jt512
Philosopher
- Joined
- Sep 24, 2011
- Messages
- 5,077
They are not competing hypotheses about how he came to exist. But now I understand how you've gotten to your argument and why you were trying to insert E in the likelihoods earlier. Refer back to my earlier example about my parents having met:
H is "my parents have met"
~H is "my parents have not met"
P(H) = P(~H)
E is "I exist" <- this is not where Jabba's argument fails
P(E|H) > P(E|~H) <- this is where his argument fails
Then (assuming I came to exist either through my parents having regular intercourse or my parents having used artificial insemination):
E n H = "I came to exist through my parents having regular intercourse"
E n ~H = "I came to exist through my parents having used artificial insemination"
The hypotheses about how I came to exist are E n H and E n ~H and not H or ~H. The latter are hypotheses about the universe in general (whether it is one where my parents have met or not) for which my existence is merely relevant.
Trivially P(E | E n H) = P(E | E n ~H) = 1, but that's neither relevant - it just says that the probability of an event conditioned on a subset is 1 - nor does "your own existence" have anything to do with it, since as you can see P(E | E n H) = P(E | E n ~H) for any events E and H.
Likewise in Jabba's argument the hypotheses are not about how he came to exist, but about the universe in general (whether it is one where our selves are mortal or not). But in his case his existence is not even relevant to them, which is, again, where it fails. You can see this by Jabba arguing that the likelihood of his existence under H is "virtually zero" and not "exactly 1".
I've explained a couple times why your argument is wrong. I think you've got a blind spot on this one. Jabba's observation that he exists is conditioned on his existence, so whether trivial or not, his conditional likelihood terms under both his hypotheses (regardless of the details) are 1. His saying they are not is due to his not recognizing that he has conditioned on his existence.