Debate manuals like the Nyaya Sutra of Gautama, the Organon of Aristotle and works by Moists in China were designed to introduce students and scholars to forms of argument, methods of attack and defense. Like Aristotle, Vatsyayana argues that debate proceeds from motives, and so a destructive skeptic debates destructively, without a committed motive or acceptable doctrine. Some have claimed that Aristotle’s syllogisms are deductively valid but Gautama’s syllogistic form of proof is not and based on induction. Actually, Aristotle has many syllogisms he openly admits in the text are not deductively valid on their own, and those forms, unlike the perfect four, weren’t studied by Islamic or Catholic logicians much. We can see induction and deduction working together in the syllogistic forms of both Aristotle and Gautama, and the similarities are quite striking. There are five formal steps to the Nyaya formal proof, but as Buddhists later perceived the first and second steps are identical to the fifth and the fourth, and can be eliminated.
To make each form of proof easier to study, I take liberties with both the Indian and Greek syllogistic forms, preserving the information but changing the order it is presented to show how the information connects in sequence. Strangely, in the original texts of Aristotle, the most famous and basic form of syllogism is not If A then B, if B then C, so if A then C, as I present it, but rather In B then C, if A then B, so if A then C, such as Aristotle’s famous example, All men are mortal, Socrates is a man, so Socrates is (or rather, was) mortal. It does work, but it works better as Socrates is a man, all men are mortal, so Socrates is mortal.
Similarly, Gautama’s central example is, Wherever there is smoke there is fire, as in a kitchen, so because there is smoke on the hill, there is fire on the hill. This is almost identical to Aristotle if we change the subjects to his, and say, Whoever is a man is moral, like Plato, so since Socrates is a man, Socrates is mortal. Thus, we can reorder Gautama’s proof in a similar A to B to C way, such that it reads, There is smoke on the hill, wherever there is smoke there is fire, as in a kitchen, so there is fire on the hill. Notice that this is not perfect, because perception of smoke is a central example of possible misperception, but it need not be, as smoke can look quite dissimilar from a dust cloud sometimes. The second example would then read, in line with Kanada’s cosmic observations, Sound is made, and whatever is made is impermanent, like a pot, so sound is impermanent. Those who say Gautama relies on induction focus on the addition of the extra example offered, and not on the clear similarities of the forms.