Tuesday, July 20, 2010

More objections to E = K

Rizzieri (forthcoming) presents a number of objections to Williamson’s claim that your evidence consists of all and only the propositions that you know (E=K). I think his criticisms of Williamson miss their mark.

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.

This entails:

(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:

(6) p.

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.


Jonathan Birch said...

Rizzieri plays on the intuition that, when you go over to your door and give the lock a quick twist to the left, you thereby obtain some evidence that no one can open the door.

This much is surely correct. But I think Rizzieri errs in claiming that this evidence is constituted by the false proposition LD. It's actually constituted by the true proposition (LD*) that a procedure which usually succeeds in locking the door has just taken place.

You do know LD*, so E=K is unthreatened.

Clayton said...

I think that's exactly right. To block this sort of move, I think he's going to try to make some points about the basis of your belief and might move to cases of more widespread error. But, I think he's playing with fire. I think it's always going to be more likely that the assumptions about justification he needs are more dubious than the claim he's attacking.

Anonymous said...

You claim that if 1) is true, so is 2). What's the ground for this claim?

I would think that someone who insists that false propositions can count as evidence would simply deny that 1) entails 2). More generally, such a person would probably say that instances of 4) don't entail instances of 5), and hence wouldn't be troubled by this argument.

But maybe I'm missing something...

Clayton said...

Hey Anon,

I'm not sure what R's view is, but in the paper he tries to use W's view that evidence raises the probability of what it is evidence for. So, the thought is this:

(i) p is evidence for q only if p "speaks in favor" of q. W cashes this out as follows:
"At least as a first approximation, we can model the first condition in probabilistic terms: e should raise the probability of h. That is, the probability of h conditional on e should be higher than the unconditional probability of h; in symbols, P(h|e) > P(h)."

(ii) When these conditions are met, there is a support fact to be explained and something that explains the support fact. The thing to be explained--why is q's probability raised. The thing that explains it--that p.

I think to deny the inference from (1) to (2), you'd have to deny that evidence explains something. You'd have to deny that p is evidence for q only if p explains a support fact concerning q (i.e., that something "speaks in favor of" q).