Probably Possible

[In Part I, I raised a problem for the Lockean Thesis. In Part II, I considered, as well as rejected, a purported resolution of the problem. Here's Part III, in which I explain why the problem arises.]

Consider, once again, the following:

(1) I’m slightly more confident that B than that A, and I believe that A is equivalent to B.

(4) I’m slightly more confident that B than that A, and I’m 95% confident that A is equivalent to B.

Contrary to what one would expect were the Lockean Thesis true, (1) seems infelicitous, whereas (4) seems fine. Where lies the source of this intuition?

Let us first observe that the following sentence sounds as bad, if not worse, than (1):

(1k) I’m slightly more confident that B than that A, and I know that A is equivalent to B.

It seems that if one knows that A is equivalent to B, then one should be equally confident in the two. And if one is slightly more confident that A than that B, then upon reflecting on whether one knows that A is equivalent to B, one should believe that one doesn’t know it. [1]

Next, observe that belief is tied to knowledge in a way that degree of belief or degree of confidence is not. It seems, for example, that

(a) Whatever one believes, one knows.

serves as a better epistemic ideal than

(b) Whatever one is highly confident of, one knows.

Suppose Jack picks one ticket out of a million tickets in a fair lottery in which there’s just one winner. Jack, it seems, should be highly confident that he’ll lose. Nonetheless, there’s also an intuition that he doesn’t know that he’ll lose, and hence, shouldn’t believe that he will. Or suppose Jill knows that the chance of the radioactive atom decaying in the next hour is very high. It seems that she should be highly confident that it’ll decay. But given that there’s a chance that it won’t decay, there’s an intuition that Jill doesn’t know, and hence, shouldn’t believe that it’ll decay.

We can now try to explain why (1) sounds bad, but (4) sounds OK. Suppose I’m slightly more confident than A than that B. Then I don’t know that A is equivalent to B. By (a), I shouldn’t believe that A is equivalent to B, even though there needn’t be anything to stop me from being highly confident that the two are equivalent. Note that there’s a similar explanation why Jack seems to be epistemically worse off if

(2′) Jack is slightly more confident that Mark Twain wrote Huckleberry Finn than he is that Samuel Clemens wrote it, and he believes that Mark Twain is Samuel Clemens.

is true of him than if

(5′) Jack is slightly more confident that Mark Twain wrote Huckleberry Finn than he is that Samuel Clemens wrote it, and he’s 95% confident that Mark Twain is Samuel Clemens.

is true of him.

Now, you might disapprove of (a) as an epistemic ideal, thinking that it’s perfectly fine to believe things that you don’t know, so long as you’re justified in believing them. If so, then instead of comparing (a) with (b), compare

(c) Whatever one believes, one should, upon reflection, believe that one knows.[2]

with

(d) Whatever one is highly confident of, one should, upon reflection, believe that one knows.

According to (c), you don’t have to believe only those things you know, but whatever you believe, you should, upon reflection, take yourself to know. For suppose that upon reflection, you don’t believe that you know that p. The reason for this would seem to be that you don’t believe that you are justified in believing that p. But if you don’t believe that you’re justified in believing that p, then you shouldn’t believe that p.

(c), as an epistemic ideal, seems much more plausible than (d). Suppose Jack picks one ticket out of a million tickets in a fair lottery in which there’s just one winner. Suppose also that although Jack believes that the chance of losing is high, he wouldn’t, upon reflection, believe that he knows he will lose. It seems that although Jack should be highly confident that he’ll lose, he shouldn’t believe that he’ll. Or suppose that upon reflection, you wouldn’t believe that you know that there’ll be a hail storm tomorrow. Then it seems that you shouldn’t believe, although you might well be highly confident, that there’ll be a hail storm tomorrow.

Let’s try to explain the difference between (1) and (4) again. Suppose I’m slightly more confident that A than that B. Were I to reflect on whether I know that A is equivalent to B, I should believe that I don’t know it. But if so, then by (c), I shouldn’t believe that A and B are equivalent, even though there needn’t be anything to stop me from being highly confident that they are. Similar reasoning explains the difference between (2′) and (5′). Jack is slightly more confident that Mark Twain wrote Huckleberry Finn than he is that Samuel Clemens wrote it. Were he to reflect upon whether he knows that Mark Twain is Samuel Clemens, he shouldn’t believe that he knows. By (c), he shouldn’t believe, although he might well be highly confident, that Mark Twain is Samuel Clemens.
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[1] As wo pointed out, some have argued that knowledge doesn’t require certainty - might this allow one to know that A is equivalent to B without being equally confident in the two? Although one who isn’t certain that A is equivalent to B might well be more confident of one than the other, I’m inclined to think that this is so only if one doesn’t know that A is equivalent to B. If one knows that A is equivalent to B, then whether such knowledge is accompanied by certainty or not, one should be equally confident in A and in B.

[2] Some version of this principle was put forward to me by Mike Pelczar a few years ago.

Posted by wenghong on 13th May 2007 under Credences, Probability, Rationality. Leave a response?