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80
Jaina Theory of Multiple Facets of Reality and Truth
(ii) We will have to use some special operator for indicating avaktavya.
Just as we signify 'It is not the case that p' by '~p' similarly we
could signify 'It is indeterminable whether p' by `«p'. Now we are in a position to formalise the seven-fold scheme of syädvāda in the following way:
(1) Mp (2) M~p (3) Mp. M~p (4) M«p (5) Mp. Mop (6) M-p. Map (7) Mp. M-p. Mąp
It is prima facie possible to justify this interpretation by relating it to the Jaina concept of naya and also with the notion of third truthvalue as may be applied to nayas. Prof. S. L. Pandey for instance in his article mentioned above, tries to show that all nayas being partial truths can be assigned the third truth-value I of Lukasiewicz's threevalued system. Now Lukasiewicz himself relates the idea of the middle truth-value with some modal logical considerations. His attempt to combine the two considerations may be used for our purpose in the following way: "Possibly p” is true when p is indeterminate. "Possibly -p" is true when -p is indeterminate. But if p is indeterminate so is ~p. (Jainas would add: if p is indeterminate, so is oop). So given any proposition p which expresses a naya (which is indeterminate), Mp, M-p, Mp.M~p, Map all are true.
8. Nicholas Rescher states this in the following way: "With a view to the future
contingency interpretation of the third truth-value I, Lukasiewicz introduced a modal operator of possibility and necessity (symbolically O and o) into his three-valued logic. These are to be subject to the truth-table: PL Op op
T
TLF FFF”
- Many Valued Logic, Op. cit., p.25. For typographical convenience I have used M and L as the respective symbols for modal operators.
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