Graham Priest on Buddhism and logic

Buddhism47gfby Massimo Pigliucci

Graham Priest is a colleague of mine at City University of New York’s Graduate Center, a world renowned expert in logic, a Buddhist connoisseur, and an all-around nice guy [1]. So I always pay attention to what he says or writes. Recently he published a piece in Aeon magazine [2] entitled “Beyond true and false: Buddhist philosophy is full of contradictions. Now modern logic is learning why that might be a good thing.” I approached it with trepidation, for a variety of reasons. To begin with, I am weary of attempts at reading things into Buddhism or other Asian traditions of thought that are clearly not there (the most egregious example being the “documentary” What The Bleep Do We Know?, and the most frustrating one the infamous The Tao of Physics, by Fritjof Capra). But I quickly reassured myself because I knew Graham would do better than that.

Second, Graham knows a lot more than I do about both logic and Buddhism (especially the latter), so surely I was going to learn new things about both topics and, more crucially, how they are related to each other. The problem is that I ended up learning and appreciating more about logic, not so much about Buddhism, and very little about their congruence. Hence this essay.

I am going to follow Graham’s exposition pretty closely, and will of course invite him to comment on my take at his pleasure. Broadly speaking, my thesis is that the parallels that Graham sees between logic and Buddhism are more superficial than he understands them to be and, more importantly, that Buddhism as presented in his essay, is indeed a type of mysticism, not a philosophy, which means that logic (and, consequently, argumentation) are besides the point. Moreover, I will argue that even if the parallels with logic run as deep as Graham maintains, Buddhism would still face the issue — fundamental in any philosophy — of whether what it says is true of the world or not, an issue that no mystical tradition is actually equipped to handle properly.

Graham’s essay begins with the complaint that many Western philosophers dismiss Buddhism as mysticism. While he claims this is due to ignorance and incomprehension, the point to keep in mind is that such opening clearly marks the charge of “mysticism” as an important motivator behind his whole essay. Keep this in mind, because it will come in handy later on.

An early example, in Graham’s piece, of what so many W-philosophers are complaining about is this famous saying by Buddhist thinker Nagarjun: “The nature of things is to have no nature; it is their non-nature that is their nature. For they have only one nature: no-nature.” At first glance, I do share the puzzlement of my W-colleagues, but I am certainly willing to let Graham help me to clear the fog of my incomprehension.

He pins much of the alleged disdain toward Buddhism to W-philosophers’ aversion to contradictions, which is rooted, of course, in Aristotelian logic, and particularly in two of its pillars: the principle of non contradiction (contradictory statements cannot both be true in the same sense at the same time) and the law of the excluded middle (either something is true or it isn’t, no third option available) [3].

Graham invites his readers to go back to the 5th Century BCE in India, when Buddhism was just beginning, and when a principle known as catuskoti (“four corners”) was being formulated. Here is how he explains it: “[catuskoti] insists that there are four possibilities regarding any statement: it might be true (and true only), false (and false only), both true and false, or neither true nor false.” The literature on this developed because of answers that the Buddha gave to questions such as what happens to enlightened people when they die. The Buddha, apparently, often simply refused to answer the question at all (wisely, I might add); but at other times Buddhist texts seem to suggest that none of the four catuskoti actually provides an answer, and that therefore there was a problem to be handled. Apparently, things got a bit more clear with the second most important Buddhist thinker of all time, 2nd Century CE’s Nagarjuna, who espoused the view that things are “empty,” which Graham tells us doesn’t mean non-existent, but rather that they are because they relate to other things. Nagarjuna spends time discussing the four catuskoti and concludes that there are instances — such as the question of what happens to an enlightened person after he dies — that are not covered by any of those cases.

Graham himself refers to Nagarjuna’s writings as “cryptic,” and to his reasoning as “opaque,” which are both highly irritating characteristics of some Western (think Heidegger!) and Eastern philosophies, and which I really wish people stopped defending or taking for granted and began to seriously criticize. At any rate, here is Graham’s summary of Nagarjuna’s position:

“The language we use frames our conventional reality (our Lebenswelt, as it is called in the German phenomenological tradition). Beneath that there is an ultimate reality, such as the condition of the enlightened dead person. One can experience this directly in certain meditative states, but one cannot describe it. To say anything about it would merely succeed in making it part of our conventional reality; it is, therefore, ineffable. In particular, one cannot describe it by using any of the four possibilities furnished by the catuskoti.”

[Notice the reference to German phenomenology, more on this in a minute.]

This amounts to a sort of catuskoti+, characterized by the four initial possibilities plus a fifth case standing for ineffability. Bear with me for a few more minutes, there’s going to be a pay off.

So far, W-philosophers would have two sources of trouble: the catuskoti is bad enough, because it violates both non-contradiction and excluded middle; but now Buddhists are talking about ineffable things, too! The thing about the ineffable is that it is defined as something of which one cannot talk, it is by definition beyond words. And yet, Nagarjuna and his followers gingerly go on telling us things about the alleged ineffable! In particular, in Graham’s rendition, they tell us why some things are ineffable, even though they cannot comment on the things-in-themselves.

Okay, if you are even superficially familiar with Western philosophy, you might have recognized parallels — which Graham duly notes, of course — with Kant, or even Heidegger. Kant makes a distinction between the phenomenal world, to which we have access through our senses and reason, and the noumenal one, which is in a sense ineffable, but about which we can tell why it is so. Heidegger, much more bizarrely and certainly more obscurely, wrote a big book about Being and then told everyone that you can’t really say anything about Being.

Graham says that all of this is a contradiction, and one that should not actually worry W-philosophers, regardless of whether they are contemplating Kant, Heidegger or Buddhism: “you can’t explain why something is ineffable without talking about it. That’s a plain contradiction: talking of the ineffable.”

I think this is a questionable move. I don’t think there is any real contradiction at play here. Let me take the case of Kant in particular, since it is by far the least obscurely put. A reasonable retelling of the story, I suspect, is that Kant identified an epistemically inaccessible zone, one the content of which we cannot know. But we can observe the contours of such zone, the epistemic perimeter, if you will, from the outside. Imagine a physical analogy: you use Google map and find out that a certain location on it, say Dick Cheney’s house, is missing from it. There is a large blacked out area around it, to which you have no access. There is no contradiction in a) acknowledging that you can’t say anything about what is inside that geographical black hole while b) you can say something about it, for instance that it exists, and that it has a certain perimeter.

What I have not told you so far is that Graham had in the meantime weaved a fascinating series of analogies between the contradictions of Buddhism and developments in logic since Aristotle. We are therefore treated to a breathtaking, and truly enlightening, overview of things like the distinction between a relation and a function in mathematics (the later relates objects in a one-to-one fashion, the former in a one-to-many); relevance logic (a non-classical system designed to deal with paradoxes) [4]; the Russell paradox (concerning the set of all the sets that are not members of themselves) [5]; many-valued logic (invented by Polish logician Jan Łukasiewicz in the 1920s to deal with the contingency of statements about the future, which are strictly speaking neither true nor false, as Aristotle himself recognized) [6]; and plurivalent logic (which deals with paradoxes originating from self-referential sentences, and was co-invented by Graham himself) [7]. It’s a veritable tour de force, and it’s worth every minute of your (focused!) attention.

But what do we get out of all of this? Graham himself acknowledges that all these developments in logic, which largely took place within the Western tradition, occurred entirely independently of Buddhism. There was pretty much no cultural cross-fertilization, going either way. That, in itself, is not a problem: a reasonable interpretation of what happened is that Western logicians and Buddhist thinkers arrived at the same conclusions independently of each other.

Except that that strikes me as a forced analysis of what is going on. Relevance logic, many-valued logic, various treatments of paradoxes, and so forth were explicitly tackled by Western philosophers as logical problems, and confronted by means of rigorously formal analysis and carefully developed arguments. This is not at all the impression of Buddhism that I get from reading Graham (and from my intro-level familiarity with Buddhism outside of taking Graham as a source [8]). Instead, Buddhist thinkers clearly arrived at their formulations by non-philosophical, and more precisely, mystical, means.

Graham seems to recognize this when he says: “Call it mysticism if you want; the label has little enough meaning. But whatever you call it, it is rife in great philosophy — Eastern and Western.” I beg to differ. It may be great mysticism (if one is inclined to take on board this approach to truth and knowledge), but not great philosophy. The term “philosophy,” in my book (and I’m sure Graham will disagree) is best reserved for the sort of argument-cum-logic approach developed by the pre-Socratics and their immediate successors (who, after all, introduced the very word!), and to confuse it with other modes of thought is, well, confusing.

This, by the way, isn’t a West-East thing at all. Graham squarely numbers Heidegger among the “call it mysticism if you want” group, which is why I really don’t like Heidegger: he may have something interesting or profound to say (unlike, say, Derrida), but if he doesn’t bother to say it in clear and logically cogent ways, the hell with it, as far as I’m concerned. (Graham also includes Wittgenstein in this group, though in his case things are more complex, both because of his famous first and second philosophical phases throughout his life, and because even his second phase is crystal clear compared to Heidegger!) And on the other side of the geographical divide we have the vibrant tradition of Indian logic and epistemology [9] which certainly counts as philosophy, and which paralleled many of the developments of the Western tradition, arriving at several of the same conclusions.

Now, I realize that the word “mysticism” almost automatically carries a negative connotation in the West (thanks, Deepak Chopra!), and I must confess to being deeply mistrustful of mystical insights myself. But if by mysticism we simply mean an intuitive, rather than a discursive, approach to thinking about the nature of reality, by all means, bring your intuitions to bear on whatever it is we are discussing and let’s hash it out. Still, this points to a major disanalogy between Western (and Indian!) logic and Buddhism as presented by Graham’s attempt to interweave them: in logic we are concerned with the formal properties of hypothetical systems, not with the way the world is. Logic and math do often have surprisingly insightful things to say about reality, but this isn’t their point. Logicians in particular are concerned with the properties inherent in the structure of sentences, not in their content — which is why logic texts read like endless streams of “if p then q; p; therefore q,” where it simply doesn’t matter what the damned p and q actually represent.

That is most definitely not the case for metaphysicians concerned with the noumenal vs phenomenal world (Kant), with Being (Heidegger) or for Buddhist disciples concerned with what will happen to them if they die after achieving enlightenment. Graham suggests that Nagarjuna’s problem with the ineffable is analogous to the Hungarian mathematician Julius König’s work on ordinals and what happens after we have been through all finite numbers (which is an infinite set, of course). I don’t feel comfortable with that analogy, precisely because questions about ordinals are questions about logical-mathematical objects, while Nagarjuna’s (and Kant’s, and Heidegger’s) attempt is at saying something about the world as it is. Not the same thing.

Graham draws two conclusions at the end of his must-read essay:

“Mathematical techniques often find unexpected applications. Group theory was developed in the 19th century to chart the commonality of various mathematical structures. It found an application in physics in the 20th century, notably in connection with the Special Theory of Relativity. Similarly, those who developed the logical techniques described above had no idea of the Buddhist applications, and would, I am sure, have been very surprised by them.”

Yes to almost all of the above, except that I see a glaring difference between applying logic to the theory of relativity and retrofitting it to a mystical tradition.

“The second lesson is quite different and more striking. Buddhist thought, and Asian thought in general, has often been written off by Western philosophers. How can contradictions be true? What’s all this talk of ineffability? This is all nonsense. The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true. That’s a different matter. But it does show that these ideas can be made as logically rigorous and coherent as ideas can be.”

Well, no. To begin with, whether Buddhist views are true is precisely the matter. Logic and math cannot be false, unless one has made a mistake in the formalism. And they cannot be false precisely because they do not deal with statements concerning the world. The same courtesy cannot be extended to any form of mysticism, philosophy or science, for that matter.

As for Buddhist ideas being just as rigorous as Western logic and math, again, no. The rigor in the latter comes out of the ability to very precisely spell out formalism, build arguments and proofs, defend or abandon axioms, and so on. Nothing of the kind appears to be the case within Buddhist tradition, though again I’m certainly more than willing to be corrected (with detailed examples?) by Graham, who knows that tradition much better than I.

Graham’s parting shot is this: “As the Buddha may or may not have said (or both, or neither): ‘There are only two mistakes one can make along the road to truth: not going all the way, and not starting.’” Being conscious of the hubris of improving on the Buddha, I’d add a third: one can get started on the wrong path.


Massimo Pigliucci is a biologist and philosopher at the City University of New York. His main interests are in the philosophy of science and pseudoscience. He is the editor-in-chief of Scientia Salon, and his latest book (co-edited with Maarten Boudry) is Philosophy of Pseudoscience: Reconsidering the Demarcation Problem (Chicago Press).

[1] He has also been, more than once, on my Rationally Speaking podcast, to talk about logic and Buddhism.

[2] Beyond true and false: Buddhist philosophy is full of contradictions. Now modern logic is learning why that might be a good thing, by G. Priest, Aeon, 5 May 2014.

[3] The third fundamental principle of classical logic is the law of identity: each thing is the same with itself and different from another.

[4] Relevance Logic, by E. Mares, Stanford Encyclopedia of Philosophy.

[5] Russell’s Paradox, by A.D. Irvine and H. Deutsch, SEP.

[6] Many-Valued Logic, by S. Gottwald, SEP.

[7] Plurivalent Logics, by G. Priest, Australasian Journal of Logic, vol 11, 2014.

[8] See the following SEP entries: Buddha, by M. Siderits; Madhyamaka, by R. Hayes; The Kyoto School, by B.W. Davis; Japanese Zen Buddhist Philosophy, by S. Nagatomo.

[9] See these SEP entries: Logic in Classical Indian Philosophy, by B. Gillon; Epistemology in Classical Indian Philosophy, by S. Phillips.


Categories: commentary

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104 replies

  1. ejw – No arguments, but here’s the thing. I believe that Nagarjuna’s proof can account for the science of today. That is, I believe that it is the correct metaphysical explanation of quantum mechanics and everything else. This would be why he was able to prove his result, that it is true. I can only point to other people’s work on this, but there is quite a bit, and Schroedinger would be with me on this. I wouldn’t want to defend this idea here, I’m no physicist, but I would defend the belief that it’s something that physicists would find it worthwhile to explore. Buddhism and its equivalents seem to me to offer us the only description of the world anything like weird enough to be a plausible interpretation of QM.

    I see what you mean about metaphysics and suffering and would agree. The latter would be like taking the medicine while the former would be like reading the label on the bottle. Many Buddhists have no time for philosophising.

    But if we’re not sure what’s in the bottle, if anything at all, then the label must be worth reading. For an academic researcher the metaphysics of mysticism would be more important than all the talk about suffering. If we are not going to do any practice then the metaphysical scheme of Nagarjuna would be the only thing we’ve got to go on to test the plausibility of the teachings. Even the Buddha tells us not to rely on the reports of practitioners.

    The trouble is that scientists often despise metaphysics. They assume that Hume, Descartes, Russell, Wittgenstein, Carnap and so on knew more about metaphysics than Nagarjuna and the Buddha, and so see a failed metaphysical project and quite naturally want nothing to do with it.

    Liked by 1 person

  2. Seth – I see your objections, but think they are wide of the mark. When someone claims ‘to have removed all contradiction or attained certain access to ‘ultimate truth’ ‘, this is two very different claims. Nagarjuna’s proof does not depend on any claim to knowledge. He just makes an argument. Many other people have made the same argument, and they are not all Buddhists.

    Also, he does not claim to have removed all contradiction. He demonstrates their removal step by step and with great rigour. It would have saved him a lot of time just to claim it.

    He proves that all positive metaphysical position are logically indefensible. The fact that he is able to prove this is not his fault. It’s just the way the world is. It just so happens that his result, which can be thought of as a ‘neutral’ metaphysical position, coincides exactly with the soteriological teachings of the Buddha. if his metaphysics is correct. then so would be the message of the sutras.

    There can be no true contradictions in a world for which no distinctions, real or conceptual, are fundamental. Kant deals with this issue. .

    The problem for philosophy is not claims to knowledge. It is whether Nagarjuna’s result is right or wrong. There are no major problems associated with understanding what he proves. He proves that Kant was right – all selective metaphysical positions can be refuted in the dialectic. Either this is the case or it isn’t. There is no evidence that it is not the case, and all the available evidence is consistent with these positions being false in reality, ‘out there’ in the world. No claim to knowledge is required to bolster the basic logic of the situation.

    I see no reason to favour any particular interpretation of Nagarjuna, He proves what he proves. Either his logical result describes what is the case or it does not. If we don’t know which it is then clearly it might be.

    I’d like to stop here if you don’t mind. I keep being beguiled by the discussion and losing hours in thought. .Thanks for the chat. I’ll still be reading if you want to come back about this. .


  3. Gregory Gaboardi,

    I have to say that I’m at something of a loss. I have thought about how to define philosophy before, but I’ve never thought about the definition of mysticism. In ordinary speech, I use the word ‘mystical’ when I mean ‘magical and mysterious.’ The combination of that with religion is what prompts me to think that there must be a supernatural element to mysticism.

    What sort of methodology would you ascribe to mysticism?


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