Since, in the case of complementary hypotheses, P(E) would be P(E|H)P(H) + P(E|~H)P(~H), I tried to estimate what-specific-hypotheses ~H would include (in this case) and how-probable-each-would-be multiplied by how-probable-each-would-be-to-result-in-E, and added up the products...
- Can you follow that, and does it make sense?
I can follow it, and no it does
not make sense. It doesn't make sense because you're trying to shoehorn one formulation of a solution into a different formulation of the problem. As I begin the list you're so terrified of: you don't know how to formulate a statistical inference.
The formulation you've chosen is "an hypothesis and its complement." And yes, numerous experts have confirmed that you're using the formula that reckons the conditional probability of the hypothesis given an event and incorporates the complement of the hypothesis, and that it's properly derived algebraically from Bayes' theorem. But you wrongly extend that endorsement to mean their approval as the right way to solve your problem. It's not.
If H were the hypothesis whose probability, given data, you were directly interested in, you might have a chance of convincing someone you were working the problem correctly. But that's not what you're doing. You've flipped it around -- the way nearly all fringe theorists err in doing -- and you're trying to establish your desired hypothesis by showing that some other hypothesis is so improbable on its own that it has to be discarded. You think you can do this by statistical legerdemain and formulating it as "a hypothesis and its complement," where "a hypothesis" is your competition and "its complement" is your theory.
But that's not what "a hypothesis and its complement" means, and you finally figured it out. If "a hypothesis" is materialism (which is the only hypothesis you've ever tested), then "its complement" is the
set of all hypotheses that aren't materialism. And that set contains hypotheses that don't lead to immortality. That means the probability of immortality, given data, cannot just be 1-P(materialism), as you originally suggested. Your plan was never to compute the probability of immortality given data. It was instead to deduce it based on smack-talking the competition and disguising the exercise as math.
Once you finally figured out that you had to deal with a
set of things that weren't materialism, you decided -- in your fumbling, pidgin-statistics way -- that you could fix your proof by enumerating all the hypotheses in the complement that weren't materialism and assigning priors and likelihoods to them in the same out-of-your-fanny way you used for all the other numbers. This is wrong not only because you're just pulling numbers out of your fanny -- thus
proving nothing -- but because you don't understand why, fundamentally, you can't take that approach even if you could get actual data for that fan-out of hypotheses.
The reason "the complement" has a sort of special status in statistics is because it's allowed to include the notion of stuff you could never know and therefore never nail down. For that reason you can't -- and shouldn't try -- to exhaustively enumerate them all. You figured this out, which is why the last bit of your enumeration exercise was "whatever I haven't thought of." And you thought you could assign a prior and likelihood function to it. By definition if you can't know what it is, you can't start assigning numbers to it and have the resulting formulation mean anything. It certainly can't prove anything.
But more importantly, by doing what you've done, you've transformed the problem into a set of discrete hypotheses. The "hypothesis and its complement" formulation really doesn't help you there, even if you tried to gimmick it and try the union of them all and the complement of their union. Why? Because the union would contain both hypotheses that lead to immortality and those that don't. Computing one number of them would not discriminate between mortality and immortality.
If you have an incomplete set of discrete hypotheses and some data, what is the best way then to evaluate them statistically? I'll leave that to you, since it's your proof. I know the answer, and I've spelled it out to you several times in the posts you insist you can ignore because I'm so mean to you. But it's not the formulation you're using, I can say that. What I will say, however, is that you'll actually have to compute the probability of immortality given the observation of your current existence, and you won't be able to do it indirectly as one-minus-something.
Even statistics, which deals with uncertainty, doesn't let you cheat the way you've been planning to cheat. Every single statistician you've consulted has told you this.