Paradox with just self-reference

T. Parent

Published 2016-11-02Version 1

If a semantically open language allows self-reference, one can show there is a predicate which is both satisfied and unsatisfied by a self-referring term. The argument amounts to diagonalization on substitution instances of 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'.