Is Time Infinite?

In the previous post on Aristotle's potential-vs-actual infinity distinction, I left a loose end hanging. Aristotle himself thought the past was infinite — that the universe had no beginning. But "the past" sounds like a completed thing, and completed infinities are exactly what the framework forbids. So which gives?

This video is my attempt at the answer.

Time Goes Both Ways

The natural picture of time is symmetric. Moments line up like points on a line, stretching off in both directions. The line just goes on. There is no last moment in the future, because whatever moment you pick, you can imagine the next one. There is no first moment in the past, because whatever moment you pick, you can imagine the one before it.

So far, so symmetric. But pull on this and the symmetry comes apart in your hand.

The Case for an Infinite Future

Imagine someone tells you, "This is the last moment that will ever happen." You can immediately ask: why? Why couldn't there be another? Whatever stops time from continuing has to be something, and that something would be located at some moment — which would itself be in time. There's no way to seal off the future without smuggling more time in to do the sealing.

So the future cannot have a final moment. Time, into the future, is infinite — but in exactly the sense the previous post was about. Potentially infinite. There is no actual infinity of future moments sitting around already, because the future hasn't happened yet. There's just the open-endedness of more, indefinitely.

That's a clean fit with the Aristotelian framework. The future is potential infinity in its purest form.

The Case for a Finite Past

Now run the same thought experiment backwards. To say the past is infinite is to say that infinitely many moments have already happened before this one. But "already happened" means completed. Infinitely many completed moments — that's an actual infinity, exactly the kind the Aristotelian framework rules out.

There's a second version of the argument that's even more direct. If the past is infinite, then to reach today, the universe had to traverse infinitely many moments. But you can't traverse an actual infinity — no matter how many moments you've gotten through, there are always more behind you. So the universe couldn't have arrived at today. But it did. So the past can't be infinite.

The asymmetry is now visible. The future is potential infinity, no problem. The past, if it were infinite, would have to be actual infinity, and that's the kind that breaks. So the past must have a beginning.

A Hidden Assumption

This argument depends on a particular theory of time, and I want to flag that explicitly. What I've been assuming is sometimes called the A-theory (and in its strongest form, presentism): the view that only the present moment is fully real, that the past has been but no longer is, and that the future will be but is not yet. On this picture, the past is a kind of completed sequence and the future is a genuinely open one — exactly the asymmetry the argument relies on.

There's a major rival view called the B-theory (or eternalism), on which all moments of time are equally real — the universe is a four-dimensional block, and "now" is just where in the block you happen to be. On the B-theory, the past doesn't have a different ontological status from the future. The asymmetry I just leaned on would soften, and the argument would need to be rerun.

I think A-theory is defensible — there are good philosophical and theological reasons to prefer it — but I want to be honest that the conclusion I just reached is sensitive to which way you go on this.

An Older Disagreement

This is also where I should mention an internal disagreement in the Christian philosophical tradition that often gets papered over. Bonaventure, in the thirteenth century, argued essentially the case I just made: the past must be finite, an eternal universe is impossible. Thomas Aquinas, his contemporary, disagreed. Aquinas held by faith that the world had a beginning — Genesis says so — but he thought that philosophically an eternally-existing universe was not provably contradictory. Aristotle had believed in an eternal universe, after all, and Aquinas didn't want to claim the Philosopher had committed a logical error he hadn't actually committed.

So when I argue here that the past must be finite, I'm landing closer to Bonaventure than to Aquinas. That doesn't make either of us wrong, but it's worth knowing the disagreement is older than the modern debates over the Kalam argument, and the smartest people in the tradition have not agreed on it.

A Note on God

If you're worried this creates trouble for the idea of an eternal God who knows all moments of time — wouldn't God's knowledge then be an actual infinity? — there are theories of divine knowledge that handle this question (Boethius's view that God knows time eternally rather than sequentially is the classic example), but they live in philosophy of religion rather than philosophy of time, and they deserve their own video.