One of the stranger things that one comes upon from atheists is the idea that the universe always existed. This is obviously impossible because it’s a simple contradiction in terms because simple observation shows that things happen because of causal linkage. Though it is more common for people to describe this model as “a causal chain that never started”, it would be more accurate to describe this model as “an infinite series that terminated.” I’m referring to the mathematical concept of an infinite series, so I think it might make sense to pause for a moment to explain what little you need to know about the mathematics of infinite series because most people don’t study higher mathematics.
Speaking a little loosely, an infinite series consists of two things:
- A starting value (optional)
- A way to generate the next value from its index in the list, the previous values, or both
One example of an infinite series, N, is: N1=1, Ni+1=Ni+1. That is, the first element in the series is 1 and each successive element is the element before it, plus one.
That’s it. That’s all infinite series are. They can be defined any way you want; you can reference more than one element, such as in the famous Fibonacci sequence where (starting with the third element) each element is the sum of the previous two. You can define them without reference to the previous element, such as a series of numbers where each is the index squared (1, 4, 9, 25, 36…). But in each case, what you have is a rule for how to generate all of the elements. What you don’t have is the elements. Yet.
This gets us to the famous mathematical fact that “infinity is not a number.” Infinity isn’t a thing, it’s rather the concept of, “you never stop.” If you ever stop, it’s not infinity. And as you can see in how we defined the infinite series above, it never stops. That’s what makes it an infinite series.
Now, the moments of time clearly form a series; they are ordered not merely by the passage of time but also by causal connections. If I push a glass off of the table, it falls after I pushed it and not before.
Now, the thing is, the set of all moments leading up to the present moment forms a sequence with a final element. A sequence with a final element, by definition, is a finite sequence. However, by the hypothesis of the world always having existed, this would be a finite sequence with infinitely many elements. That’s a contradiction, and since it is indisputable that the sequence of moments leading up to the present moment has a final element, the number of elements in that set cannot be infinite. Quod Erat Demonstrandum.
Uncowed by mere logic and obvious truth, the atheists who hold this kind of thing will then say that there’s no reason you have to stop when counting backwards. It could be infinite in that direction! Whether or not that’s true, it’s irrelevant, because time doesn’t go that way. Time moves forwards, not backwards. God, or the laws of physics, or brute facts, or a drunken elf named Fred, or something clearly already picked a direction for time to flow, and we’re all stuck with it. All manner of things might be true if we lived in a completely different universe than the one we live in, and the first rule of tautology club is the first rule of tautology club if tautology club has rules and they’re well ordered. (Mathematically, a well-ordered set is an ordered set which has a first element. Not all ordered sets do. The rational numbers greater than zero under the standard ordering are not well-ordered, for example, because for any hypothetical first element, simply divide it in half an you have a rational number which comes before it.)
Interestingly, it has been a common theme in arguments for God to simply side-step the problem and give arguments which do not rely on the universe having started. The argument from motion (change) and the the argument from contingency and necessity are the two most obvious examples. Plenty of others don’t require it, either. (The Kalam cosmological argument is the obvious exception, of course.) I can see the appeal of simply side-stepping the problem since it’s irrelevant, but I do somewhat wonder at the wisdom of it. It may be falling on the wrong side of answering a fool according to his folly; by allowing people to persist in holding as true something that’s obviously wrong, it has allowed the fools to be wise in their own eyes.
Then again, they’d do that anyway. Most of them are clearly not seriously thinking through their own ideas. But for the few of them who are, I think it’s worth at least pointing out that the universe can’t have existed forever before explaining why it doesn’t matter anyway.
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Chris Lansdown 
Just because you arbitrarily labelled the present moment (when you wrote the above) the final element of a time series doesn’t mean that time itself isn’t infinite. The fact that the present moment (as I write this) is later than your final moment proves that your final moment wasn’t the final moment anyway. If we label the integer 2024 (or any other integer) the final integer, that doesn’t mean that the set of all integers isn’t an infinite series.
(Why even mention the present moment being the final moment of a time series? It only seems to muddy your argument.)
This isn’t the ‘checkmate, atheists!’ argument you seem to think it is. Time could be past-infinite yet still “move” forwards (just as integers can be ‘negative-infinite’ but still ‘count’ positively). Your mistake (I think) might be in assuming that we have to somehow traverse all of the past moments in time to get to the present moment, which isn’t the case. If the universe is past-infinite, we can exist at any moment in time. By analogy, we don’t have to live through all of history to be alive in 2024. It appears you hold to the ‘A’ theory of time, but special relativity has essentially proven that the ‘B’ theory is correct.
Finally, I agree that all this really has nothing to do with proving whether God exists or not. That said, I’ve argued with many Christians who answer “What caused God to exist?” with “He’s always existed”, which I assume you’d have to agree doesn’t answer the question.
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“Just because you arbitrarily labelled the present moment (when you wrote the above) the final element of a time series doesn’t mean that time itself isn’t infinite.”
I didn’t say it did. It does make it the final element of that set, which is all I said. The set of all moments up to five minutes ago is a set with a final element that is also a subset of the set of all moments up to now. That a set can be a subset of another set changes nothing whatever.
“Your mistake (I think) might be in assuming that we have to somehow traverse all of the past moments in time to get to the present moment, which isn’t the case.”
Yes, in fact, you have to. That’s what time is. The mere fact that you can count backwards doesn’t matter, because no one cares what *you* can do. They care what *time actually did*. And time moves forward. The negative integers are infinite only because you can keep going in that direction. But time doesn’t go in that direction.
“I’ve argued with many Christians who answer ‘What caused God to exist?’ with ‘He’s always existed’, which I assume you’d have to agree doesn’t answer the question.”
Yes. People who hold God to be within time, rather than the creator of time, tend to be pagans with a very small pantheon, and as such their theology is always incoherent, so it’s incoherent here, too.
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(You may be confusing ordered sets and infinite series. They’re not the same thing.)
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Is it, though? Your thesis seems to assume the A-theory of time in which there is a unique present moment which “moves” forwards (can time itself “move”?), but special relativity shows that the B-theory of time is correct as there is no unique present moment, per special relativity.
Incidentally, even if the A-theory is correct, how long does the present moment itself last? If it is infinitely short, then there are infinitely many such moments even if time is past-finite.
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