RADICAL ANTI‐DISQUOTATIONALISM

Abstract

A number of ‘no-proposition’ approaches to the liar paradox find themselves implicitly committed to a moderate disquotational principle: the principle that if an utterance of the sentence ‘P ’ says anything at all, it says that P (with suitable restrictions). I show that this principle alone is responsible for the revenge paradoxes that plague this view. I instead propose a view in which there are several closely related language-world relations playing the ‘semantic expressing’ role, none of which is more central to semantic theorizing than any other. I use this thesis about language and the negative result about disquotation to motivate the view that people do say things with utterances of paradoxical sentences, although they do not say the proposition you’d always expect, as articulated with a disquotational principle. Consider a self-referential utterance, u, of the sentence ‘u is not true’. According to one widespread and appealing intuition when one makes a semantically paradoxical utterance such as u one simply does not succeed in saying anything. Call this the no proposition theory. No proposition theorists reject the disquotational assumption that utterances of ‘u is not true’ say that u is not true on the grounds that some utterances of ‘u is not true’ do not say anything at all. However, they may nonetheless subscribe to a qualified version of the principle that says that if an utterance of ‘u is not true’ says anything at all it says that u is not true. In this paper I shall show that such views are susceptible to a version of the revenge paradoxes. An examination of these paradoxes suggests a view in which paradoxical utterances such as u do say things, although they do not say what you might expect them to (in this case, that u is not true). I shall show, moreover, that this phenomena falls out of general considerations about the relation between language and the world, and is much more widespread than many have thought. In this paper we will be primarily be investigating the corner of philosophical space that accepts classical logic and that admits quantifiers that bind variables taking sentence position. Unless otherwise stated, that framework will be assumed throughout. 1 No Proposition Accounts of the Paradoxes The most straightforward version of the no proposition theory maintains that sentences like ‘u is not true’ are completely meaningless, and thus that any attempt to say something by making an utterance of this sentence would fail. Call this the non-contextual view. On the non-contextual view, then, all utterances of a paradoxical sentence are equally bad. ∗Thanks to ... 1Restrictions might exclude sentences which express different propositions in different contexts, such as sentences involving indexical expressions. 2Of course, neither of these assumptions are uncontentious; but see Prior [19] and Williamson [28] for a defense of the intelligibility of quantification into sentence position, and Williamson [29] for general methodological remarks about the application of classical logic to the liar paradox. For a recent approach to the liar that relaxes classical propositional logic, see Field [8]. For a discussion of approaches that relax the classical rules for the propositional quantifiers see Bacon, Hawthorne and Uzquiano [2].