Nyāya-prasthāna means everything, all the sūtras and codes, are there with full reasoning.
Lecture on BG 13.5 -- Paris, August 13, 1973:
The Brahma-sūtra, or Vedānta-sūtra, is called nyāya-prasthāna. There are three different processes for understanding the Absolute Truth: nyāya-prasthāna, śruti-prasthāna, smṛti-prasthāna. Brahma-sūtra is nyāya-prasthāna. Nyāya-prasthāna means everything, all the sūtras and codes, are there with full reasoning. Hetumadbhir viniścita. And whatever Brahma-sūtra says, that is viniścita, means ascertained. There is no doubt. Just like Brahma-sūtra says, athāto brahma jijñāsā. Brahma-sūtra says, "Now it is the time for inquiring about the Absolute Truth." "Now" means in this life, human form of life, or...
Just like in Europe and America it is the time now to inquire about the Absolute Truth because materially they are advanced. They have seen all material advancements. The scientists are now perplexed that "How we shall maintain ourselves because we have nothing to give anymore? Whatever stock we had, that is finished." Now they are simply to bluff, no more stock to give. They have given us motorcar and atomic bomb and aeroplane and electronic activities. So many things they have given. That's all right. Simply they could not give us relief from birth, death, old age, and disease. That's all. The real problems are there.