Among the many questions raised by Nāgārjuna’s catuṣkoṭi, the most fundamental concerns the type of objects to which its negative statements apply. These statements deny the reality of conditioned Being, which can be understood in two ways: as a negation of our concept or knowledge of conditioned Being, or as a negation of conditioned Being as such. The first interpretation can be called “epistemological” and the second “metaphysical.” Scholarship has almost unanimously accepted the epistemological approach. In this paper I object (...) to this approach and propose to reinterpret the catuṣkoṭi metaphysically, as a description of Being and its inherent principles. I ground my objection in Hegel’s “Doctrine of Being” and argue that the catuṣkoṭi exhibits similar features to the Hegelian concept of substantial negativity. In the end, I draw some conclusions for the study of Nāgārjuna in general and highlight the limits of the parallelism. (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)

In early Buddhist logic, it was standard to assume that for any state of a ff airs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time mak­ing sense of this, but it makes perfectly good sense in the se­mantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to (...) suggest that none of these options , or more than one, may hold. The point of this paper is to examine the matter, including the formal logical machinery that may be appropriate. (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)

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) 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 (1975) framework of First (...) Degree Entailment. Cotnoir (2015) 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 ponens 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. Furthermore, I shall argue that the Collapse Argument has been misguided from the outset. The last chapter suggests 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)

According to Garfield and Priest’s interpretation, the positive use of the catuskoti by Nāgārjuna in Mūlamadhyamakakārikā (MMK) shows that he endorses a four-valued semantics similar to that of Belnap’s First-Degree Entailment (FDE), while the negative use of the catuskoti by Nāgārjuna in MMK indicates that what he really has in mind is a plurivalent five-valued semantics. This paper argues that their interpretation suffers from a number of problems: adequate logic, collapse of kotis, lack of literature support, and a (...) suitable explanation of the third koti. The final part of the paper combines insights from Westerhoff, Cotnoir, Garfield and Priest together and describes the right interpretation of Nāgārjuna’s use of the catuskoti in MMK with the right semantics and the right logic of MMK. The authors argue that Nāgārjuna’s ‘rebuttal’ of all four kotis in a catuskoti should be understood as a mere denial or a mere rejection of these kotis. (shrink)

Using logic-laden terms to translate and interpret what the ancient Indian Buddhist thinkers said when we are not sure what they spoke about when they spoke about ‘contradictions’, etc. in natural languages can sometimes make things frustrating. Keeping in mind Wittgenstein’s exhortation, “don’t think, but look!”, I approach the issues of contradiction, negation, and the _catuṣkoṭi_ via case-by-case study on several pertinent passages in Dharmapāla’s _Dasheng Guangbailun Shilun_. The following are some interrelated observations which should not be overgeneralized, especially considering (...) the limited scope of this study and its methodological considerations. First, there is an implicit rule of non-opposition and there could be no real oppositions for apparent oppositions because of implicit qualifications. Moreover, these are not new since or after Dignāga. Second, Dharmapāla and his contemporaries are familiar with the two negative usages, and _prasajya-pratiṣedha_ is used for negating the opponents’ theses and is related to the no-thesis view. It’s not a good idea to assign truth values to sentences using _prasajya-pratiṣedha_ or to a thesis in which the terms have no real objects. And Dharmapāla’s theses are just therapeutic tools. Third, in Dharmapāla’s discussion of the negative _catuṣkoṭi_, one can see the rule of non-opposition, the strategy of qualifications, and the two negative usages. Although the four positions in the _catuṣkoṭi_ are regarded as mutually exclusive and jointly exhaustive, they are jointly exhaustive in pragmatic context, and are mutually exclusive under some interpretations, but not all. My tentative suggestion is that the _catuṣkoṭi_ is a loosely term-based way of categorization. Last but not least, in the text discussed, I do not see Buddhist thinkers endorsing any contradictions. (shrink)

The aim of this paper is to see whether Robinson and Kajiyama’s critiques of Nāgārjuna’s discourse of catuṣkoṭi, as contradicting formal logic, while following a dialectical formula is plausible. According to them, the 3rd koṭi is a violation of the law of non-contradiction, while the 4th koṭi, a violation of the law of excluded middle. Yet, since catuṣkoṭi can be interpreted as containing different perspectives in its expression of each koṭi, the critique of violating the law of non-contradiction fails. Further, (...) should a proper presupposition be added, the problem of excluded middle is resolved. Owing to the presence of this premise postulated as a real entity possessing intrinsic nature, it becomes perfectly valid, irrespective of all-out refutation of every option, In this context, catuṣkoṭi can be seen as an ‘expedient’, representing different views of separate schools or perspectives without violating the principle of formal logic, nor postulating any hierarchical dialectics elevating into the higher grades among these koṭis. Likewise, catuṣkoṭi in Nāgārjuna can be viewed as revealing the absurdity of postulating any identity or precondition for causal relations in perceiving intrinsic substance. (shrink)

Kajiyama Yuich understands Nāgārjuna’s logics of catuṣkoṭi in terms of Hegelian Dialectics, while interpreting the negation formula of 4th koṭi in tetralemma as the religious truth of Madhyamika, which cannot be negated as an ultimate truth. And Richard Robinson also posits this proposition as dissolving the entire dr̥sti. Examining these approaches, this thesis argues against the dialectical interpretation of catuṣkoṭi with reference to its logical structure. For this, reference will also be made to Piṇgala and Candrakīrti’s commentary comparing them to (...) Robinson’s and Kajiyama’s. Here, focus will be put on the aspect of ‘perspectives.’ Upon further examination, it was determined that a Hegelian dialectical approach is not plausible for interpreting Nāgārjuna’s logic, which is purely negative and skeptical in its character. And through reformulating the structure of catuṣkoṭi in terms of prasaṅga, this paper compares it with a dialectical formula to more clearly evaluate the implication of negative logic for catuṣkoṭi. Thereby, it was seen that Nāgārjuna has neither equated propositions on the basis of identity, nor postulated any hierarchy through classifying the grade of these koṭis. Accordingly, on the strength of various perspectives, any proposition in the catuṣkoṭi can be understood with logical clarity, without positing any metaphysical or dialectical interpretation. Further, the possible reconstruction of Nāgārjuna’s understanding of the tetralemma supports a semantic approach to truth, while revealing the absurdity of perceiving identity or causal relations as possessing intrinsic substance. (shrink)

Names name, but there are no individuals who are named by names. This is the key to an elegant and ideologically parsimonious strategy for analyzing the Buddhist catuṣkoṭi. The strategy is ideologically parsimonious, because it appeals to no analytic resources beyond those of standard predicate logic. The strategy is elegant, because it is, in effect, an application of Bertrand Russell's theory of definite descriptions to Buddhist contexts. The strategy imposes some minor adjustments upon Russell's theory. Attention to familiar catuṣkoṭi from (...) Vacchagotta and Nagarjuna as well as more obscure catuṣkoṭi from Khema, Zhi Yi, and Fa Zang motivates the adjustments. The result is a principled structural distinction between affirmative and negative catuṣkoṭi, as well as analyses for each that compare favorably to more recent efforts from Tillemans, Westerhoff, and Priest. (shrink)

Graham Priest presents an exploration of the development of Buddhist metaphysics, which is viewed through the lens of the catuskoti. In its earliest and simplest form this is a logical/metaphysical principle which says that every claim is true, false, both, or neither; but Priest shows how the principle itself evolves as the metaphysics develops.

_ The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi _, by PriestGraham. Oxford: Oxford University Press, 2018. Pp. 208.

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.

For the primary purpose of eliminating and overcoming ignorance, Buddhist philosophers put forward a method of negation. It is Nagarcuna who developed and systematized this method.- and his work is mainly on the subject of negation. Its Two Truth Doctrines, catuskoti, the Eight-Tiered Method of Existence, and finally the Middle Way, bear traces of, or even build upon, this method. In this context, we will talk about the meaning of catuskoti in Indian philosophy, try to explain the uncertainty (...) of these four alternatives, and put forward suggestions and interpretations for showing these alternatives. Then, from the perspective of classical and non-classical logic, the location of these alternatives will be discussed. (shrink)

Respected modern scholars regard the pre-Buddhist philosopher Sañjaya Belaṭṭhiputta—a significant figure in the Buddhist canon—as the originator of the important classical argument- forms known as the catuṣkoṭi and catuṣkoṭi vinirmukta. We argue that the early Buddhist texts do not in fact support this view of the origin of these argument-forms; the question of their origin is open. While it is certainly true that the Pāli Sāmaññaphala Sutta and some of its parallels portray Sañjaya as deploying the catuṣkoṭi, there is nothing (...) in these passages to suggest that he was its originator. The situation concerning the catuṣkoṭi vinirmukta is perhaps even more surprising: There is nothing in the early Pāli texts and their parallels—nor in Buddhagosa’s famous Pāli commentary on the early texts—to show that Sañjaya even deployed the catuṣkoṭi vinirmukta let alone originated it. Further, our investigations also call into question the standard portrayal of Sañjaya as an obfuscator and prevaricator. It appears he may have been a more interesting and able philosopher than the Sāmaññaphala Sutta—and modern accounts based on it—maintain. (shrink)

A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhaṅgī, and the Mādhyamika catuṣkoṭi. It is argued that the irrationality currently imputed to these logics relies upon some philosophical preconceptions inherited from Aristotelian metaphysics. This misunderstanding can be corrected in two steps: by recalling their assumptions about truth; by reconstructing their ensuing theory of judgment within a common conceptual framework.

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)

Graham Priest, ampiamente considerato una figura di tutto rilievo nel panorama filosofico contemporaneo, è conosciuto prevalentemente per i suoi contributi nel campo delle logiche non-classiche, e per essere uno dei fondatori della controversa tesi filosofica denominata dialeteismo. Non sorprende che, come per molti degli autori che vengono comunemente inseriti nella tradizione analitica, due delle aree in cui il suo pensiero è stato più fecondo siano la logica e la metafisica. Ciò che sorprende, invece, è la sua capacità di usare le (...) teorie formali e le tesi metafisiche da lui stesso concepite come via di accesso per terreni filosofici normalmente considerati distanti da quello anglosassone. In particolare, sono numerose le occasioni in cui l’attenzione di Priest si è rivolta ad Oriente, e più nello specifico al Buddismo. The Fifth Corner of Four, il suo ultimo libro, può essere considerato a buon diritto la manifestazione più evidente di questo grande e perdurante interesse. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

This is an essay in comparative philosophy and philosophy of religion building on the ontological claims espoused by two major thinkers in the Buddhist and Christian philosophical traditions: Nāgārjuna (c. 150–250) and Hegel (1770–1831). I use Nāgārjuna’s fourfold tetralemma (catuṣkoṭi) and Hegel’s threefold dialectic (Dialektik) to propose a novel understanding of the ontological status of the self in its relation to itself and to its other, the no-self. Thus, I apply the tetralemma to the self, arguing that, to attain ontic (...) completion, the self must itself reflect the tetralemmic form in the totality of its being – nothing – both-being-and-nothing – neither-being-nor-nothing. These in turn correspond to the Hegelian in-itself, for-another, both-in-itself-and-for-another, and neither-in-itself-nor-for-another. (shrink)

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to (...) the claim that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Sengzhao (c.374–414) was a Chinese Neo-Daoist who converted to Mahāyāna Buddhism, and few people doubt his influence on Chinese Buddhist philosophy. In this article, provided his Neo-Daoism (xuanxue) and Madhyamaka Buddhism, I will present how Sengzhao featured a symbolic meaning of ‘void’ (śūnya) as rooted originally in Daoism. The Daoist contradictions, in particular between ‘being’ (you) and ‘nothing [non-being]’ (wu), are essential to the development of his doctrine of ‘no ultimate void’ (不真空論, Buzhenkonglun). To understand what Sengzhao meant by ‘void’, (...) which is in denial about the ultimate reality, I broach a notion of nihil (‘nothing’ but also ‘no value’) that bears on his discursive practice. In this light, I formulate a Daoist argument for contradictions and ECN (ex contradictione nihil—nothing follows from contradictions) from Laozi’s Daodejing. Furthermore, I elaborate on Sengzhao’s defence of ECN in his Buzhenkonglun. Reconstructing his negative approach to contradictions within the scope of the four-valued expressions (catuṣkoṭi) in the Madhyamaka tradition from Nāgārjuna, I consider a likely objection that a fifth value such as the ineffable may be inferred as void. Instead of subsuming the ineffable value under his discourse, I finally endorse Sengzhao’s purpose of linguistic and conventional approximation to the ultimate reality as silence. As such, I conclude the significance of void in Sengzhao’s denials via contradictions (ECN), i.e. an early philosophical peak of Chinese Buddhism from Daoism. (shrink)

In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as _off-topic_, whereas the two classical values are read as _true and on-topic_ and _false and on-topic_. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making (...) use of our new framework, we will offer a new interpretation of the logic of Catuskoti which combines Beall’s proposal of having _FDE_ as the correct logic with the on-topic/off-topic divide. Finally, we will offer a general result that will allow us to make sense of a family of infectious logics in terms of Beall’s on-topic/off-topic reading. (shrink)

Jay Garfield and Graham Priest have attempted to make sense of Nāgārjuna’s apparently paradoxical uses of the catuṣkoṭi, or “four corners of truth”—according to which, a sentence may be true, false, both, or neither—by presenting a series of lattices. This chapter argues that Garfield and Priest’s lattices cannot ground the logic at play in Nāgārjuna’s Mūlamadhyamakakārikā; their semantic analysis cannot be an accurate analysis of Nāgārjuna’s arguments. The chapter argues for a new semantic interpretation that places greater emphasis on the (...) suggestion that the positive catuṣkoṭi requires disambiguation between the conventional and ultimate perspectives, whereas the negative catuṣkoṭi does not. (shrink)

The article considers the theoretical and practical consequences of the so-called "soft" version of epistemological realism in Bimal K. Matilal's philosophical project. The author offers an analytical view on Matilal's philosophy, which helps to understand it in a broader prospective, comparing his arguments on perception and objectivity with contemporary arguments in Western analytical philosophy; in fact, it is possible to view Matilal not only as the proponent of revised Nyāya-Vaiśeṣika approach, but also as the follower of realistic view on language, (...) following L. Wittgenstein, W. Quine, H. Putnam and M. Dummett. Despite the fact that such interpretation may sound diverse or multivocal, it nevertheless helps to better understand both lineages of argumentation: the critical review of the impossibility of private language can be compared in both Western and Indian philosophical discourses, which leads into the domain of social epistemology. The second part of the article discusses the ethical arguments on the vulnerability of moral virtues, and the place of Dharma as a term in moral philosophy. Poetical and metaphorical language appears to be a fruitful strategy to discover the ineffable - and also via negativa and catuṣkoṭi - which is shown by Matilal on the example of the unacceptability of lying. The ethical ineffability and its interconnection with Matilal's commentaries on practical wisdom play the crucial part in the interpretations of Dharmaśāstra texts. (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.

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)

An alternative semantic framework is proposed in the following to reconstruct and make sense of “Eastern logics”: a Question-Answer Semantics (thereafter: QAS), including a set of questions-answers and a finite number of ensuing non-Fregean logical values. Thus, meaning is provided by yes-no answers to corresponding questions about relevant properties. These logical values help to show that the saptabhaṅgī (and its dual, viz., the Buddhist Mādhyamaka catuṣkoṭi) is not a many-valued paraconsistent logic but, rather, a one-valued proto-logic: a constructive machinery that (...) serves as a formal theory of judgment, rather than a Tarskian-like theory of consequence. Such an explanatory model of contradiction assumes a deep redefinition of logical values. (shrink)

There is a phenomenon that often arises when a philosophy argues that there are limits to thought/language, and tries to justify this view by giving reasons as to why there are things about which one cannot think/talk---in the process appearing to give the lie to the claim. I will be concerned with that phenomenon. We will look at some of philosophies that fall into this camp (those of Wittgenstein, Heidegger, and Mahayana Buddhism). We will then see that Buddhist philosophy has (...) resources to address this kind of issue not present in Western traditions, namely the catuskoti and its developments. The catuskoti is a principle to the effect that claims can be true, false, both, or neither. Later developments add a fifth possibility: ineffability. Of course, one might be skeptical that such ideas can be made logically respectable. I will show how to do so with some simple tools from contemporary non-classical logic. (shrink)

Does it make sense to employ modern logical tools for ancient philosophy? This well-known debate2 has been re-launched by the indologist Piotr Balcerowicz, questioning those who want to look at the Eastern school of Jainism with Western glasses. While plainly acknowledging the legitimacy of Balcerowicz's mistrust, the present paper wants to propose a formal reconstruction of one of the well-known parts of the Jaina philosophy, namely: the saptabhangi, i.e. the theory of sevenfold predication. Before arguing for this formalist approach to (...) philosophy, let us return to the reasons to be reluctant at it. (shrink)

At the end of his review of The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi by Graham Priest, Mark Siderits (2019) remarks.

This paper considers the matter of representation in Vedānta by examining key claims in the Ṛgveda and the Upaniṣads, which are some of its principal texts. Specifically, we consider the logic behind the paradoxical verses on creation and the conception of consciousness as the ground on which the physical universe exists. This also is the template that explains the logical structure underlying the principal affirmations of the Upaniṣads. The five elements and consciousness are taken to pervade each other, which explains (...) how gross matter is taken to consist of all the four different kinds of atoms that get manifested in different states of the substance. The verses on creation are an example of the use of catuṣkoṭi in Indian philosophy prior to the use of it by Nāgārjuna in the Madhyamaka tradition. It also contrasts central ideas of Vedānta with the corresponding contemporary scientific ideas on consciousness. (shrink)

This research attempts to evaluate the hermeneutic characteristics of catuṣkoṭi (tetralemma) in the ‘Nirvāṇa’ Chapter of the _Mūlamadhyamakakārikā_ (Ch. 25), focusing on the identity thesis between nirvāṇa and saṃsāra. Regarding the structure of the tetralemma posited by Nāgārjuna (ca. 150-ca. 250), this study criticizes the dialectical interpretation of Robinson and Kajiyama from the perspective of Siderits and Katsura’s semantic approach to the extent that it does not deny ultimate truth. This sets it apart from the semantic view presented by Siderits (...) and Garfield (J Indian Philos 41:655–664, 2013). To support this position, the commentaries of Piṅgala (ca. 4C) and Candrakīrti (ca. 600–ca. 650) are also used, along with Nāgārjuna’s _Vigrahavyāvartanī_. From this standpoint, the meaning of non-duality of nirvāṇa and saṃsāra is evaluated, in the sense that both are negated in the ultimate sense, as opposed to the metaphysical view, which interprets the tetralemma in a dialectical way. Siderits and Katsura suggests that, as in the case of nirvāṇa, “just as the four lemmas applying to saṃsāra is rejected, ultimately there is no such state as saṃsāra,” because it is empty of its intrinsic nature. Following this line of reasoning, the thesis of Tathāgata in 25.17 and 25.18 can also be interpreted semantically as “there is no real distinction between before and after death, due to the absence of intrinsic nature (_svabhāva_) in Tathāgata.” Likewise, the semantic approach here negates the four propositions of nirvāṇa and saṃsāra only, as operated when clinging to identity. (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)

In his book review of Graham Priest's The Fifth Corner of Four, Mark Siderits, while criticising Priest's philology, suggests that Priest's work is 'of considerable interest' for two reasons. First, 'when two independent traditions use similar methods to work on similar issues, it is always possible that one may have hit on approaches that the other missed'. Second, 'the decentering that can be induced by looking at another tradition may trigger fresh insights, even if those insights are not ones that (...) were actually developed by the tradition marked 'other''. The main task of this paper is to unpack Siderits' thought. By analysing some of Priest's work, I will suggest a decentering that must have taken place in China when Buddhism was 'exported to China in Buddhist shipping containers'. For anyone familiar with the forms of Buddhist philosophy developed in India, various forms of Chinese Buddhism can often look strange. Some ideas that were debated and defended by Indian Buddhists do not appear anywhere in Chinese Buddhism and some assumptions have been quietly added to Buddhism by Chinese Buddhists. By showing that Priest's work brings out the 'innovation' that Chinese Buddhists gave to Buddhism, I will suggest that it is this decentering that Siderits suggests Priest makes use of. (shrink)