Ultralogic as Universal? is a seminal text in non-classcial logic. Richard Routley (Sylvan) presents a hugely ambitious program: to use an 'ultramodal' logic as a universal key, which opens, if rightly operated, all locks. It provides a canon for reasoning in every situation, including illogical, inconsistent and paradoxical ones, realized or not, possible or not. A universal logic, Routley argues, enables us to go where no other logic—especially not classical logic—can. Routley provides an expansive and singular vision of how a universal logic might one day solve major problems in set theory, arithmetic, linguistics, physics, and more. It circulated in typescript in the late 1970s before appearing as the Appendix to Exploring Meinong's Jungle and Beyond. With engaging, forceful prose, unsparing criticism of entrenched institutions, and many tantalizing proof sketches (is the Axiom of Choice a theorem of naive set theory?), Ultralogic? has had a major influence on the development of paraconsistent and relevant logic. This new edition makes this work available for a modern audience, newly typeset and corrected, along with extensive notes, and new commentary essays.

In this first volume of The Sylvan Jungle, the editors present a scholarly edition of the first chapter, "Exploring Meinong's Jungle," of Richard Routley's 1000-plus page book, Exploring Meinong's Jungle and Beyond. Going against the Quinean orthodoxy, Routley’s aim was to support Meinong’s idea that we can truthfully refer to non-existent and even impossible objects, like Superman, unicorns and the (infamous) round-square cupola on Berkeley College. The tools of non-classical logic at Routley’s disposal enabled him to update Meinong’s project for a new generation. This volume begins with an Introduction from Dominic Hyde, “The ‘Jungle Book’ in Context,” an essay that situates Exploring Meinong’s Jungle and Beyond historically. We provide the original Preface by Routley, followed by Chapter 1: “Exploring Meinong’s Jungle and Beyond.” In Chapter 2, Nicholas Griffin argues that Sylvan’s project was insufficiently radical with his essay, “Why the Original Theory of Items Didn’t (Quite) Go Far Enough.” Sylvan revisits his position from this time in Chapter 3, with his article, “Re-Exploring Item-Theory.” Filippo Casati, who has worked in the Routley Archives then takes up the question of the future of Sylvan’s research program in his essay, “The Future Perfect of Exploring Meinong’s Jungle.” Iconic and iconoclastic Australian philosopher Richard Routley (né Sylvan) published Exploring Meinong’s Jungle and Beyond in 1980. This work has fallen out of print, yet without great fanfare it has influenced two generations of philosophers and logicians.

In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and offers the broadest possible perspective on the debate of negation in logic and philosophy. It is a powerful tool for reasoning under contradictoriness as it investigates logic systems in which contradictory information does not lead to arbitrary conclusions. Reasoning under contradictions constitutes one of most important and creative achievements in contemporary logic, with deep roots in philosophical questions involving negation and consistency This book offers an invaluable introduction to a topic of central importance in logic and philosophy. It discusses (i) the history of paraconsistent logic; (ii) language, negation, contradiction, consistency and inconsistency; (iii) logics of formal inconsistency (LFIs) and the main paraconsistent propositional systems; (iv) many-valued companions, possible-translations semantics and non-deterministic semantics; (v) paraconsistent modal logics; (vi) first-order paraconsistent logics; (vii) applications to information processing, databases and quantum computation; and (viii) applications to deontic paradoxes, connections to Eastern thought and to dialogical reasoning.

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes .

Why are there paradoxes? This book uses paraconsistent logic to develop the mathematics to find out.

Relevance logics came of age with the one and only International Conference on relevant logics in 1974. They did not however become accepted, or easy to promulgate. In March 1981 we received most of the typescript of IN MEMORIAM: ALAN ROSS ANDERSON Proceedings of the International Conference of Relevant Logic from the original editors, Kenneth W. Collier, Ann Gasper and Robert G. Wolf of Southern Illinois University. 1 They had, most unfortunately, failed to find a publisher - not, it appears, because of overall lack of merit of the essays, but because of the expense of producing the collection, lack of institutional subsidization, and doubts of publishers as to whether an expensive collection of essays on such an esoteric, not to say deviant, subject would sell. We thought that the collection of essays was still (even after more than six years in the publishing trade limbo) well worth publishing, that the subject would remain undeservedly esoteric in North America while work on it could not find publishers (it is not so esoteric in academic circles in Continental Europe, Latin America and the Antipodes) and, quite important, that we could get the collection published, and furthermore, by resorting to local means, published comparatively cheaply. It is indeed no ordinary collection. It contains work by pioneers of the main types of broadly relevant systems, and by several of the most innovative non-classical logicians of the present flourishing logical period. We have slowly re-edited and reorganised the collection and made it camera-ready.

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

This third volume continues Richard Routley's explorations of an improved Meinongian account of non-referring and intensional discourse (including joint work with Val Routley, later Val Plumwood). It focuses on the essays 8 to 12 of the original monograph, Exploring Meinong's Jungle and Beyond, following on from the material of the first two volumes and further explores aspects and implications of the Noneist position. It begins with a discussion of the value of nonexistent objects championed by noneism, especially as regards theories of perception, universals, value theory and a commonsense account of belief. It continues with: a detailed analysis of what it means to exist; the importance of nonexistent objects to adequate accounts of mathematics and the theoretical sciences; and an account of noneisms' distinctiveness from other accounts of nonexistent objects. These essays are supplemented with scholarly essays from Naoya Fujikawa, and Maureen Eckert and Charlie Donahue.