Q&A: The Probability of a Miracle as a Refutation of the Witness Argument – Fifth Notebook
The Probability of a Miracle as a Refutation of the Witness Argument – Fifth Notebook
Question
Hello,
In the fifth notebook, the Rabbi mentions the story about a mother they wanted to put in prison on the claim that she had murdered her two children. From this he goes on to infer that if we do not know the components of the testimony, we cannot determine whether it is reasonable or unreasonable.
But there is an argument based on Bayes' formula that even if we assume a miracle is possible, in the end everyone agrees that it is very, very rare. If so, then even if we say that the witnesses to the occurrence of the miracle are very reliable, much more so than ordinary witnesses—for example, they make a mistake only once in 100,000 times—still, since the rarity of a miracle like the splitting of the Red Sea, for example, is one in a billion, then overall the chance that the witnesses are telling the truth is one in 10,000.
That is, everyone agrees that a miracle, by definition, is an event that is not at all common or widespread. If so, testimony about it, whose degree of reliability is known overall and is not as high as the frequency of the miracle, can never really "catch" the miracle and testify to it reliably.
You can see it here – https://aeon.co/essays/don-t-believe-in-miracles-until-you-ve-done-the-math
Answer
What I learned from the story is that when there is an improbable alternative, that does not mean we should not accept it. It depends on whether the alternative is more probable. Therefore, when making a decision, one must always compare alternatives. So too regarding the mother: although it is unlikely that two siblings would die of crib death, it is even less likely that a mother would murder her two children. I did not understand your wording, but it does not seem to me that it means what I wrote here.
The argument you brought here is Hume's argument, and I explain in the fifth notebook why it is mistaken, and at greater length in my book Truth and Unstable. So I do not understand what the question is.