BTW, Jabba, the form of Bayes' Theorem that you are using requires H and ~H to be complementary hypotheses, that is, they must be mutually exclusive and exhaustive. If ~H is a specific hypothesis, and there is more than one alternative to ~H, then H must comprise all the alternatives. The problem with that is how do you come up with a single P(E|H), if H represents a collection of alternative models, each implying a different value of P(E|H)?
Alternatively, if H and ~H are both specific hypotheses, then they must be the only possible hypotheses in the universe. If, on the other hand, there are more than two possible hypotheses, then you cannot use the form of Bayes' Theorem that you've been using; you must use the odds form of Bayes Theorem instead.
jt,
- The following is how I calculated the likelihood of E given ~H:
11.3. Re P(E|~H):
11.3.1. The probability (“likelihood”) of E given ~H, involves several specific hypothetical possibilities.
11.3.1.1. That only some of us have but one finite life.
11.3.1.2. That we each have numerous finite lives.
11.3.1.3. That only some of us have numerous finite lives.
11.3.1.4. That we each have an infinity of finite lives.
11.3.1.5. That only some of us have an infinity of finite lives.
11.3.1.6. That we each have an infinite life.
11.3.1.7. That only some of us have an infinite life.
11.3.1.8. That time isn’t what we think it is (to be explained).
11.3.1.9. Some other explanation.
11.3.2. Now I must estimate (roughly) the prior probability (rounded off to three decimal places) of each more specific possibility (hypothesis), given ~H.
11.3.2.1. That only some of us have but one finite life: .000
11.3.2.2. That we each have numerous finite lives: .002.
11.3.2.3. That only some of us have numerous finite lives: .000.
11.3.2.4. That we each have an infinity of finite lives; .002
11.3.2.5. That only some of us have an infinity of finite lives: 000.
11.3.2.6. That we each have an infinite life: .002
11.3.2.7. That only some of us have an infinite life: .000
11.3.2.8. That time isn’t what we think it is (to be explained): .002
11.3.2.9. Some other explanation: .002
11.3.3. And now, I must estimate the likelihood of my own current existence given the different specific hypotheses under ~Hs.
11.3.3.1. That only some of us have but one finite life: .10.
11.3.3.2. That we each have numerous finite lives: .10.
11.3.3.3. That only some of us have numerous finite lives: .25.
11.3.3.4. That we each have an infinity of finite lives; 1.00
11.3.3.5. That only some of us have an infinity of finite lives: .50.
11.3.3.6. That we each have an infinite life: 1.00
11.3.3.7. That only some of us have an infinite life: .50
11.3.3.8. That time isn’t what we think it is (to be explained): .50
11.3.3.9. Some other explanation: .50
11.3.4. And now, I must multiply each of the probabilities of ~H above by the likelihoods of my current existence, given each specific hypothesis, and add up their products. And, the total likelihood of my current existence given ~H:
11.3.4.1. P(E|~H) = (0*.5) + (.002*.10) + (0*.25) + (.002*1.0) + (0*.5) + (1*..002) + (0*.5) + (.002*.5) + (.002*.5), or
11.3.4.2. P(E|~H) = 0 + .0002 + 0 +.002 + 0 + .002 + 0 + .001 + .001, or
11.3.4.3. P(E|~H) = .0052. And,
11.3.5. P(H|E) = 0*.99/(0*.99 + .0052*.01) = (0/.000052) = 0.
11.3.6. P(H|E) = 0.
11.3.7. IOW, given my current existence, the posterior probability that I will have one, finite life is zero…