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Crap, walking perpendicular up a wall is an action so long as you consider spiders and other insects beings.
My point is, an action that cannot be achieved by any being is not an action at all, merely an IDEA in the mind.
The impossibility of ominscience is going to take some thought. I think it is key to remember that any being that is omniscient is god, in the concept that humanity in general understands what god is. So proving the impossibility of omniscience would corelate to the proving the impossibility of a god.
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Man is condemned to be free
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