – user107952
    Jul 9, 2014 at 7:49
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    @user107952 And when someone asks you if you believe in Santa Claus, you say, "I'm not sure right now, since I am focussing on other things, I'll get back to you." Later on, when you are free, how do you decide whether or not you believe in Santa Claus? Do you keep a list of previous beliefs which you review, or do you decide on the belief each time based on the available evidence? If you say you don't believe in Santa, do you caveat that saying "but that's only true for now, while I am focusing on it." However it is, it would be almost impossible to have a sensible conversation with you.
    – adrianos
    Jul 9, 2014 at 13:45
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    The point is, of course, that 'focus' adds nothing relevant to the concept of belief and so in fact obfuscates it. There are similar examples in Wittgenstein's private language arguments.
    – adrianos
    Jul 9, 2014 at 14:12

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