Actual Infinities

[Mudhammam]

A popular claim made in conjunction with the Kalam argument for God's existence is something like the following: past time cannot terminate in an infinite regress because it would take an infinite amount of time to arrive at the present moment, and one cannot reach the end - which would be the present - of an actual infinity. It's often stated that only potential infinities can exist - that is, a future continuance of time which never ceases - but not actual infinities. Is there any validity to this latter assertion? If so, how can an omniscient being, with actual infinite knowledge of the potentially infinite future, avoid the very same predicament imposed by actual infinities?

This sounds intriguing, but I am not yet entirely sure I understand the argument. Can we start from the basics - why exactly is past infinity a problem?

As I see it, it's incoherent to suggest that infinity can exist as a complete set - think of infinity as a number. You can always seemingly add to whatever that infinite number "is" - hence, it could not actually be infinite. So, if past time were infinite, the present could not arrive, for it would require an infinite amount of time for every prior successive moment to reach completion, which doesn't appear to mean anything. But if we grant infinite past time, there is no need for God. I'm more interested in granting the logical impossibility of actual infinities for the sake of argument, and then asking how it is that God is also not made logically impossible?