Indian Logic Forum

Bhadrakara · Posted: Fri Oct 07, 2005 10:32 pm Post subject: Metalogical Incompatibilities

Douglas DUNSMORE DAYE

Metalogical Incompatibilities in the Formal Description of Buddhist Logic (Nyaya)

Introduction and Background. In this paper I wish to consider two specific aspects of comparative logic. First, I wish to briefly sketch and comment upon the general post-war (rather Procrustean) methodological background regarding the Sanskrit ablative case (AC) in Buddhist logical texts and the use of the functor of material implication (MI) to describe the AC. Secondly, I wish to demonstrate the incompatibility of MI and AC by contextually examining truth-functionality, and the incompatible concepts of Stephan Toulmin's full-warrant and the Buddhist protometalogical rule of the Three Forms of the Justification (trairupyahetu).

The technical literature of philosophy of logic is saturated with warnings against assuming the interchangeability of "if p then q," "q because of p" and "p implies q." I do not wish to re-trace that ground again; rather I wish to suggest a new instance of incompatibility between "implies" and "because" (AC) based solely on the metalogical incompatibilities found in the works of Toulmin and the (supposed) author of the sixth century, the Indian Buddhist logician, Dignaga.

I have read somewhere that when the early Jesuit missionaries first arrived in China and began the study of the Chinese language in which to propagate the Christian Dharma (teachings), they began writing grammars of Chinese utilizing the non-isomorphic descriptive categories and terminology of Latin grammar. I would not wish blatently to assert that such questionable methodological activities have been carried out in all logical studies of Buddhist Nyaya. However, I do wish to suggest that one can construct a weak analogy between such activities and the expectations and methological projections of (first) scholars primarily trained in western 19th century syllogistic and 20th century mathematical logic, and (second) their subsequent attempts to describe and elucidate Buddhist logic (Nyaya) by utilizing the logical machinery of a tradition foreign to that of Buddhist Nyaya (Chinese: yin ming). The methodological presuppositions common to the over-formalized expectations of the modern logician may lead him to protect the distinctions of his discipline when he looks at the primitive nature of (here) sixth century nyaya texts. The result may be a reading into a logically less sophisticated text of an over-formal analysis, which presupposes the legitimate assumptions and distinctions shared in a more sophisticated and complex modern logical tradition. I am not arguing that such methodological projection is not possible and sometimes helpful; I am arguing that in this specific context it is not accurate.

I do not wish to suggest that I have not found such comparative inquiries both interesting and rewarding. Such cross disciplinary and cross cultural studies are, in the long run, one of the most fruitful methods by which we can attain, intellectually and culturally, what we almost seem now to have economically, namely, one multivalent world. The modern tradition in philosophy of logic, a truly international enterprise today, is the only source from which methods may be generated for a truly distortion-free analysis of comparative logic. It should not be construed from the foregoing remarks that I am assuming an anti-modern methodologicallogical position; simply stated, I am against metalogical obscuration and implicit cultural projection.

Let me briefly try to place my viewpoint in the context of the history of logic. As is well known, the western logical tradition has undergone great and convulsive changes since Frege and has changed very rapidly since the end of the 19th century. The primary emphasis is that such development, fruitful as it is, between mathematicians, logicians, and philosophers, gives a particular emphasis and direction to the development of western logic, namely, that mathematics is held to be the primary model for the development of logic. I make the assumption that the analogies between Indian logic, jurisprudence and debate are much greater than those between Indian logic, mathematics and much of formalistic logic. I suggest that we may more profitably explore the metalogical function of certain proto-metalogical machinery in Sanskrit by analyzing both the presuppositions of the ancient proto-metalogical traditions of India and the presuppositions of the formal machinery of modern (international) formal logic. Hence, I do not necessarily assume that the latter is a completely distortion-free instrument by means of which one may describe the former (Indian nyaya).

Published originally in the Notre Dame Jornal of Formal Logic 18 (1977), no. 2, 221вЂ“231.

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