In many philosophical traditions, it is held that reality is non-dual. Of course, to be non-dual, as opposed to dual, is itself to partake of a certain duality. If reality really is non-dual, it must transcend this duality too. But what could this mean? Can one make coherent sense of it? To keep the discussion focussed, I will locate it in one specific tradition: the Mahāyāna Buddhist tradition. The idea that ultimate reality is non-dual goes back to the earliest Mahāyāna (...) sūtras at the turn of the Common Era. Thereafter, the question of what it means to transcend duality plays a central role in Buddhist philosophy. The point that reality must transcend even the duality between duality and non-duality plays a significant role in the Chinese Sanlun philosopher Jizang (, 549–623). His discussion points the way to an answer to our problem which may be articulated with the techniques of contemporary paraconsistent logic, as we will see. (shrink)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (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)

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)

Per il dialeteismo ci sono contraddizioni vere. Questa concezione filosofica ha assunto una forma chiara e definita a partire dal lavoro del filosofo e logico Graham Priest – uno dei suoi padri fondatori, nonché uno dei suoi più strenui difensori. Questo libro intende portare il dialeteismo all’attenzione di un ampio pubblico, che non sia solo quello degli addetti ai lavori. Il volume è suddiviso in due parti. La prima include le cinque lezioni su "Dialeteismo e storia della filosofia" tenute da (...) Priest e Filippo Casati a Padova nel 2016, in occasione del Corso di Eccellenza per il dottorato in filosofia dell’Università di Padova. La seconda contiene quattro contributi sul dialeteismo di autori italiani. (shrink)

Nāgārjuna, the famous founder of the Madhyamika School, proposed the positive catuṣkoṭi in his seminal work, Mūlamadhyamakakārikā: ‘All is real, or all is unreal, all is both real and unreal, all is neither unreal nor real; this is the graded teaching of the Buddha’. He also proposed the negative catuṣkoṭi: ‘“It is empty” is not to be said, nor “It is non-empty,” nor that it is both, nor that it is neither; [“empty”] is said only for the sake of instruction’ (...) and the no-thesis view: ‘No dharma whatsoever was ever taught by the Buddha to anyone’. In this essay, I adopt Gricean pragmatics to explain the positive and negative catuṣkoṭi and the no-thesis view proposed by Nāgārjuna in a way that does not violate classical logic. For Nāgārjuna, all statements are false as long as the hearer understands them within a reified conceptual scheme, according to which substance is a basic categorical concept; substances have svabhāva, and names and sentences have svabhāva. (shrink)

A number of analytical philosophers have recently endorsed the view that the world itself is indeterminate in some respect. Intriguingly, ideas similar to the view are expressed by thinkers from Chinese Madhyamaka Buddhism, which may shed light on the current discussion of worldly indeterminacy. Using as a basis Chinese Madhyamaka thought, together with Jessica Wilson’s account of indeterminacy, I develop an ontological conception of indeterminacy, termed ontic indeterminacy, which centres on two complementary ideas—conclusive indeterminability and provisional determinability. I show that (...) OI is well-equipped to tackle several issues of worldly indeterminacy. My overarching aim is to present a viable and sustainable perspective on the subject of indeterminacy to enrich analytical philosophers’ insights into the intricate nature of reality. (shrink)

This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.

A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...) false. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.

This paper examines the metaphysics of interdependence in the work of the Chinese Buddhist Fazang. The dominant approach of this metaphysics interprets it as a species of metaphysical coherentism wherein everything depends upon everything else, no individual is more fundamental than any other, and so reality itself is non-well-founded in the sense that chains of dependence never terminate. I argue, to the contrary, that Fazang's metaphysics is better interpreted as a novel variety of foundationalism. I argue, as well, using set- (...) and graph-theoretic techniques, that there is a consistent way to model this alternative interpretation, and that this model differs in significant ways from a coherentist model. (shrink)

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s and Graham Priest’s interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's framework of First Degree Entailment. Cotnoir has argued (...) that the lattices of Priest and Garfield cannot ground the logic of the catuskoti. The concern is simple: on the one hand, FDE brings with it the failure of classical principles such as modus ponens. On the other hand, we frequently encounter Nāgārjuna using classical principles in other arguments in the MMK. There is a problem of validity. If FDE is Nāgārjuna’s logic of choice, he is facing what is commonly called the classical recapture problem: how to make sense of cases where classical principles like modus pones are valid? One cannot just add principles like modus pones as assumptions, because in the background paraconsistent logic this does not rule out their negations. In this essay, I shall explore and critically evaluate Cotnoir’s proposal. In detail, I shall reveal that his framework suffers collapse of the kotis. Taking Cotnoir’s concerns seriously, I shall suggest a formulation of the catuskoti in classical Boolean Algebra, extended by the notion of an external negation as an illocutionary act. I will focus on purely formal considerations, leaving doctrinal matters to the scholarly discourse – as far as this is possible. (shrink)

Recently there has been a debate on whether Pyrrho’s philosophy could be influenced by Indian Buddhist philosophy. Discussions revealing striking similarities between them often point out Pyrrho’s complicated sentence, referred to as tetralemma, as one of the most striking similarities. The central question of this paper is whether Pyrrho’s sentence is of the tetralemmatic kind. Authors argue that if Pyrrho’s sentence is not fourfold in structure it could scarcely be classified as similar to the Buddhist tetralemma. A careful analysis of (...) the question is provided, arguing that the approach to the problem of tetralemmatic structure cannot be carried out solely on syntactic grounds. An aspect of a deeper philosophical meaning of the formula is applied, which alone enables us (if at all) to link Pyrrho’s philosophy to Buddhism. (shrink)

The is a brief reply to the central objection against the construction of my The Fifth Corner of Four by Andi Kapsner in his “Cutting Corners: A Critical Note on Priest’s Five-Valued Catuṣkoṭi. This concerns the desirability of adding a fifth corner to the four of the catuṣkoṭi.

Graham Priest has offered a rational reconstruction of Buddhist thought that involves, first, modeling the Catuṣkoṭi by a four valued logic, and then later adding a fifth value, read as “ineffability”. This note examines that fifth value and raises some concerns about it that seem grave enough to reject it. It then sketches an alternative to Priest’s account that has no need for the fifth value.