Hans

I would like to presume for the sake of this inquiry that in order for the universe to have always existed an infinite regression of events prior to the present is necessary.

Is there a sound argument to support the assertion that it is impossible for an infinite regression to have occured?

Thanks for any help.

Keith Russell

Greetings:

I thought Xeno's Paradox had been soundly refuted.

Keith.

Hans

I guess I'm playing catch-up.

I presume Xeno's Paradox is the argument used to discount the possibilty of infinite regress. Are you aware of a link to the argument and/or its refutation?

I'm doing a google search now.

[ August 16, 2002: Message edited by: Hans ]</p>

Hans

Xeno's Paradox deals with an object traveling a finite distance. I'm not sure it's the same thing as discounting the possibilty of an infinite regression of events.

beausoleil

This is the link I found, which seems quite good.

<a href="http://www.mathpages.com/rr/s3-07/3-07.htm" target="_blank">http://www.mathpages.com/rr/s3-07/3-07.htm</a>

I don't find his argument about mirrors convincing, however. The calculus approach demonstrates that spac can be infinitely divisible and the hare still catch the tortoise in finite time. Similarly the light beam spends a finite time in the mirror arrangement. However, to determine which angle it emerges at one has to find the nth term of a series similar to (-1)^n in the limit n -&gt; infinity, which is undefined. The contrast with the tortoise and hare is that we can race a tortoise and hare, but can't construct the mirror arrangement. So [i]that[/i[]a feature of the mirror arrangement is hard to conceive of doesn't bother me much. Still, I'd be interested to hear other thoughts.

tronvillain

Hans:
I am not aware of one.

Bill

Gee; I just had something to say <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=1&t=002199" target="_blank">over in the Feedback Forum</a> on this same topic. There, I said: The whole matter of infinite distances in time and/or space is quite literally mind-boggling. In other words, for some reason, our minds seem to rebel at the idea of any actual infinities actually existing in reality. As finite beings, it is very difficult for us to conceptualize the idea of a truely infinite extent along any axis of dimensionality.

William Lane Craig's "greatest argument" in favor of his God is his Kalam argument, which asserts (in brief) that no actual infinity can exist, therefore time must have had a beginning. From that stepping-off point, Craig asserts that his God must have caused the beginning of time. Craig conveniently ignores the fact that his God must have also existed for an infinite amount of time and had no cause. Why, then, cannot the natural universe have existed for an infinite amount of time and had no first cause?

These matters are covered on the II <a href="http://www.infidels.org/library/modern/theism/cosmological.html" target="_blank">Cosmological Arguments</a> page. Dan Barker's <a href="http://www.infidels.org/library/modern/dan_barker/kalamity.html" target="_blank">Cosmological Kalamity</a> is one of those that asserts the idea I express, above, that any argument that denies the possibility of an actual infinite amount of past time simultaneously denies the Christian idea of a God who has existed for an infinite amount of past time.

Craig's Kalam argument is actually an ancient argument from Islamic philosophy (thus, the unusualy name, Kalam, which is an Islamic word). As such, it comes to us from a time before the invention of Calculus. That is, long before humanity had any real understanding of the idea of infinity.

The Kalam argument is set forth simply, in these terms: <ol type="1">[*]Whatever begins to exist has a cause of its existence.[*]The Universe began to exist.[*]Therefore, the Universe has a cause of its existence.[/list=a]Some physicists attack the first premise on the grounds of quantum mechanics, which holds that "uncaused effects" do occur. In other words, at least in the realm of quantum mechanics, some things do begin to exist, but have no cause. Thus, these physicists assert, premise 1 is clearly false, based upon the findings of 20th century physics.

I attack the second premise on the grounds that the so-called "Big Bang" does not involve "a beginning of existence." Thus, we have no real proof that "The Universe began to exist." Instead, we have an arbitrarily-defined T = 0 time from which we measure the progress of the "Big Bang" phenomena as it develops into the space/time continuum within which we live.

Unless you assert that the state of our space/time continuum at T = 0 time represents an instance of creation ex nihilo (literally, "out of nothing"), then the "nugget" that comprises the "Big Bang" at T = 0 time had a prior existence in some form or another within some sort of "other" space/time continuum.

First, unlike relativity, neither quantum mechanics nor string theory postulates an initial size of zero at T = 0 time. Both quantum mechanics and string theory lead to the conclusion that there is a minimum size to the energy contained within the "Big Bang" "nugget" at T = 0 time. That minimum size is small, but finite and comprehensible. Given that state of affairs for T = 0 time, it is actually incomprehensible that the "nugget" of space/time which expands into the "Big Bang" had no existence whatsoever, in any form, prior to T = 0 time.

==========

Physicists have hypothesized about just what sort of "prior existence" that "nugget" of space/time might have had "prior to" T = 0 time. One hypothesis is the so-called "many worlds" hypothesis, which seems to assert that our particular space/time continuum is just one of an infinite number of parallel space/time continuums (or "parallel universes," if you will), and that new sets of space/time continuums are continuously being created in various states (including, obviously, in the "nugget" state). Another hypothesis is that the "nugget" derives from a "fluctuation" within a "quantum vacuum" that exists within a larger space/time continuum of some sort. This one is most compatible with string theory, which seems to hold that only those space/time continuums with exactly three dimensions of space can develop into complex states of matter and energy. All larger numbers of spatial dimensions tend to "fall apart" rapidly, thus creating states of quantum vacuum, from which it is possible to obtain "nuggets" of space/time that can develop into complex states of matter and energy, much like our own.

All of these are clearly hypothetical situations, as it is (at this time) impossible to even conceive of just how one would go about attempting to test these kinds of hypotheses. Nonetheless, modern scientific thinking broadly challenges the idea that "The Universe began to exist" at T = 0 time. Instead, the best version of modern scientific thinking is that there is some larger reality (whose nature is presently unknown, and possibly unknowable) out of which the "nugget" of stuff that existed at T = 0 time somehow managed to separate itself and "cause" the "Big Bang."

"That's my story, and I'm sticking to it!"

== Bill

Plump-DJ

My own 2 cents.

I thought Thomas Aquinus had based an argument around the so called impossiblity of an infinite regress, but i can't quite remember how it goes. (something to do with their being at least one non-contingent behind it all or something which btw has always made good sense to me)

I think both the theist and atheist must address the same question if they do not accept an infinite regress -- What is the nature of ultimate or absolute reality? Is it just energy and matter? Or is it personal and spiritual like God?


To Bill...

I'd like to address a couple of the points you raised if i may.

Well i don't know if they still do. I think it's been shown that virtual particles are not analogous to creation from nothing, which btw is an absurd proposition. (Just ask David Hume ) It's one thing to say the cause is unknown, it's another thing altogether to say that stuff can spring fron the complete absense of any sort of stuff. (or non-stuff) I'd also add that if a universe can come from absolutely nothing then so can anything else, which has interesting implications for any sort of "rational" inquiry into the nature of realiy, doesn't it?

"How did this get here??"
"I have no idea mate, maybe it sprang from complete non-existence, just like the universe did?"

Well the BB represents (to the best of my knowledge) the beginning of all the matter, energy and the space/time dimensions associated with that -- which is generaly what we mean by universe. (or at least that's what i mean ) In otherwords at some point (logicaly here) the universe (MEST) emerged from something else. So i'm not sure what the real *qualitative* difference is between that and a beginning.

Plump-DJ

[ August 17, 2002: Message edited by: Plump-DJ ]</p>

beausoleil

Surely the 'resolution' of xeno's paradox shows that there can be an infinite regression of 'causes' in the past in a finite time.

Bill

Formally, you have equivocated the meaning of the word "universe." Equivocation occurs when a word takes on two different meanings according to how it is used.

The on-line dictionary defines <a href="http://www.m-w.com/cgi-bin/dictionary?va=universe" target="_blank">universe</a> this way: As you can see, it is very easy to equivocate the word <a href="http://www.m-w.com/cgi-bin/dictionary?va=universe" target="_blank">universe</a>. In fact, the more expansive definitions are fairly recent in origin (i.e., 20th century constructs).

Definition 1-a, above, is the typical theist assertion ("a systematic whole held to arise by and persist through the direct intervention of divine power"), and that is what I'm attacking in my post, above (the idea that a God is "necessary" for a "universe" to exist).

In discussions of this sort, my preference is to reserve the use of the word <a href="http://www.m-w.com/cgi-bin/dictionary?va=universe" target="_blank">universe</a> for its most-inclusive sense, which is the basic definition "1 : the whole body of things and phenomena observed or postulated." In this sense of the word "universe," if God exists, then God must necessarily be part of the "universe" of all things that are observed or postulated to exist. This idea is consistent with <a href="http://www.infidels.org/library/modern/bill_schultz/crsc.html" target="_blank">my views on the question of "intelligent design."</a>

Taken in that sense, when you say "the universe (MEST) emerged from something else," you have introduced a self-contradiction of terms, in that the "universe" of "the whole body of things and phenomena observed or postulated" would necessarily include the "something else" out of which you assert that the "universe emerged."

==========

To make matters a bit more clear, I will accept for the moment the idea that the "Big Bang" phenomena we've been discussing here is the same as what we define the word "universe" to mean. In that sense, your statement would make sense. But you would merely be aligning yourself with those physicists who postulate somes sort of "multi-verse" (a word coined to distinguish itself from the unity implied by the word "universe") as the "something else" out of which our "Big Bang" "universe" emerges. However, cosmologists believe, with some certainty, that humans will eventually discover how to explore this region of "something else," and thus at that point it will logically align as part of the "observed phenomena" which comprises our "universe" (in my sense of the word and yours both, because in your sense, if we can observe this "something else" in a lab today, it would certainly be a part of the "Big Bang universe," now wouldn't it?).

==========

We see in this discussion exactly why Wittgenstein focused almost entirely on language as the primary "problem" for philosophers to untangle. In the past, the use of multiple senses of words was not always so easy to sort out.

==========

Anyway, the main thing that I am preching against here is the idea of creation ex nihilo (literally, "out of nothing"). If you acknowledge that the "Big Bang" emerged from "something else" then you are acknowledging that the "Big Bang" had a prior cause that lies within that "something else" and is thus not the product of creation ex nihilo. Buried someplace deep within that "something else" out of which the Big Bang emerges lies either an infinite regress of causes or else a First Cause.

But Wittgenstein showed that the idea of a "First Cause" actually existing is a problem that arises due to our inability to explain our own existence. In fact, the postulated "First Cause" cannot be logically present, because the existence (or discovery) of said "First Cause" would necessarily require that we ask the question of "what caused that First Cause?" Again, as Wittgenstein showed, theists traditionally dismiss that question by responding with something along the lines of "you can't question God!" But that merely demonstrates the faith of the theist in God being the ultimate answer to every possible question. That "answer" is really a total non-answer!

Jim Still brilliantly deals with this subject in his essay <a href="http://www.infidels.org/library/modern/james_still/w_why.html" target="_blank">The Mental Discomfort of "Why?"</a> I cannot recommend his essay too highly because it clearly demonstrates that:

• The question of a "First Cause" for the entirety of existence cannot be answered by any possible scientific, philosophical, or logical investigation carried out from within the very existence whose cause is being questioned; and
• That anyone who asserts otherwise is merely asserting their faith in some particular conclusion, and also refusing to explore the idea that their alleged "First Cause" must (or at least, might) have had some sort of "cause" for its own existence.

Given the extreme clarity with which Wittgenstein answered this whole business of the "First Cause," it is a real wonder that this same sort of debate continues to arise, over and over again. However, as the above essay by Jim Still clearly shows, the idea of a "First Cause" actually existing is ludicrous, and so we must content ourselves with believing in the idea of an infinite regress of causes, and somehow seek to frame our particular worldview(s) (theist or nontheist) within that sort of overall framework.

Only then can we be truly honest with ourselves about the limits of human knowledge and what we might hope to discover before humanity and all of its descendants ultimately goes extinct.

== Bill