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I posted this text a long time ago in Danish and I translated it and used it on the forum. I think I forgot to post the English version here as well. I apologize for the low quality English in the text.

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I have earlier written a short article about why the stone-paradox not is a real paradox and therefore do not disprove omnipotent entities.

The paradox

The paradox is usually formulated thus:

Can an all-mighty [god, entity] create a rock so heavy that it cannot itself lift it? If it can, then it is not all-mighty and if it cannot, then it is not all-mighty. Given either outcome then the [god, entity] is not all-mighty.

Let us formulate the argument more explicit:

1. If god exists, then god is all-mighty.
2. Either god can a rock so heavy that he cannot lift it, or he cannot.
3. If god can, then he is not all-mighty.
4. If god cannot, then he is not all-mighty.
5. Given either outcome, god is not all-mighty. (2, 3, 4)
6. God does not exist (1, 5)

The problem

I claim that the problem lies with premise 3. It simply doesn’t follow that if god can create an object, which causes him to lose omnipotence, then he is not omnipotent. I will explain why later, let us now look at a similar argument which catches the problem mere clearly.

1. If god exists, then god is all-mighty.
2. Either god can remove his own all-mightyness or he cannot.
3. If god can, then he is not all-mighty.
4. If god cannot, then he is not all-mighty.
5. Given either outcome, god is not all-mighty. (2, 3, 4)
6. God does not exist. (1, 5)

It should be clear that premise 3 is false. If it in some way is not clear to you, then let me explain exactly where it goes wrong.

Actuality and potentiality – the root of the problem

All-mightyness is often defined as ‘can do everything’. This is too vague for us. Let us look at what one calls logical omnipotence (logical all-mightyness); one can do all which is logically possible. Logically possible is the weakest form of potentiality, because it just says that the thing is not self-contradictory.

If an entity can do all actions which are logically possible, then it can also create a rock so heavy that it cannot lift it. But this does not make it impotent; non-all-mighty. It is first when the rock becomes actual that the entity is no longer all-mighty. There being a possibility creation of a rock does not mean that it is created. Therefore there is a conflation of potentiality (can) and actuality (is) at the adherents to the argument.