WL Craig's Kalam Cosmological Argument - Page 2

Brian Bosse · #41 (**permalink**) 08-28-2007, 01:27 AM

Hello Joel,

Yes, I can see how my last post was confusing. Forgive me.

1. Cantor's diagonal argument requires the assumption that all sets (including infinite sets) are actual.
2. There is a school of mathematics that deny this. In fact, from Aristotle onward there have been people who denied actual infinity.
3. I am not so against the concept of taking a set, such as the set of natural numbers, and treating it is a complete whole.
4. However, I am completely against those who think transfinite mathematics cooresponds to the real world just because they have developed some formal system.

Quote:

I guess this is the crux of the matter...either the transfinite is an attribute of the real world or it is not. If it is, then Craig's argument fails because there has never been a point in time when the world began to exist.

I have argued against the universe being eternal independently of the transfinite. In other words, my argument does not have anything to do with the transfinite. Those who appeal to the transfinite in an effort to say the an eternal universe could be possible may as well have appealed to the Telly Tubbies. Neither speak to the issue.

Again, sorry for the confusion. The KLM is sound, but it does not prove much on its own.

Brian

sotzo · #42 (**permalink**) 08-28-2007, 01:34 AM

Thanks Brian...I see your point and it helps me understand Craig's argument better, especially where it is deficient.

Brian Bosse · #43 (**permalink**) 08-28-2007, 09:46 AM

Hello Sotzo,

You are welcome. I am not sure, though, that T.E. agrees. I think he still holds that one is not able to dispell the possibility that the universe represents an actual infinity in terms of its age, and as such KLM is not proved sound. In this regard, he has not commented on the argument I provided.

Sincerely,

Brian

tewilder · #44 (**permalink**) 08-28-2007, 08:04 PM

Quote:

Originally Posted by Brian Bosse

Hello Sotzo,

You are welcome. I am not sure, though, that T.E. agrees. I think he still holds that one is not able to dispell the possibility that the universe represents an actual infinity in terms of its age, and as such KLM is not proved sound. In this regard, he has not commented on the argument I provided.

Sincerely,

Brian

I don't see why God can't create an actual infinite, and in addition to the space time continuum we are in, perhaps in another work he did.

Brian Bosse · #45 (**permalink**) 08-28-2007, 09:14 PM

Hello T.E.,

Quote:

I don't see why God can't create an actual infinite, and in addition to the space time continuum we are in, perhaps in another work he did.

Earlier, I asked if God could create a square circle. Do you care to answer that question? Also, to be very precise here, the debate is not whether or not God can create an actual infinite, but whether the universe has been around for an infinite amount of time. Again, I have provided an argument for why it has not.

Sincerely,

Brian

tewilder · #46 (**permalink**) 08-29-2007, 09:17 AM

Quote:

Originally Posted by Brian Bosse

Hello T.E.,

Quote:

I don't see why God can't create an actual infinite, and in addition to the space time continuum we are in, perhaps in another work he did.

Earlier, I asked if God could create a square circle. Do you care to answer that question? Also, to be very precise here, the debate is not whether or not God can create an actual infinite, but whether the universe has been around for an infinite amount of time. Again, I have provided an argument for why it has not.

Sincerely,

Brian

Your argument assumes a cardinality of Aleph0 and that every moment corresponds to a natural number. Therefore every moment is only a finite time away.

But suppose we don't limit the cadinality this way. Then take moment Aleph+6. That moment is a specific moment, and it is infinitely remote.

Civbert · #47 (**permalink**) 08-29-2007, 10:51 AM

Brian,
I think the following was your argument against an "actual" infinity:

Quote:

Originally Posted by Brian Bosse

Now, let's apply this to the universe. If the universe is infinite, then there exists a point u(1) that is an infinite time span away from today T(0). Given an infinite set of intervals from u(1) corresponding to the set of natural numbers we would get something like this...

Code:

N:                1    2    3  ...   n ... 
Time Interval:  u(1) u(2) u(3) ... u(n) ...

If we are here today, T(0), then there exists a time from u(1) such that it is a finite time to T(0). (If there is no interval of time from u(1) such that it is a finite distance of time to T(0), then we cannot be here. There is no interval of time to get us here.) Since we are here, then if the universe is infinite, there exists a time from u(1) such that it is a finite time to T(0). However, by the NAT there does not exist any 'n' such that u(n) is a finite interval of time from T(0). Therefore, the universe is not infinite.

This argument establishes the truth of premise 2. Premise 1 seems uncontroversial, and as such the argument can be declared sound. Q.E.D.

I think Premise 1 is controversial. "If we are here today, T(0), then there exists a time from u(1) such that it is a finite time to T(0)." This already presumes a finite universe. I think to make this claim, you must assume that there is alway a finite distance between u(1) any u(n). But if the distance from u(1) to u(n) is infinite, then the time to T(0) is also infinite.

One could have easily said: For every point with a distance of x from here, there is a point that has distance of x+1. This seems to be an uncontroversial statement.

It applies to the material universe. One can not define a point beyond which there is no further point, because there is always the point that is 1 measure beyond it.

I also have a problem with the meaning of "reality" being assumed.

Quote:

I disagree. The mathematics of the transfinite has nothing to do with reality. It is simply a formal construct. A formal game played by mathematicians if you will. On the other hand, I presented an argument as to why the universe cannot have already existed for an infinite period of time. Let me be real clear here: appealing to the mathematics of the transfinite is nothing but a smokescreen. The mathematics of the transfinite does not substantiate an actual infinity in the real world in any way.

It appears that you are using the term "reality" to mean very specifically, the material world. In other words, you seem to imply that the set of natural numbers are"unreal" because you can not conceive of them have actual correspondence to the material universe. This seem to be a metaphysical commitment that leads to a whole slew of problems when speaking about the existence of God and spiritual things.

Brian Bosse · #48 (**permalink**) 08-29-2007, 08:07 PM

Hello T.E. and Anthony,

Quote:

Originally Posted by T.E.

Your argument assumes a cardinality of Aleph0 and that every moment corresponds to a natural number. Therefore every moment is only a finite time away.

If the universe really is infinitely old, then there exists some point in the past, say u(1), that is an infinite interval from today. Here is the point, there is no successive amount of time from u(1) that is still not an infinite amount of time from today. If there ever is, then u(1) was not an infinite amount of time from today. Therefore, there cannot be a successive interval of time from u(1) to today. However, there must be if we are here. Since we are here, then u(1) is not in the infinite past.

Quote:

Originally Posted by T.E.

But suppose we don't limit the cadinality this way. Then take moment Aleph+6. That moment is a specific moment, and it is infinitely remote.

Call this infinitely remote point u(1). There exist no successive interval of time from u(1) to today. But we are here. Therefore, there must be such an interval. Therefore, u(1) is not infinitely remote.

Quote:

Originally Posted by Anthony

I think Premise 1 is controversial. "If we are here today, T(0), then there exists a time from u(1) such that it is a finite time to T(0)." This already presumes a finite universe. I think to make this claim, you must assume that there is alway a finite distance between u(1) any u(n). But if the distance from u(1) to u(n) is infinite, then the time to T(0) is also infinite.

Don’t you have a Scripturalism thread you should be attending to?

The key point is that we are here today. Mathematicians point out that if in fact you do have an infinite sequence such as a succession of time (I used the sequence of digits in the expansion of 1/7 as an example), then no matter what point you pick in the sequence there will always be an infinite number of successions to follow. If ever this not the case, then the sequence was not infinite. So, if there really was a point in the infinite past that the universe existed, say u(1), then there is no succession of sequences, say ‘n’, such that ‘n’ is not an infinite distance from today. But since we are here today, then there must be a succession of sequences, say ‘n’, such that ‘n’ is a finite distance from today. Again, if this is not the case, then we cannot be here today.

Quote:

Originally Posted by Anthony

One could have easily said: For every point with a distance of x from here, there is a point that has distance of x+1. This seems to be an uncontroversial statement. It applies to the material universe. One can not define a point beyond which there is no further point, because there is always the point that is 1 measure beyond it.

I am not sure what the pertinence of this is. If the universe is infinitely old, then there exists a point from today, say u(1), that is an infinite distance from today. The problem is getting from u(1) to today. There is no amount of time from u(1) such that it still isn’t an infinite distance from today. If there is such a time, then u(1) was not an infinite distance away. Therfore, if u(1) really was an infinite distance away, then we can’t be here. However, we are here. Therefore, u(1) is not an infinite distance away.

Quote:

Originally Posted by Anthony

I also have a problem with the meaning of "reality" being assumed. It appears that you are using the term "reality" to mean very specifically, the material world.

Well, that is what we are talking about. We are talking about the universe itself - material existence. I am saying that it is impossible for the material universe to be eternal. I have provided an argument for why it is not. This has nothing to do with God being eternal.

Quote:

Originally Posted by Anthony

In other words, you seem to imply that the set of natural numbers are"unreal" because you can not conceive of them have actual correspondence to the material universe.

I can conceive of there being a correspondence. I just cannot conceive of the natural numbers being exhausted in terms of the age of the universe. This is what those who appeal to an actual infinity in terms of the age of the universe do. They say that the age of the universe is at least a surjection with the natural numbers. If this is actually the case, then we cannot be here today. Any point from the infinite past is still an infinite distance from today. Think of it this way: how long is eternity? Let’s say T(aleph0) represents some point in the infinite future. We are here today at time T(1). In a billion years we will be at T(10^9). What is the distance from this point to T(aleph0)? It is still an infinite distance away. There will never be a time T(x) such that the distance is finite. Yet, for those who say the universe is eternal, this must be the case for us to be here today.

Quote:

Originally Posted by Anthony

This seem to be a metaphysical commitment that leads to a whole slew of problems when speaking about the existence of God and spiritual things.

I disagree. It is incoherent to speak of a completed infinite. By definition, the infinite is potential (given any ‘x’, there exists an ‘x+1’). Speaking of an actual infinity is like speaking of a round square. If you think you need to be able to posit an actual infinity for God, then please state where. I will be happy to try and provide a formulation or explanation that is both orthodox and avoids the incoherence of an actual infinity.

Sincerely,

Brian

tewilder · #49 (**permalink**) 08-29-2007, 08:25 PM

"There exist no successive interval of time from u(1) to today."

Why not? It doesn't seem any crazier than, say, the Axiom of Choice.

sotzo · #50 (**permalink**) 08-29-2007, 11:37 PM

Quote:

Originally Posted by tewilder

"There exist no successive interval of time from u(1) to today."

Why not? It doesn't seem any crazier than, say, the Axiom of Choice.

I don't see the parallel between the AC and the issue of whether matter has existed eternally.

Also, what is your counterargument to the view that there is a Tzero, and that if there was no Tzero, there would be no Tnow?

tewilder · #51 (**permalink**) 08-30-2007, 08:59 AM

Quote:

Originally Posted by sotzo

Quote:

Originally Posted by tewilder

"There exist no successive interval of time from u(1) to today."

Why not? It doesn't seem any crazier than, say, the Axiom of Choice.

I don't see the parallel between the AC and the issue of whether matter has existed eternally.

Well, try it. Produce a pair of real numbers where one is the real number that is next larger than the other.

If you can't, why should analogous demands be expected of infinite sequences?

Quote:

Originally Posted by sotzo

Also, what is your counterargument to the view that there is a Tzero, and that if there was no Tzero, there would be no Tnow?

It's just an assertion.

tewilder · #52 (**permalink**) 08-30-2007, 09:31 AM

You might want to take a look at some of Ehrlich's work.

Here is a view of an anthology:

http://projecteuclid.org/DPubS/Repos...rml/1081878082

It is has an article by Conway on the surreal numbers, and Erhlich's work on infinity is based on Conway's earlier studies. Some essays into into the matter of infinite real numbers, infinitesimals, and their reciprocals. As an alternative to the surreal numbers (of which the reals are a part) there is a paper by H. Jerome Keisler on the hyperreals which also have infinite and infinitesimal numbers.

For some sense of what the course I took from Ehrlich was like see this:

http://www.pitt.edu/~pittcntr/Being_...pr_11_2006.htm

tewilder · #53 (**permalink**) 08-30-2007, 09:44 AM

See also:

Abstract of:
The absolute arithmetic continuum and the unification of all numbers great and small.
http://www.univ-nancy2.fr/poincare/c...ts/ehrlich.pdf

sotzo · #54 (**permalink**) 08-30-2007, 10:38 PM

Quote:

Well, try it. Produce a pair of real numbers where one is the real number that is next larger than the other.

If you can't, why should analogous demands be expected of infinite sequences?

I don't think the issue is infinte sequences per se, but infinte sequences involving time. I subscribe to a realist view of time (Newtonian time). In such a framework, of course, time is bound up with the existence of matter. If matter is eternal, then time is not eternal..if time is not eternal then tzero occurred at some point in the past.

tewilder · #55 (**permalink**) 08-30-2007, 10:46 PM

Quote:

Originally Posted by sotzo

Quote:

Well, try it. Produce a pair of real numbers where one is the real number that is next larger than the other.

If you can't, why should analogous demands be expected of infinite sequences?

I don't think the issue is infinte sequences per se, but infinte sequences involving time. I subscribe to a realist view of time (Newtonian time). In such a framework, of course, time is bound up with the existence of matter. If matter is eternal, then time is not eternal..if time is not eternal then tzero occurred at some point in the past.

That is merely the time in this creation. It does not limit what God could have created, or may have created in another act of creation.