Heterologicality and Incompleteness
Cezary Cieśliński · Mathematical logic quarterly · 2002
We present a semantic proof of Gödel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate “heterological” is itself heterological. We show that this sentence doesn't follow from T and is equivalent (provably in T) to the consistency of T. Finally we show how to construct a similar incompleteness proof for Peano Arithmetic.