Is the Kalam Cosmological Argument Logically Valid?

The kalam cosmological argument for the existence of God is the centrepiece argument for apologists such as William Lane Craig. Its power is found in the simplicity of its validity, and in the intuitive plausibility of its premises.

 

Take Craig’s formulation:

 

P1: Whatever begins to exist had a cause

P2: The universe began to exist

C: Therefore the universe had a cause

 

It may only show that the universe was caused by something, but this fact goes a long way towards identifying the God of classical theism (Craig employs a few giant leaps to reach a personal God, but they are outside the scope of this discussion for now). I am always surprised when atheists are ready to concede the conclusion. To allow that the universe had a cause is to admit that which we do not know. After all, it should worry us that we are answering a question regarding the genesis of our universe simply from a logically valid syllogism. It is a synthetic proposition, and Craig requests that we assent to its truth without leaving our armchair.

 

I will attempt to show, contrary to appearance that this argument is in fact logically invalid if analysed properly. Take the apparent form of the argument:

 

P1: Everything B is C

P2: u is B

C: u is C

 

This apparent form is of course logically valid. So what happens if we analyse the premises? Take P1. We either know this is true from experience or by intuition. If experience, we run into many problems.

 

Firstly, when do we experience something coming into existence, as opposed to the rearrangement of pre-existing matter? When a house is built, we might say that it ‘comes into existence’, but it is clear that we do not mean it in the same sense as we do when we speak of the universe ‘coming into existence’. The house is created from bricks positioned and cemented, and the high-level name ‘house’ is given to the result of this change. Even with personal identity, we ‘come into existence’ at conception (or soon afterwards) but, short of committing to dualism there is nothing created ex nihilo, in the way that we mean when we speak of the beginning of the universe. It is therefore problematic to appeal to our experience when speaking of things ‘coming into existence’.

 

Secondly, if we speak from experience we must have had a wide and comprehensive enough experience to allow our inductive conclusions to have a sound basis. Even ignoring the previous problems, if we experience things only coming into existence as a result of a cause, these things are necessarily part of a universe, and we may never encounter the birth of a universe. We would have to lay claim to experience informing us ‘whatever begins to exist, even a universe, has a cause’, which we cannot. If we choose to leave out ‘even a universe’, the later conclusion can no longer follow.

 

The strongest justification for P1 therefore, is intuition. It is inconceivable that, out of nothing something may be created without a cause. Hume answered this by noting that both cause and effect can be conceived independently, and there is no necessary connection between them. This goes some way, but we still may wish to say that accepting the truth of P1 is more rational than holding it false. This is a plausible view, and thus we turn to P2.

 

Craig employs an argument from the impossibility of an actual infinity of events to support P2. This premise is very unlikely to be denied by an atheist, as it is in line with modern cosmological science. The Big Bang theory, crudely put, postulates both space and time created out of nothing, and so there is little to say about P2 other than that it is true. However it may be said that the sort of beginning that we speak about when we talk of creation ex nihilo is a very different sort of beginning than that which we are familiar with.

 

Let us work with a reasonable definition of ‘beginning’:

D1: Something ‘had a beginning’ if and only if there was a time t₁ at which it did not exist and a time t₂ at which it did exist, where t₁ temporally precedes t₂.

 

I propose that this definition is intuitively what we mean when we speak of ‘beginning to exist’. Space and time created out of nothing, however does not satisfy this definition. Instead, we might use:

D2: Something ‘had a beginning’ if and only if there was a time t₂ at which it did exist, such that there is no time t₁ at which it did exist, where t₁ temporally precedes t₂.

 

The definitions are distinct; D1 entails D2, but D2 does not entail D1. It seems to me that when we intuit a beginning, the definition we use is D1, as it is the time at which the thing does not exist that forms the clear idea of ‘coming into existence’ that we require. Therefore it is unreasonable to accept only D2 as the definition of ‘beginning’ in P1; we must use D1. Conversely, in P2 we must use D2 as D1 is false in this context. Given that the definitions are not interchangeable, the meanings of the word ‘beginning’ in each premise are different.

 

Therefore, the syllogism is formally invalid:

P1: Everything B₁ is C

P2: u is B₂

C: u is C

 

If this seems incredible, consider an analogous argument:

P1: All Greeks are humans

P2: The Parthenon is Greek

C: Therefore, the Parthenon is human

 

Here, the word ‘Greek’ is used twice but with different meanings. For an argument in this form to be logically valid the first predicate must be identical to the predicate ascribed to the subject in the second premise.

 

I propose that this is the mistake in the kalam argument; a false equivocation between two distinct conceptions of ‘beginning to exist’. If the universe had a cause of its existence, we are not in a position to know it, and must instead hope that our empirical understanding of the creation of new universes grows, if indeed our own is not the only universe in existence and if it is not beyond our capacity for scientific inquiry.

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