Understanding Truth

Abstract Understanding Truth aims to illuminate the notion of truth, and the role it plays in our ordinary thought, as well as in our logical, philosophical, and scientific theories. Part 1 is concerned with substantive background issues: the identification of the bearers of truth, the basis for distinguishing truth from other notions, like certainty, with which it is often confused, and the formulation of positive responses to well‐known forms of philosophical skepticism about truth. Having cleared away the grounds for truth skepticism, the discussion turns in Part 2 to an explication of the formal theories of Alfred Tarski and Saul Kripke, including their treatments of the Liar paradox (illustrated by sentences like This sentence is not true). The success of Tarski's definition of truth in avoiding the Liar, and his ingenious use of the paradox in proving the arithmetical indefinability of arithmetical truth, are explained, and the fruitfulness of his definition in laying the foundations for the characterization of logical consequence in terms of truth in a model is defended against objections. Nevertheless, it is argued that the notion of truth defined by Tarski does not provide an adequate analysis of our ordinary notion because there are intellectual tasks for which we need a notion of truth other than Tarski's. There are also problems with applying his hierarchical approach to the Liar as it arises in natural language – problems that are avoided by Kripke's more sophisticated model. Part 2 concludes with an explanation of Kripke's theory of truth, which is used to motivate a philosophical conception of partially defined predicates – i.e., predicates that are governed by sufficient conditions for them to apply to an object, and sufficient conditions for them to fail to apply, but no conditions that are both individually sufficient and jointly necessary for the predicates to apply, or for them to fail to apply. While the advantages of understanding are true, to be a predicate of this sort are stressed at the end of Part 2, a theory of vague predicates according to which they are both partially defined and context sensitive is presented in Part 3. This theory is used to illuminate and resolve certain important puzzles posed by the Sorites paradox: a newborn baby is young, if someone is young at a certain moment, then that person is still young one second later, so everyone is young. The book closes with an attempt to incorporate important insights of Tarski and Kripke into a broadly deflationary conception of truth, as we ordinarily understand it in natural language and use it in philosophy.