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I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could create a round triangle" (add additional qualifiers, here and to the solution, if you feel there is not a true contradiction). If we don't want to say such a statement is true, which most theists do not, we must ask why it's not true. It seems the proposition can be divided into in three parts:

1) If X exists, it is round

2) If X exists, it is a triangle

3) God could cause X to exist.

The proposition can be sensibly said not to affect the definition of omnipotence because it is the conjunction of 1 and 2 that cannot be true. A round triangle is not a "thing." The problem has nothing to do with the truth value of 3. Perhaps we could paraphrase by saying it's not the instantiation of a round triangle that causes the problem, but the mere concept of a round triangle.

What I'm curious about is whether such a solution to omnipotence paradoxes carries any weight at all on Meinongian views. Would a round triangle, a married bachelor, or a stone too heavy for God to move exist in Meinong's Jungle? If so, is there any reason such things could not "exist in the world," so to speak, aside from God's inability to instantiate them?

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    "If X exists, it is a triangle"? I don't think this is a correct logical analysis... It follows from this that everything is a triangle. – Eliran May 21 '16 at 19:03
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    A round triangle is not a "thing." Correct: it is a concept. An inconsistent concept cannot be "instantiated", because an object instantiating it must have and have not a certian property. An "example" of round triangle would be a geometric object having three angles and at the same time not having three angles (circles have no vertices). And we "do not like" contradictions... – Mauro ALLEGRANZA May 21 '16 at 19:12
  • @EliranH Hmm, I chose that wording over "X is round" and "X is a triangle" just to be super careful about meeting anyone's criteria for ontological commitment to X. Is there a better wording that's unambiguously non-committing? – user20658 May 21 '16 at 20:07
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    Even for Meinong round triangles do not exist, they only subsist. Meinongian logics have existence predicate in addition to quantifier, and round triangles are on the negated side of it. If that's enough to deliver God then God is delivered. Trickery doesn't remove the dilemma: God is or is not bound by the laws of logic. Aquinas and most Catholics explicitly say he is, so he can not create inconsistent entities, he is also bound by his nature, e.g. can't do evil. Those who like mystics say that he is not have a very simple "explanation": God is ineffable. Either way, no tricks are required. – Conifold May 21 '16 at 23:10
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    Omnipotence in Latin does not mean can do everything it means having all authority, omni potens or all powerful. I understand that modern translation has redefined its meaning to include, “can do anything” but that is not the claim made of the God of the Bible. There are plenty He claims He cannot do but that doesn’t make Him less omnipotent because He is being described as having all power or all authority. @user20658 so a circle triangle has nothing to do with God, it has everything to do with human mind games. – Autodidact Apr 15 at 3:40
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You can look at this through the lens of "Mathematical fictionalism" http://plato.stanford.edu/entries/fictionalism-mathematics/ and the related sort of bounded dialethianism that results, allowing contradiction to harmlessly exist all over the place, even in something like Classical Logic.

The issue is not whether there is a consistent model of the universe. You can assume from the start that there just isn't. The question is how large your universe of discourse can get before it degenerates, instead. Something like Russell's paradox is a real contradiction inside Classical logic, but it is seldom entailed by anything, so it can just stay there, and other parts of the universe can still be useful. The resulting universe is huge and such large parts of it 'conserve truth', that it is worth having on hand as a tool.

If you take this notion of separate fictional universes seriously, but deny their fictionality from a Meinongian point of view, then yes, these things exist, but they cause the universes in which they would/do exist to be quite small, since they run into contradiction very quickly. Very little can be said that conserves the truth of its premises, unless none of the subjects involved have shapes.

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