“The fellow who sneers at our combined Bayes factor on the grounds that we are assuming independence appears to have overlooked the fact that we have an entire section discussing that very issue and offering, as far as I know, a new technical point in the literature concerning the question of whether assuming independence strengthens or weakens a case and relating this to the question of situations of duress.”—link
You don’t even need to read the article to see that 10^39 is just a silly number, but for those interested, it is obtained by assuming that the probability of each of the disciples believing in the Resurrection is independent of the probabilities for the other disciples. Despite the fact that the independence assumption is clearly nonsense, and they themselves describe it as a “first approximation”, they then go on to quote this 10^39 figure throughout the rest of the article, and in the interview.
Just from very quickly skimming the paper, what bentam said seems denotatively true but connotatively very incomplete, not totally untrue though.
McGrew argues that, assuming independence, the Bayes Factor would be 10^39, and they do use it throughout the paper. It is a silly number, and they do reach it by assuming independence—which is a ridiculous hypothesis.
bentam implies that, had they not done so, they would have reached a more sensible figure, and that by assuming the generous (to them) hypothesis in the paper, true they have not argued against the least convenient likely position for them, which makes the paper dismissible.
What they actually do is conclude that, the less independent the testimony of the apostles, the more likely the whole story is to be true, by virtue of the evidence going from the likelihood of the supposed apparent conviction of them to the likelihood of the event’s truth swamping out that of the evidence going the other way.
Yes, you read what I wrote correctly, and I didn’t misspeak. I think that’s what she’s saying.
So McGrew does her intellectual duty by arguing throughout the paper for what she believes to be the lower bounds of the Bayes Factor, the true least convenient possible world, contrary to as implied by bentam.
She’s not arguing dishonestly, so she has to compensate with unreasonable assumptions that lead to conclusions like 10^39 being the lower bound.
Lydia McGrew addresses your post saying:
Just from very quickly skimming the paper, what bentam said seems denotatively true but connotatively very incomplete, not totally untrue though.
McGrew argues that, assuming independence, the Bayes Factor would be 10^39, and they do use it throughout the paper. It is a silly number, and they do reach it by assuming independence—which is a ridiculous hypothesis.
bentam implies that, had they not done so, they would have reached a more sensible figure, and that by assuming the generous (to them) hypothesis in the paper, true they have not argued against the least convenient likely position for them, which makes the paper dismissible.
What they actually do is conclude that, the less independent the testimony of the apostles, the more likely the whole story is to be true, by virtue of the evidence going from the likelihood of the supposed apparent conviction of them to the likelihood of the event’s truth swamping out that of the evidence going the other way.
Yes, you read what I wrote correctly, and I didn’t misspeak. I think that’s what she’s saying.
So McGrew does her intellectual duty by arguing throughout the paper for what she believes to be the lower bounds of the Bayes Factor, the true least convenient possible world, contrary to as implied by bentam.
She’s not arguing dishonestly, so she has to compensate with unreasonable assumptions that lead to conclusions like 10^39 being the lower bound.