This paper examines the various Liar paradoxes and their near kin, Grelling's paradox and Gödel's Incompleteness Theorem. All are found to spring from circular definition – whether of statements, predicates, or sentences – a manoeuvre that generates the fatal disorders of the Liar syndrome: semantic vacuity, semantic incoherence, and predicative catalepsy. Afflicted statements, such as the Liar statement, fail to be genuine statements, and hence say nothing – a point that invalidates the arguments on which the various paradoxes rest. Formal systems are found to require disambiguators to distinguish the pseudostatements from their genuine doubles. Gödel's Theorem is shown to be fallacious, and measures are proposed to correct the conceptual mistakes on which it is based.
© Philosophia Press 2002