In his well-known 1980 paper “Externalist Theories of Empirical Knowledge” BonJour gives an internalist suggestion to the lottery paradox. The lottery paradox was previously thought to be an argument against internalism—the view that in order to be justified, an agent must have a cognitive grasp of the reason(s) why her belief is likely to be true.
In BonJour’s version of the lottery paradox, there are 100 lottery tickets, 1 of which will win and 99 of which will lose. A paradox results if one holds that a belief is adequately justified to satisfy the requirement of knowledge if there is a high probability of its truth and if one accepts the following two assumptions:
1. If one has adequate justification for believing each of a set of propositions, one also has adequate justification for believing the conjunction of the members of the set.
2. If one has adequate justification for believing a proposition, one also has adequate justification for believing any further proposition entailed by the first proposition (68).
If one holds that a person is justified in believing propositions that have a high probability of being true, then for each of the tickets, one is justified in believing that it will lose because for each ticket the probability that it will lose is 0.99. And if one is justified in believing that each will lose, then it follows that one is adequately justified in believing that no ticket will win which contradicts the given information.
This paradox has often thought to be an argument in favor of externalism:
It is at this point that externalism may seem to offer a way out. For an externalist position allows one to hold that the justification of an empirical belief must make it certain that the belief is true, while still escaping the clutches of skepticism. This is so precisely because the externalist justification need not be within the cognitive grasp of the believer or indeed of anyone. It need only be true that there is some description of the believer, however complex and practically unknowable it may be, which, together with some true law of nature, ensures the truth of the belief. (68)
BonJour, however, believes that there might be a way out for the internalist. He argues that the main problem for the lottery paradox is that the agent knows that at least one proposition in a set of highly probable propositions is false. He thinks it is necessary for justification for the agent not to know this. BonJour admits that his suggestion is incomplete but seems to be on the right track. I would like to propose two further conditions which need to be added to help solve some of the problems. Though I believe these conditions are necessary, they may not be sufficient. Additional conditions may need to be added and, in the end, we might find that an internalist account does not actually work to explain the lottery paradox.
The first worry that BonJour needs to address is a worry associated with conditions of lack of knowledge: the agent may be to blame for her lack of knowledge. Thus, the first condition that needs to be added is that it must be the case that the agent does not lack knowledge that the proposition is in a set of possibilities, one of which will be realized, due to her own irresponsibility.
Another condition that seems necessary is that the agent does not justifiably believe that the proposition is in a set of possibilities, one of which will be realized. Take the following examples:
Example 1: Harry buys a lottery ticket. There are 100 tickets sold and Harry believes that 1 of the tickets definitely will win. Harry believes that his ticket will not win.
Example 2: Lloyd buys a lottery ticket. There are 100 tickets sold and Lloyd believes that 1 of the tickets definitely will win. Lloyd believes that his ticket will not win.
Note that so far these cases are the same in the relevant ways (the only difference is the names), and that they are both instances of BonJour’s lottery paradox. Now suppose that the lottery Harry has chosen to play is legitimate. There will, in fact, be 99 losing tickets and 1 winning ticket. The lottery Lloyd has chosen to play, however, is a scam and no one’s ticket will actually win, and the person in charge of the lottery is the only one who knows this. Let’s further suppose that Harry and Lloyd both have the same strong evidence for their belief that there will be 1 winner in their chosen lottery: they were told by many extremely reliable sources that there will be 1 winner. According to the internalist account, Harry and Lloyd both would be justified in their beliefs that 1 ticket will win in their specified lottery. However, Harry knows that 1 ticket will win in his lottery case and Lloyd does not know in his lottery case (because in Lloyd’s case it is not true).
But if the required condition for being justified in the belief that one’s ticket will not win is lack of knowledge that the proposition is in a set of possibilities, one of which will be realized, then we will get a strange result concerning the justification of Harry and Lloyd’s beliefs about whether their tickets will lose. Lloyd will be justified in his belief that his ticket will not win because he does not know that one of the propositions in the set will be realized, and Harry will not be justified in believing that his ticket will not win because he does know that one of the propositions in the set will be realized. This seems false because they both have justified beliefs that 1 ticket in their lottery will win. Thus, I think that a stronger requirement than not having knowledge is necessary. In order to be justified in believing that p, the agent needs to not justifiably believe that the proposition p is in a set of possibilities, one of which will be realized. Since Harry and Lloyd both justifiably believe that one of the tickets in their particular lotteries will win, neither is adequately justified to satisfy the requirement for knowledge in believing that his ticket will not win.