In my last blog, we looked at a very common objection to the existence of God. In this objection, the skeptic essentially urges that the very concept of omnipotence leads to contradiction and absurdity, since we can imagine a case in which this omnipotent force meets an immovable object. Since such a case would entail the absurd result that the object both could and could not be moved, we should reject the claim that and omnipotent God exists.

Here’s the argument put a bit more carefully:

-----PART I--------

(1) For any X and Y, if X is omnipotent and Y is a possible state of affairs, X can bring about Y. (definition of omnipotence)

(2) It is possible for the world to contain a rock too large for anyone to lift. Call that possibility ROCK. (assumption)

(3) If God exists, he is omnipotent. (assumption)

(4) Therefore, if God exists, he can bring about ROCK. (from 1, 2, and 3)

(5) If ROCK is brought about, then there is an action that no one can do: lift that rock. (from 2)

(6) Therefore, If God exists, there is an action that he cannot do: lift that rock. (from 4 and 5)

--- PART II -------

(7) An omnipotent being can lift any rock. (assumption)

(8) Therefore, if ROCK is brought about, there is an action that God can do: lift that rock. (from 7)

(9) Therefore, if God exists, there is an action that he can do: lift that rock (from 4 and 8)

But now, if we suppose God exists, we get into trouble:

(10) God exists (assumption)

(11) God cannot lift that rock (from 6)

(12) God can lift that rock (from 9)

In the comment section of my last blog, Andrew suggested the following strategy: grant (2), show that it doesn’t lead to trouble by itself, question (7), and show that – suitably clarified – it is logically incoherent. Andrew pointed out that if (7) were true – if God really could lift any rock – then he could lift and unliftable rock. But, Andrew urges, that’s crazy. It’s already built into the description of the rock that nobody could lift it. And so, Andrew suggests, we should reject (7).

For what it's worth, upon reflection I think (7) is a little late in the game to object to the argument. After all, the skeptic is trying to show that omnipotence leads to absurdity. Telling the skeptic that (7) either is absurd or leads to absurdity isn’t going to discourage him: that’s exactly what the skeptic is aiming for! If we’ve already granted premise (2) – the possibility of the existence of an unliftable rock – it does seem to follow that, if God exists, he could lift that rock. Absurdity does seem to follow from granting (2).

Therefore, I think a better avenue is to attack premise (2). Although it makes a very weak logical claim, i.e. a claim of mere possibility, I don’t think we should accept it. What it says, substantially, is that there could be a rock such that no possible being could lift it. But suppose there even could be an omnipotent being. Suppose God at least could exist. (I think the atheist will grant this weak claim.) Wouldn’t God be able to lift any rock?

What exactly would an unliftable rock look like? I suppose we’d have to imagine a rock of infinite dimensions. Infinitely massive, infinitely long, infinitely wide, infinitely high. If the rock were of finite dimension, somebody could lift it. (I’m reminded of Archimedes’ famous boast: “Give me a place to stand and a lever long enough and I will move the world.” His point was that any rock of finite dimension could be moved by someone.) So the rock proposed in (2) must be of infinite dimension.

But can we really imagine such a rock, a rock of infinite dimensions, a rock larger than the (presumably finite) universe, a rock with no borders? Is such a rock really possible?

I don’t think so. At least I can’t make sense of such an idea.* But then we’re well within our rights to reject (2). And so the objection fails.

* Just one example of how weird the suggestion of a rock of infinite dimension is: To imagine such a rock, it's not sufficient for you to just imagine yourself walking on the surface of a really large boulder, which extends to the horizon all around you. A rock of infinite dimension would have no surfaces on which to walk, just as a number line extending infinitely in both directions has no largest or smallest number. So to imagine this unliftable rock of infinite dimension is to imagine a rock with no surfaces. Can you really imagine that? Is that really possible? I vote “no.” And so the Rock Problem for God is dissolved.