This essay presents a critique of dialetheist readings of Madhyamaka based on the philosophy of the fifteenth-century Tibetan scholar, Gorampa Sonam Senge (Go rams pa bSod nams Seng ge) (1429-1489). In brief, dialetheism is the acceptance that in a logical system there can be at least some cases in which a statement and its negation are true; that is, it involves the acceptance of true contradictions. Jay Garfield and Graham Priest's "Nāgārjuna and the Limits of Thought" attempts to reconcile apparent (...) contradictions in Nāgārjuna's Madhyamaka writings by appealing to dialetheism.1 Tom Tillemans' response to that article, "How do Mādhyamikas Think?" advocates an interpretation of Nāgārjuna that relies on a weaker .. (shrink)

Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

This is a philosophical investigation of the nature of the limits of thought. Drawing on recent developments in the field of logic, Graham Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact veridical. Beginning with an analysis of the way in which these limits arise in pre-Kantian philosophy, Priest goes on to illustrate how the nature of these limits was theorised by Kant and Hegel. He offers new interpretations of Berkeley's (...) master argument for idealism and Kant on the antimonies. He explores the paradoxes of self reference, and provides a unified account of the structure of such paradoxes. The book concludes by tracing the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida. (shrink)

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and (...) their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area. (shrink)

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

Here are the chief riches of more than 3,000 years of Indian philosophical thought-the ancient Vedas, the Upanisads, the epics, the treatises of the heterodox and orthodox systems, the commentaries of the scholastic period, and the contemporary writings. Introductions and interpretive commentaries are provided.

In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one (...) or more such values. The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics. (shrink)

In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one (...) or more such values. The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics. (shrink)