How do Sanskrit philosophers deal with solipsism?
Some Buddhist epistemologists just accepted it, as a necessary consequence of their idealism. The example of Ratnakīrti’s “Rejection of the existence of other continuous sequences [of causes and effects leading to the illusion of a separate mind]” comes to mind. In my opinion, Ratnakīrti has a specially strong argument in favour of his view, namely: The Buddhist epistemological school denies the ultimate mind-independent existence of external objects. But once one accepts that, and thus accepts idealism, how can one safeguard intersubjectivity? If there is no reality other than our representations, how comes we can understand each other? Would it not be much more economical to imagine that there is only one representation?
Others rejected it based on analogy (basically: I am a mind, i.e., a continuous sequence of causes and effects; other people behaving similarly must be a mind too). The first and main example of this reasoning is Dharmakīrti’s “Establishment of the existence of other continuous sequences” (santānāntarasiddhi).
The Pratyabhijñā and the Advaita Vedānta schools are ultimately forms of solipsism. In the former case, there is only Śiva’s mind, and the appearance of other minds is part of his līlā ‘playful activity’. In the latter (at least after Śaṅkara), there is only brahman, and the appearance of other minds is due to māyā. What is the different explanatory power of līlā vs māyā? That māyā’s ontology is hard to explain, whereas once one has committed to the existence of a personal God, with Their likes and dislikes, then līlā is a perfectly acceptable solution. Thus, AV is light on the Absolute’s ontology, but implies a leap of faith as for māyā, whereas the opposite is the case for the Pratyabhijñā school.
What about the realist schools? Some of them established the existence of the self based on aham-pratyaya, i.e., our own perception of ourselves as an ‘I’ (so the Mīmāṃsā school). Some thinkers within Nyāya (like Jayanta) used inference to establish the existence of the self.
Is this enough to establish the existence of other selves?
Yes, in the case of Mīmāṃsā, because other minds seem prima facie to exist and due to svataḥ prāmāṇya (intrinsic validity) such prima facie view should be held unless and until the opposite is proven.
Yes, according to Jayanta, because other selves can be inferred just like the own self is.
Realistic Vedāntic schools will rely on either the Mīmāṃsā or the Nyāya paradigm. Thus, the question at this point will rather be: What is consciousness like, if one subscribes to this or the other school?
Some schools (like Pratyabhijñā, Yoga…) claim that we can have direct access to other minds, through yogipratyakṣa or intellectual intuition. However, yogipratyakṣa is possible only to some exceptional individuals. Moreover, Pratyabhijñā thinkers like Utpaladeva think that even this is not an evidence of the existence of separate other minds.(Cross-posted on my personal blog, http://elisafreschi.com)