What? You give a probability P(E|H) to "the universe is fine-tuned if a god exists." Then you give a probability P(E|~H) to "the universe is fine-tuned if a god doesn't exist."
You
observe that life exists. You
presume that the universe is fine tuned.
There is evidence that the universe is fine-tuned.
How does
evidence that E is true help you do an inference? Recall, the equation is:
P(H|E)=P(H)P(E|H)/P(E)
...where P(E) has multiple forms--but essentially it's just P(E).
If E
is true, you can perform an inference. What do you do if E
may be true? If it is merely supported by evidence?
Assume it's true? Then you beg the question--and you're going down that false dichotomy road. Demonstrate so convincingly that it's true that E' doesn't become a viable possibility? Then you meet my caveat criteria for being able to maintain rationality.
Ignore it and apply the inference anyway? Then, again, you're begging the question, while sinning against mathematics.
Hedge your bets? Then you need something other than Bayes Theorem.
There are only four possibilities:
- there is a god and the universe is not fine-tuned
- there is no god and the universe is not fine-tuned
- there is a god and the universe is fine-tuned
- there is no god and the universe is fine-tuned
...at the beginning of the day. And at the end of the day, if you merely stop with the hypothetical exercise, there's no issue.
But if you accept the argument, by
presuming that the universe is fine-tuned (or guessing, or holding as a premise--however you phrase it, doesn't matter--the key is you're accepting the argument), then you're denying the two alternative not-fine-tuned possibilities, and are committing a false dichotomy.
Again, as I've repeated so many times now... if,
and ONLY if, let's suppose, you have a
good reason to suspect that it's not even viable to hold the universe as not fine tuned...
THEN you are acquitted of the accusation of false dichotomy...
Otherwise, sorry. It's a classic false dichotomy.
The only condition necessary for the fallacy of false dichotomy to be truly committed, is that at the end of the day, you have ignored n-2 of n>=3 viably possible scenarios, be you excuse yourself as holding a premise or no.
I cannot see how you can argue otherwise.
Edit:
If a higher probability is assigned to the first one than the second one, the posterior probability of the hypothesis will be higher than the prior probability.
Sure... why not? It really is, genuinely, more believable that an elephant was used to build a house that I know for sure exists than it is to believe that an elephant was used to build a house I'm not quite sure exists.