WL Craig's Kalam Cosmological Argument

Discussion in 'Apologetical Methods' started by sotzo, Aug 14, 2007.

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  1. sotzo

    sotzo Puritan Board Sophomore

    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.
  2. turmeric

    turmeric Megerator

    What's Kalam?
  3. sotzo

    sotzo Puritan Board Sophomore

    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.
  4. Beoga

    Beoga Puritan Board Freshman

    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.
  5. BrianLanier

    BrianLanier Puritan Board Freshman

    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).
    Last edited: Aug 23, 2007
  6. VictorBravo

    VictorBravo Administrator Staff Member

    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.
  7. VictorBravo

    VictorBravo Administrator Staff Member

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

    sotzo Puritan Board Sophomore

    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.
  9. VictorBravo

    VictorBravo Administrator Staff Member

    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.
  10. Davidius

    Davidius Puritan Board Post-Graduate

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

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

    tellville Puritan Board Junior

    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.
  12. cih1355

    cih1355 Puritan Board Junior

    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.
    Last edited: Aug 23, 2007
  13. Civbert

    Civbert Puritan Board Junior

    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.
  14. BrianLanier

    BrianLanier Puritan Board Freshman

    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.)
  15. Brian Bosse

    Brian Bosse "The Brain"

    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.

    N:                   1 2 3 4 5 6 7 ... n ...
    One-Seventh (1/7) : .1 4 2 8 5 7 1 ... 5 ...
    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...

    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 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.

  16. sotzo

    sotzo Puritan Board Sophomore


    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.
  17. tewilder

    tewilder Puritan Board Freshman

    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.
  18. Brian Bosse

    Brian Bosse "The Brain"

    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?


  19. tewilder

    tewilder Puritan Board Freshman

    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.
    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.
  20. Brian Bosse

    Brian Bosse "The Brain"

    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." ;)

  21. tewilder

    tewilder Puritan Board Freshman

    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.
  22. Brian Bosse

    Brian Bosse "The Brain"

    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.

  23. ChristianTrader

    ChristianTrader Puritan Board Graduate

    Does not any attempt to deny actual infinity have serious theological consequences? Either God is finite or actual infinity. No one wants any part of saying that God is finite. If one was to attempt the potentially infinite angle, then one would have to move over into completed infinity unless one wants to deny that God has exhaustive self knowledge.

  24. Brian Bosse

    Brian Bosse "The Brain"

    Hello C.T.,

    One needs to be very careful and precise in these types of discussions. The mathematical concepts of the 'finite' and 'infinite' are not the same when one speaks of creation being finite or when we speak of the everlasting God. The Cantorian actual infinity is not the same thing as saying God has no beginning or other similar sayings.

    Again, you need to be precise about what you are saying here. The idea of actual versus potential infinity is an idea that is proposed at our level of creation. So, this is the level the argument takes place in. Being that God created this level of existence there exists another level not accessible to us as creatures that necessarily is a level where God exists. We cannot comprehend this level. Things predicated at this level simply do not translate to our level of existence. So, if God is everlasting in the sense of existing always or before creation, because this necesarily is indpendent of creation, we cannot say that in our creation there is an everlasting past. The Bible speaks analogously to us. We cannot comprehend it in any other way. I have no problem saying that at the second level of existence there is no actual infinite. Regarding the other level, I cannot speak of. No created being can speak of this level except that which is revealed to us by God. Even then, God can only use second level references in analogy to describe the first level of existence. The bottom line is that this level of existence is ultimately unaccessible to us. So, when you speak of God's self-knowledge, you are necessarily speaking of something that is beyond us. It is not part of this level of creation. In other words, it is not what we are concerned with when we are speaking of concepts like actual or potential infinity, which are second level concepts. I believe any theological problems that you might see arising from this can be dealt with by making fine distinctions.


  25. CubsIn07

    CubsIn07 Puritan Board Freshman

    Although the KCA is sound in and of itself from what I have seen, you will notice that when Bahnsen debated Stein, Bahnsen said that he does not use the KCA apart from already presupposing the Christian worldview because good philosophers can get around the argument. I think Bahnsen would say that you are not allowed to use contrary premises in separate proofs. The problem is that you will have a hard time arguing the eternality of God, an uncaused cause, and the KCA to make one larger argument for Christianity. Yes an actual infinite seems impossible and the only way to get around this and maintain traditional Christianity it to postulate God's timelessness, but that is a difficult proposition. My point is that if you say that everything that begins must to have a cause, how do you know that God didn't begin to exist?
  26. Brian Bosse

    Brian Bosse "The Brain"

    Hello Cubsin7,

    Yes, Bahnsen would say that in the Christian worldview God is uncreated. As such, He is not subject the KCA. This means the Christian worldview can account for the universe being here. God created it; whereas, those worldviews not positing an uncreated creator fail. However, one needs to posit more than this because it is incoherent to speak of an uncreated creator in time. He needs to be eternal, and as such the Christian must embrace a God sans time even with the difficulties it presents. Any other alternate that I am unaware of just is not tenable.

    The only way to "prove" this is to assume it. Scripture is clear that God is the uncreated one. Therefore, the pragmatic analysis of worldviews (presuppositional apologetics) will show the sufficiency of the Christian worldview. However, KCA is not an argument for God per se. It only is an argument for the necessity of a creator for the universe whatever that is. In many ways it works the same as ID.


  27. tewilder

    tewilder Puritan Board Freshman

    What Craig is arguing against is a composed infinite, and infinite made up of an infinite number of parts.

    To make his argument is uses mathematical examples that presuppose a certain type of set theory, although he does not tells us (because he did not know himself) that other types of set theory the do not yield this result are possible.

    To make his argument he also argues that time is made up of parts, so an actual infinite time of a universe existing is a composed infinite of an infinite number of time parts, or events, or some such.

    Very quickly the argument gets complex, and not all the assumptions are out in the open.


    For the argument to not apply against the infinity of God, Craig has to argue that God is not composed, either in his being or in his duration. The sort of God that, say, the Federal Vision believes in that is essentially relational and goes through changes, emotional states, etc. would not be possible if Craig's argument is valid, but only the God of the philosophers, who is a purely simple, unchanging being.

    Of course, the Federal Vision people say that their God is Van Til's God. So if they are right, then Craig has made a dividing line between two basically different theologies.
  28. Brian Bosse

    Brian Bosse "The Brain"

    Hello T.E.,

    The issues are interesting.

    This may be the case. His appeals to things like the infinite hotel, etc... do point to non-intuitive issues that arise within Set Theory. However, I do not yet see how any set theory gets around these issues. For instance, all set theories will argue that the cardinality of the nuatural numbers equals the cardinality of the even numbers. It seems you are saying that there is a set theory where this is not the case. This is news to me, but I am no expert.

    With all of that said, I proposed an argument that does not presuppose a particular set theory. Rather, it denies the actual infinite in terms of the real world. It does not deny it in strict theoretical constructs. Most set theorists would not find this problematic. They will admit that the transfinite may not have a real world application and remain content with their construct. I love to study formal systems just for the sake of the logic behind formal systems (set theories are in this catagory).

    I disagree. The argument as stated only argues against an actual real world interval that is infinite as opposed to an interval that is finite divided into infinite parts. Also, when you speak of the infinity of God, I suspect you are equivocating on the term 'infinity'. I do not think the Bible uses the term in such a technical sense as mathematicians have defined it. A discussion regarding this would be interesting.


  29. tewilder

    tewilder Puritan Board Freshman

    Sure. But transfinite arithmetic is done with ordinal numbers, not cardinal numbers.

    What's more, there is a reason for that. Cardinality is defined as relative ordering. Two sets have the same cardinality if the members can be mapped one to one onto each other. This is the same as saying that each set can order the other (just so long as at least one can generate an order). For finite sets, this is the case when there are just as many members in each set. But if set A is mapped onto set B one to one, and set A still has members left over when B runs out, then A has a greater cardinality, and it is also the case that it has more members, is bigger than B.

    But what about infinite sets? The natural numbers vs. the real numbers. You cannot order the real numbers by the natural numbers, as Cantor's diagonal proof shows. But does that mean, in the case of infinite sets, that one has more members or is bigger? Or in the case of infinite sets is a difference of cardinality merely a matter of relative orderability and does not imply the informal concept of more?

    If you look at the standard texts: Kleene, Church, etc. the all assert without argument or even raising the question of equivalency that greater cardinality means "more", but I maintain that this is a unjustified metaphysical interpretation of set theory. Cantor just assumes this also, which I suppose is where the problem started.

    This is why in the transfinite realm, cardinal numbers fail. Cardinality, in my view, is not a fully arithmetic concept, and in the transfinite realm this becomes apparent.

    In this form it is question begging. You don't believe and actual infinite can exist in the real world, because you think that in the real would it is impossible.
    Well, we aren't talking about what the Bible says about God. We are talking about what philosophical theology says about God, and has said since ancient times. God is simple, unchanging etc.

    There are plenty of people who reject this sort of traditional metaphysics, but as far as I know only process theology people have an developed answer about what they would put in its place.

    Craig has a section in at least one of this books (I remember reading two or three) where he talks about the simplicity of God and how that exempts God from the argument, and he has a discussion trying to show that time must be thought of as consisting of moments or events and is therefore composed.

    Of course this gets Craig (if his argument is valid) only to the God of the philosophers. He then has to call on supplementary arguments as to why the God that his argument proves to exist would be the God of the Bible. Craig is well aware of that.
    Last edited: Aug 27, 2007
  30. tewilder

    tewilder Puritan Board Freshman

    Then there is this guy:


    who argues that God could create an actual infinite past, and yet Craig's argument would still be valid!
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