What is meant by saying in ordinary language that someone s believes some proposition p is not always clear. But what is normally meant (and what I have understood by ‘belief’ so far) is, I suggest, that in s's view the world is more probably one in which p is true than one in which any alternative is true, i.e. s believes p to be more probable than any alternative. I suggest that the primary concept of belief is believing this proposition as against this alternative. My grounds for this suggestion is that sometimes agents are unclear about what is meant by saying that they believe some proposition, until belief is spelled out in this way; and, as we shall see, this relative belief is the concept of belief which is
75 Sometimes a person will say that he does ‘not know what he believes’ about some matter. That assertion is, I suggest, to be taken as an assertion that he is not aware of
himself as having a belief about some matter that things are this way rather than that way; and so, it follows, he does not believe one proposition about the matter rather than its negation.
76 Two recent writers have given similar accounts, very different from the one above, of the relation between an agent's beliefs and his judgement as to what are his beliefs.
According to John Vickers (‘Judgement and Belief’ in (ed.) K. Lambert, The Logical Way of Doing Things, Yale University Press, New Haven, 1969) and D. H. Mellor (‘Consciousness and Degrees of Belief’ in (ed.) D. H. Mellor, Prospects for Pragmatism, Cambridge University Press, 1980) belief is something manifest in public behaviour, while the agent's ‘judgements’ or ‘assents’ are his views expressed to himself or publicly about that pattern of public behaviour. We have seen, however, that mere public behaviour will not show an agent's beliefs. We would use an agent's judgements as further evidence of his beliefs to the pattern of his public behaviour. Another difficulty with their view is that while any discrepancy between what an agent says about his own beliefs and the belief manifest in behaviour seems strong evidence of deceit or self- deceit, there is no reason on this account why it should do. It is simply misobservation or misinterpretation of public behaviour—which, like any other misobservation or misinterpretation of the public, may be quite lacking in any such self-deceit.
manifested in action—which is why agents have a clearer grasp upon it.
The normal alternative with which a belief is contrasted is its negation. The negation of a proposition p is the proposition not-p or ‘it is not the case that p’. The negation of ‘today is Monday’ is ‘it is not the case that today is Monday’ or ‘today is not Monday’. Normally to believe that p is to believe that p is more probable than not-p. To believe that Labour will win the next general election is normally to believe that it is more probable that Labour will win than that they will not win. In other words, normally, I suggest, to believe that p is to believe that p is probable (i.e. has a probability of greater than ½; and so not-p has a probability of less than ½). (I understand p being certain as an extreme case of p being probable; it is p having a probability of 1 or close thereto.) What can be said in favour of this claim? To start with, if I do not believe that p is probable, I cannot believe that p is true. If I believe that it is more probable that not-p than that p, I cannot believe that p. Examples bear this out. If I believe that it is not probable that Liverpool will win the cup then (barring considerations to be discussed below, arising, from the existence of a number of alternatives) I cannot believe that they will win. But what about the other way round? Suppose that I do believe that
p is probable. Must I believe that p? Clearly, if either I am to believe that p or I am to believe that not-p, I must believe
the former. But might I not believe that p is probable without believing that p or believing not-p? If I believe that p is very, very probable, surely I believe that p. Cases where we would say the former are always cases where we would say the latter. If I believe that it is very, very probable that Liverpool will win the FA Cup, then I believe that Liverpool will win. The only difficulty arises when I believe that p is marginally more probable than not. Here we might be hesitant about whether to say that I believe that p. The hesitation arises not from ignorance about any unobserved matters, but because the rules for the application of the concept of belief are not sufficiently precise. Maybe some men do use ‘believe’ so that s has to believe that p is significantly more probable than not if s is to believe that p. But certainly others are prepared to allow that s believes that p if s believes merely that p is marginally more probable than not. It seems tidier to follow this latter usage. For, if we do not follow this usage, there would have to be some value of probability θ between
½ and 1, such that only if a man believed that p had a probability greater than θ would he believe that p. But any value chosen for θ would be extremely arbitrary. I conclude that although our ordinary rules for the use of words may not be sufficiently precise for my suggestion to be clearly analytic (i.e. to bring out our current understanding of the concept of belief), there is a case, if we are to have a clear concept of ‘believe’, for tightening up usage so that the words of my suggestion do now express a logically necessary truth.
Although normally the sole alternative to a belief that p is its negation, sometimes there will be other alternatives. This will be the case where p is one of a number of alternatives being considered in a certain context. In that case to believe that p will be to believe that p is more probable than any one of these alternatives (but not necessarily more probable than the disjunction of the alternatives). Sometimes, if in answer to a question ‘Who do you believe will win the election?’ I reply ‘Labour’ I may mean simply that I believe that it is more probable that Labour will win than that the Conservatives will win; and that it is more probable that Labour will win than that the SDP-Liberal Alliance will win, and more probable that Labour will win than that no party will win. I may believe these things without believing that it is more probable that Labour will win than that they will not win (and so that election will have some other, I know not what, result). Again, the belief that Liverpool will win the Cup may be the normal strong belief that it is more probable that Liverpool will win the Cup than that they will not, but it may be simply the weak belief that it is more probable that Liverpool will win than that Leeds will win, and more probable that Liverpool will win than that Aston Villa will win. And so on. But certainly normally to believe that p is to believe that p is more probable than not-p.