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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.

Philosophy of Language Philosophy of Logic On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts. Show Abstract..

Tarski's manner of defining truth is generally considered highly significant. About why, there is less consensus. I argue first, that in his truth-definitions Tarski was trying to solve a set of philosophical problems; second, that he solved them successfully; third, that all of these that are simply problems about defining truth are as well or better solved by a simpler account of truth. But one of his crucial problems remains: to give an account of validity, one requires an account not just of truth but of truth under varying interpretations. Tarski's account has the merit of generalizing to this, to model theory and to abstract algebra.

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified (in terms of definitional complexity) account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

It is often argued that the combination of deflationism about truth and the truth-conditional theory of meaning is impossible for reasons of circularity. I distinguish, and reject, two strains of circularity argument. Arguments of the first strain hold that the combination has a circular account of the order in which one comes to know the meaning of a sentence and comes to know its truth condition. I show that these arguments fail to identify any circularity. Arguments of the second strain hold that the combination has a circular explanation of the ideas or concepts of meaning and truth. I show that these arguments identify a genuine, but acceptable, circularity.

On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts.

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

Gupta"s and Belnap"s Revision Theory of Truth defends the legitimacy of circular definitions. Circularity, however, forces us to reconsider our conception of meaning. A readjustment of some standard theses about meaning is here proposed, by relying on a novel version of the sense–reference distinction.

I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. But his test is too demanding. The inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular.

This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” uses of definienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justified, although some problems remain that future research in this field should take into account. The following assumptions constitute the typical background in which the truth paradoxes arise: (i) classical first-order logic, (ii) a language allowing for self-reference, and (iii) the “semantic” Tarskian schema: (TS) T ‘A’ ↔ A (where ‘T’ is the truth predicate, and the single quotes are a nominalization device applicable to sentences; for simplicity, we only consider homophonic versions of TS). This background can be seen as somehow part of our ordinary linguistic and conceptual background and yet, to avoid inconsistency, one or more of these assumptions must be suitably weakened. The classical, Tarskian strategy is to forbid self-reference, whereas the fixed-point approaches stemming from the work of Saul Kripke (1975) and Robert Martin and Peter Woodruff (1975) weaken the logic..