Kalam Cosmological Argument and the actual infinity

The kalam cosmological argument has received a renewed attention in philosophical literature after several presentations and defenses of its versions offered by William Lane Craig. The crux of the debate about Craig?s a priori arguments in its favor has had mainly to do with the analysis of the concept of actual infinity and its implications for the possibility that the universe has an infinite past. While Craig?s arguments point to the counter-intuitiveness of the implications of the existence such a past, his critics offer reasons to think that his analysis is flawed in different respects, mostly due to inappropriate application of mathematical concept of an infinite set. I aim to show that the criticisms on offer have flaws of their own and, hence, fail to show that Craig?s reasoning is insufficient to offer serious reasons to doubt the coherence of the notion of the infinite past. I argue that a more serious threat to Craig?s arguments lies in certain types of symmetry between the past and the future.