Paradox with just Self-Reference

T. Parent
Virginia Tech
If a semantically open language has no constraints on self-reference, one can show there is a predicate which is both satisfied and unsatisfied by a self-referring term. The argument requires diagonalization on a definition-scheme for the predicate ‘x is Lagadonian’. (The term ‘Lagadonian’ is adapted from David Lewis). Briefly, a self-referring term is counted as “Lagadonian” if the initial variable in the schema is replaced with the term itself. But the same term is not counted as Lagadonian if this variable is replaced with the quotation or other name for the term. Thus the term both satisfies and does not satisfy ‘x is Lagadonian’. Finally, a related paradox is presented, which requires no self-referring name; it rather depends on a definite description for the sentence containing the description.
Keywords Self-Reference  Circularity  Paradox  Yablo, Stephen  Tarski, Alfred  Godel, Kurt
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