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How to eliminate self-reference: a précis

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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.

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References

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  1. 2820 3rd Street No. 6, Santa Monica, CA, 90405, USA

    Philippe Schlenker

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  1. Philippe Schlenker
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Correspondence to Philippe Schlenker.

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Schlenker, P. How to eliminate self-reference: a précis. Synthese 158, 127–138 (2007). https://doi.org/10.1007/s11229-006-9054-8

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  • DOI: https://doi.org/10.1007/s11229-006-9054-8

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