How to eliminate self-reference: a précis

Author: Schlenker, Philippe

Source: Synthese, Volume 158, Number 1, September 2007 , pp. 127-138(12)

Publisher: Springer

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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 h ₀(F), h ₁(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

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11229-006-9054-8

Affiliations: 1: Email: schlenke@free.fr

Publication date: 2007-09-01