According to some believers omnipotence doesn't mean that God can do things that are logically possible. By "omnipotent" they mean can do anything that is logically possible. So Premise 3 is not necessarily true.

What about choice? Suppose God creates a stone and chooses not to lift it.

God doesn't conform to the law of the excluded middle -- after all, he is omnipotent. Why should he be contained by our preferred patterns of inference?

He isn't.

vegetarian - not made of meat
bacon - a meat product.

God cannot make vegetarian bacon, although he is omnipotent, because I have just defined it to be an impossible object. This does not restrict what God can or cannot make any more than it restricts what Global Soya Inc. can make. It just restricts what I am willing to call it.

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I would like to be able to say that an omnipotent being can create contradictions. But there's a fair point you're making here about our willingness.

Maybe I'd put it that God cannot contradict analytic truths, but that's not a restriction on God as much as it is a grammar of preference. But if he is omnipotent I'd say that he can create synthetic true contradictions -- something like the liar's paradox.

This scenario is inherently corrupt. The very word "omnipotence" excludes "cannot" by its definition. It's a stupid trick, not even worth addressing really.

The appropriate response to humor this question would be another question: "Why would God, Who can do anything, bother doing something so incredibly stupid and pointless?"

What if God IS the stone?

"Why would God, Who can do anything, bother doing something so incredibly stupid and pointless?" — Michael1981

What if God IS the stone? — gloaming

I had very much the same thought. I was thinking that God (or whoever thought about herself that she was God) would kick herself for having performed such a dumb and pointless act of creation. And then she would pause to contemplate the almighty stone that's now defeating her powers, and call it her God.

If God can create such a stone, then he is not omnipotent — Yajur

How does this follow?

How does this follow? — Michael

Because God thereby lacks the power to lift the stone.

I always take issue with the notion that divine omnipotence is a useful religious concept. I don't think it is. Some professional theologians and philosophers agree with me, hence process theology and process philosophy. See Charles Hartshorne "Omnipotence and Other Theological Mistakes". Anyway these sort of conundrums should cause you to question the conceptions of the divine which give rise to them in the first place.

We are talking about can and cannot.
So either God can or cannot make such a stone.
Let's say God chooses not to lift the rock but he possibly can, then he failed at making the described rock, hence he's not omnipotent.

God doesn't conform to the law of the excluded middle — Moliere

Is there a particular third option you have in mind?

God cannot make vegetarian bacon, although he is omnipotent, because I have just defined it to be an impossible object. — unenlightened

Yes, however, creating a rock so heavy that one cannot lift is not an impossible task. I can easily create objects so heavy that I cannot lift.

Makes no sense to talk or think about something without first giving some specification of what that something is — tim wood

I am talking about the general definition of God (you can think in terms of whatever Religion you do or don't follow).

If it's still unclear, check this out https://www.google.com/search?q=god+meaning&oq=god+meaning&aqs=chrome..69i57j0l5.4537j1j7&sourceid=chrome&ie=UTF-8

What are you talking about? You need to give us your definition of God and omnipotence. You seem to want God to exhibit human tendencies. Is God omnipotent before or after the creation of that stone? I should think that any being (not only that which is named God) is omnipotent if they have no limitation.
Your premise cannot assume omnipotence before the relevant factors have been appropriately considered. You should have said:

1. Either X can create a stone so heavy that he cannot lift, or he can't
2. If X can create such a stone, then he is not omnipotent
3. If X can't create such a stone, then he is not omnipotent
4 Therefore, he is not omnipotent

From your succeeding statements, by God you already imply omnipotence which makes your arguments (1-4) illogical.

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Ok, my definition of God is a being who is Omnipotent, Omniscient and Omnipresent.
My definition of Omnipotence is being able to do anything

So I rewrite the argument with these definitions using Modus Tollens,

1. If God exists, then he is omnipotent
2. No being is omnipotent
3. Therefore God does not exist.

Now to defend premise 3,

a. Either some being can create a stone so heavy that he cannot lift it, or he cannot
b. If he can create such a stone, he is not omnipotent
c. If he cannot create such a stone, he is not omnipotent.
d. No being is omnipotent

Is God omnipotent before or after the creation of that stone? — BrianW

I think most religions believe God is omnipotent throughout

A being (same source) is:

1. existence.

2. the nature or essence of a person.

3. a real or imaginary living creature.

None of this will do for God, — tim wood

Umm so according to you God is not a real creature. Are you arguing for atheism?

Still creating dissonance.

1. If God exists, then he is omnipotent
2. No being is omnipotent
3. Therefore God does not exist. — Yajur

If you have already concluded that no being is omnipotent, what is the purpose of this whole exercise?

If you have already concluded that no being is omnipotent, what is the purpose of this whole exercise? — BrianW

The point is to show an omnipotent God cannot exist. Apparently, using Modus Tollens here.

Think of the argument: If there is smoke, there is fire. There is not fire, so there is no smoke.

This might help further http://www.philosophy-index.com/logic/forms/modus-tollens.php

If there is smoke, there is fire. There is not fire, so there is no smoke. — Yajur

There must be context. For example, in this statement, it could mean that no fire is observed where it was expected or pointed out to be. It does not mean that fire and smoke do not exist.
So, in what context does God not exist and how have you gained such information, how have you interpreted it and what (principle, analogy, experience, proof, etc) validates your conclusion?

Ps. After the above process what you'll have given is your perspective. From it, others can analyse to see if it meets their standards of reason as well.

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Because God thereby lacks the power to lift the stone. — Pierre-Normand

What stone?

What stone? — Michael

Yes, it's true that if Her power to create such a stone remains unactualized, then, in that case, Her merely having this power doesn't entail a contradiction.

Her merely having this power doesn't entail a contradiction. — Pierre-Normand

Which I believe is the solution to the paradox. God can create the stone but doesn't.

Which I believe is the solution to the paradox. God can create the stone, but doesn't. — Michael

I rather like this purported solution, not because I am especially interested in saving the notion of an omnipotent god, but because it is a useful reminder of the general distinction between an agent (who may be an ordinary human being) lacking a power and her being in contingent conditions entailing that she will not exercise it. Failures to recognize this distinction often leads to some variations on the modal fallacy.

Yes, however, creating a rock so heavy that one cannot lift is not an impossible task. I can easily create objects so heavy that I cannot lift. — Yajur

I'm not a great creator myself, but I have come across rocks so heavy I cannot lift them. But not rocks so heavy that an omnipotent being cannot lift them, those are impossible objects by definition. As such, it does not limit God in any way, but only what we can sensibly say. God, or Bio-Med Inc. might create vat grown muscle tissue from piggy DNA, or avocados that oink, but neither would be vegetarian bacon, unless we change the definitions, because non-meat meat is impossible. A rock that cannot be lifted by someone who can lift any rock is impossible - a nonsense.

Well, I think @unenlightened has the right of it in the above with respect to the particular example you're giving.

The middle I had in mind was between truth and falsity, though. Or the notion of true contradictions. I should have probably said the law of non-contradiction, but I was just quickly typing off a response.