Virtual logic — The MetaGame Paradox

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This is column number 10. In this column we shall discuss a recent relative [1],[2] of the Russell paradox, the Metagame Paradox. This paradox is related to a set theoretic paradox about well-founded sets, the Well-founded Set Paradox. These two paradoxes are both related to the basic nature of any observing system that would include itself in its own observations. I give you these paradoxes and a comment on the nature of the observer. Judge them for yourself. Near the end of the column we show how, by turning the paradox around, there are new proofs of uncountability of certain infinities. These proofs have the remarkable quality that they use a bit of imaginary reasoning, only to have it vanish just as it appears! It is this role of the imagination that is central to our theme. We reason by an imaginary detour. And we obtain a real answer.

Document Type: Research Article

Publication date: January 1, 1999

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