Stalnaker suggests that the possible worlds analysis of propositions will correctly interpret our intuitions about attributions of tacit, or presupposed, beliefs. We may conclude, for example, that someone literally believed a tacit or presupposed belief. However, under a linguistic view of content, according to which beliefs are sentence-like representations of propositions, we should have to concede that our attributions are not literally correct. The linguistic view, in this case, may be taken to assert the following:
1. Our beliefs are sentence-like representations of propositions.
2. If (1), then our minds must represent our beliefs
3. Our minds must represent our beliefs.
4. But, our minds are finite.
5. (1) and (2) and (3). (triple conjunction, but for brevity’s sake, let’s suppose it happened in sequence)
6. If (1) and (2) and (3), then it is not the case that our minds can represent an infinite amount of beliefs
7. If it is not the case that our minds can represent an infinite amount of beliefs, then our minds cannot represent all of the tacit beliefs we take for granted
8. If our minds cannot represent all of our tacit beliefs we take for granted, then the belief attributions of tacit beliefs are not literally correct.
9. So, if (1) and (2) and (3), then the belief attributions of tacit beliefs are not literally correct. (from 5-8)
10. Therefore, the belief attributions of tacit beliefs are not literally correct.
Stalnaker wants to reject premise (1). His suggestion is that if (7) is correct, then, we should not conceive of belief as sentence – like representations of propositions. His alternative conception of beliefs goes as follows:
11. If attitudes are primarily attitudes to possible states of the world, then a belief state can be represented as a set of possible worlds and to believe that P is to be in a belief state that lacks any possible world in which P is false.
12. If a belief state can be represented as a set of possible worlds and to believe that P is to be in a belief state that lacks any possible world in which P is false, then the finite mind could have an infinite number of separate beliefs.
13. if the finite mind could have an infinite number of separate beliefs, then the mind can literally believe all of the tacit beliefs we take for granted.
14. if the mind can literally believe all of the tacit beliefs we take for granted, then the belief attributions of tacit beliefs is literally correct.
15. So, if attitudes are primarily attitudes to possible states of the world, then the belief attributions of tacit beliefs is literally correct.
16. Attitudes are primarily attitudes to possible states of the world.
17. Therefore, the belief attributions of tacit beliefs are literally correct.
18. If (16) and (17), then (1) is false.
Hopefully this does some justice to Stalnaker’s argument against the Linguistic view of propositions, though I would appreciate some feedback. My argument notwithstanding, I would like to continue to evaluate Stalnaker’s possible worlds analysis of propositions. Stalnaker’s view holds that to believe P is to be in a belief state which lacks any possible world in which P is false. What I would like to propose is that this conception of beliefs is inadequate to explain one of our less desirable traits, that is, our ability to hold two contradictory beliefs (e.g. God exists, and God does not exist). What believing two contradictory beliefs would entail under his view, it seems, is that one represents both a world in which P is true, and a world in which not-P is true, or that P is false. But this cannot happen, since to believe that P is to be in a belief state which lacks any possible world in which P is false. Contradictory beliefs are necessary falsehoods, so let’s turn briefly to what he has to say about such matters.
Stalnaker discusses a problem for his view: if mathematical truths are necessary, then there can be no doubt about the truth of the propositions themselves. So, everyone must know that mathematical propositions which are necessarily true are true (or that those which are necessarily false are false). The problem, however, lies in our inability to know right away that some given mathematical statement which is necessarily true or false is true or false. Stalnaker locates the problem in the difficulty in our assessing which proposition is being expressed by a mathematical statement (especially if it is sufficiently complex). The objects of belief in these cases, then, are propositions about the relation between statements and what they say. Such a person’s belief, according to Stalnaker, would consist in a proposition about the relation between the statement, “God exists and God does not exist”, and the necessarily false proposition P and not P. Such a person (I am supposing) would know all the relevant information about that the relation between the statement and the false proposition. Their knowing this is not in doubt. But, just because their beliefs consist of propositions about the relation between the statement and the necessarily false proposition does not appear to explain anything about how a person can hold two contradictory beliefs. My suggestion is that there appears to be something wrong with his analysis of the content of beliefs in mathematical truths and falsehoods. And if we must rely on his previous concept of beliefs as properties of belief states, we are no better off. However, perhaps I have missed Stalnaker’s point, as may be evident, so perhaps this is not a problem for his view after all.
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