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)

The logical analysis of Nāgārjuna’s catuṣkoṭi has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners’ formalization typically appears as: A, Not A, Both, and Neither. The pulse of the controversy is the repetition of negations in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa and prasajya-pratiṣedha. This paper builds off Westerhoff’s account and presents some subtleties of Nāgārjuna’s use of these (...) negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna’s use of na and a- within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā. (shrink)

The little versified treatise on the elements of Buddhist logic, often referred to as the Hetucakraḍamaru, is usually attributed to Dignāga. It is only available in a Tibetan translation and quotations from a few of its verses are extant in Sanskrit sources. On the basis of a novel interpretation that is based on a critical edition of the text, we argue that there is a good reason why its title was Hetucakraḍamaru - a ḍamaru is a two-headed drum. The “heads” (...) of the drum are circular and they refer to the sapakṣa and vipakṣa conditions of the logical reason. These “wheels” can be turned clock-wise and counter clock-wise. The nine positions that are located on the wheels do remind one of a dharmacakra, which has a center and eight positions that are placed around it as if it were a compass. We illustrate our interpretation of the text by means of various diagrams. (shrink)

This thesis is the attempt to find a logical model for, and trace the history of, the catuṣkoṭi as it developed in the Indo-Tibetan milieu and spread, via China, to Japan. After an introduction to the history and key-concepts of Buddhist philosophy, I will finish the first chapter with some methodological considerations about the general viability of comparative philosophy. Chapter §2 is devoted to a logical analysis of the catuṣkoṭi. Several attempts to model this fascinating piece of Buddhist philosophy with (...) the tools of classical logic shall be debunked. A paraconsistent alternative will be discussed but eventually dismissed. As a rejoinder, I shall propose a model for the catuṣkoṭi with the help of speech-acts. The remainder of this chapter will look at Chinese and Japanese forms of the catuṣkoṭi which I shall model in a quasi-recursive system. The third and final chapter will look at the Kyoto School's soku-hi dialectics which ties together the different threads of this essay. I will criticise an established, classical model of the soku-hi dialectics and offer an alternative with a second-order paraconsistent semantics. (shrink)

Buddhist philosophers have investigated the techniques and methodologies of debate and argumentation which are important aspects of Buddhist intellectual life. This was particularly the case in India, where Buddhism and Buddhist philosophy originated. But these investigations have also engaged philosophers in China, Japan, Korea and Tibet, and many other parts of the world that have been influenced by Buddhism and Buddhist philosophy. Several elements of the Buddhist tradition of philosophy are thought to be part of this investigation. -/- There are (...) interesting reasoning patterns discernible in the writings of Buddhist philosophers. For instance, the Mādhyamika philosopher Nāgārjuna presents arguments for the emptiness of all things in terms of catuṣkoṭi (four ‘corners’: roughly speaking, truth, false, both, neither). There are also the Indian vāda (debate) literature and Tibetan bsdus grwa (collected topics) that list techniques of debates. -/- The main interest here is the tradition of Buddhist philosophy, sometimes referred to as Pramāṇavāda, whose central figures are Dignāga (approx. 480–540 CE) and Dharmakīrti (6th– 7th CE). This philosophy is understood to be the Buddhist school of logic-epistemology. ‘Pramāṇavāda’ is not a doxographical term traditionally used to refer to a recognised school of Buddhist philosophy. It is a conventional term that is sometimes used in modern literature. Nevertheless, in what follows, we think of it as a tradition within Buddhist philosophy and ‘Buddhist logic’ refers to what is developed in this tradition. -/- Buddhist logicians have systematically analysed the kind of reasoning involved in acquiring knowledge. They hold that there are valid ways to reason that are productive of knowledge. In what follows, some of the main elements of their analyses will be described. Note, however, that, while exegetical studies of Buddhist texts are important, we must step back from them and consider what is involved in taking a Buddhist approach to logic in light of modern formal logic. This analysis will be done against the backdrop of the contemporary literature on logic and related subjects in contemporary philosophy to make sense of the logical studies by Buddhist logicians. (shrink)