Can someone explain what the Nyāya logicians meant by vyāpti (pervasion)?

Question

My training is entirely in Western formal logic, and I've started reading Matilal's The Character of Logic in India. I understand the standard example: there is fire on the hill because there is smoke, and wherever there is smoke there is fire, as in a kitchen.
I'm tempted to read vyāpti as a universally quantified conditional, "for all x, if smoke at x then fire at x". But Matilal suggests that's too quick.
Specific questions:
Is vyāpti a relation between properties, between loci, or something else?How do the Naiyāyikas think it is known? If by repeated observation, don't they run straight into the problem of induction?

Meera Kulkarni · Answer

Good questions. Short version:
Vyāpti is invariable concomitance between the reason (hetu, smoke) and the thing to be proved (sādhya, fire). Fire is the pervader and smoke the pervaded. It's asymmetric: fire pervades smoke, but not the other way round, since you can have fire without smoke, the classic case being a red-hot iron ball.
So it's a relation between properties, but always as they occur in loci. That's why the example (dṛṣṭānta) of the kitchen matters: it anchors the relation in an actual place.
As for knowing it: observation of co-presence (anvaya) and co-absence (vyatireka), plus the absence of any counterexample, plus checking for an upādhi, a hidden condition. Inferring smoke from fire fails because smoke needs wet fuel; wet fuel is the upādhi.
The Cārvākas pressed exactly your induction worry. Later Navya-Nyāya answered partly by positing an extraordinary perception through universals: seeing smoke as such, you grasp all smoke.

Vikram Sethi · Answer

The upādhi reads to me like a confounding variable. You've observed fire with smoke many times, but only because you've only seen fires with damp wood. It's surprisingly modern.

Tomasz Wójcik · Answer

This is very helpful, Meera. So upādhi works like a defeater, and the whole account is closer to defeasible reasoning than to a material conditional. I'll read Gaṅgeśa next, if I can find a translation I trust.

Arjun Iyer · Answer

For what it's worth, the Advaitins accepted much of the Nyāya account of inference and quarrelled mainly about details. Shankara's followers needed a good theory of inference to argue at all, so they borrowed it.

4 answers