Nyāya Sūtras 11

Now, the self is not grasped by perception. Is it known merely from the instruction of an authoritative person? It is answered: no, it is to be known also by inference. How?

NyS 1.1.10: Desire, aversion, effort, pleasure, pain, and cognition are the mark of the self.

When the self has experienced pleasure from contact with an object of a particular kind, on seeing an object of that very kind it desires to acquire it; this desire to acquire, which arises from the synthesis of experiences by a single [agent] who perceives multiple objects, is the mark of the self. For it is not possible if there were merely different cognitions restricted to their respective objects, just as in the case of different bodies. In the same way, aversion toward a cause of pain arises from the synthesis of experiences by a single [agent] who perceives multiple objects.

On seeing an object of the kind known to be a cause of pleasure for it, it makes an effort to acquire an object of that kind. This would not occur without a single synthesizer of experiences who perceives multiple objects. It is not possible if there were merely cognitions restricted to their respective objects, just as in the case of different bodies. By this, effort toward a cause of pain is explained. And through the memory of pleasure and pain, acquiring their means, it experiences pleasure, experiences pain, and feels pleasure and pain. The reason is the very same as stated earlier. Indeed, being desirous of knowing, it considers, 'What can this be?', and considering, it comes to know, 'It is this'; this cognition, being apprehended as having the same agent as the desire to know and the consideration, is a mark of the self. The reason is the very same as stated earlier. Here, [the phrase] 'just as in the case of different bodies' is analyzed: just as, for the proponent of non-self, different cognitions restricted to their respective objects are not synthesized across different bodies, so they would not be synthesized even with respect to a single body, because there is no difference.

This is the customary experience of a single living being: remembering what was seen by oneself, not what was seen by another, nor what was not seen. Thus, indeed, is the customary experience of multiple living beings: one does not remember what was seen by another. Neither of these two can be established by the proponent of non-self; hence it is established that the self exists.