Kātyāyana (c. 3rd century BC) was a Sanskrit grammarian, mathematician and Vedic priest who lived in ancient India.
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He is known for two works:
Kātyāyana's views on the word-meaning connection tended towards naturalism. Kātyāyana believed, like Plato, that the word-meaning relationship was not a result of human convention. For Kātyāyana, word-meaning relations were siddha, given to us, eternal. Though the object a word is referring to is non-eternal, the substance of its meaning, like a lump of gold used to make different ornaments, remains undestroyed, and is therefore permanent.
Realizing that each word represented a categorization, he came up with the following conundrum (following Matilal):
Clearly, this leads to infinite regress. Kātyāyana's solution to this was to restrict the universal category to that of the word itself — the basis for the use of any word is to be the very same word-universal itself.
This view may have been the nucleus of the Sphoṭa doctrine enunciated by Bhartṛhari in the 5th c., in which he elaborates the word-universal as the superposition of two structures — the meaning-universal or the semantic structure (artha-jāti) is superposed on the sound-universal or the phonological structure (śabda-jāti).
In the tradition of scholars like Pingala, Kātyāyana was also interested in mathematics. Here his text on the sulvasutras dealt with geometry, and extended the treatment of the Pythagorean theorem as first presented in 800 BC by Baudhayana.
Kātyāyana belonged to the Aindra school of grammarians and may have lived towards the North west of the Indian subcontinent.
See the article Indian Sulbasutras for more information on the Sulbasutras in general and the mathematical results which they contain.
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