I just ran across this post from Craig's website. Craig is responding to Carroll and, after quoting him, replies thusly:
Here Carroll claims that to have a singularity in the past does not mean to have a beginning; it means only that SOME [past-directed] geodesics come to an end. He says that others might not. On this interpretation, the BGV Theorem is consistent with some geodesics’ being infinitely extended into the past. But that is precisely what the theorem proves to be impossible. The theorem requires that ALL actual, past-directed geodesics eventually come to an end. In order for the universe to be beginningless, there must be infinite, past-directed geodesics. That’s why Borde, Guth, and Vilenkin take their theorem to prove that any universe which has, on average, been in a state of cosmic expansion throughout its history cannot be past-eternal but must have a beginning.OK, so, in my last post (yeah, I know, no apologies, I'm only going to post when I feel like it, so there), I quoted the conclusion from the actual BGV paper:
... we see that if Hav > 0 along any null or noncomovingSo, it's obvious from the paper that the requirement that a geodesic ends is not applicable to geodesics that are timelike and comoving. In other words, Craig is simply wrong when he writes that BGV requires "ALL actual, past-directed geodesics eventually come to an end."
timelike geodesic, then the geodesic is necessarily
Either Craig hasn't understood the conclusion of the paper he cites so frequently, or he is deliberately mischaracterizing the paper for his readers so that they will think he has decisively refuted Carroll.
What do you think?