By Graham Priest
Buddhist metaphysics and modern symbolic logic might seem strange bedfellows. Indeed they are. The thinkers who developed the systems of Buddhist metaphysics knew nothing of modern logic; and the logicians who developed the panoply of techniques which are modern logic knew nothing–for the most part–of Buddhism. Yet unexpected things happen in the evolution of thought, and connections between these two areas are now emerging. (As I write this, I’m on a plane flying back to Germany from Japan, where I’ve been lecturing on these matters for the last two weeks in Kyoto University) Let me try to explain as simply as I can.
At the time of the historical Buddha, Siddhārtha Gautama, c. 5c BCE, a common assumption was that there are four possibilities concerning any claim: that it is true (and true only), that it is false (and false only), that it is both true and false, that it is neither true nor false. The principle was called the catuṣkoṭi (Greek: tetralemma; meaning ‘four points’ in English).
We know this because, in some of the sūtras, the Buddha’s disciples ask him difficult metaphysical questions, such as the status of an enlightened person after death: does the person exist, not exist, both, or neither? They clearly expect him to endorse just one of these possibilities.
Until recently, Western logicians have had a hard time making sense of this. Standard logic has assumed that there are only two possibilities, true (T) and false (F)–tertium non datur. In particular, there is nothing in the third koṭi (both true and false), and even if there were, it would be in the first two as well (true, and false). So the koṭis would not be exclusive.
To those who know a little modern non-classical logic, however, the matter is easy. There is a system of logic called First Degree Entailment (FDE). This is a four-valued logic whose values are exactly those of the catuṣkoti (t, f, b, and n). Standardly, they are depicted in a diagram as follows:
Given this ordering, the values interact with other standard machinery of logic, such as negation, conjunction, and validity.
Matters, however, don’t end there. The Buddha refused to answer such tricky questions. Some sūtras suggest that this was because it was simply a waste of time. Others hint at the possibility that sometimes none of the four koṭis may be the case.
And this is just what later metaphysics suggested. Nāgārjuna (dates uncertain, 1st or 2nd c. CE) is perhaps the greatest Buddhist philosopher after the Buddha. His Mūlamadhyamakakārika (Fundamental Verses of the Middle Way) was a text which was to exert a profound influence on all subsequent Buddhisms. And in this, he appears to say that some things are simply ineffable. The state of an enlightened person after death, for example, is such.
This adds a fifth possibility, i, which is none of the above. It is distinguished from the first four, in that if something, A, has the value i, so does any more complex sentence formed out of A. (If A is ineffable, so must this be.)
This still isn’t an end to the matter, however. For Nāgārjuna, and those who follow him, not only claim that some things are ineffable: they explain why they are so (roughly, these situations pertain to an ultimate reality, which is what remains after all conceptual–and therefore linguistic–imputations are “peeled off”). Clearly, speaking of the ineffable is a most paradoxical state of affairs. It would seem to show that some claims can take more than one of the five values, such as both t and i. (And lest it be thought that this is simply a feature of Eastern mysticism, one should note how many of the great Western philosophers have found themselves in exactly the same situation: Aristotle (prime matter), Kant (noumena), Wittgenstein (form, in the Tractatus), Heidegger (being).)
Again, modern techniques of non-classical logic can show how to make sense of this possibility. In standard logics, things take exactly one of whatever values are on offer. But in a construction called plurivalent logic, things can take more than one (maybe even less than one) such value. The plurality of values interact in a perfectly natural and sensible way with the other logical machinery.
What to make of these matters? Philosophers may certainly argue about this. (This, after all, is what philosophers love to do.) However, one thing is ungainsayable: Buddhist metaphysics and formal logic can profitably inform each other.
FDE was a system of logic known independently of Buddhist considerations. (It was developed in the 1960 and 70s in a branch of logic known as relevant logic.) But the development of the five-valued logic above, and plurivalent logics, were motivated, at least in part, by trying to make sense of the Buddhist picture. The metaphysics can therefore stimulate novel developments in logic—developments whose interest is not simply restricted to applications to Buddhist metaphysics.
Conversely, those with a suspicion of metaphysics in general and Eastern systems of metaphysics in particular, might be tempted to write off such enterprises as logically incoherent. They’re not. The techniques of modern logic certainly don’t show that these pictures of reality are true. However, they show that they’re as logically coherent as can be – and, moreover, they allow us to articulate the views with a precision and rigor hitherto unobtainable, and hence to understand them and their consequences better.
Buddhist views are not, of course, the only views that can work in this dialectical way. But because Buddhist views are little known in Western philosophy, they provide a particularly fruitful domain of inquiry.
And what would the Ancient Buddhist metaphysicians themselves have made of such developments in logic? We’ll never, of course, know; but my own guess is that they would have very much appreciated the enlightenment which such techniques can bring.
Graham Priest is Boyce Gibson Professor of Philosophy at the University of Melbourne and Visiting Professor at University of St Andrews. He is the author of Logic: A Very Short Introduction.
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Image credits: 1) The Buddha, by Shivanjan (Own work) [CC-BY-SA-3.0] via Wikimedia Commons; 2) Nāgārjuna, [Public domain], via Wikimedia Commons
“I remember speaking in one of the United States’ western cities when a professor was attending the lectureship and asked me to speak against a particular eastern religion; of which I said I would not do. The professor said “I am an American and I belong to this particular eastern religion. “I have taught this religion in my lectures and elsewhere” he said. “I want you to speak on the subject of why you do not subscribe to the dogma of my religion, and my students will take you apart after your lecture.” I said “No I really don’t want to do that. I’ve learned that when you throw mud at others, not only do you get your hands dirty, but you also lose a lot of ground. But I will tell you why I am a Christian. I will speak on that subject.” At the end of the talk he was quite vociferous in his denunciation of what I had said, and he basically took me to task at the front of the lecture room attacking the fact that I didn’t understand logic. I said “Look we’re not gonna get anywhere here, lets go out for lunch; you pay and I’ll pray.”
So we got together for lunch and he brought a professor of psychology with him. The psychologist and I finished our lunch while the philosopher hadn’t even started his. His food had become congealed in front of him. He had taken the paper place mats off all the other tables in order to draw out his argument. And basically what he was trying to say was this; that there are two kinds of logic (actually there are more as we’ve already discussed). He said “One is the law of non contradiction. The law of non contradiction means if something is true, the opposite of it is false. It is called an ‘either/or’ logic. If I say to you for example there is a red car parked immediately outside near the front steps to the restaurant; if that statement is true the opposite of it is false. I am not at the same time saying that the red car is not parked out there. It is either true or false. I’ve just given you a simple illustration; if it is A then it is not non-A at the same time. You basically establish the either/or dogma.” So he said “Ravi that is the law of non contradiction; that is a western way of thinking. Westerners think either/or.” I said to him “I disagree with the last statement; why don’t you rub it off the paper?” But he wouldn’t do it.
So then he moved to the eastern way of thinking. He said “In the east you do ‘both/and’. It is a dialectic (the contradiction between two conflicting forces). You don’t say ‘it is either this or that’ you say ‘both this AND that’. Carl Marx used the dialectical system. It was not either the employer, or the employee; you put them together and you find a classless society. Both employer and employee join together in a classless society.” Funny thing is they never show you a classless society but they just talk about it. That there is a both/and dogma in the dialectic; two poles of an argument.
The professor continued saying “You see Ravi the dialectical system is Eastern.” I said “Why don’t you cross out that last line because I don’t agree with you?” but he refused to cross it out. I had talked about the many contradictions in certain pantheistic world views (Belief in and worship of all gods), very strong contradictions. And he said “You see Ravi if you took the dialectical system to be true, any time you came into a contradiction you wont be puzzled by it. You’ll say “this is the way they think. They make opposite statements and both of them are right” So if you ask one follower of religion X, “Is God personal?” he answers “Yes.” You ask a second follower of religion X “Is God personal?” and he says “No.” You go to the third person and ask “Which of these two is right?” and he says “Both of them.” That’s the Eastern way of thinking. So you’ve got the either/or which is Western, the both/and which is Eastern.”
He was waxing eloquent just going on and on; finally I interrupted and said “Can I say something to you sir?” He said “Yes” and he picked up his knife and fork and started to cut into his first morsel of food. As he was cutting into the first morsel of food I said “Here’s what you’ve told me; there is an either/or which is Western, there is a both/and which is Eastern, and you want to me to study religion X right? Now here’s my question to you professor… are you telling me when I’m studying religion X, I either use the both/and system or nothing else; is that right??” I repeated it again, “That I either use the both/and system or nothing else, is that right?” Do you know what he did? He put his knife and fork down, and with a very nervous expression he said to me “The either/or does seem to emerge doesn’t it.” I said “Yes. In fact I’ve got some shocking news for you; even in India, we look both ways before we cross the street; it is either the bus or me, not both of us.” – Ravi Zacharias
Do you see what the professor was doing? He was using the ‘either/or’ in which to prove the ‘both/and’. He was saying you either use this system (the both/and) or nothing else. So it’s got nothing to do with whether it is Western or Eastern, it has got everything to do with that which best reflects reality.
[…] Lauter nichtklassische Logiker, die ich schätze, haben eher spät in ihrer Karriere angefangen, über das Tetralemma zu reflektieren: Ulrich Blau, Matthias Varga von Kibéd und Graham Priest. […]
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