Every student of English-speaking analytical metaphysics is taught that the early twentieth century philosophical debate about truth confronted the correspondence theory, supported by Russell, Moore, the early Wittgenstein and, later, J.L. Austin, with the coherence theory advocated by the British Idealists. Sometimes the pragmatist conception of truth deriving from Dewey, William James, and C.S. Peirce is regarded as a third player. And as befits a debate at the dawn of analytical philosophy, the matter in dispute is normally taken to have (...) been the proper analysis of the concept.No doubt this conception nicely explains some of the characteristic turns taken in the debate. Analysis, as traditionally conceived, has to consist in the provision of illuminating conceptual equivalences; and illumination will depend, according to the standard rules of play, on the analysans’ utilizing only concepts which, in the best case, are in some way prior to and independent of the notion being analyzed — or, if that's too much to ask, then concepts which at least permit of some form of explication which does not in turn take one straight back to that notion. (shrink)

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...) simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

They reject the correspondence theory, insist truth is anemic, and advance an "anti-theory" of truth that is essentially a collection of platitudes: "Snow is white" is true if and only if snow is white; "Grass is green" is true if and only if grass is green. According to disquotationalists, the only profound insight about truth is that it lacks profundity. David contrasts the correspondence theory with disquotationalism and then develops the latter position in rich detail - more than has been (...) available in previous literature - to show its faults. (shrink)

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.

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...) Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics. (shrink)

Tarski showed how to give satisfactory theories of truth for a wide variety of languages, but he required that the theory of truth for a language be formulated in an essentially richer metalanguage. Since there is no human language essentially richer than a natural language and since we would like to develop consistent theories of truth for natural languages, we would like to learn how to formulate a theory of truth for a language within that very language. ;Toward this end, (...) I consider a class of formalized languages called partially interpreted languages, derived from the work of Carnap, in which sentences are classified as definitely true, definitely false, and intermediate. I give a condition of adequacy, analogus to Tarski's Convension T, requiring that is true be definitely true iff is definitely true , and show that it is possible to give, effectively and explicity, a theory of truth that meets the condition. Theories of truth that meet the condition are shown to have various pleasant properties. The construction depends heavily upon the work of Saul Kripke. ;In addition to the work of Tarski and Kripke, the "naive semantics" of Gupta and Herzberger is discussed. Of the paradoxes other than the liar, only Montague's paradox about necessity is discussed in any detail. To solve this paradox, I recommend a provability interpretation of modal logic of the type studied by Solovay. Prospects for extending Solovay's results into quantified modal logic are discussed. ;The work is entirely concerned with formal languages, although it is hoped that the tools developed can be usefully applied to natural languages. (shrink)

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

The first chapter explores the theory developed in Kripke's "Outline of a Theory of Truth." A tension in Kripke's account of the concept of truth is revealed--a conflict between two intuitions. The first intuition, called the "fixed point conception of truth," is that the whole meaning of the truth predicate is given by the formula "we may assert of a sentence that it is true iff we may assert that sentence." The second intuition, called the "thesis of the supervenience of (...) semantics," is that the interpretation of the truth predicate is determined by the interpretations of all the other non-logical constants of the language. I show that these two intuitions cannot be reconciled within the context of Kripke's theory, and I argue for the choice of the fixed point conception of truth over the principle of the supervenience of semantics. Chief among the considerations that I advance is the fact that the fixed point conception of truth yields a natural logic of truth. In the second chapter I present that logic of truth in the form of a cut-free sequent calculus. I then turn, in chapter three, to a discussion of the significance of such cut-free sequent calculi. I argue that we may view the sequent calculus introduction rules for a logical constant as giving the meaning of that constant, under certain conditions. In particular, we can see our logic of truth as providing an explication of our intuitive concept of truth which complements Kripke's original model-theoretic explication. The fourth chapter takes up some criticisms of Kripke's theory which center on the logic of truth. In addition, the general ideas developed in the first three chapters are applied in a discussion of the various schemes of three-valued logic which can be used in the development of Kripke's approach. Finally, in the last chapter, it is shown that Kripke's technical concepts, and the logical ideas developed in the second and third chapters, can be used to provide a unified account of many contexts in which paradox arises. (shrink)

According to the disquotationalist theory of truth, the Tarskian equivalences, conceived as axioms, yield all there is to say about truth. Several authors have claimed that the expression of infinite conjunctions and disjunctions is the only purpose of the disquotationalist truth predicate. The way in which infinite conjunctions can be expressed by an axiomatized truth predicate is explored and it is considered whether the disquotationalist truth predicate is adequate for this purpose.

Anil Gupta; XV*—Remarks on Definitions and the Concept of Truth1, Proceedings of the Aristotelian Society, Volume 89, Issue 1, 1 June 1989, Pages 227–246, https.

The Revision Theory of Truth has been challenged in A. M. Yaqūb's recent book The Liar Speaks the Truth. Yaqūb suggests some non-trivial changes in the original theory - changing the limit rule - to avoid certain artifacts. In this paper it is shown that the proposed changes are not sufficient, i.e., Yaqūb's system also produces artifacts. An alternative solution is proposed and the relation between it and Yaqūb's solution is explored.

In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth as a property whose applicability is given by a revision process rather than by a fixed (...) extension. The main advantage of this revision process is its ability to explain why truth seems in many cases almost redundant, in others substantial, and yet in others paradoxical. Yaub offers a comprehensive defense of the revision theory of truth by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences can be constructed. Yaqub concludes by introducing a logic of truth that further demonstrates the adequacy of the revision theory. (shrink)

This dissertation is a study of some recent theories of truth. The theories fall into three groups: The Revision Theories, the context-sensitive theories, and the "Chrysippian theories". ;The "Chrysippian theories" are based on the intuition that pathologicalities arising from the concept of truth can be recognized and acknowledged with the concept of truth itself. Thus, from the pathologicality of the Liar, for example, we can conclude that the Liar is not true. This leads to immediate difficulties since the Liar claims (...) just that--that it is not true--and it would thus seem to be true. The Chrysippian theories are designed to avoid these difficulties while preserving the motivating intuition. Haim Gaifman's Pointer Semantics, and Brian Skyrms' Intensional Fixed-Point Theory of Truth are examples of such theories. They are exposited and criticized. ;The context-sensitive theories dealt with are Tyler Burge's Indexical Theory of Truth and the theory of Jon Barwise and John Etchemendy. These theories claim that an ambiguity due to a contextual parameter is the reason for the difficulties we encounter. Burge offers a theory of Tarskian levels coupled with a pragmatic theory that explains the assignment of levels to occurrences of 'true'. Barwise and Etchemendy make explicit a situational parameter in their account of propositions. They consider the ambiguity with respect to the situation a propositions is about a main source of the paradoxes. ;Finally, the Revision Theories of Truth of Anil Gupta and Nuel Belnap and two variations of this theory are considered. One is due to Aladdin Yaqub, the other, the "fully-varied theory", is due to Gupta and Belnap but remains largely unexplored. Revision theories are put forward as the most promising account of the difficulties. They are based on a definitional reading of all Tarski biconditionals. The circularity implied by such a reading is handled by Gupta's and Belnap's general theory of definitions. ;Yaqub's objections raised against the standard theory are examined, and his proposed solution is shown to be inadequate. The fully-varied Revision Theory is shown to provide a better solution. (shrink)

Gupta’s Rule of Revision theory of truth builds on insights to be found in Martin and Woodruff and Kripke in order to permanently deepen our understanding of truth, of paradox, and of how we work our language while our language is working us. His concept of a predicate deriving its meaning by way of a Rule of Revision ought to impact significantly on the philosophy of language. Still, fortunately, he has left me something to.

This dissertation deals with the problem of truth and semantical paradox. It begins by motivating the premise that the Tarskian biconditionals are collectively exhaustive and individually constitutive of the concept of truth. That is, the concept of truth is completely and correctly defined by the totality of all the biconditionals of the form 'x is true iff p', where 'p' is replaced by any sentence and 'x' by any name of that sentence. ;The argument of the dissertation has three stages. (...) First, I argue in Chapter One that the premise above entails that the concept of truth is circular. For the Tarskian biconditionals of certain sentences specify circular truth conditions for those sentences. For example, the Tarskian biconditional of the truth-generalization 'No sentence is both true and false' shows that the truth conditions of this generalization essentially involve reference to truth itself. The circularity of the concept of truth in bivalent languages gives rise to a revision process in which the semantical status of each sentence is determined by its Tarskian biconditional once a totality of nonsemantical facts and an initial extension of the truth predicate are posited. The theory whose thesis is what the preceding sentence asserts is called the revision theory of truth. ;In the second stage, I argue that the revision theory is consistent. I describe in Chapter Two a type of formal semantics called stability semantics. Since each semantical system of stability semantics is a formal representation of the revision process, the consistency of any such system demonstrates that the revision theory is consistent. ;Finally, I show that the revision theory is materially adequate. In Chapter Four I develop a system of stability semantics that represents the revision process faithfully and that yields the intuitively correct results in a representative sample of cases. I also define and study a notion of logical consequence congruous to this semantical system. In order to understand fully how this system succeeds in representing the revision process faithfully, I first examine how other systems fail. Thus in Chapter Three I give a critical exposition of Herzberger's, Gupta's, and Belnap's systems. (shrink)