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.

[GrandizerII]

Non Sequitur. If we have to argue for the Big Bang, or say for the Beginning of the Universe, then it never happened? Doesn't follow.

Angrboda, your video presenter first of all begs the question when says, "what if you have an infinite amount of time". That an infinite amount of seconds is possible what needs to be demonstrated. Therefore, her reasoning is circular and assumes what she needs to prove. It's like this:

Proof that an infinite number formed by successive addition is (allegedly) possible:

1. Assume that you have an infinite number of seconds formed by successive addition.
2. Therefore you allegedly can get to an infinite number with an infinite number of seconds.

It's hopelessly, irremediably fallacious, and cannot get off the ground. You need to prove that an actually infinite number of things can be formed by successive addition without assuming an actually infinite number of seconds formed by successive addition of one second to another already exists.

And in 17:20 onward, the next person in the video says, indeed, you will never reach the point, where you can say, finished, I've done it, I've reached infinite. That concedes the point. That Atheism needs such fallacious claims as actual infinites formed by successive addition is enough to reject it.

Haven't seen the video yet, but going on what you're saying.

The argument from successive addition isn't an argument against the possibility of an actual infinite; it's an argument against the completion of an actual infinite and is ok with the possibility of an actual infinite. So it's not begging the question (in this context) if one starts with the premise that an actual infinite is possible.

Indeed, if you already have an infinite sequence of past moments, then it is possible to "complete" such a sequence by successive addition until you get to the present moment. This is trivially true.

[Angrboda]

I probably should be doing other things this morning, but seeing as Nishant Xavier seems to believe his work on this topic is finished, I will present two counterarguments.

First, as to whether you can achieve an infinity by successive addition of moments. There are three cases here:
1. A past infinity of moments;
2. An infinite number of successive additions of moments;
3. A finite past and a finite number of successive additions.

In cases 1 and 2, an infinite set of moments added to any finite set results in an infinite set of moments and thus proves the opposite. This is basic math. So only the third case is of any concern. However, if you are performing successive additions upon a finite set as an analogy to a past infinite universe, then you have created a false analogy because it is not being suggested that the universe at some point is past finite. If you are assuming the universe is past finite at some point in your argument, then you would be begging the question at that point. So, no, your argument about successive addition doesn't prove anything; it is a non sequitur. It's true that any finite number of successive additions to a finite set only results in a finite set, but the set of moments in a past eternal universe is not finite and so your argument simply does not apply.

The main problem is that there are equivocations in your and Craig's argument. It is never stated whether the set of moments you are adding to is finite or infinite, but since the argument requires a finite set in order to succeed, it is necessarily implying that you start with a finite set of moments. It also does not specify whether the successive additions are finite or infinite, but again, in order for the argument to work, the additions must be finite. However, the conclusion is arguing that a past eternal universe cannot arrive at the present through successive addition based upon this argument which implicitly assumes you are starting with a finite past, which you are not. So the conclusion equivocates on the initial condition and is therefore invalid. It does not follow from either you or Craig's argument that you cannot get to the present moment by successive addition to an infinite past; the argument is a non sequitur.

As to the first cause argument itself, I am going to refute Aquinas' First Way as well as the Kalam Cosmological Argument.

For the sake of argument, consider a hypothetical. Consider that there is no absolute law of uniformitarianism so that things in the past may not be consistent with things in the present. Now let us consider a hypothetical. Suppose the law that things that begin to exist have a cause was not true at some distant point in the past. There is no inconsistency here unless uniformitarianism is a law, and it is not. Under such conditions a universe began to exist, without cause, because that is simply what things did at the time, so there is no violation there. A while after the universe came into existence, a god came into existence similarly. This god need not be the Judeo-christian god, but was similar in that it was omnipotent. This god was also good, though perhaps not perfectly so. This god realized that if evils were allowed to come to exist without cause, then that could be a real problem, and so this god caused reality to no longer allow things to come into existence unbidden. Thus we have the universe we have today, the universe began to exists as postulated, and there is a law that things that begin to exist have causes. Everything that the First Way and Kalam require to be true is true in this hypothetical and yet the conclusion of those arguments is in different ways violated, primarily by suspending the assumption of uniformitarianism.

Astute readers may notice a parallel between this argument and Plantinga's Free Will Defense in that this is not attempting to prove an actuality, but rather a mere possibility, and it is the existence of that mere possibility that undermines other arguments -- The Deductive Problem of Evil for Plantinga and Aquinas and Kalam for me. As such, arguing that you don't believe that my hypothetical happened does you no good, you must show that my hypothetical is not possible or you have nothing. Get to work.

I will also point out that this is one of the problems with drawing conclusions from such arguments as Aquinas and Kalam is that all theories are necessarily underdetermined in that they all depend upon a host of auxiliary hypotheses which are not explicitly stated. If the auxiliary hypotheses do not hold, then the conclusion does not hold. In this case, I attacked uniformitarianism.

[polymath257]

Non Sequitur. If we have to argue for the Big Bang, or say for the Beginning of the Universe, then it never happened? Doesn't follow.

Angrboda, your video presenter first of all begs the question when says, "what if you have an infinite amount of time". That an infinite amount of seconds is possible what needs to be demonstrated. Therefore, her reasoning is circular and assumes what she needs to prove. It's like this:

Proof that an infinite number formed by successive addition is (allegedly) possible:

1. Assume that you have an infinite number of seconds formed by successive addition.
2. Therefore you allegedly can get to an infinite number with an infinite number of seconds.

Wrong. That is NOT the assumption.

In 1, you are assuming successive addition on top of a finite start. But, in an infinite regress there is no start. At any time when there is 'successive addition', there is *already* an infinite number of past seconds.

In other words, the 'successive addition' is on top of an already infinite number of seconds, which *does* give an infinite number of seconds total.

[Neo-Scholastic]

Scholasticism is particularly tedious when its proponents are pedantic to an unsympathetic audience...speaking from experience here.

[Nishant Xavier]

Look, its fairly straightforward:

1. A series formed by successive addition can never be an Actual Infinite.
2. The temporal series of past moments is a series formed by successive addition.
3. Therefore, the temporal series of past moments can never be an Actual Infinite.

If you want to challenge this argument, you need to show one premise is false. Which is it?

[polymath257]

Look, its fairly straightforward:

1. A series formed by successive addition can never be an Actual Infinite.
2. The temporal series of past moments is a series formed by successive addition.
3. Therefore, the temporal series of past moments can never be an Actual Infinite.

If you want to challenge this argument, you need to show one premise is false. Which is it?

1. is only true if it starts from a finite beginning. If it already has an infinite series, successive addition keeps it infinite.

2. Not *formed*. But it *is* a series of successive addition from a possibly infinite.

3. This isn't a premise, but a conclusion. But the conclusion isn't justified because the premises aren't valid in the  case of infinite regress.

[Nishant Xavier]

Grandizer said:

You can't reach -infinity from 0. No one is saying that you can.

Then that concedes the argument. We got to 0, therefore, we didn't start from - infinity.

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.

Agree with this. You could have started with 10^10Trilion^100Trillion and come to 0, but not from an actual number called -infinite seconds ago. Even one of the persons in Angrboda's video conceded this: the distance between the finite and the infinite cannot be transcended by successive addition.

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.

That would be a potential infinity, not an actual infinity. Potential infinity is ok, which just means the series keeps on expanding to a very large number like the trillion thing I mentioned above. Actual infinity you will never reach, like in the example of adding 1,2,3 etc on pages of paper I gave. And why? Because the distance between the finite and infinite cannot be traversed by the successive addition of one number to the other.

Here is Wiki on Actual Infinity contrasted with Potential Infinity: "Actual infinity is to be contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps. As a result, potential infinity is often formalized using the concept of a limit."

Taken from: https://en.wikipedia.org/wiki/Actual_infinity

[Angrboda]

Look, its fairly straightforward:

1. A series formed by successive addition can never be an Actual Infinite.
2. The temporal series of past moments is a series formed by successive addition.
3. Therefore, the temporal series of past moments can never be an Actual Infinite.

If you want to challenge this argument, you need to show one premise is false. Which is it?

And two, as pointed out has an ambiguity of terms, which as I pointed out earlier, either leads to a different conclusion, or makes the conclusion a non sequitur. Since that exhausts all the possibilities, the conclusion is not true.

If you need something more precise, two is false as an infinite past isn't formed by successive addition; it simply is infinite.

[Nishant Xavier]

What is the alleged ambiguity? Pls break it down.

To me, it looks like Atheists are trying mighty hard to avoid an unpleasant conclusion. Lol, that's fine. Keep trying.