Questioning Gödel's Ontological Proof: Is Truth Positive? - Damschen, Gregor (European journal for philosophy of religion, 2011)
In his Ontological proof, Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property f: If f is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false.