William Lane Craig's defence of the kalam cosmological argument rests heavily on two philosophical arguments against a past-eternal universe. In this article I take issue with one of these arguments, what I call the ‘Hilbert's Hotel Argument’ – namely, that the metaphysical absurdity of an actually infinite number of things existing precludes the possibility of a beginningless past. After explaining this argument, I proceed to raise some initial doubts. After setting those aside, I show that the argument is ineffective against proponents of presentism. The remainder of the article considers and rejects possible replies on Craig's behalf.
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