I've seen several critiques of Craig's argument from the atheist camp. I have heard that there are Reformed Christians who may disagree with Craig's conclusion or premises. Two questions:

1. How is the Craig's argument any different than the traditional cosmological argument?

2. Does anyone know of any critiques of Craig's Kalam argument from a Reformed Christian perspective? (BTW, not looking for a presupp critique of the Kalam argument as it relates to whether evidential vs. presupp apologetic approaches...i'm really interested in the actual validity of the argument itself.)

Here is the argument:
Premise 1: Everything that begins to exist has a cause.
Premise 2: The universe began to exist.
Conclusion 1: Therefore, the universe must have a cause.

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Joel Batts
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What's Kalam?

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I've never been able to find what "Kalam" means - of course, nobody has ever accused me of being a Google genius either.

Seriously though, that is part of my question...finding out what Kalam means and how it is different than the traditional cosmo. arguments.

Kalam I believe was a Muslim apologist who was the first to formulate the Cosmological argument for the existence of god (well, in his case Allah). Don't completely quote me on that though.

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Brian Vandenburg
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The argument is certainly vaild. I assume you are inquiring into its *soundness*. I think the argument has a prima facie persuasiveness to it, and can be used to increase the warrant of the reasonableness of Theism. However, used as a pre-dogmatic formulation of a demonstative argument for the existence of God, it will have its share of problems. So if one were to say the belief in God is properly basic, it could function as piece of natural theology. I don't think Christians should have a problem with the argument per se, just if it is used as a foundation for belief in God (pre-dogmatic).

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^Brian Lanier^
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I first heard of the word "kalam" in the context of early Islamic philosophy/theology. کلام

The word literal means "to speak", but it was used to describe a dialectic approach: Propositions and counterargument. Why it is used for this particular argument I don't know.

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R.Vic Bottomly
Providence Reformed Baptist Church, Tacoma, WA

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I'd add that it appears to depend upon an empirical observation: the universe had a beginning. That has to be established first.

Craig's response to this point is that we know the universe had a beginning because if it did not, the universe would be infinite and it is impossible to traverse an actual infinite. He then makes the point that since you cannot traverse an actual infinite we would never be at this place in time having our discussion (if the universe indeed had no beginning) since there would be an infinite series of events to get to this point...in other words, there would be no time zero from which to come to this point in time.

Wow, that seems like a bigger and more difficult argument than the first one. I see a hint of Thomas Acquinas in that one, but I'd have to go back to my books to be sure.

If you were Zeno you could just say that we don't really traverse space anyway.

Also, it seems like one could object that, even if a cause were conceded, the cause need not be the Trinity.

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No, and he admits that. That is why he then argues for the resurrection. He attempts to show that there needs to be a timeless, immaterial, personal cause that starts the universe. But why would such a cause start the universe? He then points to the resurrection. Jesus being resurrected by God is the only explanation of the facts that we have, and if this is the case then Jesus has God's "stamp of approval" (because only God could raise Jesus from the dead). Well, Jesus gave his stamp of approval to the Jewish religion as it was fulfilled in him. Thus, Christianity has God's stamp of approval. Therefore, whatever Christianity says about why we are here and who God is is true. Given that he is an evidentialist, he will then say that while this is not an infallible proof for Christianity or God, it is on the whole the most probable explanatory model we have given the evidence.

As for Kalam, it is either the name of the Muslim philosopher or the name the Muslim philosopher who thought up the argument gave it.

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Mark Maney
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I do not know if there is a traditional cosmological argument. I just know that there are different versions of the argument.

One could say that the argument does not necessarily prove the existence of the Christian God, but Craig would respond that the argument only intends to prove that God exists and that another argument is needed to prove that the God who exists is the Christian God.

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Curt Hayashida
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Although you were joking, that's actually a good point. Zeno shows that we traverse the infinite every time we move from A to B. So it is not a given that we can not traverse an actual infinite.

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R. Anthony Coletti
Midway Presbyterian Church (PCA)
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[i]et venite et arguite me dicit Dominus[/i]

Well, there are arguments on both sides. I tend to think that Craig has the better argument (i.e., the impossibility of an actual infinite). Again, I think most (if not all) Christians would agree with that the universive has not *always* existed. Perhaps not so for the unbeliever, but then again he has an metaphysical stake in denying the argument (not to say that believers don't as well!). So again, this argument may have value as a piece of natural theolgy, so long as the Christian does not use it as providing a foundation to the Christian faith. (Then there is the question as to how Craig uses the argument himself and I'm not sure that is clear either.)

Hello Gentlemen,

The argument is valid. An actual infinity is incoherent and oxymoronic. All me to make a distinction between a finite interval of time that is subdivided into an infinite number of smaller intervals, and an infinite interval of time divided into an inifite number of intervals. Zeno's arguments play on the former, whereas the latter is the claim being made by those who say that the universe is uncreated. Consider an infinite string of digits (for instance, the number one-seventh) that is put into a one-to-one coorespondence with the set of natural numbers.

Mathematicians will note that for any given 'n' in the set of natural numbers corresponding to a particular digit in the sequence of one-seventh, there are an infinite number of digits that remain. If for some given 'n' this is not the case, then the sequence is not infinite and has an ending. We will call this the non-actuality theorem (NAT). 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...

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 infinte, 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.

Brian

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Brian Bosse
Faith Community Church
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Brian

Nice proof...you've explained precisely why Zeno's paradox doesn't apply here. The famous tortoise racing Achilles example (where Achilles never catches up) that is used to illustrate the paradox would be apples to apples with Craig if there were no starting line for the race. As it stands, they have a T(0) and, therefore, the paradox resolves.

The problem with Criag is that he assumes ZFC set theory. Pick a different set theory that allows proper classes and you can build a coherent transfinite arithmetic and the paradoxes go away.

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T.E. Wilder
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Hello T.E.,

I am no expert, but Mathematical Logic and Set Theory are a hobbie of mine. I am not sure what you mean by "there being a coherent transfinite arithmetic and the paradoxes go away." Can you explain? What paradoxes go away? How do "Proper Classes" solve any of these paradoxes?

Thanks,

Brian

There is a guy named Philip Ehrlich who has worked out a transfinite mathematics. Craig argues on the basic of the old paradoxes of cardinality where, for example, the cardinality of the set of natural numbers is Aleph, and Aleph + 1 = Aleph and Aleph + 2 = Aleph, and so on, because it can't get any bigger, until you jump up to the next order of cardinality, say that of the real numbers.

So Craig says if you have an actual infinite where for example you add a moment to an already elapsed infinite number of moments you wouldn't have any more moments because the total of them is still Aleph.

Ehrlich showed that if you don't used restrictive set theories such the Zermelo-Fraenkel set theory but instead something like Hilbert-Akerman you can construct a transfinite ordinal arithmetic where Aleph does not equal Aleph + 1 which does not equal Aleph + 2 and you can do normal operations of addition and subtraction.

Ehrlich has also done interesting studies of thermodynamics. For example, he has a book Negative, infinite, and hotter than infinite temperatures.
http://www.springerlink.com/content/j45862lt261g3q34/
He said that although thermodynamics does not require an actual infinite, the math for it stands ready in case some application for it does turn up.

Craig knows nothing of this stuff, and his book does not take it into account.

Actuallly, it is a much longer story than that, but there is the main point.

A book to read along side of Craig would be Infinity: An Essay in Metaphysics by Jose Benardete. What Craig does is turn over the supposed paradoxes of the infinite until you mind boggles and you agree with his intuition that the actual infinite is impossible. But Benardete's mind does not boggle as easily as Craig's, and he does not report the same intuition.

Hello T.E.,

I am unfamiliar with Hilbert-Akerman set theory. Can you point me to the axioms that make up this formal system?

The concept of an actual (completed) infinity is incoherent to me. I can grasp potential infinity just fine. The touble with an actual infinite is that it must contain a potential infinity. The natural numbers are such an example. There is no 'n' such that 'n+1' does not exist. Yet, those who hold to an actual infinity speak of the exhaustion of such a set. In what sense can such a set be exhausted? It cannot be in the sense that there is a last 'n'. I say all of this just to say that I am suspect of anyone whose mind is not "boggled as easily Craig's."

Brian

Hilbert and Ackerman published a book on set theory in 1928. It was later translated into English. I don't have the list of axioms. But what I do know is that for a transfinite arithmetic you need a set theory, such as the Hilbert Ackerman, that allows proper classes, that is classes that are not capable of being members of classes.

"The concept of an actual (completed) infinity is incoherent to me."

I don't see why God, for example, couldn't make infinite things, even if we could never get through them.

Hello Tewilder,

Can God square a circle? Can God list all of the natural numbers? No. Just as 'square' and 'circle' are not compatible, so is 'list all' and 'natural numbers'. The natural numbers are precisely defined. There is no ambiguity. Part of that definition is that for all 'n' there exists a successor to 'n'. To speak of this as being completed (actual) is the same type of talk as squaring a circle.

Brian