In which of the following arguments is the middle term always positively…

Concept

In Nyāya, a kevalānvayi inference has an exclusively affirmative pervasion (vyāpti): the middle term occurs only where the major term occurs, and no locus is available in which both are absent. An anvaya-vyatireki inference admits both positive and negative examples, whereas a kevalavyatireki inference is established through negative concomitance.

Application

Classify each argument by the kind of concomitance available between its middle and major terms:

• In ‘All knowable objects are nameable,’ nameability is treated as universal. Therefore no vipakṣa can provide a locus where nameability is absent, so the knowable–nameable pervasion is available only through affirmative concomitance.

• ‘No non-fiery things have smoke’ states the negative side of the smoke–fire pervasion. A smoky, fiery kitchen and a smokeless, fireless lake provide positive and negative instances, so the underlying inference is anvaya-vyatireki.

• ‘All things which have smoke have fire’ states the affirmative side of the same smoke–fire pervasion. The kitchen and lake examples again make both agreement in presence and agreement in absence available.

• In the smell–difference argument, the major term ‘different from the other elements’ belongs only to earth, the subject under consideration. No separate positive similar instance is available, so the pervasion is established through negative concomitance.

Cross-check and result

The knowable–nameable case has no possible vipakṣa because nameability is universal; the two smoke–fire formulations admit both positive and negative instances; the earth–difference case has no separate positive similar instance.

Therefore, the argument ‘All knowable objects are nameable; the pot is knowable; therefore the pot is nameable’ is the kevalānvayi inference described in the question.