Now here comes the punch line. Let NO be the set of all non-ouroboric sets. NO seems like a weird thing to think about, but if Frege’s definition allows it into the world of sets, so must we. Is NO ouroboric or not? That is, is NO an element of NO? By definition, if NO is ouroboric, then NO cannot be in NO, which consists only of non-ouroboric sets. But to say NO is not an element of NO is precisely to say NO is non-ouroboric; it does not contain itself. But wait a minute—if NO is non-ouroboric, then it is an element of NO, which is the set of all non-ouroboric sets. Now NO is an element of NO
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