Minimalism and Paradoxes

This paper argues against minimalism about truth. It does so by way of a comparison of the theory of truth with the theory of sets, and consideration of where paradoxes may arise in each. The paper proceeds by asking two seemingly unrelated questions. First, what is the theory of truth about? Answering this question shows that minimalism bears important similarities to naive set theory. Second, why is there no strengthened version of Russell’s paradox, as there is a strengthened Liar paradox? Answering this question shows that like naive set theory, minimalism is unable to make adequate progress in resolving the paradoxes, and must be replaced by a drastically different sort of theory. Such a theory, it is shown, must be fundamentally non-minimalist. Why is there no strengthened version of Russell’s paradox, as there is a Strengthened Liar paradox? This question is rarely asked. It does have a fairly standard answer, which I shall not challenge. But I shall argue that asking the question helps to point out something important about the theory of truth. In particular, it raises a serious challenge to an increasingly popular version of deflationism about truth. To see what the problem is, it is useful to ask another slightly offbeat question. What is the theory of truth about? There is, of course, an obvious answer to this question: the theory of truth is about truth bearers and what makes them true. Taken at face value, this answer seems to bring with it a commitment to a substantial notion of truth. A deflationist about truth might well wish to give a very different answer: the theory of truth is not really about anything. There is no substantial property of truth, so there is nothing—no domain of objects, or properties, or phenomena—which the theory of truth describes. Not all positions called ‘deflationism’ subscribe to this view, but the important class of so-called minimalist views do. I shall argue that this sort of deflationist answer is untenable, and thus argue in broad strokes against minimalism. I shall argue by way of a comparison of the theory of truth with the theory of sets, and consideration of where paradoxes may arise in each. I shall show that deflationist positions that accept the idea that truth is not a real or substantial property are too much like naive set theory. Like naive set ∗ Thanks to Otavio Bueno, Alex Byrne, Ned Hall, Richard Heck, Jim Pryor, Susanna Siegel, Ralph Wedgwood, and Steve Yablo for valuable comments and discussions. Thanks also to two anonymous referees for this journal. A version of this material was presented at the Society for Exact Philosophy Annual Meeting, 2001. I am grateful to my audience there for many useful comments and questions. c © 2001 Kluwer Academic Publishers. Printed in the Netherlands. MinimalismParadoxes.tex; 27/12/2001; 15:29; p.1