LESSWRONG
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Yes, Virginia, You Can Be 99.99% (Or More!) Certain That 53 Is Prime
ActionItem10

Craig is just purposely conflating the likelihood of a particular result and the likelihood of given the declaration of a result by the lottery officials, that result being true.

If you and I are flipping coins for a million dollars, it's going to take a lot of convincing evidence that I lost the coin flip before I pay up. You just cannot flip the coin in another room where I can't even see, and then expect me to pay up because, well, the probability of heads is 50% and I shouldn't be so surprised to learn that I lost.

Therefore, the actual likelihood of a p... (read more)

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1wizzwizz4
A second, detailed reading might make it seem like this comment's has an error. However, the reasoning is sound; "you said the coin was heads" doesn't distinguish very well between "the coin was heads" and "the coin was tails but you lied about the bet", so doesn't provide much evidence. Likewise, the dismissing of hearsay appears to be an error, but remember that humans have finite computational power. If you take into account (at least) the hypothesis that somebody's trying to deceive you about reality, you effectively end up dismissing the evidence anyway – but then you need to keep track of an extra hypothesis for the rest of your life to avoid scatterings of hearsay consistently nudging up your probability estimate when that's not really founded. (This is assuming that it's cheap to manufacture hearsay; expensive-to-manufacture hearsay shouldn't be dismissed so lightly.)
No Universally Compelling Arguments in Math or Science
ActionItem00

I am at a loss about the true meaning of a "universally compelling argument", but from Eliezer's original post and from references to things such as modus ponens itself, I understood it to mean something that is able to overcome even seemingly axiomatic differences between two (otherwise rational) agents. In this scenario, an agent may accept modus ponens, but if they do, they're at least required to use it consistently. For instance, a mathematician of the constructivist persuasion denies the law of the excluded middle, but if he's using it in a... (read more)

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No Universally Compelling Arguments in Math or Science
ActionItem00

Nitpicking: Modus ponens is not about "deriving". It's about B being true. (Your description matches the provability relation, the "|-" operator.) It's not clear how "fundamental" modus ponens it is. You can make up new logics without that connective and other exotic connectives (such as those in modal logics). Then, you'd ask yourself what to do with them... Speaking of relevance, even the standard connectives are not very useful by themselves. We get a lot of power from non-logical axioms, with a lot of handwaving about how ... (read more)

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0ChrisHallquist
Well, if they're logically inconsistent, but nothing you can say to them will convince to give up YECism in order to stop being logically inconsistent... then that particular chain of reasoning, at least, isn't universally compelling. Or, if they have an undefeatable hypothesis, if that's literally true... doesn't that mean no argument is going to be compelling to them? Maybe you're thinking "compelling" means what ought to be compelling, rather than what actually convinces people, when the latter meaning is how Eliezer and I are using it?