The thread topic seems rather trivial until you consider that "possibility", much like the set theory problem above, is really a non-referential linguistic operation that describes our use of language rather than any particular referent or experience except the experience of using language. A statement of possibility describes a hypothetical validity rather than a factual validity because it pertains to the unknown, but as the unknown becomes known then the hypothetical possibilities narrow toward the factual reality. Thus "possibility" pertains to knowledge rather than reality. Even your set theory problem makes more sense after considering that "sets" are a useful product of psychology and language rather than empirical investigation of the world, and insofar that a set is imaginary a set is free to produce the sorts of contradictions that are necessary to guide a logical operation toward its appropriate conclusion.
err "factual *veracity*", not "validity"
A good analogy is a wrench that doesn't fit any bolts. The wrench still exists, it just doesn't work. If my cult happened to worship that mis-shapen wrench, however, that wrench would suddenly become an important aspect of my world in the minds of myself and culties.
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