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#132 Leibniz’s Cosmological Argument and the PSR

October 26, 2009

Dear Dr. Craig,

I'm impressed with the new edition of Reasonable Faith. I've read one of the older editions and found the new additions to be very insightful. Particularly, I enjoyed the new material on Meier's and Ehrman's work on the historical Jesus and Dennett's cosmological theory. There are also new additions in other areas of the book. This is a must read for serious students of apologetics.

I have a question pertaining to the Leibnizian cosmological argument from the principle of sufficient reason. I studied Leibniz with Professor Sowaal at SFSU. His Monadology is quite awesome. In several of his works he argues for the existence of God based on the need for an explanation why things should be as they are and not otherwise. Here Leibniz appeals to his famed Principle of Sufficient Reasons (PSR). Leibniz begins by asking "Why should there be something rather than nothing?"

Following Davis, you reconstruct Leibniz's cosmological argument in the following manner:

1) Anything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause [A version of PSR].
2) If the universe has an explanation of its existence, that explanation is God.
3) The universe exists.
4) Therefore, the universe has an explanation of its existence (from 1, 3)
5) Therefore, the explanation of the existence of the universe is God (from 2, 4).

The conclusion follows validly from the premises, so the only question is whether the three premises are more plausibly true than their denials. Premise 3) is not in dispute. Consequentially, the real debate centers on 1) & 2). Van Inwagen argues that the PSR is false. If van Inwagen's argument goes through, then 1) is false and the argument is unsound.

Van Inwagen confesses that the PSR seems plausible at first glance, but he finds it implausible upon closer examination. What reason does van Inwagen offer in support of this conclusion? He thinks the PSR leads to the absurd conclusion that every proposition is a necessary truth. This is an unacceptable consequence. Consequently, PSR is refuted by way of reductio ad absurdum. The strategy is to deduce the falsity of the PSR based on the assumption that there are contingent propositions. His argument runs as follows.

First, suppose there are propositions and possible worlds.

1) There are some contingent propositions.
2) Some propositions are true in some worlds and false in others.
3) There are possible worlds.
4) Suppose there are four possible worlds one of which is actual.
5) Arbitrarily, let Possible World 2 be the actual world.
6) If the Principle of Sufficient Reason is correct, there is a sufficient reason for the fact that Possible World Two is the actual world; that is, this fact has an explanation.
7) Let S stand for the explanation sufficient to identify or describe Possible World Two as the actual world [the true proposition "Possible World Two is the actual world.].
8) S cannot be true in any other Possible World save for Possible World Two.
9) S must be true in Possible World Two and in no other possible world. What propositions have this feature? Only one: the proposition that Possible World Two is the actual world.
10) But the fact that Possible World Two is the actual world cannot serve as an explanation of the fact that Possible World Two is the actual world. "Because Possible World Two is the actual world" is not an answer to the question "Why is Possible World Two the actual world?"
11) Thus, there can be no answer to the question "Why is Possible World Two the actual world?"

Van Inwagen explains: "Another way to put this point would be to say that there can be no explanation of the whole set of truthsfor the actual world is simply that possible world such that whatever is true is true in it; what makes a particular possible world the actual one is that it "contains" all the truths and none of the falsehoods. And this conclusion is not implausible. One cannot explain the fact that a given contingent proposition is a truth simply by appealing to necessary truths. Therefore, any explanation of a contingent truth must appeal to other contingent truths, and, as a consequence, the whole set of contingent truths cannot be explained because there are no contingent truths outside this set to appeal to. But then the Principle of Sufficient Reason is false." Finally, Van Inwagen repeats, "It follows that if the Principle is true, then there are no contingent propositions; if the Principle is true, every truth is a necessary truth."

My question main question is whether you think van Inwagen's argument applies to your formulation of the PSR in your version of the Leibnizian cosmological argument? Is so, then how do you propose to respond? If not, then why not? Could you explain in more detail your understanding of the PSR and why you feel it evades or does not evade van Inwagen's counter-example to the PSR. I find some version of the PSR to be intuitively plausible, more so than its denial. Something must be wrong.

Best Regards,


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Dr. craig’s response



I'm glad for your question, and for how you finally framed it as well, because it enables me to differentiate the version of the argument I defend from Leibniz's own version. The short answer to your question is that the objection raised by Van Inwagen does not apply to the formulation of the Principle of Sufficient Reason which comes to expression in premiss (1) of the argument I defend. Indeed, premiss (1) was deliberately formulated so as to avoid this traditional objection to Leibniz's own very strong formulation of the principle.

In "The Monadology" Leibniz formulates his Principle of Sufficient Reason (PSR) as follows: "no fact can be real or existent, no statement true, unless there be a sufficient reason why it is so and not otherwise." On the basis of this principle Leibniz held that there must be a sufficient reason why anything at all exists. He went on to argue that the sufficient reason cannot be found in any individual thing in the universe, nor in the collection of such things which is the universe, nor in earlier states of the universe, even if these regress infinitely. Therefore, there must exist an ultra-mundane being which is metaphysically necessary in its existence, that is to say, its non-existence is impossible. It is the sufficient reason for its own existence as well as for the existence of every contingent thing.

Undoubtedly, the most controversial premiss in the Leibnizian cosmological argument is the PSR. The Principle as stated in "The Monadology" has seemed to many, including myself, to be evidently false. Indeed, I thought it was demonstrably false. Leibniz's principle requires that there be an explanation for every fact or truth. But not every fact, it seems, can have an explanation, for there cannot be an explanation of what Alexander Pruss calls the Big Contingent Conjunctive Fact (BCCF) which is itself the conjunction of all the contingent facts there are. (The BCCF is, in effect, your Possible World Two.) For if the explanation of the BCCF is contingent, then it, too, must have a further explanation, which is impossible, since the BCCF includes all the contingent facts there are. On the other hand if the explanation of the BCCF is necessary, then the fact explained by it must also be necessary, which is impossible, since the BCCF is contingent.

What Stephen Davis saw is that a successful cosmological argument doesn't depend for its success on anything so strong as Leibniz's own version of the PSR. There are a number of weaker and more plausible candidates for a PSR which might be employed in a cosmological argument for a necessary being. For example, while rejecting the demand for an explanation of a fact like the BCCF, Crispin Wright and Bob Hale, in their discussion of Hartry Field's anti-Platonist claim that it is an inexplicable contingency whether mathematical objects exist, nevertheless maintain that explicability is the default position and that exceptions to this rule have to be explicable exceptions—some explanation is needed for why no explanation is possible.

For example, they claim that if physical existence is at issue, Leibniz's question, "Why is there something rather than nothing?" is an unanswerable question if a satisfactory explanation of why a physical state of affairs obtains has to advert to a causally prior situation in which it does not obtain, since a physically empty world would not cause anything. They believe that the demand for an explanation of the contingency of physical existence is pre-empted by the restrictive principle that the explanation of the obtaining of a (physical) state of affairs must advert to a causally prior state of affairs in which it does not obtain.

Such a principle will be seen by the theist, however, as not at all restrictive, since the explanation of why the physical world exists can and should be provided in terms of a causally prior non-physical state of affairs involving God's existence and will. The proponent of the Leibnizian cosmological argument could generate his argument by holding, in conjunction with the above principle, that the obtaining of any physical state of affairs has an explanation.

Alternatively, the theist could claim that in the case of any contingent state of affairs, there is either an explanation for why that state of affairs obtains or else an explanation of why no explanation is needed. That would exempt something like the BCCF, since it cannot have an explanation. Or, more narrowly, the theist could maintain that for any contingently existing thing, there is an explanation why that thing exists. Or again, he could assert that everything that exists has an explanation of its existence, either in the necessity of its own nature or in an external cause. All of these are more modest, non-paradoxical, and seemingly plausible versions of the PSR. Thus, the objection raised by Van Inwagen misses the target—or, more accurately, is aimed at another target.

On the basis of Alexander Pruss's work, moreover, I've come to question whether the sort of objection expressed by Van Inwagen really does succeed against a strong version of the PSR. The claim that the explanation of the BCCF cannot be found in a necessary truth presupposes that explanations must entail the facts they serve to explain. If some fact is materially implied by a necessary truth, then it may be explained by that truth without itself being necessary. Pruss suggests that the BCCF may be explained by the necessary truth that God has weighed the reasons for creating for each world and has freely chosen which world to create. Moreover, the claim that the BCCF cannot be explained by some contingent truth assumes, even more controversially, that no contingent truth can be self-explained. The reason why the BCCF is true may be simply because each of its conjuncts is true; nothing more is needed to explain why the BCCF is true than the truth of its atomic constituents, each of which has an explanation for its truth. Or again, it may be supposed that the explanation for the BCCF is the fact that God freely wills the BCCF. (Notice that the proposition Possible World Two is the actual world is not the only proposition uniquely true in that world; so is the logically equivalent proposition God freely wills that Possible World Two be actual). Since that explanation is itself a contingent fact, it is also a constituent of the BCCF willed by God. It may then be regarded as self-explained or its explanation may be that God wills that He wills the BCCF, which fact will also be a constituent of the BCCF to be similarly explained in terms of yet another conjunct. This regress seems to be as innocuous as a series of entailments like its being true that it is true that p. The entire regress is contained in the BCCF and so is willed by God.

If you want to pursue further the discussion of the strong version of PSR, check out Pruss's article in the Blackwell Companion to Natural Theology (2009) or his earlier The Principle of Sufficient Reason (2006).

In any case, the version of the PSR in premiss (1) of argument I defend is compatible with there being brute facts about the world like the BCCF or brute states of affairs like the obtaining of Possible World Two. It requires merely that there be two kinds of beings: necessary beings, which exist of their own nature and so have no external cause of their existence, and contingent beings, whose existence is accounted for by causal factors outside themselves. That seems to me an eminently plausible principle.

- William Lane Craig