Eliminating Self-Reference

Philippe Schlenker

24 Oct 2008, 2:00pm, Class of 1947 Room

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 (i) none of the translations is self-referential, but that (ii) 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, 2004) and Cook (2004), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language.