Infinite Cardinality and the Possibility of an Infinite Past

We analyze two arguments popularized by William Lane Craig for temporal finitism. Although these arguments are often advanced to support the Kalam cosmological argument for a beginning of the universe, they have broader implications for how one understands God’s relationship to time. The first argument appeals to Hilbert’s hotel to argue that if there existed an actual infinity, absurdities would follow. The second argument alleges that an infinite collection could not be formed by additive succession. Although we ultimately find the arguments to be uncompelling, we believe they serve as a meaningful point of contact between mathematics, philosophy, and theology.