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As we have already seen, every inference involves the knowledge of vyapti or a universal relation between the major and the middle term. Without a universal relation between the two, no valid conclusion can be drawn from the premises. It is only when we know that smoke is universally related to fire that we can conclusively prove the existence of fire in a hill in which we see smoke. Otherwise, the inference will be inconclusive and invalid. On the other hand, it would seem that if we know smoke to be universally related to fire, we already know the smoke in the hill to be related to fire. The truth of the universal proposition all cases of smoke are cases of fire' involves, nay, depends on the truth of the proposition 'this case of smoke is a case of fire.' Thus it would seem that the major premise of an inference, which is a universal proposition, 1 R. M. Eaton, General Logic, p. 496. 2 Op. cit., p. 501.

assumes what we want to prove in the conclusion, i.e. an inference involves the fallacy of petitio principii or begging the question. The above dilemma of inference has been anticipated and solved in Indian philosophy. The solution is generally based on the distinction between the knowledge of the universal and that of the particulars coming under it. When we know that smoke is always related to fire, we know them in their general character as two universals. This does not imply that we know the relation between all particular smokes and fires. Thus the Mimamsakas argue that the knowledge of vyapti or a universal relation between smoke and fire does not necessarily involve any knowledge of a particular instance of fire, e.g. the fire in a hill. When we know the universal proposition 'all cases of smoke are cases of fire,' we do not know anything about the hill, far less, about its relation to fire. If that were not so, or, if we knew anything about the fire in the hill, there could be no necessity for the perception of smoke in the hill, in order to know the existence of the fire in it. Hence it follows that the conclusion of the inference, namely, 'that hill is fiery,' is a new knowledge which is not involved in the knowledge of its premises. The Naiyayika view of vyapti as covering all the individual cases of a relation seems to commit inference to the fallacy of petitio principii. Thus it has been held by the Naiyayika that when we know the vyapti or the universal relation between smoke and fire, we know all the individual cases of smoke to be related to fire. Otherwise, we cannot account for the inference of fire from the smoke in a hill. If we do not know that the hill-smoke is related to fire, we could not possibly pass from the one to the other. But then the difficulty is that if we already know the hill-smoke to be related to fire, there is no room for an inference to arrive at a new truth. The conclusion of such an inference will only repeat what is already stated in the premises. This difficulty in the Nyaya view of inference may however be explained. ... Vide Sastradipika, pp. 62-63.

According to the Naiyayika, to know that smoke is universally related to fire is indeed to know that 'all cases of smoke are cases of fire.' But the knowledge we have of all fires and smokes is mediated by the knowledge of the universals 'fireness' and ' smokeness' (samanyalaksanapratyasatti). This means that we know all fires and smokes in so far as they participate in fireness' and 'smokeness,' i.e. in their general character without any reference to their specific characters. So while the vyapli gives us a knowledge of the relation between smoke and fire in general, an inference based on it gives us the knowledge of the relation of fire to a particular object, namely, the smoky hill. The major premise of the inference 'all cases of smoke are cases of fire' does not by itself lead to the conclusion that there is fire in the hill. It is only when the major premise is combined with the minor, 'there is smoke in the hill,' that we draw the conclusion there is fire in the hill.' This shows that the truth of the conclusion is not epistemically involved in that of the major premise or the universal proposition. Hence we are to conclude that inference is neither inconclusive nor a petitio principii, since it gives us a new knowledge."

1. TB., p. 11; Tattvachintamani, II. pp. 290-91. 2 Anumanasya dve ange vyaptih paksadharmata ca, etc., Tarkabhasa, p. 11. Vyapyasya parvatadivrttitvam paksadharmata, Tarkasamgraha, p. 46.