Double negation in Buddhist logic
Post on 06-Jul-2016
HANS G. HERZBERGER
DOUBLE NEGATION IN BUDDHIST LOGIC*
Enroute to this conference i , I met three nominalists. Bearing in mind that our general topic was metaphysics and logic, it occurred to me to enlist some help from these paragons of metaphysical discipline. What I found, remarkably enough, was that their common metaphysical position (or perhaps one should say, their common anti-metaphysical position) branched out in three very different semantical directions. While they all agreed ontologically, to the extent of disavowing abstract entities of all sorts, each of them embraced a different semantics. The juxtaposition of their views was interesting to me, and it was a revelation for them, because it showed how the interaction of ontology and semantics coloured their whole philosophical outlook and even influenced their prospects for a balanced philosophical life.
My first traveling companion, the one I think of as the happy nominalist, rigorously carried over his nominalism from ontology into semantics, to the point where he had a uniform overall philosophy: a nominalist ontology coupled with an equally nominalist semantics. My second companion was an unhappy nominalist, with a split philosophy. He found that language imposed upon him unacceptable ontological commitments; for he was a nominalist in ontology but a naive realist in semantics. My third companion, who might be called the resourceful nominalist, had managed somehow to accomodate his metaphysical scruples to the ontological liberality of ordinary language and naive semantics. He promised to explain later how he had worked it out.
Our discussion made us all aware of a general phenomenon, the problem of reconciling and balancing ontology and semantics. It was hardly a new discovery, and certainly not a new problem. Indeed, it seemed to have direct application to some puzzling aspects of Buddhist logic, especially to the role of double negation in the Buddhist doctrine of apoha. The conjecture I propose to develop locates the apoha doctrine within a philosophical tradition of resourceful nominalism.
From what I have been able to learn from the English literature, the Buddhist theory of negation was a many-sided doctrine of interwoven strands, some of which deserve separate treatment quite apart from narrowly
Journal of lndian Philosophy 3 (1975) 3-16. All Rights Reserved Copyright 1975 by D. Reidel Publishing Company, Dordreeht-Holland
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logical concerns: doctrines about semantic fields, perceptual error, identifying descriptions, and the verification of negative judgments. Stcherbatsky, for example, devotes four chapters of  to some of these topics, making up a small treatise on epistemology and semantics. It is quite beyond my competence to reconstruct the whole doctrine in all its ramifications. The aspect to be singled out here is the logic of negation as involved in the exclusion theory of meaning, according to which the meaning of any word is "the repudiation of its own contrary". This takes some
explaining. Scholars agree that apoha somehow involves a semantics of exclusion and
opposition. Thus B.K. Matilal writes:
Meanings, for Digngga, are fictional constructions and they have a negative function.., to exclude the object from the class of those objects to which [the name] cannot be applied. 2
Bringing in the standard example of the cow, Karl Potter writes:
Although it falsifies reality to describe it as having a certain positive character (e.g. cowness), it does not falsify [reality] to describe it as lacking a certain negative character (e.g. non-cowness). 3
and K. Kunjunni Raja expands on this example:
If the word 'cow' is to be used to mean differend kinds of cows, the red, the black and the brown, it can be only by the negation of the non-cow... The word 'cow' then does not denote a positive object cow, but means only the negation of the non-cow. 4
This is the doctrine that has recently been described as "one of the most significant Buddhist contributions to philosophy".s What can be made of all these double negatives?
It should be quite clear that the classical law of double negation would undermine any straightforward rationale for preferring doubly negative constructions. Classically, any doubly negative term not-not-A is semantically equivalent to the simple term A it is supposed to replace. Any attempt to explain the meaning of the simpler in terms of the more complex would fail on account of circularity, and insistence on the circumlocution as a privileged formulation would seem perverse. 6 This is the way things look from within the classical logical perspective. If the meaning of the word 'cow' were to be given by the doubly negative complex 'not-non-cow', what would its meaning
DOUBLE NEGATION IN BUDDHIST LOGIC 5
be within that complex? Should the complex itself be analyzed in terms of quadruple negation ('not-not-not-not-cow')? This would lead down an endless path which is hardly a path to illumination. Therefore, as most commentators have remarked, the doctrine ofapoha requires some nonclassical account of negation. My main problem will be to actually identify some viable logic of negation suited to the doctrine and adequate to its intelligibility.
It is all very well to concede that a nonclassical account of negation may be required for certain philosophical purposes, and that the law of double negation, for example, should be suspended or restricted. It is another matter altogether to identify a thoroughly satisfactory nonclassical negation on which a viable logic can be reconstructed as a foundation for those philosophies. Many initially promising efforts in this direction have come to grief. In the words of one of the greatest pioneers of nonstandard logical theory, the contemporary Polish logician Jan Lukasiewicz:
...the propositional calculus is not a heap of stones, which remains even if a few stones are removed from it. It is rather a mechanism of the greatest precision, which breaks down after the removal of a single cogwheel, and must then be reconstructed. 7
Accordingly, nothing less than a thorough reorganization of the elements of logic is apt to suffice for the Buddhist doctrine of double negation. What is initially fascinating about this problem is that nothing in the standard literature on nonstandard logic seems fully appropriate for explicating this doctrine. The hypothesis to be outlined here builds on a simple but radical departure in the theory of propositions, in terms of which a full reconstruction of a richer logic can be developed.8
The problem is to find at least one adequate semantics for apohist negation, at least one semantical operation which could reconstruct the principal features attributed to double negation by Dign~ga and his followers. To do justice to the apoha doctrine, one must be prepared to venture outside the perspective of the classical logic of negation. At the same time it is crucial to avoid going too far. Mere failure of the law of double negation is hardly a sufficient condition for adequacy of a logic to the apoha doctrine. 9 The doctrine requires a semantic distinction between terms and their double negations, and it also requires some partial semantic equivalence between them. Minimally then it requires a logic rich enough to represent a term and its double negation as equivalent on one semantic level and nonequivalent on another.
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Before proceeding, some cautionary remarks on method may be in order. It is quite idle to attribute modern concepts to ancient authors, in the absence of explicit formulations on their part. More modest claims however are worthwhile making and can be revealing, particularly in a case like the present one where the historical evidence is simultaneously meagre and confusing. When a natural scientist constructs a theoretical model for some phenomenon, he follows the hypothetical method. The model is required to organize the phenomenon and render it systematically intelligble; towards this end he employs whatever analytical tools are at his disposal. Similarly in dealing with a philosophical doctrine it is often useful to employ analytical methods which help us to understand the doctrine although they could not without anachronism be attributed to its author. Free use of truth-tables, formal semantics and the like can be justified if taken in this hypothetical spirit. So in a speculative vein we can review the logical concepts at our disposal, and inquire which if any of them exhibit the minimal features required for ingredients in a rational reconstruction of the doctrine. This kind of preliminary investigation can at least clear the air by eliminating some alternatives, and by focussing the attention of scholars more narrowly in directions that are at least minimally viable.
Towards this end, a small number of unproblematic historical assumptions will suffice. It is relevant that the authors of the apoha doctrine were nominalists, engaged in active debate with philosophical realists, and that they accorded distinguished status to negative constructions in semantics, particularly to those which were doubly negative. Proceeding from these fundamental assumptions, it is possible to organize at least one logical framework within which the distinguished status of doubly negative constructions has a philosophical rationale. So I asked my three traveling companions, on what sort of grounds a nominalist might find negative constructions congenial to his philosophical outlook.
The happy nominalist had worked on this problem and had resolved it to his own satisfaction. Nominalism as such, he assured me, requires no negative style nor any other special mode of formulation. The reason, he said, is that one can be a nominalist not only with regard to ontology but also with regard to semantics and language. A strong distinction between appearance and reality is the cornerstone of nominalism in both fields. To be sure, our ordinary modes of expression appear to carry weighty ontological c6mmitments, as when we speak of numbers, properties and the like. But all this can be
DOUBLE NEGATION IN BUDDHIST LOGIC 7
explained away and a nominalistic semantics can be provided for all intelligble discourse, by imposing on language, as we impose on experience, an appearance-reality distinction. The happy nominalist then is one who is thoroughgoing in his nominalism, to the point of carrying through a semantic analysis which explains away all apparent commitments to universals. 1
Now it seemed to me that authors of the apoha doctrine had some affinities with this happy nominalist, but they were clearly less complacent. In common with him, they were striving for a nominalist semantics, it seemed to me; but unlike him they were unsatisfied with ordinary direct formulations, at least in their semantic metalanguage. So far then I had no clue as to why this should be.
Turning to my second traveling companion, the unhappy nominalist painfully manifested the desperate situation in which he found himself. Not venturing to discount and explain away the apparent ontological commitments of language, he found them on the whole metaphysically repugnant, so that the least philosophical assertion that passed his lips threw him into an intolerable situation. Given his metaphysical position, he was unable to agree with anyone but another nominalist; and given his semantical doctrine, he found himself unable to discourse at all with anyone else, even to disagree. From the point of view of the unhappy nominalist, philosophy could only be seriously discussed from within a metaphysical standpoint, among those who already accepted it. Assuming as I did that the nominalist authors of the apoha doctrine entered into a long controversy with their realist contemporaries, I concluded they were not unhappy nominalists, in the sense of my second traveling companion.
Finally the resourceful nominalist told me that he regards language as a divided domain; and he capitalized on the semantic differences he finds between its central and its .peripheral regions. While acknowledging the metaphysical commitments of ordinary language, he has learned to live with them by confining his serious philosophical discourse to some more austere canonical idiom. As he explained to me, some regions of language are relatively free from metaphysical commitments; and those noncomittal regions, when thoroughly cultivated, he holds to be adequate for philosophy. According to the resourceful nominalist then, ordinary language does have ontological commitments which must be avoidable in philosophical discourse, and which are avoidable through disciplined restriction to some relatively noncomittal regions of language. Now it seemed to me consistent with my
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working assumptions that the authors of the apoha doctrine were resourceful nominalists.
It occurred to me that my third companion was not actually using his canonical idiom in explaining it to me. And I recalled from my reading that the same was true of the Buddhist logicians, al While insisting that terms mean the exclusion of their own contraries, they mercifully refrained from putting this formula itself negatively. Nowhere did I find them saying that terms exclude the contrary of the meaning of the exclusion of their own contraries, and things of that sort. Strictly speaking then their philosophical style was not adamantly negative. That is, they did not themselves insist on writing in their canonical idiom. When asked about this in his own case, my third companion cheerfully acknowledged leading what he called a "double life". His words, as I recall them, were: "It is one of the consolations of philosophy that the benefit of showing how to dispense with a concept does not hinge on dispensing with it". 12 So the double negative might have been a canonical idiom for the Buddhist logicians even though they were quite prepared to use ordinary formulations in expounding their philosophy.
The difference between the happy and the resourceful nominalist is therefore rather subtle. Both may be willing to use ordinary language in philosophical discourse, but for different reasons. According to the happy nominalist, ordinary language carries no metaphysical commitments, and thereby is a perfectly suitable medium for philosophical discourse. According to the resourceful nominalist, ordinary language does carry metaphysical commitments, but he is prepared to use it anyway, secure in the knowledge that he could, if challenged, reformulate in his canonical idiom whatever it is that he wants to say. Meanwhile he finds it reasonable to take advantage of the simplicity and convenience of the ordinary mode.
Now the real work of hypothetical reconstruction begins. Assuming that double negation might be intended as a device for circumventing unwanted ontological commitments, one needs to provide a semantic framework in which some form of double negation could possibly have this effect.
It is not hard to specify what it means for a language or a sublanguage to have ontological commitments. A sentence of a given language carries a commitment to entities of a certain kind if and only if it implies the existence of such entities in the sense that it is true only under conditions in which entities of that description exist. In this sense almost every sentence has some ontological commitments. To take an example from Aristotle, the sentence
DOUBLE NEGATION IN BUDDHIST LOGIC 9
Socrates is ill implies that Socrates exists, as does its denial Socrates is not ill. Whether or not it furthermore should be taken as implying the existence of
illness and perhaps other universals, depends on one's semantic theory. Many alternative accounts of semantic structure have been given. So-called platonistic semantic theories do impute a commitment to universals to almost every sentence, in requiring predicate terms to denote attributes, concepts or classes. On these accounts, a sentence like Socrates is ill would be true if and only if an appropriate relation holds between two entities, one of which is concrete (namely, Socrates) and the other of which is abstract (namely, illness). By contrast, a nominalistie semantic theory might single out words or word-inscriptions as a category of concrete individuals whose distinguishing feature is that they happen to function as symbols, much as other concrete individuals happen to function as shoes, flowerpots, and the rest. According to a radically nominalistic semantics then, the sentence Socrates is ill would be true if and only if an appropriate relation holds between two entities, each of which is concrete (namely the man Socrates and the word 'ill'). Needless to say, there are variations on both these two extreme semantic doctrines, and intermediaries between them. The happy nominalist is one who holds some radically nominalistic semantics, the unhappy nominalist is one who holds some radically platonistic semantics, and the resourceful nominalist holds some intermediate semantic doctrine.
Somehow the apohist philosophers did not arrive at the radically nominalistic semantics which formulates truth-conditions in terms of a direct relation between words and things without any intervening entities or constructs. Their pattern of semantic analysis, as it seems to me, adheres to the classical pattern on which meanings intervene between words and things. But they made an interesting effort to transpose this pattern by reinterpreting meanings as logical constructs rather than abstract entities. In a statement which Kama- laina attributes to his master "the revered Dignffga" it is claimed that:
in due course, all characteristics of the [so-called] 'Universal' - such as one-ness, eternality, complete subsistence in every component - subsist in the apoha itself. Consequently, on account of the superiority of its exellence, the only theory that is right is that "the denotation of words consists in the exclusion of other things".13
This formulation, as I read it, claims to effect a nominalistic reduction of universals through the agency of double negation, and an appearance-reality distinction. As Kamalagl-la goes on to explain:
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It is only the real positive character of the things denoted by words that is denied by us; so that the illusory positive character of the things denoted by words is accepted by us. 14
The sophistication of this approach lends itself to confusion; as one of
Dign~ga's critics complained, it seems to be an effort to make cloth without
yarn is ; for the constructs which play the role of meanings in the apohist semantics are held to be 'featureless nonentities':
the [so-called] 'denotation of words' is entirely featureless.., it is neither positive nor negative; it is neither diverse nor same: it is neither subsistent nor non-subsistent; it is neither one nor many... In reality it does not exist in the form it is apprehended; hence it cannot be positive. Nor is it negative, as it is apprehended as an entity. 16
We have a contrast then between universals like illness which are entities of a certain kind, and apohas like exclusion ofnonillness which are nonentities of a corresponding kind devised to systematically replace them in semantic
analysis. This and other formulations suggest the following logical role for
negation: that positive terms denote entities whereas negative terms denote
nonentities. This interpretation seems to have been adopted by some of
Dign~ga's critics 17 ; and I believe it leads into difficulties. Inasmuch as language
provides quite a number of coextensive pairs of terms, one of which is
positive and the other negative, this interpretation would require some
things to be both entities and nonentities at once, being both well and non-ill,
rough and non-smooth. I do not believe the texts force this interpretation
upon us; they appear to me to be consistent with a more satisfactory
interpretation, which accords negation a rather different logical import.
Advancing to a higher level of generality, let us reflect briefly on the
common philosophical predicament of trying to deal critically with a position
or doctrine whose fundamental presuppositions one finds unacceptable.
Bertrand Russell described a case of this predicament in connection with
By the law of excluded middle, either 'A isB'or '.4 is not B' must be true. Hence either 'The present King of France is bald' is true or 'The present King of France is not bald' must be true. Yet if we enumerate the things that are bald, and then the things that are not bald, we should not find the present King of France on either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig. 18
Whether one affirms the thesis ('He is bald') or the antithesis ('He is not
bald') one is caught in a dialectical commitment to their common
DOUBLE NEGATION IN BUDDHIST LOGIC 11
presupposition or ground. Russell's theory of descriptions offered a way out of the predicament which can I believe be generalized and extended to apply to the present case.
The depth of this dialectical predicament depends to some extent on the detachability of presuppositions. Consider the most favourable case, in which the presuppositions in question can be explicitly rendered as separate
propositions and detached from the rest of the doctrine. In such a favourable case, a formula for resolving the predicament would be: render the presuppo- sitions explicit, and factor the doctrine into two parts. Imagine all of the original presuppositions now entered into one book and the rest of the doctrine into a separate book. Let the first book be entitled Unexpressed Ground of the Doctrine, and the second book entitled Manifest Content of the Doctrine. When such a segmentation can be implemented, each part can be considered separately and accepted or rejected on its own merits.
The same pattern apples to the content of individual sentences. In favourable cases, the content of a sentence might be factored into two parts: its presuppositional ground, and its manifest content. Segmenting the content on this pattern is tantemount to associating two propositions with that sentence, under the principle that they bear two distinct semantic relation~ to it.
Continuing to develop this favourable case, let the ordered pair of ground and manifest content be called a two-foldproposition. All that we have done is to isolate and organize in a certain way two ingredients in the content of a sentence. To the extent that such a segmentation can be carried through systematically, the possibility of a richer logic, based on two-fold propositions, immediately arises.
The notion of a two-fold proposition adapts an idea of Emil Post, one of the founders of many-valued logic. In his celebrated dissertation , Post suggested that classical logic might be generalized to "higher-dimensional propositions" much as geometry had been generalized to higher-dimensional
spaces. Post's construction, and his way of counting dimensions, are slightly modified in my presentation, but the basic idea is essentially the same: a
two-fold proposition is an ordered pair (g,m) of classical propositions, representing the ground and manifest content of some sentence. Ground and manifest content are classical propositions, perhaps to be thought of as regions of logical space, or as sets of possible worlds. They are subject to operations like forming logical products and complements.
Several varieties of negation can now be formulated and distinguished in
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their logical import. One variety, which converts a thesis into a corresponding antithesis, might be called 'antithetical'. When applied to a two.fold proposition having a certain ground and manifest content, it results in another two-fold proposition having the same ground but the opposite manifest content. This operator, analogous to the 'internal negation' of three-valued logic, may be schematized as follows:
Antithetical Negation: N(~g,m)) = (g,~) It provides an appropriate way of denying any two.fold proposition in case one is prepared to accept its ground. Otherwise, of course, it would be ineffective, inasmuch as it commits one to the same ground. Hegel explains this by way of an illustration in his Science of Logic, in these words:
If for example it is said that the rose is not red, this negates only the determinateness of the predicate, which is distinguished from the universality which also belongs to the predicate. The universal sphere, colour, is retained; if the rose is not red, it is assumed that it has a colour - some other colour? 9
This operator did not originate with Hegel, but his thought focussed upon it and challenged the legitimacy of other forms of negation,
Antithetical negation is sufficiently classical to render it unsuitable for present purposes. It conforms to a law of double negation, inasmuch as the double antithetical negation of any two-fold proposition will have the same ground and a manifest content equivalent to that of the original proposition. This follows from the assumption that the manifest content is given by a classical two-valued proposition m, which coincides with the complement of its own complement, ~.
Now let me describe a different variety of negation which I will call 'apohist negation'. I do not mean by this terminology to attribute this operator to the Buddhist logicians, but rather to suggest it may be an operator congenial for a rational reconstruction of their doctrine:
Apohist Negation: NA (g,m) = (1,ff~ )
The presuppositional ground 'vanishes' under this negation operator, whose joint effect is to suspend the presuppositional ground and deny the manifest content. If performed twice, it has the effect precisely of suspending the presuppositional ground while leaving substantially intact the manifest content:
Double Apohist Negation: NA NA (g,m) = (1,m).
DOUBLE NEGATION IN BUDDHIST LOGIC 13
The semantic interpretation of unity (1) in this context is a tautology or otherwise necessarily true proposition, representing a vacuous presuppositional ground. Clearly the law of double negation does not hold for this operator. In general a two-fold proposition and its double apohist negation will not be fully equivalent. At the same time, a mitigated law of double negation does hold, in that any two-fold proposition and its double apohist negation will be partly equivalent in a definite sense, restricted to manifest content. So this operator meets the minimal requirements set down at the beginning of the investigation. On the standard pattern it can be applied to terms as well as to propositions, with corresponding effect.
Armed with these logical constructions, what conclusions might be drawn concerning the philosophical prospects for apohist semantics? To carry through the program of providing a canonical idiom adequate to philosophical discourse, it will not suffice merely to have the apohist negation operator. It must be assumed or hoped that the content of every sentence from some sufficiently comprehensive domain can be factored into two components, roughly on the following pattern: all the platonistic elements must be encompassed within the presuppositional ground, leaving a purely nominalistic manifest content.
All along it has been assumed that apohist semantics attributes platonistic commitments to simple sentences like Socrates is ill," and that it finds those commitments philosophically unacceptable. This is one interpretation of the claim that universals are 'apprehended' as entities but that 'in reality' they do not exist. 2 Whatever the faults of this interpretation, it has the merit at least of doing justice to both sides of the appearance-reality distinction.
Proceeding on this interpretation, platonistic commitments might be factored out and encompassed within the presuppositional ground. Thus the first component in the content of the sentence Socrates is ill might be some proposition to the effect that there exists such a property as illness; and its second component might be some proposition to the effect that the term 'ill' applies to the man Socrates. Relative to such a factoring into a platonistic ground and a nominalistic manifest content, double apohist negation would yield a sentence Socrates is not non-ill with the same manifest content and a vacuous ground, and thereby a substantially equivalent sentence with a purely nominalistic import.
Success of the program then depends on the feasibility of carrying through the underlying analysis. It requires the identification of all platonist~c
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ingredients of semantic structure, and their systematic isolation into the first component. Furthermore it depends on the assumption that nothing vital is lost under this transference. In short then, the program of the resourceful nominalist cannot be carried through successfully unless the program of the happy nominalist could in principle be carried through.
Our analysis now has led us to the brink of an Hegelian synthesis. It raises the question: why should any nominalist stop short of happy nominalism? Why indeed should an advocate of any metaphysical position stop short of a semantics in thorough harmony with his ontology? I put this challenge to my third traveling companion, who once again demonstrated his resourcefulness, in granting my point while drawing a different conclusion from it. To be sure, he conceded, his program was feasible only if that of the happy nominalist was feasible as well. But on his view there was a question of truth quite apart from feasibility. The semantic structure of language, he told me, is independent of one's philosophy. Languages have their own ontological presuppositions, and philosophers have their own ontological scruples. He would be happy if the two could be reconciled, but reconciled if they could not. And so, he told me, he would not be drawn into my synthesis.
With this rejoinder, the resourceful nominalist had completed his case for a philosophical position that was distinctive, internally coherent, and up to a point defensible. In its sophistication it lacked the simplicity of extreme nominalism, but it was interesting to me insofar as it seemed to provide a logical-metaphysical rationale for the apoha doctrine. While it certainly could not account for all aspects of that doctrine, it did seem to account for some. The conjecture that double negation might be a device for endorsing the manifest content of a sentence while evading its presuppositions, has proved to be a workable hypothesis, with some logically interesting ramifications. In application to Buddhist semantics, it will have served its purposes well if efforts to refute it advance our understanding of those doctrines.
University of Toronto
* Support from the Canada Council (Leave Fellowship W73-0169) is gratefully acknowledged. I have also benefited from the guidance of Radhika Herzberger, and from discussions with Professor Sibajiban Bhattacharya.
DOUBLE NEGATION IN BUDDHIST LOGIC 15
i Presented to the First Annual Session, Bangladesh Philosophical Association, Dacca University, January 1974. 2 ,p.44. 3 [91, p.188. 4 151, p.83. s [41, p.173. 6 The charge of circularity has a long history; see , p.87.
From his essay, 'Logic and the Problem-of the Foundations of Mathematics' (1938): p.281 in [61. s Exactly what constitutes a viable reconstruction of logic is not easy to say, but some control may be exercised through the requirement that the rejection of classical laws must in every case be based on principles which justify that rejection, and ideally those principles should provide a rationale for the classical tradition in logic. The reconstruction should aim at vindicating classical logic as a first approximation, somewhat in the way classical physics was shown to provide an approximately correct account of ordinary motion within definite boundary conditions. Further discussion and logical development of the theory of two-fold propositions, may be found in [21. 9 Some scholars have mentioned intuitionistic logic In this connection, for the law of double negation is also rejected by the intultionists. However, until it can be shown how lntuitionism actually elucidates Buddhist philosophy, the connection remains somewhat tenuous. Some broader philosophical framework has to be brought into the account, and attention given to the particular ways in which double negation fails, and to the specific grounds for such failures. 10 Two paradigms of happy nominalism might be the scholastic logician Jean Buridan, and the contemporary nominalist Nelson Goodman. 11 As noted in the controversy over the alleged 'negativity' of the apoha doctrine In [121, p.25ff. 12 These words are actually borrowed from a notably resourceful former nominalist; see [10l, Section 39, 'Definition and the Double Life'. t3 Kamalagfla, Commentary to Text 997-1000, in . 14 Kamalagfla, Commentary to Text 1095-1096, in . Is Attributed to Kum~rila, Text 1001-1002, in [31. 16 ~ntaraksita, Text 1190, in [31. 17 See , p.40: "According to the Realists, reality is two-fold: Existence and nonexistence, and therefore language too consists of two types of words, namely positive and negative. Negation is said to be the meaning of negative words whereas Existence is expressed by positive words". 18 [111, p.48. 19 , Vol. 2. Section 1, Chapter IIA, p.275. 20 ~fintaraksita, Text 1190, in 13].
 Hegel, G.W.F., Science of Logic, tr. by W.H. Johnstone and L.G. Struthers, Allen & Unwin, London, 1929.
[21 Herzberger, H.G., 'Dimensions of Truth', Journa( of Philosophical Logic, 1973.  Jha, Ganganatha (transl.), The Tattvasai~graha of S~ntaraksita, with the
Commentary ofKamalagrla, Vol. 1, Oriental Institute~ Baroda 1937.  Kajiyama, Y., 'Three Kinds of Affirmation and Two Kinds of Negation in Buddhist
Philosophy', Wiener Zeitschrift fur dm Kunde Sitdasiens, 1973. [51 Kunjunni Raja, K., Indian Theories of Meaning, Adyar, Madras, 1963. [61 Lukasiewicz, J., Selected Works, ed. by L. Borkowski, North-Holland, Amsterdam,
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 Matilal, B. K., Epistemology, Logic, and Grammer in Indian Philosophical Analysis, Mouton, The Hague, 1971.
[81 Post, E., 'Introduction to a General Theory of Elementary Propositions', 1921 ; reprinted in J. van Heijenoort, ed., From Frege to G6del, Harvard University Press, Cambridge, 1967.
 Potter, K., Presuppositions of India's Philosophies, Englewood Cliffs, N. J., Prentice-Hall, 1963.
 Quine, W. v. O., Wordand Object, MIT Press, Cambridge, Mass., 1960.  Russell, B., 'On Denoting', 1905; reprinted in R. Marsh, ed., Logic and Knowledge,
Allen & Unwin, London 1956.  Sharma, D., The Differentiation Theory of Meaning in Indian Logic Mouton,
The Hague, 1969. [ 131 Stcherbatsky, Th., Buddhist Logic, Dover, New York, 1962.