A simplified example of Greek logic is as follows
- All men die
- Socrates is a man
- Socrates will die
Compared to this, Hindu Nyāya has some additional steps. The most common example used is that of the fire in the mountain. The steps are as follows
|There is fire in the hill
|There is smoke
|If there is smoke, there is fire, like in the kitchen
|There is smoke in the hill
|Hence there is fire in the hill
One important step in Nyāya is udāhārana and just because one could not be provided an entire darshana can be refuted. An example of that would be Gaudapada (Adi Shankara’s teacher’s teacher) refuting Samkhya.
According to Samkya, the effect pre-exists in the cause, similar to how a tree pre-exists in the seed. Like how the tree is born from the seed, purusha manifests from prakriti. Gaudapada disagrees with this and among the many tactics he deploys to refute Samkhya, one of them is the lack of udāhārana.
He argues that if Samkhyans say that purusha came from prakriti, one can ask where the prakriti itself came from? If that prakriti came from another cause, it can go backward endlessly (recursion without a terminating condition or anavastha dosha). Or if you argue that prakriti is a causeless cause, he says that won’t work as well, as there is no udāhārana of a causeless cause.
अजाद्वै जायते यस्य दृष्टान्तस्तस्य नास्ति वै ।
जाताच्च जायामानस्य न व्यवस्था प्रसज्यते ॥ १३ ॥
There is no illustration to support the view of him who says that the effect is born from the unborn cause. Again, if it be said that the effect is produced from a cause which is itself born then it leads to a regressus ad infinitum.