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

[GrandizerII]

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.

Again, what do you mean by "start from -infinity"? Do you mean:

1) start from a specific past moment in time that is infinitely away from the present moment?

or

2) start with an infinite sequence of past moments?

If 1, no one is saying that's possible.

If 2, then you can get to the present moment eventually

Your argument therefore fails.

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.

And all this is true without necessarily posing a threat to an infinite past, because with an infinite past you don't start with a finite set of moments anyway. So there need not be any distance between the finite and the infinite to worry about here.

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.

If you're referring to the infinite past, that's not a potential infinity by Craig's definition. Because a potential infinity is supposed to be a finite set that's ever expanding. An infinite sequence of past moments is not a finite set.

The part where I say "no limit" is meant to illustrate what is being meant by an infinity. Infinity is not an unimaginably extreme integer. Rather, it refers to the "limitlessness" of the count of integers here. Mathematically, in the context of this debate, it's the cardinality of the infinite set itself: aleph-null.

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.

Potential infinity refers to a finite set that's ever-expanding, not to an actual infinite. Nor is it to be mistaken for an infinite set of potentialities.

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

Bolded mine.

An infinite past (with no first moment) is the opposite of finite. So not applicable here.