Craig on finitism and presentism

The kalām cosmological argument for God’s existence holds that the universe must have had a beginning.  (Not all versions of the cosmological argument make this claim.  For example, the versions I defend in my book Five Proofs of the Existence of God do not make it.)  William Lane Craig’s influential presentation of the argument defends the claim in several ways, one of which is by arguing that a beginningless universe would amount to an actual infinite, and that an actual infinite is impossible.  That judgment, in turn, is supported by appeal to examples like the Hilbert’s Hotel thought experiment, in which the idea of a hotel with an actually infinite number of rooms and guests yields a variety of bizarre consequences.