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How to Eliminate Self-Reference: A Précis
Vol. 158, No. 1 (Sep., 2007), pp. 127-138
Published by: Springer
Stable URL: http://www.jstor.org/stable/27653578
Page Count: 12
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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.
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