Paraconsistent logic, logic in which inconsistent information does not deliver arbitrary conclusions, is one of the fastest growing areas of logic, with roots in profound philosophical issues, and applications in information processing and philosophy of science. This book contains selected papers presented at the First World Congress on Paraconsistency, held in Ghent in 1997. It contains papers on various aspects of the subject. As such, it should be of interest to all who want to learn what the subject is, and (...) where it is going. (shrink)

Approaches to paraconsistency can be arranged on a spectrum similar to the way in which approaches to vagueness are often understood. On the left are the metaphysical realists; those who think that there are real contradictory facts, that are mind and language independent. On the right are those who think that although we can have inconsistent beliefs and inconsistent theories — and we need a paraconsistent logic to deal with them — the world itself is perfectly consistent. In the middle (...) are the semantic dialetheists, who claim that there are true contradictions, but that these come about because of particular features of our use of language. This chapter outlines a particular version of semantic dialetheism based on a four-valued logic. It contends that although we need such a logic to deal with our current language, we could regiment our uses of predicates (and other expressions) to eliminate all true contradictions. (shrink)

The paper contains a short story which is inconsistent, essentially so, but perfectly intelligible. The existence of such a story is used to establish various views about truth in fiction and impossible worlds.

In these essays the minimalist approach to linguistic theory is formulated and progressively developed.

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into (...) a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them. (shrink)

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

This is the first introductory textbook on non-classical propositional logics.

In this book Ludlow uses the metaphysics of time as a case study and focuses on the dispute between A-theorists and B-theorists about the nature of time.

The primary goal of Peter Ludlow's Semantics, Tense, and Time is to illustrate how one can study metaphysical issues from a linguistic/semantic perspective by addressing the debate between tenseless theorists and tensed theorists. Ludlow's book is noteworthy in part because of the novelty of its approach to this debate and in part because it addresses and endeavors to solve the metaphysical problems of temporal solipsism that other temporal solipsists have not addressed.

This article introduces three arguments that share a single conclusion: that a comprehensive science of language cannot describe relations of semantic reference, i.e. word–world relations. Spelling this out, if there is to be a genuine science of linguistic meaning, then a theory of meaning cannot involve assigning external, real-world, objects to names, nor sets of external objects to predicates, nor truth values to sentences. Most of the article tries to explain and defend this broad conclusion. The article also presents, in (...) a very limited way, a positive alternative to external-referent semantics for expressions. This alternative has two parts: first, that the meanings of words and sentences are mental instructions, not external things; second, that it is people who refer by using words and sentences, and word/sentence meanings play but a partial role in allowing speakers to talk about the world. (shrink)

The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown (...) that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial. (shrink)

Expanding on some of Chomsky’s recently expressed views of meaning in a way that is consistent with his long-held rationalist conception of mind, I show how syntax, broadly conceived, could individuate meanings and provide a science of meanings inside the head. Interpretation becomes a pragmatic matter, although a rationalist account of mind shows how internal meanings guide interpretation and, more generally, language use. In this view of meanings, interpretation, and mind, semantics as usually understood disappears.

My modest aim in this note is to sketch three interrelated critiques of public languages, and to respond to them. All are broadly Chomskyan, and all support the same conclusion: that, insofar as they even exist, the study of public languages is not a viable scientific project. (Related critiques of semantics, understood as involving word–world relations, will be touched on as well).

This book gives an overview of paraconsistent logics - that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering: Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some philosophical (...) problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed. (shrink)