The development of logic in India dates back to the analysis of inference by Aksapada Gautama, founder of the Nyaya school of Hindu philosophy, probably in the first or second centuries BCE, and so stands as one of the three original traditions of logic, alongside the Greek and Chinese traditions. Logic (from ancient Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... Aksapada Gautama (probably c. ... Nyaya is the name given to one of the six orthodox or astika Hindu schools of Philosophy - specifically the history of logic. ...

The Nyaya Sutras

Main article: Nyaya Sutras

The Nyaya-sutras were composed by Aksapada Gautama around 500 BC. The sutras contain five chapters, each with two sections. ...

Vaisheshika

Founded by Kanada, the Vaisheshika school made use of the Nyaya system of inference. Kanada was a Hindu sage who founded the philosophical school of Vaisheshika. ... Vaisheshika, also Vaisesika, (Sanskrit: वैशॆषिक)is one of the six Hindu schools of philosophy (orthodox Vedic systems) of India. ...

Dignaga's formalisation of inference

Dignaga's characterisation of inference by example and by the hetucakra (Peckhaus 2004)

The new Nyaya school

Main article: Navya-Nyaya

In the 13th century, Gangesha Upadhyaya founded the Navya-Nyaya, roughly rendered as the new school of logic, which was to become the focus for a renewed vigour in the investigation of logic and philosophical analysis . (12th century - 13th century - 14th century - other centuries) As a means of recording the passage of time, the 13th century was that century which lasted from 1201 to 1300. ... Gangesha Upadhyaya, 13th century, Mithila, established the Navya-Nyaya, New Logic, school. ...

Possible influence of Indian logic on modern logic

In the late 18th century, British scolars began to take an interest in Indian philosophy and discovered the sophistication of the Indian study of inference, culminating in Henry T. Colebrooke's The Philosophy of the Hindus: On the Nyaya and Vaisesika Systems in 1824 (in Ganeri, 2001), which provided an analysis of inference and comparison to the received Aristotelian logic, resulting in the observation that the Aristotelian syllogism could not account for the Indian syllogism. Jonardon Ganeri observed that this period was the period in which George Boole and Augustus De Morgan were making their pioneering applications of algebraic ideas to the formulation of logic, and suggested that these figures were likely to be aware of these studies in xeno-logic, and further that their acquired awareness of the shortcomings of traditional logic are likely to have stimulated their willingness to look outside the system. (17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ... 1824 was a leap year starting on Thursday (see link for calendar). ... Aristotelian logic, also known as syllogistic logic, is the particular type of logic created by Aristotle, primarily in his works Prior Analytics and De Interpretatione. ... In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). ... George Boole [], (November 2, 1815 Lincoln, Lincolnshire, England - December 8, 1864 Ballintemple, County Cork, Ireland) was a mathematician and philosopher. ... Augustus De Morgan (June 27, 1806 - March 18, 1871) was an Indian-born British mathematician and logician. ...

As a parallel, several mathematicians have suggested an influence of Indian mathematics on the European. For example, Hermann Weyl wrote: Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician and physicist, one of the first people to combine general relativity with the laws of electromagnetism. ...

Occidental mathematics has in past centuries broken away from the Greek view and followed a course which seems to have originated in India and which has been transmitted, with additions, to us by the Arabs; in it the concept of number appears as logically prior to the concepts of geometry. (Weyl, 1929)

References

• B. K. Matilal. Logic, Language, and Reality: An Introduction to Indian Philosophical Studies. Delhi, 1985.
• B. S. Gillon. Indian theories of inference (subscription), in the Routledge Encyclopedia of Philosophy, 1998.
• J. Ganeri, editor. Indian Logic: A Reader. Routledge Curzon, 2001
• V. Peckhaus. Dignaga’s Logic of Invention. In Ivor Grattan-Guinness, editor, History of the Mathematical Sciences, 2004.
• V. V. S. Sarma. Indian Systems of Logic (Nyaya): A Survey (PDF). Proc. Bombay Logic Conference, 2005.

The Routledge Encyclopedia of Philosophy is a major encyclopedia of philosophy that was first published by Routledge in 1998, and has since 2002 been made available online on a subscription basis. ...

External links

• Overview of Indian and Greek Development of Logic and Language