Kalam Cosmological Argument--Premise One

The Cosmological Argument is one of the classical "proofs" for the existence of God. It has been re-worked several times to reach its present, most widely recognized form--i.e. the Kalam Cosmological Argument. The most popular proponent of this argument is William Lane Craig.

When I considered myself a Christian I went to one of his debates and believed he did a very good job with it. He used the Cosmological Argument very effectively against his opponent--though, in fairness, the guy Craig debated was a radio announcer who did not have any kind of former philosophical training (this was apparently before Craig decided to only debate PhDs).

This is how the Cosmological Argument is commonly presented:

1. Whatever begins to exist has a cause of its existence.
2. The universe began to exist.
2.1 Argument based on the impossibility of an actual infinite.
2.11 An actual infinite cannot exist.
2.12 An infinite temporal regress of events is an actual infinite.
2.13 Therefore, an infinite temporal regress of events cannot exist.
2.2 Argument based on the impossibility of the formation of an actual infinite by successive addition.
2.21 A collection formed by successive addition cannot be actually infinite.
2.22 The temporal series of past events is a collection formed by successive
2.23 Therefore, the temporal series of past events cannot be actually infinite.
3. Therefore, the universe has a cause of its existence.


Let B = the predication "begins to exist"
Let C = the predication "has a cause of existence"
Let u = "the universe"

"For every x, if x begins to exist, then x has a cause of existence. The universe begins to exist, therefore the universe has a cause of existence."

The most devastating critique I've ever read of this argument was, ironically, from Christian philosopher, Alvin Plantinga, in his book God and Other Minds. He concentrated his critique on the second and third premises and their defenses, though he only begrudgingly conceded the first premise.

Usually, people do accept the first premise and deal with subsequent premises and their defenses (e.g. that there cannot be infinite regress, etc). I'm not sure, however, that even this first premise can be maintained.

[I am indebted to Dan Barker for the following critique. The idea and some of the examples are his and can be found here.]

In the first premise, the proponent of this argument appears to be making a category mistake. The theist says that "whatever [thing--the word is implicit]" that begins to exist must have a cause. The theist, then, switches that "thing" to "the universe." The problem, here, is that it may be inappropriate to treat the universe in the same way one treats some "thing" in the universe.

For example, let's say that I have a number set in this form: [2,4,6,8 . . .]. From studying "inside" the set, I draw the conclusion that every thing is two counts away from the next thing. My statement is perfectly valid inside the set. Two is two counts from four, four is two counts from six, etc.

But the rule that is valid within the set is not necessarily valid of the set itself. Let's say that my set above is in a list of sets. Set 1 is in the form [1,2,3,4 . . .], the set I mentioned above is Set 2, the next set in the list, Set 3, is in the form [3,6,9,12 . . .].

Now, I extracted a rule from Set 2 that says everything is two counts away from the next thing. If I applied this rule to the set itself, however, my statement would not be true. Set 2 is neither two counts away from Set 1 nor two counts away from Set 3.

This, however, is exactly what the theist is doing when he goes from the statement that "Whatever [thing] begins to exist has a cause of its existence," to his next statement and conclusion that "The universe began to exist. Therefore, the universe has a cause of its existence." This argument treats the universe as a "thing," and not "the set of all things." This is the category mistake.

[Note that it is true of all sets that a set is made up of the sum of its parts. Sometimes rules of the sets do apply to the set itself, but not necessarily so.]

Let me try to be more clear. If I asked a theist to prove his statement, "Whatever begins to exist has a cause of its existence," he would have to appeal to things inside the physical universe. He might say that a hurricane is caused by ocean temperatures, etc. His statement is a physical statement that relies on induction and on physical laws.

In other words, the first premise is not a tautology (though it may seem to be one), but rather an empirical statement demonstrated by induction.

The problem comes when the theist tries to apply natural laws to the universe itself. He is doing the same thing that I did with the number sets above. He is finding a rule that is true inside the universe (i.e. inside "the set") and saying that it must apply to the universe itself (i.e. to "the set" itself). There is no way to prove that that is the case, though. There is no way to prove that a rule inside the set (i.e. the universe) must apply to the set itself.

Let me try another way of explaining this. I saw this "ball" in a toy store the other day. It is made of plastic pieces on joints. If a child pulled on the joints, the ball would begin to expand. The ball keeps expanding to a rather large ball and can retract to a small, dense ball. The inside of the ball is hollow.

Many physicists believe the universe is similarly "ball-shaped." What the theist is doing is taking a rule that is true inside the ball and applying it to the conditions outside the ball. This may not, however, be the case. The outside conditions may be entirely unlike the inside conditions.

Let me try a hypothetical. Let's say that the universe did begin, but it began inside something I will call a "yniverse." A yniverse is a type of meta-universe.

Let's say that the physics of the yniverse are very different from the physics of our own universe. First of all, there is no indication that a yniverse had a beginning. It is like what some physicists used to call a "steady-state" universe.

Now, imagine that the physical laws in that yniverse allow for things to come into existence without a cause (I think we already made clear that the theists' assertion that something requires a cause is a statement that is true only because of our physical laws in our universe). So, in this yniverse, a universe can come into existence without any cause. If this were the case, our universe, because it is a part of another "set" with different rules, can come about without a cause at all.

I'm not saying that this is what I believe happened, but I'm simply pointing out that just because it is the case that everything that comes into existence within the universe has a cause, that does not mean that the universe itself had to have a cause. You cannot assume that a law at play within a set is true of the set itself.

The Cosmological argument falls apart if the first premise cannot be maintained.