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The hypothetical rock could be infinitely dense, so in this case size wouldn't matter. The rock would have to be so heavy that God cannot lift it, or if that is not possible, then God wouldn't be omnipotent. It is simply impossible and by presenting this problem some atheists believe that an omnipotent God who can do everything imaginable is not possible.
I'm sorry but that's simply not the question I'm asking. I think NowASaint puts it quite well; "the explanation of jumping into a mortal body does not work because if God is limited to a mortal body, He is not God....and so you would be left with your absurdity of God creating a rock so big He cannot lift it." although it would not be a rock so big He cannot lift it, but a rock so heavy.
(of a deity) having unlimited power; able to do anything.
To me the definition of omnipotent; "able to do anything" would mean that the omnipotent being could do anything conceivable, though I suppose the definition is up to interpretation.
The paradox does not go into detail about how the lifting of the rock would work. It is just assumed that if an omnipotent being were to create a rock they cannot lift then they would account for all of the factors in order to make a rock they cannot lift. If they are truly all powerful they could manipulate gravity so that they could make a rock they cannot lift.
We're talking about the abilities of an omnipotent being, so the argument about Earth makes no sense. The lifting of the rock could happen on any plane with the same laws of weight (gravity). The question itself is if an omnipotent being could make a rock that they could not lift. The place is irrelevant to the question and your argument is flawed either way as Jupiter is heavier than Earth meaning that it could take place on a planet larger than Earth. The two rocks could be stacked to use as a place to lift the one of the rocks from.
You can be omnipotent and still go into a simulation. Your physical might never changes, but your simulated might does. You are never not omnipotent in the example.
It's true that you could change your own strength as an omnipotent being, but the question is could an omnipotent being with all of their might available to them create a rock that with all of their might available to them they cannot lift.
I still am apparently not clear enough with my wording. I presented the question unspecifically not going into too much detail. The real question would then be Could God, the omnipotent being He is, create a rock that he, as an omnipotent being and with all of His strength (not downgrading His strength so that He cannot lift the rock) create a rock that could not be lifted with His omnipotent strength? This then leads to the two problems presented with both answers while still considering God (or any omnipotent being) to be omnipotent.