Heartbreak at Hilbert’s Hotel

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. For more than three decades, William Lane Craig has been the leading proponent of the kalam cosmological argument for the existence of God. The argument is formulated as follows (Craig (a), ): () Whatever begins to exist has a cause. () The universe began to exist. () Therefore, the universe has a cause. After attempting to justify the premises of this argument, Craig sets out to analyse what the cause must be like, given certain characteristics it must have. For example, he says the cause must be uncaused, timeless, spaceless, and immaterial (ibid., ). Allegedly, the only kind of cause that could plausibly fit this description would be a powerful, immaterial mind – just as God is supposed to be. In this article I examine Craig’s case for premise (). In particular, I focus on just one of the philosophical arguments he uses to establish that the universe began to exist – namely, that the metaphysical absurdity of an actually infinite number of things existing precludes the possibility of a beginningless past. Let’s call this supporting argument Hilbert’s Hotel Argument (HHA, for short). I begin by reviewing HHA, and follow by raising some initial doubts about the controversial first premise, which states that ‘an actually infinite number Religious Studies (2014) 50, 27–46 © Cambridge University Press 2013 doi:10.1017/S0034412513000140