Abstract

Central to the liar paradox is the phenomenon of 'self-reference'. The paradox typically begins with a sentence like: (L): (L) is not true Historically, doubts about the intelligibility of self-reference have been quite common. In some sense, though, these doubts were answered by Kurt Gödel's famous 'diagonal lemma'. This paper surveys some of the methods by which self-reference can be achieved, focusing first on purely syntactic methods before turning attention to the 'arithmetized' methods introduced by Gödel. It's primary lesson is that we need to be more careful than we usually have been about self-reference.