This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

In this ingenious and powerfully argued book Tim Maudlin sets out a novel account of logic and semantics which allows him to deal with certain notorious paradoxes which have bedevilled philosophical theories of truth. All philosophers interested in logic and language will find this a stimulating read.

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

Of course, for all that it may illustrate the frame of mind in which distinctively classical principles can seem unassailable, this reasoning tacitly ...

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

In this book, Scott Soames illuminates the notion of truth and the role it plays in our ordinary thought as well as in our logical, philosophical, and scientific theories. Soames aims to integrate and deepen the most significant insights on truth from a variety of sources. He powerfully brings together the best technical work and the most important philosophical reflection on truth and shows how each can illuminate the other. Investigating such questions as whether we need a truth predicate at (...) all, what theoretical tasks it allows us to accomplish, and how we are to understand the content of any predicate capable of accomplishing these tasks, Soames organizes his discussion into three parts. Part I addresses crucial foundational issues as it identifies the bearers of truth, provides a basis for distinguishing truth from other notions, and formulates positive responses to well-known forms of truth-skepticism. Part II explicates the formal theories of Alfred Tarski and Saul Kripke and evaluates the philosophical significance of their work. It discusses their treatments of the Liar paradox, the relationship between truth and proof, the notion of a partially defined predicate, the concepts of logical truth and logical consequence, and the connection between truth and meaning. Part III extends important lessons drawn from Tarski and Kripke into new domains: vague predicates, the Sorites paradox, and the development of a larger, deflationary perspective on truth. Throughout the book, Soames examines a wide range of deflationary theories of truth, and attempts to separate what is correct and worth preserving in them from what is not. In doing so, he seeks to clear up many of the most significant philosophical doubts about truth. Written for a general audience while offering engaging material to the specialist, this rich study will be profitably read by both. (shrink)

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. He has illuminated Aristotle’s syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection, and has worked to debunk the theory of descriptions. This volume brings together new articles by an international roster of leading logicians and philosophers in order to honour Smiley’s work. Their essays will be of significant interest to those working across the logical spectrum—in philosophy of (...) language, philosophical and mathematical logic, and philosophy of mathematics. (shrink)

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..

The motivation for Core Logic is explained. Its system of proof is set out. It is then shown that, although the system has no Cut rule, its relation of deducibility obeys Cut with epistemic gain.

A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.

Of the dozens of purported solutions to the liar paradox published in the past fifty years, the vast majority are "traditional" in the sense that they reject one of the premises or inference rules that are used to derive the paradoxical conclusion. Over the years, however, several philosophers have developed an alternative to the traditional approaches; according to them, our very competence with the concept of truth leads us to accept that the reasoning used to derive the paradox is sound. (...) That is, our conceptual competence leads us into inconsistency. I call this alternative the inconsistency approach to the liar. Although this approach has many positive features, I argue that several of the well-developed versions of it that have appeared recently are unacceptable. In particular, they do not recognize that if truth is an inconsistent concept, then we should replace it with new concepts that do the work of truth without giving rise to paradoxes. I outline an inconsistency approach to the liar paradox that satisfies this condition. (shrink)

Kevin Scharp proposes an original theory of the nature and logic of truth on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept, and proposes a detailed theory of inconsistent concepts that can be applied to the case of truth. Truth also happens to be a useful concept, but its inconsistency inhibits its utility; as such, it should be replaced with consistent concepts that can (...) do truth's job without giving rise to paradoxes. To this end, Scharp offers a pair of replacements, which he dubs ascending truth and descending truth, along with an axiomatic theory of them and a new kind of possible-worlds semantics for this theory. He goes to develop Davidson's idea that truth is best understood as the core of a measurement system for rational phenomena, and offers a semantic theory that treats truth predicates as assessment-sensitive and solves the problems posed by the liar and other paradoxes. (shrink)

Awarded the 1988 Johnsonian Prize in Philosophy. Published with the aid of a grant from the National Endowment for the Humanities.

First paragraph: Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true. Balking at the prospect that logical truths are made true by any particular thing, a consequence that may in fact be hard to avoid (see Restall 1996, Read 2000), this principle of truthmaking is sometimes restricted to (logically) contingent truths. I aim to show that even in its restricted form, the principle is provably false.

Model comparison games can be used not only to decide whether two specific models are equivalent or not, but also to establish a measurement of difference among a whole class of models. We show how this is possible in the case of the spatial modal logic S4u of Bennett. The approach results in a spatial similarity measure based on topological model comparison games. After establishing the theoretical framework, we move towards practice by giving an algorithm to effectively compute the similarity (...) measure for a class of topological models widely used in computer science applications: polygons of the real plane. In the appendix, we briefly overview an implemented system based on the theoretical framework. (shrink)