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NAYAVĀDA AND MANY-VALUED LOGIC
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truth-value I as we have already discussed above. Then as regards the first point we may cite the authority of Vidyānanda who interprets the seven modes (Bhangas) of Naya as Vidbikalpanã (Positive statement), Pratiședha kalpanā ( Negative statement), KramavidhiPratişedha-kalpana (consecutive or successive combination of positive statement and negative statement ), Yugapad-VidhiPratisedha-kalpanā (simultaneous combination of positive statement and negative statement), Vldhikalpanā and Yugapad-vidhipratiședha-kalpanā, pratişedha-kalpanā and Yugapad-vidhi-pratised ha-kalpanā and finally Kramena vidhi-pratiședha-kalpanā and Yugapad-vidhi-pratiședha-kalpanā. The fourth Bhanga i. e. the conjunction of a positive statement and its negative form needs a little more consideration as it is basic to Jaina logic. It is also called as avaktavya or indescribable. But, as a matter of fact, the word avaktavya here means indeterminate. Most importantly, what is remarkable on the part of the Jaina logicians is their keen observation that the indeterminate compound statement is a conjuncion of a positive statement and its negative form and that it challenges the law of contradiction. They have given a logical theory that does not accept the law of contradiction, at least in the form in which it is stated in two-valued logic. The denial of this law, therefore, has logically rendered their logic a type of three-valued logic.
Now the next question which I want to discuss in this context pertains to Syādvāda and Pramāņa Saptabhangi, If our interpretation and reconstruction of Nayavāda is accepted, then it can be said that Syadvāda is a species of Nayavāda and Pramāņa-Saptabhangi is that of Naya-Saptabhangi. Syādvāda is a true statement and Pramāņa-Saptabhangi is the table of seven true statements which are availed from a positive statement by the operations of negation, conjunction and disjunction. For example let us think that P is a true statement, then Pramāna-Saptabhangi will become as follows:
1. P (assertion of P) 2. not-P (negation of P) 3. P or not-P (disjunction of P and not-P) 4. P and not-P (conjunction of both P and not-P)
5. P and (P and not-P) (conjunction of 1 and 4) J-11
