Even though disquotationalism is not correct as it is usually formulated, a deep insight lies behind it. Specifically, it can be argued that, modulo implicit commitment to reflection principles, all there is to the notion of truth is given by a simple, natural collection of truth-biconditionals.

Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: of the system KF of Feferman formulated in classical logic, and the system PKF of Halbach and Horsten, formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the (...) reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true. (shrink)

Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory $\mathsf {T}$ or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between reflection principles (...) and principles of mathematical and transfinite induction as well as the status of the latter with respect to various foundational characterizations of number theory. (shrink)

At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the (...) philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth. (shrink)

This book is a collection of important writings on deflationism, with a detailed introduction and an exhaustive annotated bibliography. Among philosophers concerned with the theory of truth, deflationist positions have quickly gained ground and have become the most popular. Yet heretofore there has been no single book to which the readers can go for a detailed, overall view of the entire phenomenon of deflationism. This is the only available map of the whole terrain of deflationism. -/- Deflationism is a comparatively (...) new approach, though it has its roots in the thinking of some philosophers in the early twentieth century. Deflationism rejects all the traditional theories of truth: the correspondence theory (truth corresponds with facts), the coherence theory (truth is membership of a coherent set of beliefs), the pragmatist theory is provability or verifiability). This book gives complete coverage to all the different varieties of deflationism, and to earlier philosophers who anticipated deflationism. The articles and exerpts include classic works by Frege, Ayer, Ramsey, Tarsk, and Quine, and recent works by the leading deflationist authors of today: Paul Horwich, Hartry Field, Stephen Schiffer, Robert Brandom, and Stephen Leeds. (shrink)