Do we need to prove that unicorns, tooth fairies, hobbits and so on do not exist? The question is not just funny, insofar as an upholder of the existence of ghosts and the like could easily claim that —strictly speaking— there is no evidence of their non-existence. In Indian epistemology, this amounts to saying that there are no bādhakas ‘invalidating cognitions’ telling us that the existence of ghosts, etc. is invalid.
Thus, the absence of bādhakas is not enough, unless one wants to invest an aweful amount of time looking for contrary evidences about nearly every possible claim. A usueful tool, in this sense, might be the Pūrva Mīmāṃsā adherence to what is usually the case. We do not see omniscient people, nor witches, nor hobbits, nor teeth fairies, thus, the one who argues in favour of their existence has the burden to prove it.
Accordingly, the absence of bādhakas is not enough for whatever goes beyond the ordinary and one needs positive reasons to establish it. But one must be careful with such positive reasons. In fact, the same argument will be applied to more important issues, such as the existence of God or the epistemological validity of the Sacred Texts. Thus, once we have agreed that God and hobbits share the fact of being extra-ordinary, then we need to apply to God the same standard we applied to the hobbits, i.e., the asbence of evidence of the contrary is not enough to establish His/Her existence.
Now, suppose one says that God exists not just because His/Her existence cannot be invalidated, but also because of consensus gentium (or any other form of mahājanaparigraha), then, what would she do if the opponent could be able to prove that most people do in fact believe in the existence of witches (as it might have indeed been the case)? Indian epistemologists have, thus, asked for a majority of qualified people (i.e., of mahājana ‘great people’ and not just bahujana ‘many people’). Christian theologians, by contrast, have conceived the idea of a providential lead of the people’s hearts, so that God Himself/Herself will incline His/Her people in the right direction (cf. vox populi, vox Dei— the people’s voice is God’s voice).
If, however one is not persuaded by these attempts (the latter relies, again, on something extra-ordinary and has, thus, no independent probatory value; the former relies on one’s ability to discern who the ‘great people’ are, which is far from obvious) and leaves out bādhakābhāva (‘absence of invalidating cognitions’) and mahājanaparigraha (‘acceptance by many/great people’), what remains in order to prove extra-ordinary states of affairs?
Perhaps: 1. Inference (but you must really be very confident in order to hope for inference to go further than direct perception). 2. Mystical experience (but that is not communicable, or at least, its epistemic value cannot be communicated). 3. Renunciation to any need to verify.Can you think of other means?