Will_Sawin comments on Yes, Virginia, You Can Be 99.99% (Or More!) Certain That 53 Is Prime - Less Wrong

38 Post author: ChrisHallquist 07 November 2013 07:45AM

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Comment author: CarlShulman 08 November 2013 12:46:41AM *  8 points [-]

Christian apologist William Lane Craig claims the skeptical slogan "extraordinary claims require extraordinary evidence" is contradicted by probability theory, because it actually wouldn't take all that much evidence to convince us that, for example, "the numbers chosen in last night's lottery were 4, 2, 9, 7, 8 and 3." The correct response to this argument is to say that the prior probability of a miracle occurring is orders of magnitude smaller than mere one in a million odds.

This only talks about the probability of the evidence given the truth of the hypothesis, but ignores the probability of the evidence given its falsity. For a variety of reasons, fake claims of miracles are far more common than fake TV announcements of the lottery numbers, which drastically reduces the likelihood ratio you get from the miracle claim relative to the lotto announcement.

The specific miracle also has lower prior probability (miracles are possible+this specific miracle's details), but that's not the only issue.

Comment author: Will_Sawin 09 November 2013 10:39:15PM 6 points [-]

Even if true announcments are just 9 times more likely than false announcements, then a true announcment should raise your confidence that the lottery numbers were 4 2 9 7 9 3 to 90%. This is because the probability P (429783 announced | 429783 is the number) is just the probability of a true announcement, but the probability P( 429783 announced | 429783 is not the number) is the probability of a false announcement, divided by a million.

A false announcer would have little reason to fake the number 429793. This already completely annihilates the prior probability.