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Madhva Logic
[ch. sometimes mutually exclusive, yet sometimes found to be coincident; thus cooking is done by women, yet there are men who cook; cook and males are mutually exclusive, though there may be some males who cook (kvacit samāvista api kvacit paraspara-parihārenaiva vartate). The circle of cooking is divided between males and females. Here also there is a relation between cooking and males, but it is not unfailing (avyabhicāritā); unfailing relation means that, where there is one, there must be the other also.
When a man observes the coexistence of fire and smoke, he naturally revolves in his mind "is it in this place that fire and smoke are seen together, while in other places and at other times the presence of one excludes the presence of the other, or are they always found together"; then by observing in several instances, he finds that, where there is smoke, there is fire, and that, where there is no fire, there is no smoke, and that in some cases at least there is fire, but no smoke. These observations are followed by a consideration such as this: "since, though in many cases fire coexists with smoke, in some cases at least fire is found where there is no smoke, does smoke, although in all the cases known to me it exists with fire, ever remain without it, or does it always coexist with fire?” Then again the consideration arises that the relation of smoke to fire is determined by the presence of wet wood (ādrendhana), which may be called a vitiating condition (upādhi), i.e., had this condition not been there, there would have been unqualified coexistence of fire with smoke, and vice versa. This vitiating condition (upādhi) exists in all cases of smoke, but not in all cases of firel, Where the coexistence is not determined by any such vitiating condition, the coexistence is universally mutual. There are some qualities which are common to both fire and smoke (e.g., both of them are objects of knowledge: yathā prameyatvam), and these cannot determine the connection. There are other qualities which do not belong either to smoke or fire, and these also cannot determine the connection. It is only the vitiating condition of the presence of wet wood which by its absence can dissociate fire from smoke, but cannot dissociate smoke from fire. If there were any such condition which was present in all cases of fire, but not in all cases of smoke, then the inference of fire from smoke would have been faulty as the
This vitiating condition will therefore falsify an inference such as "There is smoke in the hill because there is fire."