Actual Infinities

[Mudhammam]

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?

How is the problem of an infinite regress never reaching the present different than the problem of an arrow never reaching it's mark because there are an infinite number of points between where it was shot and its mark? The arrow does reach its mark whether we can describe how it gets through an infinity of points or not.

An arrow travels through physical space, which is not infinitely divisible, whereas mathematical space is. I suppose the theoretical question could be asked, if time is infinitely divisible, but that would seem to be different from whether or not - if we can imagine a series of snapshot moments extending endlessly into the past - the present could ever arrive given an "infinite number" of such "pictures". Time is certainly weird.

I'm still trying to grasp the sense in which a being could be said to possess infinite knowledge - it seems somewhat related to this problem of an infinitely extended past - in that both are incoherent.