“The odds of that are something like two to the power of seven hundred and fifty million to one.”
As Eliezer admitted, it is a very bad idea to ascribe probabilities like this to real world propositions. I think that the strongest reason is that it is just too easy for the presuppositions to be false or for your thinking to have been mistaken. For example, if I gave a five line logical proof of something, that would supposedly mean that there is no chance that its conclusion is true given the premisses, but actually the chance that I would make a logical error (even a transcription error somewhere) is at least on in a billion (~ 1 in 2^30). There is at least this much chance that either Elizer’s reasoning or the basic scientific assumptions were seriously flawed in some way. Given the chance of error in even the simplest logical arguments (let alone the larger chance that the presuppositions about genes etc are false), we really shouldn’t ascribe probabilities smaller than 1 in a billion to factual claims at all. Better to say that the probability of this happening by chance given the scientific presuppositions is vanishingly small. Or that the probability of it happening by chance pretty much equals the probability of the presuppositions being false.
“The odds of that are something like two to the power of seven hundred and fifty million to one.”
As Eliezer admitted, it is a very bad idea to ascribe probabilities like this to real world propositions. I think that the strongest reason is that it is just too easy for the presuppositions to be false or for your thinking to have been mistaken. For example, if I gave a five line logical proof of something, that would supposedly mean that there is no chance that its conclusion is true given the premisses, but actually the chance that I would make a logical error (even a transcription error somewhere) is at least on in a billion (~ 1 in 2^30). There is at least this much chance that either Elizer’s reasoning or the basic scientific assumptions were seriously flawed in some way. Given the chance of error in even the simplest logical arguments (let alone the larger chance that the presuppositions about genes etc are false), we really shouldn’t ascribe probabilities smaller than 1 in a billion to factual claims at all. Better to say that the probability of this happening by chance given the scientific presuppositions is vanishingly small. Or that the probability of it happening by chance pretty much equals the probability of the presuppositions being false.
Toby.