Indian Logic Forum

Plamen · Posted: Sat Jan 21, 2006 7:45 am Post subject: Nature of Negation in Nagarjuna

In his 1957 PEW articles, Richard H. Robinson investigates some logical aspects of Nagarjuna's system. He says the following about negation:

* * *
A number of passages reveal that Nagarjuna maintained a concept of negation which at first sight seems nonsensical.

p.300

[30] "If entity (presence) is not established, then non-entity (absence)
is not established either, since by non-entity
people mean that alterentity (complement) of entity." (15.5)

[31] "Independent of the pure there is nothing
impure in dependence on which we may posit the
pure. Therefore, the pure does not occur either." (23.10)

[32] "If self, purity, permanence, and felicity
do not occur, then nonself, impurity,
impermanence, and suffering do not occur either." (23.22)

[33] "If nirvana is not an entity, it cannot be a
non-entity; where there is no entity, there is
no non-entity." (25.7)

[34] "Since the conditioned is not established, the
unconditioned cannot be established." (7.33)

[35] "If 'both eternal and non-eternal' were
affirmed, then 'neither eternal nor
non-eternal' might be affirmed." (27.18)

These examples seem to maintain that the presence of the negation of any variable implies the presence of that variable. However, it is more likely that Nagarjuna was thinking of a finite extension and its complement, and excluding null and universal terms from consideration. An entity (bhava) is by definition conditioned, and neither universal (sasvata) nor null (uccheda). It has a complement which is conditioned in the same way except for the property of being absent when the entity .is.present.A pacaphrase of (33) may elucidate this.

"If nirvana is not the finite extension of a
set of properties, then nirvana cannot be
the finite extension of the absence of a set
of properties; in cases where a finite
extension does not exist, the complement of
that finite extension does not exist either."

The term "nature" (prakrti equals svabhava) has no complement. (36) "If (anythings) existence is due to its nature, its non-existence will not occur, since the alter-entity (complement) of a nature never occurs." (15.8)

That is, a nature is the class of properties attributed to a class of terms Since they are necessarily present throughout the range of the subject or class of subjects, cases of their absence do not occur.

If the extension of purity is the null class or the universal class, then no part of the universal class constitutes the class of pure things, and no other part constitutes the class of impure things. Quantification

Many of Nagarjuna's terms are explicitly bound, and, since all his propositions seem to be general it is necessary to supply quantifiers in a number of propositions where they are not given.

p.301

Universal quantifications are effected both by the functor all (sarvam) and by negation of an existential functor (kascid, kadacana, etc.)

[37] "For among existents, impermanence never does
not occur." (21.4)

[38] "Since no non-dependently-arisen dharma occurs,
no non-empty dharma occurs." (24.19)

[39] "Origin and dissolution do not occur without
entity." (21.8)

[40] "For nowhere does there occur any
unconditional entity." (25.5)

[41] "Since an entity does not (occur) without
aging-and-death." (25.4)

Existential quantifications are denied by Nagarjuna, since all the terms he is repudiating are conceived as essences, and it is absurd to maintain that the essence of a thing pertains only to part of the thing.

[42] "If one part is divine and one part is human,
he would be both eternal and non-eternal; and
that is impossible." (27.17)

[43] "If one part were finite and the other part
were infinite, both finite and infinite would
pertain to the world; and that is impossible." (27.26)

[44] "Nor does it obtain that one part of the body
(upadana) perishes, while the other part
does not perish." (27.27)

Assuming that bones do not decay, "one part of the body perishes and one does not" is not an absurd statement. But manifestly Nagarjuna's point is not the denial of common-sense assertions, but the denial of the concept of entity (bhava) and own-being (svabhava) which is commonly imposed on the terms of common-sense assertions. The axiom is "that is not one (entity) of which contradictory attributes are predicated."(17)

Quantity has something to do with the two extremes (the ever-existent and the annulled).

[45] "Ever-existence-that 'that which exists by
own-being does not' not exist'-and
annulment--that 'it does not exist now but
it existed formerly'are absurd." (15.11)

Eternalism asserts that "all A is B," while annihilism asserts that "some A is B and some A is nor B." Both views are rejected on axiomatic grounds. The significant point is that the distinction is one of the quantity of the terms.