Kalam Cosmological Argument

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C.G. Weaver

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« on: June 28, 2007, 01:30:03 pm »

The New Cosmological Argument

Richard M. Gale and Alexander Pruss have proffered a valid deductive cosmological argument for the necessary existence of a powerful, intelligent creator of the actual universe. That argument contained an affirmation of Duns Scotus’ weak principle of sufficient reason which affirmed that:

(1)  W-PSR: For any proposition, p, and any world, w, if p is in w’s Big Conjunctive Fact[1], then there is some possible world, w1, and proposition, q, such that w1’s Big Conjunctive Fact (BCF) contains p and q and the proposition that q explains p.[2]

The Gale-Pruss argument requires several definitional helps for the purposes of clarification. First, a possible world is individuated by its corresponding Big Conjunctive Contingent Fact (BCCF). Given actualism[3], one can simply show this by noting how every world is identical to a maximal compossible BCF—where a BCF is understood to be a long conjunction of all true propositions in/at that world. Therefore, a BCCF in a particular world w1 will contain at least one proposition that has a different truth value then say a different world w2. Thus, every possible world contains its own unique BCCF. Interestingly enough, a world’s BCF is also individuative since each world’s BCF will contain its corresponding BCCF. It follows then that:

(2)  If a possible world w and w* have the same BCCF then w = w*. (True by definition)

The important question to pose now is whether or not the actual world a has an explanation? The Gale-Pruss argument would then like the inquirer to suppose the following:

(3)  p is a’s BCCF. (True by hypothesis).

Now there appears to me to be three ways one can arrive at the conclusion the Theist wants, viz., that p has an explanation. First, one can follow the Gale-Pruss argument all the way out by postulating the initial plausibility of W-PSR and show what interesting propositions follow from that [this I will do shortly]. Second, one can show how W-PSR entails the S-PSR[4] and then show how by necessity p has an explanation. And finally, one can show as I have tried to do in a paper which was presented at a special event of the EPS, that W-PSR entails a weak causal principle, and by showing this one need not proceed with the Gale-Pruss argument but just show the entailment relation between W-PSR and W-CP and show how W-CP is sufficient enough to launch a straightforward cosmological argument like the Kalam.[5]   PAN>

The Gale-Pruss Argument

           The first step is universal instantiation for the W-PSR. Note:

(4)   If a proposition p, is in a’s BCCF, then there is some possible world, w1, such that w1’s BCF contains p and q and the proposition qEp.[6]

(5)  Therefore, there is a possible world w1 and a proposition q, such that w1’s BCF contains p and q and the proposition qEp. [From (3), (4) modus ponens]

The key step for the argument is showing that w1 is identical to the actual world. Gale and Pruss then show that p is identical with w1’s BCCF. Let p1 be w1’s BCCF. Every conjunct of p is a contingent proposition true in w1 (from (5) and (3)), it follows then that:

(6)  Every conjunct of p is a conjunct of p1.[7] [True by definition of p]

Gale and Pruss then state:

Conversely, suppose r is a conjunct of p1. Then either r or not-r will be true in the actual world by bivalence. If not-r is true in the actual world, then not-r is a conjunct in p (since not-r is) contingent  as r is), and hence is a conjunct in p1, so that then both r and not-r are conjuncts in p1, which contradicts the fact that p1 is the Big Conjunctive Contingent fact of a possible world.[8]

Not-r must not be true in the actual world, and therefore r is true there. Proposition r is contingent and is incorporated in p. Every conjunct of p1 is a conjunct of p. Therefore,

(7)   w1 = a.

Given Leibniz’s law of the indiscernability of identicals it follows that:

(8)  There is in the actual world a proposition q, such that the actual world’s BCF contains p and q and the proposition qEp.

As a last step of this argument Gale and Pruss show how the explanation of the actual world’s BCCF is a personal explanation and not a determined “scientific” one. So:

(9)  q is either a personal explanation or a scientific explanation.

The explanation cannot be a scientific one since q would then have to be contingent since it is related to, if not determined by nomic laws. Nomicity does not coincide with metaphysical necessity, and therefore the explanation cannot be scientific since if it was q would be apart of p’s BCCF. So:

(10)                     q is not a scientific explanation.

(11)                     Therefore, q is a personal explanation.

Furthermore, q cannot report the causal or explanatory actions of a contingent being since if it did the BCCF would incorporate a proposition which reports the existence of the contingent being in question. Q itself is not able to explain why the contingent being it refers to exists, since a contingent being’s intentional action evidently must presuppose, and hence cannot explain, that being’s existence.[9] Moreover the actions of this necessary being must be free for the same reasons that Craig provides for the third stage of the Kalam argument. The only reason why a necessary being who exists explanatorily prior to the actual worlds becoming actual in all its contingent elements, would want to enter into the relevant explanatoral relation is if that being so decided. Thus, no antecedent conditions coerced the actions of this necessary being. Since the BCCF reports the existence of the actual world’s universe, it then follows that:

(12)                     It is contingently true that there exists a personal necessary being who freely personally explains p.[10]

[1] See below for definition of BCF.

[2] Richard M. Gale and Alexander R. Pruss, “A New Cosmological Argument,in Religious Studies 35 (1999): 463.

[3] I do realize that Actualism has opponents, e.g. David Lewis, On the Plurality of Worlds (Malden, MA: Blackwell Publishers, 1986 repr. 2002); but see the following works for blistering criticisms: Peter van Inwagen, “Two Concepts of Possible Worlds,” in Ontology, Identity, and Modality (Cambridge: Cambridge University Press, 2001), 206-242; Alvin Plantinga, The Nature of Necessity; Alvin Plantinga, “Two Concepts of Modality: Modal Realism and Modal Reductionism,” in Matthew Davidson (ed.), Essays in the Metaphysics of Modality (New York: Oxford University Press, 2003), 192-228; Robert Merrihew Adams, “Theories of Actuality,” in Noûs 8 (1974): 211-231; Alexander R. Pruss, “The Cardinality Objection to David Lewis’s Modal Realism,” in Philosophical Studies 104 (2001): 167-176.

[4] S-PSR = For every contingently true proposition, p, there is a proposition, q, that explains p.  

[5] C.G. Weaver, “Grounding the Causal Principle” at the Evangelical Philosophical Society (Special Event) in New Orleans “The Future of Atheism” conference in early 2007.

[6] Where qEp is read as q explains p.

[7] Remembering that p1 is w1’s BCCF.

[8] Richard M. Gale and Alexander R. Pruss, “A New Cosmological Argument,in Religious Studies 35 (1999): 464.

[9] Ibid., 465.

[10] Due to space constraints I have not defended just how it is that (12) is only contingently true, and therefore the action of this necessarily existent being is uncoerced and undetermined. I would love to explore this fact in future posts.



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« Reply #1 on: June 28, 2007, 02:36:45 pm »
I think Gale and Pruss's new cosmological argument is better than many cosmological arguments insofar as it employs an extremely plausible version of the PSR and some fairly uncontroversial modal apparatus (namely, S5). But it's an interesting question whether it's better than the Kalam. The latter seems much more elegant and concise, and to that extent it might have a dialectical one-up on Gale and Pruss's. But it looks to me like both arguments are sound. It'd be interesting to get Craig's take on Gale and Pruss's argument . Somebody should send him a 'question of the week' about it.
"I am not an atheist." - Albert Einstein



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« Reply #2 on: July 01, 2007, 06:00:34 pm »

I have heard Craig comment on the BCCF, which was my first exposure to the idea.  Perhaps he has written on it in an issue of Philosophia Christi, too(?).


C.G. Weaver

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« Reply #3 on: July 03, 2007, 07:32:14 pm »

Propositions (13) and (14) should have read:

(13) If q explains p then necessarily if q then p.

(14) Necessarily q, and necessarily if q then p, then necessarily p.


(13) qEp ¢¬ ¡à (q ¢¬ p)

(14) ¡à q & ¡à (q ©­ p) ©­ ¡à p


black apologist

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« Reply #4 on: August 01, 2007, 02:10:10 am »
Interesting post C.G. Weaver,

As I've written elsewhere, I'm a lot more partial to the Gale-Pruss argument than I am towards the kalam. While I do think that all cosmological arguments for God's existence rest on one or more disputable principles, I also think that this is true for any philosophical argument. The real task is not to discover an argument whose premises cannot be disputed (a notion which seems almost laughable) but rather those arguments which rest on principles that are less controversial than others and whose premises are more plausible than their contradictories. I think that this is the case with the Gale-Pruss argument. I do think that the kalam can be argued to an extent, but the success of the argument is very much dependent on what Craig's interlocutor thinks of his premises, especially the premise which states "the universe began to exist".

There is one weakness in the Gale-Pruss argument that I would like to have your thoughts on C.G. Weaver. Graham Oppy has criticized the "New Cosmological Argument" for being question-begging due to the fact that it has been discovered that the W-PSR entails the S-PSR. Oppy would argue that this entailment makes the W-PSR no better than the S-PSR and that atheists have good reason for rejecting that principle and (consequently) the Gale-Pruss proof altogether. I think that such a criticism is unacceptably excessive as it seems to require that one's understanding of an argument can only be closed upon deduction. If this was the case, then every valid deductive argument for anything could rightly be charged with begging-the-question once the premises have been fully deduced. This doesn't seem to be a reasonable criticism, and thus I think the W-PSR which Gale and Pruss have proferred is more plausible than Oppy's contradictory. Do you know of these criticisms that have been levied against the argument? If so, what are some of your views concerning them?



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« Reply #5 on: August 02, 2007, 06:47:53 pm »
I think Mr. Weaver is a bit busy at the moment, I haven't been receiving correspondence from him.

Your response to Oppy is entirely sufficient, and I think a bit comical, black. If the best response that can be given to Pruss' argument is that the premises entail the conclusion, then I think the argument's doing pretty well.

I think Oppy's response is extraordinarily weak. To tell the truth, though, I'm so impressed by Pruss' treatment of the PSR and his new argument that I might be a bit biased. It seems to me that the weak PSR is a far more plausible object of belief than "God does not exist." If atheists have no good reason to reject the weak PSR other than pulling a modus tollens and rejecting the PSR precisely because it leads to God's existence, they are in big trouble. There are few reasons to be an atheist, perhaps the problem of evil is a reason, but I have my doubts about that, as I've made clear elsewhere. Maybe the best reason is that those who are atheists fail to believe that any of the arguments for God's existence are really good arguments. If Pruss' argument is good, however, that reason goes out the window. In that case, it would be question-begging to reject the PSR on the premise that God does not exist.