Rob,
You write, "A while back, you wrote 'one binary choice from among an infinite set of initial conditions implies continuously branching probabilities.'
Yes.
"Consider the very first binary branch point, at *the beginning of time*, before life existed anywhere. One branch leads to the condition 'life will ultimately emerge somewhere', and the other branch leads to the condition 'life will never emerge anywhere'."
That is not an example of continuously branching probabilities. You assume but two logical possibilities, and assign probability 1 to one and 0 to the other. A continuously branching schema of equally likely universes does not assume the excluded middle -- what we can say with probability 1, though, is that at least one branch will produce life as we know it. After all, it did.
"The multiverse hypothesis ignores the latter, because, if the two conditions are equally likely, *a priori*, that is 'in the beginning', then the hypothesis can never explain why the *a posteriori*, that is 'at the present time', probability of life = 1."
Oh yes, it can. If Albrecht is right, the "beginning" is ambiguous.
"In essence, in order to make the hypothesis work, rather than prove that the emergence of life is inevitable, it had to assume (by ignoring the other branch) that the emergence of life is *necessary*, right from the start. It thus assumes the very thing it claims to prove."
Not at all. The many worlds hypothesis is not a tree with just two mutually exclusive branches. That's a strawman argument.
"If one is going to simply assume that the emergence of life is *necessary*, one might as well assume that is necessary for a *universe*, and dispense with the then unnecessary *multiverse*."
You're neglecting that the multivers is a sufficient condition for life, not necessary. The necessary condition is the equally likely hypothesis. The multiverse may, in fact, be the *only* domain where the equally likely hypothesis applies. (Personally, I think so.)
Tom