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)

In recent decades deflationary theories of truth have been challenged with a technical argument based on the notion of conservativeness. In this paper, I shall stress that conservative extensions of theories and expandability of their models are not equivalent notions. Then, I shall argue that the deflationary thesis of the unsubstantiality of truth is better understood as leveraging on the stronger notion of expandability of models. Once expandability is involved in the argument, some notable consequences follow: the strategy proposed by (...) Hartry Field in response to the conservativeness objection is strongly undermined and even simpler proposals (such as theories based on standard t-sentences) are shown to be quite problematical. (shrink)

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants of Kripke–Feferman truth. The first, \, features a consistent but partial truth predicate. The second, \, an inconsistent but complete truth predicate. It is known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability, under natural assumptions, coincides with (...) definitional equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of \ and \ raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)

One way to study and understand the notion of truth is to examine principles that we are willing to associate with truth, often because they conform to a pre-theoretical or to a semi-formal characterization of this concept. In comparing different collections of such principles, one requires formally precise notions of inter-theoretic reduction that are also adequate to compare these conceptual aspects. In this work I study possible ways to make precise the relation of conceptual equivalence between notions of truth associated (...) with collections of principles of truth. In doing so, I will consider refinements and strengthenings of the notion of relative truth-definability proposed by Fujimoto (2010): in particular I employ suitable variants of notions of equivalence of theories considered in Visser (2006) and Friedman & Visser (2014) to show that there are better candidates than mutual truth-definability for the role of sufficient condition for conceptual equivalence between the semantic notions associated with the theories. In the concluding part of the paper, I extend the techniques introduced in the first and show that there is a precise sense in which ramified truth (either disquotational or compositional) does not correspond to iterations of comprehension. (shrink)

The existence of a close connection between results on axiomatic truth and the analysis of truth-theoretic deflationism is nowadays widely recognized. The first attempt to make such link precise can be traced back to the so-called conservativeness argument due to Leon Horsten, Stewart Shapiro and Jeffrey Ketland: by employing standard Gödelian phenomena, they concluded that deflationism is untenable as any adequate theory of truth leads to consequences that were not achievable by the base theory alone. In the paper I highlight, (...) as Shapiro and Ketland, the irreducible nature of truth axioms with respect to their base theories. But, I argue, this does not immediately delineate a notion of truth playing a substantial role in philosophical or scientific explanations. I first offer a refinement of Hartry Field’s reaction to the conservativeness argument by distinguishing between metatheoretic and object-theoretic consequences of the theory of truth and address some possible rejoinders. In the resulting picture, truth is an irreducible tool for metatheoretic ascent. How robust is this characterizaton? I test it by considering: a recent example, due to Leon Horsten, of the alleged explanatory role played by the truth predicate in the derivation of Fitch’s paradox; an essential weakening of theories of truth analyzed in the first part of the paper. (shrink)

In the paper we investigate typed axiomatizations of the truth predicate in which the axioms of truth come with a built-in, minimal and self-sufficient machinery to talk about syntactic aspects of an arbitrary base theory. Expanding previous works of the author and building on recent works of Albert Visser and Richard Heck, we give a precise characterization of these systems by investigating the strict relationships occurring between them, arithmetized model constructions in weak arithmetical systems and suitable set existence axioms. The (...) framework considered will give rise to some methodological remarks on the construction of truth theories and provide us with a privileged point of view to analyze the notion of truth arising from compositional principles in a typed setting. (shrink)

Recent work on formal theories of truth has revived an approach, due originally to Tarski, on which syntax and truth theories are sharply distinguished—‘disentangled’—from mathematical base theories. In this paper, we defend a novel philosophical constraint on disentangled theories. We argue that these theories must be epistemically stable: they must possess an intrinsic motivation justifying no strictly stronger theory. In a disentangled setting, even if the base and the syntax theory are individually stable, they may be jointly unstable. We contend (...) that this flaw afflicts many proposals discussed in the literature; we defend a new, stable disentangled theory, double second-order arithmetic. (shrink)

This paper investigates a set of issues connected with the so-called conservativeness argument against deflationism. Although I do not defend that argument, I think the discussion of it has raised some interesting questions about whether what I call “compositional principles,” such as “a conjunction is true iff its conjuncts are true,” have substantial content or are in some sense logically trivial. The paper presents a series of results that purport to show that the compositional principles for a first-order language, taken (...) together, have substantial logical strength, amounting to a kind of abstract consistency statement. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? Once the question has been properly formulated, the answer turns out to be about as elegant as one could want: Adding a theory of truth to a finitely axiomatized theory T is more or less equivalent to a (...) kind of abstract consistency statement. A large part of the interest of the paper lies in the way syntactic theories are 'disentangled' from object theories. (shrink)

Deflationism about truth describes truth as a logical notion. In the present paper, I explore the implication of the alleged logicality of truth from the perspective of axiomatic theories of truth, and argue that the deflationist doctrine of the logicality of truth gives rise to two types of self-undermining arguments against deflationism, which I call the conservativeness argument from logicality and the topic-neutrality argument.

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over (...) subject matters ‘richer’ than arithmetic, such as set theory. The move to this new formal setting provides deflationists with better defence and brings a broader perspective to the debate. (shrink)

In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purposes and has additional attractive properties.

This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Several ‘internal’ categoricity results have been discussed in the recent literature. Against the background of the philosophical position called internalism, we propose and investigate truth-theoretic versions of internal categoricity based on a primitive truth predicate. We argue for the compatibility of a primitive truth predicate with internalism and provide a novel argument for (and proof of) a truth-theoretic version of internal categoricity and internal determinacy with some positive (...) properties. (shrink)

The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still lacking. We (...) provide an axiomatization of the minimal commitments implicit in the acceptance of a mathematical theory. The theory entails that the Uniform Reflection Principle is part of one’s implicit commitments, and sheds light on why this is so. We argue that the theory has significant epistemological consequences in that it explains how justified belief in the axioms of a theory can be preserved to the corresponding reflection principle. The theory also improves on recent analyses of implicit commitment based on truth or epistemic notions. (shrink)

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the philosophy of language (...) and philosophical logic, such as Kripke's possible worlds semantics for modal logic. We also examine the paradoxical decomposition of the sphere known as the Banach–Tarski paradox. Finally we examine Tarski's work on decidable and undecidable theories, which he carried out in collaboration with students such as Mostowski, Presburger, Robinson and others. (shrink)

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants Kripke-Feferman truth. The first, KF+CONS, features a consistent but partial truth predicate. The second, KF+COMP, an inconsistent but complete truth predicate. It is well-known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability under natural assumptions coincides with definitional (...) equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of KF+CONS and KF+COMP raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)