Vaisesika takes up the thread of inquiry from where Nyaya leaves it with its pramanas. According to the great sage Kanada, the founder of Vaisesika, everything ultimately is made up of atoms. Isvara created the world by different combinations of atoms. In both Nyaya and Vaisesika, the cosmos and the individual self are entities separate from Isvara.
As we inquire into the origin of conscious life and the insentient atom and go step by step ahead in our inquiry, we realise in the end the monistic truth that everthing is the manifestation or disguise of the same Paramataman. Nayaya is an intermediate stage to arrive at this truth.
Naya or Tarka (logic) gives rationalism its due place, but this does not lead to materialism, atheism or the Lokayata system. Through intellectual inquiry, Nyaya comes to the conclusion that, if the world is so orderly with so many creatures in it, all of them interlinked, there must be an Isvara to have created it. Nyaya recognises that there are areas that cannot be comprehended by human reason and that the truths that cannot be established rationally must be accepted according to how the Vedas see them. This means that Nyaya takes every care to see that reasoning does not take a course that is captious (remember what I told you about the Acarya's view that tarka should not become kutarka ) and that it leads to the discovery of truth.
To examine something with the instrument of knowledge is to purify that very knowledge. It is also a means of obtaining intellectual clarity. When there is lucidity the truth that is beyond the reach of this very intellect will appear to us in a flash. [In other words there will be an intutive perception of the truth].
It is indeed commendable to have faith in the Lord and in the sastras even without carrying out any intellectual inquiry. But are we able to have such complete faith that will take us across worldly existence? Instead of idling away one's time, without making any intellectual effort to discover the truth, would it not be better to keep thinking even if it be to arrive at the conclusion that there is no God? A person who does so is superior to the idler who has no intellectual concern whatsoever. perhaps the athesit, where he to continue his inquiry, would develop sufficient intellectual clarity to give up his atheism. But the idler has no means of advancing inwardly.
This is one reason why even "Carvakam" was accepted as a system in India. "Caru-vakam"="Carvakam" : that which is pleasing to the ear. Carvakam believes that there is no need to worry about God or any Sprit or to observe vows and fasts or to control one's senses. Live as you please according to your whims and according to the to the dictates of your senses.
Sorrow, however, is inevitable even in a life in which we consciously seek pleasure. Indeed sorrow will predominate. The purpose of religion is overcoming sorrow.
For a general background, please see here