Wednesday, August 5, 2009
A Universal Set and Illogical State-ments made Logical
So a universal set may only exist within one universe. It may not extend across universes. However, relationships (information) between sets may exist across universes. Thus a set A may be a member of a set B in one universe, and the set A not be a member of a set B in another universe. Russell's Paradox only exists if you are referring to a single universe. There must be something about Russell's Paradox which is an informatic way of creating separate universes. A paradox is when conflicting things can be held true at the same time. Each side of the paradox exists in one universe, and is a totally acceptable way of talking about it. If A holds in one universe, and not A holds in another universe, then one may say A and not A holds true. If you are only referring to one universe, then both A and not A can not hold true at the same time (but they may at different times). If you think about a single universe of logic, then A and not A must be a false statement, and A or not A must be a true statement. If you think about multiply present universes, then A and not A may or may not be true, and A or not A may or may not be true.
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