Thursday, January 31, 2008

Lotteries, closure, and conjunctive beliefs

There's a nice thread developing at FQI concerning lottery propositions and conjunctive beliefs. Suppose we have a 1,000,000 ticket lottery with a guaranteed winner. We ought to grant:

(A1) It would be irrational to believe all tickets in the lottery will be losers.

Now, consider:
(1) Henry is justified in believing that his ticket (t1) will lose.
(2) If Henry is justified in believing that t1 will lose, then Henry is justified in believing that t2 will lose, … , Henry is justified in believing that t1,000,000 will lose.

Therefore,

(3) Henry is justified in believing that t1 will lose, Henry is justified in believing that t2 will lose, … , Henry is justified in believing that t1,000,000 will lose.
(4) If Henry is justified in believing that t1 will lose, Henry is justified in believing that t2 will lose, … , Henry is justified in believing that t1,000,000 will lose, then Henry is justified in believing that t1, t2, t3, … , and t1,000,000 will lose (JC).

Therefore,

(5) Henry is justified in believing that t1, t2, t3, … , and t1,000,000 will lose.
(6) Henry is not justified in believing that t1, t2, t3, … , and t1,000,000 will lose (since he knows one ticket must win).

Therefore,

(7) Both Henry is justified in believing that t1, t2, t3, … , and t1,000,000 will lose, and Henry is not justified in believing that t1, t2, t3, … , and t1,000,000 will lose.
(8) On pain of contradiction, then, either (1), (2), (4), (6), or (7) is false.

I'm all for denying (1), but JD, Tim, and Trent seem to want to deny the closure principles that commit us to the contradiction.

Consider this exchange:
Adam: Zach will be at the party.
Ben: Who else will we know at the party?
Adam: Yolanda will be at the party.
Ben: Got it.

Ben: Chris, Adam believes that Zach and Yolanda will be at the party.
Adam: Wait! I don’t believe that.
Ben: But you said…
Adam: I said Zach will be at the party …
Ben: And you believe that, yes?
Adam: Yes. I was sincere. I also said Yolanda will be at the party.
Ben: And you were sincere in saying that as well?
Adam: Yes. But, I never said I believed Zach and Yolanda would be at the party. Listen carefully. Zach will be at the party and I’m not wrong to believe that. Yolanda will be at the party and I’m not wrong to believe that. However, it would be epistemically imprudent to believe that both Yolanda and Zach will be at the party.

An argument.
(1) Adam is out of his mind.
(2) You cannot be out of your mind _and_ epistemically rational.
(3) There is no relevant difference between Adam's firm refusal to accept the conjunction of two beliefs neither of which he will give up and the refusal of someone who believes of tickets t1 - tn that each will lose without believing the collection contains nothing but losers.

Therefore,

(4) Even if we do not assume that closure holds in full generality, insisting that the lottery case is the counterexample to closure is costly. There is no apparent explanation as to why this subject seems so completely off his nut except that now is not the time for him to refuse to accept conjunctions while refusing to suspend judgment as to either conjunct.

Tuesday, January 29, 2008

Alston on the factivity of justification

He writes:
If goodness from an epistemic point of view is what we are interested in, why shouldn't we identify justification with truth, at least extensionally? If the name of the game is the maximization of truth and the minimization of falsity in our beliefs, then plain unvarnished truth is hard to beat. This consideration, however, has not moved epistemologists to identify justification with truth ... But why should this be? It is obvious that a belief might be [deontically justified] without being true ... but what reason is there for taking [evaluative justification] to be independent of truth? I think the answer to this has to be in terms of the "internalist" character of justification. When we ask whether S is justified in believing ... we are ... asking a question from the standpoint of an aim at truth; but we are not asking whether things are in fact as S believes. We are getting at something more "internal" to S's "perspective on the world" ... With respect to [evaluative justification] the analogous point is that although this is goodness vis-a-vis the aim of truth, it consists not in the beliefs fitting the way the facts actually are, but something more like the belief's being true "so far as the subject can tell from what is available to the subject". In asking whether S is [evaluative] justified in believing that p, we are asking whether the truth of p is strongly indicated by what S has to go on; whether, given what S had to go on, it is at least quite likely that p is true. We want to know whether S had adequate grounds for believing that p, where adequate grounds are those sufficiently indicative of the truth of p. (1989:99)

There's a lot packed into this.

I've seen no explanation as to why a false belief might be deontically justified. Let that pass. I think it's funny for Alston to press this 'not internal enough' complaint in arguing that the justified belief need not be true. Leafing through the pages of Epistemic Justification, we see Alston frequently formulates perspectival internalism as follows:

PI: Justification is internal in that it depends on what support is available from "within the subject's perspective", in the sense of what the subject knows or justifiably believes about the world (1989: 107)

If you have a justified belief concerning any proposition, is that not a justified belief that the proposition in question is true? I don't see any inconsistency between the claim that justification is internal in the sense outlined by PI and the claim that there are no false, justified beliefs. If your belief concerning p is justified and that belief just is the belief that p is true, the truth of the relevant proposition is internal or "within the subject's perspective". If, however, the subject's belief concerning p is not justified, the truth of p is not internal or "within the subject's perspective". On its face, it seems that insisting that all justified beliefs are, among other things, true beliefs is consistent with perspectival internalism. So, how's truth not internal enough?

It seems that while truth might count as internal according to PI, adequacy of grounds as understood in the way that Alston does would not count as internal. While the grounds might count as internal, their adequacy would not since their adequacy would require that those grounds generally lead to the truth. I think the 'internal enough' stick is an odd one for Alston to use on those who would say that truth is necessary for justified belief.

Monday, January 28, 2008

Aaron Burr and George Hamilton

A friend thought that I had tried to erase all record of the blog. Not so. I was tired of seeing people arrive at this page by googling an ex's name, so I erased everything. Nothing of importance was lost. I've already written up everything that I thought needed to be written up.

I'm not quite ready to get back to proper philosophy blogging. I thought I'd post this little gem:

The narrator is pretty much what would happen if you spliced my genes with Ryan Prewitt's and added liberal doses of scotch. Thanks to Brent for the link.