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Katyayana



 
 
Katyayana (c. 3rd century BC) was a Sanskrit grammarian
Vyakarana

The Sanskrit grammatical tradition of is one of the six Vedanga disciplines. It has its roots in late Vedic India, and includes the famous work, ....
, mathematician
Indian mathematics

Indian mathematics—which here is the mathematics that emerged in South Asia from ancient times until the end of the 18th century—had its beginnings in the Bronze Age Indus Valley civilization and the Iron Age Vedic culture ....
 and Vedic
Historical Vedic religion

The religion of the Vedic period is the historical predecessor of Hinduism. Its liturgy is reflected in the Mantra portion of the four Vedas, which are compiled in Sanskrit....
 priest who lived in ancient India
History of India

The known history of India begins with the Indus Valley Civilization, which spread and flourished in the north-western part of the Indian subcontinent, from c....
.

He is known for two works:

Katyayana's views on the word-meaning connection tended towards naturalism. Katyayana believed, like Plato
Plato

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
, that the word-meaning relationship was not a result of human convention. For Katyayana, 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):
If the 'basis' for the use of the word 'cow' is cowhood (a universal) what would be the 'basis' for the use of the word 'cowhood'?
Clearly, this leads to infinite regress.






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Katyayana (c. 3rd century BC) was a Sanskrit grammarian
Vyakarana

The Sanskrit grammatical tradition of is one of the six Vedanga disciplines. It has its roots in late Vedic India, and includes the famous work, ....
, mathematician
Indian mathematics

Indian mathematics—which here is the mathematics that emerged in South Asia from ancient times until the end of the 18th century—had its beginnings in the Bronze Age Indus Valley civilization and the Iron Age Vedic culture ....
 and Vedic
Historical Vedic religion

The religion of the Vedic period is the historical predecessor of Hinduism. Its liturgy is reflected in the Mantra portion of the four Vedas, which are compiled in Sanskrit....
 priest who lived in ancient India
History of India

The known history of India begins with the Indus Valley Civilization, which spread and flourished in the north-western part of the Indian subcontinent, from c....
.

He is known for two works:
  • The Varttika, an elaboration on Pa?ini
    Pa?ini

    was an Iron Age India Sanskrit grammarian from Pushkalavati, Gandhara .He is known for his Vyakarana, particularly for his formulation of the 3,959 rules of Sanskrit Morphology in the grammar known as 'Ashtadhyayi' , the foundational text of the grammatical branch of the Vedanga, the auxiliary scholarly disciplines of historical Ved...
     grammar. Along with the Mahabhasya of Patañjali
    Patañjali

    Pata?jali is the compiler of the Yoga Sutras, an important collection of aphorisms on Yoga practice, and also the author of the Mahabha?ya, a major commentary on Panini Ashtadhyayi....
    , this text became a core part of the vyakarana (grammar
    Grammar

    Grammar is the field of linguistics that covers the conventions governing the use of any given natural language. It includes morphology and syntax, often complemented by phonetics, phonology, semantics, and pragmatics....
    ) canon. This was one of the six Vedanga
    Vedanga

    The Vedanga are six auxiliary disciplines for the understanding and tradition of the Vedas.#Shiksha : phonetics and phonology #Chandas : Meter ...
    s, and constituted compulsory education for Brahmin
    Brahmin

    Brahmin is the class of educators, law makers, scholars and preachers of Dharma in Hinduism. It is said to occupy the highest position among the varna in Hinduism of Hinduism....
     students in the following twelve centuries.
  • He also composed one of the later Sulba Sutras
    Sulba Sutras

    The Shulba Sutras or Sulbasutras are sutra texts belonging to the Srauta ritual and containing geometry related to fire-altar construction....
    , a series of nine texts on the geometry of altar constructions, dealing with rectangles, right-sided triangles, rhombuses, etc.


Katyayana's views on the word-meaning connection tended towards naturalism. Katyayana believed, like Plato
Plato

Plato , was a Classical Greece Greeks philosopher, mathematician, writer of philosophical dialogues, and founder of the Platonic Academy in Ancient Athens, the first institution of higher learning in the western world....
, that the word-meaning relationship was not a result of human convention. For Katyayana, 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):
If the 'basis' for the use of the word 'cow' is cowhood (a universal) what would be the 'basis' for the use of the word 'cowhood'?
Clearly, this leads to infinite regress. Katyayana'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 Spho?a
Spho?a

is an important concept in Sanskrit grammarians, relating to the problem of speech production, how the mind orders linguistic units into coherent discourse....
 doctrine enunciated by Bhart?hari
Bhart?hari

is the name of a 6th or 7th century Sanskrit grammarian, and of a Sanskrit poet of roughly the same period....
 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-jati) is superposed on the sound-universal or the phonological structure (sabda-jati).

In the tradition of scholars like Pingala
Pingala

Pingala was an Ancient Indian writer, famous for his work, the Chandas Shastra , a Sanskrit treatise on prosody considered one of the Vedanga....
, Katyayana was also interested in mathematics. Here his text on the sulvasutras dealt with geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, and extended the treatment of the Pythagorean theorem
Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a triangle#Types of triangles....
 as first presented in 800 BC by Baudhayana
Baudhayana

Baudhayana, was an Indian mathematician, whowas most likely also a priest. He is noted as the author of the earliest Sulba Sutras — appendices to the Vedas giving rules for the construction of altars — called the , which contained several important mathematical results....
.

Katyayana belonged to the Aindra school of grammarians and may have lived towards the North west of the Indian subcontinent.

See also

  • Pa?ini
    Pa?ini

    was an Iron Age India Sanskrit grammarian from Pushkalavati, Gandhara .He is known for his Vyakarana, particularly for his formulation of the 3,959 rules of Sanskrit Morphology in the grammar known as 'Ashtadhyayi' , the foundational text of the grammatical branch of the Vedanga, the auxiliary scholarly disciplines of historical Ved...
  • Indian mathematicians


See the article Indian Sulbasutras for more information on the Sulbasutras in general and the mathematical results which they contain.

External links