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This question is coming out from our conversation with @Conifold:

He believes that for creation of another omnipotent being 'strong' omnipotence is required.

Can God create a rock that he can not lift? Your copy is that rock because the meaning of omnipotence is automatically restricted with the very creation of another "omnipotent" copy. Trying to answer it you will get into a Liar-like oscillation in classical logic, and in a paraconsistent one you can settle it with a dialetheia, yes+no, however you wish to interpret that. Can God wish for things impossible even for him? I suppose yes, there is nothing logically impossible about that, I think.

I however don't see why 'weakly' omnipotent being would break logic by creating another 'weakly' omnipotent being (like copy of itself).

Is 'strong' omnipotence required to create another 'strongly' or 'weakly' omnipotent being?

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I assume you use "weak omnipotence" for the fourth definition on the Wikipedia article, namely that a weakly omnipotent entity is one that can do anything that is logically possible. In that case I agree that it is not inconsistent that a weakly omnipotent entity can create another weakly omnipotent entity. But one must be careful; the definition of "weak omnipotence" must be based on global possibility. Having two weakly omnipotent entities is then possible because they are simultaneously constrained to be unable to together do something impossible, simply by definition. Thus one weakly omnipotent entity can make it so that there are two weakly omnipotent entities, again by definition.

That said, it is philosophically unsatisfying to have such a notion of weak omnipotence, when one also wishes to ascribe a conscious volition to a weakly omnipotent entity. How on earth can one such entity create another that has an independent conscious volition but yet with both constrained not to conflict? In other words, the issue lies not with weak omnipotence but in that we cannot have two entities that are both weakly omnipotent and have independent volition, unless you also affirm that the whole world (including all whatever omnipotent entities) is totally logically determined (so that there is only a single logical possibility). This does not imply that there cannot be one weakly omnipotent entity with volition in a world that is not totally logically determined, so it may be compatible with certain belief systems ascribing weak omnipotence to their respective God[s]. For example, it is not inconsistent to have two or more weakly omnipotent entities with a unique volition, though arguably that is essentially having a single being in the traditional sense, since they logically necessarily act as one.

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  • I can explain volition of creating copy of self is in knowing oneself 'well enough' to be certain to get along...
    – Matas Vaitkevicius
    Aug 31, 2016 at 11:08
  • @MatasVaitkevicius: That's a litle misleading, since it is in fact logically necessary for there to be a unique volition, because remember the definition does not say merely that the two entities will cooperate but that they cannot conflict, since everything that is logically possible is an option for them, so if they can possibly disagree then it is an option for them to do so, but the definition also says that one can always make the other agree, which gives a contradiction.
    – user21820
    Aug 31, 2016 at 11:15
  • If entities are identical copies of one another this problem does not exist. You are right in case where one omnipotent entity creates another omnipotent entity that is not like the former in this case they can indeed conflict, but I don't see how that breaks logic - it simply makes former omnipotent guy to feel a bit silly sometimes for thinking weird for no explainable reason, and doing weird stuff like loosing his omnipotence from time to time.... :)
    – Matas Vaitkevicius
    Aug 31, 2016 at 11:30
  • @MatasVaitkevicius: Yes identical copies may not suffer the problem, but my point still stands that it is a logical necessity for all weakly omnipotent entities to have the same volition. Identical copies do indeed have the same volition. Creating a second entity with an independent volition implies that the second entity is constrained to do only what the first entity wills, simply because the first entity by definition can do anything that is logically possible, which presumably includes not creating the second entity.
    – user21820
    Aug 31, 2016 at 11:35
  • So what you are saying: It would not be possible to create second entity that is not constrained to do only what the first entity wills - as it would invalidate first ones omnipotence, but that same thing would apply to the first entity too otherwise second entity would not be created fully omnipotent. But for first one to be omnipotent it must be able to do anything (including creating second entity that is not constrained to do only what the first entity wills), and this contradicts itself.... correct?
    – Matas Vaitkevicius
    Aug 31, 2016 at 11:52
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omnipotent

adjective

  1. almighty or infinite in power, as God.
  2. having very great or unlimited authority or power.

power

noun

  1. ability to do or act; capability of doing or accomplishing something.

So an omnipotent Being's abilities are unlimited. Now, what kind of abilities can exist? Since the abilities of an omnipotent Being do not diminish in potency, in order to create another omnipotent Being, it is required that one omnipotent Being possesses the ability of reproduction or emanation of beings.

Omnipotent Being is one, unlimited and complete. However, he can expand himself in many unique omnipotent expansions and still remain intact or undiminished. This is possible in infinities or unlimited potentialities.

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