#mathematicalinduction
vyāpti (invariable concomitance)
establishing a universal, exceptionless relationship between two things
Svataḥ prāmāṇya — intrinsic validity of knowledge
Arthāpatti — postulation
Mīmāṃsā recognized arthāpatti (circumstantial implication) as a distinct pramāṇa (source of knowledge), separate from inference. It's the move of positing something that must be true to account for an observed fact — e.g., "Devadatta is alive but not at home, therefore he must be outside." This is closer to abductive reasoning (inference to the best explanation) than induction, and is arguably what physicists actually do when they posit unobserved entities or laws.
Śabda and bypassing induction
Mīmāṃsā's deeper move was to ground reliable universal knowledge not in empirical induction at all, but in śabda — Vedic testimony, which they held to be eternal and authorless (apauruṣeya). This is philosophically bold: if you need a bedrock of non-inductive, non-empirical universal truth, you appeal to something outside the empirical cycle entirely. Physicists can't do this — they have no equivalent of the Vedas — which is precisely why the induction problem bites harder in physics.
#physics
self-validity of knowledge was precisely a defense against this kind of total #skepticism
