Schlenker, P. 2005. "How to Eliminate Self-Reference: A Précis". Manuscript (9 pages), UCLA & IJN.
[Full paper in pdf]
Abstract: We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L' which contains a truth predicate and sentence names, and we associate to each sentence F of L' an infinite series of translations h0(F), h1(F), ..., stated in a quantificational language L*. Under certain conditions, we show that none of the translations is self-referential, but that any one of them mirrors perfectly the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, 2004) and Cook (2004), shows that under certain conditions self-reference is not essential to any semantic phenomena. [A longer and more technical version of the analysis is developed in 'The Elimination of Self-Reference'].