But the second way uses exactly the language that Sean Carroll uses in his talk.
This is incorrect. Aquinas’ second way [redacted]:
The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. ] Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false.
Carroll does indeed reject that there must be a first cause of the existence of the universe; something Aquinas absolutely requires due to the impossibility of actual infinite regress.
Certainly within the universe we can observe causes, but we have no reason to think that the observations we make about things inside the universe apply to the universe as a whole.
And what warrant do you have for the proposition that causation does not apply to the universe as a whole? This seems at odds with naturalism’s fundamental precepts.
The second way is invalidated simply by proposing that we don’t know whether or not the universe as a whole must have had a cause.
I think you mean here that in principle it is metaphysically impossible for anyone to know whether the universe as a whole must have had a cause. If this is true though, then why are you and Caroll affirming that it didn’t? It is perplexing that so much time has gone into a model of the universe that is based on something that in principle we can’t ever know. More to the point, we do know that the universe as a whole must have had a cause.
We find ourselves in a an ever expanding changing universe. Aquinas argues that if there is no first cause, there can be no intermediate cause(s); but there clearly are intermediate causes - say the super inflationary events during the Planck Epoch. On an eternal universe theory, there is no first cause. How then did we ever reach any of the intermediate/immediate causes we have observed?
Craig makes a similar argument using set theory to illustrate the absurdity of actually existing temporal infinities:
*f actual infinites that neither increase nor decrease in the number of members they contain were to exist, we would have rather absurd consequences. For example, imagine a library with an actually infinite number of books. Suppose that the library also contains an infinite number of red and an infinite number of black books, so that for every red book there is a black book, and vice versa. It follows that the library contains as many red books as the total books in its collection, and as many red books as red and black books combined. But this is absurd; in reality the subset cannot be equivalent to the entire set. Hence, actual infinites cannot exist in reality.
Craig goes so far as to claim that a past eternal universe is a metaphysical impossibility. Science stops once an eternal universe is claimed because it is in the business of investigating causes and effects, and it can’t investigate an infinite series of events past. The basis for the claim of an eternal universe must necessarily be a philosophical one. I have yet to see a cogent argument.*