Synthese

, Volume 158, Issue 1, pp 127–138

How to eliminate self-reference: a précis

Origina lPaper

DOI: 10.1007/s11229-006-9054-8

Cite this article as:
Schlenker, P. Synthese (2007) 158: 127. doi:10.1007/s11229-006-9054-8

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 perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language.

Keywords

Paradox Semantics Self-reference Yablo’s paradox 

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Santa MonicaUSA

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