Beyond true and false

Buddhist philosophy is full of contradictions. Now modern logic is learning why that might be a good thing

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Illustration by Fumitake Uchida

Illustration by Fumitake Uchida

Graham Priest is distinguished professor of philosophy at CUNY and professor emeritus at the University of Melbourne. His latest book, One, has just been published by Oxford University Press.

Western philosophers have not, on the whole, regarded Buddhist thought with much enthusiasm. As a colleague once said to me: ‘It’s all just mysticism.’ This attitude is due, in part, to ignorance. But it is also due to incomprehension. When Western philosophers look East, they find things they do not understand – not least the fact that the Asian traditions seem to accept, and even endorse, contradictions. Thus we find the great second-century Buddhist philosopher Nagarjuna saying:
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.

An abhorrence of contradiction has been high orthodoxy in the West for more than 2,000 years. Statements such as Nagarjuna’s are therefore wont to produce looks of blank incomprehension, or worse. As Avicenna, the father of Medieval Aristotelianism, declared:
Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.

One can hear similar sentiments, expressed with comparable ferocity, in many faculty common rooms today. Yet Western philosophers are slowly learning to outgrow their parochialism. And help is coming from a most unexpected direction: modern mathematical logic, not a field that is renowned for its tolerance of obscurity.

Let’s start by turning back the clock. It is India in the fifth century BCE, the age of the historical Buddha, and a rather peculiar principle of reasoning appears to be in general use. This principle is called the catuskoti, meaning ‘four corners’. It 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.

We know that the catuskoti was in the air because of certain questions that people asked the Buddha, in exchanges that come down to us in the sutras. Questions such as: what happens to enlightened people after they die? It was commonly assumed that an unenlightened person would keep being reborn, but the whole point of enlightenment was to get out of this vicious circle. And then what? Did you exist, not, both or neither? The Buddha’s disciples clearly expected him to endorse one and only one of these possibilities. This, it appears, was just how people thought.

At around the same time, 5,000km to the west in Ancient Athens, Aristotle was laying the foundations of Western logic along very different lines. Among his innovations were two singularly important rules. One of them was the Principle of Excluded Middle (PEM), which says that every claim must be either true or false with no other options (the Latin name for this rule, tertium non datur, means literally ‘a third is not given’). The other rule was the Principle of Non-Contradiction (PNC): nothing can be both true and false at the same time.

Writing in his Metaphysics, Aristotle defended both of these principles against transgressors such as Heraklitus (nicknamed ‘the Obscure’). Unfortunately, Aristotle’s own arguments are somewhat tortured – to put it mildly – and modern scholars find it difficult even to say what they are supposed to be. Yet Aristotle succeeded in locking the PEM and the PNC into Western orthodoxy, where they have remained ever since. Only a few intrepid spirits, most notably G W F Hegel in the 19th century, ever thought to challenge them. And now many of Aristotle’s intellectual descendants find it very difficult to imagine life without them.

That is why Western thinkers – even those sympathetic to Buddhist thought – have struggled to grasp how something such as the catuskoti might be possible. Never mind a third not being given, here was a fourth – and that fourth was itself a contradiction. How to make sense of that?

Well, contemporary developments in mathematical logic show exactly how to do it. In fact, it’s not hard at all.

At the core of the explanation, one has to grasp a very basic mathematical distinction. I speak of the difference between a relation and a function. A relation is something that relates a certain kind of object to some number of others (zero, one, two, etc). A function, on the other hand, is a special kind of relation that links each such object to exactly one thing. Suppose we are talking about people. Mother of and father of are functions, because every person has exactly one (biological) mother and exactly one father. But son of and daughter of are relations, because parents might have any number of sons and daughters. Functions give a unique output; relations can give any number of outputs. Keep that distinction in mind; we’ll come back to it a lot.

Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false truth values. Normally, and following Aristotle, it is assumed that ‘value of’ is a function: the value of any given assertion is exactly one of true (or T), and false (or F). In this way, the principles of excluded middle (PEM) and non-contradiction (PNC) are built into the mathematics from the start. But they needn’t be.

To get back to something that the Buddha might recognise, all we need to do is make value of into a relation instead of a function. Thus T might be a value of a sentence, as can F, both, or neither. We now have four possibilities: {T}, {F}, {T,F} and { }. The curly brackets, by the way, indicate that we are dealing with sets of truth values rather than individual ones, as befits a relation rather than a function. The last pair of brackets denotes what mathematicians call the empty set: it is a collection with no members, like the set of humans with 17 legs. It would be conventional in mathematics to represent our four values using something called a Hasse diagram, like so:

{T}
↗ ↖
{T, F}      { }
↖ ↗
{F}

Thus the four kotis (corners) of the catuskoti appear before us.

In case this all sounds rather convenient for the purposes of Buddhist apologism, I should mention that the logic I have just described is called First Degree Entailment (FDE). It was originally constructed in the 1960s in an area called relevant logic. Exactly what this is need not concern us, but the US logician Nuel Belnap argued that FDE was a sensible system for databases that might have been fed inconsistent or incomplete information. All of which is to say, it had nothing to do with Buddhism whatsoever.

Even so, you might be wondering how on earth something could be both true and false, or neither true nor false. In fact, the idea that some claims are neither true nor false is a very old one in Western philosophy. None other than Aristotle himself argued for one kind of example. In the somewhat infamous Chapter 9 of De Interpretatione, he claims that contingent statements about the future, such as ‘the first pope in the 22nd century will be African’, are neither true nor false. The future is, as yet, indeterminate. So much for his arguments in the Metaphysics.

The notion that some things might be both true and false is much more unorthodox. But here, too, we can find some plausible examples. Take the notorious ‘paradoxes of self-reference’, the oldest of which, reputedly discovered by Eubulides in the fourth century BCE, is called the Liar Paradox. Here’s its commonest expression:
This statement is false.

Where’s the paradox? If the statement is true, then it is indeed false. But if it is false, well, then it is true. So it seems to be both true and false.

Many similar puzzles turned up at the end of the 19th century, to the dismay of the scholars who were then trying to place mathematics as a whole on solid foundations. It was the leader of these efforts, Bertrand Russell, who in 1901 discovered the most famous such paradox (hence its name, Russell’s Paradox). And it goes like this:

Some sets are members of themselves; the set of all sets, for example, is a set, so it belongs to itself. But some sets are not members of themselves. The set of cats, for example, is not a cat, so it’s not a member of the set of cats. But what about the set of all the sets that are not members of themselves? If it is a member of itself, then it isn’t. But if it isn’t, then it is. It seems that it both is and isn’t. So, goodbye Principle of Non-Contradiction. The catuskoti beckons.

Here you might wish to pause for a brief sanity check. Do scenarios such as these really break the chains of Aristotelian logic? Well, an increasing number of logicians are coming to think so – though matters remain highly contentious. Still, if nothing else, examples of this kind might help to remove the blinkers imposed by what Wittgenstein called ‘a one-sided diet’ of examples. We’ll need to keep those blinkers off as we return to those tricky questions that the Buddha’s disciples asked him. After all, what does happen to an enlightened person after death? Things are going to get only more disconcerting from here on in.

The Buddha, in fact, refused to answer such queries. In some sutras, he just says that they are a waste of time: you don’t need to bother with them to achieve enlightenment. But in other texts there is a suggestion that something more is going on. Though the idea is never really elaborated, there are hints that none of the four possibilities in the catuskoti ‘fits the case’.

For a long time, this riddle lay dormant in Buddhist philosophy. It was only around the second century CE that it was taken up by Nagarjuna, probably the most important and influential Buddhist philosopher after the Buddha himself. Nagarjuna’s writings defined the new version of Buddhism that was emerging at the time: Mahayana. Central to his teachings is the view that things are ‘empty’ (sunya). This does not mean that they are non-existent; only that they are what they are because of how they relate to other things. As the quotation at the beginning of this essay explains, their nature is to have no intrinsic nature (and the task of making precise logical sense of this claim I leave for the reader to ponder; suffice it to say, it can be done).

The most important of Nagarjuna’s writings is the Mulamadhyamakakarika, the ‘Fundamental Verses of the Middle Way’. This is a profound and cryptic book, whose principle theme is precisely that everything is empty. In the course of making his arguments, Nagarjuna often runs through the four cases of the catuskoti. In some places, moreover, he clearly states that there are situations in which none of the four applies. They don’t cover the status of an enlightened person after death, for example.

Why might that be? Nagarjuna’s reasoning is somewhat opaque, but essentially it seems to go something like this. 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.

It is striking how useful his invention proves in the context of Buddhist metaphysics, though Buddhism played no part in inspiring it

We now have a fifth possibility. Let us write the four original possibilities, {T}, {F}, {T, F} and {}, as t, f, b and n, respectively. The way we set things up earlier, value of was a relation and the sets were the possibilities that each statement might relate to. But we could have taken value of as a function and allowed t, f, b and n to be the values that the function can take. And now there is a fifth possible value – none of the above, ineffable, that which lies beyond language. Call it i. (Strictly speaking, it is states of affairs that are ineffable, not claims, so our values have to be thought of as the values of states of affairs; but let us slide over this subtlety.)

If something is ineffable, i, it is certainly neither true nor false. But then how does i differ from n, neither true nor false? If we are looking at individual propositions, it is indeed tricky to discern any difference. However, the contrast comes out quite clearly when we try to join two sentences together.

Look at the sentence ‘Crows can fly and pigs can fly.’ You’ll notice that it is made up of two distinct claims, fused together by the word ‘and’. Expressions that are formed in this way are called conjunctions, and the individual claims that make them up are known as conjuncts. A conjunction is true only if both conjuncts are true. That means it is false if even one conjunct is false. ‘Crows can fly and pigs can fly’, for example, is false as a whole because of the falsity of the second conjunct alone. Similarly, if p is any sentence that is neither true nor false, that means ‘p and pigs can fly’ is false. By contrast, if p is ineffable, then ‘p and pigs can fly’ is ineffable too. After all, if we could express the conjunction, we could express p as well – which we can’t. So i and n behave differently in conjunctions: f trumps n and i trumps f.

What I have just described is an example of a many-valued logic, though not a common one. Such logics were invented by the Polish logician Jan Łukasiewicz in the 1920s. He was motivated, as it happens, by Aristotle’s arguments that contingent statements about the future are neither true nor false. In order to make sense of such claims, Łukasiewicz came up with a third truth value. It is indeed striking how useful his invention proves in the context of Buddhist metaphysics, though once again, Buddhism played no part in inspiring it. His innovation is entirely the product of the Western philosophical tradition.

On the other hand, if Łukasiewicz really wanted to get to grips with Buddhist thought, he shouldn’t have stopped with his many-valued logics. Perhaps you have already seen what’s coming next…

Philosophers in the Mahayana traditions hold some things to be ineffable; but they also explain why they are ineffable, in much the way that I did. Now, you can’t explain why something is ineffable without talking about it. That’s a plain contradiction: talking of the ineffable.

Embarrassing as this predicament might appear, Nagarjuna is far from being the only one stuck in it. The great lodestar of the German Enlightenment, Immanuel Kant, said that there are things one cannot experience (noumena), and that we cannot talk about such things. He also explained why this is so: our concepts apply only to things we can experience. Clearly, he is in the same fix as Nagarjuna. So are two of the greatest 20th-century Western philosophers. Ludwig Wittgenstein claimed that many things can be shown but not said, and wrote a whole book (the Tractatus), explaining what and why. Martin Heidegger made himself famous by asking what Being is, and then spent much of the rest of his life explaining why you can’t even ask this question. 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.

Anyway, what did Nagarjuna make of this problem? Nothing much. He didn’t even comment on it. Perhaps that’s not so surprising: after all, he thought that certain things might be simultaneously true and false. But later Buddhist philosophers did try to wriggle out of it, not least the influential 15th-century Tibetan philosopher, Gorampa.

Pardon? In explaining what they do, are we not talking about them? Well, yes, of course we are

Gorampa was troubled enough by the situation that he attempted to distinguish between two ultimate realities: a real ultimate reality, which is ineffable, and a ‘nominal’ ultimate reality, which is what we end up talking about when we try to talk about the real ultimate. But wait a minute – the nominal ultimate is obviously effable: by definition, it is the reality that we can talk about. In that case, if we say that ultimate reality is ineffable and we are actually talking about the nominal ultimate, what we are saying is false. Thus Gorampa’s proposal refutes itself.

Interestingly, Kant made a similar move. He distinguished between two notions of noumenon, the realm beyond the senses: a positive one and a negative one. According to him, only the negative one is legitimate. We cannot talk about things of this kind; we just need to be aware of them to mark the limit of what we can talk about. Pardon? In explaining what they do, are we not talking about them? Well, yes, of course we are.

The Gorampa/Kant predicament is, in fact, inevitable. If one wishes to explain why something is ineffable, one must refer to it and say something about it. To refer to something else is just to change the subject.

So we have now hit a new problem: the contradiction involved in talking of the ineffable. In a sense, the possibility of a true contradiction is already accommodated by that both option of the catuskoti. (Our Western thinkers could not even say this much.) Alas, our contradiction is of a rather special kind. It requires something to take both the values true and ineffable, which, on the understanding at hand, is impossible. Yet the resources of mathematical logic are not so easily exhausted.

In fact, we have met something like this before. We started with two possible values, T and F. In order to allow things to have both of these values, we simply took value of to be a relation, not a function. Now we have five possible values, t, f, b, n and i, and we assumed that value of was a function that took exactly one of these values. Why not make it a relation instead? That would allow it to relate something to any number of those five values (giving us 32 possibilities, if you count). In this construction, something can relate to both t and i: and so one can say something true about something ineffable after all.

The similarities between this and our Buddhist paradox of ineffability are, you must admit, pretty unnerving

The technique we are using here is called plurivalent logic, and it was invented in the 1980s in connection with the aforementioned paradoxes of self-reference. In fact, one of those paradoxes is not a million miles away from our ineffability predicament. It is called König’s paradox, after the Hungarian mathematician Julius König who wrote it up in 1905, and it concerns ordinals.

Ordinals are numbers that extend the familiar counting numbers, 0, 1, 2, etc, beyond the finite. After we have been through all the finite numbers (of which there is, of course, an infinity), there is a next number, ω, and then a next, ω+1, and so on, forever. These ordinals share an interesting property with the counting numbers: for any set of them, if there are any members at all, there must be a least one. How far, exactly, the ordinals go is a vexed question both mathematically and philosophically. Nevertheless, one fact is beyond dispute: there are many more ordinals than can be referred to using a noun phrase in a language with a finite vocabulary, such as English. This can be shown by a perfectly rigorous mathematical proof.

Now, if there are ordinals that cannot be referred to in this way, it follows that one of them must be less than all the others, for that is true of any collection of ordinals. Consider the phrase ‘the least ordinal that cannot be referred to’. It obviously refers to the number in question. This number, then, both can and cannot be referred to. That’s our paradox. And since it cannot be referred to, one cannot say anything about it. So the facts about it are ineffable; but we can say things about it, such as that it is the least ordinal that can’t be referred to. We have said ineffable things.

The similarities between this and our Buddhist paradox of ineffability are, you must admit, pretty unnerving. But those who developed plurivalent logic were entirely unaware of any Buddhist connections. (I say this with authority, since I was one of them.) Once again, the strange claims of our Buddhist philosophers fall into precise mathematical place.

There is, of course, much more to be said about all these matters. But we have now seen something of the lie of the land. So let me end by stepping back and asking what lessons are to be drawn from all this.

One is a familiar one. 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.

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. 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.’

Read more essays on logic, mathematics and values & beliefs

Comments

  • siddharth

    Excellent article.Beautiful coherent arguments on such diverse disciplines.
    But one point i would like to take up why is it assumed that all the teachings of the eastern Buddhist culture are in contradiction to western philosophical leanings,That sounds like a unwarranted assumption to me.Has there been any study to prove that ?
    Sid

    • Orio14

      I don't think he's saying that all teachings of the eastern Buddhist culture are in contradiction to western philosophical leanings, just that that tends to be the presumption by Westerners.

    • G

      The assumption that Buddhist teachings are either irrelevant to, or in opposition to, Western teachings, started at a time when the respective cultures knew far less about each other. It continued by force of inertia until relatively recently, but I would say that since the 1970s there has been enough cross-cultural knowledge to render it highly obsolete.

      There are still pockets of opposition based largely in a kind of ethnocentrism that holds that Western systems of logic are either superior or fully sufficient unto themselves. One example of a route to that conclusion is via the success of science-based medicine ('SBM'), whose roots are in Western science and thus Western philosophy. Supporters of SBM note the relative lack of strong empirical support for Asian theories of medicine, and then interpolate back from there to the conclusion that Asian philosophy was somehow lacking in comparison to Western philosophy.

      By analogy, 'Country X makes mediocre automobiles, therefore Country X probably doesn't have strong engineering talent.' This is the obvious error of over-generalising, and yet it still occurs.

  • http://jayarava.blogspot.com Jayarava

    The idea that Nāgārjuna is profound is moot, but if I may I'd like to take you back to one of his source texts - in fact the only source text mentioned by name in his Mūlamadhyamakakārikā. In the Kaccānagotta Sutta is a discussion of "right view" - the correct orientation to Buddhism. It begins by denying two extremes: existence (astitā) {T} and non-existence (nāstitā) {F}. Neither of these apply because the "objects" under discussion (mental events) arise in the mind and pass away without ever really existing. So with respect to ontology, not T not F, or { }. But only with respect to ontology. From the start we ought to be aware that Buddhist teachings were never meant to be an ontological theory - they primarily describe the arising and passing away of mental events. Buddhists only became interested in ontology some centuries after the death of the Buddha.

    Nāgārjuna however was writing at a much later time. His world was highly influenced by ontological Realism. This came about through two pressures. Firstly Buddhists had a problem of conditions continuing to function as conditions long after they had ceased (a requirement of the karma doctrine), and a number of suggestions to fix this were put forward. One of the most prominent was that the mental events (cetanā) most closely associated with actions always exist (sarva-asti). Secondly Buddhists used encyclopaedic categorisation of mental events to deconstruct appearances and this led first to fixed categories (defined by an essential quality or svabhāva) and then to the idea that mental events themselves were real and defined by an essence {T}. See particularly the work of Collett Cox on Sarvāstivāda approaches to dharma theory, but also work by David Barstow.

    So Nāgārjuna was writing against a background of Realism and he adopted a rhetorical strategy that first appeared in texts that pre-date him by a century or two, which we might call anti-Realism. Where some Buddhists declared {T}, anti-Realists countered by arguing {not-T} which looks quite similar to {F} but was in fact intended to nudge everyone towards { } *wrt ontology*.

    This is not mere sophistry but has important soteriological consequences for Buddhists. With respect to mental events it's important because our relationship to them determines our experience of life. Most of us see "happiness = pleasure" as the meaning of life and thus pursue pleasure as a means to happiness. This need not be gross hedonism - it might entail all kinds of mundane things like family, career, wealth (anything that makes us feel good). Mental events (such as a pleasant feeling) arise when the conditions are present and quickly cease again when the conditions are not. Since one of the important conditions is *attention* and our attention wanders around rather randomly, the thing we think will make us happy is constantly slipping away from us. Hence experience is equated with disappointment and dissatisfaction (duḥkha). Thus these mental events that are essential to our happiness are {not T not F}: {not F} because we have experiences, but {not T} because experiences are ontologically indeterminate. Experiential insight into just this is what Buddhists believe to be liberating (from the experience of suffering).

    It's not that contradictions end up being true, though that is certainly a popular reading of Nāgārjuna and the Prajñāpāramitā tradition. It's that applied to ontology the Buddhist ideas that describe how the mind works produce contradictions. If we stay in the intended domain (viṣaya), the contradictions don't arise.

    Mental events cannot be described with simple existent/non-existent dualities. The celebrated "Middle Way" is to describe mental events in terms of arising and passing away in dependence on conditions, particularly on the presence of sense objects and sense faculties which between them are said to constitute everything (sarvam), by which we mean, everything of importance to Buddhist soteriology.

    What arises in the mind does not exist in the way that objects of the physical senses exist (we cannot have shared experiences of mental events for example). Nor do they not exist. Nor are the neither existence nor non-existent - we do actually have experiences! Nor can we say that they both exist and not exist. However this last is adopted by Buddhists who couldn't help themselves and strayed into ontology - mapping descriptions of the mind onto descriptions of the world. We call this the Two Truths: something is conventionally true (I am a person) but ultimately untrue (because what I call a person is a momentary collocation of mental events that is constantly changing). But this double-speak is only necessary because we step outside the domain of application of the ideas about mental events.

    As I say once one sorts out which domain ought to be under discussion by Buddhists most of the apparent paradoxes and the need for double-speak like the Two Truths evaporate. But it so happens that religious people like paradoxes and they want to believe that their explanation of mental states is a Theory of Everything. So they keep applying dependent arising to ontology (despite warnings not to) and the paradoxes persist. This train of thought received a considerable boost in the early 20th Century from two translators and commentators that were profoundly influenced by Romanticism: D T Suzuki and Edward Conze (refer to David McMahan's book, The Making of Buddhist Modernism and the chapter on Romanticism as a key influence). They embraced the irrational for various reasons, though with Conze one suspects it was at least partly to piss off the Oxford Dons who insisted on calling him "Mr Conze" as they refused to recognise his German DPhil equivalent.

    So while this is certainly an interesting take on logic and paradox in Buddhism I think that it really only repeats popular misconceptions (popular amongst Buddhists that is). I don't find apologetics for nonsense very helpful and have been writing about the problem for a number of years now (though my publications are so far in other areas). The mainstream of Indian logic is also intolerant of paradox and nonsense. Buddhists were not doing sophisticated plurivalent logic, they were simply confused. It was never profound. And Buddhists never really considered bodhi to be ineffable to start with, indeed the early Buddhist texts have a great deal to say about it - "effing the ineffable" my fellow blogger David Chapman calls it. Even those Buddhists who these days embrace paradox for religious reasons go on incessantly about what enlightenment is like - people might say in principle that enlightenment is ineffable but that doesn't stop them effing away ad nauseum. Now that is a contradiction.

    The fundamental work on unravelling of this misconception was done by Sue Hamilton - see especially "Early Buddhism: A New Approach". It was she who really demonstrated the problems caused by ontology and highlighted the domain of knowledge in which Buddhist thought is both sensible and helpful. In her words "the Buddha was always talking about experience".

    The message of the Buddha was that if you treat mental objects like objects of the physical senses then you will become confused. And this is exactly what happened. Repeatedly.

    I've been discussing these issues on my blog for a few years now, and most recently exploring the Sarvāstivāda Realism which forms the backdrop to Nāgārjuna's anti-Realism. http://jayarava.blogspot.co.uk/

    • G

      Nicely done; though I don't think your points constitute an either/or with respect to Graham's points, or, at minimum, I haven't reflected on them long enough to conclude with any assurance that they do.

      In the end there's convergence on the value of an expansion of philosophy as usually understood in the West, to include other well-developed intellectual traditions such as those that come from Buddhism. Of course this produces areas of agreement and areas of disagreement, all the more so in interaction with mathematics and the sciences. Yet there is great joy in knowing or at least anticipating that our view of 'life, the universe, and everything,' becomes more comprehensive.

      I've marked your blog for further reading.

      • Gino

        Science and religion do not pursue the same purpose. Western positivist vision has improved our ability to control objects but has much depleted our ability to think the being and existence. Consciousness and existence are not objects. A consciousness objectified becomes a simple object, that is, the consciousness and life of anyone. This is to say that one must be very careful when applying the concepts and thought forms suitable for objects (Hipokeimenon) to the phenomena of existence. We can not approach the existence in the same manner of a shoe or a stone.

        • http://jayarava.blogspot.com Jayarava

          Hi Gino, I don't think the Western vision is positivist at all - positivism was always a minority sport. I think perhaps you want to talk about Scientific Rationalism which is something else altogether.

          Who is to say that consciousness is not an object? That's an ontological claim with no epistemological backing. Ditto for existence and anyway Nāgārjuna denies existence (as well as non-existence). so a conversation of his views on that subject will be short.

          I don't think the distinction you want to make between "objects" and "existence" make much sense in any philosophical view, but they are not distinctions relevant to Nāgārjuna. Indeed you seem to have a view that would be considered eternalistic by Buddhist criteria and thus wrong.

          • ApathyNihilism

            "Who is to say that consciousness is not an object? "

            Consciousness can perhaps be "objectified", that is, considered as an object, but that seems to deprive consciousness of its most distinctive feature, the first-person, subject, which appears irreducible to purely objective description.

          • http://jayarava.blogspot.com Jayarava

            There are a number of assumptions about consciousness that are being treated at true without ever being tested. Neuroscientists have been studying consciousness as an object for a few decades now.

            The fact is that since we started sharing jokes and laughing together, maybe a 100,000 years ago, the first-person, subjective aspects of consciousness have been much less interesting and important than the aspects we share. It is shared experience that makes humans interesting as a species.

        • G

          Agreed, science and religion do not pursue the same purpose.

          The purpose of science is to ascertain measurable facts and develop empirically supported theories, having to do with subject matter in the natural universe. The purpose of religion is to develop wisdom related to ultimate questions of existence, meaning, morals, and praxis.

          Each can inform the other in ways that contribute to our wellbeing. (Or, each can attempt to impose upon the other in ways that are inimical to our wellbeing.)

          Here in the USA, science and religion have become polarised via extreme fundamentalism in religion, and a backlash in the form of the New Atheism. This has become highly destructive, for example with the deadlock over climate change. Science tells us that human activity is disrupting global climate; religion _should be_ telling us that we are morally obligated to change our behaviour accordingly, but instead has dug in its heels, perhaps in anticipation of bringing the fundamentalist eschatology into being.

          There is a desperate need to reconcile the worldviews of science and religion, and for religion to evolve beyond crude fundamentalism. Science could help religion to evolve, but for the reciprocal hostility that has led many scientists (and many laypeople who are rationalists or empiricists) to deprecate the value of religion altogether, rather than parsing its more progressive elements from its more primitive ones. Religion could help science to grapple with issues of values, but for the hostility that its more primitive elements have stirred up with the science community.

          Graham's article is one example of precisely what is needed to reconcile worldviews and promote a spirit of mutuality between them. While it won't directly stop those who would blow up womens' clinics or buses full of passengers, it contributes to the rise of a worldview in which science and religion both contribute to the common good rather than fighting each other at our collective expense.

        • Christy Sands

          "This is to say that one must be very careful when applying the concepts and thought forms suitable for objects (Hipokeimenon) to the phenomena of existence."

          I would also say one must be careful when applying thought forms suitable to existence to objects. Imo, it's important to find a balance between realism and anti-realism.

    • Eric Zsebenyi

      Surely Conze embraced contradiction not out of a Romantic impulse, but from the influence of Marxism on his interpretation of the Mahayana, and from the thought of various other philosophers through the ages who practiced what Conze called dialectical, as opposed to formal, logic. See, for example, "Contradictions in Buddhist Thought" in Lamotte's festschrift. Also, Conze wrote Der Satz vom Widerspruch several years before the indignities inflicted upon him by the Oxford Dons, so perhaps his idiosyncratic view of the principle of contradiction derived from something more fundamental in his nature than irascibility.

      • http://jayarava.blogspot.com Jayarava

        Hi Eric, I respect your opinion, you know Conze better than I do. But I find McMahan's characterisation of him as a Romantic fits with what I do know. His Prajñāpāramitā commentaries reek of it. And Marxism too has a touch of the Romantic about it, so I don't see that as disqualifying him.

        I want to take him seriously, but frankly dealing with his work makes it difficult. I hope to touch on this in a forthcoming publication with respect to errors in his Sanskrit Heart Sutra edition, but the wheels grind slowly.

        • Eric Zsebenyi

          I never thought of Marxism as Romantic (in fact, quite the opposite), though I suppose the humanist inclinations of Marx and Engels qualify to some extent.

          McMahan's book has been on my reading list, and has now moved to the top.

          I look forward to reading your forthcoming publications. I'm especially interested to know the specific examples of the scent of Romanticism you detect in Conze's Prajñāpāramitā commentaries.

          • http://jayarava.blogspot.com Jayarava

            Romanticism focusse on emotion rather than intellect - a reaction against the classical scientific rationalism of the 19th century (pre-quantum, pre-relativity). Indeed Romantics are rather anti-intellectual. Reason is a poor tool for exploring truth. It's explicitly vitalist. Mind/body dualistic - the idea of the pure spirit is central. And Romantics embraced the irrational - a lot of the Romantic poets were out of their skulls on drugs a lot of the time. It emphasises individual, personal experience, but interprets experience as ineffable - expressible perhaps in artistic expression and in imagery but not in prose. It's also associated with German Idealism.

            Conze embracing of the irrational reading of Prajñāpāramitā was pretty consistent with all of this. His assertion of Absolute truths, anti-intellectualism, and emphasis on esoteric nature of the teachings - that the truths he hints that he as access to cannot be put into words (and yet as far as I know he had no direct Buddhist teacher!).

            Drop me a line when you've read McMahan - I'll be interested to know what you make of it.

    • http://www.executivemandala.com.au Simon Mundy

      Thank You Jaya! I've been stumbling towards this understanding of these confusions (Buddhism talking about mental events v ontology) for a couple of years now and your sometimes hilarious discussion above is most welcome.

  • Michael

    'How can contradictions be true? What’s all this talk of ineffability? This is all nonsense.'

    This is hardly news to western thought. The Christian God is supposed to be ineffable but Christians have been writing and editing his profile for centuries.

    • http://jayarava.blogspot.com Jayarava

      effing the ineffable :-)

  • notmike64

    its all about the grey ..or gray or is it all black and white...there is beauty in the break down ...

  • http://wildernessvagabonds.com/ Mike Lewinski

    Nagarjuna’s writings defined the new version of Buddhism that was emerging at the time: Mahayana. Central to his teachings is the view that things are ‘empty’ (sunya). This does not mean that they are non-existent; only that they are what they are because of how they relate to other things. As the quotation at the beginning of this essay explains, their nature is to have no intrinsic nature (and the task of making precise logical sense of this claim I leave for the reader to ponder; suffice it to say, it can be done).

    I think I got part of this while pondering my own version of the Liar's Paradox, where instead of This statement is false I substituted I am a liar.

    I could see the way that identity and behavior intercreate each other. By taking on the identity 'liar' then lying becomes not just permissible but the foundation of my identity.

    Yet it is impossible to lie all the time as my modified paradox shows. By admitting myself as a liar I tell the truth and corrode the truth value while not wholly negating it. Am I still a liar while I tell the truth about being a liar?

    I came eventually to see that, of the idea that identity and behavior create each other, identity is largely an illusion. There's only the behavior, the relating to other things.

    • http://jayarava.blogspot.com Jayarava

      The trouble is that the liars paradox is not very profound. It's a quirk of language and not much more. The days of language tricks masquerading as philosophy are pretty much over.

      In practice no one lies all the time and no on tells the truth all the time. So the liars paradox tells us nothing about the real world.

      • G

        'The days of language tricks masquerading as philosophy are pretty much over.' That's good to hear, and I've observed similarly.

        • http://jayarava.blogspot.com Jayarava

          Given what the guy in this thread is writing, language games are far from dead.

          • G

            That's what turned me off to academic philosophy when I was an undergrad: it all seemed to be about logic games with words, and lacked a grounding in observables. Whereas I've always been something of a mongrel between empiricism and mysticism (defined respectively and briefly as: discernment of the facts of nature via observation and hypothesis-testing; and, direct engagement with the ground of being; in Huxley's terms I'm a contemplative).

            But the situation with philosophy seems to have changed over the past 20 years, for example with folks such as David Chalmers who take empirical methods and findings into account. We also see the rise of new philosophical outlooks based largely in current science, notably in physics & astrophysics, for example Max Tegmark's stuff about the multiverse and the limits of observation, and the implications of various schools of physics and computer science on the issue of free will. I'm interested to know what you think of all this.

          • http://jayarava.blogspot.com Jayarava

            When we talk about "the multiverse" what we actually mean is an abstract mathematical implication of string theory which has no practical reality that we can possible imagine, and which predicts no communication between universes. I don't see how this kind of speculation is relevant to the task at hand, or different from other kinds of metaphysical speculation.

            I'm not familiar with Tegmark, but I've been reading Patricia Churchland on the brain and mind. She's extremely doubtful about the idea that we do not have free will - very doubtful about this interpretation of the results of neural studies (and she is the neuroscientists neuroscientist). She points out that we unequivocally have self-control, that we do not act on every urge that we have. And that in many ways this is more important than free will. Free will is primarily a problem for theologians trying to explain the problem of evil. I'm not convinced that free will is even an interesting problem. From a Buddhist point of view we have a certain amount of influence over our actions, largely through self-control, to the extent to which we are conscious of the process of responding to stimulus - a view informed by spending a lot of time in samādhi (not me, but I do know people who do).

            I think most people misunderstand quantum mechanics and don't realise it. Having studied quantum mechanics I'm at least aware that I do not understand it! I've written one blog on this and plan one or more follow ups quite soon. First essay is "Erwin Schrödinger Didn't Have a Cat" http://jayarava.blogspot.co.uk/2010/10/erwin-schrodinger-didnt-have-cat.html I've sketched out an essay on how we misunderstand the role of the "observer" in quantum physics which I plan to put on my blog in a few weeks.

            I agree that philosophy has changed. I find Thomas Metzinger quite informative and useful. I also find George Lakoff and Mark Johnson's work on metaphor and embodied cognition useful. But most Buddhists seem not to get beyond either Nietzsche or Schopenhauer. Their views of science are even more archaic which is a bit depressing.

          • G

            Agreed, multiverse theory has thus far been unfalsifiable, for which reason I haven't paid it much attention until recently. Lately it appears that there may be some testable implications, and Tegmark is on the trail of those. That makes it interesting in a scientific sense. I'll admit I do take an interest in metaphysics in the sense of frameworks for organising our knowledge and making inferences.

            'The task at hand' as I understand it, traditionally and to this day, is concerned with enlightened mind and compassionate action. Long story made short, the way I take the commitment to work for the enlightenment of all sentient beings, is to work for the conditions that enable all persons to seek enlightenment if they so choose. That also translates to a commitment to sustainability, as the physical precondition for all else is that we have a world in which we can live, and that living must be more than a struggle for survival in a social darwinist culture that arises from the consequences of the lack of sustainability.

            Per Feynman, nobody really understands QM; and yet even those of us without adequate maths background can understand the words written by scientists, so we can begin to approach the subject. I'm also presently reading Schrödinger (_What is Life?_), whose views about certain things seem surprisingly similar to mine. I've got your essay open in another page that I'll be reading shortly.

            I'll also be looking up Churchland and Metzinger, I have some bare familiarity with Lakoff, and I'll look up Johnson as well.

            I'm inclined to believe that the issue of free will is important for reasons in addition to the issue of morality. If the predominant cultural attitude is that free will is illusory, that attitude legitimises all manner of manipulation of others, and control-based paradigms of government and economics. Keyword search 'nudge' and read up: the stuff is utterly chilling.

            However it would appear that work by Brembs et.al., by Hameroff et.al., and others, points toward a neurological basis for free will, which supports the cultural attitudes that make for respect for free will, and also make the idea of _good will_ truly meaningful and operative. To be clear, I'm not arguing ontology based on consequentialism: 'nature goes along her way, regardless of what humans say,' and ours isn't to wish facts away but to use them as the strong foundation for building something good and worthwhile. In the end, based on Brembs, Hameroff, and others, it would appear that the facts of nature support free will and thus lead to the cultural attitudes that arise from it. (Also to be clear, I am not advocating for Neitzsche, much less for Ayn Rand, or anything in that part of the spectrum.)

            One of the important benefits of mindfulness is, as you said, becoming conscious of the process of responding to stimuli. That necessarily entails an increase in self-control, and I would say it also entails an expansion of the scope of free will: not only in choosing to not-do harm, but in choosing to do good wherever possible, and act with compassion rather than reacting with whatever impulse might be at hand.

            More later, I'm going to read your item on Schrödinger now and copy the rest of those references to my look-up list. If you have an email address on your website I'll be in touch via email so we can continue whatever of this you might find interesting, via means that aren't subject to the technical quirks of this webpage.

          • Andy Smith

            Churchland admits outfront that the traditional notion of free will--something independent of the brain able to transcend the laws of biological causality--is dead. The problem is that the traditional view is what most people have in mind when they argue for free will. What she calls self-control is clearly not free will in this sense. It's built up from causal events like everything else.

            I think it might be useful to distinguish "freedom to" from "freedom from". If everything is cause and effect (some things may be truly random, but that is not free will, either), then we can't say we have freedom to do anything. Indeed, what we call "we" or "I" is as much a product of causation as everything else. There is no freedom of choice.

            OTOH, we can say that we have freedom from. We are free from the traditional consequences of many environmental factors. This is what makes us so different from other organisms. Much of this kind of freedom is the result of evolution and development, and further freedom in this sense may be possible through certain individual actions--even though we don't choose these actions freely.

            I use an analogy with weather (it can be an actual example, but is better as an analogy). For the most part, we can't control the weather. We can't choose whether it will rain or not. But we are most of the time free from most of the consequences of rain. It does not for most people most of the time have much effect on what they do. Again, what they do is not freely chosen, but it is freer in this sense than it used to be. For those of you familiar with Dennett's Freedom Evolves, I would say this is the kind of freedom he's talking about. And I think one could say it's more or less the same as Churchland's self-control, as well.

          • http://jayarava.blogspot.com Jayarava

            "With some disappointment, I am bound to say that I suspect that the claim that free will is an illusion is often made in haste, in ignorance, and with an eye for the headline and the bottom line" (Churchland. Touching a Nerve. p.185 - see also previous para)

            The distinction she makes between Kantian contra-causal free will and causal free will is very useful. Contra-causal free will was bad philosophy to start with. But I don't think this is what Theologians had in mind when they started arguing about free will as a solution to the Problem of Evil. So it seems to me that your "traditional" freewill is a rather obscure way of putting it. Which tradition?

          • Andy Smith

            Well, why don’t you just ask yourself what you mean when you
            claim you or someone else has free will. Maybe we could go from there.

            As I said before, the problem begins with the assumption that there is an “I” that is choosing among various forms of behavior. But the modern scientific view, which Churchland pretty clearly subscribes to, is that “I” itself is a product of causes. “I” in fact is not distinct from the behavior.A choice is being made, but I don't see where the notion of freedom comes in if everything is causal.

          • http://jayarava.blogspot.com Jayarava

            Actually I'm not very interested in the issue of "free will" as I see most people try to frame the discussion - even Churchland, though she is more interesting than most.

            We clearly have will, because as you say we make choices. The question is then to what extent is will a contributor to decision making. Or even what contributes to experiencing a decision as willed, since a lot of willing is unconscious and automatic.

            The idea that because behaviour has causes that this eliminates the role of will in behaviour is ludicrous. Will is a cause of behaviour. Clearly it is not the sole cause, but then why would we look for simplistic causes for something as complex as human behaviour?

            A choice implies degrees of freedom. Or it is not a choice. A decision implies some exertion of will. Or it is not a decision.

          • Andy Smith

            What do you mean by will? The scientific WV strongly implies that will, whatever it is or means to someone, is just another product of causes. In that view, what is commonly called will is just a particular cause or set of causes that is very strong, so it overrules other causes, which in that situation and with other individuals, may have more of an effect on the outcome.

            I agree that a choice implies degrees of freedom, the question is who or what isn exercising this choice. A choice is made when an animal does one thing instead of another, or for that matter, when the weather manifests in one way rather than another.

            When you say a decision implies some exertion of will, I think you mean a human decision, rather than a decision in a much broader sense. But again, the decision is the result of various causes.

            I'll admit i find it strange that people who are interested in mediation should be arguing about free will, since one of the very first lessons of the practice is that we in fact don't have free will. Indeed, that realization is often what compels someone into this life in the first place.

          • http://jayarava.blogspot.com Jayarava

            I'm not sure what you mean by the first lesson of practice being that we don't have free will. This is definitely *not* the first less of Buddhist meditation. It's not a Buddhist view *at any stage*. Buddhism, and Buddhist meditation, is predicated on the notion that each sentient being is capable of making choices. Whether we are free to or not is a separate issue, we do have the capability.

            Buddhists view morally significant action as motivated by a decision to act. This encompasses some unconscious actions, but only when there is an unconscious decision. An accident doesn't count. The initial goal is to bring decision making more into consciousness so as to gain more freedom to decide.

            A decision to act may not be very free. People who are unreflective may well make many unconscious decisions based on neurotic grasping or aversion. Most people are blindly driven by greed and hatred, but even though decisions are blind and unconscious they are still decisions, and thus still morally significant.

            The metaphysical problem for Buddhists is explaining this in the absence of a metaphysical self. Of course we all have a first-person perspective on our own mental states. But Buddhists argue that there is no entity which observes, no life essence, no self. (Similar to the Damasio school of thought on the self, including Thomas Metzinger). Decisions are made, but there is no one who decides.

            Buddhists say that all experiences - including the experience of being "someone" - only arise when the conditions are in place. Consciousness is a process not an entity. Always consciousness of (something or other). Teaching morality is often done in a pragmatic way however - "your" actions rebound on "you". Such ideas are apparently unnecessary for people with insight.

            Of course there are other meditative traditions, but Buddhism always assumes the capacity to make decisions and carry out willed actions. Whether than capacity is conscious or unconscious is to some extent up to us. We can be more or less mindful of decisions.

          • Andy Smith

            I’m talking about meditation, not Buddhist philosophy, which may or may not understand meditation. Of course, people are free to define meditation in different ways, and frequently do, but the process I’m talking about has enough in common with what most Buddhists do or say they are doing or trying to do that I believe it’s their goal. I can’t of course prove that this process will show you that you have no free will, but it’s something I’m every bit of certain as the sun coming up tomorrow. This kind of knowledge is not something I can debate the fine points about. It’s literally a matter of life and death for me. But you have to get a certain ways before you can’t go back and your life is on the line.

            This knowledge is quite different from, though confirms in this case, the scientific understanding of causality that comes to the same conclusion. From the latter point of view, it isn’t just that we don’t have free will. The concept is incoherent. It makes no sense in a world of causality. The only point in doing anything is because of a certain expected outcome, and this is just another way of saying, in response to certain causes.

            The distinction between conscious and unconscious actions is often appealed to in arguments about free will, but just because a decision is conscious, or very slightly conscious in the usual case, does not make it free. Awakening or becoming conscious means becoming more aware of the fact that we are not free, not more capable of acting freely (again, in the sense of choosing one act over another).

            Awakening is associated with a self or observer that is aware of the ordinary selves. It’s certainly nothing like any of these ordinary selves, and maybe self is not the best term for it. But it represents the only way of observing mental states without the use of still other mental states. It's not introspection, which is simply thinking about thinking.

          • http://jayarava.blogspot.com Jayarava

            "but the process I’m talking about has enough in common with what most Buddhists do or say they are doing or trying to do that I believe it’s their goal"

            And as a Buddhist of 20 years, ordained 9 years, and a peer-reviewed published author on Buddhist ideas, I'm telling you, you are wrong. Just wrong. About Buddhism anyway. And your Vedanta style views on meditation are not my cup of tea. I know Gary Weber and other Vedantins deny free will, and they are free to do so in my book, but that view has nothing in common with the goals of Buddhism.

            I think our conversation naturally concludes here. Or at least I choose not to respond further. Make of that what you will.

      • http://wildernessvagabonds.com/ Mike Lewinski

        It doesn't have to be profound to be useful. Consider a related claim with a broader scope: "there are no universal truths". Someone might try to build an epistemology around this, except it apparently negates itself in a way very much like the liar's paradox. It purports to be a universal truth, right? Can we dismiss this claim on that basis alone with no further consideration? Or does it lead us into the problem of induction?

        As formulated in "this statement is false" we can examine this class of self-negating statements in the most narrow possible sense. We don't have to look outside of it as we might in "there are no universal truths". The latter might actually be true in all cases, except of itself.

        Expanding from there, we have Heraclitus, translated variously:

        "Nothing endures but change"
        "Change is the only constant"
        "It is in changing that things find repose."

        He was at least wise enough to put this in a way so as to provide the exception not given in "there are no universal truths". Whether this meets your bar for profundity or not, it helps illuminate the larger problems of epistemology.

        • http://jayarava.blogspot.com Jayarava

          Mike. I'm not finding anything useful or profound in what you've written. It's not grounded in experience and has no practical implications that I can see.

          Sure everything changes, but so what? Heraclitus strikes me as rather pedestrian. Any twelve year old can tell you that everything changes.

          Take half an hour, sit completely still and follow the sensations of breathing with uninterrupted attention, not allowing your mind to drift or wander. If your attention is undivided and unbroken for just 30 minutes, you will have an experience which may interest you. It may take some practice to achieve unbroken concentration for that long. (Don't try it without qualified help if you suffer from what these days is called "mental illness").

          Buddhism is primarily about that kind of experience. The most astute Buddhist thinkers had no interest in "the world" changing, except perhaps as a metaphor for the main event - the arising and passing away of mental states. It's the change in experience itself that interests us.

          Thinking about it is insufficient.

          • http://wildernessvagabonds.com/ Mike Lewinski

            We have different goals for philosophy and that's fine.

          • http://jayarava.blogspot.com Jayarava

            Chicken?

          • http://wildernessvagabonds.com/ Mike Lewinski

            This attempted insult harms your cause and sets a bad example here. It is particularly unfortunate in the context of this article about the conciliation of eastern and western thought.

            Philosophy is not a zero-sum pursuit. Your goals are not mutually exclusive of mine. I'm most interested in logic and epistemology: how do we know what we know? I care about these things as part of my effort to refine my own critical thinking skills. A healthy democracy requires not just informed voters, but critical thinkers who vet the information they receive carefully.

            The problem of induction touches on just about every major social issue that science can inform, such as abortion, gun control, gay rights, marijuana legalization, GMO food labels, water fluoridation and more. If voters don't understand the limitations of the sources of knowledge, they might incorrectly believe that science can definitively tell us when a human life begins, or whether GMO foods, marijuana or fluoride can be "proven" safe. Bad information can produce bad policies. Uncritical thinkers are more susceptible to propaganda. I have an interest in scientific skepticism as a path to more rigorous evaluation of evidence in pursuit of the best possible political choices I can make.

            The liar's paradox is not taught as profundity, but rather as an aid to exploring issues related to epistemology, including the problem of induction. It is almost certain that it will continue to exist in curricula because it has value, not as profundity but as an example in a class of self-negating paradoxical statements. That it may be mentioned in a course on logic doesn't infringe on the ability of students to learn meditation techniques in a course on Buddhism.

            The study of logic and epistemology are valid methods of self improvement in and of themselves. They also have practical applications both to democracy as a whole as well as to the individual pursuit of happiness. That you may not appreciate it the way I do doesn't make it less practically useful to me or less important to healthy democracy.

            Your previous posts contain some unwarranted assumptions about my practices and beliefs. I'm not offering you the suggestion to take a logic course because for all I know you already have but didn't obtain the same value from it as I have. That's OK. We have different goals for philosophy and that's fine.

          • http://jayarava.blogspot.com Jayarava

            It's not an attempted insult. It's a challenge - interrogative mood, not imperative. As you say philosophy is not a zero-sum game. You have nothing to lose by exploring new approaches or having new experiences. Since the topic under discussion is Nāgārjuna, lest we forget, it seems relevant that you at least give some thought to his views which would have been grounded in the kind of exercise I suggested.

            That you dismiss it out of hand makes me wonder why. That's all. But you seem not to be interested in Nāgārjuna and his methods. In which case aren't you commenting on the wrong thread?

          • Greg Fatbert

            Pompous?

          • zubinwadia

            or Egg?

          • G

            Nicely done. 'Sit still and observe (if you can)' is a subtle challenge that most people today will find as difficult as, or more so than, physical training exercises of the kind required in the military.

            Question, and this is an important issue to me: What do you make of the continued reinforcement of completely fragmented attention by various factors of the modern economy? Here I'm thinking of relentless multi-tasking, and of the way advertising and consumerism encourage impulsiveness. To my mind this is as dangerous to humanity's collective future as promoting anti-vaccination conspiracy theories, if not more so: we need to reduce consumption impacts in order to reduce climate impact, or we are headed for a cliff at high speed.

            How can we go about promoting, in the culture at-large, the ideas and practices that lead people to value attention and in particular value the deliberate focus of attention more than the popular scatterbrain mindset? 'You will have an experience that may interest you' is a truly brilliant way of saying this one-to-one; would that also apply to reaching a wide audience?

          • http://jayarava.blogspot.com Jayarava

            I think there is a war going on for our attention. And it's driving us mad. Personally I avoid advertising as much as possible.

            I think the ideas are being promoted quite effectively in the form of Kabat-Zin style Mindfulness - yesterday the UK reported that an all party working group of commons MPs, peers and senior civil servants met in the Parliament buildings to learn about the techniques and start to put them into practice. Converting the leadership has always been the key to establishing Buddhist ideas and techniques in the past. I suspect the same is true now.

          • G

            Most interesting. 'Kabat-Zin,' keyword search coming right up, or if you have any URLs to suggest, I'm all ears (with a couple of exceptions: I don't do Facebook-anything or Google-anything, due to work-related security rules).

            Agreed re. adverts, though I find advertising to be an interesting cultural medium in an abstract sense (akin to studying sociology or clinical psych). I've also got my blocking software turned up to 11 and I don't much watch the telly (perhaps a few hours a year).

            You have a lot of good and and well-thought-out ideas and perspectives, so I'm going to start reading your blog and would like to get in touch via email if possible. If you have a contact address or form on your site I'll pop up in your inbox;-) otherwise I can post one of my public email addresses to start out, though I'll have to post it in small pieces to prevent it getting harvested by spam bots.

          • http://jayarava.blogspot.com Jayarava

            My email is on my blog website - on the right. basically [myname]@gmail.com

      • David Krueger

        I absolutely disagree. In my mathematical logic class, we used a variant ("this statement cannot be proved") to prove Godel's incompleteness theorem.

        Simply put, the idea is to encode provable mathematical theorems as words in a language, and see if the quoted statement is a valid word of the language.

        If it is, then the language is inconsistent, because it proves a false statement.

        If it is not, then the language is incomplete, because it does not contain a proof for a certain true statement.

        While there's a bit more too it than that, this sort of self-referential contradiction is at the heart of the proof.

        I consider this to be one of most philosophically important mathematical ideas. I believe this is a popular opinion among mathematicians.

        Mathematics is abstract and it is debatable how directly it applies to reality, but I think it is clear that it does apply in some very useful ways.

        • http://jayarava.blogspot.com Jayarava

          "Mathematics is abstract and it is debatable how directly it applies to reality, but I think it is clear that it does apply in some very useful ways."

          Could you give an example of a practical consequence of this? Something useful?

          thanks

    • G

      Identity also assumes the existence of a singular and unified personality, which is questionable at best. 'The self' may be another example of 'personification,' just as the Abrahamic traditions 'personify' the deity, or various pagan traditions 'personify' elements of nature.

      We evolved to recognise faces and similar patterns that denoted various types of 'persons' with agency, such as animals we sought to eat, and animals that sought to eat us. The personal and darwinian cost of failing to recognise the face of a predatory animal in a tree (false negative), is higher than that of imputing personhood to a pattern that turns out to only be the way the sunlight is reflected through leaves and branches (false positive).

      From an agnostic perspective one can ask 'is the deity real?', and similarly one can ask 'is the self real?'

      As for the person who says 'I am a liar,' I would understand that to mean that the person lies with much greater frequency than normal, rather than that every statement they make is a lie. Human behaviour is very often probabilistic rather than rigidly determined, so this would be a safe guess.

  • http://vaickerviews.wordpress.com DPV

    Why does eastern philosophy seek to validate itself by the truths uncovered by the Western thinkers? Conversely, how does it become “invalid”,an “embarrassment” or “the strange claims of our Buddhist philosophers”, if eastern concepts had no counterparts in the West? And, therefore could be regarded as suspect, or dismissed as “mystical”? Or worse, why does it have to be that such western thoughts are also regarded as suspect if it had been originally inspired by the East? The author seems to be very particular about emphasizing their separate/ independent origins again and again.

    The essay is less about Buddhist logic than an apologia for it ; a kind of groveling appeal before the West to let it in – as, according to the author, it seems that it is being kept out by “high orthodoxy in the West ”. In this he seems to go “all the way”

    Overall, it is so embarrassing to find Buddhist logic being introduced thus.

    • Gene Linet

      Who is seeking validation from Westerners? It's rather Priest, in his distinctly Western/analytic style, who feels the need to parse Buddhism into some kind of calculus. The notion of consistency and is less relevant to Easterners, I suspect. As the old saying goes, "When the sage points at the moon, all the idiot sees is the finger."

      • http://vaickerviews.wordpress.com DPV

        Even when the sage points to the moon, I would still want to look at his finger to make sure what he is pointing at – at the risk of being called an idiot. I would want to know which moon the finger is pointing toward; or whether he points to the moon or a star ; or whether the finger points downwards at the ground ; or whether he is pointing backwards towards himself; or whether he is pointing towards a million other things that exist. The point is I am not comfortable
        with what the sage says is the moon and when you start off from such a position of doubt there are endless possibilities, all of them have to start off with the direction of the finger.

        While the others seem to be delving into the intricacies and discussing the finer points, it might seem odd that I want to spoil all that by the seemingly petty issues that I want to drag in.

        Nonetheless,it is important to bring it to everybody’s attention.

        Mr.Graham Priest starts off with the premise that “Asian
        traditions seem to accept, and even endorse, contradictions “, they are mystical and inconsistent. He goes on to establish that at least some of them can be redeemed. How? Why? Simply because
        the West thinks so.

        Mr.Priest opens his essay with the most well known of the
        Buddhist philosophers Nagarjuna by saying that his thoughts produce “blank incomprehension”. Think about it, it is like blaming Einstein for being abstruse just because you do not understand his theory.

        What gives Mr.Priest the special privilege to pick up or dump
        an idea of eastern thought? It is exactly what Edwards Said had argued against in his book on Orientalism.

        Further, Mr.Priest gives the impression of being ever so conscious
        of a reverential orthodoxy in the west and is eager to measure up to them. This orthodoxy has the ultimate authority of picking up the Eastern thoughts selectively and put them on the pedestal. The criterion? They are as absurd and arbitrary as Mr.Priest’s . At the end of the day, Eastern thoughts are presented as poor copies of the West or as Edward Said put it as “surrogates” or “an underground self” but never granted the legitimacy they deserved.

        What irked me the most was the way the author took a revered
        Buddhist thinker and presented him in such a cavalier manner as representative of Eastern thought.

        If he was so interested in presenting the views and ideas of
        Eastern thought, there are other less contentious ways. But if this is the way Mr.Priest wants to do it, then, most of Eastern thought would be out of bounds of the world because it would be difficult to find ‘equivalents’ that can validate and present them as acceptable.

        To the incomprehensibility of Narayana’s statements, he was
        only merely presenting his observations as best as he could. To start off by saying that he was hopelessly incomprehensible and contradictory, and then to redeem him by pointing to recent and similar predicament of Western thinkers is being too patronizing.

        But even then, a careful distance was maintained and from
        identifying too closely with the Eastern thought, as can be seen from the following statements:

        “It is indeed striking how useful his invention proves in the context of Buddhist metaphysics, though once again, Buddhism played no part in inspiring it. His innovation is entirely the product of the Western philosophical tradition.”

        “But those who developed plurivalent logic were entirely unaware of any Buddhist connections. (I say this with authority, since
        I was one of them.) Once again, the strange claims of our Buddhist philosophers fall into precise mathematical place.”

        If Mr.Priest’s intention is to enlighten the world about the
        wonders of the Buddhist logic, I do not see any evidence of it in the
        essay. What happens is that some of the great thinkers are dragged and made to look as perfect idiots just because some in the “western orthodoxy” think that their ideas are “suspect”. It does not enter the mind of Mr.Priest that intellectual integrity of an established thinker
        whether eastern or western cannot be questioned thus. You do not expect them to stoop down to the level of making incoherent and contradictory statements just to get attention. Their integrity would not allow them to do it. But it seems such a proposition only
        applies to Western thinkers.

        • Gene Linet

          I think you're right, if I understand you correctly. The assumption in this article is that Buddhism is "problematic", and therefore needs to be "redeemed" or at least in some way "explained"... specifically through Western exegesis. But it misses the point. From the Eastern POV contradiction is not a problem at all. If anything, it is intended to "trip you out" of the analytic mindset and to focus your attention away from the language itself. If you were to start drawing charts to explain zen koans you'd probably get laughed at... and deservedly so.

          • http://vaickerviews.wordpress.com DPV

            This is the first time I am hearing about this “trip you out”. But let us stick to well established practices and not delve on some deviants.

            That is the problem that usually happens when you start evaluating other distant cultures; you are easily tempted to develop stereotypes with some shockingly outlandish
            practices that readily draws your attention as your feeds. As this article shows, even academics are not exempt from it.

            In the interest of developing a genuine focus (on any subject) and accumulate reputable literature of it, it is always advisable to keep away from these pitfalls.Otherwise, you end up losing momentum and discredit not only yourself but also bring a bad name to the subject you study – which I am sure is not your original intention.

            Let us end this argument with hope on that front.

  • ShakaUVM

    Bart Kosko has a better way of dealing with paradox than the paraconsistent logics that Priest prefers. Fuzzy Logic discards the Principle of the Excluded Middle, but retains the Principle of Non-Contradiction. When you allow true to equal false, as Priest does, you indeed do not suffer problems with paradoxes, but your logic can also be used to prove anything is true, and so is empty and useless.

    Instead of looking at just four or five possible values of truth, Fuzzy Logic allows all truth values along a closed continuum between 0 (false) and 1 (truth). This allows us to express the truth value T for statements like "This statement is a lie" as T = 1 - T. Solving for T, we see its truth value is 0.5.

    But Fuzzy Logic is a consistent logic, and so it does not run into the empty and useless problems that paraconsistent logics do, and so is completely superior.

    I highly recommend reading Kosko's philosophical papers on Fuzzy Logic, which were, apropos to this subject, inspired by his Buddhist philosophy. (Sorry, Priest, but not all people working on multivariate logic in the 80s were non-Buddhists.)

    • LittleFuzzy

      "When you allow true to equal false, as Priest does, you indeed do not suffer problems with paradoxes, but your logic can also be used to prove anything is true, and so is empty and useless."

      This is false. Paraconsistent logics avoid explosion (this is in fact, a part of their definition). I don't have an opinion about whether or not fuzzy logics are preferable, but your reason for dismissing paraconsistent logics is simply false and would require a minimal amount of research on them to correct.

      You can read more about it here: http://plato.stanford.edu/entries/logic-paraconsistent/

      • ShakaUVM

        Allowing "both true and false" as an option is not the same as saying true equals false, which is what Priest is using in his proof here. If you allow 1 to equal 0, you can literally prove any statement, and trying to argue that it doesn't contradicts mathematics.

        • SomeLogic!

          I'd disagree with that! You can't/won't just go proving things willy nilly like that at random levels in these logics - LittleFuzzy is right that these logics specifically are built to avoid "explosion" (you can read about that on wikipedia) which is the relevant equivalent to "can prove any statement from a contradiction" that matters in the logic here. (It's probably true that your statements like "A&~A" might not be useful for proving anything interesting when used alone, but they won't break your whole system because you can't take them out of context). Source: concentrated in mathematical logic at Brown U.

  • Matt O’Brien

    Very interesting article, Professor. I also enjoyed learning non-classical logic from your book in grad school.

    "So we have now hit a new problem: the contradiction involved in talking of the ineffable."

    "Consider the phrase ‘the least ordinal that cannot be referred to’. It obviously refers to the number in question. This number, then, both can and cannot be referred to. That’s our paradox. And since it cannot be referred to, one cannot say anything about it. So the facts about it are ineffable; but we can say things about it, such as that it is the least ordinal that can’t be referred to. We have said ineffable things."

    I'm not sure that I see the paradox in making claims about ineffable things. Actually, I'm not sure I understand what an ineffable thing is supposed to be.

    It seems to me that we talk about ineffable things all the time. 'Blue' is in some sense ineffable. Take Frank Jackson's example. http://plato.stanford.edu/entries/qualia-knowledge/#2. Suppose Mary is a brilliant neuroscientist who has been raised for her entire life in a black-and-white room, wearing googles that allow only shades-of-gray stimulation of her retinas. Suppose further that she has learned every piece of scientific knowledge there is to know about light and colors and human visual processing. Still, she's never actually experienced blue. Given this setup, there seems to be nothing I can say to her which will give her that last piece of understanding. And yet, I talk about blue all the time, and I can even talk about it with Mary.

    The Mary example, in my view, isn't a special case. Every concept that we think about and refer to in speech is handled by the brain as an array of associations. Your associations with the term "London" might have a lot of analogs to my associations with the term "London", but I have had experiences of London that you haven't had, and vice versa.

    For any concept, we each have our own idiosyncratic nest of associations that gives life to that concept in our own mental world. We can only hope that there's enough 'overlap' between our individual understandings that when we communicate, we'll share a mutual understanding sufficient for the purposes at hand.

    I’m not sure by what principle(s) we would privilege some associations over others such that when you're talking about these kinds of associations, you're talking about the real thing (effing it?), and if you can't talk about these kinds of associations, then the thing is ineffable.

    Given this understanding, I'm not sure what you mean when you say that some experiences are ineffable -- for example,

    "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.”

    As someone who's done some intense meditation training, I know what it's like to have experiences while meditating that it's difficult or impossible to communicate to people who haven't had those experiences. But I think this is just a more perspicuous example of the same thing that's going on when I talk to you about blue, or London, or to another experienced meditator about a certain meditative state.

  • Adrianos

    The author thinks of madhyamaka, and Western philosophy too, as a branch of logic, as Wittgenstein did in the Tractatus. WIttgenstein came to reject this view. Madhyamakas never held to begin with. Wittgenstein came to see that metaphysics comes from a confused interpretation of the rules of logic, which are rules of grammar, not of ultimate reality. Madhyamakas thought of ultimate reality as inaccessible to logic.

    • G

      If one views logic as a subset of ultimate reality, rather than as a metaprogram for describing ultimate reality in its entirety, then it's true that the entire whole of ultimate reality is larger than the subset of logic and therefore inaccessible to logic alone. (There is a quasi-Gödelian paradox here, whereby those who assert that all can be known by logic must necessarily though usually implicitly posit logic as a metaprogram.)

      This is where we run into the limits of our various systems of knowledge, and the need to assemble a number of them together in order to increase our understanding of the whole.

  • http://riskoverreward.com Vega

    You repeated over and over that it's surprising that Buddhism and western math would stumble across the same concepts. But these ideas are so simple and universal, it would be shocking if most cultures HADN'T tackled the non-duality of true/false. It'd be strange if most cultures hadn't encountered "this statement is false" and come up with at least a 3rd if not a 4th category value in response.

    • G

      And yet it's also the case that the Western intellectual traditions have been dominated in every practical sense, by duality and the excluded middle. Our ancestors developed these ideas into such useful tools that they, and we, began to ignore or forget the existence of other tools in the kit. It took contact with other traditions that used these tools routinely, to remind us and also get us to recognize similar threads in our own history.

  • http://thewayitis.info/ Derek Roche

    Great stuff. Thank you. Thank you for airing the logic that dare not speak its name in a world of such bigotry and hatred. A free world whose so-called leader could openly declare that if you're not with me, you're on the side of evil - and be re-elected.

    Logic is simply that which is necessarily the case. When we shed our primitive prejudices, it is necessarily the case that the world be self-created, self-propagating, self-governing. And, yes, self-referential. It stands to reason. Plurivalent or, more precisely, quantum logic rules.

  • Sivaswamy Mohanakrishnan

    This clearly shows the limit and no limit functionality of human brain in thinking through stuff...and that the limit becomes limitless as soon as one thinks about it...And Buddhists might have been thinking of the concept of God when they realised God can be True, False, Both True and False, Neither True or False, and Ineffable. Many other concepts can be all that too. And the brain in expanding the limit conquers each concept one by one, in different parts of the globe.

  • PeteJ

    I wish to differ with the whole thrust of this interesting article. Buddhism does not endorse the idea of true contradictions. For a true contradiction either x is true or not-x is true, and the other is false. Where this is not the case there is no contradiction. For all of Nagarjuna's examples there is no case of x/not-x where one is true and the other false. So, using Aristotle's definition as given in De Interpretatione, Middle Way Buddhism states there are no true contradictions. It states that we make a category-error when we see such contradictions. Aristotle's rules are what Nagarjuna uses for his proof, and it would not work if he broke them.
    The article is interesting in any case and makes some nice points, although the comment that Buddhism played no part in Nagarjuna's logic is incomprehensible and clearly wrong. Perhaps I misunderstood it.
    George Spencer Brown is better on Buddhist logic. This article discusses something more like dialethism, for which contradictions can be true.

    • http://jayarava.blogspot.com Jayarava

      Indeed. Nāgārjuna was trying to argue for a single ultimate truth (paramārthasatya), despite appearances of contradiction (saṃvṛttisatya). He uses contradiction rather in the same way that Schrödinger used it. By showing that the ontological implications of his opponents views on the nature of dharmas are contradictory.

      For Schrödinger it was the ridiculous and unbelievable consequence that the cat is both alive and dead until observed that ought to have discredited Bohr et al. For Nāgārjuna it was the problem of Sarvāstivāda Realism with respect to mental events (dharmas). In fact dharmas cannot either exist or non-exist, nor neither nor both because none of those categories apply to mental events.

      And just like Schrödinger, what Nāgārjuna was trying to do was turned around. Schrödinger's cat now epitomises the "truth" of Quantum Mechanics and paradox now epitomises the "truth" of Madhayamaka. Ironic.

      And yes he was deeply embedded in a Buddhist milieu, writing about Buddhist problems, for others Buddhists in a way that is incomprehensible without a Buddhist background.

  • Charles Eaton

    It's both a blessing and a curse to use a word not in common use to refer to a critical concept. How does the meaning of the word "ineffable" differ from that of "indescribable" or from Sensei Rumsfeld's "unknown unknowns"?

  • David Malek

    And oddly enough, human kind is on the verge of making the first Quantum Computer. A Quantum Computer, is essentially working on a set of Quantum Bits, AKA QBits, which can be false and true (0 or 1) at the same time. WOW . . .

  • Bodhipaksa

    "The Gorampa/Kant predicament is, in fact, inevitable. If one wishes to explain why something is ineffable, one must refer to it and say something about it. To refer to something else is just to change the subject."

    Surely, to say that something is ineffable is to say that there is something about it that cannot be communicated in words, not that nothing about it can be said. After all, to say that bodhi is ineffable is to say something about the ineffable.

    All experience is, in my understanding, ineffable. There is always something about our experience that can never be communicated in words. The difference between the ineffability of bodhi and the ineffability of my experience of tasting humus is that when I talk about eating humus you can compare it to your own experience and thus think that we're talking about the same thing, while if you've experienced bodhi then you've had an experience with which I have no point of comparison.

  • http://portonvictor.org Victor Porton

    Something loosely related with your topic:

    I had an unfortunate experience of living accordingly a self-contradictory philosophy (not some weird logic but just contradictions in "normal" Aristotelian logic in my mind) what has lead me to conflict with everyone, extreme poverty, and enmity. I got this philosophy from a wrong interpretation of Bible.

    See this link about some of my contradictions:
    http://endofgospel.org/online/hardquestions.xhtml

    Fortunately, my religion has changed eliminating contradictions.

  • Vaccandra

    The professor who introduced me to Nagarjuna, Ashok Gangadean, was of the opinion that as far as logic was concerned, Nagarjuna and Aristotle were essentially in agreement. It is certainly true that as far as Nagarjuna's method is concerned, he adheres rigorously to the law of the excluded middle (at least -- if not also the law of non-contradiction).

    As for the catuskoti, that distinction is famous because of Nagarjuna -- but neither he nor Buddha nor some other Buddhist was the author per se. The catuskoti represents the basic alternatives of what is asserted -- commonsensically or otherwise -- to be the case in conventional discourse. And none of the alternatives holds water under a particular form of analysis -- let us call it ultimacy-seeking analysis. Taken to its extreme, that form of analysis (known as prasanga, or reductio ad absurdam) leads to "utimacy seeking rational cognition" which is a technical synonym of prajna or gnosis. That is the context of what you describe as a fifth alternative or "ineffability".

    Theoretically ineffability is a consequence, (or perhaps a function?) of the catushkoti. But for practical intents and purposes, ineffability is a result an analytical and an experience -- not a theoretical or logical alternative to the catushkoti, nor (as you observe) a real attribute of something.
    As for our readings of Gorampa, and other Tibetan commentators on Nagarjuna and Madhyamaka, there tends to be much confusion when it comes to the (translation) terms "real", "true" and "existent". In Sanskrit "real" (sat, or satya, < sat- 'to be', 'to exist') implies"existent" in the sense of real, generally (that is adjectivally) speaking. But those words (sat and satya) are typically translated into Tibetan as _bden pa_ which is almost invariably translated into English as either "real/reality" or "true/truth" (and almost never simply as "existent"). However in Sanskrit and Madhyamaka generally, _sat_ and its opposite _asat_ also mean "existence" and "non-existence", that is logical predications of a subject (e.g. tasya asati idam nopapadyate 'given the non-existence of this, that does not obtain'). Tibetan commentators sometimes evince a lack of awareness of this nuance implicit in the Sanskrit originals -- precisely because the translations they use tend to obfuscate that nuance where it applies.

    Moreover Sanskrit _bhava_ ('existent' ie. a substantive) and the related _bhuta_ ('real', 'existing') are most often translated into Tibetan as _yod pa_ ('existing', or possibly 'existent'). The term _yod pa_ in turn is usually translated, or mistranslated as the case may be, sometimes as a substantive ('existent', 'thing') and sometimes as a qualifier ('existing') -- notwithstanding that in Sanskrit the corresponding term (e.g., _bhuta_) could also mean "real" in a metaphysical, as opposed to merely epistemological, sense.

    This is all by way of suggesting that the present discussion -- while certainly provocative and worthy of much discussion and analysis -- might suffer from the same basic infirmity of most contemporary discussions of Nagarjuna, especially when those have recourse to Tibetan commentators whose writings have been translated, sometimes well and sometimes not so well, into English. It is very easy to miss the point of those commentators -- and of Nagarjuna himself -- because of deeply ingrained and all-but-irremediable obfuscations of terminology, embedded in the conventions of Tibetan translations from Sanskrit. Adding to those our English-language appropriations of those Tibetantranslations -- or even of the original Sanskrit -- in using terms such as "real", "true" and "existent", with all the complex implications of each of those, we are easily led into a multitude of possible interpretations of Nagarjuna's intent, with little or no recourse to unambiguous source-text validations thereof.

    • http://jayarava.blogspot.com Jayarava

      Vaccandra, these are important caveats. When we try to compare what Nāgāruna with modern commentators we have to be sure we understand his terminology: satya, bhāva, dharma, are all multivalent. And his context. His anti-Realism was part of a long tradition of rejecting exist/non-exist dualities for dependently arisen dharmas, i.e. mental events. And his rhetoric was deeply influenced by the Buddhist milieu of India at the time, which was strongly Realist. His writing is not simply abstract philosophy it is polemic at the same time. I've been exploring how that realism might have come about given the early Buddhist critique of it on my blog recently - the last of a trilogy of essays on Sarvāstivāda is out on friday: http://jayarava.blogspot.com

  • http://portonvictor.org Victor Porton

    An other comment by me:

    Does eastern concept of reincarnation contradict to Christian paradise and hell?

    I think, there is no contradiction here:

    I consider possible that a man (or woman) has, so to say for a lack of a better term, two spirits or two souls (a Buddhist would know a better term for one of these two).

    One spirit goes to the heaven or hell and the other of these two may reincarnate.

    It can be compared with Navier-Stokes equations which have two equivalent forms: Where will be a specific point in a flowing fluid after 5 seconds? Surprisingly there are two answers both of which are valid: 1. in the same point of our 3D space; 2. it moves with the fluid. One of this can be compared with Christian and the other with Buddhist point of view.

    Personally I am a Christian and believe that the biblical concept it true, but I allow to think that in this question the Buddhist concept may also be true.

  • http://portonvictor.org Victor Porton

    Aristotle considered future events neither true nor false. In the modern logic it could be more adequately described as both true and false.

    The idea behind this is simple: current and past events can be modeled as values of monovalued functions, while future events may have more than one possible outcome and thus may be described by relations. You suggest that these can be considered both true and false.

    In this comment I don't try to be rigorous on the positions of modern quantum mechanics. But my idea to consider future both true and false is evident.

  • http://portonvictor.org Victor Porton

    One more paradoxical statement (about physics): Everything is relative, but relativity is absolute. More exactly (and now not contradictory) formulated: Everything is relative, except of relativity itself which is absolute.

    This expressed in exact mathematical terms is presented at my blog:
    http://portonmath.wordpress.com/2012/12/15/complete-relativity-theory/

    • http://portonvictor.org Victor Porton

      By the way, I got the idea of "absolute relativity" from so called "Christian Science" cult.

      You had not got your non-binary logic from Buddhism but later have found a connection to Buddhism.

      But I've got my idea about complete relativity of Universe straight from these cultists. I just formulated it exactly.

      (I don't endorse this cult however. My faith is different.)

      • G

        Ideas stand or fall on their own, regardless of source.

        I've got your blog on my to-read list. The idea you describe is interesting and I'm inclined to feel (subjectively and with no reasoned basis as of yet;-) that it may have some unexpectedly wider applications.

  • Akiva Cohen

    Maimonedes was getting at the concept of ineffability, and proposing a solution to the paradox of referring to the ineffable, when he wrote that God can only be understood in the negative. For instance, in your examples, "the least ordinal that cannot be referred to" is comprised of words that are in and of themselves defined solely in the negative. An "ordinal" is defined by not being a counting number and therefore extending beyond the infinite (itself a contradiction in terms, but a useful one). "Least" simply means "no others are smaller", and "cannot be referred to" means "cannot be positively described".

  • CHEMST

    And here lies the reason that technology and science developed in the West (those succeeding the Greeks: Jewish, Christian and Muslim ) and not in the East.

    • G

      Without some further explanation, you're at risk of sounding like some variety of racist.

      In any case, each of the Abrahamic traditions also contains elements that are thoroughly, aggressively, and violently obscurantist. In Christianity it's American fundamentalism. In Islam it's the Wahhabi and the Taliban (Boko Haram is similarly brutalist but for the moment is only regional). In Judaism it's a sect whose name escapes me at the moment but, along with its comparable branches of Islam and Christianity, is also identified with the extreme political right wing.

      If Darwinian fitness can be measured by the duration of persistence of a species, we are still at a toss-up as to which threads of philosophy have the greatest adaptive value. (Since this discussion page is badly broken on this website I'll have to continue this in an additional comment.)

    • G

      (Continued from preceding comment, which may appear below this one since the page is broken):

      Western science gives us a potential route to interstellar civilisation, by which the lineage of humanity could persist until the last star blinks out. But the abuse of Western science has also given us the addiction to fossil fuels that has produced climate disruption and may, according to climate scientists, lead to the extinction of humanity in a few hundred years.

      Asian philosophy has influenced the development of mathematics in places such as India, which may prove necessary for interstellar travel. But beyond that, it appears wholly consilient with, the perspectives advanced in climate science in terms of sustainability. So while Buddhism alone might not get us to the stars, it could produce the worldview that enables humans to persist on Earth as long as possible before the expansion of the Sun renders Earth uninhabitable: approx. 1/2 billion years.

      • CHEMST

        My point is that the development of science and technology are based on the concepts of PEM and PNC. No viable alternative has arisen, even with access to the knowledge gained by modern science, from alternative viewpoints. If quoting the obviously true is racist than Truth is racist. If you and Jared Diamond (who by the way chooses to live most of his life in modern society) see a life of the type experienced by those of native people of Papua New Guinea as better than the one I lead, then that is fine, but we disagree. As to extinction by climate, that is the stupidest idea ever raised. Humans are the only animals to inhabit all Continents and live successfully at every latitude on the planet. Given our innate ability to succeed in the harshest environments, it it preposterous to imagine a shift in climate causing our extinction Loss of our civilization and culture, maybe, but extinction no.

  • Sam Lang

    We begin with truth-value-of defined as a function whose value is either T or F. Then we move to truth-value-of defined as a relation whose value is either {T}, {F}, {T,F}, or {}. Then we assign name these sets (t, f, b, n), and define truth-value-of as a function whose value is either t, f, b, n. The set {t, f, b, n} constitutes the set of possible functions whose domain is {T, F} and whose range is {in the set, not in the set}.

    I think that instead of adding i to the range of the truth-value-of function, it makes more sense to modify the range of the function from "the set of possible functions whose domain is {T, F} and whose range is {in the set, not in the set}" to something like "the set of possible functions whose domain is {T, F} and whose range is {in the set, not in the set, in the set and not in the set, neither in the set nor not in the set}".

    This creates a recursive definition for the truth-value-of function that correctly represents the impossibility of pinning a truth value to any idea. It also, I think, matches the Buddhist ideas that you present very well. Unfortunately it provides very little assistance when trying to reason about practical problems, which I think is why it is eschewed by Western philosophy.

  • bobthechef

    I think we're confusing metaphysical, psychological, and epistemic concerns, as well as existential concerns, and perhaps this has to do with the Cartesian/critical trajectory Western philosophy has taken since Descartes, one I despise abd one which shifts the emphasis from being to knowing in a grand gesture of self-defeat. If you read Lukasiewicz's book on he POC, he distinguishes three kinds of such principle (using his terminology): the ontological, the psychological, and the logical. To say that a thing cannot *be* and *not be* simultaneously and under the same aspect is to talk about *being*, how things are. When Aristotle makes his case in the Metaphysics, he isn't contradicting himself in the Organon, he's talking about things which are and the future simply isn't even on the table because the future isn't (and not in the way you might say that the incumbent queen of England is Michelle Obama; here I admit different ways in which a statement is false). The Organon is not primarily concerned with being but logic and contemporary philosophers seem to have a real problem understanding the that these two corpuses concern different things (for instance, you can easily find treatments of A's substance theory that focus erroneously on the Categories when they should be focusing on the Metaphysics and if you add an analytic philosopher into the mix, then "tortured" won't begin to describe the wrongheadedness of the analysis). Ineffability isn't metaphysical, it's epistemic, psychological: it is a reflexive judgement about one's knowledge in the face of the real, that something encountered exceeds one's grasp in some way. You can make an analogous case for "nothing": it isn't something, it isn't even a substrate for anything, it's the absence of anything (and indeed purely nominal). While we can perhaps find Aristotle vague, especially those of us poorly versed in Greek, I find that usually it's the interpreter that is lacking in sound mind or insight.

    As far as appealing to mathematical logic, that's always a weak style of argumentation, philosophically speaking. It is perhaps admissible in the confines of geometric methods where finding a suitable model or interpretation is a secondary concern to deduction, but fiddling with parameters and axioms with no reference to reality is not metaphysically sound and at best an accommodating hack.

    Btw, admitting your definitions for function and relation (and here elucidation and elaboration is likewise necessary, but I'll refrain) , you say that "mother of" is a function while "son of" is a relation", but your explanation is wrong. "Mother of" is a relation because X may be the mother of Y, Z, etc. "Son of" is a relation not because some X may have many sons but because there are necessarily two parents Y and Z for any son X that is a son of Y and Z.

  • fduch

    Why do we need the B and N objects in the relation, resulting 2^5 possibilities?
    Why not just have T, F and I for 2^3 possibilities?

  • Yves Reymen

    This all makes me think of system theory with state space representation where you could have observable states and non-observable states (whats called ineffable in the essay)
    Questions this raises with me are: Should we care about these ineffable concepts? Could we have influence on them or not? (similarly also for this a concept exists in system theory called controlability)

  • Alex

    My question is: besides the example of the "the least ordinal that cannot be referred to," what is an example of something that is both true and ineffable, i.e. {t,i}, {t,f,i}, {t,b,i}, {t,f,b,i}, or {b,i}?

  • Brian Genda

    "this statement is false" is NOT both true and false. It is neither.

    A: "I'm lying right now"
    B: "what are you lying about?"
    A: "about what I just said"
    B: "What did you just say?"
    A: "That I'm lying about what I'm saying"
    B: "but you are not saying anything"
    A: "Yes I am, I'm saying that my statement is false"
    B: "What statement did you make?"
    A: "That my statement is false"
    B: "then your claim is not both true AND false, it is meaningless"
    A: "Why?"
    B: "Because, it doesn't say anything about anything"

    MC Escher's visual illusions trick the mind just as grammar tricks do. He took one one visual element and combined it with another, and the meeting of the two seems to make sense, but does not. Yes, both competing elements are true, but the fact that they compete does not make the image both true AND false, it makes it nonsensical. That this part and that part make sense but not both together highlights the nonsensical nature of the union, not that both are true simultaneously.

    And therein lies the value in paradox. Not in the "both/and". But in the "neither". This is the nature of the zen koan tradition. The question, "what is the sound of one hand clapping" sounds pretty silly. A nonsense question. But that's the whole point. It isn't to get you to go further into logical distinctions, but to realize their absurdity.

    There's a reality beyond definitions, that does not deny them, but recognizes them as absurd. Illusions. Paradox isn't about having to hurt your head trying to combine or separate competing ideas, but realizing the absurdity and illusory nature of the mind itself.

    • Tam Hunt

      I think it's both true and false and neither true nor false. Uh oh, is that a new category?

  • bathieme@hotmail.com

    It seems to me that Nagarjuna in no way rejects the principle of
    non-contradiction - on the contrary, his fundamental method in MMK
    relies on it. He employs a reductio ad absurdum precisely to demonstrate
    that if you accept inherent existence in any way whatsoever, you must
    also accept contradictory consequences that are entailed, and thus, the
    view is to be rejected.

  • Tam Hunt

    Nice piece and I generally agree with your assertions. I've made some similar points comparing Eastern and Western logic in this piece: http://www.independent.com/news/2011/apr/04/logic/

  • Felix Erwin

    Clearly we can describe logic in any way we want. The (after) life is ineffable; the path to enlightenment leads to the absence of repetition. Mathematics is abstract and paradoxical, but... Qubits are loveable! ♥

  • margaret wertheim

    Lovely piece. I am reminded here of the 15th century champion of mathematical science, Cardinal Nicholas of Cusa and his enigmatic discussions about the infinite. Cusa declared that the cosmos was not infinite (for only God could be so) but that it was unbounded; it was a non-infinite infinity. His book "On Learned Ignorance" is an astonishing piece of Christian mysticism deeply informed by logical thinking about the possibilities for physical reality. He too was dealing with the question of the ineffable - what could we know about the universe through mathematics, while staying true to the final un-knowingness that must always be our state of knowledge about the Ultimate. Cusa and Nagarjuna might have a lot to agree about.

  • Constant Illumination

    Graham, hi, I'm Constant Illumination, Buddhist practitioner.
    Your inquiry seem to start from the purpose to widen some formal system. To make its elements somehow correspond to something otside, which didn't fit in.
    Thus you start within the boundaries of a system which is crucially limited. It will unlikely really solve these paradoxes and give a really consistent view which Buddhist great thinkers actually have.
    For example, when you say that paradoxal claims are both true and false, that's only putting some mechanical correlation between contradiction and some abstract object "true and false". Instead, you could use any other abstract object - such as "kergoodoo" or "bambarbeeyah". Calling contradiction "both true and false" has no real sense, because that paradoxal claim is refuted both as being true and as being false. So it could be called "nor true nor false" exactly as soundly. ((How can you really claim it's "b" when it's "n" on the very same ground?))
    Thus, what is the point there to invent mechanical cells and put there things that you don't know how to think about?
    Instead, start from the other side. Explore what is the natural system of those outside-of-this-system things. Move from the purpose of solving real tasks such as understanding how our mind works, how our knowledge forms.
    If you wish to really find the system that solves these problems, I invite you to dialog in our wiki. Here is a little introduction into the question why "flat" logical means that you use do not reflect actual relations correctly:
    http://earth.zen-do.ru/mind/dualism_self_and_no-self
    Without seeing what actually relates to what, we make such obvious mistakes:
    > In explaining what they do, are we not talking about them? Well, yes, of course we are.
    Not at all! When we seem to "speak about ineffable", we actually speak about our relations to it, which is not the "ineffable itself".
    Moreover: why should we accept as real objects (of examination) something that just could be mentally constructed (such as ordinals etc., etc.)? If they have no relation to reality? We could construct "flying pigs", precisely the same way. And then seriously discuss how to solve the paradox that pigs can't fly, and here we have an object "flying pig"...

    • Justin Chapweske

      This is a very good point. The unawake mind can only view these logics from "inside the box". You need to practice shamata/vipassana, wake up to the ineffable itself, and you will be able to more powerfully explore these logics from the outside looking in.

      • http://earth.zen-do.ru/ Constant Illumination

        Yes, without practical study of that what relates our mind to ineffable, we would only play with symbols.
        By the way, there is a tool for developing mind algorythms, called The Book of Changes (Yi Jing). People who use it often fall to 2 extremes: they either get only poetical metaphors to feel, not studying the underlying structure; or they play with combinatorics and build systems that look like geometrical puzzles, but have no real sense.
        The means for the actual study of Yi Jing is through practice, day by day, trying to take both metaphorical meanings and the structure. That practice is through meditation, especially when you divide and count Achillea Millefolia stems in a traditional way. It's very calming, peaceful and thoughtful process.

        This way you get both sides: learn optimal steps for performing activity processes... And guide your mind to be open, perceptive to the slightest signals of the intent.
        Maybe that meditative quality is more important, and getting a teaching on the poetical level is better than just playing with abstract puzzles. But, in my experience, those who want to practise only meditation and neglect logic, also might lack clarity, and might spend much time without getting stable results. (Because, for example, our states of mind are more impermanent than logic). Thus if we don't support exercises with understanding, it may happen that after the meditation "is finished" we return to the people around and stumble over habitual daily situations. Without developed understanding, it may be hard to keep meditative states of mind under all those influences.
        Therefore, people who don't cultivate both calming and seeing, tend to hide from the world, either in theories or in cozy little roleplaying.

        Delusion may be yet heavier when we don't see the way of our purpose. Then "spiritual practice" may serve something opposite: enslaving play, instead of liberation.
        In case of Yi Jing, some people practise it for the foretelling, instead of finding the way of intention in present situations. Thus people burden themselves with expectations and labels cast onto the future.
        Therefore, good practice has all the three sides: knowing correct procedure, opening the mind to reality, seeing and keeping the purpose. And, of course, it must be practice, not words. (Even not words about "practice instead of words"). :)
        In the internet... we at least can collect some correct words, that may help to practice well!
        If you wish, consider joining us in that, at our wiki
        http://earth.zen-do.ru

  • Ray Madison

    "This statement is false" is not a paradox if's a lie.
    Also it's false that the each and all of logical systems you've described as mathematical are truly that. You've assigned truth symbols that can't be precisely quantified. Mathematicians can attempt the process, but it's an after the fact attempt at measurement at best. It's neither predictive nor analytic.

    • Ray Madison

      Sorry for the typos. It should have been written "not a paradox if it's a lie.
      And also should have been, It's neither mathematically predictive nor analytic.

  • Vir Narain

    Does the wave-particle duality in physics exemplify the truth of this approach?

  • Justin Chapweske

    I applaud this effort to tie together emptiness realization with logic. But, don't let yourself get seduced by these systems of logic and lose sight of the true prize, which is to realize the ineffable itself.

    This present experience is already known to itself and is completely beyond describing.

  • bob dobolina

    good luck have fun

  • http://www.livinginthehereandnow.co.za/ beachcomber

    So do I re-incarnate or not?

    • jack

      both and neither

      • http://www.livinginthehereandnow.co.za/ beachcomber

        Looks like I will have to stay in a state of superposition à la Schrödinger's cat http://en.wikipedia.org/wiki/Schrödinger's_cat

        • jack

          Excellent. You are learning.

          • http://www.livinginthehereandnow.co.za/ beachcomber

            How comforting to discover that one need not travel all the way to an icy cave in the Himalayas for enlightenment, when it is available at the click of a mouse on the internet!

          • jack

            it can come only from inside.

  • William Hurley

    Many of the comments here add to an already rich commentarial history attached to Nagarjuna and in doing so echo a number of strengths and weaknesses those ex parte comments contain.

    To my mind, its crucial to consider the catuskoti - as articulate by Nagarjuna in the MMK - in context of the MMK in its entirety. Of the several specific points within the MMK that can be drawn on as examples, concision leads me to point to one example alone (this 1 example alone because space herein does not properly afford the breadth and depth my claim should necessarily provide).

    The passage that asserts itself as a corrective to many of the analytical amplifications found here and in the ~2000yrs of commentarial literature is found in stanza 19 of Chpt 25, the section in which Nagarjuna addresses Nirvana. In this couplet, Nagarjuna declares that "nirvana is not different that samsara" and that "samsara is no different than nirvana".

    It is this pairing that most convincingly forecloses on interpretive moves that seek to uncover "2 truths" and other similar modes of binary and/or dialectical ephemera within the MMK. Nagarjuna embraces the Buddha's empiricist purview, concerning himself with the problem of suffering first, last and always. As such, conjuring a cosmology out of Nagarjuna's MMK (or reductively from singular subjects within it) reduces the Buddhist soteriological project to a minor domain of investigation and practice subsumed to cosmologies that mimic vedic moral systems - all of which the Buddha declared to be failures in service of the question and resolution of dukkha.

    I'd add that Jan Westerhoff has published a number of valuable articles on Nagarjuna and his works beyond the MMK. Westerhoff puts forward strongly evidenced argument that MMK and Dispeller of All Disputes were tomes Nagarjuna wrote as part of his defense of the Buddha's Buddhism against proto-Nyaya logicians in academic-like forums where the modes of debate were rigidly structured - not unlike our legal system's mode of "process" is today.

  • Steve Scott

    What happens to an enlightened spirit after death? Choice.

    • jack

      The same as happens to an electron that is not observed.

  • Eli Horowitz
  • marxist

    Dear Graham Priest,
    You might benefit by paying some attention to the previous voluminous scholarship related to these questions. In particular, why have you not mentioned the work of the renowned historian and philosopher Debiprasad Chattopadhyaya? I hope this lacuna is not because he was a Indian? or because he was a marxist? And why have you not mentioned the connections to dialectical materialism? For a start, I suggest you take a look at Chattopadhyaya's "What is Living and What is Dead in Indian Philosophy?"

  • yzzzd

    Go though the whole page, only the picture seems understands what is eastern philosophy. Using logic, even the function things, to describe Buddhist philosophy is too scientific, at least to me. Just like the picture in the beginning of this article, the crane standing in the water is connected to its reflection. So, which one is real? Entity or the shadow? It seems strange if I say both, or at strange at all. The contradictions inside eastern philosophy may be interpreted by Asian using another word: balancing which teaches you how to keep distance to mass society, but still connected, how to remember by forgetting, how to enjoy the bliss, but still feel the pain.

  • I.K.

    Interesting. Now, I can replace the T's and F's in the pretty Hasse diagram with T=Tea and F=Fish and the relation will still hold. You could have neither Tea nor Fish, or just drink Tea, or just eat Fish, or take both Tea and Fish together for dinner.

    You can do similar substitutions too, like T=Twitter and F=Facebook. You can be on neither, or just be browsing Twitter, or just Facebook, or both.

    See, it is a fun play with names andy symbols, which, I'm sure has a great deal to with with PNC and PEM.

    This is the type of thing many non-mathematicians think is terribly interesting and informative, and where their thinking ends by becoming very distracted with little plays as such.

    Mathematics is a field which results (or resulted) from taking PNC and PEM to the extreme. So modeling the absence of PNC and PEM in mathematics, or what is the same, modeling contradictions and ineffability in mathematics, is to model it on a foundation which assumes PNC and PEM by default and tries to leave out contradictions. They aren't modeling what they claim to be modeling. You're just using words to make it look like they are and betraying with a warm kiss.

    There is a great difference between 'making mathematical models of contradiction' and 'finding contradictions within mathematics'. The former is just PNC with makeup and really won't tell you anything. But people tend to love these things so terribly because they are clear, simple, easy for the mind and 'make sense'. Things like that Hasse diagram and so-called models of truth values belong here. The latter, on the other hand, happens when you pursue math far enough, i.e. when you actually try to go all the way with things like PNC and PEM instead of swimming in shallow waters, and reach a point where math seems to collapse in on itself. These are the true gems, and things like the popular Godel's incompleteness theorems and Russell's paradox belong here. The great misfortune/advantage of these though, is that unlike the pretty simplistic models that people like, these gems don't make anything easy for us. Rather, they are absurd and make things more difficult. But that is why they are profound.

    You won't understand Buddhism-- or any other deep idea, including math --at all this way, but continue betraying with kisses and misunderstanding it by thinking you've understood it so well. Of course, shallow swimmers have the luxury of placing bets on things beyond their time and responsibility: “Who knows, it might be possible in the future. There is no proof that it isn’t.” Good luck to them.

    • Frank Fourth

      Talk down much?

  • Milkshake

    Things are neither this way nor that, nor are they otherwise.

  • Nope

    Any xian westerner or islamist embraces contradictions in their unholy babble daily. Buddhism actually make sense and embracing their tenets doesn't even require a belief in man made gawds. Of all the religions (and it barely squeaks in as one) it is by far the most sensible and least contradictory, if you are capable of critical thought and compassion.

  • Nitin Jain

    Awesome!!

  • HaakonKL

    When you make a function point to sets, it does not cease being a function.

    f(x) = {x} is a function, not a relation.

    It seems dishonest to first state that functions are relations (which is true), and then state that you're turning your function into a relation (which is true, you're turning it into another function and functions are relations), and then you give us a new codomain for the same function.

  • Don DeHart Bronkema

    in a quantum kosmos, contradiction & ambiguity are ineluctable.

  • rob hollander

    The ineffable strikes me as an epistemic modal notion and should, or at least can, be treated in a modal logic without compromising the classical values.