Illusion and Reality

I. Introduction The proof of Gödel's incompleteness theorem is found mainly in Chapter I and Chapter II of his 1931 paper [1]: in Chapter I, Gödel introduces the main idea of his proof, which is to construct a paradoxical proposition saying that it is itself unprovable by using the traditional Cantor’s diagonal method; in Chapter II, Gödel translates directly this paradoxical proposition in the formal system he defines, and claims that this paradoxical proposition is a « factual »  « undecidable proposition » in his formal system, thus concludes that his formal system is incomplete. Gödel's paradoxical proposition is a replica of Liar's Paradox, so deciphering Liar's Paradox becomes a key point in deciphering the proof of Gödel's Incompleteness theorem! II. Liar's paradox, self-reference and general processes Liar's Paradox represents a class of paradoxes that are closely related to self-reference, and it can be said that self-reference is the « cause »