As I pointed out in the Preface to Oppy (2006), a full discussion of cosmological arguments would need to be very extensive indeed. Even with our focus restricted primarily to considerations about the role of the concept of the infinite in cosmological arguments, we shall need to give a fairly summary treatment of some of the relevant issues.

After some initial considerations about the classification of cosmological arguments – and of the way in which one ought to distinguish between cosmological arguments and teleological arguments – we shall begin with a discussion of the first three of Aquinas' Five Ways. Next, we shall consider the cosmological arguments that Descartes defends in Meditation III and that Leibniz advances in his essay “On the Ultimate Origination of Things”. Then, we shall consider much more recent versions of cosmological arguments involving causation and contingency due to Meyer (1987), Koons (1997), and Gale and Pruss (1999). Finally, before turning to some concluding observations, we consider the recent defence of kalām cosmological arguments in the work of Craig (1979a), and the recent construction of an atheological cosmological argument in the work of Smith (1988).

SOME INITIAL CONSIDERATIONS

There are many different kinds of a posteriori arguments for the existence of God. Following Kant, we shall suppose that it is possible to sort many of these arguments into two major classes: the cosmological arguments and the teleological arguments.