 The paradoxes above are all quite similar in structure. In the case of the paradoxes of Grelling and Russell, this can be seen as follows. Define the extension of a predicate to be the set of objects it is true of. For a predicate \(P\) we denote its extension by ext\((P)\). Grelling’s paradox involves the predicate heterological, which is true of all those predicates that are not true of themselves. Thus the extension of the predicate heterological is the set \(\{ P \mid  P \not\in\) ext\((P) \}\). Compare this to the Russell set \(R\) given by \(\{ x \mid  x \not\in x \}\). The only significant difference between these two sets is that the first is defined on predicates whereas the second is defined on sets. The proofs of contradictions based on these two sets also share the same structure, as seen below (where “het” abbreviates “heterological”):