This question has implications for the kalam argument. Proponents of kalam claim (roughly) that an actually infinite series by successive addition is impossible, therefore the past must be finite, and the universe must have a beginning. Of course, if an actually infinite series is impossible, then God couldn’t create a universe with an infinite past, because even omnipotence can’t bring about an impossible state of affairs. But the question remains: is an actually infinite series impossible? If not, couldn’t God create a universe with an infinite past if he so chose?
The answer to this question depends on one’s intuition about whether or not supertasks are possible. Perhaps we can pump these intuitions by taking an example. Could God create a Hilbert’s Hotel (HH)? HH is a hotel with infinitely many rooms. William Lane Craig famously argues that such a scenario generates contradictions and is therefore impossible. For example, let’s suppose that the hotel is full and an infinite number of new guests arrive. The clerk simply moves all of the original guests to a room double their original room number. They now occupy all the even numbered rooms, leaving the odd numbered rooms vacant for the new guests. So far, so good. But let’s suppose all the guests in the odd numbered rooms check out the next morning. How many check out? An infinite number. How many are left? An infinite number. But let’s suppose instead that all the guests in rooms 4 and up check out. How many check out? Again, and infinite number. How many are left? Three. However, in both cases the same number of guests check out. This contradictory result is designed to show that a HH is impossible; ditto for an actually infinite series.
HH shows that the concept of infinity is strange, paradoxical even. But lots of philosophical notions are strange. I’m not convinced that HH shows that an actual infinite is contradictory and therefore impossible. So we return to the question: Could God create a HH? Wes Morriston seems to think so. He argues that God could create a HH by successive addition in two hours. Here’s how (quotation in italics):
During the first hour, God creates the first room. During the next half hour, He creates the second room, during the next fifteen minutes, He creates the third room, during the next seven and a half minutes, He creates the fourth. He continues in this manner until two hours have elapsed. At that point, God has created infinitely many rooms.
This seems like a plausible way for God to perform a supertask given the requisite (plausible) assumptions. Of course, this does not show that all supertasks are possible, but it does seem to show that an omnipotent God could create an actually infinite series by successive addition. Since ‘an infinite series by successive addition’ is the very thing that kalam proponents declare is impossible, this conclusion should give them pause. It also implies that God could create a universe with an infinite past.
But kalam proponents may have a response available. For example, one doesn’t need to maintain that an actually infinite series is impossible; one could offer a weaker claim, namely that while an actually infinite series may be possible, it is not possible to have an infinite number of causal influences in the history of the event. This is demonstrated by the Grim Reaper paradox. This tack is advantageous because it allows for the possibility of God creating an infinite series by successive addition and thus needn’t rely on the alleged impossibility of HH. It also avoids one of Morriston’s other objections: the possibility of an actually infinite future. The kalam proponent could accept the possibility of HH and an infinite future while still maintaining the modified premise. Finally, it’s neutral with respect to one’s theory of time (presentism or eternalism). For all of these reasons, I think this is the tack that the kalam proponent should take.