Faith and Philosophy

Volume 38, Issue 3, July 2021

On the Varieties of Finitism

Defenders of the Kalām Cosmological Argument appeal to the so-called Hilbert’s Hotel Argument to establish the finitude of the past based on the impossibility of actual infinites. Some of their opponents argue that this proves too much because if the universe cannot be beginningless due to the impossibility of actual infinites, then, for the same reason, it cannot be endless either. Discussing four different senses of the existence of an actual infinite, I criticize both sides of the debate by showing, on the one hand, that the Hilbert’s Hotel Argument is not powerful enough to rule out the possibility of the infinitude of the past and, on the other hand, that the soundness of the argument for the finitude of the past from the impossibility of actual infinites does not establish the soundness of the parallel argument for the finitude of the future.