Consider an example:
I believe that nobody can enter my office (O for now) because I believe that I have just locked the door (LD for now). Let us stipulate that I have inferred (O) from (LD). I pushed the lock in and gave it a quick twist to the left, which usually does the trick; however, my lock is damaged and does not work. Hence, (LD) is false.
About this example, Rizzieri remarks:
If Williamson’s proposal that (E = K) is correct then (LD) cannot serve as an evidential ground for (O). This generates problems for (E = K). The first difficulty is that it is very plausible that (LD) does partially constitute my evidence for (O). After all, I am justified in believing (LD), (LD) supports (O), and an explicit inference from (LD) is my most immediate basis or ground for (O).
It is hard to know what to make of this remark because it is hard to tell whether LD and O are propositions or propositional attitudes. If they are propositional attitudes, Williamson will (rightly) say that it is a category mistake to say that LD partially constitutes my evidence for O because beliefs do not partially constitute evidence for beliefs. Evidence consists of propositions.
Let’s fix this. Let’s say that the objection is this. LD is the proposition expressed by, ‘I have just locked the door’. O is the proposition expressed by, ‘Nobody can enter my office’. LD is supposed to be evidence for believing O. So, the worry is that Williamson has to deny:
(1) That I have just locked the door is evidence that nobody can enter my office.
If (1) is true, so is:
(2) Because my door is locked, it is more likely that nobody can enter my office than it would have been had my door been unlocked.
(3) My door is locked.
But, (3) is false. So, (1) must be false. So, Williamson has to deny something false.
Each of the cases involving false, justified beliefs face the same problem. In each such case, Rizzieri wants to say that the content of such beliefs is part of the subject’s evidence, but we know this is not so because the problem with his first objection generalizes. Suppose S justifiably believes p but p is false. If he says that p is part of S’s evidence for q, he has to say that this is true:
(4) That p is evidence that q.
In turn, he has to say that:
(5) Because p, q is more likely to be true.
In turn, this entails:
Owing to the factivity of ‘because’ and the further fact that evidence for has to explain why it is that the propositions it serves as evidence for are more likely than they would have been had things been different, (4) is true only if (6) is.