Waterman,
- It looks backwards to establish the probability of an hypothesis, given that a certain event has occurred.
Nope, try again. It determines the probability of a hypothesis
relative to another hypothesis, given that a certain event has happened.
E is our data, our event. It is that you exist and have a sense of self. H is the materialist hypothesis that E is an emergent property of the organism. ~H is all other hypotheses that aren't materialism. You wrongly believe ~H to be "immortality." But as so many statisticians have told you, ~H is not a single hypothesis. It is a set of hypotheses, not all of which can be true -- in fact, only one of which can be true -- and which don't all lead to immortality.
Two answers come out of Bayes: P(H|E) and P(~H|E). While these must sum to one, you wrongly consider P(~H|E) to be the probability that you have an immortal soul, given that you exist and have a sense of self. That is wrong. The probability of a specific claim like that is P(K|E), where K is one of the individual hypotheses that isn't materialism. K is a member of ~H, but it is not all of ~H. You have no basis for claiming P(K|E) is even an appreciably large portion of the vast outcomes you calculate must be ~H. You arrive at the conclusion that P(H|E) is very, very small, but you never compute P(K|E). You just assume it must be very large because it comes from a very large set. In fact it could be even smaller than P(H|E), but you wouldn't know that because you didn't compute it.
We know you know this.
There was a time when this lesson sank in, at least partially. There was a time when you took a stab at trying to formulate P(K|E) and P(L|E) and P(M|E) and basically all the individual, contradictory hypotheses that together make up the set ~H. But because you don't fundamentally understand how Bayesian inference works, you couldn't figure out how to formulate the model of all those individual theories. So in true fringe fashion, you just ignored it and simplified the problem down to where it fit your understanding whether that resulted in a correct model or not.
But wait, there's more. Bayes' theorem is not the only statistical relationship that holds here. We know P(K|E) must be smaller than P(H|E) because it requires everything that H provides, plus more -- that soul, and its ability to hook up with a particular body. We proved earlier that such a hypothesis K can never be more probable than H if it subsumes H. It can ever only be just as probable.
We know you know this.
Sadly, just at the point where you exhausted all your equivocations and variable-switching and realized your critics had you "dead to rights," you sent Befuddled Old Man out to apologize for not understanding. And just like that you excused yourself from responsibility for discussing it further.
See, here's the problem with that. A few days ago you said that the reason you couldn't make headway in this debate is because your critics just didn't understand what you were trying to claim. But you can't hold that position and then also put on Befuddled Old Man's costume and apologize for your shortcomings in a folksy, disarming manner as a means of cutting off a debate you're losing. If you're going to play at being confused or befuddled, you don't get to tell your critics they're the ones who don't understand or the ones who are being discourteous.
Admitting you don't understand your critics' rebuttals doesn't mean they aren't true and doesn't mean they don't refute your claims. It means you lose the debate and have no one to blame but yourself.
We're not trying to establish the probability of an event; we're trying to establish the probability of the hypothesis, given new information.
Except that in your formulation E isn't new information. You reckon P(E|H) as if E were assumed to be improbable before it happened.