Gautama is the founder of the Nyaya school and the author of the Nyaya Sutra, the greatest text on logical debate of ancient India, and he is also known as Akshapada, (eyes in the feet, or gazes at his feet), which, like Kanada’s name, could mean someone who is gathering up many particular things in the lower world into higher universal concepts, or someone lost in thought, much as Thales, the first famed Greek thinker, was gazing at the stars as he fell into a well. A legend says that the same happened to Gautama, who fell into a well while lost in thought, so Brahma gave him eyes in his feet.
Nyaya means right, just, justified or justifiable, the same way we use logical to mean justifiable and defendable debate or speech. The Nyaya school reached its height in 150 CE, but it traces itself back to Gautama and his teachings. In ancient India, a king, authority or rich patron could organize a debate and banquet, invite participants from various schools of thought to debate. A story from the period says that a scholar who gave up on the Vedas and turned entirely to logic turned into a Jackal. This story was obviously told by Vedic scholars and priests who found the new systems a threat to the old established traditions. The other famed Nyaya logicians, each writing commentaries on the Nyaya Sutra of Gautama and the others before them, are Vatsyayana (c. 450 CE), Uddyotakara (c. 550 CE), Vacaspatimishra (c. 900 CE) and Udayana (c. 1000 CE).
The Nyaya Sutra presents many debates that raged at the time, with many centered on dividing the mortal and particular from the eternal and universal, such as whether or not the self, or world, or laws of the cosmos are permanent or fixed in this or that way. One of these questions, asked previously by Kanada, is whether or not sound is temporary, and Kanada, like a Buddhist, says it is, though Kanada and the Nyaya following Gautama would insist that the self and laws of the cosmos, unlike sound, are eternal, following orthodox, established Hindu positions. These debates, as well as those about whether or not luxury or pleasure are good or bad, often take the form of a basic bifurcating disjunction: Is A B or not-B? Vedic priests argued that the individual self is eternal, while the Charvakas and Buddhists argued that it is temporary. Buddhists who debated the Nyaya often used relative qualifiers such as A is sometimes B, or A is somewhere B, or A is B in some things, in some ways.