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Negation: Some Indian theories
positive thesis the Nyaya concept of negation cannot be equated with a term-negation or with a proposition-negation or with a propositional function-negation.
According to the Nyaya what is negated is the second member of a dyadic relation. A relation itself can be negated provided it is a second member of another dyadic relation. Let us explain in terms of the form 'a R b', where a is the first member, b is the second member, and R is the relation between them. According to the Nyaya what is negated is is not b in insolation, but b as the second member of the relation R. This concept is expressed when it is said that the property of being the counterpositive or the counterpositiveness resident in b is limited by the limiting relation R. We cannot state a never type of absence and a mutual absence without mentioning a limiting relation of the property of being the counterpositive. The negation of a R b, according to the Nyaya, cannot be represented by any of the following forms :
(1) a R not-b, (2) a not-R b, (3) not-a R b, (4) not-(aR) b, (5) a not-(Rb),
(6) not-(a R b),
(7) not-(....R b) or not-(x R b)
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If by a term-negation we mean any expression of the form (1) or (3), then the Nyaya concept of negation is not a term-negation. If by an element-negation we mean any expression of the form (1) to (5), then also the Nyaya concept of negation is not an element-negation. If by a proposition-negation we mean any expression of the form (6), then also the Nyaya concept of negation is not a propositionnegation. Moreover, the Nyaya concept of negation cannot be represented by (7) which is a propositional function-nega. tion, because ....Rb' or 'xRb' is not the second member of
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