What type of semantics can we give ‘believe’/‘think’ that would explain the kind of behavior I outlined above? What do the semantic considerations above tell us, if anything, about the nature of the mental states we commonly call beliefs? I will go through a few proposals.
Believing as being sure
Some philosophers want to equate belief with certainty or probability one.Footnote 25 While it may be that certainty plays an essential role in our mental lives, my arguments here suggest that ‘be certain’ is not even a contextually possible meaning of ‘believe’. For this reason, I think it is a mistake to use the English verb ‘believe’ as a philosophical term for the state of being sure or certain.
Here is Foley (1992) explicating a classic version of the Lockean thesis:
To say that we believe a proposition is just to say that we are sufficiently confident of its truth for our attitude to be one of belief. Then it is epistemically rational for us to believe a proposition just in case it is epistemically rational for us to have sufficiently high degree of confidence in it, sufficiently high to make our attitude towards it one of belief.
This view equates belief with having sufficient confidence in a proposition. HRS argue that the behavior of the word ‘believe’ would seem to support such a Lockean view as long as the threshold is sufficiently low to account for the data. In particular, while the threshold may exhibit some context sensitivity, some of the cases above show that in many cases we cannot access a reading of ‘believe’ with a high threshold, even where it is strongly favored by context.
There are a number of unresolved problems facing the Lockean view, however, perhaps the most pressing being the failure of closure (Kyburg 1961). It seems, after all, a basic datum of natural language inference that belief is closed under conjunction:Footnote 26
? John believes it will rain today and he believes it will rain tomorrow, but he doesn’t believe it will rain today and tomorrow.
Another worry about the Lockean view comes from considering epistemic contradictions involving belief. Both (37) and (38-b) sound as though they attribute contradictory beliefs to John.Footnote 27
? John thinks [it’s raining but it might not be raining].
John thinks/believes it’s raining but he knows/realizes/acknowledges it might not be.
? John thinks it’s raining but he thinks it might not be raining.
The Lockean needs to explain why these examples sound contradictory: To believe might not-p seems generally just to require having not-p being compatible with one’s belief.Footnote 28 Then if believing p only requires believing p is likely, it should be possible to both believe p and believe that p might not be true. Luckily Beddor and Goldstein (2017) have already done the work of explaining why (37) is bad despite belief being weak. However, what explains the contrast between (38-a) and (38-b) remains an open question and a pressing one for the Lockean.Footnote 29
Knowledge first (belief last)
Here is Williamson’s description of his knowledge-first account of belief.
...to believe p is to treat p as if one knew p—that is, to treat p in ways similar to the ways in which subjects treat propositions which they know. In particular, a factive propositional attitude to a proposition is characteristically associated with reliance on it as a premise in practical reasoning, for good functional reasons; such reliance is crucial to belief. A creature which lacks a concept of knowing can still treat a proposition in ways in which it treats propositions which it knows. The primitive creature does not treat the proposition that food is present like that when merely desiring that food is present; it does not use the proposition as a premise in practical reasoning. By contrast, the person who genuinely believes that there is a god by a leap of faith does rely on that premise in such reasoning. The unconfident examinee who tentatively gives p as an answer is little disposed to rely on p as a premise, and for that reason does not clearly believe p, but for the same reason does not clearly know p. Although a full-blown exact conceptual analysis of believes in terms of knows is too much to expect, we can still postulate a looser connection along these lines. (Williamson 2000, pp. 46–47)
One feature of this view which HRS picked out to criticize is Williamson’s claim that knowledge is the ‘norm’ of ‘believe’ (i.e. believe p only if you know that p). We pointed out that this view seemed improbable since it does not suggest any form of error or irrationality to both attribute a belief to an individual and deny that they know it.
John doesn’t know Bill is his friend, but he believes he is.
Rather (39) simply seems to say, on one prominent reading, that John lacks the kind of evidence or confidence necessary for knowledge. In this example, then, whatever state we are attributing to John is not one of which knowledge could be the norm of. Thus at least some attributions of belief appear to be attributing a different kind of state from the one Williamson describes.
Williamson (2018) has responded to many of the arguments in HRS, conceding in effect that there is a use of ‘believe p’ in which it expresses a relatively weak form of commitment (presumably rationally compatible with taking oneself not to know p). However, Williamson insists that ‘believe’ can and often does express the stronger ‘full belief’ or ‘outright belief’ of his knowledge-first account. While Williamson does not think full belief in p requires certainty in p in the usual sense, it would seem to be incompatible with taking oneself not to know p. There does not seem to me to be good evidence that ‘believe’ gets to have such a strong reading.
To support his view, Williamson suggests that our locution ‘fully believe’ directly expresses the paradigmatic state of outright belief that comes out of his knowledge-first account. However, consideration of actual usage of ‘fully believe’, I think, tells against this suggestion. Consider (40):Footnote 30
Amanda doesn’t know Peter will come home, but she fully believes he will.
As far as I understand it, Williamson takes full belief in p to be a state in which one accepts p to the same extent that one would accept p if one knew p. However, as I read (40) it is attributing to Amanda a belief which self-consciously lacks the normal support enjoyed by knowledge.Footnote 31 Similarly a first person case is no admission of irrationality:
I don’t know Peter will come, but I fully believe it.
More generally, I worry that Williamson’s account has too little to say about the semantics of ‘believe’ to give a satisfying explanation of its behavior. For instance, if ‘believing p’ expresses as its primary meaning a commitment to p similar to the commitment we would have if we knew p, it is mysterious why it should be so easy to use ‘believing p’ to express a relatively weak state such as merely thinking p likely. Williamson (2018) argues these weaker states are similar to knowledge states, but he gives no particular account of why ‘believe’ should express the particular range of states that it does.Footnote 32\(^,\)Footnote 33 Thus, even if believing does involve being in knowledge-like states, this connection does little to explain how we talk about belief. The Lockean view, by contrast, directly explains why belief attributions are true of those propositions that we think more likely than not: as on the Lockean view that is just what ‘believe’ means.Footnote 34