Musings about omnipotence and perfection.

[Minimalist]

It is impossible for anything to defeat logic. There can be no square circles. God may exist but a god that can defeat logic must not.

Yeah...but far more likely that all gods were mere human creations for various reasons. That explanation works a lot better.

[theVOID]

Most half-decent theists define omnipotence in terms of the ability to do anything that is logically possible - That is more than a reasonable definition.

What specifically is unimpressive about the ability to do anything that is logically possible? I would be amazed by such a thing, especially considering that I personally can do but a minute fraction of possible things.

Perfection seems like it has dual meanings, one is related to subjective aesthetics and the other is related to mathematics and logic, in that sense I could be equally valid in saying both "Jimmy's make the perfect steak and mushroom pie" and "1 + 1 = 2 is a perfect application of mathematics".

Flawlessness also has the same dual meaning (it actually to me seems exactly equivalent to perfection), for some objective flawlessness I believe you need two things, you need an absolute and objective truth to the object/proposition (otherwise you're talking about subjectivism or relativism) and you need to have correct the method by which you determine this proposition to be true, for instance; A wall can't be objectively flawless because it is subject to aesthetics and the environment it is in. A blue 10 meter wall might be flawless in the circumstances where it fits a 10 meter roof and the person observing it finds blue aesthetically pleasing but under the circumstances where the roof sits 11 meters above the floor and the person in question likes red it could not be deemed flawless. A wall that fits any size building and appears to the observer in their preferred color (or whatever other attributes are considered) could however be objectively flawless.

[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

[Ryft]

That to me is either the exact same thing or I've missed something.

With all due respect to you (and I do), it should be self-evident that they do not say the same thing. To say "God cannot actualize X" says something about God and nothing about X; it could be that X is capable of being actualized but God is limited by some inability. But that is at once both obfuscating and necessarily false, where X is a self-contradicting state of affairs, because it carries the implication that the law of non-contradiction is only contingently true, that self-contradictions are only impossible extrinsically, that there is no such thing as logically impossible, tossing logic out the window as meaningless. It implies that self-contradicting states of affairs are not necessarily (intrinsically) impossible; they are just contingently (extrinsically) impossible but actualizable given the right circumstances.

Thus it is more correct to say "X is incapable of actualization," which says something about X and nothing about God; it makes the crucial and substantive point that self-contradictions are impossible intrinsically, that there is such a thing as logically impossible, that the law of non-contradiction is necessarily true, affirming logic as meaningful. It implies that self-contradicting states of affairs are necessarily (intrinsically) impossible, never actualizable by definition regardless of circumstances.

If statement A says something about God and nothing about X, and statement B says something about X and nothing about God, then statement A and B do not say the exact same thing—especially when statement A implicitly denies the fundamental laws of logic and statement B explicitly upholds them.

I see no problem in saying, "I cannot produce that which is logically impossible."

The problem lies in the implication that you COULD if given the right circumstances.

[theVOID]

With all due respect to you (and I do), it should be self-evident that they do not say the same thing. To say "God cannot actualize X" says something about God and nothing about X;

If that is all you were trying to claim then I agree that they don't say the same thing so much as they mean the same thing, we are talking about the abilities of an omnipotent entity that has the power to perform all members of U, to ask what this being could not perform yeilds the same answer as asking 'what statements are not things that can be performed' thus I see no reason to think it is more exact to use one over the other.

it could be that X is capable of being actualized but God is limited by some inability.

An inability such as?

But that is at once both obfuscating and necessarily false, where X is a self-contradicting state of affairs, because it carries the implication that the law of non-contradiction is only contingently true, that self-contradictions are only impossible extrinsically, that there is no such thing as logically impossible, tossing logic out the window as meaningless. It implies that self-contradicting states of affairs are not necessarily (intrinsically) impossible; they are just contingently (extrinsically) impossible but actualizable given the right circumstances.

For clarity, do you have an example?

Thus it is more correct to say "X is incapable of actualization," which says something about X and nothing about God; it makes the crucial and substantive point that self-contradictions are impossible intrinsically, that there is such a thing as logically impossible, that the law of non-contradiction is necessarily true, affirming logic as meaningful. It implies that self-contradicting states of affairs are necessarily (intrinsically) impossible, never actualizable by definition regardless of circumstances.

I'm on board with all of this already, my point put simply was that they yeild the same results. Perhaps the example I requested above of the exception might help...

If statement A says something about God and nothing about X, and statement B says something about X and nothing about God, then statement A and B do not say the exact same thing—especially when statement A implicitly denies the fundamental laws of logic and statement B explicitly upholds them.

What exactly are you using as example A and for what reasons does it deny the fundamental laws of logic?

I see no problem in saying, "I cannot produce that which is logically impossible."

The problem lies in the implication that you COULD if given the right circumstances.

How so? I could say "I cannot produce a square circle" and that doesn't in any way imply that i could create such a thing given different circumstances.

[Edwardo Piet]

The statement "God cannot do X" would mean there is something that is possible that God cannot do, which would mean God is not omnipotent.

The statement "X is logically impossible and therefore nothing to be done by God or anything else" is consistent with God's omnipotence.

Have I got this right?

[Ryft]

If statement A says something about God and nothing about X, and statement B says something about X and nothing about God, then statement A and B do not say the exact same thing—especially when statement A implicitly denies the fundamental laws of logic and statement B explicitly upholds them.

What exactly are you using as example A and for what reasons does it deny the fundamental laws of logic?

Statement A was, "God is not capable of actualizing self-contradiction X"—in other words, the problem with actualizing X is an extrinsic one (God). It denies the fundamental laws of logic because it implies that actualizing X is possible given the right extrinsic circumstances and that God cannot satisfy those. But its impossibility is not due to some extrinsic feature (that which it has in relation to some thing outside itself); what makes it impossible is not the fact that no agent can produce it. Rather, it is due to an intrinsic feature (that which it has in and of itself); what makes it impossible is the fact that it is incapable of production in and of itself, regardless of any circumstances real or supposed, because a self-contradiction is a logically impossible non-entity.

This is reminiscent of discussion I had early last year, where I had an atheist suggest to me that self-contradictions present a limitation to God's power (because they are something he cannot actualize) so therefore an omnipotent God is impossible. Rather baffled at how he could think that a non-existent nothing can limit anything, I nevertheless tried to answer him carefully with the following.

Let me explain this as carefully as I can. By claiming that actualizing self-contradictions (e.g., making a square circle) is something God cannot do and thus presents a limitation to his power, you are claiming that contradictions are impossible for extrinsic reasons, that they are impossible only because God's power is insufficient for the task. There are two problems with this, which my post earlier addressed.

First, such a claim violates how contradictions are defined; namely, contradictions are logically impossible for intrinsic reasons, not just metaphysically impossible for extrinsic reasons. The logically impossible "carries its impossibility within itself," as Lewis explained. Philosophers articulate the difference between two important categories of truth, necessary and contingent; the former refers to that which is necessarily true and cannot be otherwise (a square has four sides of equal length), while the latter refers to that which happens to be true but could be otherwise (stop signs are red). The fundamental laws of logic are necessary truths, not contingent truths; that is, the law of non-contradiction does not just happen to be true extrinsically (in relation to something else) and could be otherwise, but rather it is necessarily true intrinsically (in and of itself) and cannot be otherwise. So for you to claim that self-contradictions are impossible for extrinsic reasons, a limit of God's power, is to completely redefine the terms and toss logic on its head.

Second, it is true that nearly all the definitions of omnipotence use the word "unlimited" but please give attention to what is unlimited: power. This stems from the Latin potens, from posse (to be able) and therefore refers to the ability to actualize any state of affairs. And Scripture concurs by saying that all things are possible with God. But self-contradictions are neither things nor possible; they are logically impossible non-entities, nothing more than a meaningless combination of words. As non-existent nothings they are not a task to be performed nor an obstacle against the accomplishment of one. As I pointed out earlier, to hold that self-contradictions are only metaphysically impossible for extrinsic reasons is to hold that self-contradictions are possible, albeit extraordinarily difficult; i.e., that the logically impossible is logically possible (itself a meaningless logical contradiction).

I could say, "I cannot produce a square circle," and that doesn't in any way imply that I could create such a thing given different circumstances.

JOHN: Why can't God produce a square circle?

ADAM: Because he does not have sufficient power.

JOHN: An all-powerful being should be able to produce a square circle?

ADAM: Yes, because a being who cannot is thus NOT all-powerful.

JOHN: So the logically impossible is logically possible?

ADAM: [blank expression] Wait, what?

JOHN: You said an all-powerful being should be able to produce a square circle.

ADAM: Right.

JOHN: And a square circle is a logically impossible self-contradiction.

ADAM: Okay.

JOHN: Thus, you think the logically impossible is logically possible, given an all-powerful being.

ADAM: Start over. Ask me the question again.

JOHN: Why can't God produce a square circle?

ADAM: Because it is a logical contradiction.

JOHN: Then why can't God produce a logical contradiction?

ADAM: Because they are incapable of production.

JOHN: And there you have it. That is why the second statement is to be preferred, and the first statement should be rejected. That is, we do not say, "God is incapable of actualizing self-contradiction X," but rather we say, "Self-contradiction X is incapable of actualization."

[Godscreated]

Your minds go to an impossibly illogical place when it comes to the omnipotence of God. God is omnipotent because He states He is and as such the definition to omnipotence lies with God and not man.
God can not do all things and says He can not, He says I can do all things that are within My attributes ie. sin is outside of God so He can not sin. Thus God's power lies within what is righteous and perfect according to His attributes, this in fact means nothing is impossible for Him to do in His perfection. So my God has the perfect power to do the perfect thing at the perfect time and nothing can possibly stop Him.

[Captain Scarlet]

So my God has the perfect power to do the perfect thing at the perfect time and nothing can possibly stop Him.....

....apart from a fig tree which wasn't bearing any fruits, something stopping him returning in the lifetime of his followers and some Romans with a large wooden crucifix....oh no wait he wanted that last thing to happen didn't he?

[Speakeasy]

You guys are smart...Square circles....