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

[GrandizerII]

Grandizer, ok, thanks for that; any comments on what I said to Polymath earlier on, that if you start writing 1,2,3, etc on pieces of paper, will you, or others after you, ever get to infinity? If not, and he seemed to agree this series formed by successive addition would always be finite, so if you do too, then why doesn't that apply in reverse? If we imagine points on the timeline to be -15 BN (give or take), when time began, then it is clear that, with the elapse of seconds, we can finally get to the present, t=0, at some point, which is today. But if it was actually infinite, how did it ever become a finite number in the first place? I asked the same in reverse when I said, if you did get to an Actual Infinite on one page, what number were you on 10 pages earlier? You see, the difference between the finite and the infinite cannot be transcended by successive addition; that's what we're saying. So would you agree with that, or would you dispute it? It seems to me that, if we agree that by writing numbers on pieces of paper, we, or others after us, could never reach an Actual Infinite, then the same applies in reverse. Granted that we got to 0, we did not start infinitely many years ago. We started, according to some, around 13.7 BN years ago, and according to others, around 15-20 BN years ago.

I get what you're saying, and I sympathize with the intuition that leads you to think this way. The problem, however, is what does it even mean to start from infinity? Just as we can't make sense of "ending in infinity", we can't make sense of "starting from infinity". Or at least, I can't. So you will have to make clear what you mean by this exactly, to make your conclusion as persuasive as possible.

Ok. Here's a formulation I can think of:

1. If we started from -infinity, we would never get to -15 BN years (or any other finite number).
2. If we never got to -15 BN years, we would never get to t=0, today.
3. We got to today, ergo 1 is false.

The challenge is with the phrasing "started from -infinity". P1 doesn't make sense. Just as you can't reach infinity moving forwards, you can't reach -infinity moving backwards. So how can we even speak of starting from -infinity, if it's not really an origin?

Again, I get what you're really trying to say, but you have to understand this is an intuitional problem on your part, not a problem with logic itself.

The issue here is we can never transcend the difference between the finite and the infinite by successive addition, any more than we can reach an actual number called infinite by adding digits on a piece of paper. Infinity conceived in thus way is a theoretical abstraction. When we say something goes on until infinity, we mean it will never end. Therefore if something did end, it did not go on till infinity. For the same reason, if we did get to the present time, we did not start an infinite amount of time ago (otherwise we would never get to a finite point in the past), but a finite time ago. Why can I count backward and allegedly reach -infinity from 0 but clearly not reach +infinity starting from 0?

You can't reach -infinity from 0. No one is saying that you can. What some people are saying is that there is nothing logically wrong with counting backwards forever. If you have a moment t0, you can have a moment prior to that called t(-1), then t(-2), t(-3), and so on forever. And if you then reverse direction so you're moving back forwards, you can start from any moment prior to t0 and come back to t0 eventually. But just as you can't reach a specific moment called -infinity counting backwards, you can't start from a specific moment called -infinity counting forwards. But you can go as far back as you want in time, then start counting from there all the way back to t0. And if there is no limit to how far back you can go, then that's what indicates a negative infinity.

Keep in mind the argument that brought us to this point (1) for every contingent being Bn, by definition of being contingent, it depends on a prior being Bn-1. You, me, our parents, the Earth and Universe etc being examples. (2) but if Bn-1 itself is contingent, then it depends on Bn-2 etc. And since this series cannot go on forever, otherwise it would not have terminated with us, we have (3) the First Being in existence, B1, is not contingent, since there is no B0, but exists non-contingently.

Which is a separate argument altogether and not really to do with the Kalam argument. You could have contingent (or rather, dependent) things having always existed.

One doesn't even have to bring Infinity into it were it not that Atheists feel obligated to do so to avoid the unpleasant conclusion (3). For all finite n, whether n is 10 BN or 10 TN, the above conclusion holds. One can only evade it by arbitrarily postulating that the number of beings in existence is infinite.

It's not just atheists who think it can't be shown logically that a temporal infinite series is false. Aquinas himself agreed you can't demonstrate that it's logically impossible.