A response to a Platonistic and to a set-theoretic objection to the Kalam cosmological argument

The first premise of the Kalam cosmological argument has come under fire in the last few years. The premise states that the universe had a beginning, and one of two prominent arguments for it turns on the claim that an actual infinite collection of entities cannot exist. After stating the Kalam cosmological argument and the two approaches to defending its first premise, I respond to two objections against the notion that an actual infinite collection is impossible: a Platonistic objection from abstract objects and a set-theoretic objection from an ambiguity in the definition of ‘=’ and ‘<’ as applied to sets. The thought-experiment involving Hilbert’s Hotel is central to the dialectic, and the discussion clarifies its use in supporting the Kalam cosmological argument. In recent decades, there has been a veritable revival of activity in the philosophy of religion, and central to this revival has been renewed interest in theistic arguments, especially the cosmological argument. There are three basic forms of the cosmological argument. First, there is the Thomist argument, which asserts the current existence of finite, contingent beings and proceeds, by way of rejection of an infinite regress of concurrent causes, to a de re metaphysically necessary being as the ground for the current existence of those contingent beings. Central to the argument is the distinction between essence and existence and the nature of the infinite regress – involving an essentially ordered series of causes – employed by its advocates. Second, there is the Leibnizian argument which begins with the question ‘Why is there something rather than nothing?’ and proceeds, by way of the principle of sufficient reason, to the truth of a de dicto logically necessary proposition ‘God exists ’. Central to the argument is the plausibility and range of application of the principle of sufficient reason. The third argument is the Kalam cosmological argument. It is safe to say that this form of the argument has been more prominent in recent years than the other two, largely due to the writings of William Lane Craig. Along with its rise in prominence has come a wave of criticisms of the argument. These criticisms have Religious Studies 39, 373–390 f 2003 Cambridge University Press DOI: 10.1017/S0034412503006565 Printed in the United Kingdom