tronvillain

luvluv:
Well, "less than two" extends from two to negative infinity, and "less than three" extends from three to negative infinity. Both are infinite.

luvluv

tronvillian:

This really doesn't solve the problem for me. I don't really have a reason to believe that the future events in the infinite series of events already exist.

Indeed, if they are causally related, as the infinite regress would suggest, future events in the "regress" CANNOT exist yet. They have yet to be caused.

So, I don't see how this helps. (Sorry I missed it before)

Clutch

What are infinite events? Completed? How? On the IP model, there was no start. How can something that does not start be completed? Well, I don't know how many more times to define the model in terms of the properties of an infinite series. I've done this explicitly and directly, and repeatedly now. If you think this is ignoring the infinity bit of the infinite past model, then I'm at a loss.

But let me try again. No, I am not ignoring the infinity of the past, on the model in question. Here's what the past looks like: for every event, there is exactly one unique immediate predecessor. Before each event, there was an earlier one. Punkt.

-- "But then how did we get to now?"

Simple question-begging. How did we get to now from when? The mistaken presupposition: Why, from the beginning, of course! Newsflash: There is no beginning on the IP model. There's just a series of events. And how did we get from any one of these events to the present? By a strictly finite series of intermediate events.

-- "Well, how many events have occurred by now, then?"

This is tricky; it's one of those areas where lay intuitions will let you down. (Viz, like your mistaken lay intuitions about not being able to add anything to an infinite collection.) The answer is, infinitely many events have occurred.

-- "Aha, you admit it! An infinite series has been completed!"

No. No infinite series has been completed, because, by definition on the IP model, no infinite series has started. And without the aspect of completion, there is no problem.

The problem is supposed to spring from the idea that, loosely speaking, there isn't enough time to complete an infinite task. But without the implication of completion, all we have is a situation in which past events and past times are in one-one correspondence. Each past event happened at some time or other, hence there are precisely enough times for infinitely many events to have occurred -- namely, infinitely many times. But this infinite past by definition does not contain any event infinitely remote from the present, no more than the natural number series contains any number infinitely remote from zero. (Compare: "Oh, you must be ignoring the infinity of the natural numbers!" )
This is certainly not tangential. It goes to the heart of understanding the various well-defined concepts of infinity. Seriously, if you don't know this very basic fact about infinite collections, you really have to learn more before taking a view on what is and is not entailed by the prospect of an infinite past. Not only can you add or subtract elements from an infinite collection and still have an infinite collection (of the same size), but you can do this in a radical way. For instance, it is trivial that the sets {0, 1, 2, 3...} and {2, 4, 6, 8...} are not only both infinite, but are the same size. Moreover, this does not mean that all infinite sets are the same size; by the hierarchy of the transfinite, there are infinitely many different sizes of infinities.

I am by no means a mathematician, but I find this stuff weird and wonderful and exciting -- I urge you to learn something about it, not just to bolster your understanding of the regress argument, but because it's just damned interesting.

Garbles18

So why is this a problem? What natural law or universal rule is being broken by an infinite series of events occuring before the present?

Aside from that, even if time has to have a beginning and can not be infinitely regressive, you still haven't shown that there aren't an infinite number of events to be completed between any two points in time. In other words, even if there was a t = 0, you would still have to COMPLETE an infinite number of events before arriving at the present unless you have reason to believe that time is discrete instead of continuous. If this is the case, I'd be interested to hear your thoughts on why time is discrete.

HRG

Not necessarily. This holds only for cardinal transfinite numbers, not for ordinals or Conway's surreal numbers etc. Cardinals look at the "size" of a set as a whole, while ordinals count through it, as it were.

If w (the smallest infinite ordinal) is {1,2,3, ....}, then w+1 is simply {1,2,3, ....., 0}, w+w is {1,3,5,....., 2,4,6 ....} etc.

The problem that luvluv has with an infinite regress is exactly that {....,3,2,1} is not an ordinal (not every subset has a first element). He looks at it as if it was {0, ..... 3,2,1}, which isn't an ordinal either.

We cannot say that the process has run for an infinite time interval; it has never begun.


Regards,
HRG.

luvluv

HRG:

This sounds like sophistry to me.

I do understand what you're saying HRG, you're saying sure it sounds nearly impossible, but you can't prove it's impossible.

Well, assuredly, I agree with you. But your explanation sounds to me like my theological explanations must sound to you. This wordplay by no means gives me one reason to believe that it is possible, nor can I make any sense of a series of cause-effect events in time that exists, and yet never began. If I attributed the same principle to you about God you would laugh me out of the room. But I find around here that no principle that is absurd in asserting God's existence is ever absurd in denying it.

I appreciate your effort to try and explain it to me, but it is not something I am likely to ever think possible, and modern cosmolgoy gives me no real reason to worry over it at any rate.

Clutch

luvluv, since the quote was from me, I assume you were replying to me.
No. If the principle you invoked was a fundamental definition of mathematics, nobody would laugh you out of the room.

This was why I pointed out that "common sense" is a lousy guide to thinking about infinity. If your final position is that getting sufficiently clear on infinity, in order to make sense of what is and isn't a contradiction, is too hard, or finicky, or abstruse, the lesson surely is that you should not advance the Cosmological Argument.

Eudaimonist

I find that the Ontological argument doesn't really make sense unless you've already accepted a Platonic metaphysics, and the Cosmological and Teleological arguments don't make perfect sense unless you accept an Aristotelian physics and biology, respectively.

I think all these arguments are dated. The only half-way serious arguments around today are irreducible complexity and presuppositionalism. I think these arguments fail, but at least they are something different from the tired old ones.