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PIOTR BALCEROWICZ
IMPLICATIONS OF THE BUDDHIST-JAINA DISPUTE
very contents that is important for syllogistic inference, but the arrangement itself. Accordingly, letters are employed [to represent) general notions and to show, that conclusion will always follow and from any assumption."
indeed seems rather trivial. A good example of a reasoning of universal denotation is the one provided by Dharmakirti: 'Thus is the formulation of the logical reason based on (essential] identity: whatever is existent, is without exception impermanent, for instance the pot - this is the simple (unqualified) formulation of the logical reason based on (essential] identity, with the thesis and the logical reason having most broadly conceivable universal reference: sarvam anityam, sattat (everything is impermanent, because it is existent')." But we have countless instances when Dharmakirti, and Indian logicians in general, draws inference with regard to a very particular situation ('here, on this particular spot') following a general rule of invariable concomitance, for example: 'The formulation of the logical reason based on effect is as follows): wherever there is smoke, there is fire, for instance in the kitchen, etc. And there is smoke here, (hence there is fire here)," where the implied thesis (or conclusion)*astihágnih ("there is fire bere') pertains to an individual case." But even then, in both earlier cases these formulations instantiate only some ideal patterns, or semi-symbolic formulas, even though no symbolic expressions occur in the formulations. That is clear from Dharmakirti's commentary itself, when the general rule is first stated and than instantiated, or applied to a particular case, for example:
If x-s are observed, y-characterised by (i.e. dependent on these (r-s) (previously) unobserved - is observed and [y] is not observed, even if one of xs is absent, (then) y is the effect of x; and (in this case) this [effect) is smoke. 18
Two additional considerations that are taken for granted and speak in favour of the method resting upon the employment of symbols in formal logic were added in one breath at the moment of formulating the first theory to represent formal logic with the help of symbolic means that remain at the disposal of algebra, the result of which is symbolic logic, or mathematical logic or logistic: the need for a necessary instrument, or methods, or 'aids' (or, to intimate the name of the symbolic culprit' mnew, TÖ o pyavov) to facilitate the progress of scientific discovery, on the one hand, and, on the other, the demand of the discipline of the intellect.
Our list of benefits can be further extended with two more features, that is, that of concision and manageability as well as amenability to and capability of expressing abstract concepts absent from natural language. Every student of philosophic Sanskrit knows how indefinite or imprecise - and logically unsatisfactory-the conjunctions ca or vă (especially in negated sentences) in the natural language can be, how their meaning in certain contexts may overlap and how much intuitive their interpretation sometimes is. Conspicuous examples are furnisbed, for instance, by the problem of catus-koti, wherein the first bemstitch of one of its formulations naiva svatah prasiddhir na parasparatah para-pramanair val could theoretically be represented in a number of ways (p stands for svarah prasiddhir,g for parasparatah prasiddhir, and r for para-pramānair prasiddhir): (1) p ovr, (2) p-qur, (3) -p/-qvar, (4) apvqvær, (5) -p/-(qur) or (6) p (qv) etc., but it is the reader who intensionally interprets it not as an alternative (the usual meaning of va) but as a disjunction (7) -p-q/-r. The inadequacy of, say, such ambiguous words as 'and' or 'or', or its equivalents, to express certain abstract relations, that are not present in the natural language but are casily definable with the help of truth tables (1110, 0111 and 0110) in the two-vakue logic and can be represented with symbols (pla, pvq. p.4), is well-known.
Having said that, could such a symbolic and formalised language have any drawback? Apart from the earlier-quoted remark uttered jokingly by Bertrand Russell, two crucial disadvantages can be seen in the way any formalised language, alongside symbols as its corollaries, operates at the expense, where necessary, of brevity and facility of communication'.
But there is one more to be mentioned of extralogical consequence and of sociological import. However, before I come to speak of it, let us consider what actually happens when, say, Dharmakirti avails himself of examples of proof formulas or of the fallacies of proof formula? Notoriously, Indian logicians did not use symbols in the proper sense. In which sense does be then use sentences that stand for proof formulas? While formulating an inference for others, does he refer to a panicular situation or does he articulate general rules? The question
Clearly, Dharmakirti - and Indian logicians in general - does not use symbols; however, particular terms such as ghata, akasa, paramánu, Sabda, etc., stand for certain classes of objects, for example the class of material perceptible things (mūrta - pratyakşády-anupalabdha), the class of imperceptible things (amirta), the class of produced things (otaka), etc. His formulations are 'replaceable', namely they stand for general symbols, and the actual contents of a proposition is rather secondary; being of exemplary, illustrative character, its meaning is hardly of any relevance. However, their meaning is not entirely irrelevant such semi-variables, for example ghata, that occur in proof formulas denote a particular class, for example either the class of material perceptible things (märta) or the class of produced things (kytaka), and its particular denotation range is determined by the context. Thus, intensional logic possesses some indistinct aspects of extensionality.
A good exemplification of this is furnished by a comparison of two varieties of the fallacious example found in Sankarasvamin's Nyaya-pravesa (NP) and in Dharmakirti's Nyaya-bindu (NB). The former avails himself of one and the same sentence word for word (nityah Sabdo martatvat paramánuvar) to exemplify two different kinds of drstantábhasa, namely of sadhana-dharmasiddha (of the sadharmya type) and sadhyávydvetta (of the vaidharmya type), the only difference being in stating the invariable concomitance (vāpti) either in the positive
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