Refuting Craig's Kalam Argument

[Westmiller]

I very much enjoyed Arnold Guminski's "The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities", though it seems to me that a more economic refutation of Craig might have been achieved by simply faulting his application of set theory terms to reality.
While the AV of Cantorian conversion premises is useful in its own right, the fundamental problem seems to be Craig's invocation of aleph zero as a "real" cardinal value. The premise for his case against actual infinities seems to be that they are incongruous with this purely mathematical "term of art".
From one perspective, Craig is right: the incongruities fault the SV translation... but he consequentially faults reality, rather than the formulation. If real infinities are not incoherent (I don't see that they are), then the Kalam argument disintegrates.

William Westmiller

[Alhazred]

Which is simply to deny that it is possible to enumerate real infinites. That is in mathematical set theory one does not need to enumerate a set in order to operate on it, but in the real world THIS IS NECESSARY. One cannot perform REAL operations on REAL INFINITES without necessarily enumerating them. This means you simply cannot operate on (ie count) a real infinte, therefore one cannot possibly say whether or not the real infinite of an infinite number of human's hands corresponds to the real infinite of the same infinite number of humans.

In fact to even talk about 'an infinite number of humans' is ridiculous. As soon as you do so you leave reality behind, so why in tarnation would you expect to get non-absurd results when you have an absurd postulate (that infinite humans actually exists).

As near as I can tell this line of reasoning actually SUPPORTS Kalam, but even so I see no reason to accept that a METAPHYSICAL infinite is absurd simply because a PHYSICAL infinite is absurd. Granted I haven't studied the original Kalam argument, but I don't find any reason to believe that part of the whole house of cards is particularly sturdy either.

[Westmiller]

Originally posted by Alhazred
One cannot perform REAL operations on REAL INFINITES without necessarily enumerating them. This means you simply cannot operate on (ie count) a real infinte, therefore one cannot possibly say whether or not the real infinite of an infinite number of human's hands corresponds to the real infinite of the same infinite number of humans.


Guminski allows the possibility of undenumerated infinities, but counters Craig's analysis by acknowledging the incongruency that he attaches to what I'd call the "density" of infinities (ie: there are more human hands than humans). He could have accomplished the same analysis by denying that there is any *real* cardinal number of an infinity.

[Paul Ricci]

Westmiller,Alhazred:

Sorry for the late entrance into this discussion regarding the Kalam Argument by Guminski.However, I have read a few different versions of the Kalam argument and your responses challenged me to raise a few questions.
Can anyone give me a good, clear example (other than the one postulated by Craig)of a "metaphysical impossibility" that does not reduce to our commonly known impossibilities (logical, physical and/or technical)? I have a suspicion this new kind of impossibility was invented, ad hoc, simply to make room to incorporate a metaphysical, non-material entity.

Second, it's been my understanding that any actual (real) infinities are impossible since, if causes go on forever, the universe itself would have run down because of entropy and we wouldn't be here today. However, if God himself is an infinite source of energy then his energy should have run out by now as well, and we shouldn't be here. If entropy doesn't apply to God (for whatever ad hoc reasons), then there is no reason to suspect that it must apply to the universe as a whole either. The question remains: Why are real (actual) infinities impossible, metaphysically or physically?

But, of course, the argument really doesn't apply to our universe in the first place since it is not infinitely old, but only some 15 billion years. Beyond that, there was no time, nor matter, nor causes as we understand them today. Even the idea of a created universe is suspect today by some cosmologists. What existed before the "Big Bang"? I'm not sure, nor is anyone else to my knowledge. Before the Planck time, the Uncertainty Principle tells us nothing. Shouldn't the question of what existed before the Big Bang (if anything)be left to cosmologists to determine? They don't yet need supernatural entities (see articles by Victor Stenger in this regard), as an explanation. So, is not the Kalam Argument, in any form, just an academic exercise of a unreal situation?
P.O.R.

[Westmiller]

Originally posted by Paul Ricci
Can anyone give me a good, clear example (other than the one postulated by Craig) of a "metaphysical impossibility" that does not reduce to our commonly known impossibilities (logical, physical and/or technical)?

Craig's objective is to invalidate "real" infinities, presumptively leaving "supernatural" infinities to resolve first cause. He does that by applying pure mathematical set theory to show multiple counter-intuitive incongruities. Since this is the only field that treats postfinite values, there aren't many options.

Second, it's been my understanding that any actual (real) infinities are impossible since, if causes go on forever, the universe itself would have run down because of entropy and we wouldn't be here today.

Entropy ain't what it used to be. :rolleyes:
The new "cyclic universe" theories incorporate an entropy cycle that follows the Big Bang >> Big Crunch cycle. The theory is a step beyond the ekpyrotic model, which 'fizzes out'. The universe is an infinitly past and future sequence of states.

But, of course, the argument really doesn't apply to our universe in the first place since it is not infinitely old, but only some 15 billion years. Beyond that, there was no time, nor matter, nor causes as we understand them today.

The frothing multiverse models allow our little universe to pop and die, perhaps seeding adjacent big bang events.

Shouldn't the question of what existed before the Big Bang (if anything)be left to cosmologists to determine? They don't yet need supernatural entities (see articles by Victor Stenger in this regard), as an explanation.

It's a little difficult to experiment on models - or even simulations - to determine pre-big-bang conditions. It's always going to be a theoretic - and therefore metaphysical issue.

I'm on Vic's debate-prep e-team and he seems very well prepared for his contest with Craig in a few weeks at the Univ. of Hawaii. He essentially argues a natural creation as a consequence of fluctuations in the false vacuum at a Planck level, with several other "sound-bite" slashes at Craig's case.

William

[Alhazred]

I simply state flatly that real infinites are physically impossible, there is not an infinite amount of matter and energy from which to compose one in the real universe, thus any attempt to invoke them is NECESSARILY contrary to the known physical conditions prevalent in the real physical universe!

Even were you to postulate an infinitely extensive physical universe you would STILL have to actually enumerate a real infinite in order to compose it, which would require infinite time and thus is in effect impossible.

My definitions of 'possible' and 'impossible' are the most literal ones, if its possible you can show me, otherwise its impossible (granted many things are 'beyond our means' in practice but still possible in a more abstract sense).

The point is, given that a real infinite cannot exist, what does this really say about the nature or existence of God? IMHO nothing. Kalam aside I see no argument based on postulates proveable in the real world of ANY kind at the moment that creates a requirement for the existence of God. I doubt that by its very nature such a postulate even CAN be formulated in principle.

[Westmiller]

Alhazred
I simply state flatly that real infinites are physically impossible, there is not an infinite amount of matter and energy from which to compose one in the real universe...
I'm glad that you've settled that question. ;)

...if its possible you can show me, otherwise its impossible
By your definition, I couldn't show you, because it isn't possible to enumerate an infinity.

...what does this really say about the nature or existence of God? IMHO nothing.
Kalam says if the universe is not infinitely old, it must have begun. It remains an open question about how it came into existence. God is only one hypothesis.
But, I do agree that there is no proof of God, either from evidence or logic. That hasn't precluded theists from postulating it in principle and inviting falsification. That's all Kalam is: an argument that claims to be logically valid.

[Abdul Alhazred]

Originally posted by Westmiller
I'm glad that you've settled that question. ;)

LOL! It was a rather definite formulation, yes. In general what I am trying to get across is that 'POSSIBLE' means 'it can really be done in the real universe'. So your next comment is exactly right on the mark, the definition of a real infinite IPSO FACTO makes it an impossibility. At least I posit such to be true, and thus I have disposed of real infinites and all their messiness in one swell foop!

...if its possible you can show me, otherwise its impossible
By your definition, I couldn't show you, because it isn't possible to enumerate an infinity.

...what does this really say about the nature or existence of God? IMHO nothing.
Kalam says if the universe is not infinitely old, it must have begun. It remains an open question about how it came into existence. God is only one hypothesis.
But, I do agree that there is no proof of God, either from evidence or logic. That hasn't precluded theists from postulating it in principle and inviting falsification. That's all Kalam is: an argument that claims to be logically valid.

Kalam wants to be more than 'logically valid', thats pretty plain from the subtext. In any case logic and the real world don't always coincide. Something can be 'logical' and utter gibberish at the same time, as we all know.

[-DM-]

[Thank you for your feedback regarding The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities (http://www.infidels.org/library/modern/arnold_guminski/kalam.shtml) by Arnold T. Guminski (http://www.infidels.org/library/modern/arnold_guminski/). E-mail notification has been sent to the author. He is on vacation, but expects to be back--and to respond--sometime after September 10th. Although there are no guarantees, you might want to check back from time to time for a further response following this post. -DM-]

[Arnold T. Guminski]

Refuting Craig's Kalam Argument – A Response by Arnold T Guminski

I am gratified that my article prompted feedback, and I read the contributations with great interest. What I shall do is to comment upon the principal points made by each of the contributors, and in so doing make a few general statements by way of explanation of my position.

Re: William Westmiller: Naturally I am very pleased that Westmiller "fully enjoyed" my article, and that my Alternative Version (AV) of applying Cantorian theory to the real world is judged by him to be "useful in its own right." He suggests, however, that there is a more economic refutation of Craig because "the fundamental problems seems to be Craig's invocation of aleph zero as a 'real' cardinal value." It would be helpful were Westmiller to flesh out his contention. Presently I see no need to take the radical step that he suggests since it would totally deny the application of Cantorian theory to the real world. Since Westmiller agrees that "the incongruities fault the SV [Standard Version] translation" of Cantorian theory to the real world, all we need do is to use the AV in order to avoid the "incongruities." After all, no natural number can serve as the cardinal number of an infinite set of real entities; yet each such set must have a cardinality (i.e., size or power). My point is that, athough two real infinites (e.g., the sets of humans and of their hands, each human having exactly two hands) may not be in one-to-one correspondence with each other, each set is nevertheless in one-to-one corresponse with the infinite set of natural numbers (or any other denumerably infinite mathematical set). Since aleph-zero is the cardinal number of the set of natural numbers, it is the cardinal number of each real infinite.

Re: Abdul Afhazred: I do not fully understand the the substance of Afhazred's remarks, and have great difficulty in following his argument. He declares that "an even easier way to refute Kalam ... is simply to deny that it is possible to enumerate real infinites." He explains that: "That is in mathematical set theory one does not need to enumerate a set in order to operate on it, but in the real world THIS IS NECESSARY. One cannot perform REAL operatons on REAL INFINITES without necessarily enumerting them. This means you simply cannot operate on (ie count) a real infinite []." What does Afhazred mean by the term "enumeration" of an infinite set if the "operation" on such a set consists in counting? Apparently, he conceives of an operation on an infinite set as involving sequential acts. But how can the members of an infinite mathematical set be operated on (i.e., counted)? He proceeds to say that since a real infinite cannot be operated on one cannot possibly say whether or not the real infinite of human hands corresponds one-to-one to that of humans. On the contrary, I say that since (by hypothesis) each human has exactly two hands, there must be a two-to-one correspondence between the infinite set of human hands and the infinite set of humans. There is no need to count the two sets-—even were such a procedure possible. That a real infinite cannot be counted does not entail that a real infinite cannot. exist. That there is a one-to-one correspondence between any real infinite and the set of natural numbers does not entail that there is any hypothetical Mind which all-at-once assigns a natural number to each member of the real infinite—which, and I stand to be corrected, may be what Afhazred may mean by the "enumeration" of an infinite. In any case, Afhazred's position is that a real infinite, unlike a mathematical infinite, cannot be enumerated (whatever he means by that term), and goes on to argue that a real infinite cannot exist.

Afhazred writes that even talk about a real infinite is ridiculous because "[a]s soon as you do you leave reality behind." Here I shall have to agree with him. But then neither Craig nor any supporter of the Kalam Cosmological Argument grounds his objection to the metaphysical possibility of real infinites upon the physical impossibility of real infinites in this world of spatially related entities or in any other world composed of entities having physical properties more-or-less similar to those in this world. In note 11 of my article, I remarked: "Indeed, virtually all instances of counterintuitive absurdities cited by Craig and other writers are, or appear to be, instances of what are factually impossible for nonmathematical reasons in any real world of spatially and causally related objects.... However, to suppose that there are infinitely many worlds of spatially and causally related objects, none of which are spatially related to another world, seems prima facie coherent and presents most clearly the problem of the metaphysical possibibility of real infinites based upon mathematical considerations." [Please note that endnote 11 in the Secular Web version of my article has now been amended to correct the erroneous omission of "non" immediately before "mathematical" in the opening sentence of the endnote.] So, the counterintuitive absurdities incident to applying SV (Standard Version) may clearly appear to the reader (without his/her being distracted by coping with factually imposible scenarios), provided he/she acknowledges the coherence of the notion of there being two or more worlds none of which is spatially related to any other. So consider, for example, that there are infinitely many worlds each one more or less similar to this world and with each such world containing finitely many humans each with exactly two hands. There would then be infinitely many humans and infinitely many human hands. According to SV, there is a one-to-one correspondence between the infinite sets of humans and of their hands; whereas according to my AV there is a one-to-two correspondence between the two sets.

I do not see how or why Afhazred maintains that his doctrines constitutes an easier way to refute Kalam. Indeed, what he says serves to support Craig's position. As a matter of fact, in his second posting, he expressly states: "given that a real infinite cannot exist." In his first posting Alhazred asserts that "I see no reason to acccept that a METAPHYSICAL infinite is absurd simply because a PHYSICAL infinite is absurd." But in his second posting he appears to hold that that a metaphysical infinite (whatever Alhazred means by that term) is not possible, since he flatly asserts that a real infinite cannot possibly exist. Given the general structure of what I understand Alhazred to hold, I think that he slipped when he wrote of a "METAPHYSICAL infinite" in his first posting. What I think he intended was to refer to a "MATHEMATICAL infinite"—but perhaps he can tell us what he actually meant to say. But whatever he meant to say, I do not understand why he says that denying the possibility of real infinites (which would pertain to natural and supernatural beings—if any) makes it even easier to refute the Craig's first form of the Kalam Cosmological Argument – unless it is true, which I suspect, that Alhazred does not understand that the argument includes the denial of the possibility of a real infinite as a premise.

Re: Paul Ricci: Ricci first raises the question of the meaning of "metaphysical impossibility" and asks whether "anyone [can] give [him] a good, clear example (other than the one postulated by Craig) ... that does not reduce to our commonly known impossibilities (logical, physical and/or technical)?" He then states his "suspicion this new kind of impossibility was invented, ad hoc, simply to make room to incorporate a metaphysical, non-material entity." I am sorry to disappoint Ricci by replying that the notion of metaphysical possibility or impossibility is neither recent, nor ad hoc, nor contrived simply to support some theory of natural theology. Here we must be careful. There is a difference between logical possibility and metaphysical possibility. Craig, for example, acknowledges that the notion of a real infinite is logically possible. However, according to Craig, real infinites are metaphysically impossible because they could not actually obtain with respect to any coneivable world, whether natural or supernatural.

Whether or not Craig can be legitimately faulted for concluding that real infinites are metaphysically impossible, he should not be faulted simply because he holds that some things are metaphysically impossible. To maintain that some things are metaphysically impossible is not an intellectual property right exlusively belonging to theists. Whether one agrees with it or not, one very good example of what is commonly cited as a metaphysical impossibility is the uncaused beginning of the existence of any substance or continuant, whether natural or supernatural. (This doctrine is not to be confused with that concerning causal determinism.) The doctrine in question is considered to assert a metaphysical impossibility if it is believed to factually obtain as to any conceivable natural or supernatural world. Those who adhere to the doctrine do not generally consider it to be simply an empirical generalization which is potentially falsifiable, or that it is true of this world only. Rather, it is thought to be one of those principles which are implictly presupposed as true in the course of rational inquiry. It is ironic that before the emergence of Big Bang cosmology, the doctrine that the beginning of the existence of any substance of continuant must have been caused was (or at least appears to have been) generally common to both atheists and theists. Where they differed chiefly in this matter pertained to the issue of whether this world had a beginning in time. But even as to this issue, there have been (most notably Thomas Aquinas) and are now theist philosophers who maintain that God has the power to create a temporal world without a beginning but nevertheless willed to create this one with a beginning in time. Those atheists who commendably persist in maintaining the principle in question need not be reduced to perplexity if it is indeed true that this physical world has a temporal beginning. This is the case because it is open for them to maintain that the cause of that beginning is a natural event—albeit not one which belongs to the history of this world.

This brings us to Ricci's second major point: that this world is not infinitely old given what he considers to be the findings of scientific cosmology. He asks: "Shouldn't the question of what existed before the Big Bang (if anything) be left to [scientific] cosmologists to determine?" Not completely. Just as wars should not be the exclusive domain of generals, so too cosmology should not be the exclusive domain of scientists whose methological concerns with respect to the framing and testing of theories and hypotheses are not adequate for the consideration, let alone the resolution, of the Big Questions. I must add that I am loathe here to discuss philosophical issues of what occurred before the Big Bang because I did not discuss the matter in my article. My article focuses on whether a real infinite is metaphysically impossible since that contention serves as a premise in one form of Craig's Kalam Cosmological Argument that an infinite temporal series is metaphysically impossible. Craig naturally holds, or should hold, that the question of what existed before the Big Bang (if anything) cannot be entirely left to scientific cosmologists to determine if indeed real infinites and real infinite series are metaphysically impossible. Craig's argument based upon the alleged metaphysical impossibility of real infinites is completely independent of the argument grounded upon what he holds are the findings of scientific cosmology. It is relatively unimportant except for polemical purposes whether or not the findings of scientific cosmology support or confirm the former form of KCA if that argument is valid and sound,. Craig would be the first to say that were the received findings of scientific cosmology actually supportive of the theory of, say, an infinitely old oscillating universe, such findings must be subordinated to the conclusion that it is metaphysically impossible for there to be an infinite temporal series. Any KCA subargument based upon the real or supposed findings of scientific cosmology have to be separately considered whether or not Craig's arguments against the metaphysical possibility of real infinties or infinite temporal series fail. One thing Craig cannot legitimately do: he cannot construct a plausible theory of the nature of God grounded both upon scientific cosmology and the premise that real infinites are metaphysically impossible.

In philosophical controversies, it is is often the case (very much as in political controversies) that there are shifting alliances. My paper, proposing as it does my alternative version (AV) of how Cantorian theory is to apply to the real world, may disturb some of those Cantorians who adhere to the standard version (SV). They should be gently roused from their dogmatic slumbers. My hope is that they will find that the thesis of my paper is not so bad after all. My paper, with a few additional flourishes and trappings, could just as easily have been written by a theist, particularly one in the thomistic tradition. It could have been written by a theist, even were he/she to maintain that the world (or that temporal series which includes its history) must be finitely old, who is disposed to think that divine omnipotence and omniscience encompasses the possibility of divine creation of infinitely many worlds and that divine knowledge extends to infinitely many things. Alternatively, my paper could have been written by a theist who believes that God, the God of Abraham, Jacob, and Joseph, is everlastingly temporal and whose mental life includes a succession of states or events without beginning or end. But as a matter of fact, my paper just happens to have been written by someone who does not believe that God exists and who maintains, not only that infinite sets of real infinites are metaphysically possible, that that that temporal series which includes the history of this world is necessarily infinite. Because I believe that real infinites (including infinite temporal series) are metaphysically possible, so much of natural theology which presupposes the soundness and validity of the Kalam Cosmological Argument should be deemed to fail.

[Abdul Alhazred]

He declares that "an even easier way to refute Kalam ... is simply to deny that it is possible to enumerate real infinites." He explains that: "That is in mathematical set theory one does not need to enumerate a set in order to operate on it, but in the real world THIS IS NECESSARY. One cannot perform REAL operatons on REAL INFINITES without necessarily enumerting them.

And I reiterate (and yes I DO understand the mathematical construction of infinite sets by rule etc, though I don't claim to possess the level of understanding of the subject you command... ;o) that in the PHYSICAL WORLD of our reality you cannot operate on sets of things, only on individual things or finite collections of things like say "all the air molecules in this room" (and even then there is some discrete event associated with each one of these molecules, we just lump them together for convenience sake).

Your argument appeals to the existence of putatative 'other universes' and has to suppose an infinity of such. Furthermore your argument rests apon another and far more interesting axiom, that the structure of 'reality' (the some total of everything that exists) including your infinite universes must conform to some 'rational' structure. So what you need to say is 'IN LIEU OF THOSE ASSUMPTIONS' you postulate your AV to refute Craig's argument. I realize that the lack of the rationality axiom pretty well throws metaphysics out the window, but ah well... The actuality of affairs does not conform to the convenience of philosophers. If it did we would live in a much different world!

[-DM-]

Abdul:

It seems to me that Guminski has adequately responded to the feedback thus far presented, so I think it would be a good idea at this point to move this discussion to one of the open discussion forums so as to facilitate open discussion and so as not to expect too much of an author of a Library article. I am therefore moving this to the Philosophy forum (which may or may not be the best place; I'll leave that up to the Philosophy forum moderators who may be inclined to move it again).

-Don-

[the_cave]

Originally posted by Westmiller
Entropy ain't what it used to be.
The new "cyclic universe" theories incorporate an entropy cycle that follows the Big Bang >> Big Crunch cycle. The theory is a step beyond the ekpyrotic model, which 'fizzes out'. The universe is an infinitly past and future sequence of states.
Yes, but even if so, why does the series of states exist?

The frothing multiverse models allow our little universe to pop and die, perhaps seeding adjacent big bang events.
Sure--maybe!

It's a little difficult to experiment on models - or even simulations - to determine pre-big-bang conditions. It's always going to be a theoretic - and therefore metaphysical issue.

I would love to see it if scientists began treating multiverses as accepted fact. "We don't need to test the theory; but we're compelled to accept it due to metaphysical arguments." Boy, that'll be the day!

He essentially argues a natural creation as a consequence of fluctuations in the false vacuum at a Planck level
But again, where did the false vacuum come from?

[wiploc]

Originally posted by Alhazred
I simply state flatly that real infinites are physically impossible, there is not an infinite amount of matter and energy from which to compose one in the real universe, thus any attempt to invoke them is NECESSARILY contrary to the known physical conditions prevalent in the real physical universe!

Is that just infinities of time that are impossible, or infinities of anything at all? If we can't have infinities of space, then all movement must consist of teleportation, since space must consist of discrete grains of location.

Do we have any reason to believe that space is grainy? I don't know of any. I suspect that movement does consist of quantum leaps, but I don't know of any reason to think there is no space between the places where the leaps begin and end.

crc