The Leap Year got me thinking about the nature of time. I’m certainly no expert in this domain, although I find it utterly fascinating. There are roughly three (realist) philosophical positions on the nature of time: eternalism, possibilism, and presentism. Eternalism basically states that time exists as a block, analogous to space. “Now” is just an arbitrary point, like “north.” An interesting consequence of eternalism is that the past and the future are just as real as the present. It’s not the case that the past is gone and the future isn’t there. Moreover, past and future persons, objects, and events are just as real as present ones. Possibilism agrees with eternalism about the past, but not the future. The past is just as real as the present, but the future isn’t. The future is still open, still ‘becoming.’ Presentism differs from both views in saying that only the present is real. The past is gone and the future isn’t real yet.

I don’t want to go into the nuances of these positions. Rather, I’d like to explore the implications of these different theories for the Kalam Cosmological Argument. This argument is a temporal version of the cosmological argument that argues that the past must be finite and must, therefore, have a beginning and, hence, a Beginner. The argument has been stated by its foremost contemporary defender, William Lane Craig, as follows: P1: Whatever begins to exist has a cause. P2: The universe began to exist. Conclusion: Therefore, the universe had a cause. Some further argumentation is provided to the effect that this cause is personal, immaterial, powerful, intelligent, etc. What interests me is the philosophical defense of premise 2. It goes something like this: P1: An actual infinite cannot exist. P2 A beginningless series of past events is an actual infinite. Conclusion: A beginningless series of past events cannot exist.

In defense of premise 1, Craig appeals to “Hilbert’s Hotel.” Imagine a hotel with an infinite number of rooms and all the rooms are occupied. Imagine now a new guest arrives. The clerk simply moves everyone ‘up’ a room. The guest from room 1 is now in room 2, the guest from room 2 is now in room 3, etc. So room 1 is now available and the new guest checks in. But now imagine that infinitely many new guests arrive. No problem! The clerk simply moves everybody into the room double their original room number. So the guest from 1 is now in room 2, the guest in room 2 is now in room 4, etc. so that all the odd numbered rooms are now available and the infinitely many new guests check in. Suppose the next morning, the infinitely many new guests check out. How many guests checked out? Infinitely many. How many guests are left? Infinitely many. But suppose instead that all the guest in rooms 4 and up check out. How many guests checked out? Infinitely many. How many are left? Three. Note, however, that in both cases the same number of guests check out. This paradoxical result is supposed to show that the notion of an actual infinite is contradictory and therefore impossible.

So Craig and other defenders of the Kalam argument conclude that the past must be finite. However, Craig, like most Christian theists, holds that there is an afterlife that goes on forever. He is quick to point out that the future is only potentially infinite, whereas the past would have to be actually infinite if the universe didn’t have a beginning. Craig’s argument assumes that there is a relevant difference between the past and the future, and this is where one’s philosophy of time will effect one’s evaluation of the Kalam argument. If one is a presentist, as Craig is, one won’t have a problem. If there is something special about “now” and we would have to traverse an actual infinite to arrive at the present, and traversing an actual infinite is impossible, then we’d never get to “now.” With respect to the future, it’s not real, so we are not “going anywhere” i.e. some point infinitely distant. So Craig can say that the future is only potentially infinite. No problem with an afterlife. I suspect one could also be a possibilist and accept the Kalam argument. On possibilism, the future is relevantly different from the past and, as far as I know, nothing commits the possibilist to the infinity of the past.

On eternalism, however, one runs into problems. If eternalism is true, the future is not relevantly different from the past. All of time is just a block. The future is already there, and if it goes on forever, as in Christian theology, it makes sense to speak of it as infinite. What about the Hilbert’s Hotel objection? I think it shows the notion of an actual infinite is counter-intuitive, but not necessarily contradictory. Wes Morriston, a theistic critic of the Kalam argument, has envisioned a scenario that yields the same paradoxes as Hilbert’s Hotel, but with regard to a “potentially” infinite future. Suppose God has decreed that Bill and Wes offer praises to God alternating every celestial minute for all eternity. How many praises will Bill and Wes offer? Morriston thinks the only sensible answer is ‘infinitely many.’ But now suppose that God decrees that Bill and Wes take every other of their celestial minutes off to allow a third worshiper to join in. How many praises will the third worshiper offer? Again, Morriston thinks the only sensible answer is ‘infinitely many.’ We’re beginning to generate the same paradoxes we encountered with Hilbert’s Hotel. But this future scenario certainly seems possible. Couldn’t God decree this? In a dialogue between Craig and Morriston on the Kalam argument (which sadly wasn’t recorded), Craig responded by saying that the number of praises offered would be indefinite. For Morriston, given the constraints of the scenario, this is not a possible answer. Craig responded by appealing to presentism, which strengthens my intuition (I doubt it’s original) that one’s evaluation of the strength of the Kalam argument has a lot to do with one’s philosophy of time. If you have presentist or possibilist leanings, the argument seems like a good one. If you’re an eternalist, you probably won’t give it the time of day. Sorry, couldn’t resist.