I. Aquinas’ Contingency Argument
In his classic treatise, the Summa Theologica, the 13th century theologian Thomas Aquinas proposed five arguments for the existence of god, known as the “Five Ways”. Among them is a particular kind of cosmological argument commonly called the argument from contingency. Aquinas explains his third way:
Aquinas’ main argument can be summarized thus: (i) Some things in the universe are contingent in that they can either exist or not exist; (ii) Everything in the universe could not be contingent, because that would mean there was a time when nothing existed, and things do not begin to exist out of nothing; (iii) Therefore, there must be a being whose existence is not contingent, but is necessary, and this being is god.
There are numerous points at which one can object to this argument. First, it’s entirely appropriate to ask why the necessarily existing thing must be a being. Aquinas draws on our experience of contingent things, elaborates on the two types of necessary things, and yet seems to offer no explanation for jumping to the conclusion that the necessarily existing thing is specifically a being. Why could it not be matter itself? One might counter-argue that matter, unlike god, does not have existence as part of its essence, and so, according to Aquinas, would require some other necessary cause even if it were itself necessarily existing. However, this understanding of god seems to come out of The Ontological Argument, which I believe rests on an antiquated idea of existence, and makes an unwarranted leap from conceptual to metaphysical necessity.
In light of the last statement, a second objection would be that Aquinas’ criteria for necessity are quite inadequate. It’s dubious at best that existence can be ascribed as a property to any thing, even a necessary being, and a necessary thing that relies on another necessary thing for its existence seems to be an odd sort of “contingently necessary” thing, implying a contradiction in terms. Why could it not be that matter is permanent, even if it doesn’t have existence as part of its essence, or rely on a necessary thing as its cause? Perhaps Aquinas’ criteria are also guilty of a bit of special pleading in that they form a false dichotomy pointing in the direction of a being that exists by definition, which has long been a popular description of god among theologians.
A third objection to the contingency argument is that it demands a causal explanation for why something would come from nothing, although causality presupposes existence. This problem can be easily seen in my summation of Aquinas, where the descriptive phrase “in the universe” from (i) and (ii) suddenly disappears in (iii) regarding the necessary being. Aquinas builds his case on our experience of contingent things in this universe, and endeavors to show from that basis that a necessary being exists, but his argument does not stipulate that this being exists outside the universe, and following the first two premises would even seem to lend greater credence to the thought that it actually exists in our universe, or is part of it.
To assert the contrary is to argue against our experience of causality, which is obviously exclusively within the context of this universe, by positing the senseless claim that a cause can occur outside of space and time, prior to the origins of what we understand as existence. As George H. Smith puts it,
Although I hesitate to use the words “cannot” and “require” in relation to explaining the universe, it does seem that Smith accurately describes the immense difficulty the theist faces in making any rational sense of a cause existing outside of existence.
We will return to the subject of causality and touch on the infinite regress issue later in the article, but for now we move on to another sort of cosmological argument.
II. Leibniz’s Contingency Argument
The German mathematician and philosopher Gottfried Leibniz offered another formulation of contingency argument in his 1714 work, Monadologie.
Leibniz’s contingency argument differs from Aquinas’ in a couple ways. Most notable is that Leibniz articulates the claim that something does not come from nothing into what he terms the Principle of Sufficient Reason (PSR), which makes the stronger statement that nothing occurs without a sufficient reason for why it is so and not otherwise. Unlike Aquinas’ causal principle, the PSR applies to all entities, events, and propositions, not just to causation ex nihilo. The other difference is that Leibniz understands the necessary being to be necessary in the sense that it constitutes a sufficient reason for the existence of contingent things, rather than that it contains existence as part of its essence.
With this in mind, we can make a few objections to Leibniz. First, the conception of a necessary being in this formulation is still restricted to conceptual necessity. No argument is made for metaphysical necessity or for logical necessity, and so one seems justified in asking how it is that this necessary being is its own sufficient reason if all the argument could successfully show is that it is necessary to our thinking.
A second objection is that, like all forms of the cosmological argument, Leibniz’s version makes the unstated assumption that the universe as a whole is contingent. To infer from the fact that the universe contains contingent things that the universe itself must be contingent is to commit the fallacy of composition. What is true of the parts of something is not necessarily true of the whole, just as a wall made of short bricks is not necessarily a short wall. Of course, it could be true that a certain wall made of short bricks is a short wall, but such a determination cannot be reliably made a priori, as cosmological arguments attempt to do with respect to the contingency of the universe.
But what if the universe is just the set of existing things, as David Hume suggested in his Dialogues Concerning Natural Religion? Would this make the supposition of contingency more plausible? It’s hard to imagine how it would, when one could contend that there is something in or about the set that makes it necessary. Many theistic philosophers and apologists also reject the idea that explaining everything in a set explains the set itself, identifying counter-examples.4 Though I haven’t found any compelling counter-examples, it appears to me that the cosmological arguer is stuck in the uncomfortable position of either having to suppose that: i) the set with all its members explained is open to additional questions; or ii) the set with all its members explained is not open to additional questions. If i) is the case, then the fallacy of composition has to be addressed, and it looks to be more an assertion than argument to propose that the universe is contingent. If ii) is the case, on the other hand, it is simply inappropriate to demand an explanation of the universe.
Finally, a third objection can be directed at the PSR itself. Christian philosopher Peter van Inwagen has criticized the PSR for its insistence that everything can have an explanation, since at least one fact looks as if it can’t have an explanation.5 Van Inwagen identifies this fact as the hypothetical explanation of what he calls the Big Conjunctive Contingent Fact (BCCF), which is the conjunction of all contingent facts (this is practically another way of describing what I above called the “set with all its members explained”). If the explanation for the BCCF is itself contingent, then according to the PSR it must be explained. But since the BCCF already includes all the contingent facts, it cannot be explained. If the explanation for the BCCF is necessary, though, then the fact explained by it (the BCCF) is necessary, too, which cannot be true, since the BCCF is contingent. Since the explanation of the BCCF cannot both explain itself and not explain itself, the PSR appears false.
Van Inwagen’s argument seems a sound refutation of the PSR. Perhaps another way of going about it could be to simply ask what sufficient reason we have for presuming the truth of the principle. The PSR has been controversially taken as a law of logic by some philosophers, but even if it is regarded as a self-evident axiom like other logical laws apparently are – such as the law of noncontradiction and the law of identity – it still admits of no explanation.6 If the PSR is not a law of logic, on the other hand, why should it not call for an explanation, given that it is a proposition which might either be true or false?
Defenders of the Leibnizian contingency argument have mostly responded to such criticisms by introducing a weaker PSR that is closer to Aquinas’ causal principle, which we have already touched on in the last section. Now we move on to the third and final cosmological argument to be discussed in this article.
III. The Kalām Cosmological Argument
The medieval Muslim theologian Al-Ghazali put forward a cosmological argument that has become very popular today, thanks in large part to its adoption by Christian apologist and philosopher William Lane Craig. The argument, known as the Kalām cosmological argument, is quite like the famous first cause argument made by Aquinas, except with a few revisions.
2. The universe began to exist.
3. Therefore, the universe has a cause of its existence.7
Craig defends the second premise by way of two arguments against the existence of actual infinities, or infinite regresses. One argument attacks the formation of an actual infinite by successive addition, claiming that it is impossible to traverse an infinite series. Think of a man who has been counting down from eternity and is now finishing, Craig suggests. Why didn’t he finish yesterday or the day before? “Since one can always add one more before arriving at infinity, it is impossible to reach actual infinity.” The other argument attacks the possibility of an actual infinite by reference to paradoxes like Hilbert’s Hotel.
In The Miracle of Theism, the late J.L. Mackie responded to Craig’s two defenses as follows:
…what [the second] brings out is that we ordinarily have and use a criterion for one group’s being smaller than another – that it is, or can be correlated one-one with, a proper part of the other – and a criterion for two groups being equal in number – that they can be correlated one-one with each other – which together ensure that smaller than and equal to exclude one another for all pairs of finite groups, but not for pairs of infinite groups. Once we understand the relation between the two criteria, we see that there is no real contradiction.8
Responding to Mackie’s first counter-argument, Craig writes, “on the contrary, the beginningless character of an infinite temporal series serves only to underscore the difficulty of its formation by successive addition.”9 Bill reiterates his point, referred to above, about the man counting down from eternity. On Mackie’s second counter-argument, Craig asserts that “the question is not whether infinite set theory, granted its conventions and axioms, constitutes an internally logically consistent system. The issue is whether such a system can be instantiated or obtain in the real world.” Thus, he declares, Mackie has really done nothing to challenge the supporting arguments of the Kalām’s second premise.
Interestingly, Craig now seems content to place the burden of proof at the feet of the Kalām’s opponents, rather than offer compelling arguments against an infinite temporal series. Conceding that infinities are not logically impossible, he rests his case on their seeming absurdity when applied to the real world. On the face of it, this already looks like quite a weak support of premise two, but Craig’s replies to Mackie also leave much to be desired.
On the first reply, it appears that Bill is simply stating that the problem with infinities that have no first member is that they have no first member. Indeed, if his primary objection is asking where one would start from in traversing an infinity, Mackie’s description of this as a mere “prejudice against an actual infinity” seems dead right. The implicit assumption is that any temporal series must have a first member, which Craig neglects to defend.10
On the second reply, Craig’s concession to logical possibility looks like it yanks the carpet out from under his own feet. If there is nothing logically impossible about infinities, which consequently implies there are logically possible worlds where infinities can exist, then a persuasive argument against an actual infinite will need to be a posteriori rather than a priori. Unfortunately for all of us, we still struggle to understand what laws of nature there are, but I don’t find it the least bit controversial to say that there are presently no such laws under serious consideration by scientists that obviously preclude an infinite temporal series.
Another objection that can be made to the Kalām concerns the argument’s first premise, that whatever begins to exist has a cause. Whether or not this seems intuitive, it certainly is questionable in what exactly it means by “begins to exist”. We have a fairly decent working concept of what it means for something to exist, but what have we observed beginning to exist? When we produce offspring, we do not bring them into being out of nothing. They are assembled from already existing materials, if you will. Likewise, if you break a rock into two halves, at what point do those two distinct rocks ‘begin to exist’? Our experience of causation, if we reflect on it beyond basic and naive intuitions, does not provide any good grounds for accepting premise one. Sadly, Craig’s anticipation of this objection amounts to little more than a very weak reductio ad absurdum packaged with an argument from ignorance:
As already noted, the principle is problematic even in spite of intuitions, so Dr. Craig’s refusal to provide the arguments in support of it that he passingly refers to is not as forgivable as he would like it to be. I find it particularly amusing that while Craig happily criticizes Mackie for not distinguishing between what is logically possible and what metaphysically exists, Bill suddenly omits this concern from his little attack on uncaused beginnings. Perhaps it is logically possible for anything to just spring into existence, even now, and yet the laws of nature – whatever they may be – allow only certain kinds of things to happen. Craig’s last sentence exhibits nothing but a lack of imagination.
A final objection, similar to the previous one, can also be raised against the notion of an atemporal cause, or a cause existing outside time. Though Dr. Craig seems quite unwilling to assent to the possibility of an uncaused beginning to the universe, he finds it perfectly plausible that there is an uncaused cause of that beginning, which is outside space and time, and which he calls god. Certainly it is true that we have no experience of causes outside of time, so what can the theist martial to support such an arguably counter-intuitive notion? What precisely makes it more believable to Craig that things can pop into existence out of nothing when they’re caused by a powerful being? Here it doesn’t seem the difficulty stems from any logical or metaphysical problem, but rather from the absence of an agent possessing the ‘right’ attributes. But what attributes would make something able to suspend laws of nature, bend metaphysical possibilities, and do what Craig otherwise regards as absurd? If the answer is not simply begging the question in favor of a god, it will be hard to see why there’s any reason such things could not occur without a god.
In sum, the Kalām argument, while seemingly more sophisticated and modernistic than the other cosmological arguments discussed, nonetheless joins them in being built upon undemonstrated assumptions and counter-intuitive suppositions.
1. Paul Halsall, Thomas Aquinas: Reasons in Proof of the Existence of God, 1270, The Internet Medieval Sourcebook. Retrieved Feb. 6, 2014.
2. George H. Smith, Atheism: The Case Against God (Prometheus, 1989), p. 240.
3. Gottfried Leibniz, Monadologie (1714), trans. Jonathan Bennett. EarlyModernTexts.com. Retrieved Feb. 7, 2014.
4. Pruss’ Cannonball and the Leibnizian Cosmological Argument, Ex-apologist (Sept. 2, 2012). Retrieved Feb. 7, 2014.
5. Peter van Inwagen, An Essay on Free Will (1983).
6. A self-evident axiom like the law of noncontradiction is self-evident in the sense that any attempt to refute it would be self-defeating. To show the law of noncontradiction false would be to assume that it cannot be both true and false – the very law allegedly being refuted. This self-defeating tendency is not really an explanation for the law, though, as much as it is a peculiarity of it.
7. William Lane Craig, The Existence of God and the Beginning of the Universe, Truth: A Journal of Modern Thought (1991), p. 85-96. Retrieved Feb. 7, 2014.
8. J.L. Mackie, The Miracle of Theism (Oxford, 1982), p. 93.
9. William Lane Craig, Professor Mackie and the Kalam Cosmological Argument, Religious Studies, 20 (1985): 367-375.
10. Graham Oppy, Craig, Mackie, and the Kalam Cosmological Argument, Religious Studies, 27 (1991): 189-197.
11. Craig, “Professor Mackie…”, see 9.