The Pope

Originally posted by bbarr
Close enough to the Lottery paradox to suffer from the same failing.

[b]It seems to me that the union of justified beliefs should also be justified...

This is a version of the dubious closure principle I was referring to earlier. Make the relevant probabilities explicit in the beliefs above and see if the same putative paradox follows.

EDIT: H ...[text shortened]... n false is sufficient for justification? I was presenting that as merely a necessary condition.[/b]

Are you saying that the union of justified beliefs is not necessarily justified itself?

Originally posted by bbarr

EDIT: Have I claimed that showing a belief more likely true than false is sufficient for justification? I was presenting that as merely a necessary condition.

Would you humor me with the sufficient conditions? I took your response to LH to be both a necessary and sufficient condition.

Originally posted by DoctorScribbles
Are you saying that the union of justified beliefs is not necessarily justified itself?

Suppose you have a lottery with a million tickets. For each ticket, there is a .000001% chance that it will win. If it is the case then one can be justified in believing P without being certain of P, then it is likely that one can be justified in believing of any particular ticket that it will not win (as we can, by increasing the number of tickets in the example, get as close to certainty as we wish). But, of course, one cannot be justified in believing that no ticket will win, for one ticket surely will.

So, how do you think we should deal with this apparent paradox? We could deny that the inference from "it is .000001 likely that X will win" to "X will not win" is justified. This would also work with your ball example and with all examples of this sort.

Alternatively, we could deny that being justified in believing that P is sufficient for being justified in believing all the deductive consequences of P.

Originally posted by DoctorScribbles
Would you humor me with the sufficient conditions? I took your response to LH to be both a necessary and sufficient condition.

No, I will not humor you with the sufficient conditions. If you and Lucifer want sufficient conditions, we'll have to arrive at them together. I'm not your philosophical trick monkey, dammit!

Originally posted by bbarr

So, how do you think we should deal with this apparent paradox? We could deny that the inference from "it is .000001 likely that X will win" to "X will not win" is justified. This would also work with your ball example and with all ex ...[text shortened]... justified in believing all the deductive consequences of P.

Of the two alternatives you present, the first seems more appealing to me.

The latter denial seems like a worse option because the essential power of deduction is mechanical preservation of truth. To take this away from deduction -- to allow for true premises, valid deduction, and false conclusions -- is a serious crippling of a powerful tool.

The former denial seems like a better option because to infer "X will not win" from "X will very likely not win" is clearly a non sequitur -- you just get lucky in being right most of the time, but you're guaranteed to eventually be wrong. In the lottery example, if all the lottery players accept your criterion, you are certainly dooming one of them to get the short end of the belief stick, even though that person gets the money and thus may not give a rat's ass about being shafted by his belief system.

Originally posted by DoctorScribbles
Of the two alternatives you present, the first seems more appealing to me.

The latter denial seems like a worse option because the essential power of deduction is mechanical preservation of truth. To take this away from deduction -- to allow for true premises, valid deduction, and false conclusions -- is a serious crippling of a powerful tool.....

I think the main weakness of deductive logic is it can never be used to justify the belief in future events - no matter how likely they are.

The weakness of inductive logic is it will always be deductively fallacious - and rarely supplied a solid justification of belief.

Originally posted by Coletti
I think the main weakness of deductive logic is it can never be used to justify the belief in future events - no matter how likely they are.

The weakness of inductive logic is it will always be deductively fallacious - and rarely supplied a solid justification of belief.

Is it a weakness of my coffee that it doesn't taste like scotch? Each has a role for which it is suited.