This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (shrink)

What is the property of being true like? To answer this question, begin with a Canberra-plan analysis of the concept of truth. That is, assemble the platitudes for the concept of truth, and then investigate which property might satisfy them. This project is aided by Friedman and Sheard’s groundbreaking analysis of twelve logical platitudes for truth. It turns out that, because of the paradoxes like the liar, the platitudes for the concept of truth are inconsistent. Moreover, there are so many (...) distinct paradoxes that only small subsets of platitudes for truth are consistent. The result is that there is no property of being true. The failure of the Canberra plan analysis of the concept of truth, points the way toward a new methodology: a conceptual engineering project for the concept of truth. Conceptual engineering is assessing the quality of our concepts, and when they are found defective, offering new and better concepts to replace them for certain purposes. Still, there are many aletheic properties, which are properties satisfied by reasonably large subsets of platitudes for the concept of truth. We can treat these aletheic properties as a guide to the multitude of new aletheic concepts, which are concepts similar to, but distinct from, the concept of truth. Any new aletheic concept or team of concepts might be called on to replace the concept of truth. In particular, the concepts of ascending truth and descending truth are recommended, but the most important point is that we need a full-scale investigation into the space of aletheic properties and new aletheic concepts—that is, we need an Aletheic Principles Project. (shrink)

This paper compares the roles classical and intuitionistic logic play in restricting the free use of truth principles in arithmetic. We consider fifteen of the most commonly used axiomatic principles of truth and classify every subset of them as either consistent or inconsistent over a weak purely intuitionistic theory of truth.

This paper explores the interface between principles of self-applicable truth and classical logic. To this end, the proof-theoretic strength of a number of axiomatic theories of truth over intuitionistic logic is determined. The theories considered correspond to the maximal consistent collections of fifteen truth-theoretic principles as isolated in Leigh and Rathjen.

This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.

As is mentioned in Leigh :845-865, 2015), it is an open problem whether for several axiomatic theories of truth, including Friedman–Sheard theory \ and Kripke–Feferman theory \ :690-716, 1976), there exist cut-elimination arguments that give the upper bounds of their proof-theoretic strengths. In this paper, we give complete cut-elimination results for several well-known axiomatic theories of truth. In particular, we treat the systems \, and \ \\) of Friedman and Sheard’s theories and \.

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection principle, (...) are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

Against the backdrop of the frequent comparison of theories of truth in the literature on semantic paradoxes with regard to which inferences and metainferences are deemed valid, this paper develops a novel approach to defining a binary predicate for representing the valid inferences and metainferences of a theory within the theory itself under the assumption that the theory is defined with a classical meta-theory. The aim with the approach is to obtain a tool which facilitates the comparison between a theory (...) and its competitors within the theory itself, thereby expressing the disagreement between the theories within the theories. After discussing what we can and should require of an object-linguistic representation of a theory for that purpose, this paper proposes to restrict the representation of valid metainferences to locally valid metainferences, a requirement which turns out to be \-consistent and conservative over classical first-order arithmetic. This approach is then applied to four theories definable on strong Kleene models using a labelled nested sequent calculus. (shrink)

Why is it that even strong formal theories of truth fail to prove their own consistency? Although Field has addressed this question for many theories of truth, I argue that there is an important and attractive class of theories of truth that he omitted in his analysis. Such theories cannot prove that all their axioms are true, though unlike many of the cases Field considers, they do not prove that any of their axioms are false or that any of their (...) rules of inference are not truth preserving. I argue that it is the fact that such theories are not finitely axiomatizable that stops them from proving their own consistency. (shrink)

The article shows a simple way of calibrating the strength of the theory of positive induction, ${{\rm ID}^{*}_{1}}$ . Crucially the proof exploits the equivalence of ${\Sigma^{1}_{1}}$ dependent choice and ω-model reflection for ${\Pi^{1}_{2}}$ formulae over ACA 0. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of ${{\rm ID}^{*}_{1}}$ in Probst, J Symb Log, 71, 721–746, 2006.

Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...) -- Reflection -- Ontological reduction -- Applying theories of truth. (shrink)