The Form of the Cosmological Argument

The cosmological argument for the existence of God is a perennial line of reasoning for those wanting to bolster their belief in God. It is an argument I haven’t looked into deeply until it’s recent revival as the Kalam Cosmological Argument, beloved of evangelists like William Lane Craig. When I was doing my theology undergraduate degree I wrote a thesis on the ontological argument, this has to be brief as a blog post, but here’s a breakdown of the cosmological argument.

The cosmological argument has a number of different forms, but ultimately they all seem to reduce to the same basic structure.


  1. There are two sets of things. Call them ‘stuff’ and ‘gods’: the actual naming depends on the form of words being used in a particular cosmological argument.
  2. The ‘stuff’ set is finite.
  3. The ‘stuff’ set is not-empty.
  4. There is a directed relationship which connects members of either set to one another; call the roles in this relationship ‘from’ and ‘to’.
  5. This relationship is such that, all members of the ‘stuff’ set are in the ‘to’ role of at least one such relationship.
  6. The relationship also has the characteristic that there are no loops: starting from any element, of either set, there is no way to move along the relationship in a sequence of moves from ‘from’ to ‘to’ and get back to where you started.


  • From 4 and 6, we know that the relationship is a partial order on the elements.
  • From the above and 2 and 3, we  know that there must be some set of elements that do not take the ‘to’ role.
  • From the above and 5, we know that the elements that do not take the ‘to’ role in any relationship must be in the ‘gods’ set.
  • From the above, we can conclude that the ‘gods’ set is not empty. QED


Lets dress this in some classic cosmological argument terms then.

Everything has a cause, therefore there must be a first cause. This is the original form of the argument, which strictly is logically invalid. It is rescued in various ways, however.

Everything that comes into being (i.e. ‘stuff’) has a cause (i.e. is in the ‘to’ role of the ‘causation’ relationship). Therefore there must be something that has not come into being (i.e. there must be something in ‘gods’)

Every contingent thing (i.e. ‘stuff’) must have a cause (i.e. is in the ‘to’ role of the ‘causation’ relationship). Therefore there must be something that is not contingent (i.e. ‘gods’).

And the teleological argument: every created thing (i.e. ‘stuff’) has an ultimate purpose (i.e. is in the ‘to’ role of the ‘fulfilled-by’ relationship). Therefore there must be something that isn’t created (i.e. ‘gods’).


The argument seems to me to be completely sound. In fact the way I’ve presented the axioms and derivation above would directly map into a valid mathematical proof.

So if the reasoning is flawless,  what’s the problem? The problem is in the assumptions.

2. Is there actually only a finite amount of stuff? It seems intuitive but not at all certain.

3. For the teleological argument I’ve put down here, I’m not sure this holds (are there any ‘created things’? doesn’t that assume the conclusion?) But I’m sure better wording could rescue this.

4. This can be defined to be true in the abstract sense. But in most formulations of the argument a real relationship is posited here (such as causation). It isn’t clear that causation is a relationship with these characteristics, however. That failure is more obvious when considering the teleological form of the argument (it isn’t obvious to me that everything has a purpose). For the causation forms, for example, you’d need to take into account that the probability seen in quantum mechanics does not arise from some hidden determinism (i.e. there isn’t some deeper level of causation that could possibly give you QM – I might post more on this in due course).

5. This can be trivially true, because one can say that this is what defines membership in the ‘stuff’ set. But in most cosmological arguments the ‘stuff’ set is defined through some other criteria (see the examples above). It isn’t clear a priori that the definitions used to create the ‘stuff’ set might not mean that 5 is volated. In other words, why can’t just normal stuff be the first cause, why does it have to be a God? Also (and this is the intuition, I believe, that is at the root of Dawkins’ (unfortunately invalid) argument against a creator) how can we say that members of the ‘gods’ set aren’t also required to take the ‘to’ role in the relationship. In other words, on what grounds can we assert that God isn’t caused?

6. This is also very suspect, and there is again no reason other than base intuition that I can think for accepting this. Causation, in particular, seems to me to be inextricably linked to my notion of time. And I know that time is not linear in the way my intuition tells me it is. So I can’t accept this without justification either.

And even if the argument does hold, it doesn’t do the theological work that it is often put to. All you end up with is the conclusion that there is at least one element in your ‘gods’ set. There could be thousands, and the elements don’t have to correspond in any way to what you think of as God. For any reasonable reframing of the argument with viable assumptions, you’re likely to get a very watered-down ‘gods’ set at the end of it.

In short, it is an interesting argument, but not convincing unless you’re already convinced that the ‘god’ set is not empty.


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