property-theoretic

Kurt Gödel is reported to have remarked ‘‘There never were any set-theoretic paradoxes, but the property-theoretic paradoxes are still unresolved.’’ The idea behind the first part of his remark is presumably that the notion of set was hierarchical from the start, so that it should have been obvious all along that there was no Russell set (in the mathematical sense of ‘set’). The idea behind the second part is that this obvious resolution of Russell’s ‘‘paradox’’ for sets simply doesn’t carry over to the paradox for properties.