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