Formalized Self-Reference

Abstract

Elsewhere [1] I have argued that the concept of self-reference has important applications in philosophy. These applications are a reason for trying to handle the concept as rigorously and formalistically as possible. In this connection, I have constructed asystem of logic CΓ [3] which can be shown to be consistent if the rule for ‘η’ is omitted, and within which at least some aspects of self-reference can be represented. I will now sketch this logic and show how it deals with the Russell Paradox and the Grelling Paradox.