Spiritual Life
Reasons to Believe
Religions & Sects
Church History
In the News
Faith & Reason Press Speaker's Forum Links Resources About Us

The Kalam Cosmological Argument

William Lane Craig

...I find the kalam cosmological argument for a temporal first cause of the universe to be the most plausible argument for God’s existence. I have defended this argument in two books, The Kalam Cosmological Argument and The Existence of God and the Beginning of the Universe. Let me explain and supplement what I say there. The argument is basically this: both philosophical reasoning and scientific evidence show that the universe began to exist. Anything that begins to exist must have a cause that brings it into being. So the universe must have a cause. The argument may be formulated in three simple steps:

         - Whatever begins to exist has a cause.

         - The universe began to exist.

         - Therefore, the universe has a cause.

The logic of the argument is valid and very simple: it is the same as when we reason, “All men are mortal; Socrates is a man; therefore, Socrates is mortal.” So the question is, are there good reasons to believe that each of the steps is true? I think there are.

Whatever Begins to Exist Has a Cause

The first step is so intuitively obvious that I think scarcely anyone could sincerely believe it to be false. I therefore think it somewhat unwise to argue in favor of it, for any proof of the principle is likely to be less obvious than the principle itself. And as Aristotle remarked, one ought not to try to prove the obvious via the less obvious. The old axiom that “out of nothing, nothing comes” remains as obvious today as ever. In a sense, I find it an attractive feature of this argument that it allows the atheist a way of escape; he can always deny the first premise and assert that the universe sprang into9 existence uncaused out of nothing. For he thereby exposes himself as a man interested only in an academic refutation of the argument and not in really discovering the truth about the universe.

The late J.L. Mackie appears to have been such a man. In refuting the kalam cosmological argument, he turns his main guns on this first step: “there is a priori no good reason why a sheer origination of things, not determined by anything, should be unacceptable, whereas the existence of a god [sic] with the power to create something out of nothing is acceptable.” 1 Indeed, creation ex nihilo raises problems: (i) If God began to exist at a point in time, then this is as great a puzzle as the beginning of the universe. (ii) Or if God existed for infinite time, then the same arguments would apply to His existence as would apply to the same arguments would apply to His existence as would apply to the infinite duration of the universe. (iii) If it be said that God is timeless, then this, says Mackie, is a complete mystery.

Now notice that Mackie never refutes the principle that whatever begins to exist has a cause. Rather, he simply demands what good reason there is a priori to accept it. He writes, “As Hume pointed out, we can certainly conceive an uncaused beginning-to-be of an object; if what we can thus conceive is nevertheless in some way impossible, this still requires to be shown.” 2 But, as many philosophers have pointed out, Hume’s argument in no way makes it plausible to think that something could really come into being without a cause. Just because I can imagine an object, say a horse, coming into existence from nothing, that in no way proves that a horse really could come into existence that way. The defender of the kalam argument is claiming that it is really impossible for something to come uncaused from nothing. Does Mackie sincerely believe that things can pop into existence uncaused, out of nothing? Does anyone in his right mind really believe tht, say a raging tiger could suddenly come into existence uncaused, out of nothing in this room right now? The same applies to the universe: if there were originally absolute nothingness–no God, no space, no time–how could the universe possibly come to exist?

In fact Mackie’s appeal to Hume at this point is counterproductive. For Hume himself clearly believed in the causal principle. In 1754 he wrote to John Stewart, “But allow me to tell you that I never asserted so absurd a Proposition as that anything might arise without a cause: I only maintain’d, that our Certainty of the Falsehood of that Proposition proceeded neither from Intuition nor Demonstration, but from another source.”3 Even Mackie confesses, “Still this [causal] principle has some plausibility, in that it is constantly confirmed in our experience (and also used, reasonably, in interpreting our experience.)4 So why not accept the truth of the causal principle as plausible and reasonable–at the very least more so than its denial?

Because, Mackie thinks, in this particular case the theism implied by affirming the principle is even more unintelligible than the denial of the principle. But is this really the case? Certainly the proponent of the kalam argument would not hold (I) tht God began to exist or (ii) that God is, prior to creation, timeless? I would argue that God exists timelessly prior to creation and in time subsequent to creation. This may be “mysterious” in the sense of “wonderful” or “awe-inspiring,” but it is not, so far as I can see, unintelligible; and Mackie gives us no reason to think that it is. It seems to me, therefore, that Mackie is entirely unjustified in rejecting the first step of the argument as not intuitively obvious, implausible, and unreasonable.

The Universe Began to Exist

I we agree that whatever begins to exist has a cause, what evidence is there to support the crucial second step in the argument, that the universe began to exist? I think that this step is supported by both philosophical arguments and scientific confirmation of those arguments.

Philosophical Arguments

Argument from the impossibility of an actually infinite number of things. An actually infinite number of things cannot exist, because this would involve all sorts of absurdities, which I shall illustrate in a moment. And if the universe never had a beginning, then the series of all past events is actually infinite. That is to say, an actually infinite number of past events exists. Because an actually infinite number of things cannot exist, then an actually infinite number of past events cannot exist. The number of past events is finite, therefore the series of past events had a beginning. Since the history of the universe is identical to the series of all past events, the universe must have begun to exist. This argument can also be formulated in three steps:

         - An actually infinite number of things cannot exist.

         - A beginningless series of events in time entails an actually infinite number of things.

         - Therefore, a beginningless series of events in time cannot exist.

Let us examine each step together.

An actually infinite number of things cannot exist. In order to understand this first step, we need to understand what an actual infinite is. There is a difference between a potential infinite and an actual infinite. A potential infinite is a collection that is increasing toward infinity as a limit but never gets there. Such a collection is really indefinite, not infinite. An actual infinite is a collection in which the number of members really is infinite. The collection is not growing toward infinity; it is infinite, it is “complete.” This sort of infinity is used in set theory to designate sets that have an infinite number of members, such as {1,2,3...}. Now I am arguing, not that a potentially infinite number of things cannot exist, but that an actually infinite number of things cannot exist. For if an actually infinite number of things could exist, this would spawn all sorts of absurdities.

Perhaps the best way to bring this home is by means of an illustration. Let me use on of my favorites, Hilbert’s Hotel, a product of the mind of the great German mathematician David Hilbert. 5 Let us imagine a hotel with a finite number of rooms. Suppose, furthermore, that all the rooms are full. When a new guest arrives asking for a room, the proprietor apologizes, “Sorry, all the rooms are full.” But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are full. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. “But of course!” says the proprietor, and he immediately shifts the person in room #1 into room #2, the person in room #2 into room #3, the person in room #3 into room #4, and so on, out to infinity. As a result of these room changes, room #1 now becomes vacant and the new guest gratefully checks in. But remember, before he arrived, all the rooms were full! Equally curious, according to the mathematicians, there are now no more persons in the hotel than there were before: the number is just infinite. But how can this be? The proprietor just added the new guest’s name to the register and gave him his keys–how can there not be one more person in the hotel than before? But the situation becomes even stranger. For suppose an infinity of new guests show up at the desk, asking for a room. “Of course, of course!” says the proprietor, and he proceeds to shift the person in room #1 into room #2, the person in room #2 into room #4, the person in room #3 into room #6, and so on out to infinity, always putting each former occupant into the room number twice his own. As a result, all the odd numbered rooms become vacant, and the infinity of new guests is easily accommodated. And yet, before they came, all the rooms were full! And again, strangely enough, the number of guests in the hotel is the same after the infinity of new guests check in as before, even though there were as many new guests as old guests. In fact, the proprietor could repeat this process infinitely many times and yet there would never be one single person more in the hotel than before.

But Hilbert’s Hotel is even stranger than the German mathematician made it out to be. For suppose some of the guests start to check out. Suppose the guest in room #1 departs. Is there not now one less person in the hotel? Not according to the mathematicians–but just ask the woman who makes the beds! Suppose the guests in rooms ##1,3,5,... In this case an infinite number of people have left the hotel, but according to the mathematicians there are no less people in the hotel–but don’t talk to that laundry woman! In fact, we could have every other guest check out of the hotel and repeat this process infinitely many times, and yet there would never be any less people in the hotel. But suppose that the persons in rooms ##4,5,6,...checked out. At a single stroke the hotel would be virtually emptied, the guest register would be reduced to three names, and the infinite would be converted to finitude. And yet it would remain true that the same number of guests checked out this time as when the guests in rooms ##1,3,5...checked out. Can anyone believe that such a hotel could exist in reality?

Hilbert’s Hotel is absurd. As one person remarked, if Hilbert’s Hotel could exist, it would have to have a sign posted outside: NO VACANCY–GUESTS WELCOME. The above sorts of absurdities show that it is impossible for an actually infinite number of things to exist. There is simply no way to avoid these absurdities once we admit the possibility of the existence of an actual infinite. William J. Wainwright had suggested that we could reduce the force of these paradoxes by translating them into mathematical terms; for example, an actually infinite set has a proper subset with the same cardinal number as the set itself. 6 But this amounts only to a way of concealing the paradoxes; it was to bring out the paradoxical character of these mathematical concepts that Hilbert came up with his illustration in the first place. And the whole purpose of philosophical analysis is to bring out what is entailed by unanalyzed notions and not to leave them at face value.

But does the possibility of an actual infinite really entail that such absurdities are possible, or could an actual infinite be possible, as Wainwright suggests, without thereby implying that such absurdities are possible? The answer to that question is simple: the possibility of the existence of an actual infinite entails, that is, necessarily implies, that such absurdities could exist. Hilbert’s illustration merely serves to bring out in a practical and vivid way what the mathematics necessarily implies; for if an actual infinite number of things is possible, then a hotel with an actually infinite number of rooms is impossible, then so is the real existence of an actual infinite.

These considerations also show how superficial Mackie’s analysis of this point is.7 He thinks that th