Musings about omnipotence and perfection.

[theVOID]

I disagree with Rayaan here, and for an important reason. Taking my cue from his statement, I should like to point out that under Christianity it is not the case that God is unable to actualize a self-contradicting state of affairs. Rather, it is that a self-contradicting state of affairs is incapable of actualization—as DvF astutely observed. The former is a statement about God (and incompatible with omnipotence). The latter is a statement about self-contradicting states of affairs (and says nothing about omnipotence). This is why Thomas Aquinas notes, "It is more exact to say that the intrinsically impossible is incapable of production, than to say that God cannot produce it."

That to me is either the exact same thing or i've missed something. You (and Aquinas) seem to be suggesting that the former ("the intrinsically impossible is incapable of production") is somehow more valid a statement than the latter ("God cannot produce it").

Omnipotence describes the ability of God to perform every member of the universal set of tasks. But a self-contradiction is an intrinsically impossible non-entity—it cannot be analytically conceived in itself without contradiction—which means that it is neither a task to be performed nor an obstacle against the accomplishment of one.

I agree with that, but how does that relate to Aquinas' statement? I cannot produce the intrinsically impossible either, but I see no problem in saying "I cannot produce that which is logically impossible" nor do I see any reason to think that it is any less valid a statement than "the intrinsically impossible is incapable of production".

I shall borrow from an argument presented roughly ten years ago by Chuck Johnson (an atheist from the newsgroup talk.atheism) to underscore this distinction.

Let U stand for "the universal set of tasks" and let T stand for "some proposed task."

1. Omnipotence is the ability to perform every member of U.
   
2. If T is logically possible, then T is a member of U.
   
3. If T is logically impossible, then T is not a member of U.
   
4. If T is not a member of U, then T is a non-task nT.
   
5. All nT form a null set Ø.

So it is immediately obvious that to ask if an omnipotent being can perform any members of a null set Ø is very absurd. It would be incorrect to say that he cannot; rather, it is that there is nothing there to perform. Aquinas again: "It is more exact to say that the intrinsically impossible is incapable of production, than to say that God cannot produce it."

I love the structure of that argument, but I still don't see why "Omnipotent being cannot produce" and "There is nothing to produce" are at odds, they to me convey the same meaning, for example:

1. An omnipotent being can perform every member of U
2. That which is not a member of U does not exist to be performed
3. God is omnipotent
4. Therefore, God cannot perform ~U