Mercury’s perihelion precession • A discrepancy that Newtonian mechanics could not account for. Physicists trained purely in the Newtonian tradition, for whom it was unquestioned dogma, initially could not even properly perceive the anomaly as significant. It was a rounding error, a measurement artifact, something to be explained away. The framework was so thoroughly internalised as certain truth that the friction point was invisible. Einstein’s general relativity resolved it.
But the deeper point is epistemological: physicists who had engaged seriously with the limits and assumptions of Newtonian mechanics • who had asked what it required to be true, where it might break down, what a competing framework would even look like • were better positioned to recognise what the anomaly meant.
~ From my own Quote toot
Mathematical induction is one of the most powerful tools in a mathematician’s arsenal. Yet the moment you try to carry it into the physical world, it quietly falls apart. The reasons why are deep — and, strikingly, Indian philosophers of the Mīmāṃsā school were circling the same problem over a thousand years before Hume gave it its canonical Western formulation.
What Mathematical Induction Actually Requires
Induction in the mathematical sense is a proof technique operating over well-ordered discrete sets. You establish a base case, then prove that truth at step \(n\) necessarily implies truth at step \(n+1\). The key word is necessarily — the implication must hold without exception, without approximation, by the rules of the formal system itself.
\[P(0) \land \forall n\,(P(n) \Rightarrow P(n+1)) \;\Longrightarrow\; \forall n\, P(n)\]
This works in mathematics because the rules are stipulated. We defined the system; we own it completely. There are no surprises lurking at step \(10^{100}\).
Why Physics Cannot Use It
Physics offers none of those guarantees. Several distinct problems arise:
The empirical gap. Physical laws are inferred from observation, not derived from axioms. “It has held for every case we’ve tested” is inductive reasoning in the informal, Humean sense — which is precisely the problem philosophers worry about, not a solution to it.
Continuity breaks the step structure. Induction runs over discrete, well-ordered steps. Physical quantities — position, energy, time — are continuous, or at least we have no proof they are discrete at the fundamental level. There is no clean “next step” to induct over.
Measurement has irreducible uncertainty. Even if you verified a claim for a billion cases, physical measurement carries error bars. You can never confirm exact equality between your inductive hypothesis and a new experimental result. Mathematics demands exact truth; physics traffics in approximations.
The universe is not obligated to be uniform. Mathematical induction works because the rules of the system do not change — \(n+1\) follows \(n\) by the same logic everywhere. But physics could behave differently at extreme energies, scales, or regions of spacetime. We assume uniformity (the cosmological principle, spatial isotropy), but we cannot prove it the way a mathematician proves a lemma.
Classical mechanics “worked” inductively for centuries — until special relativity and quantum mechanics showed it fails at high velocities and small scales. No accumulation of prior successes could have proven it universally true.
This is the core of what Karl Popper formalised: science does not prove theories, it only falsifies them. The best a physical theory can do is survive every attempt to break it.
Enter Mīmāṃsā: The Same Problem, Different Vocabulary
The Mīmāṃsā school of Indian philosophy developed a rich epistemological framework that engages directly with this cluster of problems — arriving from a completely different direction, roughly a millennium earlier.
Vyāpti and the Induction Problem
Both Nyāya and Mīmāṃsā grappled with vyāpti — establishing an invariable, universal concomitance between two things. The classic example: yatra yatra dhūmas tatra tatra vahniḥ — wherever there is smoke, there is fire. This is exactly the induction problem rephrased: how do you get from finitely many observed instances to a universal law?
Kumārila Bhaṭṭa and other Mīmāṃsā philosophers debated at length whether vyāpti could ever be established through perception (pratyakṣa) alone. The consensus was that it cannot — you would need to perceive all instances, which is impossible.
Svataḥ Prāmāṇya: Flipping the Burden of Proof
Mīmāṃsā’s distinctive response to this impasse is the doctrine of svataḥ prāmāṇya — the intrinsic self-validity of cognition. A belief or cognition is valid by default; it stands unless actively defeated by counter-experience.
This is a striking inversion of the Western skeptical tradition. Where Hume demands positive justification for inductive claims and finds it lacking, Mīmāṃsā dissolves the problem by flipping the burden of proof. You don’t need to prove your inductive generalization is valid — it stands until falsified.
Popper arrived at a structurally similar position from a completely different direction: theories are presumed provisionally true and we proceed until a falsifying instance defeats them.
Arthāpatti: Abduction Over Induction
Mīmāṃsā also recognised arthāpatti (circumstantial implication or postulation) as a distinct pramāṇa, irreducible to the others. The classic illustration: Devadatta is alive but not at home — therefore he must be outside. You posit whatever is necessary to account for an observed fact.
This is closer to abductive reasoning — inference to the best explanation — than to induction. And it is arguably what physicists actually do in practice: positing fields, dark matter, quarks — unobserved entities or laws that must exist to explain what we do observe.
Śabda and the Limits of the Empirical
Mīmāṃsā’s deepest move was to ground universal knowledge not in empirical induction at all, but in śabda — specifically Vedic testimony, held to be eternal and authorless (apauruṣeya). If you need bedrock, non-inductive, universal truth, you appeal to something outside the empirical cycle.
Physicists have no equivalent of the Vedas. There is no authorless eternal text to appeal to. This is precisely why the induction problem bites harder in physics than in any framework that permits a non-empirical epistemic anchor.
Jayarāśi Bhaṭṭa: The Radical Endpoint
The most extreme position in this tradition belongs to Jayarāśi Bhaṭṭa (8th century), whose only surviving work, the Tattvopaplavasimha (“The Lion that Devours All Principles”), was lost for centuries before being rediscovered and published in 1940.
Jayarāśi did not just question whether vyāpti can be established by induction. He systematically dismantled every pramāṇa — perception, inference, testimony, all of them. Where Mīmāṃsā offered svataḥ prāmāṇya as a bulwark against skepticism, Jayarāśi attacked the foundations of that doctrine too.
His position is more radical than Hume’s. Hume doubted the rational justification of induction; Jayarāśi doubted the coherence of the very categories (tattvas) that inference operates over. The lion doesn’t just eat the prey — it eats the jungle.
The framing of the Khabargaon Mīmāṃsā series — “the philosophy that destroys both atheist and theist arguments” — is accurate. Jayarāśi’s skepticism is symmetric: it undermines the orthodox schools (including Mīmāṃsā itself) just as thoroughly as it undermines materialist or atheist positions.
The Deeper Convergence
Both traditions are, at root, asking the same question:
How do we justify the claim that what has held in all observed cases will hold universally and in the future?
Western philosophy, from Hume through Popper, tends to conclude that this cannot be fully justified — it is a rational leap of faith that science makes because it has no alternative. Mīmāṃsā’s svataḥ prāmāṇya offers a pragmatic alternative: treat universal claims as valid by default and revise when defeated — which is, empirically, how working scientists actually behave.
Jayarāśi goes further: even this pragmatic settlement is philosophically unstable. The lion is still hungry.
What makes this convergence remarkable is not just the similarity of conclusions but the complete independence of the paths that led there. Indian epistemology was not responding to Hume; it was responding to its own internal pressures, over a millennium earlier, with a conceptual vocabulary that in some respects is more fine-grained than anything the Western tradition developed until the 20th century.
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