Nyaya is a school of thought in Hinduism. It believes vedas are divine and authored by God?
What are the arguments that Nyaya make to support their claim?
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In his book A Critical Survey of Indian Philosophy (https://archive.org/details/IndianPhilosophyACriticalSurvey), Professor Sharma writes in the section entitled 'God" in his Chapter on Nyaya:
...Udayana's arguments for the existence of God have becomes classical for theism and may be briefly noted here. He gives the following arguments to prove the existence of God:
(5) God is the author of the infallible Veda (pratyayatah).
(6) The Veda testifies to the existence of God (shruteh).
(7) ...The Vedic commands are the Divine commands. God is the creator and promulgator of the moral laws (vakyat).
In his book A History of Indian Philosophy by Professor Dasgupta, Volume 1, Chapter VIII (https://www.wisdomlib.org/hinduism):
This world therefore bing an effect must be proceded by a cause, and this cause is Isvara... He has infinite knowledge and is all merciful. At the beginning of creation He created the Vedas. He is like our father who is always engaged in doing us good. (footnote- See Jayanta's Nyayamanjari, pp. 190-204, and Udayana's Kusumanjali with Prakala and Isvaranumana by Raghunatha.)
Fianlly, In the Bhasa Pariccheda with Siddhanta-Muktavali by Visvanatha-Nyaya-Pancanana (Swami Madhavananda translator), Visvanatha-Nyaya-Pancanana says in his commentary on verse 151:
The fact that no author of the Vedas is recalled, is no bar (to their springing from a person); for to this day we find rather a mention of their author by Kapila, Kananda and others. Otherwise even the Smritis would be regarded as being without any authors. Should it be urged that therein is mention of their authors, the answer is that in the Vedas too there is indeed a mention of their author is such passages as, 'From Him sprang the Vedas,' etc. (Rg-Veda X.xc.9, etc.). Likewise the passage, 'In the regime of each Manu, a different Sruti is produced,' may also be cited. As for the passage, 'Thou has recited in times past these blessed Vedas that are self-manifested; from Siva down to the seers, all are but their recallers, not authors,' it is only a eulogy of the Vedas. It cannot be urged that if they be composed by a person, there would be a chances of error in them, which would take away their authoritativeness; for since (the Author) is eternal and omniscient, He is unimpeachable. Hence, any other person being liable to error etc. even Kapila and the rest are not authors of the Vedas.