In chapter 2, we argued (among other things) for three preliminary conclusions regarding fine-tuning as evidence for multiverse hypotheses:
Fine-tuning favors (other things equal) hypotheses h+ on which it is likely that one or more observer-containing universes exist over hypotheses h- on which this is unlikely.
If two competing general hypotheses each imply that there is at least some observer-containing universe, but one of them implies a greater number of observer-containing universes, then fine-tuning is not a reason to favor the latter (other things equal).
Although P(e|hM) may be much closer to zero than to one (hM being the multiverse hypothesis, and e the evidence we actually have), it could nonetheless easily be large enough to make the multiverse hypothesis supported by e.
We can now reexamine these theses in the new light of our theory. To begin with (1), let’s determine under what circumstances we will have .
Suppose that
.
Since P(A|B) = P(A&B) / P(B), this can be expressed as
.
Share with your friends: |