Virtual Logic — The Flagg Resolution
Louis Hirsch Kauffman · 1999
Consider the statement: J= ‘This statement is false.’ If J is true then J states that J is false. If J is false then J states that J is true. Thus we can write J = Not J. One might shun such a statement, but perhaps there is a way to deal with it. One solution that has been proposed is to say that J has a new kind of truth value, neither true nor false, and to devise a logic with more than two truth values in which the statement J can live. In this 3 (or more) — valued logic some rules of standard logic and set theory have to be sacrificed. To see how this sacrifice comes about, consider the following statement S =J or Not J. If S were a statement in ordinary logic, we would say that S is true, since (P or Not P) is true for any statement P in ordinary logic. Thus True = J or No J.