The Burrito Paradox.

[Ace]

My dad presented me with this funny twist on an old question. I thought you all might enjoy the humour.

Can God microwave a burrito so hot that He can't eat it?

Ace

[AgeGap]

Good, but can you tell me what the old question is?

[paximperium]

Good, but can you tell me what the old question is?

What else?
"How much wood could a woodchuck chuck chuck if a woodchuck would chuck wood?"

[Ace]

Good, but can you tell me what the old question is?

of course. :rolleyes: but its not funny.
Ace

[mijopaalmc]

Good, but can you tell me what the old question is?

Can God create a stone so heavy he cannot lift it?

More generally:

Can God create a task he cannot do?

[quixotecoyote]

To which the best answer I've seen is "Yes, but then he would no longer be omnipotent."

Omnipotence implies the ability to self-limit.

[mijopaalmc]

To which the best answer I've seen is "Yes, but then he would no longer be omnipotent."

Omnipotence implies the ability to self-limit.

Next question:

Is "God" by definition omnipotent?

[quixotecoyote]

Next question:

Does "God" by definition omnipotent?

If it's not, the question doesn't really make much sense.

[mijopaalmc]

If it's not, the question doesn't really make much sense.

I edited it after I read what I had posted.

[quixotecoyote]

I edited it after I read what I had posted.

I read it the way you meant it.

If God is not defined as omnipotent, then there's no real point in asking questions about God's omnipotence.

[mijopaalmc]

I read it the way you meant it.

If God is not defined as omnipotent, then there's no real point in asking questions about God's omnipotence.

Yeah, yeah, I saw "... doesn't make sense" and assumed that it was about what I had written, because it didn't make sense as originally written. It appears that I have made yet another mistake.:o

[RandFan]

Thomas Aquinas resolved the paradox 7 centuries ago. It's amazing that this dead horse get's beaten so often.

God cannot do anything that is logically impossible. God can't make square circles, 2+2=5, etc.

ETA: God cannot do anything period because god does not exist but that's another discussion.

[ServiceSoon]

Logically impossible to whom?

[fuelair]

Actually, based on the trinity thing, In the Father form he creates it, then he switches to the Son form which, being human born, can't lift it. Obviously a load given no god, but.....

[RandFan]

Logically impossible to whom? The question answers itself.

ETA: Here is another. Is X not X?

Oh, wait, let me guess, "not X to whom?"

[kmortis]

Next question:

Is "God" by definition omnipotent?

Depends on the god. Almost all of the pagan gods were distinctly not omnipotent. That seems to be a monotheist, specifically middle eastern monotheist thing. Wasn't the Zoroastrian god supposed to be omnipotent? I don't think that any of the Hindu gods are with the possible exception of Brahma, but he's taking a nap right now so he can't answer.

[ServiceSoon]

The question answers itself.

ETA: Here is another. Is X not X?

Oh, wait, let me guess, "not X to whom?"Just becuase us mortals can't comprehend it that doesn't mean it isn't possible.

[RandFan]

Just becuase us mortals can't comprehend it that doesn't mean it isn't possible. Your statement is nonsensical. The issue has nothing to do with comprehension.

[ServiceSoon]

Just because something is beyond our understanding that doesn't make it impossible or illogical. What is nonsensical about that?

[triadboy]

Your Dad is a Simpsons fan.

HOMER
Oh right, the God dude. Hey, I got a question for you. (pulls out a piece of paper) "Could Jesus microwave a burrito so hot that he himself could not eat it?"

NED
Well sir, of course, he could, but then again... wow, as melon-scratchers go that's a honey-doodle.

[quixotecoyote]

Just because something is beyond our understanding that doesn't make it impossible or illogical. What is nonsensical about that?

It is not illogical because we cannot comprehend it. We are comprehending that it is illogical.

[RandFan]

Just because something is beyond our understanding that doesn't make it impossible or illogical. What is nonsensical about that?

RF: The impossible is not possible.

SS: Just because you don't understand it doesn't mean that the impossible is not possible.

RF: No SS, the impossible is by definition not possible. That's what impossible means.

SS: ...

[Sunstealer]

Next question:

Is "God" by definition omnipotent?No, he's impotent and non-important.

[triadboy]

Can God microwave a burrito so hot that He can't eat it?


No - He would roll it around in His mouth like I do with a hot burrito. Surely He can do what I do.

[Tsukasa Buddha]

Can God color the sky -65 meters?

[RandFan]

Can God color the sky -65 meters?Yes and make it taste like violins.

[kmortis]

Yes and make it taste like violins.

Mmmmm, violins! Crispity, crunchity violins, now with 1/3rd less sphincter.

[Dogdoctor]

Well if the burrito reached a certain temperature it would be incinerated so there is a limit to the temperature he/she/it can microwave it to. And no matter how hot he/she/it makes the burrito, he/she/it can always wait for it to cool down. My vote is for no.

[kmortis]

Well if the burrito reached a certain temperature it would be incinerated so there is a limit to the temperature he/she/it can microwave it to. And no matter how hot he/she/it makes the burrito, he/she/it can always wait for it to cool down. My vote is for no.

What if the deity made it with an asbestos wrap?

[Mobyseven]

Thomas Aquinas resolved the paradox 7 centuries ago. It's amazing that this dead horse get's beaten so often.

God cannot do anything that is logically impossible. God can't make square circles, 2+2=5, etc.

Mmm - that solution has never sat well with me. There's nothing actually logically impossible about creating something so heavy that it cannot be lifted. Humans do it all the time, making things that are far too heavy to lift.

As it is possible for a human to create an object too heavy for it to lift, that means that when you introduce an omnipotent god into the equation, that omnipotent god cannot do something that even a human can do. That doesn't make the initial task logically impossible, it makes omnipotence logically impossible.

This stands in stark contrast to square circles and making 2+2=5, because both those things are analytically logically impossible; no one can do it, not an omnipotent god, not humans, not...er...cute little bunny rabbits.

But yeah - the logical impossibility in the omnipotence paradox is misplaced. The logical impossibility lies with omnipotence itself, not with the creation of the super-hot burrito.

[RandFan]

Mmm - that solution has never sat well with me. There's nothing actually logically impossible about creating something so heavy that it cannot be lifted. Humans do it all the time, making things that are far too heavy to lift.

As it is possible for a human to create an object too heavy for it to lift, that means that when you introduce an omnipotent god into the equation, that omnipotent god cannot do something that even a human can do. That doesn't make the initial task logically impossible, it makes omnipotence logically impossible.

This stands in stark contrast to square circles and making 2+2=5, because both those things are analytically logically impossible; no one can do it, not an omnipotent god, not humans, not...er...cute little bunny rabbits.

But yeah - the logical impossibility in the omnipotence paradox is misplaced. The logical impossibility lies with omnipotence itself, not with the creation of the super-hot burrito. There's one thing wrong with your argument. Humans are not defined as omnipotent.

To be able to not lift a rock would render god not omnipotent.

Omnipotent is not not omnipotent.

A = ~A

Logicaly invalid. Logically impossible.

Give Aquinus his due. He was actually quite on the ball.

ETA: As usual for me I respond without fully understanding your point. I've got to do a better job. I'm going to change my mind. I think you might have a point. There is a difference. I'm gouing to mull this one over some more.

Thanks Moby.

ETA2: God I could save myself so much trouble if I would fully understand posts before I respond.

[Ace]

That doesn't make the initial task logically impossible, it makes omnipotence logically impossible.(snip)...The logical impossibility lies with omnipotence itself, not with the creation of the super-hot burrito.

Well put.


Your dad is a Simpsons fan.


Indeed he is...I heard this from him many years ago, I'm going to ask him if he stole it.
Ace

[Mashuna]

Mmmmm, violins! Crispity, crunchity violins, now with 1/3rd less sphincter.

I am philosophically opposed to the use of violins. There is always a better solution than to resort to violins.

[Egg]

Mmm - that solution has never sat well with me. There's nothing actually logically impossible about creating something so heavy that it cannot be lifted. Humans do it all the time, making things that are far too heavy to lift.

As it is possible for a human to create an object too heavy for it to lift, that means that when you introduce an omnipotent god into the equation, that omnipotent god cannot do something that even a human can do. That doesn't make the initial task logically impossible, it makes omnipotence logically impossible.

This stands in stark contrast to square circles and making 2+2=5, because both those things are analytically logically impossible; no one can do it, not an omnipotent god, not humans, not...er...cute little bunny rabbits.

But yeah - the logical impossibility in the omnipotence paradox is misplaced. The logical impossibility lies with omnipotence itself, not with the creation of the super-hot burrito.

The human can only do this because of something humans cannot do. It is the the limit of not being omnipotent that allows for it.

An omnipotent being that can do anything logically possible cannot logically do things that would mean not being omnipotent, such as "be anything other than omnipotent" or "demonstrate a failing of a lack of omnipotence".

If we turn the question around:

Can a human eat the hottest burrito he/she can make?
Can an omnipotent god eat the hottest burrito he/she/it can make?

...now it's something that humans cannot do and an omnipotent god can.

The task is illogical because there can be no such thing as a burrito that is too hot for an omnipotent god to eat, whereas there is such a thing as a burrito that is too hot for a human to eat.

[ServiceSoon]

RF: The impossible is not possible.

SS: Just because you don't understand it doesn't mean that the impossible is not possible.

RF: No SS, the impossible is by definition not possible. That's what impossible means.

SS: ...At one point in history people said it was logically impossible to sail around the world.
Just because we don't understand something that doesn't make it logically impossible. That is why I disagree with God cannot do anything that is logically impossible.

[Egg]

At one point in history people said it was logically impossible to sail around the world.
Just because we don't understand something that doesn't make it logically impossible. That is why I disagree with

I'm sure it used to be impossible to sail around the world, but was it really logically impossible?

ETA...doh! You're making a reference to people thinking the earth was flat, aren't you?

[bobcarp]

If god fell in the forrest, and there were only atheists around, would he make a noise?

[triadboy]

If god fell in the forrest, and there were only atheists around, would he make a noise?

If He fell on something like a Redwood and it was 'inserted' in Him - I think you know what I mean - I believe He would give a Godly yelp. But His voice is so booming - it would sound like thunder to us. So please tell your children - when they hear thunder - that's God being rectally violated by a Giant Redwood. (It's as good as the other stories)

[cafink]

At one point in history people said it was logically impossible to sail around the world.

That's because those people believed the world to be flat. They were mistaken about the shape of the world, not about the logic of sailing around it. Even those people would have conceded that it is logically possible to sail around a (roughly) spherical world. Furthermore, they were, in fact, correct in their belief that it is logically impossible to sail "around" a flat world.

Just because we don't understand something that doesn't make it logically impossible. That is why I disagree with

Microwaving a burrito so hot that an omnipotent god cannot eat is logically impossible, but not because we're unable to understand how to do it. It's logically impossible because it is a nonsensical, paradoxical statement.

[Bob Klase]

At one point in history people said it was logically impossible to sail around the world.

It's much more likely that they said it was merely impossible and meant physically impossible.

It would also depend on what people said it. You can find individuals and groups of people that say just about anything.

[Bob Klase]

To which the best answer I've seen is "Yes, but then he would no longer be omnipotent."

Omnipotence implies the ability to self-limit.

Self-limiting would mean he 'wouldn't' do it, not that he 'couldn't' do it.

I could eat a 24 ounce steak every day for a year. But I wouldn't. Doesn't mean I couldn't.

[Mobyseven]

The human can only do this because of something humans cannot do. It is the the limit of not being omnipotent that allows for it.

An omnipotent being that can do anything logically possible cannot logically do things that would mean not being omnipotent, such as "be anything other than omnipotent" or "demonstrate a failing of a lack of omnipotence".

If we turn the question around:

Can a human eat the hottest burrito he/she can make?
Can an omnipotent god eat the hottest burrito he/she/it can make?

...now it's something that humans cannot do and an omnipotent god can.

The task is illogical because there can be no such thing as a burrito that is too hot for an omnipotent god to eat, whereas there is such a thing as a burrito that is too hot for a human to eat.

But when you turn the question around, you create a completely different question - you've changed things so that it appears to be the same question just rephrased, but is actually not. The burrito in the first question is different to the burrito in the second question, because the burrito in the first question merely has to be made hot enough that a human cannot eat it, whereas in the second question it must be the hottest burrito possible to make.

The problem here is that people always lump the agent and the action together when considering this question, rather than evaluating them separately. There is nothing logically impossible about the action in this case, as can be shown by the fact that it is physically possible to undertake it (and that which is physically possible cannot be logically impossible). Things only become logically impossible when the agent is introduced and defined as omnipotent.

That tells you something, therefore, not about the logical possibility of the action, but of the logical possibility of the agent - in this case, an omnipotent being.

[RandFan]

At one point in history people said it was logically impossible to sail around the world. There are two fatal flaws in your logic SS.

1.) I'm speaking in the abstract. I'm formulating a hypothetical. A hypothetical does not need to be true to be valid?



Let's assume for the sake of argument that we don't know whether or not if there is in fact any thing that is impossibile. We suspect so but we could be wrong.

Hypothetical: If it is impossible to sail around the world then to attempt to do so would be a waste of time and money.
Is the hypothetical true? No.
Is the hypothetical valid? Yes.

Therefore if there is something that is logically impossible then there is something that even an omnipotent god cannot do.

The hypothetical is valid whether or not there exists anything that is impossible, logical or otherwise.


2.) There are, in fact, logical impossibilities. That is not arguable. There might be things that we THINK are impossible and some day we will find out that we are wrong about that but in fact there are logical impossibilities.
God cannot make a round square.
God cannot truthfully say that he always lies.
It can't happen. No amount of understanding will ever make it happen.

[Egg]

But when you turn the question around, you create a completely different question - you've changed things so that it appears to be the same question just rephrased, but is actually not. The burrito in the first question is different to the burrito in the second question, because the burrito in the first question merely has to be made hot enough that a human cannot eat it, whereas in the second question it must be the hottest burrito possible to make.

The problem here is that people always lump the agent and the action together when considering this question, rather than evaluating them separately. There is nothing logically impossible about the action in this case, as can be shown by the fact that it is physically possible to undertake it (and that which is physically possible cannot be logically impossible). Things only become logically impossible when the agent is introduced and defined as omnipotent.

That tells you something, therefore, not about the logical possibility of the action, but of the logical possibility of the agent - in this case, an omnipotent being.

As far as I can see, what you're saying is that for omnipotence to really be omnipotence it has to be able to do the logically impossible, but because that would be illogical, omnipotence can't exist. From what I understand, the original point of the rock dilemma was to help define omnipotence. What it does is to show human limitations by self-referencing. An omnipotent being cannot logically do things that only a non-omnipotent being could do because of non-omnipotent limitations, but that doesn't stop it from being omnipotence, it just defines it as being able to do anything logically possible.

Of course, the other option is to agree that omnipotence must, by definition, include the logically impossible, in which case an omnipotent being can do things that an omnipotent being can't do without any issues.

Imagine a computer programmer making a world on the computer. The inhabitants of this world, whether just with artificial intelligence or people playing online, might have limited crafting abilities. They could for instance make a large chair which they cannot lift. The programmer is outside of the game and can manipulate anything in-game by changing the coding, so there are no objects that can be created that he couldn't lift. Does that mean that he isn't all powerful relative to that computer world?

[Ryan O'Dine]

Two points.

1. If God cannot do the logically impossible, then there are rules to which God is subject. This goes beyond questions of mere omnipotence. It suggests there is something that preexisted God, or something within which God is contained -- the laws of logic. So there’s something “higher” than the “Most High.”

2. On the other hand. Conceivably, God could make all the instruments measuring the temp of the burrito register in the uneatable range, while the burrito itself was actually eatable. We'd have no way of proving otherwise -- problem solved. :cool:

[Mobyseven]

As far as I can see, what you're saying is that for omnipotence to really be omnipotence it has to be able to do the logically impossible, but because that would be illogical, omnipotence can't exist. From what I understand, the original point of the rock dilemma was to help define omnipotence. What it does is to show human limitations by self-referencing. An omnipotent being cannot logically do things that only a non-omnipotent being could do because of non-omnipotent limitations, but that doesn't stop it from being omnipotence, it just defines it as being able to do anything logically possible.

Of course, the other option is to agree that omnipotence must, by definition, include the logically impossible, in which case an omnipotent being can do things that an omnipotent being can't do without any issues.

Imagine a computer programmer making a world on the computer. The inhabitants of this world, whether just with artificial intelligence or people playing online, might have limited crafting abilities. They could for instance make a large chair which they cannot lift. The programmer is outside of the game and can manipulate anything in-game by changing the coding, so there are no objects that can be created that he couldn't lift. Does that mean that he isn't all powerful relative to that computer world?

That is indeed not what I was saying at all. My point isn't that an omnipotent being must be able to do the logically impossible, my point is that omnipotence is logically impossible.

As for your programmer's example - yes, the programmer isn't all powerful relative to the computer world. There are things that the programmer cannot do. Doesn't matter if his creations don't know it - the definition of 'omnipotence' isn't, "The ability to be, like, really really powerful from the point of view of an entity with very little power."

[Robin]

Mmm - that solution has never sat well with me. There's nothing actually logically impossible about creating something so heavy that it cannot be lifted. Humans do it all the time, making things that are far too heavy to lift.Actually, in traditional theology God can create a rock that he cannot lift.

In fact the rock paradox was used by Christian theologians to illustrate the nature of omnipotence long before it was ever used by an atheist to disprove the concept.

The medieval schoolmen made the distinction between potentia Dei absoluta (God’s absolute power) and potentia Dei ordinata (God’s ordained power), so in other words God has the absolute power to lift the rock, but has ordained that it cannot be lifted and so it cannot, even by God, (since God cannot lie).

So omnipotence is not the ability to do anything, it is the ability to do any intrinsically possible thing - God cannot do anything that creates a contradiction.
As it is possible for a human to create an object too heavy for it to lift, that means that when you introduce an omnipotent god into the equation, that omnipotent god cannot do something that even a human can do. That doesn't make the initial task logically impossible, it makes omnipotence logically impossible.
Humans cannot create an object too heavy to lift and lift it, which is what you are asking God to do.
This stands in stark contrast to square circles and making 2+2=5, because both those things are analytically logically impossible; no one can do it, not an omnipotent god, not humans, not...er...cute little bunny rabbits.
But creating a rock too heavy to lift and then lifting it is in the same category.

[Marquis de Carabas]

The problem here is that people always lump the agent and the action together when considering this question, rather than evaluating them separately.
That is because they cannot be separated. They are intrinsically linked. The problem is you have too narrowly defined what constitutes the action. The action is not merely creating a rock (or heating a burrito). It is creating a rock an omnipotent being cannot lift. Therein lies the contradiction. The phrase a rock an omnipotent being cannot lift is utter nonsense. It is nothing more than an artifact of a limitless combinatorial grammar. It has no possible referent.

[Robin]

That is because they cannot be separated. They are intrinsically linked. The problem is you have too narrowly defined what constitutes the action. The action is not merely creating a rock (or heating a burrito). It is creating a rock an omnipotent being cannot lift. Therein lies the contradiction. The phrase a rock an omnipotent being cannot lift is utter nonsense. It is nothing more than an artifact of a limitless combinatorial grammar. It has no possible referent.
It is not nonsense at all, it is a perfectly sensical phrase.

An omnipotent being is not defined as a being who can do anything, it is defined as a being who can do any instrinsically possible thing. So a rock that an omnipotent being cannot lift does have a referent - a rock that it is intrinsically impossible to lift.

[Bri]

Mmm - that solution has never sat well with me. There's nothing actually logically impossible about creating something so heavy that it cannot be lifted. Humans do it all the time, making things that are far too heavy to lift.

As it is possible for a human to create an object too heavy for it to lift, that means that when you introduce an omnipotent god into the equation, that omnipotent god cannot do something that even a human can do. That doesn't make the initial task logically impossible, it makes omnipotence logically impossible.

This stands in stark contrast to square circles and making 2+2=5, because both those things are analytically logically impossible; no one can do it, not an omnipotent god, not humans, not...er...cute little bunny rabbits.

But yeah - the logical impossibility in the omnipotence paradox is misplaced. The logical impossibility lies with omnipotence itself, not with the creation of the super-hot burrito.

I think I disagree. You are simply observing that even a human can be non-omnipotent, but that an omnipotent god cannot be non-omnipotent and therefore cannot do anything. I do think that falls into the logically impossible bin.

If omnipotence is defined as being able to do all that is logically possible, then there is no conflict. Similarly, omniscience can be defined as knowing all that is knowable since even the omniscient being cannot know the unknowable (otherwise it wouldn't be unknowable).

Two points.

1. If God cannot do the logically impossible, then there are rules to which God is subject. This goes beyond questions of mere omnipotence. It suggests there is something that preexisted God, or something within which God is contained -- the laws of logic. So there’s something “higher” than the “Most High.”

We could potentially define omnipotence as being able to do the logically impossible (or omniscience as being able to know the unknowable). But once you allow the illogical into the equation we cannot expect to understand the results. For example, if you define "omnipotence" as being able to do the illogical as well as the logical, then an omnipotent being could lift the unliftable (or an omniscient being could know the unknowable). That the result is a logical contradiction is to be expected because you've defined the term to allow (even require) logical contradictions.

-Bri

[Marquis de Carabas]

It is not nonsense at all, it is a perfectly sensical phrase.

An omnipotent being is not defined as a being who can do anything, it is defined as a being who can do any instrinsically possible thing. So a rock that an omnipotent being cannot lift does have a referent - a rock that it is intrinsically impossible to lift.
That only works if you can create a convincing argument that a rock that is intrinsically impossible to lift is not also nonsense. I'm afraid I feel it is, but I am open to being convinced otherwise.

[Robin]

That only works if you can create a convincing argument that a rock that is intrinsically impossible to lift is not also nonsense. I'm afraid I feel it is, but I am open to being convinced otherwise.
Take one God. Take one rock. God says "this rock shall never be lifted".

[quixotecoyote]

Self-limiting would mean he 'wouldn't' do it, not that he 'couldn't' do it.

I could eat a 24 ounce steak every day for a year. But I wouldn't. Doesn't mean I couldn't.

By self-limiting I mean that he could render himself non-omnipotent. He could create the burrito/rock in such a way as to remove his uber-powers so that after the creation he would be unable to eat/lift it.

More akin to sewing your mouth shut or removing your stomach in the steak example.

[Marquis de Carabas]

Take one God. Take one rock. God says "this rock shall never be lifted".
That does not sound too intrinsic to me. Its non-liftability if not a property of the rock, but a property of the command of the deity.

[Bri]

By self-limiting I mean that he could render himself non-omnipotent. He could create the burrito/rock in such a way as to remove his uber-powers so that after the creation he would be unable to eat/lift it.

More akin to sewing your mouth shut or removing your stomach in the steak example.

That also seems like a good point, although not really in the spirit of the question. In this case you're asking if an omnipotent god could make itself non-omnipotent. Sure it could, but then it would no longer be an omnipotent god.

I think the nature of the question (which I believe to be a nonsense question) is whether an omnipotent god can do the impossible (in which case it's not impossible).

-Bri

[Robin]

That does not sound too intrinsic to me. Its non-liftability if not a property of the rock, but a property of the command of the deity.
No, the deity's command is not unliftable. The rock is unliftable. Who can lift it?

[Bri]

You're asking if an omnipotent being can lift the unliftable. That's a nonsense question, similar to "Is the statement 'this statement is a lie' a lie?" The concept of lifting the unliftable is logically inconsistent. The question assumes that "omnipotent" includes the ability to do the logically inconsistent but that the result must be logically consistent.

-Bri

[Marquis de Carabas]

No, the deity's command is not unliftable. The rock is unliftable.
But the non-liftability does not come from the "rockness" of the rock. It is not intrinsic. It is a bestowed trait by extrinsic action of the deity.

[Robin]

Self-limiting would mean he 'wouldn't' do it, not that he 'couldn't' do it.

I could eat a 24 ounce steak every day for a year. But I wouldn't. Doesn't mean I couldn't.
If God says he won't then he can't.

If you say you wouldn't eat a 24 ounce steak every day for a year and you were unable to lie, then you wouldn't does mean couldn't.

[Beerina]

To which the best answer I've seen is "Yes, but then he would no longer be omnipotent."

Omnipotence implies the ability to self-limit.

More accurately, can one give up omnipotence and never simply re-assert it in the future?

One could choose to voluntarily limit oneself for a period of time, but that's a different thing than you can't re-assert it, no matter what you try.

It's like the old questions can a parliament permanently bind future parliaments? Can a person with inalienable rights like life and liberty voluntarily and irrevocably give up those rights?

Generally speaking, the answers are no, and no. Parliaments can and do simply throw out the old law they don't want, which binds them, thus retroactively asserting their authority. And you cannot give up your rights irrevocably (e.g. signing a contract to become someone's slave for ever) because you can, at any point, just reassert your right to freedom and walk away (and, at worst, you may be liable for financial costs of violating your contract.)

The latter, far from limiting your freedom, actually speaks to the fundamental, inalienable nature of certain things. They cannot be given up permanently by you by contract, end of story. Furthermore, the government has no business "enforcing" that type of contract.

[quixotecoyote]

More accurately, can one give up omnipotence and never simply re-assert it in the future?

One could choose to voluntarily limit oneself for a period of time, but that's a different thing than you can't re-assert it, no matter what you try.

It's like the old questions can a parliament permanently bind future parliaments? Can a person with inalienable rights like life and liberty voluntarily and irrevocably give up those rights?

Generally speaking, the answers are no, and no. Parliaments can and do simply throw out the old law they don't want, which binds them, thus retroactively asserting their authority. And you cannot give up your rights irrevocably (e.g. signing a contract to become someone's slave for ever) because you can, at any point, just reassert your right to freedom and walk away (and, at worst, you may be liable for financial costs of violating your contract.)

The latter, far from limiting your freedom, actually speaks to the fundamental, inalienable nature of certain things. They cannot be given up permanently by you by contract, end of story. Furthermore, the government has no business "enforcing" that type of contract.

I'm not sure the almighty power of the living god is based in contract law.

See post 53 where I explained what I meant a little better.

[Robin]

But the non-liftability does not come from the "rockness" of the rock.
So what? Who can lift it?
It is not intrinsic. It is a bestowed trait by extrinsic action of the deity.
And once bestowed this trait can never be separated from the rock, it is intrinsically impossible to lift the rock.

God can make a rock that even He cannot lift.

[Robin]

You're asking if an omnipotent being can lift the unliftable. That's a nonsense question, similar to "Is the statement 'this statement is a lie' a lie?" The concept of lifting the unliftable is logically inconsistent. The question assumes that "omnipotent" includes the ability to do the logically inconsistent but that the result must be logically consistent.

-Bri
Who are you addressing this question to? As far as I can see nobody has asked if an omnipotent being can lift the unliftable.

[Bri]

One could choose to voluntarily limit oneself for a period of time, but that's a different thing than you can't re-assert it, no matter what you try.

I can see no reason that an omnipotent being couldn't choose to permanently give up its omnipotence the same way that I could chop off and incinerate both of my hands and thereby give up my ability to raise my middle finger to you.

In fact, it wouldn't be omnipotent if it couldn't do that. Of course, having the ability to do something and actually choosing to do it are two different things.

-Bri

[Robin]

I can see no reason that an omnipotent being couldn't choose to permanently give up its omnipotence the same way that I could chop off and incinerate both of my hands and thereby give up my ability to raise my middle finger to you.

In fact, it wouldn't be omnipotent if it couldn't do that. Of course, having the ability to do something and actually choosing to do it are two different things.

-Bri

Again you are defining omnipotence as the abilty to do anything, but it has never meant that.

If God is necessarily an essential being then God cannot stop being God.

[Bri]

Who are you addressing this question to? As far as I can see nobody has asked if an omnipotent being can lift the unliftable.

I was responding to your post immediately preceeding mine. The rock is defined as being unliftable because the omnipotent god deemed it so. The question becomes whether an omnipotent god can then lift it (i.e. the unliftable rock). The notion of lifting the unliftable is nonsense.

If you define "omnipotent" as the ability to do anything that is (logically) possible to do, then no an omnipotent being cannot lift the unliftable (there is no conflict).

If you define "omnipotent" as the ability to do the logically impossible, then of course the result will be the logically impossible (the possibility of lifting the unliftable without making it "liftable").

-Bri

[Bri]

Again you are defining omnipotence as the abilty to do anything, but it has never meant that.

I'm defining omnipotence as the ability to do anything that is logically possible to do.

I was saying that the notion of defining "omniscience" as the ability to do the logically impossible is nonsense (i.e. will result in the logically impossible). If the question assumes a definition of "omniscience" as the ability to do only the logically possible, then it's not a paradox at all. The omnipotent being could make the rock unliftable at will, or could lift the rock at will (thereby making the rock liftable), but couldn't do both at the same time given that liftable = !unliftable.

I'm not sure we are in disagreement -- I was simply commenting on your comment.

If God is necessarily an essential being then God cannot stop being God.

What do you mean by "essential being?"

Sure God could stop being God (assuming "being God" involves being omnipotent). If you define "ant" as a creature with 6 legs, then you can make an ant stop being an ant by removing one of its legs (or it could do so itself by gnawing off one of its own legs).

-Bri

[Robin]

I was responding to your post immediately preceeding mine. The rock is defined as being unliftable because the omnipotent god deemed it so. The question becomes whether an omnipotent god can then lift it (i.e. the unliftable rock).
I didn't ask the question and the question is not implied by what I said.
If you define "omnipotent" as the ability to do anything that is (logically) possible to do, then no an omnipotent being cannot lift the unliftable (there is no conflict).
Which is just what I said.

[Bri]

I didn't ask the question and the question is not implied by what I said.

It was implied by the question posed in the OP.

Which is just what I said.

Yes, and I was agreeing with you. I think I already said that.

-Bri

[Robin]

I'm defining omnipotence as the ability to do anything that is logically possible to do.
So when you say "In fact, it wouldn't be omnipotent if it couldn't do that." you are also assuming that it is logically possible for a God to give up his omniptence.
What do you mean by "essential being?"
I will let St Tom field this one:
The same line of reasoning clearly shows that God necessarily exists. For everything that has the possibility of being and of not being, is mutable. But God is absolutely immutable, as has been demonstrated. Therefore it is impossible for God to be and not to be. But anything that exists in such a way that it is impossible for it not to exist, is necessarily Being itself, ipsum esse. Necessary existence, and impossibility of nonexistence, mean one and the same thing. Therefore God must necessarily exist.

Chapter 6 Compendium Theologicaie
...
Sure God could stop being God (assuming "being God" involves being omnipotent). If you define "ant" as a creature with 6 legs, then you can make an ant stop being an ant by removing one of its legs (or it could do so itself by gnawing off one of its own legs).

Again, St Thom:
Clearly, therefore, no succession occurs in God. His entire existence is simultaneous. Succession is not found except in things that are in some way subject to motion; for prior and posterior in motion cause the succession of time. God, however, is in no sense subject to motion, as has been shown. Accordingly there is no succession in God. His existence is simultaneously whole.

Again, if a being’s existence is not simultaneously whole, something can be lost to it and something can accrue to it. That which passes is lost, and what is expected in the future can be acquired. But nothing is lost to God or accrues to Him, since He is immutable. Therefore His existence is simultaneously whole.

From these two observations the proper meaning of eternity emerges. That is properly eternal which always exists, in such a way that its existence is simultaneously whole. This agrees with the definition proposed by Boethius: “Eternity is the simultaneously whole and perfect possession of endless life.”

Chapter 8 Compendium Theologicaie
So when you say "God can .." you have to be sure you are talking about the same thing that the majority of Theists mean when they say "God".

The God of Aquinas could not voluntarily give up his omnipotence.

[Robin]

It was implied by the question posed in the OP.
No, I said:
And once bestowed this trait can never be separated from the rock, it is intrinsically impossible to lift the rock.

God can make a rock that even He cannot lift.
I don't know how you got from there to:
You're asking if an omnipotent being can lift the unliftable.
when I was clearly stating he couldn't.

[Bri]

So when you say "In fact, it wouldn't be omnipotent if it couldn't do that." you are also assuming that it is logically possible for a God to give up his omniptence.

Yes it is logically possible for a God to give up his omnipotence, unless you're defining "God" as a being that cannot be non-omnipotent, in which case God would stop being "God" by becoming non-omnipotent just as the ant (defined as a creature with 6 legs) would stop being an ant by gnawing off its leg.

Logically, there is no conflict with an omnipotent being making itself non-omnipotent.

So when you say "God can .." you have to be sure you are talking about the same thing that the majority of Theists mean when they say "God".

The God of Aquinas could not voluntarily give up his omnipotence.

He is assuming further attributes to "God" than were posed by the question of whether an omnipotent being could make a rock heavier than it could lift (which only assumes omnipotence defined as the ability to do anything that is logically possible). Whether or not the "God of Aquinas" could make himself non-omnipotent (or can do evil or anything else one might conclude about such a God) would depend on further definition of "God of Aquinas."

-Bri

[Bri]

I don't know how you got from there to ... when I was clearly stating he couldn't.

I don't see much point to arguing this since I've already stated that I agree with you.

-Bri

[Robin]

Yes it is logically possible for a God to give up his omnipotence, unless you're defining "God" as a being that cannot be non-omnipotent, in which case God would stop being "God" by becoming non-omnipotent just as the ant (defined as a creature with 6 legs) would stop being an ant by gnawing off its leg.

Logically, there is no conflict with an omnipotent being making itself non-omnipotent. In fact, one could argue that not being able to do so would make it non-omnipotent to being with if "omnipotence" is defined as being able to do anything that is logically possible.
I am not sure what you mean by that last sentence.
He is adding further attributes to "God" than were posed by the question of whether an omnipotent being could make a rock heavier than it could lift (which only assumes omnipotence defined as the ability to do anything that is logically possible).
On the contrary he is defining the attributes that are logically implied by such a being.

If it is possible for a being to be more powerful, then your being is not omnipotent. A necessary God would be more powerful than a contingent God, therefore a non-necesary being is not, by definition, omnipotent.
Whether or not the "God of Aquinas" could make himself non-omnipotent (or can do evil) would depend on further definition of "God of Aquinas.
No, it is contained in the parts that I quoted.

[Bri]

I am not sure what you mean by that last sentence.

It wasn't very clear, and I removed it from my post before you responded (but not fast enough). Sorry.

If it is possible for a being to be more powerful, then your being is not omnipotent. A necessary God would be more powerful than a contingent God, therefore a non-necesary being is not, by definition, omnipotent

In what way is a being who can do anything that is logically possible except make itself no longer able to do anything that is logically possible "more powerful" than a being that can do anything that is logically possible?

-Bri

[cyborg]

God cannot do anything that is logically impossible. God can't make square circles, 2+2=5, etc.

The problem is that it is not logically impossible - the problem is that "omnipotence" is in a class of properties that always allows for something more powerful.

The problem is infinity.

[Safe-Keeper]

RandFan "won this thread" a page ago. As he says, it's ridiculous that this still gets discussed.

It's impossible for God to be omnipotent, because there are things that are simply impossible to do. Like make 2+2=5, draw a circle with five edges, etc. The number of cop-out answers to this question is really mind-boggling.

[cyborg]

It's impossible for God to be omnipotent, because there are things that are simply impossible to do. Like make 2+2=5, draw a circle with five edges, etc.

A "circle with five edges" is not a circle - that's a matter of linguistics, not logic. This is trivially impossible by definition.

[Robin]

In what way is a being who can do anything that is logically possible except make itself no longer able to do anything that is logically possible "more powerful" than a being that can do anything that is logically possible?
Well for a start there is a possibility that there will be a more powerful being than the convertible model. With the necessary omnipotent being that possibility does not exist.

And you have to think it through - no part of existence is inaccessible to an omnipotent being, neither what was nor what will be.

If he then downsizes and becomes non-omnipotent there are two possibilities:

a) He becomes a part of existence that is unaccessible to his omnipotent self or
b) He becomes a part of existence that is accessible to his omnipotent self

For a) he wasn't omnipotent in the first place (accessible/inaccessible parts of existence are no less nonsensical than liftable/unliftable rocks).

For b) he didn't really become non-omnipotent, because he is existing simultaneously with his omnipotent self.

And it is no good to suggest he voluntarily chose not to access this part of existence with his omnipotent self, because the very fact of it being accessible means that he is existing simultaneously with his non-omnipotent self.

You see Aquinas was not just thinking up a bunch of attributes he would like God to have, he was really thinking through all the ramifications and logical consequences of the concept of an omnipotent being.

"Clearly, therefore, no succession occurs in God. His entire existence is simultaneous"

[Bri]

Well for a start there is a possibility that there will be a more powerful being than the convertible model. With the necessary omnipotent being that possibility does not exist.

The definition I was assuming was simply that omnipotence means the ability to do anything that is logically possible. Whether or not a being might exist that is somehow "greater" isn't an issue as far as whether or not it is possible for an omnipotent being to make itself non-omnipotent.

According to The Stanford Encyclopedia of Philosophy (http://plato.stanford.edu/entries/omnipotence/):


The intelligibility of the notion of omnipotence has been challenged by the so-called paradox or riddle of the stone. Can an omnipotent agent, Jane, bring it about that there is a stone of some mass, m, which Jane cannot move? If the answer is ‘yes’, then there is a state of affairs that Jane cannot bring about, namely, (S1) that a stone of mass m moves. On the other hand, if the answer is ‘no’, then there is another state of affairs that Jane cannot bring about, namely, (S2) that there is a stone of mass m which Jane cannot move. Thus, it seems that whether or not Jane can make the stone in question, there is some possible state of affairs that an omnipotent agent cannot bring about. And this appears to be paradoxical.

A first resolution of the paradox comes into play when Jane is an essentially omnipotent agent. In that case, the state of affairs of Jane's being non-omnipotent is impossible. Therefore, Jane cannot bring it about that she is not omnipotent. Since, necessarily, an omnipotent agent can move any stone, no matter how massive, (S2) is impossible. But, as we have seen, an omnipotent agent is not required to be able to bring about an impossible state of affairs.

If, on the other hand, Jane is an accidentally omnipotent agent, both (S1) and (S2) are possible, and it is possible for some omnipotent agent to bring it about that (S1) obtains at one time, and that (S2) obtains at a different time. Thus, there is a second solution to the paradox. In this case, Jane's being non-omnipotent is a possible state of affairs; thus, we may assume that it is possible for Jane to bring it about that she is non-omnipotent. So, Jane can create and move a stone, s, of mass, m, while omnipotent, and subsequently bring it about that she is not omnipotent and powerless to move s. As a consequence, Jane can bring about both (S1) and (S2), but only if they obtain at different times.

The confusion may have to do with essential omnipotence vs. accidental omnipotence. I agree with you if you assume a being that is essentially omnipotent, but I see no reason why the being couldn't be accidentally omnipotent offering a second solution. You may be assuming maximal greatness rather than maximal power (omnipotence):

Omnipotence is maximal power. Maximal greatness (or perfection) includes omnipotence. According to traditional Western theism, God is maximally great (or perfect), and therefore is omnipotent.

-Bri

[ServiceSoon]

A "circle with five edges" is not a circle - that's a matter of linguistics, not logic. This is trivially impossible by definition.By whose definition? :boxedin:

[UnrepentantSinner]

Well if the burrito reached a certain temperature it would be incinerated so there is a limit to the temperature he/she/it can microwave it to. And no matter how hot he/she/it makes the burrito, he/she/it can always wait for it to cool down. My vote is for no.

That's my response. Yes God could, but would then have an eternal time to wait for it to cool down sufficiently before eating it.

[RandFan]

The problem is that it is not logically impossible - the problem is that "omnipotence" is in a class of properties that always allows for something more powerful.

The problem is infinity.I'm affraid Moby beat you to it. But it's a good point.

[cyborg]

I'm affraid Moby beat you to it. But it's a good point.

I think I can extend on what Moby said:

Although we can perceive of an infinite number of agents on a line - with ever increasing power - any instance of an agent can only ever have a finite amount of power and hence there must always be an instance of an agent more powerful.

I.e. infinity is not a number so you can't "be" infinity - so you can't "be" omnipotent.

(I suppose what one might do is define GOD as the "ground of being" which covers the infinite possibilities but isn't actually any of them - which is touched upon here.)

[Bri]

If you define omnipotence as the ability to bring about any possible state of affairs, then there cannot be an entity that is "more powerful" (the only thing more powerful would perhaps be the ability to bring about an impossible state of affairs, which as already discussed leads to nonsense).

Additionally, two such omnipotent entities cannot possibly coexist. If they could then possibly at some time omnipotent entity A, while retaining its omnipotence, might attempt to move a feather while at the same time omnipotent entity B, while retaining its omnipotence, attempts to keep that feather motionless.

Perhaps you mean that there may be a "greater" entity than an omnipotent entity in some sense, but I would think that would depend on what you mean by "greater."

-Bri

[Robin]

The definition I was assuming was simply that omnipotence means the ability to do anything that is logically possible. Whether or not a being might exist that is somehow "greater" isn't an issue as far as whether or not it is possible for an omnipotent being to make itself non-omnipotent.
I was also using that definition. If Being A is greater than Being B then Being A can do something that Being B can't. Therefore Being B cannot do something that is logically possible and is not omnipotent.

Therefore it follows that if there is a Being greater than Being B, then Being B is not omnipotent.
According to The Stanford Encyclopedia of Philosophy (http://plato.stanford.edu/entries/omnipotence/):
And as I always point out at this stage, the Stanford Encyclopedia of Philosophy tells us that Ernst Mach and Rudolf Carnap are Neutral Monists! I think we can judge the reliability of the SEP on that basis.

Nevertheless I am happy to adjudicate between Aquinas and SEP on the basis of their relative arguments.
The confusion may have to do with essential omnipotence vs. accidental omnipotence.
There cannot be two kinds of omnipotence, it is illogical. If both types of omnipotence are equivalent in power then the are equivalent full stop. If they are not equivalent in power then one is omnipotence and the other is not.

I agree with you if you assume a being that is essentially omnipotent, but I see no reason why the being couldn't be accidentally omnipotent offering a second solution. You may be assuming maximal greatness rather than maximal power (omnipotence):
No, I am assuming the same definition of omnipotence that you are.

You will have to admit that it does not sound plausible for there to be an accidentally omnipotent agent, because wouldn't the being it was contingent upon be able to do something that it could not?

But let us say it is possible for an accidentally omnipotent agent to exist, therefore there can be two omnipotent agents.

Again, if their power differed one would be able to do something that the other couldn't and the other would therefore not be able to do something that was logically possible and would not be omnipotent.

So if there is an accidentallly omnipotent then there could be no essentially omnipotent agent. I am fine with that.

But then the same argument comes into play. B1 and B2 are both omnipotent and therefore there is no part of existence that is inaccessible to them.

B1 decides to become non-omnipotent and there are two choices:

a) B1 becomes a part of existence inaccessable to omnipotent B1
b) B1 becomes a part of existence accessible to omnipotent B1

As before, in a) B1 was not omnipotent in the first place and with b) B1 is still omnipotent after divesting himself of omnipotence.

In other words the matter of essential vs accidental omipotence does not affect my previous argument one way or the other.

And, as your source points out, traditional western Theism holds accidental omnipotence to be impossible.

[Robin]

If you define omnipotence as the ability to bring about any possible state of affairs, then there cannot be an entity that is "more powerful"
Exactly. So if there was an omnipotent entity able to divest itself of power, then it would be possible for there to be a more powerful entity than it.

But it would not be possible in any circumstances for there to be a being more powerful than an essentially omnipotent being. So the accidentally omnipotent being is just not omnipotent.
Additionally, two such omnipotent entities cannot possibly coexist. If they could then possibly at some time omnipotent entity A, while retaining its omnipotence, might attempt to move a feather while at the same time omnipotent entity B, while retaining its omnipotence, attempts to keep that feather motionless.
But since it is logically impossible for one omnipotent being to countermand another omnipotent being then this inability would not rule them out from being omnipotent under your definition.

[Bri]

I was also using that definition. If Being A is greater than Being B then Being A can do something that Being B can't. Therefore Being B cannot do something that is logically possible and is not omnipotent.

Therefore it follows that if there is a Being greater than Being B, then Being B is not omnipotent.

Then you are equating "greater" with "more powerful" but that's fine. If Being B cannot bring about any possible state of affairs (and Being A can) then I agree that Being B isn't omnipotent and Being A is.

There cannot be two kinds of omnipotence, it is illogical. If both types of omnipotence are equivalent in power then the are equivalent full stop. If they are not equivalent in power then one is omnipotence and the other is not.

The two "kinds" of omnipotence mentioned in the SAP article I cited (accidental and essential) have to do with the agent rather than the omnipotence itself. Specifically, it has to do with whether or not the agent could potentially lack the property of omnipotence. More information here (http://plato.stanford.edu/entries/essential-accidental/):

The distinction between essential versus accidental properties has been characterized in various ways, but it is currently most commonly understood in modal terms along these lines: an essential property of an object is a property that it must have while an accidental property of an object is one that it happens to have but that it could lack.

The "omnipotence" in question is the same in both cases, and an omnipotent being is equally powerful whether its omnipotence is accidental or essential -- either way, it can bring about any possible state of affairs. The difference is that there is no possible state of affairs in which an essentially omnipotent being can ever become non-omnipotent.

Now, you can argue whether one is "greater" than the other, but then you're using a different definition of "greater" than simply "more powerful" and it is irrelevant to the discussion of whether or not an omnipotent being could potentially make itself non-omnipotent.

I think you may be suggesting that accidental omnipotence is impossible, but if you've explained that I have missed it or misunderstood it.

No, I am assuming the same definition of omnipotence that you are.

You will have to admit that it does not sound plausible for there to be an accidentally omnipotent agent, because wouldn't the being it was contingent upon be able to do something that it could not?

What being must the accidental agent be contingent upon and in what way?

But let us say it is possible for an accidentally omnipotent agent to exist, therefore there can be two omnipotent agents.

No there cannot. If there were two, then neither would be omnipotent. If we're assuming that an omnipotent agent exists, it must be the only omnipotent agent in existence.

Again, if their power differed one would be able to do something that the other couldn't and the other would therefore not be able to do something that was logically possible and would not be omnipotent.

So if there is an accidentallly omnipotent then there could be no essentially omnipotent agent. I am fine with that.

Even if it were possible for two omnipotent agents to exist simultaneously, by definition the power of the two agents wouldn't differ if both are omnipotent. It would make no difference if the omnipotence of one is accidental and the other is essential -- they are both equally powerful (both can bring about any possible state of affairs).

But then the same argument comes into play. B1 and B2 are both omnipotent and therefore there is no part of existence that is inaccessible to them.

B1 decides to become non-omnipotent and there are two choices:

a) B1 becomes a part of existence inaccessable to omnipotent B1
b) B1 becomes a part of existence accessible to omnipotent B1

As before, in a) B1 was not omnipotent in the first place and with b) B1 is still omnipotent after divesting himself of omnipotence.

In other words the matter of essential vs accidental omipotence does not affect my previous argument one way or the other.

Here you've completely lost me.

I'm trying to understand this. I looked back at your previous post where you made a similar argument and I cannot follow it there either. Can you please explain your argument again in a different way perhaps?

The part I'm having trouble with are the two cases you lay out ("a" and "b"). What do you mean that the agent becomes a part of existence that is accessible/inaccessible to the agent before becoming non-omnipotent?

What do you mean by an agent being "accessible or inaccessible" to itself?

And, as your source points out, traditional western Theism holds accidental omnipotence to be impossible.

Sure, if we're assuming Western theism then of course we'd be talking about a God that is essentially omnipotent and only the first solution would make sense (the answer would simply be "no" God isn't required to bring about an impossible state of affairs in order to be "omnipotent").

But I was making no such assumption -- I was simply saying that there is another possible solution to the paradox posed in the OP if the being is accidentally omnipotent. At least according to the SAP this is a possible scenario.

Exactly. So if there was an omnipotent entity able to divest itself of power, then it would be possible for there to be a more powerful entity than it.

Here I disagree. In what way could any other being be more powerful? In other words, what possible state of affairs could this theoretical other being bring about that the entity in question (that we've already defined as being able to bring about any possible state of affairs) could not?

But it would not be possible in any circumstances for there to be a being more powerful than an essentially omnipotent being. So the accidentally omnipotent being is just not omnipotent.

You seem to be using a different definition of "all-powerful" than simply the ability to bring about any possible state of affairs. Using this definition, it would be impossible for another being to be "more powerful" than either an essentially or accidentally omnipotent being. In other words, an essentially omnipotent being is not "more powerful" than an accidentally omnipotent being unless you're using a different definition.

Perhaps you mean that one is "greater" than the other (which can be argued, but only if you use a different definition of "greater" than "more powerful").

That said, wouldn't a being that could divest itself of power be "greater" than one that couldn't? Certainly if the being is accidentally omnipotent, it would be a possible state of affairs for it to become non-omnipotent, and therefore if it were unable to achieve that state of affairs it couldn't be omnipotent by definition.

But since it is logically impossible for one omnipotent being to countermand another omnipotent being then this inability would not rule them out from being omnipotent under your definition.

I understand what you're saying, but if one or both are accidentally omnipotent, then it seems that the scenario described would not be logically impossible since either one becoming non-omnipotent is a possible state of affairs. It is only impossible for them to countermand one another while both remain omnipotent. Therefore, if an omnipotent being exists (whether accidentally or essentially), it must be the only omnipotent being in existence.

Even if we accept that two accidentally omniscient beings could exist simultaneously, my point still stands that by definition neither would be more powerful than the other.

-Bri

[Robin]

The part I'm having trouble with are the two cases you lay out ("a" and "b"). What do you mean that the agent becomes a part of existence that is accessible/inaccessible to the agent before becoming non-omnipotent?

What do you mean by an agent being "accessible or inaccessible" to itself?
Suppose I am an accidentally omnipotent being and have divested myself of my omnipotence.

Naturally when I was omnipotent I had power over every single part of existence and was not bounded by time in any sense.

So could my omnipotent self now reach out and give me a poke in the eye?

If it couldn't I was never omnipotent.

If it could then I am still omnipotent.
I understand what you're saying, but if one or both are accidentally omnipotent, then it seems that the scenario described would not be logically impossible since either one becoming non-omnipotent is a possible state of affairs. It is only impossible for them to countermand one another while both remain omnipotent. Therefore, if an omnipotent being exists (whether accidentally or essentially), it must be the only omnipotent being in existence.
Why? If two omnipotent beings existed simultaneously then what logically possible thing would they be unable to do?

[Robin]

Even if we accept that two accidentally omniscient beings could exist simultaneously, my point still stands that by definition neither would be more powerful than the other.
Well of course neither would be more powerful than the other, I said the same thing earlier. What is your point here?

[Bri]

Suppose I am an accidentally omnipotent being and have divested myself of my omnipotence.

Naturally when I was omnipotent I had power over every single part of existence and was not bounded by time in any sense.

So could my omnipotent self now reach out and give me a poke in the eye?

If it couldn't I was never omnipotent.

If it could then I am still omnipotent.

Why would your past self reaching forward in time and poking your present self in the eye in any way make your present self omnipotent?

That said, the SEP article discusses in detail temporal restrictions on omnipotence, and also restrictions on an omnipotent agent's ability to cause another agent's free (in the libertarian sense) decision.

An omnipotent agent cannot, for example, cause something that has already occurred to occur differently. Doing so will result in an impossible state of affairs.

Why? If two omnipotent beings existed simultaneously then what logically possible thing would they be unable to do?

Let's say there are two accidentally omnipotent beings. Being 1 could easily move a feather at time t. Doing so would be a possible state of affairs. But being 2 could make the feather stay still at time t -- also a possible state of affairs.

Therefore, either state of affairs possible at time t. Yet if they both attempted to obtain at the same time, it would lead to a stalemate. I think the problem is that if there are two omnipotent beings, both could attempt to obtain possible states of affairs that contradict one another at the same time, even though neither state of affairs is logically impossible separately.

Well of course neither would be more powerful than the other, I said the same thing earlier. What is your point here?

If you follow this thread backwards, you'll see that I was originally commenting on cyborg's post, which implied that there would always be a being more powerful:


Although we can perceive of an infinite number of agents on a line - with ever increasing power - any instance of an agent can only ever have a finite amount of power and hence there must always be an instance of an agent more powerful.

I.e. infinity is not a number so you can't "be" infinity - so you can't "be" omnipotent.

If you define omnipotence as the ability to bring about any possible state of affairs, then there cannot be an entity that is "more powerful" (the only thing more powerful would perhaps be the ability to bring about an impossible state of affairs, which as already discussed leads to nonsense).

Additionally, two such omnipotent entities cannot possibly coexist. If they could then possibly at some time omnipotent entity A, while retaining its omnipotence, might attempt to move a feather while at the same time omnipotent entity B, while retaining its omnipotence, attempts to keep that feather motionless.

Perhaps you mean that there may be a "greater" entity than an omnipotent entity in some sense, but I would think that would depend on what you mean by "greater."

But since it is logically impossible for one omnipotent being to countermand another omnipotent being then this inability would not rule them out from being omnipotent under your definition.

Even if we accept that two accidentally omniscient beings could exist simultaneously, my point still stands that by definition neither would be more powerful than the other.

Well of course neither would be more powerful than the other, I said the same thing earlier. What is your point here?


So I was just saying that even if I concede my second point that you replied to (that multiple omniscient beings cannot exist simultaneously), my original point to cyborg still stands -- that there couldn't be another being more powerful than a being able to achieve any possible state of affairs.

That said, I'm still not convinced that there could be two omniscient beings in existence without causing some conflict if each attempts to obtain a different possible state of affairs at the same time.

-Bri

[cyborg]

there couldn't be another being more powerful than a being able to achieve any possible state of affairs.

This is the heart of the paradox Bri - restating it doesn't resolve it. As soon as you state there is a being "powerful enough to achieve any possible state of affairs," then it can bring about a state of affairs that only a being more powerful than it can resolve.

[Bri]

What do you mean by "resolving" a state of affairs?

-Bri

[RandFan]

What do you mean by "resolving" a state of affairs?

-BriOmnipotence, the ability to create a rock to big to create and the ability to lift any rock regardless of how big.

Achieve would be to lift the rock.

Resolve would be to overcome the seeming paradox. One can't do both but one can imagine an ever increasing higher benchmark of difficulty.

"Infinity", aint it a bitch?

[Bri]

Define "omnipotent" as the ability to achieve any possible state of affairs.

Such a being could, by definition, lift any rock. Also, by definition, any rock is liftable by this being.

To create a rock that is unliftable by a being that can lift any rock (i.e. to create a rock that is both unliftable and liftable) is an impossible state of affairs, not a possible state of affairs.

There is no infinitite recursion -- the answer to the paradox about whether an omnipotent being could create a rock larger than it could lift would be "no" -- by the definition above, an omnipotent being isn't required to be able to achieve an impossible state of affairs.

If you hold a different definition (that omnipotence would require a being to be able to bring about an impossible state of affairs) then yes, the being could create a rock that is both liftable and unliftable at the same time. Again, no infinite recursion.

-Bri

[RandFan]

Define "omnipotent" as the ability to achieve any possible state of affairs. I don't necassarily accept the argument by Moby and Cyborg. I can only concede or disagree with the logical validity of what they are saying. They have a logically valid point whether you like it or not.

There is no resolution to the paradox for a number of reasons but primary among those reasons is that here is no absolute when it comes to the meaning (definition) of "omnipotence" (http://en.wikipedia.org/wiki/Omnipotence#Meanings_of_omnipotence). It's an abstract concept with a great deal of controversy as to how to define it.

"The ability to achieve any possible state of affairs." Is absolutely one definition and "to resolve any state of affairs" is another.

Pardon the pun but the devil is in the details.

[cyborg]

Define "omnipotent" as the ability to achieve any possible state of affairs.

Yes, but the point you keep missing is that, "creating a rock too heavy to lift," is a possible state of affairs for anything but your omnipotent being which means there are beings who can bring about a state of affairs with respect to themselves that your omnipotent being cannot!


In other words:

To create a rock that is unliftable by a being that can lift any rock (i.e. to create a rock that is both unliftable and liftable) is an impossible state of affairs, not a possible state of affairs.

It is possible as long as you're not omnipotent.

[gdnp]

I have to jump in here on the side of no paradox

Omnipotence is a concept derived from the human mind. As such it can be defined by humans. If we define omnipotence as the ability to do anything that is logically possible, then there is no contradiction in the burrito or rock paradox. As there is no such thing as a rock to heavy for an omnipotent being to lift, or a burrito too hot for an omnipotent being to eat, it makes no sense to ask whether an omnipotent being can create one: it is logically impossible for an omnipotent being to create something that cannot possibly exist.

I would also argue that the concept of a rock too heavy to lift is nonsense. Remember Archimedes statement: with a long enough lever and a place to stand he could move the world. A rock too heavy to lift would have to have infinite mass, which would make it a black hole, not a rock. You can't even make a rock too heavy for a human to lift, with the proper equipment, much less an omnipotent being.

We are still left with other questions of omnipotence: can, for example, and omnipotent being travel faster than the speed of light? My guess is that this is also considered a logical impossibility for the Christian god, because he is also defined as being omnipresent: Something that is already everywhere cannot move. I'm not so sure how this works out logically for a non-omnipresent omnipotent god in a relativistic universe, since simultaneity is not even fixed.

Relativity makes my brain hurt.

[cyborg]

As there is no such thing as a rock to heavy for an omnipotent being to lift, or a burrito too hot for an omnipotent being to eat, it makes no sense to ask whether an omnipotent being can create one: it is logically impossible for an omnipotent being to create something that cannot possibly exist.

And as such this means that in the set of all possible abilities there exists an ability that the omnipotent being does not have - it is incomplete.

[RandFan]

I have to jump in here on the Bri / Marquis / Randfan etc. side here.

Omnipotence is a concept derived from the human mind. As such it can be defined by humans. If we define omnipotence as the ability to do anything that is logically possible, then there is no contradiction in the burrito or rock paradox. Which is what I said in my first post in this thread. Yes this is one way to define omnipotence but it raises a number of questions including, why can't I simply define omnipotence to mean anything that is not theoretically impossible for a person to do?

I accept the resolution of Aquinas but I can't deny that it isn't an absolute resolution free of criticism. Cyborg's point still stands.

"God can do x?" Not always true.

[gdnp]

Which is what I said in my first post in this thread. Yes this is one way to define omnipotence but it raises a number of questions including, why can't I simply define omnipotence to mean anything that is not theoretically impossible for a person to do?

Yeah, sorry I posted before realizing there was a second page.

We can define omnipotence any way we want, but if we define it in such a way that it is self-contradictory, what is the point? All we have done is prove that that particular definition of omnipotence causes a paradox and thus cannot exist. The definition worth discussing is the one that causes no such paradox--that of a single essential omnipotent being that can perform any logically permissible action. Or, if you prefer, bring about any logically permissible state of affairs.

Two simultaneous omnipotent beings: We might as well start a thread "what would happen if God got into a fight with Superman?"

Just as an omnipotent being doesn't need to be able to bring about impossible states of affairs, we don't have to waste our time debating definitions of omnipotence that couldn't possibly exist.

I accept the resolution of Aquinas but I can't deny that it isn't an absolute resolution free of criticism. Cyborg's point still stands.

"God can do x?" Not always true.

ETA: yes, but there is a simple test: Is X logically possible, consistent with the other properties that you have ascribed to God? then yes. If not, then no.

[Ron_Tomkins]

My dad presented me with this funny twist on an old question. I thought you all might enjoy the humour.

Can God microwave a burrito so hot that He can't eat it?

Ace


Good, but can you tell me what the old question is?

I believe the old question was something like: If a burrito falls in the middle of a desert forest, with no one to hear it, did it make any sound at all?

[Bri]

Yes, but the point you keep missing is that, "creating a rock too heavy to lift," is a possible state of affairs for anything but your omnipotent being which means there are beings who can bring about a state of affairs with respect to themselves that your omnipotent being cannot!


In other words:



It is possible as long as you're not omnipotent.

OK, I see what you're saying. But the question is whether an omnipotent being can create a rock that is heavier than an omnipotent being can lift. While a human can potentially create a rock that is heavier than a human can lift, a human cannot create a rock heavier than an omnipotent being can lift.

The problem is that a rock that would be too heavy for an omnipotent being to lift is nonsense given that an omnipotent being can lift any rock. Creating such a rock is an impossible state of affairs period.

Furthermore, according to the Stanford Encyclopedia of Philosophy article (http://plato.stanford.edu/entries/omnipotence/):

A second sense of ‘omnipotence’ is that of maximal power, meaning just that no being could exceed the overall power of an omnipotent being. It does not follow that a maximally powerful being can bring about any state of affairs, since, as we have seen, bringing about some such states of affairs is impossible. Nor does it follow that a being with maximal power can bring about whatever any other agent can bring about. If a can bring about s, and b cannot, it does not follow that b is not overall more powerful than a, since it could be that b can bring about more states of affairs than a can, rather than the other way around...

(emphasis mine)

-Bri

[Bri]

And as such this means that in the set of all possible abilities there exists an ability that the omnipotent being does not have - it is incomplete.

The ability to create a rock that is both liftable and unliftable is not within the set of all possible abilities.

-Bri

[Bri]

"The ability to achieve any possible state of affairs." Is absolutely one definition and "to resolve any state of affairs" is another.

Pardon the pun but the devil is in the details.

Sure, we can come up with any number of incoherent definitions, and we shouldn't be surprised that they result in logical incoherence.

If we define omnipotence to allow an omnipotent being to be able to achieve logically impossible states of affairs, we shouldn't be surprised that the result will be logically impossible!

My point is that using a logically coherent definition such as the ability to achieve any possible state of affairs, the paradox can be resolved, and there isn't an infinite recursion of more and more powerful beings.

-Bri

[RandFan]

My point is that using a logically coherent definition such as the ability to achieve any possible state of affairs, the paradox can be resolved, and there isn't an infinite recursion of more and more powerful beings.Given the premise that "God can do X" is not always true then I agree. In fact, that was the subject of my first post and it is my position now. So long as we all agree that the definition includes an infinte number of states of affairs that humans can perform that god can't then that's fine. That's not the definition of some people.

That said, I think Cyborg and Moby have a perfectly good point and I think you are trying a bit too hard to resolve an issue that has plagued philosophers for some time. One that really can't be solved in any absolute way. So long as we agree on the premises then sure. The problem is that not all people agree on the premises.

[Bri]

Of course "God can do X" isn't always true if "X" is incoherent (as in "God can make a married bachelor").

But like I said above in my response to cyborg, I don't think a human can make a rock that an omnipotent being cannot lift given that making something that an omnipotent being cannot lift is an impossible state of affairs. In other words, it seems that you're relying on a shifting pronoun in the phrase "that he cannot lift" to say that a human can accomplish what the omnipotent being cannot (that the "he" for the omnipotent being refers to the omnipotent being while the "he" for the human refers to the human). If you substitute "he" for the same entity, it's clear that there is no possible state of affairs that the human can accomplish that the omnipotent being cannot.

If you disagree, then what state of affairs do you propose a human can accomplish that an omnipotent being cannot given that humans are limited to a subset of possible states of affairs and an omnipotent being can accomplish any possible state of affairs?

So long as we agree on the premises then sure. The problem is that not all people agree on the premises.

I agree. My premise was the definition of omnipotence posted above (the ability to achieve any possible state of affairs). As long as your God is omnipotent by that definition, the paradox isn't unresolvable for your God.

-Bri

[gdnp]

In Christian theology the omnipotence is usually further limited by the phrase "consistent with his nature". The Christian God, for example, is considered to be perfectly benevolent. Thus God can not perform any act that is evil. He cannot lie. He cannot murder. The fact that "innocent" people die through "acts of God" is usually explained by our limited understanding of good and evil. If God did it, it is good by definition, no matter how evil it looks to us. So if a large asteroid strikes earth and extinguishes all life, it is just part of God's perfect loving plan.

I suppose you could also talk your way around this by saying that God could lie or murder, he just doesn't want to.

[Robin]

Why would your past self reaching forward in time and poking your present self in the eye in any way make your present self omnipotent?
It is not my "past" self if it is still active. It is my timeless self. My omnipotent self's omnipotence has remained unaffected.

So an omnipotent being cannot become unomnipotent.
That said, the SEP article discusses in detail temporal restrictions on omnipotence, and also restrictions on an omnipotent agent's ability to cause another agent's free (in the libertarian sense) decision.

An omnipotent agent cannot, for example, cause something that has already occurred to occur differently. Doing so will result in an impossible state of affairs.
And that is relevant - why?
Let's say there are two accidentally omnipotent beings. Being 1 could easily move a feather at time t. Doing so would be a possible state of affairs. But being 2 could make the feather stay still at time t -- also a possible state of affairs.
It is not logically possible to move a feather which an omnipotent being is keeping still.

It is not logically possible to keep still a feather that an omnipotent being is moving.

So neither of these is an example of a logically possible thing they would be unable to do.

Therefore, either state of affairs possible at time t. Yet if they both attempted to obtain at the same time, it would lead to a stalemate. I think the problem is that if there are two omnipotent beings, both could attempt to obtain possible states of affairs that contradict one another at the same time, even though neither state of affairs is logically impossible separately.
But they are not trying to obtain possible states of affairs, they are trying to obtain impossible states of affairs - overrulling an omnipotent being. Exactly the same problem arises with a single omnipotent being - trying to create an unliftable rock and then lifting it.

If this does not contradict omnipotence in a single omnipotent being then you have to be consistent and say it does not contradict omnipotence in multiple omnipotent beings.

Naturally omnipotence might be said to include common sense, so B1 and B2 would not try to compete, any more than two intelligent people would try to beat each other at Tic-Tac-Toe (or any more than an omnipotent being would try to create a liftable-unliftable rock).

So multiple omnipotent beings would have at least one ability that the single omnipotent being doesn't - the ability to co-operate.

[Robin]

The ability to create a rock that is both liftable and unliftable is not within the set of all possible abilities.
Nor is the ability to move a feather that an omnipotent being is keeping still.

[Robin]

Two simultaneous omnipotent beings: We might as well start a thread "what would happen if God got into a fight with Superman?"

Just as an omnipotent being doesn't need to be able to bring about impossible states of affairs, we don't have to waste our time debating definitions of omnipotence that couldn't possibly exist.
Why couldn't two omnipotent beings exist simultaneously?

Can you identify any logically possible thing that they would be unable to do?

[Robin]

In Christian theology the omnipotence is usually further limited by the phrase "consistent with his nature". The Christian God, for example, is considered to be perfectly benevolent. Thus God can not perform any act that is evil. He cannot lie. He cannot murder. The fact that "innocent" people die through "acts of God" is usually explained by our limited understanding of good and evil. If God did it, it is good by definition, no matter how evil it looks to us. So if a large asteroid strikes earth and extinguishes all life, it is just part of God's perfect loving plan.

I suppose you could also talk your way around this by saying that God could lie or murder, he just doesn't want to.
I have never understood why they say God can't lie. If allowing a child to die in agony of a disease could be justified by some greater good then surely a fib could also be thus justified?

[gdnp]

Why couldn't two omnipotent beings exist simultaneously?

Can you identify any logically possible thing that they would be unable to do?

Now I guess it comes down to a definition of "logically possible"

Let us say we have two omnipotent beings. And a rock.
Omnipotent being #1 states that he will allow anyone to move the rock except omnipotent being #2.

Omnipotent being #2 tries to lift the rock, and cannot. I try to lift the rock and can. I am more powerful than being #2, and thus being #2 is not omnipotent.

Or look at it this way: Omnipotent being #1 says "at noon I will move that rock 1 foot to the right". Omnipotent being #2 says "at noon I will move the rock 1 foot to the left". What happens at noon?

[Robin]

Now I guess it comes down to a definition of "logically possible"
Same as for any discussion on omnipotence - level playing field.
Let us say we have two omnipotent beings. And a rock.
Omnipotent being #1 states that he will allow anyone to move the rock except omnipotent being #2.

Omnipotent being #2 tries to lift the rock, and cannot. I try to lift the rock and can. I am more powerful than being #2, and thus being #2 is not omnipotent.
So if I land a ball 10 yards from the hole and Tiger Woods lands a ball 100 yards from the hole because someone else is holding onto his golf club, does that make me a better golfer than Tiger Woods?
Or look at it this way: Omnipotent being #1 says "at noon I will move that rock 1 foot to the right". Omnipotent being #2 says "at noon I will move the rock 1 foot to the left". What happens at noon?
What happens at noon is that neither #1 nor #2 will fail to bring about any logically possible state of affairs. So whatever happens they will still both satisfy the definition of omnipotence.

What logically possible thing do you think they would fail to do at noon?

Suppose only one omnipotent agent were possible. Said omnipotent agent says "at noon I will move that rock 1 foot to the right" and also says: "at noon I will move the rock 1 foot to the left". What happens at noon?

[gdnp]

So if I land a ball 10 yards from the hole and Tiger Woods lands a ball 100 yards from the hole because someone else is holding onto his golf club, does that make me a better golfer than Tiger Woods?We are not talking about "better" we are talking about "the best." And not just the current "the best" but "the best there can ever be". Perfect. Hole in 1 every shot, regardless of the conditions.

What happens at noon is that neither #1 nor #2 will fail to bring about any logically possible state of affairs. So whatever happens they will still both satisfy the definition of omnipotence.

What logically possible thing do you think they would fail to do at noon?

Is the rock 1 foot to the left a logically possible state of affairs? Yes. Is the rock 1 foot to the right a logically possible state of affairs? yes. Therefore, if a being cannot achieve that state of affairs, he is not omnipotent.

Suppose only one omnipotent agent were possible. Said omnipotent agent says "at noon I will move that rock 1 foot to the right" and also says: "at noon I will move the rock 1 foot to the left". What happens at noon?The rock moves to the left. He changed his mind.

If he says "at noon I will simultaneously move the rock to the right and to the left 1 foot"...well, he has either just declared that he will perform a logical impossibility, or he plans on changing the rules of space-time.

[Robin]

Let us say we have two omnipotent beings. And a rock.
Omnipotent being #1 states that he will allow anyone to move the rock except omnipotent being #2.

Omnipotent being #2 tries to lift the rock, and cannot. I try to lift the rock and can. I am more powerful than being #2, and thus being #2 is not omnipotent.
Or put it this way:

Let us say we have one omnipotent being. And a rock.
Omnipotent being states that he will allow anyone to move the rock except himself.

Omnipotent being tries to lift the rock, and cannot. I try to lift the rock and can. I am more powerful than the being and thus the being is not omnipotent and by implications no omnipotent being is possible.

[gdnp]

Or put it this way:

Let us say we have one omnipotent being. And a rock.
Omnipotent being states that he will allow anyone to move the rock except himself.

Omnipotent being tries to lift the rock, and cannot. I try to lift the rock and can. I am more powerful than the being and thus the being is not omnipotent and by implications no omnipotent being is possible.

This comes back to the argument of conditionally omnipotent and essentially omnipotent. If the being is essentially omnipotent, then a rock he cannot move is illogical and need not be considered. To me, the only type of omnipotent being that makes sense is a single essentially omnipotent being.

If you meet one, have him give me a call.

[Robin]

We are not talking about "better" we are talking about "the best." And not just the current "the best" but "the best there can ever be". Perfect. Hole in 1 every shot, regardless of the conditions.
Nope, you only said "more powerful".

It is a non-sequitur for you to state you are more powerful than #2 on the basis of something that #1 did, not you.
Is the rock 1 foot to the left a logically possible state of affairs? Yes. Is the rock 1 foot to the right a logically possible state of affairs? yes. Therefore, if a being cannot achieve that state of affairs, he is not omnipotent.
Is it logically possible to move a rock 1 foot to the left while an omnipotent being is moving it 1 foot to the right? No.

By the same reasoning it is logically possible to create an unliftable rock. It is logically possible to lift a rock. So if a being cannot achieve these states of affairs it is not omnipotent.
The rock moves to the left. He changed his mind.
So if you allow a level playing field then #1 or #2 change their mind. Being omnipotent they possess the ability to co-operate.
If he says "at noon I will simultaneously move the rock to the right and to the left 1 foot"...well, he has either just declared that he will perform a logical impossibility, or he plans on changing the rules of space-time.
And by the same virtue #1 and #2 have also just declared that they will perform a logical impossibility or that they plan on changing the rules of space-time.

You have got to come up with some argument that will disqualify the omnipotent dyad, but not disqualify the omnipotent singleton.

[Robin]

This comes back to the argument of conditionally omnipotent and essentially omnipotent. If the being is essentially omnipotent, then a rock he cannot move is illogical and need not be considered.
Not illogical at all as I pointed out at the beginning. Omnipotence means the ability to do any logically possible thing. So a rock that cannot be moved by an omnipotent being is a rock that is logically impossible to move.

For example God truthfully says "This rock shall never be moved".

Thereafter if he moves the rock then he made a mistake in the previous declaration.

But since it is logically impossible for an omnipotent being to have made a mistake then it is logically impossible for him to move the rock - ever.

So it is easy for God to create a rock he cannot lift.
To me, the only type of omnipotent being that makes sense is a single essentially omnipotent being.
An accidentally omnipotent being is logically incoherent, as I have shown (well actually Aquinas showed). But there is no logical objection to multiple essentially omnipotent beings.
If you meet one, have him give me a call.
I'll have mine call yours.

[Darth Rotor]

The God of Aquinas could not voluntarily give up his omnipotence.
Not could not, would not. There would be no point in doing so, in a general sense. The short term decision to manifest in a mortal and thus profoundly limited framework had a point.

(Whether or not you agree with the point is another topic.)

Abstractions such as purpose are not easily measured, but they nonetheless exist.

As to a later point,
I suppose you could also talk your way around this by saying that God could lie or murder, he just doesn't want to.
And if He did, what do you suppose you could do about it? Presume only relative omniscience: for the moment, let's assume that God is only really the deity in charge of the Milky Way Galaxy. Once again, the humans got the message cocked up. No surprise.

For you and I, that role is as near full omniscience as the whole monty.

Quibbling over how many orders of magnitude more powerful this deity is strikes me as not only frivolous, but given the practical limitations of travel to find a leverage point to wedge beneath this deity on his rock, laughable.

As powerful as the human mind and reason is, against the universe it's a fart in a tornado.

DR

[gdnp]

Nope, you only said "more powerful".

It is a non-sequitur for you to state you are more powerful than #2 on the basis of something that #1 did, not you.If I can achieve a state of affairs that being #2 cannot-- that is, a rock 1 foot to the left--for whatever reason, then being #2 is not omnipotent.

Is it logically possible to move a rock 1 foot to the left while an omnipotent being is moving it 1 foot to the right? No.

By the same reasoning it is logically possible to create an unliftable rock. It is logically possible to lift a rock. So if a being cannot achieve these states of affairs it is not omnipotent.
Actually, I argued before that it is not logically possible to create an unliftable rock, because an unliftable rock would have to have infinite mass. A rock to heavy for any human to lift is logical. A rock too heavy for an omnipotent being to lift is not.

So if you allow a level playing field then #1 or #2 change their mind. Being omnipotent they possess the ability to co-operate.Still, if they are forced to cooperate then they are not omnipotent. As has been said with company boards, if too people always agree, one of them is unnecessary. Perhaps that is how you can have 3 gods-1 god in the Christian triumvirate. You can only have more than one omnipotent being if they always agree.

And by the same virtue #1 and #2 have also just declared that they will perform a logical impossibility or that they plan on changing the rules of space-time.

You have got to come up with some argument that will disqualify the omnipotent dyad, but not disqualify the omnipotent singleton.

Sigh. More and more assumptions. I assume that it is illogical for an omnipotent being to make a claim that is self-contradictory, and therefore I do not need to deal with this paradox. As long as there is only one omnipotent being, then he cannot be forced into an illogical situation by another omnipotent being. But as long as there is more than one omnipotent being, there will always be the potential for paradox unless they always agree, which begs the question of whether they really are two beings or just two aspects of the same being.

[Robin]

If you disagree, then what state of affairs do you propose a human can accomplish that an omnipotent being cannot given that humans are limited to a subset of possible states of affairs and an omnipotent being can accomplish any possible state of affairs?
I can learn to make a cherry pie. But it is logically impossible for God to learn to make a cherry pie.

[Bri]

It is not my "past" self if it is still active. It is my timeless self. My omnipotent self's omnipotence has remained unaffected.

I don't know if it's a requirement that an omnipotent being be timeless. Is timelessness a possible state of affairs that an omnipotent being must be able to achieve?

I will admit that I don't know much about timelessness, but it would seem that there would still need to be some sort of cause and effect occurring atemporally, otherwise wouldn't an omnipotent being have to be unchanging? If an omnipotent being can change, then it must have accidental properties which can change, which would mean that its omnipotence could potentially be one of them.

Anyway...I don't know the answer here. It seems like timelessness might bring about all sorts of paradoxes. The SEP seems to disagree with you (or ignores timelessness for the purposes of the article) but again that doesn't mean you're wrong.

It is not logically possible to move a feather which an omnipotent being is keeping still.

It is not logically possible to keep still a feather that an omnipotent being is moving.

I see what you're saying. But you may be changing the definition in a subtle way. I can see a possible distinction between whether an action is logically possible or not and whether a state of affairs is possible or not.

It would be an impossible state of affairs for an object to have a property with two different values at the same time (a married bachelor or square circle for example). In the case of the rock paradox, a single omnipotent being is attempting to achieve an impossible state of affairs by assigning two opposing properties at once to a "movable" property of the rock.

But in the case of the feather, it is a possible state of affairs for the feather to be moving (the property "moving" = true). It is a possible state of affairs for the feather to be stationery (the property "moving" = false). Neither omnipotent being is attempting to achieve an impossible state of affairs, and therefore it seems like each should be able to do so.

Again, I'll concede that I don't know the answer.

-Bri

[Robin]

If I can achieve a state of affairs that being #2 cannot-- that is, a rock 1 foot to the left--for whatever reason, then being #2 is not omnipotent.
I see. So I am a better golfer than Tiger Woods if someone is holding onto his club. I wonder if the tournament organisers would agree with you.

But that said my counter-example still goes. God says "you can move this rock but I can't". So I can move a rock that God can't (for whatever reason - your rules, remember?) so God cannot be omnipotent.
Actually, I argued before that it is not logically possible to create an unliftable rock, because an unliftable rock would have to have infinite mass. A rock to heavy for any human to lift is logical. A rock too heavy for an omnipotent being to lift is not.
Why do you assume it would have to have infinite mass? Why couldn't it be the lightest object in existence?

In the Kena Upanishad the immovable, indestructible object is a single piece of straw.
Still, if they are forced to cooperate then they are not omnipotent.
Only if the alternative to co-operation is logically possible. It is not.

And if a being is unable to co-operate with an omnipotent being then it is not, by definition, omnipotent.
As has been said with company boards, if two people always agree, one of them is unnecessary.
Not if one is the CIO and the other is the CFO. And "unnecessary" is not the same as "non existent". And if an omnipotent being exists then it is, by definition, necessary.
Sigh. More and more assumptions. I assume that it is illogical for an omnipotent being to make a claim that is self-contradictory, and therefore I do not need to deal with this paradox.
You have changed your mind. You said that #2 claimed it would move the rock to the left at noon at the same time that #1 was going to move it to the right. Claiming to perform a logically impossible act is self-contradictory.

So if you assume that an omnipotent being would not make a self-contraditory claim then I don't have to deal with your paradox either.

Or are you saying that an omnipotent being might not know about something?
As long as there is only one omnipotent being, then he cannot be forced into an illogical situation by another omnipotent being. But as long as there is more than one omnipotent being, there will always be the potential for paradox unless they always agree, which begs the question of whether they really are two beings or just two aspects of the same being.
Non-sequitur, "A always agrees with B" does not even remotely imply "A is B".

There is no potential for paradox whatsoever unless one omnipotent being attempts to perform a logically impossible action. And even if it did there would be no actual paradox since it would not have failed to achieve any logically possible state of affairs.

So you have still not answered my original question - what logically possible action would either of the omnipotent agents be unable to acheive?

[Bri]

I can learn to make a cherry pie. But it is logically impossible for God to learn to make a cherry pie.

I think this is similar to the case of the shifting pronoun I mentioned in a previous post. Yes, assuming you don't know how to make a cherry pie, you have the capacity to learn it. Assuming that omniscience is inherent in omnipotence (I'm not sure it is, but let's just assume it is for a moment) and that this omniscience is an essential property, then God cannot both know everything but not know something at the same time.

So, yes, an omniscient being who doesn't know everything is an impossible state of affairs (the property of "omniscience" must be both true and false at the same time). Neither you nor God can achieve this state of affairs (you cannot cause God to learn something, nor can God cause himself to learn something).

But you not knowing something is not an impossible state of affairs. You can only learn how to bake a cherry pie if you don't already know how, but God could make you learn how to bake a cherry pie even if you already know how (he could first make you forget, and then make you learn).

-Bri

[Robin]

I don't know if it's a requirement that an omnipotent being be timeless. Is timelessness a possible state of affairs that an omnipotent being must be able to achieve?
If it is a possible state of affairs then an omnipotent being must be able to achieve it.
I will admit that I don't know much about timelessness...
You appeared to feel quite at ease with the subject in previous discussions. You had, as I recall, quite an ingenious argument against certain timelessness paradoxes that involved a computer program and dots. Am I confusing you with someone else?
, but it would seem that there would still need to be some sort of cause and effect occurring atemporally, otherwise wouldn't an omnipotent being have to be unchanging?
Yes, just as Aquinas says "immutable".
If an omnipotent being can change, then it must have accidental properties which can change, which would mean that its omnipotence could potentially be one of them.
Yes, if an omnipotent being is mutable then it can become non-omnipotent.

It would also imply that a non-omnipotent being could become omnipotent.

It would also imply the existence of a whole raft of logically possible states of affairs that the allegedly omnipotent being could not bring about.

It would also imply that there might be a situation in which there existed no essential being, in other words that all beings were contingent. Upon what?

That is why Aquinas says that it must be immutable - that all states of God must be simultaneous, not sequential.
Anyway...I don't know the answer here. It seems like timelessness might bring about all sorts of paradoxes.
No doubt, but then so does the idea that existence is exhausted by time and space
The SEP seems to disagree with you (or ignores timelessness for the purposes of the article) but again that doesn't mean you're wrong.
And Aquinas seems to disagree with you. But that does not mean that you are wrong either.

But in fact the particular SEP article you quoted does not come down on any particular side, merely canvasses the arguments and it does not "ignore" timelessness, it explicitly states that God in the sense of Western theism would not be temporally constrained.
I see what you're saying. But you may be changing the definition in a subtle way. I can see a possible distinction between whether an action is logically possible or not and whether a state of affairs is possible or not. It would be an impossible state of affairs for an object to have a property with two different values at the same time (a married bachelor or square circle for example). In the case of the rock paradox, a single omnipotent being is attempting to achieve an impossible state of affairs by assigning two opposing properties at once to a "movable" property of the rock. But in the case of the feather, it is a possible state of affairs for the feather to be moving (the property "moving" = true). It is a possible state of affairs for the feather to be stationery (the property "moving" = false). Neither omnipotent being is attempting to achieve an impossible state of affairs, and therefore it seems like each should be able to do so.
Your definition was "the ability to achieve any possible state of affairs"

A "moving stationary feather" is not a possible state of affairs. The failure of B1 and B2 to achieve this state of affairs would not therefore disqualify them from omnipotence, by the definition you have suggested.

[gdnp]

I see. So I am a better golfer than Tiger Woods if someone is holding onto his club. I wonder if the tournament organisers would agree with you.
This is a non-sequitor. No one can hold the club of an omnipotent golfer if he wishes to swing it, or he is not omnipotent.

But that said my counter-example still goes. God says "you can move this rock but I can't". So I can move a rock that God can't (for whatever reason - your rules, remember?) so God cannot be omnipotent.Once again, an unmovable rock makes no logical sense. It is a rock which does not follow physical laws. And since motion is relative, both in a relativistic sense and a newtonian sense, "unmovable" itself makes no logical sense.

Why do you assume it would have to have infinite mass? Why couldn't it be the lightest object in existence?

In the Kena Upanishad the immovable, indestructible object is a single piece of straw.indestructible: I guess the point here is, can an omnipotent being perform actions that violate the laws of the universe? Or does he just have to be able to perform any action compatible with the laws of the universe? The problem here is that if we say he can't violate the laws of the universe, then he can't do a whole heck of a lot: he can't make planets move without acting on them with some known force, he must conserve mass/energy, etc. If he can violate the laws of the universe, then just about anything becomes logically possible: two things can occupy the same space at the same time, for example.


And if a being is unable to co-operate with an omnipotent being then it is not, by definition, omnipotent.But if it is required to cooperate with an omnipotent being, it is also not omnipotent, because it cannot refuse.

You have changed your mind. You said that #2 claimed it would move the rock to the left at noon at the same time that #1 was going to move it to the right. Claiming to perform a logically impossible act is self-contradictory.

So if you assume that an omnipotent being would not make a self-contraditory claim then I don't have to deal with your paradox either.
Here I like the "state of affairs" definition better than the "action" definition. It is self-contradictory and thus logically impossible to have an object in 2 separate places at once. It is not, however, logically impossible to have a rock 1 foot to the left or 1 foot to the right. Thus if only one omnipotent being exists, there is no location to the rock which is logically impossible. If two omnipotent beings exist, however, there is the potential for an unresolvable conflict because they cannot both have full freedom in rock placement.


There is no potential for paradox whatsoever unless one omnipotent being attempts to perform a logically impossible action. And even if it did there would be no actual paradox since it would not have failed to achieve any logically possible state of affairs.
I seem to recall having struggled with this many years ago while trying to read Goedel, Escher, Bach. The book was discussing the question of the genii in the lamp and the ever-popular wish for more wishes. It claimed that such was not a wish, but a meta-wish. I wonder if a similar situation is extant here. Omnipotence only makes sense within a system, so actions which change the system or act on actors outside the system are meta-actions. Needs more thought and/or reading. Not tonight.

So you have still not answered my original question - what logically possible action would either of the omnipotent agents be unable to acheive?An omnipotent boxer could beat anyone in a boxing match.

[Robin]

This is a non-sequitor. No one can hold the club of an omnipotent golfer if he wishes to swing it, or he is not omnipotent.
But we are not talking about an omnipotent golfer we are talking about your claim that you have power by virtue of an action you did not perform.

But if your point is valid then so is my counter argument:

God says "you can move this rock but I can't". So I can move a rock that God can't (for whatever reason - your rules, remember?) so God cannot be omnipotent.

If you accept one argument you must accept the other.
Once again, an unmovable rock makes no logical sense. It is a rock which does not follow physical laws. And since motion is relative, both in a relativistic sense and a newtonian sense, "unmovable" itself makes no logical sense.
You mean it makes no physical sense. It makes perfect logical sense.
indestructible: I guess the point here is, can an omnipotent being perform actions that violate the laws of the universe? Or does he just have to be able to perform any action compatible with the laws of the universe? The problem here is that if we say he can't violate the laws of the universe, then he can't do a whole heck of a lot: he can't make planets move without acting on them with some known force, he must conserve mass/energy, etc. If he can violate the laws of the universe, then just about anything becomes logically possible: two things can occupy the same space at the same time, for example.
Again you are confusing physical impossibility with logical impossibility. If the laws of physics were inviolable then violating them would be logically impossible. If they were violable then it would become logically possible.

You are simply pursuing a red herring and missing the point. We have surely stipulated that "moving the feather to the left" is an action that is logically inconsistent with "moving the feather to the right", the actual physics of the thing is beside the point. We can begin the argument with "God(s) create(s) an Aristotlean universe then ...."
But if it is required to cooperate with an omnipotent being, it is also not omnipotent, because it cannot refuse.
We have been through this already. If the alternative to co-operation were logically impossible then inability to refuse co-operation would not disqualify it from omnipotence.

You are demanding an uneven playfield where the omnipotent dyad must be able to bring about logically impossible states of affairs in order to be omnipotent, but the omnipotent singleton does not.

Can you identify any situation at all in which "overruling an omnipotent being" would be a logically possible state of affairs?
Here I like the "state of affairs" definition better than the "action" definition. It is self-contradictory and thus logically impossible to have an object in 2 separate places at once. It is not, however, logically impossible to have a rock 1 foot to the left or 1 foot to the right. Thus if only one omnipotent being exists, there is no location to the rock which is logically impossible. If two omnipotent beings exist, however, there is the potential for an unresolvable conflict because they cannot both have full freedom in rock placement.
If the conflict is "unresolvable" then the state of affairs "resolved conflict" is then logically impossible.

So again you are saying that if the omnipotent dyad cannot bring about a logically impossible state of affairs then they are not omnipotent, but allowing the omnipotent singleton out of your special rule.

But again, if the omnipotent dyad possesses the ability of "co-operation" then there is no unresolvable conflict, they can decide between themselves the best placement of the object.

And if they do not have the logically possible ability of "co-operation" they are not omnipotent.

Please identify some logically possible state of affairs that the omnipotent dyad cannot bring about.
I seem to recall having struggled with this many years ago while trying to read Goedel, Escher, Bach. The book was discussing the question of the genii in the lamp and the ever-popular wish for more wishes. It claimed that such was not a wish, but a meta-wish. I wonder if a similar situation is extant here. Omnipotence only makes sense within a system, so actions which change the system or act on actors outside the system are meta-actions. Needs more thought and/or reading. Not tonight.
But if meta-actions resulted in logically possible states of affairs not available to mere actions then a being not capable of meta-actions would be unable to bring about some logically possible state of affairs and would not be omnipotent.
An omnipotent boxer could beat anyone in a boxing match.
Except for another omnipotent boxer, that would always be a draw.

[gdnp]

Look, forced cooperatation between two omnipotent beings creates absurd contradictions. Being #1 places the world in state A. Being #2 wants the world in state B. Being #2 cannot change a single state of affairs in the world, and yet by your definition he is still omnipotent. This is an absurd definition of omnipotence.

It is like arguing that God has perfect, inviolable plan and that humans have free will.

[Bri]

If it is a possible state of affairs then an omnipotent being must be able to achieve it.

I'm not sure if it would be considered a possible state of affairs though, particularly for an accidentally omniscient being.

You appeared to feel quite at ease with the subject in previous discussions. You had, as I recall, quite an ingenious argument against certain timelessness paradoxes that involved a computer program and dots. Am I confusing you with someone else?

Nope, that was me. My argument was far from ingenious but thank you for the compliment. I seem to recall that we had terminology for discussing timeless cause and effect. In my example of the programmer, the programmer acted timelessly in comparison to the simulated world and could manipulate the timeline of the simulation at will, but had his own timeline. Therefore, the programmer in the example could potentially change his own properties over "time" (his own time) but they would appear timeless to the simulated world.

Yes, just as Aquinas says "immutable".

Yes, if an omnipotent being is mutable then it can become non-omnipotent.

It would also imply that a non-omnipotent being could become omnipotent.

But you are saying that a mutable, omnipotent being (omnipotent using our working definition of being able to achieve any possible state of affairs) is impossible?

It would also imply the existence of a whole raft of logically possible states of affairs that the allegedly omnipotent being could not bring about.

Such as? I can think of many states of affairs that a mutable being could accomplish that an immutable being could not -- namely, any state of affairs that would involve a change in the being itself.

It would also imply that there might be a situation in which there existed no essential being, in other words that all beings were contingent. Upon what?

That is why Aquinas says that it must be immutable - that all states of God must be simultaneous, not sequential.

Aquinas held that God is perfect, which was the rationale for much of his philosophy concerning God. In other words, Aquinas was ascribing properties to God other than omnipotence as we've defined it (certainly his God was omnipotent because it was perfect, but also had other properties such as immutability because it was perfect). I'm not certain that immutability is necessary for omnipotence though, using our working definition of being able to obtain any possible state of affairs.

No doubt, but then so does the idea that existence is exhausted by time and space

And Aquinas seems to disagree with you. But that does not mean that you are wrong either.

I'm not certain that Aquinas disagrees with me (or more accurately, the SEP article) on this point at all. I think he ascribes properties such as perfection to God and thereby arrives at the conclusion that God must also be omnipotent and immutable. I'm not certain that he would conclude that any omnipotent being must be immutable though.

But in fact the particular SEP article you quoted does not come down on any particular side, merely canvasses the arguments and it does not "ignore" timelessness, it explicitly states that God in the sense of Western theism would not be temporally constrained.

Your definition was "the ability to achieve any possible state of affairs

The definition is the one used in the SEP article. That two omnipotent beings cannot exist simultaneously (using the example of the feather) and the possibility of an accidentally omnipotent being are concluded in the article. If you contend that two omnipotent beings can exist simultaneously and that an accidentally omnipotent being cannot exist, then you are in opposition to the article.

A "moving stationary feather" is not a possible state of affairs. The failure of B1 and B2 to achieve this state of affairs would not therefore disqualify them from omnipotence, by the definition you have suggested.

I can see your point, but also can see a possible distinction between the rock and feather examples. The rock example is an impossible state of affairs because it involves the omnipotent being defining two differing values for a single property of the same object at the same time. Not only is it an unliftable liftable rock, but the being itself is also both omnipotent and non-omnipotent at the same time. The feather example involves two different possible states of affairs for the feather (and doesn't involve any changes to intrinsic properties of the omnipotent beings at all).

As I've already stated, I don't know the answer to these questions, but I can see your argument as well as the article's argument on the matter.

ETA: If we are to discuss immutability (specifically whether an omnipotent being must be immutable), it would seem that we'll need to make some distinctions between real/unreal and intrinsic/extrinsic changes. We'll also need to discuss full immutability vs. partial immutability. There's a pretty good article from the SEP here (http://plato.stanford.edu/entries/immutability/#4). Full immutability does not allow real, intrinsic changes. But it is unclear to me whether non-real, intrinsic changes would be allowed and whether omnipotence might qualify.

-Bri

[gdnp]

Let us see if we can reduce the confusion by simplifiying the system.

I would like to define the world as a standard checkerboard with a single checker. For the pursposes of this example, omnipotence applies only to the world of the checkerboard, and is defined to place or move the checker anywhere one wishes. I think this agrees with my intuitive sense of what omnipotence should mean: if I am omnipotent, I can place the checker on any square I want, and move it whenever I want. I cannot remove the checker from the board, or change the size or number of squares on the board, or place the checker in two places simultaneously. Those actions are illogical.

For me, there is no state of affairs in this world I cannot achieve. There is no action I cannot perform.

It is impossible to have two beings who both possess these powers. You cannot have two omnipotent checker-placers playing on the same board.

If two omnipotent beings cannot coexist in this simplified system, they cannot coexist in a more complex system.

[Robin]

Look, forced cooperatation between two omnipotent beings creates absurd contradictions. Being #1 places the world in state A. Being #2 wants the world in state B. Being #2 cannot change a single state of affairs in the world, and yet by your definition he is still omnipotent. This is an absurd definition of omnipotence.
The definition is that "the ability to bring about any logically possible state of affairs. If you don't accept the definition you should have said so earlier.

But you are just making the same argument over again, using different phrasing. The answer is always the same. "The world in a state that an omnipotent being does not want" is logically impossible. A meaningless phrase does not gain meaning by prepending either "B1 wants" or "B2 wants" to it.

If you do accept that definition then you must identify a logically possible state of affairs that either could not bring about
It is like arguing that God has perfect, inviolable plan and that humans have free will.
Where have I argued that B1 and B2 can do a logically impossible thing? I haven't!

I am arguing that the inability of an being to do a logically impossible thing does not imply that it is not omnipotent.

It is more like arguing that God could not have a perfect, inviolable plan if humans have free will, and yet still be omnipotent.

It is like arguing that God could not prevent evil actions while preserving free will and still be omnipotent.

But your argument is akin to arguing that God could not be omnipotent if he could not prevent evil actions and simultaneously preserve free will.

[Robin]

Let us see if we can reduce the confusion by simplifiying the system.

I would like to define the world as a standard checkerboard with a single checker. For the pursposes of this example, omnipotence applies only to the world of the checkerboard, and is defined to place or move the checker anywhere one wishes. I think this agrees with my intuitive sense of what omnipotence should mean: if I am omnipotent, I can place the checker on any square I want, and move it whenever I want. I cannot remove the checker from the board, or change the size or number of squares on the board, or place the checker in two places simultaneously. Those actions are illogical.

For me, there is no state of affairs in this world I cannot achieve. There is no action I cannot perform.

It is impossible to have two beings who both possess these powers. You cannot have two omnipotent checker-placers playing on the same board.
Why not? What logically possible action could they not perform?

[Robin]

I'm not sure if it would be considered a possible state of affairs though, particularly for an accidentally omniscient being.
But you can't define omnipotence as "O can bring about any state of affairs that is logically possible for O". Otherwise we would all be omnipotent. I can do anything that I can do.
Nope, that was me. My argument was far from ingenious but thank you for the compliment. I seem to recall that we had terminology for discussing timeless cause and effect. In my example of the programmer, the programmer acted timelessly in comparison to the simulated world and could manipulate the timeline of the simulation at will, but had his own timeline. Therefore, the programmer in the example could potentially change his own properties over "time" (his own time) but they would appear timeless to the simulated world.
But you see the problem, don't you? If it is logically possible for the programmer to stand outside of the timeline of the dots, then it is logically possible for some other agent to stand outside the programmer's timeline.

We can repeat the argument ad infinitum. So as long as any being is constrained by some cause-effect continuum there is a logically possible state of affairs it cannot bring about.

This appears to support Aquinas' contention that an omnipotent being must be immutable and that all states of God are simultaneous.
But you are saying that a mutable, omnipotent being (omnipotent using our working definition of being able to achieve any possible state of affairs) is impossible?
See above.
Such as?
Such as poking it's non-omnipotent self in the eye.

In fact if I am an ex-omnipotent being then my omnipotent self could not have poked either George Bush or Al Gore in the eye - two logically possible and highly desirable actions this allegedly omnipotent being could not achieve.

A timeless omnipotent being could poke anybody in the eye irrespective of when and where they existed, just so long as they had at least one eye.
I can think of many states of affairs that a mutable being could accomplish that an immutable being could not -- namely, any state of affairs that would involve a change in the being itself.
It can exist in more than one state where the power of each state with respect to the other is limited. But a timeless omnipotent being could acheive the logical equivalent by existing in more than one state and refraining from the interactions that would be impossible for a mutable being.

So the ability to change does not imply the ability to achieve any state that an immutable agent cannot.
Aquinas held that God is perfect, which was the rationale for much of his philosophy concerning God. In other words, Aquinas was ascribing properties to God other than omnipotence as we've defined it (certainly his God was omnipotent because it was perfect, but also had other properties such as immutability because it was perfect). I'm not certain that immutability is necessary for omnipotence though, using our working definition of being able to obtain any possible state of affairs.
No, Aquinas does not ascribe perfection as a property "other than omnipotence", he defines it as a property logically implied by omnipotence. Aquinas derives God's omnipotence first and then derives his perfection from that fact (via his infinity).

And it makes sense - can an imperfect being really bring about any logically possible state of affairs?
I'm not certain that Aquinas disagrees with me (or more accurately, the SEP article) on this point at all. I think he ascribes properties such as perfection to God and thereby arrives at the conclusion that God must also be omnipotent and immutable. I'm not certain that he would conclude that any omnipotent being must be immutable though.
I am certain that he would and did conclude just that.
The definition is the one used in the SEP article. That two omnipotent beings cannot exist simultaneously (using the example of the feather) and the possibility of an accidentally omnipotent being are concluded in the article. If you contend that two omnipotent beings can exist simultaneously and that an accidentally omnipotent being cannot exist, then you are in opposition to the article.
Please quote the part of the article that concludes that accidentally omnipotent beings can exist. I can't find that at all. All I can see is a discussion of the argument without coming down on one side or the other.
I can see your point, but also can see a possible distinction between the rock and feather examples. The rock example is an impossible state of affairs because it involves the omnipotent being defining two differing values for a single property of the same object at the same time. Not only is it an unliftable liftable rock, but the being itself is also both omnipotent and non-omnipotent at the same time. The feather example involves two different possible states of affairs for the feather (and doesn't involve any changes to intrinsic properties of the omnipotent beings at all).
It does not make any difference. If you have two meaningless sentences then one is not rendered even more meaningless by virtue of both subject and predicate being meaningless.
ETA: If we are to discuss immutability (specifically whether an omnipotent being must be immutable), it would seem that we'll need to make some distinctions between real/unreal and intrinsic/extrinsic changes. We'll also need to discuss full immutability vs. partial immutability. There's a pretty good article from the SEP here (http://plato.stanford.edu/entries/immutability/#4). Full immutability does not allow real, intrinsic changes. But it is unclear to me whether non-real, intrinsic changes would be allowed and whether omnipotence might qualify.
Read the last sentence of your cite:

"Perhaps, then, defending DDI requires commitment to divine timelessness."

Of course it does. Immutability implies timelessness and vice versa, that appears to have been Aquinas' point in the first place..

I have to disagree that the article is pretty good. It is pretty poor. Any decent university tutor or lecturer would fail it for it's lack of proper citation.

It states that Aquinas derives immutability from simplicity. Not true, Aquinas derives immutability from the primacy of God's power. He derives simplicity (much later and indirectly) from this.

And there is this part:
Another argument against DDI appeals to God's power. Before Creation, God could assure that no universe ever existed. God has this power now only if he can alter the past. Few think he can.

Immutability - Stanford Encyclopedia of Philosophy
But Aquinas has already forseen and dealt with the objection:
Thus we say that before the world existed there was nothing except God, and that there is no body lying outside the world. But in thus speaking of “before” and “outside,” we have in mind nothing but time and place as they exist in our imagination.

St Thomas Aquinas - Compendium Theologiciae, chapter 98
In fact chapter 98 deals entirely with the paradox of an immutable being that is able to do anything at all.

[gdnp]

Why not? What logically possible action could they not perform?

We are not talking logically possible states of affairs here. We are defining omnipotence as the ability to place or move the checker anywhere one wishes. Two people cannot have this power simultaneously. If being 1 states "I wish to place the checker in the top left corner and leave it there" and being 2 states "I wish to place the checker in the top right corner and leave it there" a physical impossibility is created, since the system is defined as having only one checker and a single checker cannot be in two places simultaneously.

[Robin]

Here is the SEP at its best:
There are many arguments against DDI. One that some find particularly forceful begins from the fact that God is omniscient. If God is omniscient, they say, God knows what time it is now. What he knows, then, is constantly changing, since what time it is now is constantly changing. But knowledge of what time it is is intrinsic to God. And change with respect to something intrinsic is intrinsic change. So it seems that God cannot be intrinsically immutable.
An argument that seems to be taken from the following classic argument, no?
Bluebottle: What time is it Eccles?
Eccles: Err, just a minute. I, I've got it written down 'ere on a piece of paper. A nice man wrote the time down for me this morning.
Bluebottle: Ooooh, then why do you carry it around with you Eccles?
Eccles: Well, umm, if a anybody asks me the ti-ime, I ca-can show it to dem.
Bluebottle: Wait a minute Eccles, my good man...
Eccles: What is it fellow?
Bluebottle: It's writted on this bit of paper, what is eight o'clock, is writted.
Eccles: I know that my good fellow. That's right, um, when I asked the fella to write it down, it was eight o'clock.
Bluebottle: Well then. Supposing when somebody asks you the time, it isn't eight o'clock?
Eccles: Ah, den I don't show it to dem.
Bluebottle: Ooohhh...
Eccles: [Smacks lips] Yeah.
Bluebottle: Well how do you know when it's eight o'clock?
Eccles: I've got it written down on a piece of paper!

Spike Milligan The Mysterious Punch-up-the-Conker 1957

[Robin]

We are not talking logically possible states of affairs here. We are defining omnipotence as the ability to place or move the checker anywhere one wishes.
Ah! I see, we are changing the definition. We are allowed to arbitrarily change the definition now are we?

See my sig line.

[gdnp]

Ah! I see, we are changing the definition. We are allowed to arbitrarily change the definition now are we?

See my sig line.

The definition of "logically possible state of affairs" was not working. It creates a tautology. It led to absurd situations of omnipotent beings who could do nothing, which is my definition of impotent. I thus attempted to simplify the system to demonstrate the logical impossibility of two omnipotent beings in the same system.

[Robin]

The definition of "logically possible state of affairs" was not working. It creates a tautology. It led to absurd situations of omnipotent beings who could do nothing, which is my definition of impotent. I thus attempted to simplify the system to demonstrate the logical impossibility of two omnipotent beings in the same system.Just as I said, you changed the definition.

See my sig.

[Robin]

And incidentally, why exactly do you think the definition "able to achieve any logically possible state of affairs" leads to a tautology or a being unable to do anything?

You have not demonstrated that anywhere.

And just what exactly is your new definition of omnipotence?

And if your player has the checker on the top right hand square and says "I wish to move the checker one square to the right" he cannot.

And so, by your new definition, cannot be omnipotent.

[gdnp]

By your definition I am omnipotent. I can lift any rock that I can lift. It is not logically possible for me to be able to lift any rock that I cannot lift, therefore it does not violate your definition of omnipotence. It is a tautology.