Hmm, I don't think you're saying anything. What I said was true.

If he could do anything at all - than how hasn't he done anything at all?

If you don’t know how one does anything, how can you be sure they haven’t done anything?

In this argument, you state that you are sympathetic to Descartes’ view. The following is Descartes view on the omnipotence of God in a modus ponens argument:

1. If God can perform both actions in the boulder paradox, then he is omnipotent.
2. God can perform both actions in the boulder paradox.
3. Therefore, God is omnipotent. (1,2 MP)

It seems that you want to find this argument to be true because accepting anything otherwise would make God incapable of certain abilities, and therefore fail in the category of omnipotence (as per your definition of omnipotence), which could potentially discredit his Godlike nature.
However, Descartes’ argument nonetheless seems ridiculous. So in order to make sense of that, you offer the following modus ponens argument:

1. If God can do anything logically possible, then he is omnipotent.
2. God can do anything logically possible.
3. Therefore, God is omnipotent. (1,2 MP)

This argument seems to be the more relevant view of what you are trying to decipher. So I will make my objection in terms of this modus ponens argument.
The key issue here is your definition of omnipotence. You seem to have a good attempt to define it, but it falls short for the following reason. I object to premise 2, that God can do anything logically possible. My modus tollens argument is as follows:

1. If God can do anything logically possible, then he is omnipotent.
2. There are some logically possible things that God can’t do.
3. Therefore, God is not omnipotent.

There are some logical possibilities that God cannot do. An example of this would be lying. Lying is objectively logically possible. But God cannot lie, because it goes against his nature. Therefore, that presents a contradiction. A similar example would be the logical possibility of making a mistake – God can’t do this either.

So it seems that you need to redefine omnipotence. In my argument, my conclusion claims, “Therefore, God is not omnipotent,” only in terms of your definition of omnipotence, specifically, that an omnipotent being can do anything logically possible. I would also like to accept that God is omnipotent. But to do this, you need to redefine omnipotence, not just using the ability do any logically possible things as the basis for the definition. It’s more than just logical possibility.

For example, you can maintain the claim that God is omnipotent if you alter the antecedent in your original premise to “God can do anything that is logically possible for God.” This narrows the scope of what is logically possible to whatever is both logically possible in general and what does not contradict God’s nature (e.g., lying, erring).

A final important note – The fact that there are logically possible things that God cannot do does not undermine him as God. We wouldn’t want him to lie or make a mistake. So the fact that he is unable to do some of these logically possible things is actually a good thing, as it preserves his good nature.

Hmm, I think bringing God into it muddies the waters. What I'm sympathetic to is Descartes' idea that being omnipotent involves being able to do anything at all.

Imagine a person who can do anything logically possible. Well, that person has a lot of power, to be sure. But they do not have as much as one who can also do the logically impossible. So I think true omnipotence involves the latter.

Yep, agreed!

By definition, it assumes that a Deity can do or be, both logical and illogical or possible and impossible things.

Those unresolved paradox's are clues to the probability of that description or idea, and can be reasonably inferred as such. Good points!!

By definition, it assumes that a Deity can do or be, both logical and illogical or possible and impossible things. Those unresolved paradox's are clues to the probability of that description or idea, and can be reasonably inferred as such. Good points!! — 3017amen

What escapes me is why people who ask that kind of questions stubbornly refuse to learn from the history of Russell's paradox.

1) They are incredibly ignorant but they always know everything better.
2) They draw utterly dumb conclusions about religion.

Some people are simply beyond repair ...

Descartes' idea that being omnipotent involves being able to do anything at all.

Imagine a person who can do anything logically possible. Well, that person has a lot of power, to be sure. But they do not have as much as one who can also do the logically impossible. So I think true omnipotence involves the latter. — Bartricks

Yep, I agree. Everything else is changing the definition of omnipotent (adding "limits" to something that is, by definition, "unlimited").

But God cannot lie, because it goes against his nature. Therefore, that presents a contradiction. A similar example would be the logical possibility of making a mistake – God can’t do this either. — philorelkook

Ideas like this suggest that the "omnipotent" being under discussion has no will. Why can't an all-powerful being be wrong? Don't we need to include "all knowing" before that is an issue? Even all-knowing, couldn't it choose to be wrong?

Also when you mention "his nature" you are claiming much more knowledge of god than I think belongs in this discussion - I think many of the people involved in this thread are agnostic or atheist, and most religious people will disagree on god's "nature" (I am not saying you are wrong, just that what you are describing is a whole 'nother debate).

Also, isn't the concept of "omnipotence" in religion the result of the thousands of years of an arms race that claimed "my god is more powerful than yours"? Well if "your" god is limited by logic and having to tell the truth, then "my" god is more powerful.

Question: Can an omnipotent being create a stone which he cannot lift?
Answer: SORRY, CANNOT COMPUTE. THE PREMISE DOES NOT CONFORM TO VALID LOGICAL PARAMETERS. — BrianW

How exactly do you mean this? I view the idea of an omnipotent being as problematic, but if the premise starts with the omnipotent being existing, I don't see a problem with the rest?

It seems that you are giving an argument similar to the one as follows:

1. If God is truly omnipotent, then God must be able to successfully perform both the logically possible and the logically impossible.
2. God is omnipotent.
3. Therefore, God must be able to successfully perform both the logically possible and the logically impossible.

While this argument is valid in form, I do not think this argument is sound because of premise 1. I think we both agree with premise 2 that God is omnipotent, but I think our definition of what "omnipotence" means and looks like for God are different.

I think this difference comes from your abuse of the term "logically impossible." It is clear that you argue that a being who can do both the logically possible as well as the logically impossible is more powerful and omnipotent than a being who cannot. However, I think that to say that God cannot perform the logically impossible is not infringing on His omnipotence.

The definition of "logically impossible" is something that is contradictory or contrary to the laws of logic, such as a round square or a tall man not being tall. Your misuse of the term is seen when you claim that an omnipotent being can create a stone so heavy that it cannot lift it and then proceed to lift it, because if it can lift the stone then the stone was not too heavy for the being to lift it after all, and thus would fall into the realm of "logically possible" rather than "logically impossible," because logical impossibilities simply cannot exist. Logical impossibility infers that one cannot perform both action "x" and action "not x." Thus, God could not create a stone so heavy that He could not lift it and then lift it because it would be logically impossible, e.g. performing both "x" and "not x."

On another point that I will not dive too deeply into but think is worthy of bringing to light, do we even want to say that God can perform logical impossibilities? I think not, as this would have absurd implications, such as God being able to be both maximally just and unjust, loving and not loving, omnipotent and not omnipotent, etc.

In conclusion, I think what you are arguing to be unsound due to the misuse of the term "logically impossible," for it is not infringing upon the omnipotence of God to say that what is logically impossible, i.e. what is contradictory and therefore cannot occur, exist, or be done, cannot be done by God; if it could be done by God, then it would not be impossible but rather possible, because logical impossibilities cannot exist.

I would have agree with the view that an omnipotent being is only able to do anything that is logically possible. It only makes sense that an omnipotent being would not be able to do the impossible, or else the impossibility would not be impossible anymore. Things like “making a stone heavier than he can life” or anything that is contradictory are not doable, even for an infinitely powerful being. Not being able to do impossible or contradicting acts does not make God any less powerful simply because no being would be able to do what God cannot do.
So rather having God be something like this:
1. If God is an omniscient being that can do anything, he should be able to make a stone heavier than he can lift.
2. God cannot make a stone heavier than he can lift.
3. God is not an omniscient being that can do anything.
I would argue for it to go more like this:
1. If God is an omniscient being, he is infinitely powerful to do anything that is possible/doable.
2. God cannot make a stone heavier than he can lift.
a. But there is no being that can exist that can do this task as it is impossible for any being to make a stone heavier than it can lift.
3. God is still an omniscient being.
God as an omniscient being that has created this universe, including what is possible and impossible, would also have to abide by the rules he set for the universe. I also believe that God would be able to do the impossible outside the realms of this universe, but it will in be in ways where we cannot comprehend because we are beings that live and die by the rules of this universe.

My understanding of the “being unable to do the impossible” argument is a little different. I understand the argument as something like this:

If God has perfect qualities, God does not fail.
If God does not fail, God’s actions necessarily do not cause God’s failure.
If God has perfect qualities, God’s actions necessarily do not cause God’s failure. (1,2 MP)
God has perfect qualities.
God’s actions necessarily do not cause God’s failure. (3, 4 MP)

If we apply this argument to the boulder case (or the Jesus microwaving a burrito case as so many memes have been parodying recently), it implies that God cannot create a boulder that God cannot lift. It is impossible not simply on a logical basis, that being that an omnipotent being cannot create something it cannot lift. God cannot perform the action of creating the boulder because God’s actions cannot cause God to fail because that jeopardizes God’s other perfect qualities.

I do not have to conclude that God is not omnipotent; I have to shift my understanding of omnipotence. Omnipotence means God can do all things except the one thing that would jeopardize God’s perfection: fail. If God could do all impossible, it seems like argument would allow for God to do other impossible things. What other things might we initially consider impossible for God? Considering God’s perfect nature and qualities, we could imagine it is impossible for God to not know something. It is impossible for God to kill God’s self. It is impossible for God to sin. Are we okay with saying that God can be perfect, in the sense that God cannot sin, and still say God is entirely capable of sinning despite God’s perfectly good nature? That might imply that God is only arbitrarily good, which seems like a very unsatisfactory conclusion for theists. I am content to view God as incapable of imperfection, of failure. Here is a potential argument that may come from the “God can do the impossible” train of thought:
God is perfectly good (in the sense that all of God’s qualities necessitate perfect goodness).
If God is perfectly good, then it is impossible for God to commit evil.
It is impossible for God to commit evil. (1, 2 MP)
God can do the impossible.
God can commit evil. (inferred from 3, 4)

If someone wanted to object to say that that gives humanity an ability that God does not have, I would say “I sure hope so! I can envy and lie and cheat and all manner of evil things if I am not trying to live a good life.” All of those things lead to my failure to be a perfect being. God is a perfect being. God cannot fail. If God could do the impossible, God could do all manner of things that contradict his perfect qualities.

You say, “But they (one “who can do anything logically possible”) do not have as much [power] as one who can also do the logically impossible.”

First, I would like to clarify the definition of logical impossibility. This doesn’t mean just anything that would seem illogical to achieve — for example, me eating ice cream before working out might seem illogical. But when we refer to logical possibility, we really mean anything that does not cause a logical contradiction to properly think of it. For example, claiming that both “P” and “not P” are true at the same time and in the same way would be a logical contradiction. Another example would be asking someone to think of a square circle. These contradictions are instances of logical impossibilities.

So referring back to your claim, then, that a being that could do the logically impossible has more power than one that cannot, is in and of itself a contradiction. By definition, what is logically impossible is that which one cannot do (my first and second premises below). There is no reason to think omnipotent beings are not included in this (my fourth premise below). So when you assert that there is a being that can do something which, by definition, no one can do, I think it fails to grasp the definition of omnipotence correctly.

My argument takes the following form:

1. If a being can do the logically impossible, then that being can make a contradiction true.
2. No one can make a contradiction true.
3. Therefore, no one can do the logically impossible (1, 2 MT).
4. An omnipotent being is someone.
5. Therefore, an omnipotent being cannot do the logically impossible (3, 4, MP).

So since no one can do the logically impossible, then it is not a decrease in anyone’s power to not be able to do the logically impossible. So, an omnipotent being still maintains the highest possible level of power without being able to do the logically impossible. Because there is no contradiction between an omnipotent being and a being that cannot do the logically impossible, then, I think your argument, and your conclusions regarding Descartes’ paradox, fail to succeed.

I believe the boulder case does not depend on whether God can or cannot create the heavy stone but the argument merely focuses on a dilemma where either choice tries to convince you that God is not omnipotent. Probably, the flaw is in the premise itself, which defines God as not omnipotent if God cannot create such a stone.
Moreover, the definition of omnipotence plays a big role in each's perspective. As God who has infinite power can create infinitely heavy stone and has infinite strength to lift the stone.
I think, our definition of omnipotence in terms of a deity goes beyond logical and illogical possibilities as God is not bounded by these limits.

1. Either god can create a stone so heavy that God cannot lift, or God cannot create such a stone
2. If God can create such a stone, then God is not omnipotent
3. If God cannot create such a stone, then God is not omnipotent
4.Omnipotence is not bounded by human's logic
5. We cannot know whether God is omnipotent or not

Hm, I would say that premise 2 is false.

It seems to me that what you're doing is treating the idea of 'logical impossibility' as synonymous with the idea of 'something no-one can do'. However, for something to be 'logically impossible' is for it to be inconsistent with the laws of logic. My point is that those are not equivalent - that being an act that is inconsistent with the laws of logic is not one and the same as it being an act that no-one can do.

For example, as you yourself note, it is a basic law of logic that no proposition can be true and false at the same time (the law of non-contradiction). And thus making a proposition true and false at the same time is logically impossible, but that does not necessarily mean that it is not possible for someone to do it. If they did it, their act would violate the laws of logic. But it would still be something they did.

To illustrate, consider this proposition: "What I am saying now is false". Well, that proposition is true if it is false, and false if it is true. In creating that proposition, then, I seem to have done something that violates the law of non-contradiction. Creating that proposition was something I did. Yet what I did - if I did what I seem to have done - violates the law of non-contradiction because the proposition I created is both true and false at the same time (precisely what the law forbids).

I myself seem to be a counter-example to 2, then. And as what I just did anyone can do, we can all violate the laws of logic - we can all do something that is logically impossible, namely create propositions that are true and false at the same time.

Now, perhaps I did not violate a basic law of logic in creating that proposition. There's a debate to be had about that. The point is just that being logically impossible does not seem to be one and the same as being something no-one can do.

yes, omnipotence does not mean doing all things; it means all powerful. self-contradiction is not power. rather, it is inability.

But that's the opposite of what I said. Omnipotence does mean being able to do anything. I mean, it doesn't get more powerful than that. And being able to do things that logic says cannot be done is not an inability at all - it is an ability (quite an impressive one!). So I am confused by the 'yes'.

well omnipotent does mean being able to anything. He is also transcendent in all things.

There is technically not anything logically impossible about an omnipotent being creating something that it then cannot move. That's just equivalent to resigning a small piece of its omnipotence. Before the creation of the thing, it's omnipotent. Then it creates a limit to its omnipotence, which is within its power to do. After that it's not omnipotent anymore. But while it was omnipotent, it had the power to create limits to its own omnipotence, without contradiction.

But a being who could create a rock too heavy to lift, and lift it, is even more powerful than one who could only do the former.

There is technically not anything logically impossible about an omnipotent being creating something that it then cannot move. That's just equivalent to resigning a small piece of its omnipotence. Before the creation of the thing, it's omnipotent. Then it creates a limit to its omnipotence, which is within its power to do. After that it's not omnipotent anymore. But while it was omnipotent, it had the power to create limits to its own omnipotence, without contradiction. — Pfhorrest

This is reasonable. But it suggests an understanding of "omnipotent" that I don't think we can ever have. Omnipotence is like saying black holes have INFINITE density. It means something in the abstract, that doesn't match reality. Why can't it be perfectly possible for an omnipotent being to do ANYTHING? Even if it contradicts physics, or logic, or human language...so what?

I will agree with @Bartricks on this one.

:smirk:

No, exactly what omnipotence involves is the issue under discussion. I am saying that it involves being able to do anything, not just the possible. — Bartricks

If it can be done then it is possible. So what you are saying just amounts to saying that an omnipotent being can (in some unfathomable way) do things which are, by our limited definitions, impossible.

An omnipotent being could, for example, according to your argument, create an object that is both black all over and white all over, or even every possible colour (as well as all the impossible ones) all over.

It's just silly vacuous nonsense, in other words.

If you don’t know how one does anything — Possibility

What/who is 'one' ... (X)? OP's question fits under the hypothetical that omnipotent being exists.

Let's let X represent: 'omnipotent being' and as used in the OP.

If X denotes an 'omnipotent' being that exists,
If X denotes that such 'being' belongs to existence,
If X denotes that such a being has the power to do any thing at all.
Than it will follow that, X being does any thing at all, and this 'any thing at all' will be unique to such a being and detectable without in depth knowledge of 'how it works' because there is no such thing as X being capable of doing 'no such thing.' (Non-omnipresence, non-existence, etc..)

If X is not doing 'anything at all' .. then it follows that X cannot do 'anything at all' .. and X is not omnipotent and does not exist. So it seems clear to me that X cannot do anything at all, because it does not exist.

"How" he does any thing at all is not readily apparent how that is at all relevant. Thoughts?

If he could do anything at all - than how hasn't he done anything at all? — Swan

My point was that if you had a clear understanding of how X does things, of what is involved in the doing, then you could determine whether or not such a thing was done or could be done, regardless of whether you were aware that it has been done.

But we don’t have any idea how X would do anything at all, let alone do things that we are unaware of. All we can do is assume based on what we are aware of that has been done, and how we might do things that we are unaware of being done.

FWIW, I don’t think X exists either, but I do think the potential to do anything at all exists. It’s just not a being.

My point was that if you had a clear understanding of how X does things, — Possibility

But instead: How can anyone have a 'clear understanding' of any thing X does, if X has not done any thing at all, and because X does not do any thing at all, does not exist.

Your question of "how" being a relevant question does make sense to me. Demonstrating/knowledge that an omnipotent being cannot do anything at all does not require it to exist.

of what is involved in the doing, then you could determine whether or not such a thing was done or could be done, regardless of whether you were aware that it has been done. — Possibility

This is a concern for after the fact: ... in the case of X, first, doing any thing at all. X cannot do any thing at all, so it is not at all (currently) necessary to have a 'clear understanding' about how X does any thing at all.

I am aware X cannot do any thing at all, and also (know) such because X does not do any thing at all, because there is "no such thing" of 'nothing that X cannot do'.

But we don’t have any idea how X would do anything at all, let alone do things that we are unaware of. — Possibility

Sure we do.

All we can do is assume [...] — Possibility

What exactly are we 'assuming' if not all things 'possible' > any thing at all.. and 'known' things, that X should be knowingly doing.

FWIW, I don’t think X exists either, but I do think the potential to do anything at all exists. It’s just not a being. — Possibility

...? Sorry I'm not following.

'Potential' implying a probable, by necessary existing attributes = belong to existence ... "any thing at all..." including, every thing at all, correct?

If it's just a possible you're talking about, I'm not sure what point you're trying to make.

No, exactly what omnipotence involves is the issue under discussion. I am saying that it involves being able to do anything, not just the possible. — Bartricks

It's the same to say: "The possible is impossible." It's a trick language doesn't do.

It may be possible for an omnipotent being to do the impossible. But it's not possible for us to talk about it.

Possible: anything we can imagine happening
Potential: anything that can happen
Probable: anything that is likely to happen

Most discussions like this fail to make the distinction between potentiality and possibility. To actually do something, one needs to be aware (although not necessarily conscious of that awareness) that the something can be done.

There are plenty of things we can think of that we say cannot be done, because we are unaware of any potential for it to be done. We often say these are ‘impossible’ - but sometimes what we once thought impossible we soon discover to be possible. So in reality it was always possible, but we were only unaware of the potential.

One doesn’t have to do anything to be considered omnipotent - it only requires the potential. And you can only prove potential after the fact, so one cannot actually be omnipotent until everything is already achieved. So the concept of an ‘omnipotent being’ is a subjective perception at best, and in my view can only refer to the potential of the unfolding universe itself, of which we are a part.

Possible: anything we can imagine happening
Potential: anything that can happen
Probable: anything that is likely to happen

Most discussions like this fail to make the distinction between potentiality and possibility. To actually do something, one needs to be aware (although not necessarily conscious of that awareness) that the something can be done.

One doesn’t have to do anything to be considered omnipotent - it only requires the potential. — Possibility

So "potentiality" denotes any necessary existing attributes present & unique to X (omnipotent being), correct?

Possible: anything we can imagine happening — Possibility

I disagree. Any thing 'possible' is not just 'possible' because we imagined them to be so. Any thing 'possible' is 'all things possible.'

So "potentiality" denotes any necessary existing attributes present & unique to X (omnipotent being), correct? — Swan

I can’t say I agree with that interpretation. I don’t believe an ‘omnipotent being’ exists to present unique attributes, let alone necessary ones.

I disagree. Any thing 'possible' is not just 'possible' because we imagined them to be so. Any thing 'possible' is 'all things possible.' — Swan

You can’t clarify the meaning of a term by applying the term.

Well, I don't know then. We don't really have to agree/disagree with each other. I have nothing else to say.