Skip to main content

None of the Above: The Catuṣkoṭi in Indian Buddhist Logic

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 152)


The catuṣkoṭi (Greek: tetralemma; English: four corners) is a venerable principle of Indian logic, which has been central to important aspects of reasoning in the Buddhist tradition. What, exactly, it is, and how it is applied, are, however, moot—though one thing that does seem clear is that it has been applied in different ways at different times and by different people. Of course, Indian logicians did not incorporate the various interpretations of the principle in anything like a theory of validity in the modern Western sense; but the tools of modern non-classical logic show exactly how to do this. The tools are those of the paraconsistent logic of First Degree Entailment and some of its modifications.


Mathematics Subject Classification (2000)

This is a preview of subscription content, log in via an institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions


  1. 1.

    For FDE, see Priest [10], Chap. 8.

  2. 2.

    I note right at the start there are some Buddhist logicians in whose thinking the catuṣkoṭi played no role. This is true, in particular, of the school of Dignāga and Dharmakīrti. Like the Nyāyā, this school of logic endorsed both the Principles of Non-Contradiction and Excluded Middle. See Scherbatsky [18], pt. 4, Chap. 2.

  3. 3.

    Radhakrishnan and Moore [14], p. 289 f. The word ‘saint’ is a rather poor translation. It refers to someone who has attained enlightenment, a Buddha (Tathāgata).

  4. 4.

    See Ruegg [17], p. 1.

  5. 5.

    Tillemans [20], p. 189.

  6. 6.

    For a survey, see Ruegg [17], p. 39ff. And for a critique, see Priest [12], 2.2.

  7. 7.

    See Priest [10], Chap. 8.

  8. 8.

    As observed in Garfield and Priest [4].

  9. 9.

    See Priest [7], 4.6.

  10. 10.

    See Ruegg [17], pp. 1, 2.

  11. 11.

    Thanissaro [19].

  12. 12.

    Radhakrishnan and Moore [14], p. 290.

  13. 13.

    All translations from the MMK are from Garfield [2].

  14. 14.

    Instead of \(\varphi (A)\) (etc.), one could have any sentence that contained all the propositional parameters in A.

  15. 15.

    For the proof, see the technical appendix of Priest [12].

  16. 16.

    The Buddhists tadition was not alone in appearing to reject all four of the koṭis sometimes. See Raju [15].

  17. 17.

    The translation is taken from Kassor [5].

  18. 18.

    It is not just Gorampa who finds himself in this position. Any theory according to which there is something ineffable and which explains why it is ineffable is going to be in the same situation. There are many such theories, East and West. See Priest [9].

  19. 19.

    See Priest [8], 5.5.

  20. 20.

    See Garfield and Priest [3], and Deguchi et al. [1]. The contradiction we are dealing with here is closely related to Nāgārjuna’s paradox that the ultimate truth is that there is no ultimate truth. (See Garfield and Priest [3], Sect. 5.) One can say nothing true about ultimate reality—either because there is no such thing, or because it is ineffable. But either way, that is itself an ultimate truth.

  21. 21.

    See [10], 8.2.

  22. 22.

    For a fuller discussion of the construction described in this section, see Priest [13].

  23. 23.

    For details of what follows, see Priest [11].

  24. 24.

    See Priest [11], Sect. 5.

  25. 25.

    In [11], this is formulated not as a relational semantics but equivalently as a functional semantics, where the functional values are sets of truth values. The possibility of applying this construction to the Buddhist four (or five) values, as we hae done here, is noted there in footnote 15.


  1. Deguchi, Y., Garfield, J., Priest, G.: The way of the dialetheist: contradictions in buddhism. Philos. East West 58, 395–402 (2008)

    Article  Google Scholar 

  2. Garfield, J.: The Fundamental Principles of the Middle Way: Nāgārjuna’s Mūlamadhyamikakārikā. Oxford University Press, New York (1995)

    Google Scholar 

  3. Garfield, J., Priest, G.: Nāgārjuna and the limits of thought. Philos. East West 53, 1–21 (2003) (Reprinted as ch. 5 of Garfield’s, Empty Words. Oxford University Press, New York (2002) and as ch. 16 Priest (2002))

    Google Scholar 

  4. Garfield, J., Priest, G.: Mountains are Just Mountains (2009) (ch. 7 of D’Amato, M., Garfield, J., Tillemans, T. (eds.): Pointing at the Moon: Buddhism, Logic, Analytic Philosophy. Oxford University Press, New York)

    Google Scholar 

  5. Kassor, C.: Is Gorampa’s “Freedom from Conceptual Proliferations” dialetheist? A response to Garfield, Priest, and Tillemans. Philos. East West 63, 399–410 (2013)

    Article  Google Scholar 

  6. Priest, G.: Hypercontradictions. Logique et Analyse 107, 237–243 (1984)

    MathSciNet  Google Scholar 

  7. Priest, G.: Paraconsistent Logic. In: Gabbay, D., Guenther, D. (eds.) Handbook of Philosophical Logic, 2nd edn, Vol. 6, pp. 287–393. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  8. Priest, G.: Beyond the Limits of Thought, 2nd edn. Oxford Unversity Press, Oxford (2002)

    Google Scholar 

  9. Priest, G.: The Limits of Language. In: Brown, K. (ed.) Encyclopedia of Language and Linguistics, 2nd edn, Vol. 7, pp. 156–159. Elsevier, Amsterdam (2005)

    Google Scholar 

  10. Priest, G.: Introduction to Non-Classical Logic: From If to Is. Cambridge University Press, Cambridge (2008)

    Google Scholar 

  11. Priest, G.: Jaina logic: a contemporary perspective. History Philos. Logic 29, 263–278 (2008)

    Google Scholar 

  12. Priest, G.: The logic of the Catuṣkoṭi. Comp. Philos. 1, 32–54 (2010)

    Google Scholar 

  13. Priest, G.: Plurivalent logic. Australas. J. Logic 11 (2014) article 1.

  14. Radhakrishnan, S., Moore, C. (eds.): A Source Book in Indian Philosophy. Princeton University Press, Princeton (1957)

    Google Scholar 

  15. Raju, P.: The principle of four-cornered negation in Indian philosophy. Rev. Metaphys. 7, 694–713 (1953)

    Google Scholar 

  16. Robinson, R.: Some logical aspects of Nāgārjuna’s system. Philos. East West 6, 291–308 (1956)

    Article  Google Scholar 

  17. Ruegg, D.: The uses of the four positions of the Catuṣkoṭi and the problem of the description of reality in Mahāyāna buddhism. J. Indian Philos. 5, 1–71 (1977)

    Article  Google Scholar 

  18. Scherbatsky, Th: Buddhist Logic, vol. 1. Matilal Banarsidass, Delhi (1993)

    Google Scholar 

  19. Thanissaro: Cula-Malunkyovada Sutta: the shorter instructions to Malunkya. Accessed Mar 2010

  20. Tillemans, T.: Is buddhist logic non-classical or deviant? Chap. 9 of Scripture, Logic, Language: Essays on Dharmakīrti and his Tibetan Successors. Wisdom Publications, Boston (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Graham Priest .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer India

About this paper

Cite this paper

Priest, G. (2015). None of the Above: The Catuṣkoṭi in Indian Buddhist Logic. In: Beziau, JY., Chakraborty, M., Dutta, S. (eds) New Directions in Paraconsistent Logic. Springer Proceedings in Mathematics & Statistics, vol 152. Springer, New Delhi.

Download citation

Publish with us

Policies and ethics