Truth predicate

Abstract: It is conceded by most philosophers of language, and recently even by some linguists, that a satisfactory theory of meaning must give an account of how the meanings of sentences depend upon the meanings of words. Unless such an account could be supplied for a particular language, it is argued, there would be no explaining the fact that we can learn the language: no explaining the fact that, on mastering a finite vocabulary and a finitely stated set of rules, we are prepared to produce and to understand any of a potential infinitude of sentences. I do not dispute these vague claims, in which I sense more than a kernel of truth.1 Instead I want to ask what it is for a theory to give an account of the kind adumbrated.

Abstract: Preface Introduction PART ONE: A SELECTIVE BACKGROUND 1. Chapter 1: Self-Reference and Tarski>'s Theorem 2. Validity and the Unprovability of Soundness 3. Kripke>'s Theory of Truth (Strong Kleene Version) 4. Adding a Conditional? Curry and Lukasiewicz 5. Interlude on Vagueness, and the Paradoxes of Konig and Berry PART TWO: BROADLY CLASSICAL APPROACHES 6. Introduction to the broadly classical options 7. Truth-Value Gaps in Classical Theories 8. Truth-value Gluts in Classical Theories 9. A Second Interlude on Vagueness 10. Introduction to Supervaluational Approaches to Paradox 11. A Survey of Supervaluational and Revision-Rule Theories 12. Are Supervaluational and Revision Theories Self-Undermining? 13. Intersubstitutivity and the Purpose of Truth 14. Stratified and Contextual Theories STRATIFIED AND CONTEXTUAL THEORIES 15. What Is To Be Done? 16. Fixed Points and Revision Rules for Conditionals 17. More on Revision-theoretic Conditionals 18. What Has Been Done PART FOUR: MORE ON PARACOMPLETE SOLUTIONS 19. Validity, Truth-Preservation and the Second Incompleteness Theorem 20. Other Paradoxes 21. Do Paracomplete Solutions Depend on Expressive Limitations? 22. Determinateness, Hyper-determinateness, Super-Determinateness and Revenge PART FIVE: PARACONSISTENT DIALETHEISM 23. An Introduction to Paraconsistent Dialetheism 24. Some Dialetheic Theories 25. Paraconsistent Dialetheism and Soundness 26. Hyper-determinacy and revenge Bibliography

Abstract: In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological contexts. The latter include, for instance, contexts that generate Liar Paradox. Their central claim is that truth is a circular concept. In support of this claim they provide a widely applicable theory (the "revision theory") of circular concepts. Under the revision theory, when truth is seen as circular both its ordinary features and its pathological features fall into a simple understandable pattern. The Revision Theory of Truth is unique in placing truth in the context of a general theory of definitions. This theory makes sense of arbitrary systems of mutually interdependent concepts, of which circular concepts, such as truth, are but a special case.

Abstract: This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning—one which takes meaning to be constituted by assertibility and deniability conditions—and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system—ST—that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a ...