The Infinite Regress Step of Cosmological Arguments

Arguments for the existence of God purporting to show that there must have been a creator ex nihilo, first mover, or ultimate sustainer of physical reality all share a step that the particular sort of infinite regress that there would otherwise be is a metaphysical impossibility. I will here defend one particular kind of "no infinite regress" premise, although I don't think it goes very far in buttressing even the species of cosmological argument that can claim this true premise.

The cosmological argument premise on which I am focusing  is often put in some such as, “a completed actual infinity is impossible.” Probably it would be better to say “physical infinity” as on standard theology God is actual and has properties that sound like completed infinities. The natural numbers are, on the majority view of philosophers of math, also actual infinities. 

Let me take an example. The Kalam argument  denies the possibility that physical time could have existed forever. (As a set theory wonk would put it, the order type *ω, is supposed to be impossible for time.) No contradiction, however, can be produced from time having already gone on forever.  So the argument is of the form “I cannot imagine how time could extend infinitely into the past; therefore time does not extend infinitely into the past.”  

The progress of science, time and time again, has shown arguments of this form to be unsound, the supposed necessity of Euclidean space being the poster child.  Moreover, in the case of time, as Kant argued in his “Antinomies of Pure Reason,” the idea of a first second, with nothing before it, is hardly more easily imaginable than time’s having no beginning.

There is one form of the cosmological argument, however, for which the impossibility of an infinite regress seems to me to be on much better footing. This is where what is denied is explanation that goes on infinitely – infinitely many steps, infinitely far back, or infinitely deeper.  By explanation, here, I mean an explanation for us. I make no claims about explanation for a being of infinite intelligence or knowledge. Indeed, I am not sure what understanding for such a being would be like or whether the being would ever need explanations.  We, however, being quite finite, cannot  handle an infinite explanation.  

If in order to understand F₁ we need an explanation of F₂ for which we need an explanation of F₃, and so on, then we will never understand F₁. (This all needs a few technical caveats. We can understand explanations that involve certain well behaved sorts of infinity – a proof by mathematical induction, for example. What will not do is an explanation that requires us independently and individually to understand infinitely many stages.)

If a cosmological argument premise denying infinite explanations is true, however, that does not put the whole argument in the clear. There remains the regress stopper – God’s existence -- purporting to preclude the need for any further explanation.  God can be such a stopper only if the concept of God has some very special properties. 

Sometimes this is put as “God is self-explanatory.”  Were the existence of God self-explanatory, however, we would not need any cosmological arguments. We would not need to observe that stuff exists or that things happen. The concept of God would be enough. This would amount to a form of the ontological argument. 

 

To keep the cosmological argument cosmological, the stopper stage is often put in this way: "If God exists, then his existence is necessary," and, for that reason, "if he exists, then his existence is self- explanatory."  The first is called being “necessity prone.” I am not sure that anyone has used the phrase “self-explanation prone,” but it is, though awkward, just as apt.

The problem, of course, is that many perfectly smart and sophisticated philosophers do not accept either that God is self-explanatory or self-explanation prone.  They do not find an explanation of his existence in the concept of God, and find no conceptual impermissibility in asking “what explains God?” 

Quite a different problem with an explanation based cosmological argument is that there may well be no explanation for some phenomena. That this uranium atom, and not that one, gave off an alpha particle at a particular time has no explanation at all under the quantum theory interpretation now in vogue. 

So, even were I right that some cosmological arguments have a true “no infinite regress” premise, that does little to show these arguments sound.