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#190 The Leibnizian Cosmological Argument

December 06, 2010

Dr. Craig,

I have some questions about your version of the Leibnizian Cosmological Argument (which you call the argument from contingency--is there a difference?). Although I once used to think that the LCA was the most powerful argument natural theology had to offer, reading some material by its atheist critics has led me to doubt its soundness. Mainly, these objections are not against the PSR (principle of sufficient reason) that you use in the argument’s first premiss (which states that everything that exists has an explanation of its existence, either in the necessity of its own nature or an external cause) but are against the second premiss of the argument (which states that if the universe has an explanation of its existence, then that explanation is God).

The first group of objections attempts to use your own PSR to undermine the second premiss. The first rejoinder in this group asserts that the first premiss makes a distinction between explanations that are (i) external causes or (ii) internal necessity. But why can’t one make the two additional categories of (iii) external necessity or (iv) internal causes. One of the critiques of the LCA I read argues that so long as these latter two are even conceivable and logically and epistemically possible, then they remain viable options for the nature of the universe’s explanation. The second rejoinder in this group asserts that the explanation of the universe need not be a cause per se, because some abstract objects like numbers and the laws of mathematics and logic, though causally powerless, can explain certain facts and things, such as why 2+2=4 or the existence/nature of properties, respectively. The third, and I think most powerful, rejoinder in this category contends that you confuse dependency with possibility. Dependency, in the ontological sense, refers to the causal relationship between beings. Possibility, in the modal sense, refers to the existence of a being or the truth of a proposition in all, some, one, or no possible worlds. Possibility is silent on the dependency of beings. However, your LCA would then imply that there are two kinds of beings, (a) necessary, independent beings and (b) contingent, dependent beings. But if the objection so far is sound, it would then seem that one has no justification to conclude that a being is ontologically dependent or independent on the alleged grounds that it is modally contingent or necessary, respectively. Furthermore, there are several counterexamples to this dichotomy. For example, necessary, dependent beings are epistemically possible (since you use conceivability as a guideline for the modality of the universe, this use here cannot be rejected). Under theism, moral values are necessary in the sense that they exist in all possible worlds, yet they are still dependent upon God for their existence. Similarly, the world would fall into this category as well. If God, a necessary being, created the world, then He must have had a reason for doing so. This reason, as indicated by the PSR, must be a necessary one, or else you’d need an explanation of that. Therefore, the world, as a product of a necessary being with necessary intentions, is also necessary. But because it was created, it is still dependent on God. Accordingly, there should be four categories of beings:

(a) necessary, independent beings
(b) contingent, dependent beings
(c) necessary, dependent beings
(d) contingent, independent beings

Since your LCA deals with only the first two, it cannot show that the universe, even if contingent, depends on a being as its cause. Under this exhaustive proposal, the quarks which comprise the universe (since you rightly avoid the fallacy of division and see that intuitive evidence for the possibility of the universe’s non-existence is distinct from any evidence for the possibility of the non-existence of the material constituents of the universe) could fall under (d) and be factually necessary. Richard Swinburne has offered a model of how this would work. Like Swinburne’s god, the universe, if factually necessary, would be contingent, yet eternal, everlasting, and indestructible in the worlds in which it did exist, free of any explanation (however that might be defined). Since contingent, independent beings are conceivable and epistemically possible, this category cannot be (apparently) ruled out as viable one under which the universe could fall.

The second group of rejoinders tries to defend the claim that the universe is necessary, in the case that the first group of rejoinders were to fail. Now, I agree with your critics here that you too hastily dismiss the idea that the universe could be necessary. You rely on conceivability as a guideline to modal possibility; you say in Question 25: “Now it seems obvious that a different collection of quarks could have existed instead of the collection that does exist.” The first problem here, though, is that this proves too much. One could conceive of God’s non-existence, yet you and I would both deny that He is contingent (although Swinburne wouldn’t). Peter van Inwagen has also argued that the concept of a “knowo,” a contingent being who knows that there are no necessary beings, is conceivable and therefore possible, which would thwart God’s being necessary. Now, according to one of the LCA critiques I read, you appeal to Charles Taliaferro to escape this issue, but Taliaferro’s modal epistemology is of little help. It basically states that the move from conceivability to possibility is only prima facie valid if the state of affairs conceived is internally consistent and coherent with known facts. But it does not appear that No Necessary God thought experiments mentioned above violate this. You would need to find a modal epistemology that would non-arbitrarily prevent the No Necessary God thought experiments from working while allowing the universe to remain contingent. The second rejoinder states that conceivability does not entail possibility, because what we can conceive is always governed by a background of knowledge, which varies with location and era. For example, an ancient scholastic philosopher could have argued, “Water and H2O are different because I can conceive of a possible world where water exists without H2O. Thus, they are not identical and are therefore distinct from one another.” This argument uses the same sort of jump from conceivability to possibility used in the LCA, yet we know it is unsound because of modern chemistry. Another good example features Spider-Man, whose secret identity is Peter Parker. Suppose that Mary Jane Watson believes that Spider-Man and Peter Parker are distinct individuals. Therefore, according to your modal epistemology, because Mary Jane could conceive of a possible world wherein Spider-Man fails to exist while Peter remains existent, such a world actually exists. This is obviously impossible since they are, unknown to Mary Jane, the same person. This thought experiment therefore proves that conceivability is a poor guide to possibility because the former is heavily influenced by varying background knowledge. But also, there is the problem of conflicting intuitions. What happens if your modal intuitions conflict with mine? Who if any of us is right?

The last set of rejoinders deals with how we are to define the universe in the LCA. What definition are you using in it? If the word “universe” is defined as “all reality (including God),” the “universe” would have no external explanation because such an explanation would have exist outside of reality, which is impossible since reality is all the exists. If “universe” is defined as “the particular arrangement and number of quarks that we know of in our local area of space-time,” the “universe” would be necessary since when someone conceived of a different universe, they would be thinking of something else, and not the “universe” as earlier defined. This is similar to arguing that because God is the greatest conceivable being, it is impossible to conceive of anything greater, since that would be God and not what you were originally referring to.

These are therefore the best rejoinders to the LCA I have found in my research on it. I am a Christian theist, by the way, but I am now very skeptical about the success of this particular argument. Do you have any ideas on how these problems might be alleviated, preferably without appealing to other arguments? If the theist is forced to appeal to other arguments, he will be caught engaging in circular reasoning, which is obviously not good.



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Dr. craig’s response


Let me back up to get a running start at your questions, Midas. In my early work on the cosmological argument, I myself was dubious of the Leibnizian cosmological argument on such grounds as you suggest. In particular, I thought of God, not as a logically necessary being, but as what my doctoral mentor John Hick called a factually necessary being, that is to say, a being which is uncaused, eternal, incorruptible, and indestructible. (Swinburne still holds to this view.) It is to that sort of being that the kalam cosmological argument concludes. I even tried to “save” Leibniz by construing his metaphysical necessity in terms of factual necessity. It wasn’t until I came fully to appreciate the difference between strict logical necessity/possibility and broadly logical necessity/possibility that I could see how God might and should be thought of as necessary in the broadly logical sense. A cosmological argument for God as a broadly logically necessary being was at the same time re-opened as an option.

Of course, any such argument must feature a plausible version of the Principle of Sufficient Reason, and Leibniz’s own version seemed to me too strong. But it seemed to me that weaker versions were available, plausible, and adequate to the job. In particular, I found Stephen T. Davis’s version of the argument to be disarmingly simple and convincing. So after much thought my initial reservations were overcome, and I came to see the argument as a good one.

Now keep in mind what I mean by a “good argument.” I mean an argument which (i) is logically valid; (ii) has true premisses; and (iii) has premisses which are more plausible than their negations. In order to show that an argument is no good, it is not enough for the sceptic to show that it’s possible that a premiss is false. Possibilities come cheap. I’m puzzled that so many laymen seem to think that merely stating another possibility is sufficient to defeat a premiss. This is mistaken, for the premisses of an argument need be neither necessary nor certain in order for that argument to be a good one. The detractor of the argument needs to show either that the premiss in question is false or that its negation is just as plausibly true as the premiss itself.

Similarly, it’s not enough for critics of an argument to show that one of the premisses may be rationally denied. A good argument need not compel the assent of a rational person. Hence, I’ve never claimed that those who reject the theistic arguments I defend are irrational for doing so. Since plausibility is to a good degree person-relative, I’m not even unduly bothered by the fact that some people may not find one of the premisses more plausible than its contradictory. If someone, for example, thinks that it’s just as plausible as not that things can come into being utterly uncaused, I figure that’s his problem, not mine. My different assessment of the plausibility of the causal principle is perfectly reasonable whether or not he sees the point. Hence, my confidence in the argument’s worth as a good one is not shaken by the sceptic’s merely saying that a premiss doesn’t seem more plausible than not to him.

These considerations are important because these three groups of objections take mutually contradictory positions. Group I objections finally take the universe to exist contingently. But Group II objections take the universe to exist necessarily. Since these positions are logically incompatible, you know that at least one of the positions is false. If our goal is get at what is most plausibly true, we have to get beyond throwing out bare possibilities and try figure out what is most plausibly the case.

So with that in mind, let’s consider the argument in light of the objections you’ve encountered. For those who are unfamiliar with the argument, here is a statement of it:

1. Anything that exists has an explanation of its existence (either in the necessity of its own nature or in an external cause).
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)

Group I Objections

The first objection of this group attempts to delineate further categories of explanation, namely, external necessity and internal causes. O.K., and—? What’s the objection? Merely listing other possibilities does nothing to defeat premiss (2) of the argument. Possibility doesn’t imply viability.

And what are we talking about anyway? The idea here, I guess, is that in addition to something that exists by a necessity of its own nature and hence is uncaused, there might be things which exist by a necessity of their own nature and yet are caused. But this is plainly incoherent, since if something depends on a cause for its being, then its own nature alone does not suffice to explain why it exists. I agree that, for all we know, there might be things which exist in every possible world but are caused (numbers? moral values?). Still, such things would not exist by a necessity of their own natures even though they exist necessarily (here we see the subtlety and strength of Davis’s argument). So the category of things which exist by a necessity of their own nature and yet are caused is empty.

It is also suggested that there might be things which exist by “internal necessity.” If this is supposed to be different than something that exists by a necessity of its own nature, the only sense I can make of this suggestion is something that is self-caused. But that notion doesn’t make sense, since it would require something to be explanatorily prior to itself. So again, this category is empty.

The point of premiss (1) is to distinguish between two types of beings: those that exist by a necessity of their own natures and those that do not. This is a mutually exclusive and exhaustive distinction. It is further claimed that those things that do not exist by a necessity of their natures have causes apart from themselves which serve to explain why they exist. In other words, there are no brute contingents. This premiss strikes me as very plausible.

The second objection under Group I is that there could be a non-causal explanation for the existence of things akin to how mathematical objects explain truths like “2+2=4.” This objection just seems to be based on a false analogy. In so far as I can make sense of explaining why 2+2=4, we’d say something like the terms “2+2” and “4” designate the same entity. Or maybe we could say that “2+2=4” is derivable as a theorem from the axioms of Peano Arithmetic. But neither of these senses of “explanation” is relevant to explaining why some entity exists. Again, the strength of Davis’s formulation of his Principle of Sufficient Reason is that it does not demand that every truth have an explanation but merely that anything that exists has an explanation why it exists.

The third objection of Group I just re-turns ground already ploughed. It is inattentive to the fact that the distinction the argument draws is not between logically necessary beings and logically contingent beings but between beings which exist by a necessity of their own natures and those that do not. The argument as stated is entirely compatible with there being things that exist in every possible world and yet are causally contingent. That’s one of the strengths of the argument.

Now the claim that the world is precisely such a being is a very radical claim! But note that it gives the proponent of the Leibnizian cosmological argument exactly what he’s arguing for, namely, a transcendent cause of the universe! This is an objection? No, it’s a total concession (ironically, one that Leibniz himself would not have been altogether unhappy about, given his views on the necessity of creation)! What this “objection” questions is merely God’s freedom in creating the world. It suggests that God is not free to refrain from creating, that in every possible world God creates our universe.

So what argument is there to adopt this radical view that the universe exists necessarily but causally contingently? Like a good Leibnizian, you argue,

If God, a necessary being, created the world, then He must have had a reason for doing so. This reason, as indicated by the PSR, must be a necessary one, or else you’d need an explanation of that. Therefore, the world, as a product of a necessary being with necessary intentions, is also necessary.

I, too, used to think that this was a good argument. Therefore, I was glad that Davis’s version of the Principle of Sufficient Reason avoids it! For Davis’s version of that principle, unlike Leibniz’s own stronger version, doesn’t require that there be a reason why God chooses everything He does. Indeed, there’s a long tradition, extending back through the mediaeval Muslim theologian al-Ghazali, which sees the very essence of free will as the ability to distinguish like from like, that is, to choose one of two exactly similar alternatives (e.g., whether to have the system of cosmic spheres rotate clockwise or counter-clockwise). So Davis’s version of the argument does not require God to have a (necessary) reason for creating the world.

More recently, through reading the excellent work of Alexander Pruss on the Leibnizian argument, I’ve come to see that it is also by no means clear that there cannot be a necessary explanation of why a contingent world exists. Have you read Pruss’s article in the Blackwell Companion to Natural Theology? That’s a must! So now I’m sceptical of the objection itself and not just of its relevancy to the cosmological argument.

So the four categories of beings you list are more perspicuously labeled:

(a) A logically necessary, uncaused being
(b) A logically necessary, caused being
(c) A logically contingent, caused being
(d) A logically contingent, uncaused being

The claim of the argument is that (a) is God, (b) may or may not exist, for all we know, but depends causally upon God if it does, (c) is the stuff we see all around us every day, and (d) is empty, since everything that exists has an explanation of its existence. (What a great argument!)

Finally, you suggest that quarks might fall under (d). But that just is to reject premiss (1) of the argument. It’s to say that there are brute contingents after all. Fine, that’s what atheists typically do say (“If God does not exist, the universe has no explanation of its existence,” the logical equivalent of premiss (2)). But I find premiss (1) more plausible than not for the reasons I’ve explained in my work. The atheist’s merely stating his alternative does nothing to undermine the argument. (I mean, didn’t you expect him to say that, Midas?)

Group II

The objections of Group II suddenly do an about-face and claim, contrary to the objections of Group I, that the universe exists necessarily. Now notice that there is a certain hypocrisy on the part of those who claim that “the universe is necessary, in the case that the first group of rejoinders were to fail.” Why is this the fallback position? The objections of Group I accept that we have a reliable intuition of the universe’s contingency and so regard the universe’s existence as inexplicable, a brute fact. If it is implausible to regard the universe’s existence as a brute fact, why should we not say that the universe then has a cause of its existence? Why instead try to take back what has already been granted, namely, that the universe exists contingently?

But to consider the objections on their own, you first object to my appeal to modal intuition as prima facie justification for thinking that the universe exists contingently. That we do have such an intuition is indisputable, I think, for I can’t think of any contemporary philosopher who would defend the proposition that the universe exists necessarily. That shows that we do have a powerful intuition that the universe doesn’t exist by a necessity of its own nature. Now my claim is the modest one that this provides at least prima facie justification for thinking that the universe is contingent. As I write in Reasonable Faith:

We generally trust our modal intuitions on other familiar matters (for example, our sense that the planet Earth exists contingently, not necessarily, even though we have no experience of its non-existence). If we are to do otherwise with respect to the universe’s contingency, then the non-theist needs to provide some reason for his scepticism other than his desire to avoid theism.

So why should we regard our intuition that the universe exists contingently as unreliable?

Your rejoinder at this point seems to be that we can think of cases where our modal intuitions are unreliable: something seems conceivable but it’s really not possible. Therefore, we should not trust our modal intuition of the universe’s contingency. The problem with this line of argument is that it would invalidate all modal intuitions and result in virtual scepticism about modal matters, which is surely an implausible, not to say undesirable, outcome. Indeed, this is like arguing that because there are cases where our sensory input is unreliable (e.g., a mirage), therefore we should discount the evidence of our senses.

Notice, by the way, that the sceptic can’t appeal to the case of God’s necessary existence as an illustration of the unreliability of our modal intuitions without granting that God exists! For if you say that although our modal intuitions are that God could fail to exist even though He exists necessarily, then you have just admitted His necessary existence. Nor is the theist stuck in the uncomfortable position of affirming God’s necessary existence while affirming that His non-existence is conceivable, for I deny that once one understands the concept of God as a maximally great being, one can conceive (as opposed to merely imagine) God as non-existent. In general, I think your objection confuses imaginability with conceivability. I can imagine all sorts of things (e.g., a horse popping into being without a cause, or someone’s finding a proof that the Continuum Hypothesis follows from the axioms of traditional set theory) which are metaphysically impossible. Imaginability does not imply conceivability.

So I’m not ready to embrace the sort of modal scepticism required to make Group II objections work. Nor are most philosophers.

In Reasonable Faith I make the modest claim that we have a modal intuition of the contingency of the universe and that this provides prima facie warrant for thinking that it doesn’t exist by a necessity of its own nature. I then go on to say, “Still, it would be desirable to have some stronger argument for the universe’s contingency than our modal intuitions alone,” and I present two arguments for the contingency of the universe: first, an argument from the contingency of the fundamental constituents of the universe and, second, an argument from the universe’s temporal finitude.

With respect to the first argument, I point out that no one thinks that quarks are metaphysically necessary—it is routine to speak of universes operating according to different laws of nature and having different fundamental particles. More implausible still would be the suggestion that each and every individual quark that does exist is an independently existing, metaphysically necessary being. Now I notice that your sceptics don’t actually affirm so outlandish a hypothesis. Rather they just try to undermine our confidence in our modal intuitions. But as said above, modal intuitions needn’t be infallible in order for us to have confidence in specific cases like this one.

You don’t mention any response to the second argument. By showing that the universe had a beginning we show that it is not necessary in its existence, right in line with our modal intuitions. Perhaps you mean to close off appeal to this argument by saying, “If the theist is forced to appeal to other arguments, he will be caught engaging in circular reasoning.” If that’s your meaning, it’s mistaken. To appeal to such a consideration is not question begging, since there is no circularity in reasoning here.

The second objection of Group II is similar to the first in that it again tries to undermine the reliability of our modal intuitions by tying our modal intuitions to changing circumstances. You give some examples of people’s thinking something possible, even though it is metaphysically impossible, because they were not fully informed. Now this is interesting. How can you trust your modal intuitions that it is metaphysically necessary that “Water is H2O” and “Peter Parker is Spiderman[1],” if our modal intuitions are so unreliable? Your objection is self-defeating, since it relies on our modal intuitions to defeat our modal intuitions. Or do you think that we should doubt the necessary truth of “Water is H2O”? I see no reason to. Notice that had the scholastic philosophers known that water is H2O, their intuitions would have been exactly the same as ours. In the case of the quarks constituting the universe, is the suggestion supposed to be that if only we knew more about them empirically, we’d discover that they have some hitherto undetected property that renders their existence metaphysically necessary? Fat chance! The sceptical objectors are grasping at straws here.

In cases of conflicting intuitions, we may not be able to prove the other party wrong. But that doesn’t imply that we’re not within our rights in going with what we see clearly. Moreover, in this case, thankfully, there are no conflicting intuitions. I know of no philosopher or physicist who thinks that quarks are metaphysically necessary beings, each and every one of which exists by a necessity of its own nature. Don’t let the anti-theistic sceptics intimidate you, Midas. Their backs are to the wall, and it’s only their desire to avoid theism at all costs that would impel them to embrace so extreme a view as that no quark in the universe could have possibly failed to exist.

Group III

By “the universe” I mean spacetime and all its contents. I obviously don’t include God as part of the universe, since He is its transcendent cause. Nor do I mean just our local area of spacetime and its contents. I have to confess that I don’t understand the comment “the ‘universe’ would be necessary since when someone conceived of a different universe, they would be thinking of something else.” To be sure, the universe, defined as our local patch, is not the same thing as another patch. But that does nothing to show that our patch and its contents exist necessarily and so could not have failed to exist.

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    It would be better to use a real life example like “Cicero is Tully” rather than fictional characters, since most philosophers would say that your statement is only fictionally true.

- William Lane Craig