In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...) usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

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. (shrink)

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...) and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

The catuṣkoṭi or tetralemma is an argumentative figure familiar to any reader of Buddhist philosophical literature. Roughly speaking it consists of the enumeration of four alternatives: that some propositions holds, that it fails to hold, that it both holds and fails to hold, that it neither holds nor fails to hold. The tetralemma also constitutes one of the more puzzling features of Buddhist philosophy as the use to which it is put in arguments is not immediately obvious and certainly not (...) uniform: sometimes one of the four possibilities is selected as ‘the right one’, sometimes all four are rejected, sometimes all four are affirmed. It seems that this confusion is only exacerbated by the plethora of treatments we find in the modern commentarial literature, many of which try to analyze the tetralemma by recourse to notions of modern logic. Despite some important work done during the last decades a comprehensive study of the origin and development of the catuṣkoṭi from its use in the earliest Buddhist literature up to its later employment in the Buddhist philosophical works of Tibet, China, and Japan remains yet to be written. The present paper is obviously not intended to fill this gap, but has the specific objective of giving an interpretation of Nāgārrjuna’s employment of the tetralemma which makes both logical sense and is in accordance with his general philosophical position. (shrink)

Is Buddhism’s attitude towards accepted forms of knowledge sceptical? Are Pyrrhonian scepticism and classical Buddhist scholasticism related in their respective applications and expressions of doubt? In what way and to what degree is Critical Buddhism an offshoot of modern scepticism? Questions such as these as well as related issues are explored in the present collection, which brings together examinations of systematic doubt in the traditions of Buddhism from a variety of perspectives. What results from the perceptive observations and profound analytical (...) insights of the seven essays is a rich and multi-faceted picture of two families of philosophical systems—scepticism and Buddhism—that seem both akin and at odds, both related and distant at the same time. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.

Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...) paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; and finally, I highlight how ambiguous connectives can explain our intuitions about logical rivalry. (shrink)

Abstract This essay discusses the paradox of the N?g?rjunian negation as presented in his Vigrahavy?vartani. In Part One it is argued that as the Naiy?yika remarks, N?g?rjuna's speech act ?No proposition has its own intrinsic thesis? seemingly contradicts his famous claim that he has no negation whatsoever. In Parts Two and Three I consider the traditional as well as modem responses to this paradox and offer my own. I argue that N?g?rjuna's speech act does not generate a paradox for two (...) reasons: (a) the equivalence thesis of the kind??P = ?P is obviously false; and (b) since N?g?rjuna's speech act is situated in the dialogical/conversational universe of discourse as opposed to the argumentative/systematic universe of discourse, the teaching of the non?intrinsic thesis of all statements that it purports, holds for all statements in its class, including itself. Lastly, it is argued that even though the N?g?rjunian speech act is not a negation situated in the argumentative universe of discourse, it serves both philosophical and soteriological purposes. (shrink)

Through a philosophical analysis of realist interpretations of Madhyamaka Buddhism, I will argue that the Madhyamaka is not well represented when it is represented as nihilism, absolutism or as some non-metaphysical alternative. Indeed, I will argue that the Madhyamaka is misrepresented when it is represented as anything; its radical context sensitivity entails that it cannot be autonomously volunteered. The Madhyamaka analysis disrupts the ontic and epistemic presuppositions that consider inherent existence and absolute truth to be possible and necessary, and so (...) the ultimate truth, śūnyatā, is not an absolute truth or ultimate reality. However, I will argue that śūnyatā does qualify as a universal truth and should be understood as a context-insensitive, non-propositional truth in a non-dual dependent relationship with the multitudinous context-sensitive, propositional truths. This analysis will prove helpful in an investigation of those tensions, discernible within Buddhist modernism and the discourse of scientific Buddhism, that arise when Buddhist apologists claim a timeless modernity and a non-hostility with respect to contemporary worldviews. I will argue that apologists can resolve these tensions and satisfy their intuitions of timelessness, but only if they are willing to foreground the crucial distinction between their Buddhist worldview (their context-sensitive propositional truths) and their Madhyamaka attitude towards that worldview (the context-insensitive truth of śūnyatā). I will go on to generalise this result, showing that this Madhyamaka analysis opens up the possibility for frictionless co-operation between any and all worldviews, and that we therefore have a philosophical basis for a workable and sensitive theory of worldview pluralism. I will find it necessary to defend this position by demonstrating that, despite its context-insensitivity, the ultimate truth’s non-dual relationship with conventional truth mitigates against moral and epistemic relativism. I will further substantiate my claim as to the universal truth of śūnyatā by showing that, in Karan Barad’s ‘agential realism’, we find a revealing example of śūnyatā being articulated from within a non-Buddhist context. Thus, I hope to demonstrate some of the good effects of the Madhyamaka message, and show that this message can only be communicated clearly when it is distinguished from the discourses of Buddhism. In this manner, not by giving it a voice but through finding its voiceless authority, I hope to enable the Madhyamaka speak to the West. (shrink)