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, 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.
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, 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 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. 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.
(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. [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.
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:
( 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. 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.
 See below for definition of BCF.
 Richard M. Gale and Alexander R. Pruss, “A New Cosmological Argument,” in Religious Studies 35 (1999): 463.
 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.
 S-PSR = For every contingently true proposition, p, there is a proposition, q, that explains p.
 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.
 Where qEp is read as q explains p.
 Remembering that p1 is w1’s BCCF.
 Richard M. Gale and Alexander R. Pruss, “A New Cosmological Argument,” in Religious Studies 35 (1999): 464.
 Ibid., 465.
 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.
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(?).
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