We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.

A common argument in support of a beginning of the universe used by advocates of the kalām cosmological argument (KCA) is the argument against the possibility of an actual infinite, or the “Infinity Argument”. However, it turns out that the Infinity Argument loses some of its force when compared with the achievements of set theory and it brings into question the view that God predetermined an endless future. We therefore defend a new formal argument, based on the nature of time (...) (just as geometrical reasoning is based on the nature of space), which addresses more directly the question of beginningless time. (shrink)

Yishai Cohen raises three related objections to the kalam cosmological argument. Firstly, Cohen argues that, if the argument against the possibility of an actual infinite, which is used to support the kalam cosmological argument, is sound, then a predetermined endless future must also be impossible. Secondly, Cohen argues that the possibility of a predetermined endless future entails the possibility of an actual infinite. Finally, Cohen maintains that Robert C. Koons’ Grim Reaper paradox shows that a predetermined endless future is impossible. (...) I intend to show that Cohen’s three arguments are not sound and that the possibility of an endless future is not a thorn in the kalam cosmological argument. (shrink)