Big Bang - Evolution

[_MrStakhanovite]

Why is this so? What evidence do have for the proposition that within the presently understood big bang cosmological framework of the universe an actual infinity exists?

We have to be careful here, there is a vast difference between saying (a) the possibility of a physical actual infinity versus (b) the physical possibility of an actual infinity. I take Craig to be claiming the negation (a) instead of (b), and the negation (a) is the much stronger claim. Kalaam cosmological arguments lose all their force if there is a possibility of a physical actual infinity left open, the arguments hinge on the impossibility of a temporal regress, and the concept of time isn’t something that we can talk about as if it has material constituents.

[_mikwut]

Hi Stak,

We have to be careful here, there is a vast difference between saying (a) the possibility of a physical actual infinity versus (b) the physical possibility of an actual infinity. I take Craig to be claiming the negation (a) instead of (b), and the negation (a) is the much stronger claim.

I agree, but more specifically I think he is claiming the negation of the possibility of a physical actual infinity within our present Standard Model universe that includes a temporal historical regress in real time. It is also my understanding that if David Hilbert is correct, then Craig does negate (a), but that is what I am seeking further clarity on.

and the concept of time isn’t something that we can talk about as if it has material constituents.

This is where I got somewhat confused. What do you mean time can't be talked about as a kind of material constituent? Do you mean it isn't real? I understand that a view of time corresponding to the notions of “real time” implied by contemporary physics (particularly the General Theory of Relativity) is just that. To my understanding science has revealed that time not only has real effects on motion, change, and energy emission, but also that motion, change, and energy emission had real effects on the measurement of time. Time isn't a mere accidental property of motion or a mere subjective quality imposed on motion by someone measuring it. Time has been found to be an ingredient to both change and existence. It is the necessary condition for change and motion and produces the effect of duration. A finitely small minimum possible interval of time, (“Planck time” (tp= 5.39 × 10-44 s) is just like space, or information and can be talked about just like matter. This is why Bergson, Whitehead, Prigogine etc.. theorized that something like a non-contemporaneous distensive magnitude (earlier-later) has to condition reality, which is in a state of changing, becoming, and even enduring. Existence is not mere facticity at an instant, but rather a non-contemporaneous distension allowing for everything from continual transition (becoming) to continual enduring (the real flow of time).

This definition of time makes events into a real non-contemporaneously distended, interactive, asymmetrically related whole. Then, this (what I at least understand to be the present state of Big Bang Cosmology and physics which Craig relies on) is utilized by Craig and he is supported by Hilbert (who coined the Cantor's paradise in the first place) who shows an actual infinity to be inapplicable to any reality to which the axioms of finite mathematics can be applied.

To my understanding, Hilbert attempted to clarify the notion of an infinite numeric series which was thought to exist as a completed totality:

Just as in the limit processes of the infinitesimal calculus, the infinite in the sense of the infinitely large and the infinitely small proved to be merely figures of speech, so too we must realize that the infinite in the sense of an infinite totality, where we still find it used in deductive methods, is an illusion. (Hilbert, On the Infinite)

Hilbert is speaking about C-Infinity's (the existence of a mathematical infinity within a finite or aggregative structure) the same that Craig speaks of. He states that it contradicts the very axioms of finite mathematics. He goes on to state that the Russell-Zermelo paradox presents so many contradictions that it undermined deductive procedure in finite mathematics, these paradoxes of set theory are what Craig bases his absurdities on.

I admit I don't have the mathematical acumen to mathematically follow the discussion, but the historical discussion seems to support Craig, at least from my current vantage point.

my regards, mikwut

[_MrStakhanovite]

Hi Mik,

I agree, but more specifically I think he is claiming the negation of the possibility of a physical actual infinity within our present Standard Model universe that includes a temporal historical regress in real time.

I have to stop you here, because Craig does differ with the Standard Model in that he holds to an A-theory of time which says that the present is uniquely real (Presentism). Most physicists understand the Standard Model in B-theory, which time doesn’t have tense and that the present is no more real than the past or future. Craig is pretty upfront about what is at stake:

From start to finish, the kalam cosmological argument is predicated upon the A theory of time. On a B-theory of time the universe does not in fact come into being or become actual at the Big Bang; it just exists tenselessly as a four dimensional space-time block which is infinitely extended in the earlier than direction. If time is tenseless, then the universe never really comes into being, and therefore the quest for a cause of its coming into being is misconceived. (The Blackwell Companion to Natural Theology, pages 183-184)

In my opinion, Craig has some pretty big costs here. He has to deny Special Relativity and put forward his own theory (one that he got from Lorentz, an old aether theory) so he can get his A-theory, so he can then argue the Kalam argument.

This is where I got somewhat confused. What do you mean time can't be talked about as a kind of material constituent? Do you mean it isn't real?

Sorry about the confusion here, I was referring to something in my head that I forgot to put on my post. I was thinking of an example of how something could be mathematically necessary by physically impossible. Suppose we found a particle that was indivisible (call it a Blixa) that was the building block for all things in the universe. While 5.5 is mathematically necessary, it would be impossible for a thing to be made up of 5.5 Blixas.

Hilbert is speaking about C-Infinity's (the existence of a mathematical infinity within a finite or aggregative structure) the same that Craig speaks of. He states that it contradicts the very axioms of finite mathematics. He goes on to state that the Russell-Zermelo paradox presents so many contradictions that it undermined deductive procedure in finite mathematics, these paradoxes of set theory are what Craig bases his absurdities on.

It is my understanding that Hilbert was speaking about an actual infinite collection that was made through successive addition, where the finite becomes infinite. Sort of like how there isn’t a point where adding one more sock to a group of socks doesn’t change the whole from a non-pile to a pile. Craig summed it up as:

[F]or every element one adds, one can always add one more. Therefore, one can never arrive at infinity. (from the Finitude of the Past and the Existence of God book, page 31)

But there is another important distinction we need to draw here, particular creation of actual infinities through successive addition and procedural creation of actual infinities. Procedural creation is not impossible, and we can (at least, I can) see this in the actual infinite collection of natural numbers created via the implementation of the successor relation to zero.

[_mikwut]

Hi Stak,

Thanks for the vine.

Most physicists understand the Standard Model in B-theory, which time doesn’t have tense and that the present is no more real than the past or future.

I am interested in your thoughts here. This is where your materialism/naturalism divide becomes substantive for me. I view the B-theory as simply a discussion about the actual nature of consciousness. And I am not sure on the statistics of "most physicists". Here is an interesting piece:

http://fqxi.org/data/essay-contest-file ... i_time.pdf

If everything is an illusion from conscious experience, free will, God, the flow of time - they all are simply dismissed by mere materialism but that ultimately just begs the question of materialism/idealism. But if you accept actual infinities, a neo-platonic idea of the forms - why dismiss the flow of time just because some physicists can't plot it as easily on graph paper? I am being somewhat trite, but why do you dismiss so many of your philosophy brothers that don't dismiss the A-theory?

But there is another important distinction we need to draw here, particular creation of actual infinities through successive addition and procedural creation of actual infinities. Procedural creation is not impossible, and we can (at least, I can) see this in the actual infinite collection of natural numbers created via the implementation of the successor relation to zero.

I need more background information here, a good book perhaps?

mikwut

[_mikwut]

Stak,

I didn't get to ask you how you would dismiss or consider in context with our previous discussion Vilenkin's proof? His often stated quote does seem to provide Craig with solid scientific backing:


"It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape: they have to face the problem of a cosmic beginning."

- Alexander Vilenkin

mikwut