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Nyaya Methodology and Western Mathematical Logic: Origins and Implications

  • Martin Schmidt
  • Bharath SriramanEmail author
Living reference work entry

Abstract

In this chapter, we compare the Nyaya school of logic, one of the six major schools of Hindu philosophy to Aristotelian logic. In particular, we compare the intent, nature, and structure of syllogisms in Nyaya to that in Western mathematical logic to highlight differences in premises and conclusions. In doing so, we draw on the foundational writings and commentaries on Nyaya methodology from both Hindu and Buddhist sources, as well as the major sources of Aristotelian logic. We explore the possibility of Nyaya methodology being influenced by Aristotelian logic before arguing that the Nyaya system developed on its own trajectory. Some modern implications of Nyaya methodology are given.

Keywords

Indian philosophy Hindu philosophy Mathematical logic Nyaya logic Aristotelian logic Syllogisms Milinda Law of contrapositive Buddhist logic 

References

  1. Aristotle. (350 BC) Prior analytics (trans: Jenkinson AJ). Massachusetts Institution of Technology, BostonGoogle Scholar
  2. Aristotle. (350 BC) Posterior anlytics (trans: Jenkinson AJ). Massachusetts Institution of Technology, BostonGoogle Scholar
  3. Aristotle. (350 BC) Physics (trans: Hardie RP and Gaye RK). Massachusetts Institution of Technology, BostonGoogle Scholar
  4. Chakrabarti KK (1989) Contraposition in European and Indian logic. Int Philos Q 29(2):121–127. Issue No. 114CrossRefGoogle Scholar
  5. Dasgupta S (1922) A history of Indian philosophy, volume I. Cambridge University Press, CambridgeGoogle Scholar
  6. Davies J (1881) Hindu philosophy: the Sankhya Karika of Iswara Krishna. Trubner & Co., Ludgate Hill, LondonGoogle Scholar
  7. Fathi K (2013) Logic in Buddhism. In: Runehov ALC, Oviedo L (eds) Encyclopedia of sciences and religions. Springer, DordrechtGoogle Scholar
  8. Ganeri J (1996) The hindu syllogism: nineteenth-century perceptions of Indian logical thought. Philos East West 46(1):1–16CrossRefGoogle Scholar
  9. Ganeri J (2001) Philosophy in classical India. Routledge, LondonzbMATHGoogle Scholar
  10. Ganeri J (2004) Indian logic. In: Handbook of the history of logic volume 1. Elsevier North Holland, LondonzbMATHGoogle Scholar
  11. Ghose, A (1970) Singular propositions and Aristotle’s conception of logic. Indian Inst Manag: 327–331CrossRefGoogle Scholar
  12. Gokhale, PP (1993) Vadanyaya of Dharmakirti: the logic of debate. Motilal Banarsidass, DelhiGoogle Scholar
  13. Hiriyanna M (1932) Outlines of Indian philosophy. George Allen & Unwin Ltd., LondonGoogle Scholar
  14. Kattsoff LO (1947) A philosophy of mathematics. The Iowa State College Press, AmeszbMATHGoogle Scholar
  15. Keith A (1921) Indian logic and atomism. Greenwood Press, New YorkGoogle Scholar
  16. King R (1999) Indian philosophy: an introduction to Hindu and Buddhist thought. Georgetown Press, WashingtonGoogle Scholar
  17. Lukasiewicz J (1955) Aristotle’s syllogistic. Oxford University Press, LondonzbMATHGoogle Scholar
  18. Matilal BK (1968) Gangesa on the concept of universal property. Philosophy East and West 18(3):151–161CrossRefGoogle Scholar
  19. Merriam-Webster’s Collegiate Dictionary, 10th edn. (1993) Merriam-Webster, SpringfieldGoogle Scholar
  20. Moravcsik J (2004) Logic before Aristotle: development or birth? In: Handbook of the history of logic volume 1. Elsevier North Holland, LondonzbMATHGoogle Scholar
  21. Nicholson, H (2009) The shift from agonistic to non-agonistic debate in early Nyaya. Springer Sci: 75–95Google Scholar
  22. Phillips SH (1995) Classical Indian metaphysics. Open Court, ChicagoGoogle Scholar
  23. Raju PT (1952) Intuition as a philosophical method in India. Philosophy East West 2(3):187–207CrossRefGoogle Scholar
  24. Raju PT (1971) The philosophical traditions of India. George Allen & Unwin Ltd., LondonGoogle Scholar
  25. Russell B (1945) A history of western philosophy. Simon and Schuster, New YorkGoogle Scholar
  26. Scharf PM (1996) The denotation of generic terms in ancient Indian philosophy: Grammar, Nyāya, and Mīmāṃsā. Transactions of the American Philosophical Society, New Series,86(3):i-x+1–336CrossRefGoogle Scholar
  27. Shaw JL (1982) From the Nyaya to Frege-Russell. Stud Logica 41(2/3, Proceedings of the 1981 annual conference of the Australasian Association of Symbolic Logic):283–291MathSciNetCrossRefGoogle Scholar
  28. Simonson S (1946) The categories of proof in India logic. Philos Phenomenol Res 6(3):400–409CrossRefGoogle Scholar
  29. Stcherbatsky T (1962) Buddhist logic: volume 2. Dover, New YorkGoogle Scholar
  30. Vidyabhusana MMSC (1918) Influence of Aristotle on the development of the syllogism in Indian logic. J R Asiat Soc Great Britain Ireland: 469–488Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Western Nevada CollegeCarson CityUSA
  2. 2.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

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