ISSA Proceedings 2006 – Contradiction In Madhyamaka Buddhist Argumentation

What happens when one utters a contradiction, something of the form ‘p and not p’? To do so is to challenge one’s audience to work out the Gricean conversational implicature (Grice 1975). One of Grice’s rules governing conversation is that one utter only statements that one takes to be true. And by the laws of classical logic, any statement of the form ‘p and not p’ must be false. If the utterance is clearly of that form, it will be evident to the audience that this is evident to the speaker. And so there is open flouting of a rule governing conversation. Such flouting is the mechanism whereby Gricean conversational implicatures are generated. The question in the case of a contradiction is, which implicature? What might the speaker intend to communicate through uttering something that is transparently false?
So-called paradoxes are a staple of religious discourse. This is especially evident in expressions of religious mysticism, such as the writings of Eckhart, Śankara and the masters of Sufiism and Zen. But one also finds this element in what are taken to be expressions of quite sane religious doctrine, such as the Christian teaching of the trinity. The sort of statement I have in mind here is not strictly speaking paradoxical in the logical sense: a statement that if true is false and if false is true.[i] It is rather a statement that is evidently false; it is called a paradox simply because its assertion seems to defy the rules of communication. We can see why use of such a trope might be common in the religious context. Through it the speaker can convey the sense that something quite esoteric is being communicated, thereby contributing to the perceived value of the religion’s teachings by suggesting that they may hold the answer to some of life’s persisting problems. People expect religious teachings to have an element of the mysterious about them: if ‘the answer’ were perfectly straightforward, wouldn’t everyone have worked it out already?
Such language can also serve to mark a separation of the sacred from the profane. The Christian doctrine of the trinity works this way. We know that one person cannot be three persons (particularly when at least one of them is necessarily omniscient). So when God is said to be three persons, this will suggest that things work quite differently where the divine is concerned. We see an extreme form of this in certain explicitly contradictory teachings of the Upanishads and Advaita Vedānta concerning Brahman, where the language seems intended to be taken as apophatic. Thus when Śankara says it can be neither affirmed nor denied that Brahman is cause of the world, the intended implicature is that we understand Brahman to be beyond the representational capacities of rational discourse.
There is a class of Mahāyāna Buddhist texts containing what appear to be similar claims. In the Prajñāpāramitā literature one often encounters statements such as, ‘All feeling is devoid of the nature of feeling’, and ‘Space is neither existent nor non-existent’. That these statements are meant to function as part of a soteriological discourse is clear both from context and from the fact that they make clear reference to some of the Buddha’s most basic teachings. It is thus tempting to suppose that the intention here is likewise to convey that the object of Buddhist wisdom is something inexpressible, perhaps something that can only be apprehended through a kind of non-rational intuition.

But this temptation should be resisted. For the use of apparent contradiction has a long history in Buddhist literature, beginning with some key discourses of the Buddha himself. When the Buddha was asked whether the enlightened person or arhat is reborn after death, the Buddha replied that this could not be said (Horner 1957, pp.162-7). But when it was then asked whether the arhat was not reborn after death, the Buddha replied that this too could not be said. When asked how it could be that someone is neither reborn nor not reborn after death, the Buddha replied with the analogy of the fire that has gone out: if it were asked where this no longer visible fire had gone, it could not be answered that it had gone to the north, to the south, to the east or to the west. For the question ‘Where has the fire gone?’ has a false presupposition, namely that the fire continues to exist. Likewise the question whether the arhat is or is not reborn after death has a false presupposition, namely that there is such a thing as a person. For according to the Buddha’s teaching of non-self, while there is a causal series of psychophysical elements, the person as owner of these elements is a mere conceptual fiction, something we take to be real only because we take too literally what is just a useful way of talking.
In this case the contradictory statement ‘The arhat is neither reborn nor not reborn’ generates the following conversational implicature: the question concerning the post-mortem status of the arhat contains a false presupposition, that persons are ultimately real. And Buddhists claim that our ignorance about the falsity of this presupposition is an important source of the suffering we seek to mitigate. Thus statements with the form of a contradiction may function quite differently in the Buddhist context. They need not generate the implicature that the subject matter of the statement is ineffable and accessible only through some special non-discursive faculty. They may instead generate the implicature that strictly speaking the statement lacks a subject matter. The seeming failure of the law of bivalence – that every well-formed statement is either true or false – may be due to simple failure of reference. And given the soteriological context, this may be important to our well-being.

The founder of the Madhyamaka school of Mahāyāna Buddhism, Nāgārjuna (2nd c. CE), gave arguments for many of the seemingly contradictory claims of the Prañājpāramitā literature, such as that space is neither existent nor non-existent. The overall conclusion he wishes us to draw is that all things lack intrinsic nature, i.e., are empty. Since prior Buddhist philosophers had presumably established that only things with intrinsic nature are ultimately real, the claim that all things are empty has an air of paradox about it. For if it is true that all things are empty, then ultimately there are no things of which it is true that all things are empty. So if it is true, then it is not true. But we are also made to understand that realization of the truth that all things are empty is crucial to our attaining liberation from suffering. What are we to make of this situation?

There seem to be three options: that Nāgārjuna failed to see that his view was inconsistent; that he intends us to conclude that the ultimate nature of reality transcends the capacities of the intellect; or that he intends us to reject the presupposition that there is such a thing as the ultimate nature of reality. But there are textual reasons for rejecting the first option.[ii] And the second, apophatic interpretation may be called into question by the point just made about Buddhist uses of bivalence failure. Thus the third option seems the most plausible. Since Buddhists use the term ‘ultimate truth’ to mean both the realization which brings about liberation from suffering, and the correct account of how things ultimately are, this may be put as ‘The ultimate truth is that there is no ultimate truth’.
This is the understanding of the Madhyamaka doctrine of emptiness that I have championed in my own work. But I have also long been interested in showing that the Buddhist philosophical tradition and the Western tradition may have important things to say to one another. The doctrine of emptiness is, I think, a case in point. The position known as semantic anti-realism, developed by Michael Dummett and Hilary Putnam, holds that the truth of true statements cannot be said to depend on a world the nature of which is independent of the concepts we happen to employ (Dummett 1993; Putnam 1981). In effect it challenges the naive conception of truth as correspondence to an ultimate reality that transcends our interests and cognitive limitations. On my understanding of the doctrine of emptiness, this doctrine is a form of semantic anti-realism. But it differs in at least one important respect from the anti-realisms developed by Dummett and Putnam. The latter rely on some form of semantic internalism, the view that meanings must be internally accessible to the speaker.[iii] This may be seen most readily by reflecting on the Kantian pedigree of contemporary semantic anti-realism. Kant’s dictum, ‘Concepts without intuitions are empty’ is an expression of semantic internalism. And the anti-realist denial of verification-transcendent truth-conditions might be seen as an updated formulation of this dictum. Semantic internalism is, however, controversial. Thus it is of some interest that the Madhyamaka doctrine of emptiness does not depend on any internalist assumptions. If this doctrine is a semantic anti-realism, it is one that does not rely on internalism.

A word may be in order as to why I think a Buddhist philosopher might have been in the business of denying the semantic realist conception of truth. The Buddhist project of obtaining liberation from sansāra is said to depend on realizing the truth of non-self. The key move in this project is to see that our sense of ‘I’, of there being an enduring person, comes from taking too seriously what is actually just a useful way of talking about a causal series made up of many discrete and impermanent entities. Out of this move there developed a distinction between how things seem to us given our interests and cognitive limitations, and how things truly are independently of those interests and cognitive limitations. In the Abhidharma schools of Buddhist philosophy this became the distinction between conventional truth and ultimate truth – with ultimate truth being the privileged member of the pair. The latter is, of course, just the semantic realist conception of truth. And it requires that there be things with natures that are independent of the concepts that we happen to employ due to our interests and cognitive limitations. These things are what are called dharmas. And it turns out that they have their natures intrinsically, independently of the existence or nature of other things. They are to be contrasted with things whose natures are dependent on the natures of other things, which turn out to be mere conceptual fictions (such as the chariot, the forest, the person).[iv]

To say that all things are empty is to say that there are no things with intrinsic natures. For emptiness is just the being devoid of intrinsic nature. When Madhyamaka asserts this, it is denying that there are the sorts of things that ultimately true statements could be about. So it is in effect denying that there is such a thing as ultimate truth. And it also holds that realizing this has great soteriological significance – hence ‘The ultimate truth is that there is no ultimate truth’. Presumably this is because the distinction between conventional truth and ultimate truth involves a valorizing of the latter, and this can serve as the ground for a subtle form of clinging or self-assertion. Hence full realization of non-self requires that one come to see the semantic realist conception of truth as itself merely another useful tool.
But this reading of Madhyamaka is based on the presupposition that classical logic holds, and that contradictions must be false. Some recent developments in logic call this into question. Under classical logic, allowing a contradiction leads to what is called ‘explosion’ – the fact that any proposition whatever may be derived, so that there is a population explosion among the propositions to which we are committed. This means that anyone who affirmed a contradiction would be thereby committed to affirming any and all propositions. Since it is a requirement on meaningful discourse that speakers be prepared to affirm some propositions and deny some others, explosion provides a good reason to reject contradictions. One who will say anything is in fact saying nothing. So-called relevance logics and Routley’s paraconsistency system provide ways of halting explosion. Hence the adoption of one of these non-classical systems removes the principal reason for saying that all contradictions must be false.
Relevance logics were first developed as a way to get around the so-called paradoxes of material implication. On the standard interpretation of first-order predicate calculus, and in particular the introduction rule for the conditional, given the truth of p, q→p can always be derived for any q. Relevance logics prevent this result by placing constraints of relevance on what can be introduced into a derivation. What Routley pointed out is that these constraints also provide a way of halting explosion. Explosion results from the fact that given a contradiction p&~p, one can obtain both p and ~p by detachment, from ~p one can derive p→q, and from this in turn one can derive q by modus ponens given p. Since q can be any proposition whatever, one is thereby committed to affirming every proposition. But relevance logics block the derivation of p→q from ~p alone. The same relevance constraints that prevent the derivation of q→p for arbitary q from p alone, likewise block the derivation of p→q for arbitrary q from ~p alone.

Graham Priest’s dialetheism uses Routley’s result to show how there can be true contradictions ‘at the limit’ or at the boundaries of intelligibility.[v] Priest claims that dialetheism sheds light on the thought of such major philosophers as Kant, Hegel, Heidegger and Wittgenstein. To this list, Priest and Garfield add N~g~rjuna (Priest 2002, pp.249-70; Garfield 2002, pp.86-105). But before coming to their defense of that claim, I should say something about another of Priest’s claims. He asserts that the view that there can be true contradictions is widespread in Asian philosophy, e.g., in Taoism, Zen, and among those Indian philosophers who employ the device known as the catushkoti or tetralemma (Priest 2004). I shall only discuss the last claim, since I think it is important that the record be set straight. The example cited above concerning the question of what happens to the arhat after death is actually an example of the catushkoti, for the Buddha’s interlocutor puts not just two but four questions to the Buddha:
Is the arhat reborn?
Is the arhat not reborn?
Is the arhat both reborn and not reborn?
Is the arhat neither reborn nor not reborn?

The Buddha replies to each question in turn that it would not be correct to say so. Priest claims that this format embraces the possibility of true contradictions, for instance in the third lemma. But this seems unlikely given what is actually said by the Buddha in actual cases following this scheme. Take the case of the question concerning the post-mortem status of the arhat. The four possibilities are existent, non-existent, both, and neither. The Buddha rejects each. Now the occurrence of the third might seem to suggest the possibility of true contradictions. But it is significant that this lemma is put forth only after the Buddha has rejected the first and second. That fact suggests that the third possibility involves equivocation on ‘existent’: that the arhat does exist when ‘existent’ is taken in one sense, but does not exist when it is taken in some other sense. For when the Buddha rejects both of the first two lemmas, this generates an apparent contradiction. And one way of seeking to resolve this contradiction is to suppose that there is equivocation at work. We do this, for instance, when we interpret the statement, ‘She is the same and yet not the same’ to mean she is the same person (numerical identity) but has undergone significant qualitative change and so lacks qualitative identity. So when the Buddha rejects this lemma, he is ruling out the possibility that there are different senses of ‘exists’ at work here.

The fourth possibility also looks to be formally contradictory. (Indeed it seems logically equivalent to the third.) But the tradition treats this as quite different from the third lemma. It is taken to be the claim that there is some alternative characterization of the subject at hand that is not contained within the pair p and ~p. For instance, when Nāgārjuna examines the relation between cause and effect at the outset of his foundational work Madhyamakakārikās, the four possibilities considered are that these are identical, distinct, both and neither. The last possibility is explained as the view that origination is without cause. This is likewise a way of trying to resolve the apparent contradiction resulting from rejecting what look to be all the possibilities: that things arise from themselves, from distinct things, or from both. So this would be a way of saying that one does not contradict oneself when one rejects each of the first three possibilities. To consider this possibility is not to envision that there might be true contradictions. It is a way of trying to avoid attributing to the speaker the view that a contradiction holds.
Priest and Garfield claim that certain of Nāgārjuna’s statements about emptiness represent examples of contradictory statements that may meaningfully be said to be true. Nāgārjuna’s commentator Candrakīrti says, for instance, that the intrinsic nature of all things is to lack intrinsic nature (de la Vallée Poussin 1970, pp.264 – 265). This statement says that things both have and lack an intrinsic nature, so it is formally contradictory. Yet it may nonetheless be true according to the dialetheist.
Notice that the dialetheist reading differs markedly from the false presupposition reading. According to the former, the statement in question is true. According to the latter the statement lacks a truth value. There is an important difference between saying that the ultimate nature of reality is contradictory, and saying there is no such thing as the ultimate nature of reality. The former reinstates the presupposition that the latter rejects. There is, according to this presupposition, something we are talking about when we inquire into the ultimate nature of reality. Indeed Priest and Garfield think there is reason to believe ultimate reality must be contradictory in nature. For, they argue, the ultimate nature of reality is how things are independently of the concepts we happen to employ. But any attempt to specify its nature must employ concepts. And so the ultimate nature of reality must be such as not to be expressible using our concepts. And yet if this is true, then there is something about the ultimate nature of reality that can be expressed using our concepts, namely the fact that it is indescribable. So the ultimate nature of reality is contradictory in nature.

The dialetheist reading is also said to have the advantage that it gives the enlightened person something to be right about. (To put it in the terms I used earlier, it preserves the gap between the sacred and the profane.) Thus it achieves the goal of the second option described above, of preserving a transcendent subject-matter. But it does this without requiring that one work out a conversational implicature – at least not if one knows there can be true contradictions. So the dialetheist reading might seem preferable to the false presupposition reading.

I must confess that I am not persuaded, though. For one thing, I think the argument concerning the inexpressibility of the ultimate nature of reality is flawed. For another, I think this turns Madhyamaka and Advaita Vedānta into notational variants of each other – something that would be unacceptable to both sides. I also fail to see why the appeal to the insight of the enlightened should have any force. While there may be an epistemic difference between those who are enlightened and the rest of us, it is not clear to me why this would have to be explained in terms of some transcendent subject-matter about which we are ignorant and they have insight. Why could this not be accounted for instead in terms of a mistake that we make and they do not, but a mistake concerning a shared world constructed in conformity with classical logic?
To elaborate on this last point, I want to say something about a matter on which I think Garfield, Priest and I agree. When Mādhyamikas claim that all things are empty, they do not exempt emptiness itself from this claim. They say that emptiness is itself empty. In commenting on the consequences of this, Garfield and Priest say:
The emptiness of emptiness is the fact that not even emptiness exists ultimately, that it is also dependent, conventional, nominal, and in the end it is just the everydayness of the everyday. Penetrating to the depths of being, we find ourselves back on the surface of things and so discover that there is nothing, after all, beneath those deceptive surfaces. Moreover, what is deceptive about them is simply the fact that we assume ontological depth lurking just beneath. (Garfield 2002, p.101)
With this characterization I am in complete agreement. What I would suggest, however, is that it opens up the possibility of giving the enlightened something about which they can be right without requiring that there be a sphere of the ultimate that they perceive and we do not. For what the enlightened perceive might be just the same world we perceive, only without the illusion of hidden depths.

But perhaps the more interesting question is what dialetheism would do to the Mādhyamika’s ability to argue for their claim that all things are empty. I think the result would be rather dire. Nāgārjuna’s strategy is to use only reductio arguments. He seeks to demonstrate that the opponent’s various theses concerning the ultimate nature of reality invariably lead to contradiction, and so cannot be maintained. Now suppose he took this to show that ultimate reality has a contradictory nature, for instance in its having an inexpressible nature that is expressible, or in having as its nature that it lacks a nature. If he is willing to countenance true contradictions, then the opponent might insist on revisiting the reductio arguments that presumably refuted their theses. Such refutations employed a modus tollens argument from the falsity of the derived contradiction to the falsity of the thesis from which the contradiction was derived. But if some contradictions may be true, perhaps the contradiction derived from the opponent’s thesis is among them. Of course the opponent is unlikely to be someone who believes that there are true contradictions. The present point, though, is that the Mādhyamika is not well positioned to claim that only those contradictions that favor their own position are true, while the contradictions derived from the opponent’s theses are simply false. In that case the modus tollens argument to the falsity of the opponent’s thesis cannot get off the ground. The Mādhyamika would be left without a way of showing that all things are empty.

Mādhyamikas say that only mad people accept contradictions (de la Vallée Poussin 1970, p.15). We have just seen why this might be. Embracing dialetheism would threaten their use of reductio arguments. And the alternatives do not look very promising. Suppose they sought to construct independent arguments for their claim that all things are devoid of intrinsic nature. The opponent is someone who will only accept reasons that are grounded in the ultimate nature of reality. If the Mādhyamika proffers reasons that appeal to the ultimate nature of reality, then they will contradict their thesis that all things are devoid of intrinsic nature. Suppose they claim that since ultimate reality is contradictory in nature, they are entitled to employ reasons that contradict their thesis. The opponent will then justifiably charge the Mādhyamika with question-begging. It is up to the Mādhyamika to establish some such thesis as that all things are empty, or that the ultimate nature of reality is inexpressible, before they can claim to have reason to believe that ultimate reality is contradictory in nature. The burden of proof rests with them, since it is they who propose that we abandon a logic that has served as common currency until now.[vi]
There are also historical reasons to reject the attribution of dialetheism to Nāgārjuna. These have to do with an approach to contradictory statements that was widely shared among classical Indian philosophers. I bring this up because I think it is an approach that is worth our consideration. On this approach, there is no proposition that is expressed by a contradictory statement. This is because in order for a word string to express a proposition, the words must be ‘semantically fit’, that is, their referents must be such as can be related as the syntax of the string says them to be. The stock example of a word-string that lacks semantic fitness is ‘Devadatta waters the plants with fire’. Since fire cannot perform the function of irrigating plants, this word string fails to denote a possible state of affairs, and so does not express any meaning. It is neither true nor false. And the same holds for statements that have the form of a contradiction. The statement, ‘Feeling lacks the nature of feeling’ fails to denote any state of affairs, since anything that is a feeling has the nature of feeling, and its having that nature stands in the way of its lacking that nature. So the statement is neither true nor false. And likewise for any other contradiction. On this approach there can be no true contradictions.[vii]
This might appear incompatible with the use of reductio arguments. If a contradiction can be neither true nor false, then there can be no modus tollens argument from the falsity of the contradiction to the falsity of the opponent’s thesis. But the Mādhyamika has a way to get around this difficulty. They do not assert that the contradiction derived through the reductio is false. They say instead that the derived contradiction should not be asserted by the opponent. And realizing that this statement should not be asserted, the opponent will realize that the thesis from which this contradiction was derived should likewise not be asserted. This strategy allows the Mādhyamika to set about disabusing us of the notion that there is such a thing as the ultimate truth without themselves saying anything that could be construed as a characterization of how things ultimately are (or are not). They thus avoid being put in the odd (and potentially embarrassing) position of claiming that some contradictions are true.

NOTES
[i] Logical paradoxes typically involve sets of statements. Such is the case for instance with sorites paradoxes. But there are formulations of the Liar that involve a single statement, e.g., ‘This statement is false’.
[ii] For instance, at Vigrahavyāvartanī 5-6, Nāgārjuna has the opponent raise the objection that if all things are empty then there can be no means of knowledge whereby it is known that all things are empty. In verses 29-51 of the same text he replies to this objection. Regardless of whether or not the reply is successful, this shows that Nāgārjuna was aware of the paradoxical consequences of the doctrine of emptiness. Thus a conversational implicature is generated by his utterance of the doctrine.
[iii] The British empiricist doctrine that the meaning of a word is an idea is a form of semantic internalism, as is the logical positivist doctrine of verificationism.
[iv] I develop this in some detail in Chapters 1-4 of Siderits 2003.
[v] For technical details see Priest 1987. For various applications of dialetheism see Priest 2002.
[vi] Garfield and Priest note that in employing reductio arguments, Nāgārjuna shows himself to be committed to the falsity of contradictions in the conventional plane (Garfield 2002, 94-6). They claim he holds that it is only ‘at the limit’ in the domain of the ultimate truth that there may be true contradictions. But they do not explain how such a distinction can be shown to be principled.
[vii] That Candrakīrti takes this view of contradictions is at least suggested by his comments on MMK xxvii.28, which concerns the rejection of the possibility that existence both has and does not have a limit: ‘Because the object of the negation cannot really be, so the negation is not possible’ (de la Vallée Poussin p.590).

REFERENCES
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Priest, G. (2002). Beyond the Limits of Thought. Oxford: Clarendon.
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Putnam, H. (1981). Reason, Truth and History. Cambridge: Cambridge University Press.
Siderits, M. (2003). Personal Identity and Buddhist Philosophy: Empty Persons. Aldershot, UK: Ashgate.