The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[Angrboda]

Ok. So, while, I was away, I was thinking of another way the argument could be formulated: for a Being Bn, if it is contingent, it depends on a prior Being Bn-1. But Bn-1 likewise, if it too is contingent, further depends on Bn-2. And so on and so forth until we come to B1 and B0. Since we are speaking of real beings, there is no B0. Therefore, B1, the First Being, is non-contingent.

But perhaps these words "contingent" and "necessary" don't indicate too much to the average reader, though they are well known in modal logic and other fields. Very well, then, we will use simpler terminology. Let's use temporal/eternal instead. For every Being Bn, if it is temporal, it depends on a prior being in the timeline, Bn-1. Nevertheless, this series cannot go on backward to infinity (will come to why, and the objections raised in a minute), Therefore, at some point we will reach the very beginning of time, and the final temporal being, B2, will have been caused by B1. And B1, the First Being, is thus proven to be a Non-Temporal Being, an Eternal Being, the First Cause of the Universe.

Hence, Axiom I is: B1, i.e., an Eternal First Being exists, owing to whom B2 to Bn, i.e. the Sub-Set or Universe of Temporal Beings, began to exist.

This conclusion is confirmed by Empirical Science. Wikipedia says: https://en.wikipedia.org/wiki/Borde%E2%8...in_theorem

"The Borde–Guth–Vilenkin theorem, or the BGV theorem, is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout its history cannot be infinite in the past but must have a past spacetime boundary.

---

Therefore, we have a certain conclusion of Empirical Science that the Universe is not infinite in the past but temporal and thus is not B1.
This is also intuitively obvious: if in fact the universe were already infinitely old, it would follow that everything that could happen in the future has in fact already been taken place; and why? because an infinite time has already elapsed sufficient for it to take place. These are the kinds of absurdities to which apply the mathematical theoretical concept of infinity to a collection of things such as moments of time will lead to.
Also, the argument is not that an actual infinite cannot exist, but that: an actual infinite cannot be formed by successive addition. And since the past series of temporal moments is a series formed by successive addition, it clearly follows that that series cannot be actually infinite.
This intuitive mathematical and logical conclusion in fact is what the BGV Theorem, from leading experts in the field, has established scientifically.

Finally, if you think, you can reach Infinity by Successive Addition, I have a simple proposal for you, dear friends: start writing 1,2,3 etc on notes of paper. And then keep going. As soon as you get to Infinity, get back to me, and I'll immediately concede the Argument. Lolol. You see what I'm saying? And if btw you object you won't have enough time to since you die, then ok, entrust it to other contingent/temporal beings, before you do. Then let them continue the series. Will they ever get to an actual number called Infinite by Successive Addition? No, in fact they will not. But supposing they ever do. Now go back 10 pages and tell me what number they were on. How did they transcend the difference from a finite number to Infinite all of a sudden? They could not have. The number formed by successive addition will always be finite. Again, the conclusion clearly follows: a series formed by successive addition cannot be actually infinite. Hence, the universe is not actually infinite in the past, etc.

---

Regards,
Xavier.

This has already been adequately answered. The theorem requires classical spacetime which may not be a valid assumption and Alan Guth disagrees with Vilenkin about the possibility of a past eternal universe.