I know you are trying to be rigorous, but your logic has far too many assumptions to be so. Firstly you assume that a property is eternal. Predicate logic would probably assume that if A exists, than that does not change, but the entire message I'm proposing is that this property can change. That is, God can create a stone and then make it uncrushable. Does God turning a stone from crushable into uncrushable imply that God has done something which God cannot do? I submit that no it does not because God can simply change that property back to crushable once more, and then crush the stone.
You are assuming that God is singular, but nothing in your logic requires that. You are also assuming that God is omnipotent.
So that's at least three pre-requisites that you did not state clearly. If you want to be rigorous perhaps you should start from a more basic set of axioms.
Will
In a message dated 8/1/2009 7:45:12 A.M. Pacific Daylight Time, brewhaha@freenet.edmonton.ab.ca writes:
Please allow me to start this proof from scratch and try to go from the paradox that is most interesting to the simple answer of no, and generalizing it to all paradoxes, refuting objections in a monologue, because it does not seem to contain equally powerful participants. Can God crush an uncrushable stone? In mechanically verifiable predicate logic notation, I can write "exists(God) implies not exists(UnCrushableStone)". Spelled out in plain English, that means God can do any thing, and that is singular, because if God can do any combination of things, then he can contradict himself and crush the stone, which does not allow for a self-consistent proof, because that allows God to prove that the uncrushable stone did not exist in the first place. exists(UnCrushableStone) implies not exists(God). Translation: If the uncrushable stone exists, then God does not, because the stone's existence implies something God cannot do and God can do any thing. Either God exists or the UnCrushableStone exists (and not both). exists(God) xor exists(UnCrushableStone). For God to crush the uncrushable stone requires both God and the uncrushable stone to be present at the same time. not(exists(God) and exists(UnCrushableStone)). Their existence is mutually exclusive. In any true paradox that demands a contest between two beings with an ultimate power, and where those two beings exclude each other, the answer is no, because those two beings cannot exist at once. So, what happens if God creates the uncrushable stone? He cannot do that without changing himself in the same move. In creating the uncrushable stone, he creates something that is not possible, so God would no longer be omnipotent. If God is no longer omnipotent, then no God is. _______ "Another round, Mr. Descartes?" "I think not," said Descartes, who promptly vanished. "Can you think?", I asked, putting Descartes before the horse. We are Descartes of Borg: We assimilate, therefore we are.
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