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YKY comments on Deleting paradoxes with fuzzy logic - Less Wrong
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A conjecture (seems easy to prove):
"If, in a fuzzy logic where truth values range from [0,1], we allow logical operators (which are maps from [0,1] to [0,1]) or predicates that does not intersect the slope=1 line, then we can always construct a Liar's Paradox."
An example is the binary predicate "less-than", which has a discontinuity at 0.5 and hence does not intersect the y=x line.