Chris M,
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I would debate this point as well, but I'd agree that it's a different discussion.
LOL looking back I made an error, it's the Platonic world view that was being destroyed. If you have a chance check out "Philosophy in the Flesh: The embodied mind and its challenge to western thought" Lakoff and Johnson.
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Regarding your math, in what way is C a mapping from pSA (powerset of SA) to SA? It seems to me like pSA is larger than SA regardless of C, which seems to me like an additional function applied to S that changes neither SA nor pSA. Can you clarify?
For every possible subset S of SA there is a unique possible action C(S)
The power set (set of all subsets) therefore has one C(S) per subset S; a 1-to-1 mapping. All C(S) must be in SA by definition; so given that there are actions other than C in the set SA, this leads to the conclusion that SA is larger than its own power set. Which is a contradictory conclusion.
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Regarding Christianity, insofar as it seems to be the main object in our discussion, monotheism is at least as indebted to Hellenic philosophy as to Judaism.
Can you site me examples in Hellenistic Philosophy that affirms your statement that an omnipotent being is bound by logic. The trinity is most certainly a Hellenistic construct where God or should I I say "Gods" are breaking the law of identity.
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In this case, the ideological motivation behind omnipotence is not at all as you describe, but rather because omnipotence arises as a natural property of the agent being conceived. For instance, there is no action, nor even one possible, to whose causation cannot be traced ultimately to the Unmoved Mover, by very definition.
Aristotle, Kalam, Aquinas... no one really has been able to make this argument work without contradictory propositions.
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To this I would add only, that you may be enticed to argue that I am able to defend the logical consistency of the monotheistic God on my own terms, but that this is a hollow, or perhaps only narcissistic, victory insofar as it has no implications beyond my personal terms and into the tradition of monotheism as such. To this I would object most strongly, noting that the terms I describe are not at all personal to me, but rather derived from the tradition of philosophical thought which I described at the beginning of this post, and which is most central to monotheistic concepts in the Western tradition.
Okay, now you're anticipating my response and answering before I get a chance to respond. In the interest of a charitable discussion I suggest that we each refrain from this type of debate.