In a series of recent papers, 1 Hartry Field has proposed a novel class of solutions to the semantic paradoxes, and argued that the new solutions are ‘revenge-immune’. He has argued, in particular, that by building on a sufficiently expressive language one can get a language which is able to express its own semantic theory, including its own truth predicates and any intelligible determinacy predicates. The purpose of this note is to argue that the plausibility of Field’s revenge-immunity claim depends crucially on the status of higher-order languages. We show that by availing oneself of higher-order resources one can give an explicit characterization of the key semantic notion underlying Field’s proposal, and note that inconsistency would ensue if the languages under discussion were expressive enough to capture this notion. 1 Field’s Proposal For the sake of concreteness, we shall consider the version of the proposal developed in Field (2003a) and further elucidated in Field’s contribution to the present volume. Start with a standard first-order language L containing the set-theoretic primitives ‘∈’ and ‘Set(...)’, together with an arbitrary selection of non-set-theoretic predicates. On

Die Wahrheit liegt weder in der unendlichen Annährung an einer objektiv Gegebenes noch in der Mitte, sondern rundherum wie ein Sack, der mit jeder neuen Meinung, die man hineinstopft, seine Form ändert, aber immer fester wird. R. Musil We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of those sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games are simple, those over the natural model of arithmetic being all within the arithmetical class of Σ 0 3. 1

We consider notions of truth and logical validity defined in various recent constructions of Hartry Field. We try to explicate his notion of determinate truth by clarifying the path dependent hierarchies of his determinateness operator. Hartry Field in a recent series of papers ([2],[3],[5] in [1]) has indicated how we might approach a theory of truth and associated semantic paradoxes, by providing an inventive alternative to the current semantic theories of Kripke [10], Herzberger [9],[8], Gupta & Belnap [6], et al. In his recent book ‘Saving Truth from Paradox ’ ([4]), building on his earlier papers, he provides both a deep analysis of those currently available constructions of theories of truth, and an account of his own. The book is perhaps the culmination of his thinking and insights in this topic to date. It is a very rich and detailed tapestry that he weaves. A thumbnail sketch of Field’s project might run as follows: (I) the current

This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed. 1 New questions for the Revision Theory of Truth The Revision Theory of Truth is a class of models for the language of truth (LT). This language of truth is intended to be a toy model for a natural language such as English. It is intended to contain all the features that are relevant for the logical properties of the notion of truth, and no more than that. LT contains the first-order language of arithmetic (LPA), so as to enable sentences to talk about themselves relative to some coding scheme. Versions of this article have presented at the Truth Be Told conference in Amsterdam