A Mathematician Reads the Kalam Cosmological Argument

Abstract: Some Christian apologists, notably William Lane Craig, have championed something called the kalam cosmological argument for the existence of God. One version of the argument leans heavily on the claim that the existence of an actual infinite in the physical world is a metaphysical impossibility. We strongly criticize this claim, showing that it involves dogmatically insisting that certain metaphysical premises are absolutely inviolable, when in fact said premises are not only optional, but are far flimsier than other metaphysical claims (eventually shown to be untenable) that great thinkers of the past, including Einstein, have misguidedly clung to. While our criticisms strike most mathematicians and physicists as straightforward and uncontroversial, they have encountered resistance from philosophers, suggesting that there is a communication gap between the scientific and philosophical communities. We hope this paper will help bridge that gap.