Buddhist logic – Viewpoints which Matter

The Fifth Corner of Four: Catuskoti in Buddhist Logic

Key Terms

Logic
Classical Logic
Non Classical Logic
Many Valued Logic
Multi Valued Logic
Three Valued Logic
Four Valued Logic
Catuskoti
Buddhist Logic
Lukasiewicz Logic
Kleene Logic
Intuitionistic Logic
Five Valued Logic

Researchers

Graham Priest
Kreutz, Adrian
Kapsner, Andreas
Jan Westerhoff
Hans Rudolf Kantor
Gunaratne, R. D.

The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi

Source: The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi. By Graham Priest. New York: Oxford University Press, 2018. / Matthew T. Kapstein

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Key Sources of Research

“Understanding Nāgārjuna’s Catuṣkoṭi.”

Gunaratne, R. D.

Philosophy East and West 36, no. 3 (1986): 213–34. https://doi.org/10.2307/1398772.

https://www.jstor.org/stable/1398772

“The Logical Form of Catuṣkoṭi: A New Solution.”

Gunaratne, R. D.

Philosophy East and West 30, no. 2 (1980): 211–39. https://doi.org/10.2307/1398848.

https://www.jstor.org/stable/1398848

Na ̄ga ̄rjuna’s Logic

Aaron J. Cotnoir | aaron.cotnoir@uconn.edu| January 28, 2010

in G Priest , K Tanaka , Y Deguchi & J Garfield (eds) , The Moon Points Back . Oxford University Press . 2015

https://research-repository.st-andrews.ac.uk/handle/10023/11329

“The Catuskoti as a bilattice.”

Onishi, Takuro.

“Rationality, Argumentation and Embarrassment: A Study of Four Logical Alternatives (Catuṣkoṭi) in Buddhist Logic.”

Bharadwaja, V. K.

Philosophy East and West 34, no. 3 (1984): 303–19. https://doi.org/10.2307/1398631.

https://www.jstor.org/stable/1398631

RECAPTURE, TRANSPARENCY, NEGATION AND A LOGIC FOR THE CATUSKOTI

Kreutz, Adrian (2019).

Comparative Philosophy 10 (1).

https://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=1264&context=comparativephilosophy

https://philpapers.org/rec/KRERTN-3

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.

On the relationship of Advaita Vedānta and Mādhyamika Buddhism

Reynolds, Eric T.

University of British Columbia
Date Issued. 1975

https://open.library.ubc.ca/media/stream/pdf/831/1.0093585/1

https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/831/items/1.0093585

Paradox and Negation in the Upanishads, Buddhism and the Advaita Vedanta of Sankaracarya (India)

Thompson, Heather. California Institute of Integral Studies

ProQuest Dissertations Publishing, 1982. 8400050.

This dissertation explores the uses of Paradox and Negation–in contrast and comparison–through the Upanishads and Buddhism to the Advaita Vedanta of Sankara. Paradox and Negation employed are not of ordinary parlance but are philosophic and dialectic tools indicating a state beyond the world of appearances–the Supreme.The Upanishads indicate the Supreme state by positing the Transcendent Atman–The Transcendent Subjectivity–and the Transcendent Brahman–the Transcendent Existentiality. In both aspects, the Supreme is seen as the antecedent state to the nest of appearances: Its existence supports all phenomena. By juxtaposing two apparently incongruous statements–thus producing a Paradox–the Upanishadic seers pushed the mind beyond its normal boundaries into a meditative insight. Similarly, through Negation, the seers denied the self-sustaining validity of phenomena.The Buddha, in contrast, forwarded a pragmatic’ philosophy, refusing to speculate about the existence or nature of the Supreme. Rather, he examined the conditions of daily life, their cause, their cessation and the route to their cessation. Passing through the nominalist teachers of the Hinayana school to the Mahayana school, a growing use of Paradox and Negation is seen and culminates in the dialectics of Nagarjuna. Nagarjuna pushed Paradox and Negation to extremes in his Catuskoti, four-fold argument, which revealed the logical inadequacies of all concepts. They have only causal or relational validity within the boundaries of the intellect. Outside that boundary, they have no self-nature or existence.Sankara, in his Advaita Vedanta, rising to another level on the spiral of Indian philosophy, takes from the teachings of the previous two traditions and elaborates and develops both. He recognizes that the phenomenal world has reality–but a temporary one. It exists only so long as the mind is held in sway by illusion and ignorance. Once the mind has been restored to its true state–which is a meditatively disciplined one–the phenomenal world is seen as having relative existence only and as totally dependent on the Supreme Brahman.The uses of Paradox and Negation by the three schools will be examined as contrasts and complements to each other.

“Who Understands the Four Alternatives of the Buddhist Texts?”

Wayman, Alex.

Philosophy East and West 27, no. 1 (1977): 3–21. https://doi.org/10.2307/1397697.

https://www.jstor.org/stable/1397697

THE LOGIC OF THE CATUSKOTI

GRAHAM PRIEST

Comparative Philosophy Volume 1, No. 2 (2010): 24-54 Open Access / ISSN 2151-6014 http://www.comparativephilosophy.org

https://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=1032&context=comparativephilosophy

CONTRADICTION AND RECURSION IN BUDDHIST PHILOSOPHY:
FROM CATUṢKOṬI TO KŌAN

Kreutz, Adrian (2019).

In Takeshi Morisato & Roman Pașca (eds.), Asian Philosophical Texts Vol. 1. Milano: Mimesis International. pp. 133-162.

https://philarchive.org/rec/KRECAR-2

Click to access contradiction_and_recursion_in_buddhist.pdf

Cutting Corners: A Critical Note on Priest’s Five-Valued Catuṣkoṭi.

Kapsner, Andreas (2020).

Comparative Philosophy 11 (2).

https://philpapers.org/rec/KAPCCA-3

https://scholarworks.sjsu.edu/comparativephilosophy/vol11/iss2/10/

The Fifth Corner Re-Examined: Reply to Priest

Andreas Kapsner January 24, 2022

Click to access The-Fifth-Corner-Re-Examined-Reply-to-Priest.pdf

“Don’t be so Fast with the Knife: A Reply to Kapsner,”

PRIEST, Graham (2020)

Comparative Philosophy: Vol. 11: Iss. 2, Article 11.
Available at: https://scholarworks.sjsu.edu/comparativephilosophy/vol11/iss2/11

The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuskoti.

Priest, Graham (2018).

Oxford, England: Oxford University Press.

https://philpapers.org/rec/PRITFC

Interpreting Interdependence in Fazang’s Metaphysics.

Jones, Nicholaos (2022).

Journal of East Asian Philosophy 2:35-52.

On Buddhist Logic

Adrian Kreutz

Thesis
MA by Research
University of Birmingham
Department of Philosophy

https://philpapers.org/rec/KREOBL

Click to access Kreutz2020MRes.pdf

Abstract

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.

Indian Logic

Wikipedia

https://en.wikipedia.org/wiki/Indian_logic

“The Logic of Four Alternatives.”

Jayatilleke, K. N.

Philosophy East and West 17, no. 1/4 (1967): 69–83. https://doi.org/10.2307/1397046.

https://www.jstor.org/stable/1397046

A Russellian Analysis of Buddhist Catuskoti.

Jones, Nicholaos (2020).

Comparative Philosophy 11 (2):63-89.

https://scholarworks.sjsu.edu/comparativephilosophy/vol11/iss2/6/

The Catuskoti

by Peter Fumich

An essential principal to Buddhism is non-dualism. However, the Catuskoti is clearly a system still immersed in dualism. This sort of dualism is more like that of the dual in Tao. Taken by themselves, the two relative states contain within themselves the nature of the absolutes. The only thing which differentiates are the notions both, neither. It is much like the yin and yang symbol. However, more accurately as we go on we see a fractal emerge. Hence, the ultimate truth, one in which we seem to conceptually call the more subtle truth is an illusion. The infinite recursion of this extension hints at an ultimate truth arising at ¥. The conception which takes within it this very fractal nature is truly enlightened. A truth which is free from dualism is either entirely immersed within dualism, or it lacks the distinction of truth all together. The use of the Catuskoti serves the purpose to hint ultimately at a non-truth. Speaking in terms of tautologies and ineffables, we will see the Catuskoti is a conceptual elaboration of traditional dualism, absolute true and false. While this itself is a conceptual elaboration of the union of true and false, Sunyata or 0. Sunyata is a conceptual elaboration of itself, which of course cannot be explained conceptually because then it emerges from non-conceptual Sunyata to conceptual Sunyata of 0. We can hint at it by saying, as a truth space, the non-conceptual Sunyata be U, then the set of ineffables of U and tautologies of U forms the conceptual elaboration of U. It should be clear that careful attention to our use of V4, the Klein 4 group, will be sufficient to realize a conceptual grasp of the non-conceptual Sunyata. See http://jcer.com/index.php/jcj/article/view/420

https://jcer.com/index.php/jcj/article/view/420/445

https://11prompt.com/?q=node/491

Buddhist Logic and Quantum Dilemma

by Jayant Burde

ISBN: 9788120835528, 8120835522
Year of Publication: 2012
Binding: Hardcover
Edition: 1st

Graham Priest

Handbook of the History of Logic

Volume 8, 2007, Pages 129-204

https://www.sciencedirect.com/science/article/abs/pii/S1874585707800069

The Many Valued and Nonmonotonic Turn in Logic

Graham Priest, in Handbook of the History of Logic, 2007

https://www.sciencedirect.com/topics/computer-science/valued-semantics

3.3 Contradiction in Eastern Philosophy

We have not finished with the Neoplatonist tradition yet, but before we continue with it, let us look at Eastern Philosophy, starting in India. Since very early times, the Law of Non-Contradiction has been orthodox in the West. This is not at all the case in India. The standard view, going back to before the Buddha (a rough contemporary of Aristotle) was that on any claim of substance there are four possibilities: that the view is true (and true only), that it is false (and false only), that it is neither true nor false, and that it is both true and false. This is called the catuskoti (four corners), or tetralemma.⁴⁸Hence, the possibility of a contradiction was explicitly acknowledged. The difference between this view and the orthodox Western view is the same as that between the semantics of classical logic and the four-valued semantics for the relevant logic of First Degree Entailment (as we shall see). In classical logic, sentences have exactly one of the truth values T (true) and F (false). In First Degree Entailment they may have any combination of these values, including both and neither. Just to add complexity to the picture, some Buddhist philosopers argued that, for some issues, all or none of these four possibilities might hold. Thus, the major 2nd century Mahayana Buddhist philosopher Nāgārjuna is sometimes interpreted in one or other of these ways. Arguments of this kind, just to confuse matters, are also sometimes called catuskoti. Interpreting Nāgārjuna is a very difficult task, but it is possible to interpret him, as some commentators did, as claiming that these matters are simply ineffable.⁴⁹

The Law of Non-Contradiction has certainly had its defenders in the East, though. It was endorsed, for example, by logicians in the Nyaayaa tradition. This influenced Buddhist philosophers, such as Darmakārti, and, via him, some Buddhist schools, such as the Tibetan Gelug-pa. Even in Tibet, though, many Buddhist schools, such as the Nyngma-pa, rejected the law, at least for ultimate truths.

Turning to Chinese philosophy, and specifically Taoism, one certainly finds utterances that look as though they violate the Law of Non-Contradiction. For example, in the Chuang Tzu (the second most important part of the Taoist canon), we find:⁵⁰

That which makes things has no boundaries with things, but for things to have boundaries is what we mean by saying ‘the boundaries between things’. The boundaryless boundary is the boundary without a boundary.

A cause of these contradictions is not unlike that in Neoplatonism. In Taoism, there is an ultimate reality, Tao, which is the source and generator of everything else. As the Tao Te Ching puts it:⁵¹

The Tao gives birth to the One.

The One gives birth to the two.

The Two give birth to the three —

The Three give birth to every living thing.

It follows, as in the Western tradition, that there is nothing that can be said about it. As the Tao Te Ching puts it (ch. 1):

The Tao that can be talked about is not the true Tao.

The name that can be named is not the eternal name.

Everything in the universe comes out of Nothing.

Nothing — the nameless — is the beginning…

Yet in explaining this situation, we are forced to say things about it, as the above quotations demonstrate.

Chan (Zen) is a fusion of Mahayana Buddhism and Taoism. As might therefore be expected, the dialetheic aspects of the two metaphysics reinforce each other. Above all, then, Zen is a metaphysics where we find the writings of its exponents full of apparent contradictions. Thus, for example, the great Zen master Dōgen says:⁵²

This having been confirmed as the Great Teacher’s saying, we should study immobile sitting and transmit it correctly: herein lies a thorough investigation of immobile sitting handed down in the Buddha-way. Although thoughts on the immobile state of sitting are not limited to a single person, Yüeh-shan’s saying is the very best. Namely: ‘thinking is not thinking’.

or:⁵³

An ancient buddha said, ‘Mountains are mountains, waters are waters.’ These words do not mean that mountains are mountains; they mean that mountains are mountains. Therefore investigate mountains thoroughly…

Now interpreting all this, especially the Chinese and Japanese writings, is a hard and contentious matter. The writings are often epigrammatic and poetical. Certainly, the writings contain assertions of contradictions, but are we meant to take them literally? It might be thought not. One suggestion is that the contradictions are uttered for their perlocutionary effect: to shock the hearer into some reaction. Certainly, this sort of thing plays a role in Zen, but not in Mahayana Buddhism or Taoism. And even in Zen, contradictions occur in even the theoretical writings.

More plausibly, it may be suggested that the contradictions in question have to be interpreted in some non-literal way. For example, though ultimate reality is literally indescribable, what is said about it gives some metaphorical description of its nature. This won’t really work either, though. For the very reason that ultimate reality is indescribable is precisely because it is that which brings all beings into being; it can therefore be no being (and so to say anything about it is contradictory). At least this much of what is said about the Tao must be taken literally, or the whole picture falls apart.⁵⁴

Indian Logic

https://tibetanbuddhistencyclopedia.com/en/index.php/Indian_logic

The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi

Graham Priest, The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi, Oxford University Press, 2018, 172pp., ISBN 9780198758716.

Reviewed by Mark Siderits, Seoul National University (Emeritus)
2019.05.18

https://ndpr.nd.edu/reviews/the-fifth-corner-of-four-an-essay-on-buddhist-metaphysics-and-the-catuskoti/

The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi

Reviewed by Ronald S. Green

Journal of Buddhist Ethics
ISSN 1076-9005 http://blogs.dickinson.edu/buddhistethics Volume 27, 2020

Click to access Green_Review_of_Priest_The_Fifth_Corner_of_Four-1.pdf

Review of Graham Priest: The Fifth Corner of Four. An Essay on Buddhist
Metaphysics and the Catuṣkoṭi, Oxford University Press, Oxford, 2018.

Mind, 2019, forthcoming.
Jan Westerhoff

https://ora.ox.ac.uk/objects/uuid:d8fa6404-3e65-4711-a7c9-e7c696e6602c/files/rb8515n415

https://ora.ox.ac.uk/objects/uuid:d8fa6404-3e65-4711-a7c9-e7c696e6602c

The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi. By Graham Priest. New York: Oxford University Press, 2018. 208 pages.

Matthew T. Kapstein
École Pratique des Hautes Études, Paris, and the University of Chicago

Click to access 4-4-Kapstein-review.pdf

Review: The Fifth Corner of Four

“Graham Priest, “The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuskoti.””.

Kreutz, A.

Philosophy in Review, Vol. 39, no. 3, Aug. 2019, pp. 146-8, https://journals.uvic.ca/index.php/pir/article/view/18802.

https://journals.uvic.ca/index.php/pir/article/view/18802

The Catuṣkoṭi, the Saptabhaṇgī, and “Non-Classical” Logic.

Priest, G. (2022).

In: Sarukkai, S., Chakraborty, M.K. (eds) Handbook of Logical Thought in India. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2577-5_50

https://link.springer.com/referenceworkentry/10.1007/978-81-322-2577-5_50

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https://link.springer.com/chapter/10.1007/978-81-322-2719-9_24?fromPaywallRec=true#citeas

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“Doxographical Appropriation of Nāgārjuna’s Catuṣkoṭi in Chinese Sanlun and Tiantai Thought”

Kantor, Hans Rudolf. 2021.

Religions 12, no. 11: 912. https://doi.org/10.3390/rel12110912

https://www.mdpi.com/2077-1444/12/11/912

One Negation, Two Ways of Using It: Prasajyapratiṣedha in Bhāviveka and Candrakīrti’s Argumentation1

Chen Hsun-Mei
National Taiwan University / Kyoto University / Harvard Yenching Institute Wang Wen-Fang
Professor, National Yang Ming University

Click to access Chen-Hsun-Mei-National-Taiwan-University-Kyoto-University-Harvard-Yenching-Institute-Wang-Wen-Fang-2020.pdf

Nāgārjuna’s Tetralemma in Yamauchi Tokuryū’s Philosophy

Romaric Jannel

https://philarchive.org/archive/JANNTI

Three new genuine five-valued logics

Mauricio Osorio1 and Claudia Zepeda2
1 Universidad de las Am ́ericas-Puebla,
2 Benem ́erita Universidad Ato ́noma de Puebla {osoriomauri,czepedac}@gmail.com

Click to access paper8.pdf

https://www.sciencedirect.com/science/article/pii/S1571066120300888

Many-Valued Logic

SEP

https://plato.stanford.edu/entries/logic-manyvalued/

Many-valued logics. A mathematical and computational introduction..

Augusto, Luis M. (2020).

London: College Publications.

https://philarchive.org/rec/AUGMLA

Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics.

“Many-valued logic and its philosophy.”

Malinowski, Grzegorz.

In The Many Valued and Nonmonotonic Turn in Logic (2007).

Improving the efficiency of using multivalued logic tools.

Suleimenov, I.E., Vitulyova, Y.S., Kabdushev, S.B. et al.

Sci Rep 13, 1108 (2023). https://doi.org/10.1038/s41598-023-28272-1

https://www.nature.com/articles/s41598-023-28272-1

Improving the efficiency of using multivalued logic tools: application of algebraic rings.

Suleimenov, I.E., Vitulyova, Y.S., Kabdushev, S.B. et al.

Sci Rep 13, 22021 (2023). https://doi.org/10.1038/s41598-023-49593-1

https://www.nature.com/articles/s41598-023-49593-1

An Introduction to Many-valued Logics

by Robert Ackermann

https://www.routledge.com/An-Introduction-to-Many-valued-Logics/Ackermann/p/book/9780367426040

“Foreword: Three-Valued Logics and Their Applications.”

Cobreros, Pablo, Paul Égré, David Ripley, and Robert van Rooij.

Journal of Applied Non-Classical Logics 24, no. 1–2 (2014): 1–11. doi:10.1080/11663081.2014.909631.

https://www.tandfonline.com/doi/full/10.1080/11663081.2014.909631

The Two-Valued Iterative Systems of Mathematical Logic.

Post, Emil L..

(AM-5), Volume 5, Princeton: Princeton University Press, 1942. https://doi.org/10.1515/9781400882366

Indian Modernity: Contradictions, Paradoxes and Possibilities

Author Avijit Pathak

Avijit Pathak is Professor at the Centre for the Study of Social Systems, Jawaharlal Nehru University, New Delhi.

Publisher Taylor & Francis, 2023
ISBN 1003830838, 9781003830832
Length 254 pages

‘Quintum Non-Datur‘, The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuskoti

Priest, Graham,

(Oxford, 2018; online edn, Oxford Academic, 20 Dec. 2018), https://doi.org/10.1093/oso/9780198758716.003.0002, accessed 21 May 2024.

Levels of truth and reality in the philosophies of Descartes and samkara.

Schroeder, Craig (1985).

Philosophy East and West 35 (3):285-293.

https://doi.org/10.2307/1399157.

https://www.jstor.org/stable/1399157

https://www.proquest.com/openview/877c873a024f65b35ce731710fbca754/1?pq-origsite=gscholar&cbl=1820847

In the West, the general tendency of philosophers has been to understand things as being either real or unreal and to view propositions as either true or false. It is assumed that that which is real or true is opposite and exclusive of that which is unreal or untrue and that there can be no mediating ground. Only rarely does one find a philosopher who attempts to qualify truth and reality, that is, to hold that one thing might be, to some degree, more or less real than another, or to hold that one proposition could be more true than a second, while remaining less true than a third. On the contrary, philosophy in the West has generally been a quest to determine more clearly what is real and true and to contrast it more sharply with what is held to be unreal and untrue.

Often in this quest, however, philosophers display a tendency to qualify truth and reality even while trying to deny or exclude the possibility of such qualification. In Descartes’ writings, this qualification is set forth through his method of radical doubt as exercised in the Meditations. In his search for the real and the true, Descartes proceeds to doubt all of his former, commonsense beliefs. In this process, starting with that which is most easily doubted, that which seems the least ontologically and epistemologically well-grounded, he proceeds to submit to radical doubt beliefs of firmer and firmer ontological and epistemological footing, in search of something indubitable upon which to rebuild the structure of truth and reality. In spite of the fact that this method of radical doubt results in a reassertion of that which Descartes had more naively believed all along, it is instructive to compare the mediating levels observed by Descartes in his method to those of a non-Western philosopher who admits to qualified levels of truth and reality. Thus, while Descartes’ conclusions follow the more general Western pattern of drawing strict lines of demarcation between reality and nonreality, truth and untruth, we will concentrate more on his method, which stratifies and qualifies reality and truth prior to the drawing of these lines. Qualified levels of truth and reality are less of a problem for Indian philosophers. While India, too, has its schools of philosophy which admit to only two ontological or epistemological possibilities, one also finds in other schools a very careful and deliberate grading of reality and truth from levels of varying qualification to a level of ultimacy. Samkara’s Advaita Vedanta is one such school, and it is Samkara that will be considered in a comparison with Descartes. There are, strictly speaking, only one level of full truth and reality and one level· of full untruth and nonreality for Samkara. These extremes, however, are mediated by at least two other levels which are sadasadvilaksana,” other than real and unreal.” The reality or nonreality of these middle levels can only be understood in relation to the highest and lowest levels of reality. This ambiguity in their nature renders them anirvacanTya,” that about which we cannot speak.” For Samkara, there are only two sorts of things which are fully unreal,(1) the

The Problem of Two Truths in Buddhism and Vedānta

Author G.M.C. Sprung
Edition illustrated
Publisher Springer Science & Business Media, 2012
ISBN 9401025827, 9789401025829
Length 132 pages

The Uses of the Four Positions of the “Catus-koti” and the Problem of the Description of Reality in Mahayana Buddhism

RUEGG, D SEYFORT.

Journal of Indian Philosophy; Dordrecht, Holland Vol. 5, (Jan 1, 1977): 1.

https://www.proquest.com/openview/f02b0f810d35117b1b575d06325787f1/1?pq-origsite=gscholar&cbl=1818354

https://www.jstor.org/stable/23438780

Four Corners—East and West.

Priest, G. (2011).

In: Banerjee, M., Seth, A. (eds) Logic and Its Applications. ICLA 2011. Lecture Notes in Computer Science(), vol 6521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18026-2_2

https://link.springer.com/chapter/10.1007/978-3-642-18026-2_2

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YU-KWAN, NG.

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Journal of Indian Philosophy 10, no. 4 (1982): 309–37. http://www.jstor.org/stable/23445371.

On Garfield and Priest’s interpretation of the use of the catuskoti in Mūlamadhyamakakārikā.

Wang, C., & Wen-fang, W. (2024).

Asian Philosophy, 1–21. https://doi.org/10.1080/09552367.2024.2309769

https://www.tandfonline.com/doi/abs/10.1080/09552367.2024.2309769

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The Deconstructionist Interpretation of Nagarjuna’s Catuskoti∗

Shi, Ruyuan (Chien-Yuan Hsu) PhD candidate, the Dep. of Religious Studies, the University of Calgary, Canada Sessional instructor, Mount Royal University, Canada

Click to access 龍樹四句的解構詮釋.pdf

“INTRODUCTION: BUDDHISM AND CONTRADICTION.”

Tanaka, Koji.

Philosophy East and West 63, no. 3 (2013): 315–21. http://www.jstor.org/stable/43285829.

“DOES A TABLE HAVE BUDDHA-NATURE?”

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Philosophy East and West 63, no. 3 (2013): 373–86. http://www.jstor.org/stable/43285836.

Buddhist Formal Logic, Part 1

Richard See Yee Chi

Edition reprint
Publisher Motilal Banarsidass Publ., 1984
ISBN 8120807308, 9788120807303
Length 304 pages

Reviewed Work: Buddhist Formal Logic

Richard S. Y. Chi

Review by: Douglas Dunsmore Daye
Philosophy East and West
Vol. 23, No. 4 (Oct., 1973), pp. 525-535 (11 pages)
Published By: University of Hawai’i Press

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Alam Nizar, Syed Moynul.

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Journal of Indian Philosophy 8, no. 3 (1980): 303–6. http://www.jstor.org/stable/23440331.

Early Buddhist Theory of Knowledge

By K N Jayatilleke

Edition 1st Edition First Published 1963

eBook Published 15 August 2013

Pub. Location London Imprint Routledge

DOI https://doi.org/10.4324/9781315888347

Pages 524

eBook ISBN 9781315888347

https://www.taylorfrancis.com/books/mono/10.4324/9781315888347/early-buddhist-theory-knowledge-jayatilleke

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Journal of Chinese philosophy 20, no. 3 (1993): 313-347.

Nagarjuna’s Madhyamaka: A Philosophical Introduction

Author Jan Westerhoff
Publisher Oxford University Press, 2009
ISBN 0199705119, 9780199705115
Length 256 pages

Izutsu’s Zen Metaphysics of I-Consciousness vis-à-vis Cartesian Cogito

Takaharu Oda
2020, Comparative Philosophy

Issue: 2
Volume: 11
Page Numbers: 90-112
Publication Date: 2020
Publication Name: Comparative Philosophy

https://doi.org/10.31979/2151-6014(2020).110207

https://www.academia.edu/43756980/Izutsu_s_Zen_Metaphysics_of_I_Consciousness_vis_à_vis_Cartesian_Cogito

What Can’t be Said: Paradox and Contradiction in East Asian Thought

Authors Yasuo Deguchi, Jay L. Garfield, Graham Priest, Robert H. Sharf
Publisher Oxford University Press, 2021
ISBN 0197526209, 9780197526200
Length 256 pages

Relation and Negation in Indian Philosophy

Key Terms

Para consistent logic
Non-classical logic
Paradoxes
Contradictions
Catuskoti
Saptabhangi
Tetralemma
Trilemma
Dilemma
Buddhist logic
Unanswerable questions
Nagarjuna
Mula madhya maka karika
Truth predicate
Para consistency
First Degree Entailment
Many-valued logic
Relational semantics
Nyaya
Navya Nyaya
Neti Neti
Logic
Indian Philosophy
Hindu Logic
Jaina Logic
Principle of the Excluded Fifth
Principle of the Excluded Third
Nasidya Sukta
Relation
Negation

Researchers

Kalidas Bhattacharyya
Purushottama Bilimoria
Matilal, Bimal Krishna
Satis Chandra Vidyabhusana
George Bosworth Burch
Graham Priest
J. F. Staal
Westerhoff, Jan
Gunaratne, R. D.
Rahlwes, Chris
Ruegg, D.S.

A History of Indian Logic (ancient, Mediæval and Modern Schools.)

Source: A History of Indian Logic (ancient, Mediæval and Modern Schools.)

Relation in Indian Philosophy

Source: The Problem of Relation in Indian Philosophy

Negation and Negative Facts in Western and Indian Logic

Source: Negation and Negative Facts in Western and Indian Logic

My related Posts

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Chinese Tiantai and Japanese Tendai Buddhism
Dialogs and Dialectics
Meditations on Emptiness and Fullness
Dhyan, Chan, Son and Zen Buddhism: Journey from India to China, Korea and Japan
What is Yogacara Buddhism (Consciousness Only School)
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Five Types of Systems Philosophy
On Holons and Holarchy
Networks and Hierarchies
Boundaries and Networks
Boundaries and Relational Sociology
Semiotic Boundaries
Social and Symbolic Boundaries
Boundaries and Distinctions
Relational Consciousness: Subjectivity and Otherness
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From Individual to Collective Intentionality
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Networks, Narratives, and Interaction
Multilevel Approach to Research in Organizations
Relational Turn in Economic Geography
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Key Sources of Research

Nāgārjuna, Śaṅkara, Krishnamurti: Negation as a Spiritual Exercise.

Tubali, S. (2023).

In: The Transformative Philosophical Dialogue. Sophia Studies in Cross-cultural Philosophy of Traditions and Cultures,

vol 41. Springer, Cham. https://doi.org/10.1007/978-3-031-40074-2_11

https://link.springer.com/chapter/10.1007/978-3-031-40074-2_11

Abstract

To gain a deeper insight into the role that negation played in the Krishnamurti dialogue, I compare it to two well-researched negation-based philosophies. The first is Nāgārjuna’s Buddhist philosophy of the ‘middle way’ (madhyamaka), in particular his most prominent work The Fundamental Wisdom of the Middle Way (Mūlamadhyamakakārikā). The second is the eighth-century Śaṅkara’s Hindu system of Advaita Vedānta, mainly his commentary on the Bṛhadāraṇyaka Upaniṣad and his independent work A Thousand Teachings(Upadeśasāhasrī). I start by introducing the Buddha’s imponderables and the way that Nāgārjuna developed these segments of the Buddha’s Dharma into the system of the middle way (madhyamaka). In this section, I demonstrate the transformative nature of this system, based on the original text as well as scholarly sources. The next section is dedicated to the presentation of Śaṅkara’s Advaita Vedānta as a negative philosophy and to the ways in which his method corresponds to and stands in contrast to Nāgārjuna’s negation. Finally, I highlight the uniqueness of Krishnamurti’s dialectical negation: while the two classical paragons of the negative approach practised by Nāgārjuna and Śaṅkara are tools for the elimination of metaphysical views and epistemological approaches, Krishnamurti’s is a psychological and post-traditional negation whose aim is to do away with past, knowledge, and authority. More generally, I argue that, as a feature of the transformative dialogue, negation is a spiritual exercise that prepares for a particular experience and facilitates it: the discussant’s ability to perceive reality with naked eyes and a bare mind.

Notes

I shall return to Sañjaya’s form of negation in the following section.

It is worth mentioning that the scriptures that inspired Nāgārjuna’s and Śaṅkara’s practices of negation – the Buddha’s Dharma talks in the Pāli Canon and the Bṛhadāraṇyaka Upaniṣad, as well as a significant number of other Upaniṣads – had also been largely narrated in the explicit form of a dialogue.

This reading of the text is supported by Nāgārjuna scholars such as Jay L. Garfield (for example, 1995: 209; Garfield and Priest 2003: 11).

For a contrary view, see Raju (1954: 703), who perceives Nāgārjuna’s and Śaṅkara’s negation (particularly, their use of four-cornered negation) as ‘a principle expressive of ultimate reality’.

See, for instance, the debate between Stafford L. Betty (1983: 123–138, 1984: 447–450) and David Loy (1984: 437–445).

In Śaṅkara’s case, as I will show in the second section, all metaphysical claims but one.

However, the logical gulf separating Indian thought from Western logical traditions seems to be gradually being bridged as a result of efforts initially made by twentieth-century Western philosophers in response to logical paradoxes. Two important developments have been the emergence of paraconsistent logic, which accommodates inconsistency in a controlled way, viewing inconsistent information as potentially informative, and the subsequent modern form of dialetheism (“two-way truth”), which transcends the law of non-contradiction by maintaining that there are indeed true contradictions (Priest et al. 2022a, b).

We know of Sañjaya only through early Buddhist literature which refers to him critically (Jayatilleke 1963: 135).

Jayatilleke (ibid., 138) maintains that this formula was not only Sañjaya’s, but was shared by all classical Indian sceptical schools of thought.

The Brahmajāla Sutta contains a thorough negation of sixty-two views that prevailed among recluses in the time of the Buddha.

Or ‘eel-wrigglers’, a term which should be understood as either denoting verbal jugglery or as an analogy that likens sceptics to eels that constantly squirm about in the water and are difficult to get hold of (Jayatilleke 1963: 122).

.Jones (2016: 13) convincingly unveils the reasoning behind the Buddha’s strategy of negation in the Vacchagotta dialogue.

This brings us back to negation as a practice among mystics who tend to defend their experiences as ‘ineffable’. Blackwood (1963: 202–206) suggests that it is not that mystics argue that all descriptive statements are false, but rather that all descriptive statements are ‘inapplicable or inappropriate’ when it comes to their transcendent realizations. Thus, mystics simply disregard syntactic and logical rules, such as the law of non-contradiction, which are only relevant as long as one wishes to ‘make learning possible’ (ibid., 207–209).

See also Ganeri’s (2013a: 51–53) useful point that the Buddha’s negation in the Vacchagotta dialogue was not to keep secret knowledge in his fist but to ensure that he would not impart knowledge that is unnecessary and therefore ultimately harmful. Thus, using negation he could challenge the premise of the question itself (ibid. 53).

Nāgārjuna clearly deems the refutation of all views the centrepiece of the Buddha’s Dharma, since he concludes his work by praising Gautama Buddha for teaching the ‘true doctrine which leads to the relinquishing of all views’ (XXVII: 30).

In this sense, the Mūlamadhyamakakārikā is in line with the general tendency of some forms of Indian and Buddhist debate to value reasoning and argumentation not only for their truth-preserving and truth-validating properties, but also for their ability to promote truth (Ganeri 2013a: 125).

With the word ‘trans-logical’ I also indicate that contrary to Betty’s qualm (1984: 448), the ladder of logic is not a mere apparatus that one ought to kick out from beneath oneself after climbing up it, but a form of discriminating wisdom on which one builds.

This is stated cautiously, since certain forms of South Asian argumentation, including four-cornered negation and Nāgārjuna’s use of it, can help Western thought to accept other forms of logic and thus to arrive at broader logical formulas.

In the collective memory of mainstream Hinduism, Śaṅkara is honoured as a philosopher-saint whose efforts to give a coherent structure to disparate Hindu beliefs and practices have safeguarded Hinduism from the challenges posed by the rise of Buddhism (Shearer 2017: xiii). There are also substantial examples of criticism of Buddhist views in Śaṅkara’s works (e.g. Brahmasūtrabhāṣya II.2.18–32).

Shearer (2017: xxiii) considers Śaṅkara’s employment of relentless reasoning, logic, and dialectic a part of his methodological toolkit (upāya, or useful means), which is only utilized to either defend or advance the radical cognitive insight (jñāna) which lies at the core of the Advaitin perspective of non-dualism. Thus, Shearer concludes, Śaṅkara is not a philosopher since he does not maintain a consistent conceptual position and does not believe that truth can be proven or brought about by any of these methodological tools (ibid.). This brings us back to the concept of transformative philosophers.

Raju (1954: 704), who contrasts Śaṅkara’s negation with that of Nāgārjuna, mentions that while śūnya in Sanskrit means both the mathematical and metaphysical zero, another word employed by the Sanskrit writers to describe the mathematical zero is Pūrṇa, which means the full rather than the empty.

Raju (1954: 709–710) effectively classifies Nāgārjuna’s conception of fourfold negation as ‘metaphysical relativism’ and Śaṅkara’s negation as ‘metaphysical absolutism and phenomenal relativism’.

For a supportive view, see King (1957: 112–113), who concludes that Nāgārjuna’s outer scepticism is intended to serve his inner truth.

Since Krishnamurti is not as philosophically coherent as Nāgārjuna and Śaṅkara, this should be stated with reservation: while his dialogical negation generally avoids affirmative assertions about the ultimate truth, Krishnamurti’s diaries, biographies, and public discourses include numerous contradictory descriptions of the nature of the already existing reality (see Chap. 8).

This distinction will be elaborated on in the concluding chapter.

Nevertheless, Krishnamurti mainly abandoned this structure only in his close group discussions and one-on-one conversations. His public discourse generally retained the traditional guru–student dialogue.

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Bilimoria, P.

Log. Univers. 11, 13–33 (2017). https://doi.org/10.1007/s11787-017-0161-8

https://link.springer.com/article/10.1007/s11787-017-0161-8

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Silence and Contradiction in the Jaina Saptabhaṅgī

Draft Version
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Chris Rahlwes

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Tripathi, Chhote Lal.

East and West 27, no. 1/4 (1977): 345–55. http://www.jstor.org/stable/29756390.

Negation and Negative Facts in Western and Indian Logic

NS Dravid

Nagpur

Click to access 22-3-2.pdf

The Navya-Nyaya Doctrine of Negation

The Semantics and Ontology of Negative Statements in Navya-Nyaya Philosophy

Bimal Krishnal Matilal

ISBN 9780674606500
Publication date: 01/01/1968

DAYA KRISHNA ON SOME INDIAN THEORIES OF NEGATION: A CRITIQUE

Sen, Prabal Kumar
Philosophy east & west, 2013-10, Vol.63 (4), p.543-561

The Splendour of Negation: R. S. Bhatnagar Revisited with a Buddhist Tinge.

Sebastian CD.

J. Indian Counc. Philos. Res. 2020;37(3):343–60. doi: 10.1007/s40961-020-00214-6. Epub 2020 Jul 25. PMCID: PMC7382565.

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Raju, P. T. (1954).

Review of Metaphysics 7 (4):694 – 713.

https://philpapers.org/rec/RAJTPO-2

Semantics of Nothingness: Bhartrhari’s Philosophy of Negation – I

Sthaneshwar Timalsina

sthaneshwar.timalsina@ifrc.in’

The linguistic philosophy of Bhartrhari needs to be addressed in his milieu. His speculations about the nature of language and his analysis of Sanskrit both transcend the boundaries of language and relate to metaphysics, epistemology, and ontology.
Indology | 14-12-2017

https://indiafacts.org/semantics-nothingness-bhartrharis-philosophy-negation-1/

Semantics of Nothingness: Bhartrhari’s Philosophy of Negation – II

Semantics of Nothingness: Bhartrhari’s Philosophy of Negation – II

“Indian Tradition and Negation.”

Upadhyaya, K. N.

Philosophy East and West 38, no. 3 (1988): 281–89. https://doi.org/10.2307/1398867.

ON THE CONCEPTS OF RELATION AND NEGATION IN INDIAN PHILOSOPHY

by Kalidas Bhattacharya (Author)

(Calcutta Sanskrit College research series ; no. 109)

Unknown Binding – January 1, 1977

https://darshanmanisha.org/publications/on-the-concepts-of-relation-and-negation-in-indian-philosophy/embed#?secret=EqbvEWUYqV#?secret=Q2FFjN6zJK

‘Negation: Can Philosophy Ever Recover from it?’,

Bhushan, Nalini, Jay L. Garfield, and Daniel Raveh (eds),

in Nalini Bhushan, Jay L. Garfield, and Daniel Raveh (eds), Contrary Thinking: Selected Essays of Daya Krishna (New York, 2011; online edn, Oxford Academic, 27 May 2015), https://doi.org/10.1093/acprof:osobl/9780199795550.003.0010, accessed 17 May 2024.

NAGARJUNA’S REASONING WITH NON-IMPLICATIVE NEGATIONS

SAROJ KANTA KAR

Click to access Nagarjuna’s%20Reasoning%20With%20Non-Implicative%20Negations.pdf

THREE ABSOLUTES AND FOUR TYPES OF NEGATION
INTEGRATING KRISHNACHANDRA BHATTACHARYYA’S INSIGHTS?

By Stephen Kaplan
Book
The Making of Contemporary Indian Philosophy
Edition 1st Edition
First Published 2023
Imprint Routledge
Pages 14
eBook ISBN 9781003153320

STUDY ON FOUR LOGICAL ALTERNATIVES (CATUṢKOṬI AND CATUṢKOṬI-VINIRMUKTA) IN INDIAN MĀDHYAMIKA SCHOOL

sherry shi

https://www.academia.edu/42911366/Study_on_Four_Logical_Alternatives_catuṣkoṭi_and_catuṣkoṭi_vinirmukta_in_Indian_Mādhyamika_School

THE NAVYA-NYĀYA DOCTRINE OF NEGATION. BY BIMAL K. MATILAL.

Cambridge: Harvard University Press;

Canada: Saunders of Toronto, Ltd. 1968. Pp. xi, 208

Cyril Welch

https://www.academia.edu/100223324/The_Navya_Nyāya_Doctrine_of_Negation_By_Bimal_K_Matilal_Cambridge_Harvard_University_Press_Canada_Saunders_of_Toronto_Ltd_1968_Pp_xi_208_7_50?rhid=28320110724&swp=rr-rw-wc-42911366

ABHAVA : NEGATION IN LOGIC, REAL NON-EXISTENT, AND A DISTINCTIVE PRAMANA IN THE MIMAMSA

Purushottama Bilimoria PhD
2008, Logic Navya Nyaya and Applications Homage to Bimak Krishna Matilal

https://www.academia.edu/25897487/Abhava_negation_in_logic_real_non_existent_and_a_distinctive_pramana_in_the_Mimamsa?rhid=28320110724&swp=rr-rw-wc-42911366

THINKING NEGATION IN EARLY HINDUISM AND CLASSICAL INDIAN PHILOSOPHY

Purushottama Bilimoria PhD

https://doi.org/10.1007/s11787-017-0161-8
Publication Date: 2017
Publication Name: Logica Universalis

https://www.academia.edu/44596936/Article_Full_text_available_Thinking_Negation_in_Early_Hinduism_and_Classical_Indian_Philosophy&nav_from=ae9bfa80-5dc0-49a3-9dca-0a214b7e931f&rw_pos=0

https://www.researchgate.net/publication/313941478_Thinking_Negation_in_Early_Hinduism_and_Classical_Indian_Philosophy

https://link.springer.com/article/10.1007/s11787-017-0161-8

NEGATION AND THE LAW OF CONTRADICTION IN INDIAN THOUGHT: A COMPARATIVE STUDY

Published online by Cambridge University Press: 24 December 2009

J. F. Staal

https://www.cambridge.org/core/journals/bulletin-of-the-school-of-oriental-and-african-studies/article/abs/negation-and-the-law-of-contradiction-in-indian-thought-a-comparative-study/949A3A5C169D71859EF3440FA5A84D04

PART 19 – NEGATION IN NYĀYA-VAIŚEṢIKA

https://www.wisdomlib.org/hinduism/book/a-history-of-indian-philosophy-volume-1/d/doc209826.html

BASHAM, KOSAMBI, AND THE NEGATION OF NEGATION

Ramkrishna Bhattacharya

https://www.academia.edu/11965736/Basham_Kosambi_and_the_Negation_of_Negation

Negation in Indian Philosophy

Encyclopedia

https://www.encyclopedia.com/humanities/encyclopedias-almanacs-transcripts-and-maps/negation-indian-philosophy

Negative facts in classical Indian philosophy

Gillon, Brendan S.

DOI 10.4324/9780415249126-F049-1

Article Summary

Like their European counterparts, the philosophers of classical India were interested in the problem of negative facts. A negative fact may be thought of, at the outset at least, as a state of affairs that corresponds to a negative statement, such as ‘Mr Smith is not in this room.’ The question that perplexed the philosophers of India was: How does someone, say Ms Jones, know that Mr Smith is not in the room? There are essentially four possible metaphysical positions to account for what it is that Ms Jones knows when, after entering a room, she comes to know that her friend is not present there. Each of the positions has been adopted and defended by certain classical Indian philosophers. On the one hand, some take the absence of the friend from the room as a brute, negative fact. Of these, some hold knowledge of this fact to be perceptual, while others hold it to be inferential. On the other hand, some hold that the absence of the friend from the room has no real ontic status at all, and believe that what there really is in the situation is just the sum of all the things present in the office. These latter philosophers hold that knowledge of one’s friend’s absence is just knowledge of what is present, though some believe the knowledge results from perception, while others believe it to result from inference. These four positions were maintained by, respectively, the Nyāya philosopher Jayanta, the Mīmāṃsā philosophers Kumārila Bhaṭṭa and Prabhākara, and the Buddhist Dharmakīrti.

The Negation of Self in Indian Buddhist Philosophy

Sean M. Smith
University of Hawai‘i at Mānoa

https://quod.lib.umich.edu/cgi/p/pod/dod-idx/negation-of-self-in-indian-buddhist-philosophy.pdf?c=phimp;idno=3521354.0021.013;format=pdf

Logic in Classical Indian Philosophy

SEP

https://plato.stanford.edu/entries/logic-india/

Nāgārjuna’s Negation.

Rahlwes, C.

J Indian Philos 50, 307–344 (2022).

https://doi.org/10.1007/s10781-022-09505-5

https://link.springer.com/article/10.1007/s10781-022-09505-5

Abstract

The logical analysis of Nāgārjuna’s (c. 200 CE) catuṣkoṭi (tetralemma or four-corners) 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 (¬A), Both (A &¬A), and Neither (¬[A∨¬A]). 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 (nominal or implicative negation) and prasajya-pratiṣedha (verbal or non-implicative negation). 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 (not) and a(n)- (non-) within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā.

Nāgārjuna’s Catuṣkoṭi.

Westerhoff, J. (2006).

Journal of Indian Philosophy, 34, 367–395.

Immediate Negation.

Kreutz, A. (2021).

History and Philosophy of Logic, 42(4), 398–410. https://doi.org/10.1080/01445340.2021.1928851

https://www.tandfonline.com/doi/full/10.1080/01445340.2021.1928851

What happened to the third and fourth lemmas in tibet?

Tillemans, T. (2015).

Journal of Buddhist Philosophy, 1, 24–38.

The uses of the four positions of the “Catuṣkoṭi” and the problem of the description of reality in Mahāyāna Buddhism.

Ruegg, D. S. (1977).

Journal of Indian Philosophy, 5(1/2), 1–71.

The Navya-Nyāya Doctrine of Negation: The Semantics and Ontology of Negative Statements in Navya-Nyāya Philosophy.

Copi, Irving M. (1972).

Philosophy East and West 22 (2):221-226.

https://philarchive.org/rec/MATTND-2

Negation in Intuitionistic Logic and Navya Nyaya

BANI SENGUPTA
PUBLISHER: RADHA PUBLICATIONS, DELHI
LANGUAGE: ENGLISH
EDITION: 2001
ISBN: 9788174872104
PAGES: 124

https://www.exoticindiaart.com/book/details/negation-in-intuitionistic-logic-and-navya-nyaya-uah154/

RECAPTURE, TRANSPARENCY, NEGATION AND A LOGIC FOR THE CATUSKOTI

ADRIAN KREUTZ

Comparative Philosophy Volume 10, No. 1 (2019): 67-92
Open Access / ISSN 2151-6014 / http://www.comparativephilosophy.org https://doi.org/10.31979/2151-6014(2019).100108

https://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=1264&context=comparativephilosophy

‘The Role of Negation in Nāgārjuna’s Arguments’,

Westerhoff, Jan,

Nagarjuna’s Madhyamaka: A Philosophical Introduction (New York, 2009; online edn, Oxford Academic, 1 May 2009), https://doi.org/10.1093/acprof:oso/9780195375213.003.0003, accessed 17 May 2024.

https://academic.oup.com/book/9039/chapter-abstract/155552008?redirectedFrom=fulltext

Paradox and Negation in the Upanishads, Buddhism and the Advaita Vedanta of Sankaracarya (India)

Thompson, Heather. California Institute of Integral Studies

ProQuest Dissertations Publishing, 1982. 8400050.

Negation

SEP

https://plato.stanford.edu/entries/negation/

Contradiction, Negation, and the Catuṣkoṭi: Just Several Passages from Dharmapāla’s Commentary on Āryadeva’s Catuḥśataka

Chih-chiang Hu
https://doi.org/10.1007/s10781-023-09554-4

Three kinds of affirmation and two kinds of negation in Buddhist philosophy.

Kajiyama, Y. (1973).

Wiener Zeitschrift Für Die Kunde Südaisiens Und Archiv Für Indische Philosophie,17, 161–174.

The Mādhyamika “Catuṣkoṭi” or Tetralemma.

Chakravarti, S. S., & Chakrabarti, S. S. (1980).

Journal of Indian Philosophy, 8(3), 303–306.

The use of four-cornered negation and the denial of the law of excluded middle in Nāgārjuna’s logic.

Mohanta, D. (2010).

In A. Schumann’s (Ed.), Logic in religious discourse(pp. 44–53). Berlin: De Gruyter.

The logic of The Catuskoti.

Priest, G. (2010).

Comparative Philosophy, 1(2), 24–54.Google Scholar

None of the above: The Catuṣkoṭi in Indian Buddhist logic.

Priest, G. (2015).

In M. C. Jean-Yves Beziau, and Some Dutta (Eds.), New direction in paraconsistent logic (pp. 517–527).London: Springer.

OBJECT CONTENT AND RELATION

Publication Category Philosophers of Modern India
Publication Author Kalidas Bhattacharyya
Publication Language English
Publisher Name Das Gupta & Co.Ltd.
Publication Place Calcutta
No. of Pages 167

https://darshanmanisha.org/publications/object-content-and-relation/embed#?secret=DLwuy56Nmo#?secret=KOcnumHL02

This book by Kalidas Bhattacharyya considers the relation between Consciousness and it’s Object. Once we ask the question “Is there anything intermediate between consciousness and object?”, we come up with the answer “Content”. Now, what is this Content and is there such an intermediate thing between Consciousness and Object? This is a question that needs to be answered. This book explores the relationship between Objects and Consciousness via the idea of Content. The book is divided into two chapters. This first chapter is on “Object and Content”. The second is on “Relation”. The first chapter deals with:

Analysis of Thought and Memory

Analysis of Perception: Idealism and Realism

Analysis of Perception – Illusion as to Judgment

Some Theories of Illusion Examined

Content and Object as Alternatives

Criterion of Reality

Real and Non-Real Appearances

The second chapter deals with

The Notion of Relation

Classification of Relations

The So-called Puzzles of Relation

Relation – Is it Subjective, Objective or Dialectical?

External and Internal Relation

Some Theories of Relation

Two Indian dialectical logics: saptabhangi and catuskoti.

Schang, Fabien (2010).

Journal of the Indian Council of Philosophical Research 27 (1):45-75.

https://philarchive.org/rec/SCHTID-9

None of the Above: The Catuṣkoṭi in Indian Buddhist Logic.

Authors: Graham Priest

In book: New Directions in Paraconsistent Logic (pp.517-527)
January 2015

DOI:10.1007/978-81-322-2719-9_24

https://www.springerprofessional.de/en/none-of-the-above-the-catuskoti-in-indian-buddhist-logic/7456120

https://www.researchgate.net/publication/297713276_None_of_the_Above_The_Catuskoti_in_Indian_Buddhist_Logic

https://www.semanticscholar.org/paper/None-of-the-Above%3A-The-Catuṣkoṭi-in-Indian-Buddhist-Priest/e441318845b51b12ddddc060d3064d943b48dc42

The uses of the four positions of the Catuskoti and the problem of the description of reality in Mahāyāna Buddhism.

Ruegg, D. Seyfort (1977).

Journal of Indian Philosophy 5 (1-2):1-71.

Nāgārjuna’s Negation.

Rahlwes, Chris (2022).

Journal of Indian Philosophy 50 (2):307-344.

A Grammarian’s View of Negation: Nāgeśa’s Paramalaghumañjūs.ā on Nañartha.

Lowe, John J. & Benson, James W. (2023).

Journal of Indian Philosophy 51 (1):49-75.

The logic of the catuskoti.

Priest, Graham (2010).

Comparative Philosophy 1 (2):24-54.

https://www.semanticscholar.org/paper/THE-LOGIC-OF-THE-CATUSKOTI-Priest/c2a46106ad68d2f7625872ff13dbbbd02fa1929a

Nāgārjuna’s Negation.

Rahlwes, Chris (2022).

Journal of Indian Philosophy 50 (2):307-344.

Nāgārjuna’s Catuṣkoṭi.

Westerhoff, Jan (2006).

Journal of Indian Philosophy 34 (4):367-395.

https://www.jstor.org/stable/23497268

Thinking Negation in Early Hinduism and Classical Indian Philosophy.

Bilimoria, Purushottama (2017).

Logica Universalis 11 (1):13-33.

The uses of the four positions of the Catuskoti and the problem of the description of reality in Mahāyāna Buddhism.

Ruegg, D.S.

J Indian Philos 5, 1–71 (1997). https://doi.org/10.1007/BF00200712

https://link.springer.com/article/10.1007/BF00200712

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Two Indian Dialectical Logics: saptabhangi and catuskoti

Fabien Schang
2011, Studies in Logic: Logic and Philosophy Today

https://www.academia.edu/42017816/Two_Indian_Dialectical_Logics_saptabhangi_and_catuskoti

https://philarchive.org/rec/SCHTID-9

A Many-valued Modal Interpretation for Catuskoti

Liu Jingxian

Click to access prospectus_16_7.pdf

A Vedic Touch To Logic In Indian Thought – Part One

SUBHASH KAK
Oct 09, 2016,

https://swarajyamag.com/culture/a-vedic-touch-to-logic-in-the-indian-thought

A Vedic Touch To Logic In Indian Thought – Part Two

SUBHASH KAK

Oct 09, 2016,

https://swarajyamag.com/culture/a-vedic-touch-to-logic-in-indian-thought-part-two

“Understanding Nāgārjuna’s Catuṣkoṭi.”

Gunaratne, R. D.

Philosophy East and West 36, no. 3 (1986): 213–34. https://doi.org/10.2307/1398772.

The Deconstructionist Interpretation of Nagarjuna’s Catuskoti∗

Shi, Ruyuan (Chien-Yuan Hsu) PhD candidate, the Dep. of Religious Studies, the University of Calgary, Canada Sessional instructor, Mount Royal University, Canada

Click to access bm054137877.pdf

Logic in Indian Thought

Subhash Kak

2009, Chapter In Logic in Religious Discourse, Ontos Verlag

Does a Table Have Buddha-Nature? A Moment of Yes and No. Answer! But Not in Words or Signs: Reply to Siderits

Yasuo Deguchi
Kyoto University
Jay L. Garfield
Smith College, jgarfield@smith.edu
Graham Priest
University of Melbourne

https://scholarworks.smith.edu/cgi/viewcontent.cgi?article=1009&context=phi_facpubs

Nagarjuna

IEP

Nagarjuna

An Introduction to Non-Classical Logic.

Priest, G . (2008).

New York: Cambridge University Press.

Doxographical Appropriation of Na ̄ga ̄rjuna’s Catus.kot.i in Chinese Sanlun and Tiantai Thought

Hans Rudolf Kantor

2021

Graduate Institute of Asian Humanities, Huafan University, New Taipei City 223011, Taiwan; kantorsan@hotmail.com

Religions 12: 912. https://doi.org/10.3390/ rel12110912

Click to access religions_12_00912%20HRK.pdf

Graham Priest on Buddhism and logic

by Massimo Pigliucci

Graham Priest on Buddhism and logic

CONTRADICTION AND RECURSION IN BUDDHIST PHILOSOPHY:
FROM CATUṢKOṬI TO KŌAN

adrian Kreutz (university of aMsterdaM)

https://adriankreutz.weebly.com/uploads/1/2/4/9/124988441/contradiction_and_recursion_in_buddhist.pdf

Nāgārjuna’s Catuskoti

Nāgārjuna’s Catuskoti

A Gricean Interpretation of Nāgārjuna’s Catuskoti and the No-thesis View

2020, History and Philosophy of Logic (link)

The central thesis of Buddhism is emptiness, a view saying that all entities have no essence Nāgārjuna (c. 150–250 CE), 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 (a) substance is a basic categorical concept; (b) substances have svabhāva, and (c) names and sentences have svabhāva.

“The Logical Form of Catuṣkoṭi: A New Solution.”

Gunaratne, R. D.

Philosophy East and West 30, no. 2 (1980): 211–39. https://doi.org/10.2307/1398848.

The mādhyamika catuko i or tetralemma.

Chakravarti, S.S.

J Indian Philos8, 303–306 (1980). https://doi.org/10.1007/BF00166298

“Understanding Nāgārjuna’s Catuṣkoṭi.”

Gunaratne, R. D.

Philosophy East and West 36, no. 3 (1986): 213–34. https://doi.org/10.2307/1398772.

The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuskoti.

Priest, Graham (2018).

Oxford, England: Oxford University Press.

https://academic.oup.com/mind/article-abstract/129/515/965/5553059

Extract

If Euthyphro and Agrippa secured places in the history of philosophy for the dilemma and trilemma, Nāgārjuna did so for the tetralemma (catuṣkoṭi in Sanskrit). Even though this second-century Indian thinker did not invent the argumentative pattern in which the four alternatives of a position, its negation, both, or neither are considered, it became inextricably linked up with his philosophical approach, and Nāgārjuna (and the philosophical school of Madhyamaka he founded) plays a central role in Graham Priest’s ‘essay on Buddhist metaphysics and the catuṣkoṭi’. The book might remind readers of his landmark 2002 Beyond the Limits of Thought; even though the historical and conceptual scope in the present volume is narrower, many of the key features are still there: a chronological exposition following along with the history of philosophy, a focus on dialetheism in different manifestations, and descriptions of various formal constructions (in the present case drawn primarily from non-classical logic and graph theory) to elucidate complex and often quite obscure ideas of past masters.

Abstract

The book charts the development of Buddhist metaphysics, drawing on texts which include those of Nagarjuna and Dogen. The development is viewed through the lens of the Catuṣkoṭi At its simplest, and as it appears in the earliest texts, this is a logical/metaphysical principle which says that every claim is true, false, both, or neither; but the principle itself evolves, assuming new forms as the metaphysics develops. An important step in the evolution incorporates ineffability. Such things make no sense from the perspective of a logic which endorses the principles of excluded middle and non-contradiction, which are standard fare in Western logic. However, the book shows how one can make sense of them by applying the techniques of contemporary non-classical logic, such as those of First Degree Entailment, and plurivalent logic. An important issue that emerges as the book develops is the notion of non-duality and its transcendence. This allows many of the threads of the book to be drawn together at its end. All matters are explained, as far as possible, in a way that is accessible to those with no knowledge of Buddhist philosophy or contemporary non-classical logic.

Paraconsistent Logic

https://plato.stanford.edu/entries/logic-paraconsistent/

Graham Priest on Dialetheism and Paraconsistency

Volume 18 of Outstanding Contributions to Logic
Editors Can Başkent, Thomas Macaulay Ferguson
Publisher Springer Nature, 2020
ISBN 3030253651, 9783030253653
Length 704 pages

Chains of Being: Infinite Regress, Circularity, and Metaphysical Explanation

Author Ross P. Cameron
Publisher Oxford University Press, 2022
ISBN 0192596195, 9780192596192
Length 256 pages

A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind

Author Roy Sorensen
Publisher Oxford University Press, 2003
ISBN 0190289317, 9780190289317
Length 416 pages

What are Paradoxes?

CHRISTOPHER COWIE

Journal of the American Philosophical Association 2023

https://doi.org/10.1017/apa.2021.48

Published online by Cambridge University Press

Click to access what_are_paradoxes.pdf

“The Paradox of Negation in Nāgārjuna’s Philosophy.”

Patel, Kartikeya C.

Asian Philosophy 4, no. 1 (1994): 17–32. doi:10.1080/09552369408575386.

https://www.tandfonline.com/doi/abs/10.1080/09552369408575386

In Contradiction

Author Graham Priest
Edition 2
Publisher Clarendon Press, 2006
ISBN 0191532487, 9780191532481
Length 352 pages

Dialetheism

SEP

https://plato.stanford.edu/entries/dialetheism/

One: Being an Investigation Into the Unity of Reality and of Its Parts, Including the Singular Object which is Nothingness

Author Graham Priest
Edition illustrated
Publisher OUP Oxford, 2014
ISBN 0199688257, 9780199688258
Length 252 pages

The Law of Non-Contradiction: New Philosophical Essays.

GRAHAM PRIEST, JC BEALL, and BRADLEY ARMOUR-GARB, editors.

Oxford: Clarendon Press, 2004. ISBN 0-19-926517-8. Pp. xii + 443., Philosophia Mathematica, Volume 13, Issue 2, June 2005, Page 235, https://doi.org/10.1093/philmat/nki019

What is a Contradiction?

Patrick Grim

Click to access contradictionweb2.pdf

Reflexivity: From Paradox to Consciousness

Authors Nicholas Rescher, Patrick Grim
Edition illustrated
Publisher Walter de Gruyter, 2013
ISBN 3110320185, 9783110320183
Length 190 pages

“Jaina Logic: A Contemporary Perspective.”

Priest, Graham.

History and Philosophy of Logic 29, no. 3 (2008): 263–78. doi:10.1080/01445340701690233.

https://www.tandfonline.com/doi/full/10.1080/01445340701690233

Jaina Logic and the Philosophical Basis of Pluralism

JONARDON GANERI
Department of Philosophy, University of Liverpool
Revised 2 October 2002

HISTORY AND PHILOSOPHY OF LOGIC, 23 (2002), 267±281

https://philarchive.org/archive/JONJLA

Jaina Philosophy

SEP

https://plato.stanford.edu/entries/jaina-philosophy/

Seven-Valued Logic in Jain Philosophy

International Philosophical Quarterly
Volume 4, Issue 1, February 1964
George Bosworth Burch
Pages 68-93
https://doi.org/10.5840/ipq19644140

https://www.semanticscholar.org/paper/Seven-Valued-Logic-in-Jain-Philosophy-Burch/e828cdbadba3a52cf9338a1bd8cea359c12f6351

A History of Indian Logic (ancient, Mediæval and Modern Schools.)

Author Satis Chandra Vidyabhusana
Publisher Calcutta University, 1921
Original from Princeton University
Digitized Nov 20, 2008
Length 648 pages

https://books.google.com/books?id=wcEwAAAAYAAJ&pg=PA158&lpg=PA158&dq=jaina+logic%C2%A0&source=bl&ots=DB_iKAtfet&sig=ACfU3U311z5-nGex2rP1hMVTgVQYdKxbpQ&hl=en&sa=X&ved=2ahUKEwi6gpP8sJCGAxVEF1kFHaKxC0A4UBDoAXoECAQQAw#v=onepage&q=jaina%20logic%C2%A0&f=false

A History of Indian Logic: Ancient, Mediaeval and Modern Schools

https://archive.org/details/in.ernet.dli.2015.188696

History of the Mediæval School of Indian Logic, Volume 6

History of the Mediæval School of Indian Logic, Satis Chandra Vidvabhusana
Issue 1 of University studies, University of Calcutta
Author Satis Chandra Vidyabhusana
Publisher Calcutta University, 1909
Original from the University of Michigan
Digitized Feb 19, 2008
Length 100 pages

https://books.google.com/books?id=sK5YAAAAMAAJ&pg=PR13&lpg=PR13&dq=jaina+logic%C2%A0&source=bl&ots=5M_7I5xvaT&sig=ACfU3U1QEBEAg8ivhUsDqadscEsUKqjvyw&hl=en&sa=X&ved=2ahUKEwi6gpP8sJCGAxVEF1kFHaKxC0A4UBDoAXoECAMQAw#v=onepage&q=jaina%20logic%C2%A0&f=false

Possibilities as the foundation of reasoning

P. Johnson-Laird, P. Johnson-Laird, Marco Ragni
Published in Cognition 1 December 2019
Psychology

https://www.semanticscholar.org/paper/Possibilities-as-the-foundation-of-reasoning-Johnson-Laird-Johnson-Laird/ae7e961199497ca9a99ecf348fc500db5996ebb6

“Saptabhaṅgī: The Jaina Theory of Sevenfold Predication: A Logical Analysis.”

Jain, Pragati.

Philosophy East and West 50, no. 3 (2000): 385–99. http://www.jstor.org/stable/1400181.

“Anekāntavāda and Dialogic Identity Construction”

Barbato, Melanie. 2019.

Religions 10, no. 12: 642. https://doi.org/10.3390/rel10120642

https://www.mdpi.com/2077-1444/10/12/642

Hindu Logic As Preserved in China and Japan

Publications of the University of Pennsylvania Series in Philosophy Series
Author Sadajiro Sugiura
Editor Edgar Singer
Publisher CreateSpace Independent Publishing Platform, 2015
ISBN 1514745216, 9781514745212
Length 114 pages

Click to access 196174216674_10153659077911675.pdf

https://books.google.com/books?id=wcEwAAAAYAAJ&pg=PR19&lpg=PR19&dq=%22+Hindu+Logic+as+preserved+in+China+and+Japan+%22+by+Sadajiro+Sugiura+w+h+o+h+a+d+offered+it+as+a+dissertation+for+the+Degree+of+Doctor+of+Philosophy+at+the+University+of+Pennsylvania.&source=bl&ots=DB_iKBtfet&sig=ACfU3U1z-DiU_PDcbsk2sDbE6kYCb_F6Kw&hl=en&sa=X&ved=2ahUKEwjcxqWc1pCGAxXUFVkFHX-LBCkQ6AF6BAgFEAM#v=onepage&q=%22%20Hindu%20Logic%20as%20preserved%20in%20China%20and%20Japan%20%22%20by%20Sadajiro%20Sugiura%20w%20h%20o%20h%20a%20d%20offered%20it%20as%20a%20dissertation%20for%20the%20Degree%20of%20Doctor%20of%20Philosophy%20at%20the%20University%20of%20Pennsylvania.&f=false

https://archive.org/details/hindulogicaspreservedinchinaandjapanbysadajirosugiuraededwardsingera._202003_941_U

Dignāga and Dharmakīrti on Fallacies of Inference: Some Reflections.

Kukkamalla, Bhima Kumar (2020).

Journal of the Indian Council of Philosophical Research 37 (3):403-419.

Logic in Classical Indian Philosophy

SEP

https://plato.stanford.edu/entries/logic-india/

Buddhist Logic (2 volumes)

by TH. Stcherbatsky (Author)

Publisher ‏ : ‎ Motilal Banarsidass Pub; First Edition (December 17, 2008)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 1030 pages
ISBN-10 ‏ : ‎ 8120810198
ISBN-13 ‏ : ‎ 978-8120810198

Buddhist logic reveals itself as the culminating point of a long course of Indian philosophic history. Its birth, its growth and its decline run parallel with the birth, the growth and the decline of Indian civilisation. The time has come to reconsider the subject of Buddhist logic in its historical connections. This is done in these two volumes. In the copious notes the literary renderings are given where needed. This will enable the reader to fully appreciate the sometimes enormous distance which lies between the words of the Sanskrit phrasing and their philosophic meaning rendered according to our habits of thought. The notes also contain a philosophic comment of the translated texts. The first volume contains a historical sketch as well as a synthetical reconstruction of the whole edifice of the final shape of Buddhist philosophy. The second volume contains the material as well as the justification for this reconstruction.

Content:
Preface, Abbreviations, Introduction, Part I – Reality and Knowledge (pramanya-vada), Part II-The Sensible world, Ch. 1 The theory of Instantaneous being (ksanika-vada),Ch. II Causation (pratitya-samutpada), Ch. III. Sense-Perception (pratyaksam), Ch. IV – Ultimate reality (paramartha-sat), Part III-The constructed world, Ch. I-Judgment, Ch. II – Inference, Ch. III – Syllogism (pararthanumanam), Ch. IV. Logical Fallacies, Part IV – Negation, Ch. I-The negative judgment, Ch. II. – The Law of Contradiction, Ch. III-Universals, Ch. IV. Dialectic, Part V-Reality of the External World, Conclusion, Indices, Appendix, Addenda et corrigenda. Preface, Appendices, Indices, Errata

Introduction to the Non-dualism Approach in Hinduism and its Connection to Other Religions and Philosophies

Sriram Ganapathi Subramanian S2GANAPA@UWATERLOO.CA Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada
Benyamin Ghojogh BGHOJOGH@UWATERLOO.CA Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada

https://philarchive.org/archive/SUBITT

Self and World: Major Aspects of Indian Philosophy.

Patel, Ramesh N. (2020).

Beavercreek, OH, USA: Lok Sangrah Prakashan.

https://philpapers.org/rec/PATSAW-3

Logic and Belief in Indian Philosophy

Second Revised Edition
edited by Piotr Balcerowicz

Click to access Logic_and_Belief_in_Indian_Philosophy_2016.pdf

References:

1. Vidyahhusana, Satis Chandra. A History of Indian Logic: Ancient, Mediaeval and Modern Schools. Calcutta University, 1921.
2. S. S. Barlingay. A Modern Introduction to Indian Logic. Delhi: National Publishing House, 1965.
3. D. C. Guha. Navya Nyaya System of Logic. Delhi: Motilal Banarsidass, 1979.
4. Nandita Bandyopadhyay. The Concept of Logical Fallacies. Delhi: Sanskrit Pustak Bhandar, 1977.
5. B. K. Matilal. The Navya Nyaya Doctrine of Negation. Michigan: Harvard University Press, 1968.
6. S. R. Bhatt. Buddhist Epistemology. USA: Greenwood Press, 2000.
7. B. K. Matilal. Logic, Language and Reality. Delhi: Motilal Banarsidass, 2008.
8. Sastri, Kuppuswami.S. A Primer of Indian Logic: According To
Annambhatta’s Tarkasamgraha. Madras: Kuppuswami Sastri Research Institute, 1951.

How Do Theories of Cognition and Consciousness in Ancient Indian Thought Systems Relate to Current Western Theorizing and Research?

Peter Sedlmeier1 *and Kunchapudi Srinivas2

Institut für Psychologie, Technische Universität Chemnitz, Chemnitz, Germany, 2 Department of Philosophy, Pondicherry
University, Puducherry, India

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4791389/

Epistemology in Classical Indian Philosophy

SEP

https://plato.stanford.edu/entries/epistemology-india/

Logic, Language, and Reality: An Introduction To Indian Philosophical Studies

by Matilal, Bimal Krishna

https://archive.org/details/in.ernet.dli.2015.461051

Absence: An Indo-Analytic Inquiry

December 2016 Sophia 55(4)

DOI:10.1007/s11841-016-0547-8
Anand Jayprakash Vaidya
San Jose State University
Purushottama Bilimoria
University of California, Berkeley and San Francisco State University
Jayshankar L. Shaw

https://www.researchgate.net/publication/305482510_Absence_An_Indo-Analytic_Inquiry

Abstract

Two of the most important contributions that Bimal Krishna Matilal made to comparative philosophy derive from his (1968) doctoral dissertation The Navya-Nyāya Doctrine of Negation: The Semantics and Ontology of Negative Statements in Navya-Nyāya Philosophy and his (1986) classic: Perception: An Essay on Classical Indian Theories of Knowing. In this essay, we aim to carry forward the work of Bimal K. Matilal by showing how ideas in classical Indian philosophy concerning absence and perception are relevant to recent debates in analytic philosophy. In particular, we focus on the recent debate in the philosophy of perception centering on the perception of absence. In her Seeing Absence, Anya Farennikova (2013) argues for the thesis that we literally see absences. Her thesis is quite novel within the contexts of the traditions that she engages: analytical philosophy of perception, phenomenology, and cognitive neuroscience. In those traditions there is hardly any exploration of the epistemology of absence. By contrast, this is not the case in classical Indian philosophy where the debate over the ontological and epistemological status of absence (abhāva) is longstanding and quite engaging. In what follows, we engage Farennikova’s arguments, and those of John-Rémy Martin and Jérome Dokic in their (2013) response to her work, through the use of classical Indian philosophers and their twentieth century proponents. Using the work of Matilal (1968, 1986), Bilimoria (2015) and Shaw (2016) we show that there are several engaging ideas that can be taken from Indian philosophy into the terrain explored by Farennikova, and Martin & Dokic. Our aim is to provide an updated comparative engagement on absence and its perception for the purposes of enhancing future discussions within analytic philosophy. However, we do not aim to merely show this by focusing on the history of primary texts or on twentieth century commentary on primary texts. Instead, we hope to show that the living tradition of Indian philosophy that Matilal embodied carries forward in his students and colleagues as they revive and extend Indian philosophy.

Negation (Abha¯va), Non-existents, and a Distinctive pramana in the Nya¯ya-Mı¯ma¯ṃsa

January 2016
DOI:10.1007/978-3-319-17873-8_12
Authors:
Purushottama Bilimoria
University of California, Berkeley and San Francisco State University

https://www.researchgate.net/publication/307634171_Negation_Abhava_Non-existents_and_a_Distinctive_pramana_in_the_Nyaya-Mimamsa

Why Is There Nothing Rather Than Something? An Essay in the Comparative Metaphysic of Nonbeing

October 2019
DOI:10.1007/978-3-030-18148-2_13
In book: Considering Religions, Rights and Bioethics: For Max Charlesworth (pp.175-197)
Authors:
Purushottama Bilimoria
University of California, Berkeley

https://www.researchgate.net/publication/336630065_Why_Is_There_Nothing_Rather_Than_Something_An_Essay_in_the_Comparative_Metaphysic_of_Nonbeing

https://www.researchgate.net/publication/257761935_Why_Is_There_Nothing_Rather_Than_Something

Abstract

This essay in the comparative metaphysic of nothingness begins by pondering why Leibniz thought of the converse question as the preeminent one. In Eastern philosophical thought, like the numeral ‘zero’ (śūnya) that Indian mathematicians first discovered, nothingness as non-being looms large and serves as the first quiver on the imponderables they seem to have encountered (e.g., ‘In the beginning was neither non-being what nor being: what was there, bottomless deep?’ ṚgVeda X.129). The concept of non-being and its permutations of nothing, negation, nullity, etc., receive more sophisticated treatment in the works of grammarians, ritual hermeneuticians, logicians, and their dialectical adversaries variously across Jaina and Buddhist schools. The present analysis follows the function of negation/the negative copula, nãn, and dialetheia in grammar and logic, then moves onto ontologies of non-existence and extinction and further suggestive tropes that tend to arrest rather than affirm the inexorable being-there of something. (This chapter is to be read in tandem with two aligned papers that have appeared since the first publication of this chapter (see above), namely, ‘Thinking Negation in Early Hinduism and Classical Indian Philosophy’ (Bilimoria 2017); and ‘Negation (Abhāva), Non-existents, and a Distinctive Pramāṇa in the Nyāya-Mīmāṃsā’ (Bilimoria 2016)).

Catuṣkoṭi

Wikipedia

https://en.wikipedia.org/wiki/Catuṣkoṭi

Neti-Neti or Apophatic Theology: Knowledge Obtained by Negation

Neti-Neti or Apophatic Theology: Knowledge Obtained by Negation

The Transformative Philosophical Dialogue: From Classical Dialogues to Jiddu Krishnamurti’s Method

Volume 41 of Sophia Studies in Cross-cultural Philosophy of Traditions and Cultures
Author Shai Tubali
Publisher Springer Nature, 2023
ISBN 3031400747, 9783031400742
Length 258 pages

Logic: A Short Introduction

Collection of 6 Youtube Videos on introduction to Logic.

Graham Priest

Professor at CUNY, NYC

History of Indian Philosophy

Routledge History of World Philosophies
Editor Purushottama Bilimoria
Edition illustrated, reprint
Publisher Routledge, 2017
ISBN 1317356179, 9781317356172
Length 638 pages

Chapter 6 – Nyāya-Vaiśeṣika theory of Relation

Reality of Relation
Different types of Relation
Saṃyoga (Conjunction)
Samavāya
Viśeṣaṇatā Sambandha (Attributive Relation)
Vṛttyaniyāmaka-sambandha (Non-Occurrent-Exacting Relation)

https://www.wisdomlib.org/hinduism/essay/nyaya-vaisheshika-categories-study/d/doc1149907.html

Relations in Indian Philosophy

(Sri Garib Dass Oriental Series) (English and Sanskrit Edition) Hardcover – January 1, 1993
Sanskrit Edition by V. N. Jha (Editor)

ISBN-10 ‏ : ‎ 817030329X
ISBN-13 ‏ : ‎ 978-8170303299

Delhi, India: Sri Satguru Publications.

https://philpapers.org/rec/JHARII

Contributed research papers presented at the National Seminar on Relations in Indian Philosophy, held during 25th-27th March 1991 at the Centre of Advanced Study in Sanskrit, University of Poona.

https://www.exoticindiaart.com/book/details/relations-in-indian-philosophy-old-and-rare-book-nas077/

The present volume contains 17 articles presented and discussed at the National Seminar on Relations in Indian Philosophy which was held on 25th to 27th March, 1991, at the Centre of Advanced Study in Sanskrit, University of Poona. The papers focusses on nature of a relation, the role played by a relation in generating a cognition, the role played by a relation in creating a precise language of philosophical and logical communication. and the philosophical implication of a relation. Any philosophical analysis requires clear idea about these aspects of a relation. The studies included here cover a very wide range of philosophical and logical literature in Sanskrit. Although the main source of information has been the literature on Pracina-Nyaya and Navya-Nyaya, some articles also have taken into account the position of relation and the problems of relation in other systems of Indian Philosophy. There are views on relation being Ontological facts and also there are views which deny the Ontological reality of a relation. The discussions in this volume in- corporate both the ranges.

Preface

The present volume contains 17 articles presented and discussed at the National Seminar on Relations in Indian Philosophy which was held on 25th to 27th March, 1991 at the Centre of Advanced Study in Sanskrit, University of Poona.

It gives me pleasure to present these articles in the hands of scholars of Indology, Logic and Philosophy. Briefly speaking, focus has been put in these papers on the following aspects.

1. Nature of a relation.

2. The role played by a relation in generating a cognition.

3, The role played by a relation in creating a precise language of philosophical and logical communication.

4. The Philosophical implication of a relation.

Any Philosophical analysis requires clear idea about these aspects of a relation. The studies included here cover a very wide range of philosophical and logical literature in Sanskrit. Although the main source of information has been the literature on Pracina Nyaya and Navya-Nyaya, some articles also have taken into account the position of relation and the problems of relation in other systems of Indian Philosophy. As can be seen, there are views on relations being Ontological facts and also there are views which deny the Ontological reality of a relation. The discussions in this volume incorporate both the ranges.

The Navya-Nyaya system of Indian Logic started paying more attention to the problem of relation because it was the necessity of the time. There was a great need for evolving a precise language of communication for logical and philosophical discussions. The Indian logicians realised that this cannot be achieved without introducing the idea of delimitations through property and relations and this is why they had to pay more attention to the discussion on relations. I wish that the readers will read this volume with the perspective presented above.

I thank the Indian Books Centre, New Delhi for undertaking the publication of this volume. I am sure, the scholars in the field will highly appreciate this venture.

The Problem of Relation in Indian Philosophy

N S Dravid

Nagpur

Click to access 5-1-3.pdf

Problem of Relations in Indian Philosophy

Author Sarita Gupta
Publisher Eastern Book Linkers, 1984
Original from the University of Michigan
Digitized Jun 8, 2006
Length 111 pages

https://www.exoticindiaart.com/book/details/problem-of-relations-in-indian-philosophy-old-and-rare-book-nap580/

Quantum Entanglement and the Philosophy of Relations – Jaina Perspective

By Prof Sisir Roy
August 2017

https://www.esamskriti.com/e/Spirituality/Science-ad-Indian-Wisdom/Quantum-Entanglement-and-the-Philosophy-of-Relations-~-Jaina-Perspective-1.aspx

Causation In Indian Philosophy

Apu Sutradhar
Guest Lecturer, Department of Philosophy,
A.B.N Seal College, Cooch Behar, W.B, India.

IOSR Journal Of Humanities And Social Science (IOSR-JHSS)
Volume 23, Issue 9, Ver. 3 (September. 2018) 35-39
e-ISSN: 2279-0837, p-ISSN: 2279-0845.
http://www.iosrjournals.org

Click to access F2309033539.pdf

Causation, Indian theories of

Perrett, Roy W.

DOI 10.4324/9780415249126-F055-1

https://www.rep.routledge.com/articles/thematic/causation-indian-theories-of/v-1

Article Summary

Causation was acknowledged as one of the central problems in Indian philosophy. The classical Indian philosophers’ concern with the problem basically arose from two sources: first, the cosmogonic speculations of the Vedas and the Upaniṣads, with their search for some simple unitary cause for the origin of this complex universe; and second, the Vedic concern with ritual action (karman) and the causal mechanisms by which such actions bring about their unseen, but purportedly cosmic, effects. Once the goal of liberation (mokṣa) came to be accepted as the highest value, these two strands of thought entwined to generate intense interest in the notion of causation. The systematic philosophers of the classical and medieval periods criticized and defended competing theories of causation. These theories were motivated partly by a desire to guarantee the efficacy of action and hence the possibility of attaining liberation, partly by a desire to understand the nature of the world and hence how to negotiate our way in it so as to attain liberation.

Indian philosophers extensively discussed a number of issues relating to causation, including the nature of the causal relation, the definitions of cause and effect, and classifications of kinds of causes. Typically they stressed the importance of the material cause, rather than (as in Western philosophy) the efficient cause. In India only the Cārvāka materialists denied causation or took it to be subjective. This is unsurprising given that a concern with demonstrating the possibility of liberation motivated the theories of causation, for only the Cārvākas denied this possibility. The orthodox Hindu philosophers and the heterodox Buddhists and Jainas all accepted both the possibility of liberation and the reality of causation, though they differed sharply (and polemically) about the details.

The Indian theories of causation are traditionally classified by reference to the question of whether the effect is a mode of the cause. According to this taxonomy there are two principal theories of causation. One is the identity theory (satkāryavāda), which holds that the effect is identical with the cause, a manifestation of what is potential in the cause. This is the Sāṅkhya-Yoga view, though that school’s particular version of it is sometimes called transformation theory (pariṇāmavāda). Advaita Vedānta holds an appearance theory (vivartavāda), which is often considered a variant of the identity theory. According to the appearance theory effects are mere appearances of the underlying reality, Brahman. Since only Brahman truly exists, this theory is also sometimes called satkāraṇavāda (the theory that the cause is real but the effect is not).

The other principal theory of causation is the nonidentity theory (asatkāryavāda), which denies that the effect pre-exists in its cause and claims instead that the effect is an altogether new entity. Both adherents of Nyāya-Vaiśeṣika and the Buddhists are usually classified as nonidentity theorists, but they differ on many important details. One of these is whether the cause continues to exist after the appearance of the effect: Nyāya-Vaiśeṣika claims it does, the Buddhists mostly claim it does not.

Finally, some philosophers try to take the middle ground and claim that an effect is both identical and nonidentical with its cause. This is the position of the Jainas and of some theistic schools of Vedānta.

“ANĀDITVA OR BEGINNINGLESSNESS IN INDIAN PHILOSOPHY.”

Tola, Fernando, and Carmen Dragonetti.

Annals of the Bhandarkar Oriental Research Institute 61, no. 1/4 (1980): 1–20. http://www.jstor.org/stable/41691856.

Six Systems of Indian Philosophy

By Sanjeev Nayyar

https://www.esamskriti.com/e/Spirituality/Philosophy/Six-Systems-Of-Indian-Philosophy-1.aspx

Theory of Error and Nyāya Philosophy: A Conceptual Analysis

Gobinda Bhattacharjee
PhD Research Scholar,
Department of Philosophy,
Tripura University, Suryamaninagar – 799022, Tripura, INDIA

2021 IJRAR September 2021, Volume 8, Issue 3

http://www.ijrar.org (E-ISSN 2348-1269, P- ISSN 2349-5138)

https://philarchive.org/archive/BHATOE

A History of Pre-Buddhistic Indian Philosophy

Author Beni Madhab Barua
Publisher University of Calcutta, 1921
Original from Princeton University
Digitized Oct 9, 2008
Length 444 pages

https://books.google.com/books?id=XEkuAAAAYAAJ&pg=PA283&lpg=PA283&dq=relation+in+indian+philosophy&source=bl&ots=fENI15Xw4Y&sig=ACfU3U0f-3mtieyj-s4nEtmvqmCFmUafug&hl=en&sa=X&ved=2ahUKEwidvbufopWGAxXCMlkFHaczB984qgEQ6AF6BAgDEAM#v=onepage&q&f=false

Indian Philosophy Volume 1

Volume 1 of Indian Philosophy
Author Jadunath Sinha
Publisher Motilal Banarsidass, 2016
ISBN 8120836510, 9788120836518
Length 944 pages

Indian Philosophy Volume 2

Volume 2 of Indian Philosophy
Author Jadunath Sinha
Publisher Motilal Banarsidass, 2016
ISBN 8120836529, 9788120836525
Length 762 pages

Indian Philosophy Volume 3

Volume 3 of Indian Philosophy
Author Jadunath Sinha
Publisher Motilal Banarsidass, 2016
ISBN 8120836537, 9788120836532
Length 487 pages

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The Fifth Corner of Four: Catuskoti in Buddhist Logic

Key Terms

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The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuṣkoṭi

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INTEGRATING KRISHNACHANDRA BHATTACHARYYA’S INSIGHTS?