Disjunctions
Disjunctions create difficulties for many philosophical views. So, it is worth asking whether they create any special problems for the view that knowledge is to be understood in terms of adequate information.1
Suppose a fair coin has been flipped and lies covered on the back of S’s hand. Let P be that the flipped coin has landed heads and Q that it has landed tails. S does not believe P and does not believe Q, but she does believe (P or Q). Suppose it is P that is true, that is, the coin has landed heads. Although P is a truth that S lacks, we are not likely to regard this as preventing her from knowing the disjunction (P or Q), but why not?
The answer is that even without the information that P is true, S can have adequate information about the truth of the disjunction (P or Q). She is aware that P and Q are only two possibilities here and hence one or the other of them is true. In this respect, the case is analogous to a lottery case, where S knows that the lottery is fair and hence knows that either ticket T1 or ticket T2 . . . or ticket Tn will be the winning ticket without being aware of which specific ticket will win. Her not being aware which ticket will be the winner need not prevent her from having adequate information about the disjunction’s truth, given that she has lots of information about the workings of the lottery and why it is that one of the tickets must be the winner. What would be surprising to her and hence undermining of knowledge is if none of the tickets won, but one of ticket’s winning is just what she expects. And so it is with the coin case; S can have enough information to know that either heads has come up or tails has come up without being aware which is true.2
Among the lessons here is that it cannot be assumed that if one truth entails another, S’s being unaware of the former prevents her from knowing the latter. Conjunctions are the most obvious example. Let A be that Kuala Lumpur is the capital of Malaysia and B that Quito is the capital of Ecuador. The conjunction (A and B) entails A, but if S is aware of the truth of A but not the truth of B, (A and B) is not necessarily the kind of truth we would regard as preventing her from having adequate information about A. We see the connection between the two, of course, but when evaluating whether she knows A, we narrow our focus to it and accept that it is possible for her to know A without believing (A and B).
Disjunctions are merely another instance of this. If P is true and Q is false, then (P or Q) is true, but S’s not being aware of P does not necessarily prevent her from having adequate information about the disjunction (P or Q). Once again we see the connection, but we narrow our focus to (P or Q), not the truth P that entails it. Accordingly, as in the coin case, we think that S can have enough information to know (P or Q) even if she is unaware that it is P that is true.