Logic and Buddhist metaphysics. Buddhist metaphysics and modern symbolic logic might seem strange bedfellows. Indeed they are. The thinkers who developed the systems of Buddhist metaphysics knew nothing of modern logic; and the logicians who developed the panoply of techniques which are modern logic knew nothing–for the most part–of Buddhism. Yet unexpected things happen in the evolution of thought, and connections between these two areas are now emerging. (As I write this, I’m on a plane flying back to Germany from Japan, where I’ve been lecturing on these matters for the last two weeks in Kyoto University) Let me try to explain as simply as I can.
At the time of the historical Buddha, Siddhārtha Gautama, c. 5c BCE, a common assumption was that there are four possibilities concerning any claim: that it is true (and true only), that it is false (and false only), that it is both true and false, that it is neither true nor false. The principle was called the catuṣkoṭi (Greek: tetralemma; meaning ‘four points’ in English).
We know this because, in some of the sūtras, the Buddha’s disciples ask him difficult metaphysical questions, such as the status of an enlightened person after death: does the person exist, not exist, both, or neither? They clearly expect him to endorse just one of these possibilities.
This still isn’t an end to the matter, however. For Nāgārjuna, and those who follow him, not only claim that some things are ineffable: they explain why they are so (roLogic and Buddhist metaphysicsughly, these situations pertain to an ultimate reality, which is what remains after all conceptual–and therefore linguistic–imputations are “peeled off”). Clearly, speaking of the ineffable is a most paradoxical state of affairs. It would seem to show that some claims can take more than one of the five values, such as both t and i. (And lest it be thought that this is simply a feature of Eastern mysticism, one should note how many of the great Western philosophers have found themselves in exactly the same situation: Aristotle (prime matter), Kant (noumena), Wittgenstein (form, in the Tractatus), Heidegger (being).)
Again, modern techniques of non-classical logic can show how to make sense of this possibility. In standard logics, things take exactly one of whatever values are on offer. But in a construction called plurivalent logic, things can take more than one (maybe even less than one) such value. The plurality of values interact in a perfectly natural and sensible way with the other logical machinery.
What to make of these matters? Philosophers may certainly argue about this. (This, after all, is what philosophers love to do.) However, one thing is ungainsayable: Buddhist metaphysics and formal logic can profitably inform each other.
FDE was a system of logic known independently of Buddhist considerations. (It was developed in the 1960 and 70s in a branch of logic known as relevant logic.) But the development of the five-valued logic above, and plurivalent logics, were motivated, at least in part, by trying to make sense of the Buddhist picture. The metaphysics can therefore stimulate novel developments in logic—developments whose interest is not simply restricted to applications to Buddhist metaphysics.
Conversely, those with a suspicion of metaphysics in general and Eastern systems of metaphysics in particular, might be tempted to write off such enterprises as logically incoherent. They’re not. The techniques of modern logic certainly don’t show that these pictures of reality are true. However, they show that they’re as logically coherent as can be – and, moreover, they allow us to articulate the views with a precision and rigor hitherto unobtainable, and hence to understand them and their consequences better.
Buddhist views are not, of course, the only views that can work in this dialectical way. But because Buddhist views are little known in Western philosophy, they provide a particularly fruitful domain of inquiry.
And what would the Ancient Buddhist metaphysicians themselves have made of such developments in logic? We’ll never, of course, know; but my own guess is that they would have very much appreciated the enlightenment which such techniques can bring.
First, let me say that Massimo and I agree on more than we disagree. I agree, for example, that the point of philosophy is to come to a reasoned — and of course, fallible — evaluation of truths about metaphysics, ethics, and so on. That was just not my aim in the piece I wrote, which was to show how the techniques of modern logic can help to understand certain Buddhist views. To evaluate, one must first understand. Secondly, I agree on the virtue of clarity, and abhor obscurantism as much as he does. But, again, having said that, many issues in mathematics and the natural sciences are complex and difficult. One should not expect that they can be spelled out in a way that can be understood without a lot of hard work. Philosophy is no different.
So let me turn to the things about which we disagree. First some general comments. Let us start with logic. Massimo claims that one cannot be wrong in logic since it is purely formal. I find this a historical view surprising from someone who has such a grasp of the history of science. Logic (in one of the many senses of the word) is a theory about what follows from what. Western logicians have been producing such theories for about two and a half thousand years. The received view has changed over time, and later views often hold earlier views to be false. Thus, for example, some of the syllogisms Aristotle took to be valid are not held to be so by contemporary logicians. Aristotle held that contradictions do not imply everything; most modern logicians would disagree. One of the great early Medieval logicians, Abelard, held that any conditional of the form ‘if A then it is not the case that A’ is false; most modern logicians would disagree. In the 1960s most logicians held that the conditional ‘if the theory of evolution is false, people have evolved’ is true; few would now subscribe to this view. Are we at the end of history in the process of revising our views about logic.
Second, Buddhism. There is no one thing which is Buddhism, any more than there is one thing which is Christianity. Theravāda Buddhism is very different from Tantric Buddhism, which is very different from Zen Buddhism, and so on. And each of these, in turn, is many things. Each is a religion, a set of meditative and disciplinary practices, an organizational structure, a player in political structures. But each also endorses various philosophical views. It was some (and only some) of these views which were the concern of my article. Next, Buddhist philosophy — as engaged in by its notable historical practitioners — is no different from Western philosophy. For over two thousand years, Buddhist philosophers have been putting forward different views of metaphysics, ethics, and arguing with each other about which is right. Of course, if one’s only knowledge of Buddhism comes from contemporary popular works, one will not see this. One has to read the philosophers themselves, such as Candrakīrti, Tsongkhapa, Fazang — though I would not advise anyone to jump into this literature without a guide, any more than I would do this with Aristotle, Kant, or Wittgenstein.
In fact, Buddhist thought is one of the most rationalistic of views connected with a religion. There is no god, and so one is not expected to believe something simply because god is supposed to have revealed it. There is no distinction between natural and revealed thought, as there is in Christianity. Indeed, in the Kālāma Sūtra, the Buddha himself urges people not to believe something simply because some authority figure tells them (an attitude many contemporary Western philosophers would do well to take to heart). A person should accept something only if it makes sense to them.