This is a brief addendum to the last post, which I hope was easy enough to follow for anyone still reading the series. I’m sure I don’t always make it easy, and I’m hoping by the exercise of writing these things out that I will become better at articulating them.
Moreover, the subject of infinity is challenging enough, and I find myself in a peculiar position of understanding somewhat more than I used to, and yet not very much at all. There are things like “infinite set theory” that are beyond the scope of anything I have studied, though I hope to approach such things in the future.
But what can be said now about infinity as it relates to God and the large stone?
In the last post, I am essentially describing a “potential infinity,” a series of ever larger numbers that can be supposed to go on forever. One never reaches the number “infinity,” because it is impossible to count to infinity, but the fact that the series can go on forever is what makes it “potentially” infinite. For all we know, there is no end to the series, just as, for all we know, there is no end to the future.
To ask whether, in the end, God was either unable to make the rock or unable to lift it is like asking whether the last number you count before infinity is even or odd. There’s no answer to the question – we might say the question is the “wrong” question.
In this way, I offer that the theist has escaped the riddle. But, then, what about an actual infinity? Couldn’t the skeptic say, “Well, God, create a rock that is actually infinite in size – then, can you lift that rock?”
In the post on Hilbert’s Hotel, I give a well-known argument against actual infinities. The argument stands on the basis that an actual infinity leads to logically absurd conclusions. Rather than accept those conclusions, we instead reject that an actual infinity could exist.
So, our author (and God) might reject outright the challenge to build an actually infinite rock. The existence of such a rock would lead to logical absurdities which are not useful to the telling of a story.
They might, of course, be useful to the telling of a particular kind of story – science fiction, for a start – and that’s an interesting subject to explore. Again, we are not saying that an actually infinitely sized rock is logically impossible, or that the conclusions are logically contradictory. Rather, we are saying that the conclusions are absurd, not seeming to have any relation to the world we find ourselves in.
If it is possible to create a rock of actually infinite size (residing, as it surely must, in a Universe of actually infinite size), then the answer whether it can be lifted is probably only known to an all-knowing creator (he says with sheepish grin). I do suspect that such a Universe is only a possible one, and not necessarily one God has or would actually create; at least, it seems not to be possible in this Universe, and just as well, since the story of that Universe is probably far less useful to God’s purposes.
In any event, even with this caveat, it would seem that a consideration of actual infinities renders the riddle absurd, and therefore it does not fare better here than it does with potential infinities. Even if we have to retreat to the notion that God only do one thing or the other, this simply means there is one less thing that any one can do, and God can still do all things that can be done.