Elizer, your post above strikes me, at least, as a restatement of verificationism: roughly, the view that the truth of a claim is the set of observations that it predicts. While this view enjoyed considerable popularity in the first part of the last century (and has notable antecedents going back into the early 18th century), it faces considerable conceptual hurdles, all of which have been extensively discussed in philosophical circles. One of the most prominent (and noteworthy in light of some of your other views) is the conflict between verificationism and scientific realism: that is, the presumption that science is more than mere data-predictive modeling, but the discovery of how the world really is. See also here and here.

I have to bet on every possible claim I (or any sentient entity capable of propositional attitudes in the universe) might entertain as a belief? That is highly implausible as a descriptive claim. Consider the claim "Xinwei has string in his pockets" (where Xinwei is a Chinese male I've never met). I have no choice but to assign probability to that claim? And all other claims, from "language is the house of being" to "a proof for Goldbach's conjecture will be found by an unaided human mind"? If Eliezer offers me a million dollars to bet on someone's pocket-contents, then, yes, if the utility is right, I will calculate probabilities, meager though my access to evidence may be. But that is not life. The null action may be an action, but lack of belief is not a belief. "I've never thought about it" is not equivalent to "it's false" or "it's very improbable".

(Did Neanderthals assign probabilities, or was it a module that emerged at about the same time as the FOXP gene? Or did it have to wait until the invention of games of chance in western Europe? Is someone who refuses to bet on anything for religious reasons ipso facto irrational?)

And you don't take the belief "2 + 2 = 4" as having probability of 1? Nor "2 + 2 = 5" as 0?

I'm off, out of ISP range for a day, so I won't reply for a bit. Cheers.

By "suspending judgment" I mean neither accepting a claim as true, nor rejecting it as false. Claims about the probability of a given claim being true, helpful as they may be in many cases, are distinct from the claim itself. So, pdf, when you say "The proper attitude towards the claim "Rooney has string in his pockets" is that it has about an X% chance of being true", where X is unknown, I don't see how this is materially different from saying "I don't know if Rooney has string in his pockets", which is to say that you are (for the moment at least) suspending judgment about whether the claim (call it 'string') is true or false. And where X is estimated (on the basis of some hypothetical evidence) to be (say) .4, what is the proper attitude toward 'string'? Saying "'string' has a 40% chance of being true" doesn't answer the question, it makes a different claim, assigning probability. In such situations, the rational course of action is to suspend judgment about 'string'. You may of course hold beliefs about the probability of 'string' being true and act on those beliefs accordingly (by placing real or hypothetical bets, etc.), but in such cases you're neither accepting nor rejecting 'string'.

Eliezer, I think we are misunderstanding each other, possibly merely about terminology.

When you (and pdf) say "reject", I am taking you to mean "regard as false". I may be mistaken about that.

I would hope that you don't mean that, for if so, your claim that "no evidence in favor -> almost always false" seems bound to lead to massive errors. For example, you have no evidence in favor of the claim "Rooney has string in his pockets". But you wouldn't on such grounds aver that such a claim is almost certainly false. The appropriate response would be to suspend judgment, i.e., to neither reject nor accept. Perhaps I am not understanding what counts as a suitably "complicated" belief.

As for Archimedes meeting Bell's theorem, perhaps it was too counter-factual an example. However, I wouldn't say it's comparable to the "high utility" of the winning lottery ticket: it the case of the lottery, the relevant probabilities are known. By contrast, Archimedes (supposing he were able to understand the theorem) would be ignorant of any evidence to confirm or disconfirm it. Thus I would hope that he would refrain from rejecting it, merely regarding it as a puzzling vision from Zeus, perhaps.

Eliezer, I agree that exactly even balances of evidence are rare. However, I would think suspending judgment to be rational in many situations where the balance of evidence is not exactly even. For example, if I roll a die, it would hardly be rational to believe "it will not come up 5 or 6", despite the balance of evidence being in favor of such a belief. If you are willing to make >50% the threshold of rational belief, you will hold numerous false and contradictory beliefs.

Also, I have some doubt about your claim that when "there is no evidence in favor of a complicated proposed belief, it is almost always correct to reject it". If you proposed a complicated belief of 20th century physics (say, Bell's theorem) to Archimedes, he would be right to say he has no evidence in its favor. Nonetheless, it would not be correct for Archimedes to conclude that Bell's theorem is therefore false.

Perhaps I am misunderstanding you.

The error here is similar to one I see all the time in beginning philosophy students: when confronted with reasons to be skeptics, they instead become relativists. That is, where the rational conclusion is to suspend judgment about an issue, all too many people instead conclude that any judgment is as plausible as any other.