Friday, May 30, 2008

Lotteries and the norm of belief

Correct me if I'm wrong. At the very least, try to correct me if you think I'm wrong.

(1) To use lottery propositions to motivate the knowledge account of belief, we have to assume:

(A1) Beliefs in lottery propositions won't constitute knowledge (assuming that the grounds for such beliefs do not include insider's information).
(A2) You oughtn't believe what you don't know.

(2) If you accept single-premise closure, you have to say that overt and covert lottery beliefs share the same epistemic status (i.e., that either both constitute knowledge or neither do). By 'overt lottery belief', I mean a belief in a lottery proposition (e.g., the belief that I'll lose tomorrow's lottery). By 'covert lottery belief', I mean a belief whose truth depends on the outcome of a lottery proposition when this isn't known to the believer (e.g., the belief that I'll not be able to go on safari held by a subject whose friend has just slipped a lottery ticket into his coat pocket).

(3) If you think that safety is necessary for knowledge, you have to say that overt and covert lottery beliefs share the same epistemic status (i.e., that either both constitute knowledge or neither do).

If (1)-(3) are correct, and I think they are, then we ought to ask the further question as to whether (4) is true:

(4) Overt and covert lottery beliefs share the same deontic status (i.e., either beliefs are both types may be permissibly held or neither may).

I take it that if you buy into the knowledge account, (4) is a consequence of (1)-(3). However, I take it that the following goes against our ordinary intuitions:

(5) You ought never believe if the belief that p is a covert lottery belief.

If we reject (5), we can only retain (A2) by rejecting (A1). That undercuts one of the primary motivations for the knowledge account. If we reject (5), we can only accept (4) by rejecting (A1). If we reject (4), we have to reject both (2) and (3) and that comes at a mighty high cost. It's an ad hominem argument, but the main defenders of the knowledge account tend to accept (2) and I think offer (3) as an essential part of their explanation as to why overt lottery beliefs do not constitute knowledge. Myself, I'm happy to accept the disjunction of (4) and (5) and use that as the basis of an attack on the knowledge account.

(Q1) Am I alone in thinking that intuition speaks in favor of (5)?
(Q2) Am I right in thinking that (2) and (3) are true?

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