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Negation : Some Indian theories
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Let us consider the in junction na bhakşayet 'he shall not cat'. It is said that this type of injunction should not be translated as he shall not eat, but as 'he shall not eat. This injunction does not prescribe an action different from eating. It simply prohibits eating. If the positive injunction bhaksayet 'he shall eat' is symbolized by 'N[F(x)]', where 'N' stands for the obligation operator, then its negation would be symbolized by 'N ~[F(x)]'. This type of negation is called 'pras. ajya-pratisedha' or 'nişedha' type of negation. In this context it is to be noted that the negative injuction has not been symbolized by' ~N[F(x)]' but by 'N ~[F(x))'. In standard deontic modal logic '~N[F(x)]' would be equivalent to ‘P ~[F(x)}', where 'P' stands for the permissibility operator. So '~N[F(x)]' would not express a negative injuction.
Now let us discuss whether negations of the form ‘N[ ~ F(x)] or 'N[F(-X)]' are permissible according to the Mimāņsā philosophers.
According to these philosophers all cases of negation other than prasajya-pratişedha which is symbolized by the form 'N [F(x)]', are called "paryudāsa' 'exclusion' type of negation. It is also said that the paryudāsa 'exclusion type of negation is to be understood where the negative is connected either with the verbal root or with the noun, and the prasajya-pratişedha 'prohibition' type of negation is to be understood where the negative is connected with the verbal ending.
In the injunction nekşeta 'he shall not look', the 'not is attached to the verb or the verbal root. Hence the sentence nekseta should be translated as 'he shall not-look’, and this type of negation is to be considered as a paryudāsa 'exclusion' type of negation. In this case the injunction positively prescribes something other than looking This type of negation can be symbolized by the form 'N[~ F(x)]'.
Now let us consider the injunctions where a noun is negated. As an example of this type of negation the Mimāmsā philosophers have discussed the injunction nānuyājesu ye-yajāmaham karoti at the after-scrifices he shall not say
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