The Kalam Cosmological Argument for the Existence of God

as popularized by Dr. William Lane Craig

I would like to preface by saying that these ideas are not primarily mine! They were formulated by much smarter individuals than I, and I am merely defending and popularizing these arguments. I will attach their defenses of these arguments below for you to reference as well.

The Kalam is one of the historical arguments from natural theology for the existence of God. The purpose of the argument is not to prove that one specific religion’s conception of God is correct, but the only purpose of this argument is to prove that such a being exists necessarily. That is, the universe is contingent upon the existence of God. This is a deductive argument in that if the first two premises are true, then the conclusion is inescapable.

The argument reads as follows:

(1) Everything that begins to exist has a cause.

(2) The universe began to exist.

(3) Therefore, the universe has a cause.

I do not see a need to defend (1) as I think no sincere seeker of truth can deny it and maintain credibility. To assert that something can begin to exist uncaused is to appeal to magic.

I will then articulate some basic points in support of (2) so that we can all be on the same page when engaging with this argument. Two basic arguments in support of (2) are as follows: (2.1) An actually infinite number of things is impossible, and (2.2) It is impossible to pass through an infinite number of elements one at a time.

Dr. Craig formulates them in this way:

(2.11) An actual infinite cannot exist.

(2.12) An infinite regress of events is an actual infinite.

(2.13) Therefore, an infinite temporal regress of events cannot exist.


(2.21) A collection formed by successive addition cannot be an actual infinite.

(2.12) The temporal series of events is a collection formed by successive addition.

(2.13) Therefore, the temporal series of events cannot be an actual infinite.

In support of (2.1): Let’s discuss some of the absurdities that would occur if we could actualize an infinite by using the analogy of Hilbert’s Hotel. Imagine that there existed a hotel with infinite rooms, but all of the rooms were occupied by an infinite amount of guests. There is not a single vacancy throughout the entire hotel. However, if a new guest were to show up asking for a room, the manager would have no problem accommodating him since there are infinite rooms! He would simply move the occupants of room 1 into room 2, room 2 into room 3…ad Infinitum. As a result of these room changes, room 1 is now unoccupied and available for our guest.

Furthermore, if an infinite number of guests were to show up asking for rooms, they could also be accommodated as the manager would simply move each current occupant into the room number which is double his current number. The current guests would all end up in even-numbered rooms, and all the odd-numbered rooms would become vacant! Therefore, the infinite hotel that is already full can accommodate an infinite number of new guests (and this could be done an infinite amount of times)! Now, what would happen if guests started to check out? If all of the guests in the odd-numbered rooms checked out, an infinite number of people would have just left the hotel and an infinite would be left. The manager could move his occupants back into the odd-numbered rooms in reverse order of what we already witnessed above, and he would still have a full hotel! Now, imagine if the guests all checked out from numbers 6, 7, 8…ad Infinitum. Then, the infinite has been reduced to just 5 guests, and the same amount of guests just checked out as when the guests staying in odd-numbered rooms checked out. This exercise shows some of the incredible absurdities that we should expect if an actual infinite were able to exist (ability to exist is defined as a metaphysical actualization, not a mathematical ability). It’s also important to note that the existence of these incongruities is not because we do not understand the concept of infinity. Modern set theory is very advanced, and these absurdities arise only because we understand the nature of actual infinities, not out of a lack of understanding.

When we subtract quantities such as all the odd positive numbers from all the positive numbers, we end up with all the even positive numbers. When we subtract 4, 5, 6…ad Infinitum from all the positive numbers, we end up with 4 numbers. In both of these cases, we subtract identical quantities of infinity from identical quantities of infinity and end up with nonidentical answers. The second example can be repeated using a different starting point to produce any number until infinity, and this is precisely where the contradiction lies in Hilbert’s Hotel. While subtracting and dividing infinities is forbidden in trans-infinite mathematics, one cannot stop guests from checking out of a hotel! It’s also important to note that the argument is not that an infinite is mathematically impossible but that an actual infinite is metaphysically impossible. The actualization of such a hotel in the mind-independent universe would be ontologically absurd. If an actual infinite were metaphysically possible, then such a hotel would be metaphysically possible. Therefore, the real existence of an actual infinite is not metaphysically possible. Dr. Graham Oppy’s solution to “move the guests in room N to room 2N (for all N)” does little to alleviate my doubts that such a hotel is ontologically absurd and does not answer the contradictions that occur from subtracting infinities.

Let’s consider the grim reaper paradox: you are alive at 12:00 am, and there are infinitely many numbers of grim reapers waiting to kill you. The first grim reaper will kill you if you are still alive at 1:00 am, and he does nothing if you are already dead. The second grim reaper will kill you at 12:30 if you are still alive, and the next at 12:45…ad Infinitum. Due to this paradox, you cannot survive past 12:00, but no grim reaper will ever swing his scythe to kill you because an earlier one would have already done so. Dr. Oppy’s solution to this paradox involves a quite bizarre form of retro-causation that would result in the collective action of the grim reapers causing your death, but not any one grim reaper specifically being responsible (unless I misunderstand him). But of course, this retro-causation does not apply to this particular form of the paradox popularized by Dr. Rob Koons and Dr. Alexander Pruss (sic ‘em bears!) because no grim reaper would ever swing his scythe once you are dead which rules out collective action.

We can also modify this paradox to deal with an infinite past. The same basic rules apply of grim reapers waiting to kill you, but none of them actually swinging their scythe to kill you provided you are dead before their appointed time comes. Suppose you are an everlasting being that could only be killed by a grim reaper. If you were alive today, a grim reaper would kill you. If you were alive yesterday, a different grim reaper would have killed you. If you were alive the day before yesterday, a different grim reaper would have killed you…ad Infinitum. Since the series of past days has no beginning, it makes no sense to say that though you were once alive, you cannot live to the present. Then, if you were a finite being, you would never even exist because of the mere intention of an infinite amount of grim reapers to kill you! The key here is that you are an everlasting being, so this key element is what creates the paradox. We cannot rely on the notion that space-time is infinitely divisible as each grim reaper is equidistant in time from the one before and after it, and we cannot rely on the notion that there cannot be an actual infinite or Hawthorne’s mereological totalities as there never has to be an actually infinite amount of reapers. Therefore, the results are similar to the first formulation in that you cannot live to the present, but no grim reaper can kill you because a prior one would have already done so.

Dr. Pruss formulates everything we have covered so far in this way:

(2.121) If there could be a backwards infinite sequence of events, Hilbert’s Hotel would be possible.

(2.122) If Hilbert’s Hotel were possible, the Grim Reaper Paradox could happen.

(2.123) The Grim Reaper Paradox cannot happen.

(2.124) Therefore, there cannot be a backwards infinite sequence of events.

Dr. Pruss argues that causal finitism solves the problem in that all causal sequences have only finitely many members, and no member is causally dependent on infinitely many members. On causal finitism, the grim reaper paradox is impossible because each grim reaper’s action is causally essential to the outcome. There also cannot be an infinitely dense sequence of grim reaper actions since time is discreet (Aristotelian discreteness perhaps since the Kalam assumes A-theory). Besides, the infinite past example is impossible because an ungrounded infinite causally connected chain cannot actually exist as will be demonstrated shortly. It follows logically from these ideas that an infinite past is impossible, and therefore, there must have been a beginning to the universe some finite distance in the past.

In support of (2.2): No series formed by adding one event after another can ever reach infinity. In support of this, I suggest that you attempt to count to infinity. You will see very quickly that, no matter how many numbers you have counted, there is still an infinite number left to count. Well, if we cannot count to infinity, how could we expect to count down from infinity to reach the present day? This is like being forced to count all of the negative numbers backward before we can count zero; i.e. you must count -1 before 0, -2 before -1…ad Infinitum. You would never reach zero and would be driven back into the past so that no number could ever be counted! So then we see that if an infinite number of non-zero moments have preceded this one, we would never have reached today. This shows, by nature of us being in the present moment, that the number of past events must be finite and have a beginning.

Addressing the issue of infinite causal sequences: I think that while an infinite causal sequence is certainly possible to conceive of mathematically, I’m not sure that I see an infinite causal sequence as a more plausible metaphysical alternative than a concrete beginning a finite time away to the mind-independent universe. So that we’re all on the same page, this idea is usually formulated as follows: “There is a beginning infinitely distant in time, that is, while there are infinitely many past events, time nevertheless did have a first instant.” Let’s picture this causal sequence as a chain: this is a chain with two definite ends (i.e. the present and a beginning), but there are infinitely many links between the two ends. This analogy reads like two ships passing in the night since the two subsets of chains (beginning and ending) would never actually connect. We never actually reach two links that would complete this chain. If we think of the beginning as x and the end as y, then the chain, not being transitively closed, will never insatiate a causal sequence that terminates on y. I think this rules out that the universe has an infinite regress of causes at least as it relates to infinite causal chains that begin to exist. Therefore, if the universe began to exist, that beginning must be a finite duration from the present.

Now, this has only ruled out infinite causal chains that have beginnings. What about infinite causal chains that are beginning-less? If we think of an infinite causal loop as another chain of causes that must eventually reconnect to one of its prior links, then it must eventually reach its predecessor. If our causal chain is infinite, we will end up with an infinite chain possessing two starting points only that the two ends have been somehow connected! Since we cannot reach the end of the chain from a starting point, such a causal loop is impossible as well. Since no such ungrounded infinite causal chain exists, the space-time universe must have a beginning.

Based on the above reasoning, I think that (2.1) and (2.2) are true and thus validating the premise that the universe did have a beginning some finite distance in the past. This necessarily leads to (3); namely, that the universe has a cause. I will make another post discussing (3) and what is commonly called the “gap problem.” This problem deals with what the possible causes of the universe could be, and I think that the best answer to the gap problem is God. I made some jumps in logic for the sake of space on this post, but I can explain the jumps I made if you have questions (or you can read the essays below). As always, I welcome conversations around these ideas!

References for this post:

The Blackwell Companion to Natural Theology/Philosophical Foundations for a Christian Worldview! Buy one! Read it!

Here is Dr. William Lane Craig’s website where you can read more about this argument and watch him debate it with top academics:

Here is Dr. Alexander Pruss’ blog:

Here is Dr. Robert Koons’ website:

Here are some resources from Dr. Alvin Plantinga:

Relevant academic works:

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