How to eliminate self-reference: A précis

Synthese 158 (1):127 - 138 (2007)
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
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References found in this work BETA
Roy T. Cook (2004). Patterns of Paradox. Journal of Symbolic Logic 69 (3):767-774.
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Stephen Yablo (2004). Circularity and Paradox. In Thomas Bolander, Vincent F. Hendricks & Stig Andur Pedersen (eds.), Self-Reference. Csli Publications. 139--157.
Citations of this work BETA
Ming Hsiung (2013). Equiparadoxicality of Yablo's Paradox and the Liar. Journal of Logic, Language and Information 22 (1):23-31.
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