Synthese

, Volume 158, Issue 1, pp 127–138 | Cite as

How to eliminate self-reference: a précis

Origina lPaper

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 

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References

  1. Cook R. (2004). Patterns of paradox. Journal of Symbolic Logic, 69(3): 767–774CrossRefGoogle Scholar
  2. Kripke S. (1975). Outline of a theory of truth. Journal of Philosophy, 72, 690–716CrossRefGoogle Scholar
  3. Leitgeb H. (2002). What is a self-referential sentence? Critical remarks on the alleged (non-)circularity of Yablo’s paradox. Logique et Analyse, (177–178): 3–14Google Scholar
  4. Schlenker, P. (2006). The elimination of self-reference. Journal of Philosophical Logic (to appear)Google Scholar
  5. Yablo S. (1993). Paradox without self-reference. Analysis, 53, 251–252CrossRefGoogle Scholar
  6. Yablo, S. (2004). Circularity and paradox. In: Self-reference, CSLI.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Santa MonicaUSA

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