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 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.