I’ve been reading The Sheed and Ward Anthology of Catholic Philosophy (ed. James Swindal & Harry Gensler, 2005). Apparently, William of Ockham, though a Christian, argued against several traditional arguments for God’s existence (pp 220-222 in the anthology, taken from Ockham’s Quodlibeta, p 1, q 1).
Some folks have argued for a prime mover based on the supposed impossibility of an infinite regress of causes. The regress of causes must stop somewhere and so must stop with a cause that is not itself caused. This is supposed to be a piece of evidence for God; medieval theologians understood this to establish that the universe had a cause, though the other properties of that cause needed to be filled in through other arguments. (This is one version of the cosmological argument.)
Here’s Ockham’s response. Consider a continuous piece of matter (i.e. a piece of matter can be infinitely subdivided). If you strike the piece of matter at one point, the forces will move through the matter, transmitted to all other points. Since the matter is continuous, the force will have to be transmitted through an infinite number of points before the force reaches any other point. And that means that there will be an infinite series of causes and effects throughout the material. Thus, infinite regresses are possible after all.
One objection that could be thrown at Ockham — and that William Lane Craig would be likely to use — is to distinguish between potential and actual infinities. Potentially, you could decompose the continuum into an infinite number of pieces, but no one actually has infinitely subdivided the continuum, so it’s not an actual infinity. However, this response strikes me as rather poor. For any given time, there is a corresponding cause-effect pair in the continuum and, as time marches forward, all of those cause-effect pairs are passed through. We don’t need to decompose the continuum ourselves for it to be an actual infinity.
Another kind of response would point out that continua do not exist. Matter cannot be infinitely subdivided, not because it would take forever, but because matter is made of atoms. However, this doesn’t work either. The prime mover argument is supposed to demonstrate on the basis of a priori reason — and not on the basis of empirical observation — that the universe requires an unmoved mover. Yet there is no a priori argument that decides between continua theories of matter and atomic theories of matter; historically, that issue was settled only through scientific experimentation. Thus, continua are not conceptually impossible. But if continua are not conceptually impossible, then an actual infinite series of causes cannot be impossible.