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P.183 The history of Indian logic is usually divided into three periods, Old Nyaaya (circa 250 B.C. ) , Buddhist logic (sixth century A.D.) and New Nyaaya. The Buddhist logic text, Nyaayaprave`sa (Introduction to Logical Methods) , had great influence upon Indian and Chinese Buddhism and also among the Jains. As a pivotal work, the Nyaayaprave`sa has received critical attention from historians of religion, philologists, philosophers, and logicians. As with all advances in scholarship, there is controversy over interpretation, but in the case of Buddhist logic, the controversy cuts to the very heart of the issue of whether Buddhist logic is in any recognizable contemporary sense a "logic." The received view holds that Buddhist logic bears very close similarities to syllogistic forms and that it can be represented and analyzed by standard deductive techniques.(1) A much different and opposing view has been argued by Professor Douglas Daye in a series of papers. Daye maintains that "... the descriptive utility of mathematical logic with early Nyaaya texts has simply been overrated";(2) that although the Nyaaya texts contain metalogical rules for evaluating the "legitimacy or illegitimacy" of arguments, the distinction between validity and invalidity does not apply;(3) that Nyaaya models are not inferences but "formalistic explanations"; and that "... Buddhist logic is not deductive, nor can it be formally valid nor is it an inference."(4) The cumulative effect of these claims is to assert that Buddhist logic is not a "logic" at all, at least not in any sense which is recognized by Western philosophers. There is a radical incompatibility between the Nyaaya methods of logic and those of the Prior Analytics or Principia Mathematica. Of course, there will be differences, possibly very great differences, between any two traditions so diverse as fourth century (B.C.) Greece and sixth century (A.D.) India, but are we to go so far as to say that the Nyaaya does not contain inferences? The radical incompatibility thesis is, I maintain, a mistake; moreover, it is a mistake which can readily be uncovered by examining the typical Nyaaya inference scheme. Of the notion that a Nyaaya scheme could be a "formalistic explanation" without being an inference, I shall say very little because I do not see how anything which functions as an explanation could not involve inferences of some kind or other. It is important to know whether the Nyaaya scheme is deductive or not, and if it is, whether all of its parts are essential to the deduction. I will demonstrate that there are two ways of reading the Nyaaya form: one which is straightforwardly deductive and a second which is best understood by what the American pragmatist, C.S. Peirce, and later Norwood Hanson, call "retroduction." To begin with, consider this representative example from the Nyaaya:(5) 1. pak.sa (thesis) Sound is imprrmanrne 2. hetu (mark or Reason) - Because of its property of being produced P.184 3. d.r.s.taanta (Exemplification)--Whatever is produced, is impermanent 4. sapak.sa (similar case)- As with a pot, and so forth 5. vipak.sa (dissimilar case)- As (not with the case) of space, and so forth Tachikawa proposes the following scheme for what he calls the "three-membered Indian syllogism:(6) 6. There is property p in locus L 7. (because) there is property q (in L). 8. Wherever there is property q, there is property p, as in locus w Clearly, if this schema is reversed, (8) and (7) become premises for a valid deductive inference of (6) as the conclusion.
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