Is Nyāya tarka a kind of counterfactual reasoning, and does it need possible worlds?

Question

I teach mathematics, and when I read Nyāya I am always delighted by how close their techniques are to the proofs I teach. One that puzzles me is tarka, which I have seen translated as "hypothetical reasoning", "suppositional reasoning" or "reductio".
The classic example seems to go like this: we see smoke on the hill and infer fire. Someone doubts the link. We answer: "If there were no fire there, there would be no smoke", and since there plainly is smoke, the doubt collapses.
That is a counterfactual: it supposes something false and draws a consequence. In Western philosophy, counterfactuals are now usually explained with possible worlds (the nearest world where there is no fire, and so on). Did the Naiyāyikas have anything like that? Or did they manage counterfactual reasoning without any theory of other worlds at all? And is tarka a source of knowledge for them, or something else?

Meera Kulkarni · Accepted Answer

Lovely question, Vikram. A few points from the texts.
First, tarka is old in the school: it is one of the sixteen topics listed at the very start of the Nyāya-sūtra. But it is not one of the pramāṇas. It does not by itself produce knowledge. It is an auxiliary that supports a pramāṇa, usually inference, by removing a doubt that would otherwise block it.
Second, the place where it does most work is in later Navya-Nyāya, especially Gaṅgeśa, in establishing vyāpti, the invariable concomitance between smoke and fire. You cannot observe every case, so the worry arises that somewhere smoke occurs without fire. Tarka answers by showing that the supposition leads to something unacceptable: smoke would then not be an effect of fire, which contradicts everything we rely on.
Third, there is a limit. Udayana has a well-known point that doubt itself has a boundary: you cannot go on doubting the fire–smoke link while lighting a fire to make smoke, because your own action contradicts the doubt. Doubt that contradicts your practice is not genuine doubt.
As for worlds: no, there is no possible-worlds semantics. Tarka is a technique of argument, a way of using a false supposition, not a theory of what makes counterfactuals true.

Oskar Nyberg · Answer

Meera's answer suggests the right comparison is not with Lewis or Stalnaker but with reductio ad absurdum, and with what logicians call suppositional reasoning. Stalnaker's semantics answers "what makes 'if there were no fire, there would be no smoke' true?" Tarka answers "how may I use such a supposition in a debate?" Different projects. The Nyāya never needed the first because they were not trying to give truth conditions for conditionals in general.

Tomasz Wójcik · Answer

Udayana's point about doubt and practice is remarkably close to things Peirce and Wittgenstein said much later about doubt needing a reason and not being unlimited. I did not know it. Is there a translation of the passage you would recommend, Meera?

Meera Kulkarni · Answer

Tomasz, the most accessible discussion I know is in Matilal's essays on Indian logic; he treats tarka and Udayana's limit on doubt quite carefully, and he was always alert to the Western parallels without forcing them.

Vikram Sethi · Answer

Thank you. So: tarka is a method, not a pramāṇa, and not a semantics. It is closer to what I do on the board when I say "suppose there were a largest prime" than to anything about other worlds. That makes me feel even more at home with it.

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