Note: this transcription was produced by automatic voice recognition software. It has been corrected by hand, but may still contain errors. We are very grateful to Tim Wittenborg for his production of the automated transcripts and for the efforts of a team of volunteer listeners who corrected the texts.
PA: We're going to be talking about Buddhist logic or logic and Buddhist logic, because these are two areas you've worked in. You're very well known for your work in contemporary logic. And during your career, you turned your attention to the resources that Buddhism has to offer in logic. And I was wondering if you could start by just telling us why you got interested in Buddhist logic.
GP: Okay, so a bit of autobiography. My training was as a mathematician. So my doctorate is in mathematics. But by the time I finished my doctorate, I knew that philosophy is an awful lot more fun than mathematics for me. So, I was very fortunate to be offered a job in the philosophy department. But I knew virtually no philosophy. So I've spent a lot of my career teaching myself philosophy, which has been great fun. So I guess I'd been around as an academic for something like 20 years, and I'd learned a lot of Western philosophy in that time. I hadn't really come across much Eastern philosophy just because in the Western Academy, no one really knows much about it. But I had a stroke of very good luck. I met someone who's since become a very close friend, a guy called Jay Garfield. At that time, Jay was professor in Tasmania, and I was professor in Brisbane. Okay, quite a long way apart. But Australia is relatively small in terms of you know, the philosophical community. So I got to know Jay well. And Jay was also trained as a Western analytic philosopher, but he also has moved into the Asian traditions as well. And then Jay knew a lot about the Asian traditions. Jay is kind of amazing because he taught himself Tibetan. I learned Tibetan anyway. And then he made one of the best translations of the Mūlamadhyamakakārikā, which is probably the most important famous book or text written by Nāgārjuna, second century, first century ADE. In India, no one knows exact dates, but it's one of the most important philosophical texts in Buddhism.
PA: Yeah, I just read his translation, actually. To write some other of these scripts.
GP: Well, Jay had just finished that translation and I had just finished my own book Beyond the limits of thought. And we started to chat about things. And I realized that many of the things he was engaged in was so fascinating and related to a number of things that I was engaged with. So it was talking to Jay that I came to realize that I knew at best half of the world's philosophy, the sort of European derived stuff. So I knew nothing about China. I knew nothing about India. But Jay showed me that there was so much more that was interesting in philosophy. So then I made a point of teaching myself, I'll try to teach myself that as well. So I mean, you do that by talking to people who know by teaching, teaching is a great way of learning. Because you can't teach it unless you get your head around it to a certain extent first.
PA: Podcasting is also actually a good technique.
GP: I understand entirely.
PA: I recommend it.
GP: And I went to study in India, and I've studied in Japan. So over the last 20 years or so, I guess I've learned quite a lot about certain aspects of Asian philosophy. So that's how I got into this stuff.
PA: And was it really the resonance between technical issues you were working on in logic and the Buddhist tradition? Or was it more, oh, well, I don't know about this. And I should, just generally speaking.
GP: There's certainly a resonance with the logical issues. We can talk about that in a minute. But it wasn't it wasn't just that. I think there are so many fascinating philosophical ideas that come out of China and India and Tibet and Japan and Korea. And even without any logic connection, I would have found those ideas fascinating. The views about the nature of reality, the ethics, the political philosophy. I mean, these are just fascinating ideas, even without logic connection.
PA: Right. So you weren't just mining the Buddhist tradition for material to use in logic.
GP: No, not at all.
PA: Just looking for whatever you would find interesting.
GP: Sure. So you know, I've learned lots of Western philosophy. And some of that's got something to do with logic. Some of it hasn't. But I find philosophy fascinating, just as it’s philosophy.
PA: Now a lot of your work in logic, I mean, not Buddhist logic, but logic, generally speaking, has been about what's sometimes called non-classical logic. And in fact, some of the work that you and also Jay Garfield have contributed on Buddhism suggests that Buddhist logic is non-classical logic. And not only because it developed independently of classical logic, but because it makes some of the same technical moves, perhaps we could say. And so I was wondering whether you could maybe tell us before we get into the Buddhist material, what non-classical logic is and what some of the issues are that arise.
GP: Okay, a little bit of history of Western logic. Classical logic is something of a misnomer, because it has absolutely nothing to do with the great classical civilizations of the West, like Egypt and Greece and Rome. Classical logic essentially was invented at the end of the 19th century. And the most important, important person here was Gottlob Frege, who I think did not get the credit he deserved initially. So when these new ideas were taken up in Europe and other European derived countries like North America and Australia, the people who got the credit were in the first instance people like Russell, sometimes Wittgenstein. And it wasn't really till the mid 50s that people recognize how much was owed to Frege.
PA: Even though Russell at this made it quite clear that he was drawing on Freger, didn't he?
GP: Oh, yes. Yeah, he didn’t, he didn't hide this. But people read Principia [Mathematica], that's Russell's 1910 book, where he deployed what was essentially something like Frege’s logic. So people read that. And they didn't go back and read Freger. One reason they didn't was because Frege's notation is terrible. It's really hard to read. Whereas Russell's symbolism was much more familiar to mathematicians. Anyway, the point was that classical logic is an invention of the late 19th century. I don't know who coined the term classical logic, but it's a master stroke of propaganda, because it makes you think how cool it is. It's been around since ancient Greece. And this is not true. So logic has developed in the West for two and a half thousand years. And logic as modern logicians understand it is a theory about what follows from what. So if I give you certain things, claims that I make, you know, what can I infer from that? That's what logic deals with. And different theories of that have been proposed since ancient Greece through the great medieval period into the end of the 19th, 20th, 21st century. So logic is a very dynamic subject, which has evolved over a long period of time. Unfortunately, the way that logic is taught nowadays is anything but historical. So you're just given a logic book and you're told this is logic. And it's probably some form of classical logic. So you can get the impression that this has dropped from the sky. Or maybe some kind of Moses has brought it down from Mount Sinai, you know, and you just learn the tablets.
PA: It's more like learning physics nowadays than it is like learning let’s say, ethics.
GP: Yeah, except that most physicists, or most people who learn physics, know that physics has a history. Most logic students don't know that logic has a history. It's taught very ahistorically. Okay, that's a bit of a gripe. Okay, so that's fine. So it's important to say that classical logic is a product of its time. And it was a fantastic advance in logic. Classical logic was so much more powerful than anything that had preceded it that it soon became in 20 or 30 years fairly orthodox. And there are many great investigations of it by brilliant mathematicians such as Hilbert and of course, Gödel. So Hilbert's working in Göttingen in the 1920s, 1910s. Gödel is working in Vienna in 1920s, 1930s before he goes to the US and works in Princeton. So these are great logicians. And what they were able to do was develop the logic that had been invented by people like Frege and shows so much of its wealth. And philosophers caught on. And they thought: hey! You know, we've got this great new philosophical tool, let's do everything we can with it! So the next 30 years of logic, or rather philosophy from about 1920 to 1960 is philosophers who want to apply logic, take logic as the tool and try to apply it to philosophy of science, philosophy of language, thinking, you know, finally, we've got logic right. Now we can go about applying it.
PA: This is sort of the heyday of analytic philosophy.
GP: Yeah, that's probably true.
PA: Or certainly you have developments like logical positivism.
GP: Yeah, it's very much connected with logical positivism, logical empiricism in the United States. But when you start to use a tool, one thing that you quickly discover is its limitations. Well, quickly, it takes 40, 50 years in this case. And it's clear that classical logic has limitations. Now, everyone is, all logicians are aware of this. You might think that there are ways of work of a workaround of the limitations.
GP: But you might come to think that there are better ways of approaching logic, that you don't need to work around what you need is a kind of revamping of logic. So what we've seen, especially in the last 40 years, I guess, but actually it goes back way before that, is people working on systems of logic, which are now called non-classical logic. So these are logics, which deviate from classical logic in some way or other. And roughly speaking, deviant logics, non-classical logics fall into two kinds. The ones that think that they're the expressive resources of classical logic are too, too limited. So you add extra expressive machinery. And the sort of paradigm example of that is modal logic, where you add a logic to deal with things, claims about possibility, necessity, and so on. And in the 20th century, that goes back to C.I. Lewis, who's working in the 1920s. But then there are people who say no, classical logic gets it wrong in a much more profound way. There are just things about logical, there are just things about classical logic, which are just wrong. And that movement starts very early. So probably the first person to work on this area was the Dutch mathematician Brouwer, who's working on something called intuitionist logic, really about 1910. So about the same time as Prinkie B. Mathematica. And then by about the 1920s, you get another Dutch mathematician, Arend Heyting, producing intuitionist logic, which says: hey, classical logic is wrong. So I won't go into all the differences because they get technical. But in classical logic, there's a principle called the principle of excluded middle. So every statement is either true or false. And what intuitionist did was say, no, no, that's not true. There are some things which are neither true nor false. So they construct a system of logic in which that is not a logical truth. So for every A, A or it's not the case today, it's just not true. So the origins of non classical logic really go back very close to the origins of classical logic, except no one paid much attention to them. Just because classical logic was such a fabulous theory, it's so powerful, it did such a good job of so many things. People didn't worry about the kind of the places where it didn't seem to fit so well. But by about the 1960s, 1970s, then lots of logicians started to feel, well, we shouldn't ignore these non classical systems, because maybe they can actually do a lot better job of some areas where classical logic seems to suck a pair of shoes that bite. You know, you can live with the biting shoes for a while. But after a while, do you think, well, maybe I can do better with a new pair of shoes?
PA: Does the classical logician think that this idea that the statement could be neither true nor false? I mean, in a way, that's an obvious observation that we actually talked about in the Nāgārjuna episodes, that, for example, category mistakes, right? How heavy is the color blue? This kind of question? I mean, there's no there's no good answer to that. And the reason is because the question makes a false assumption, namely that colors have weight. But what couldn't a classical logician say, well, I don't need this value because if I'm just precise enough and I avoid category mistakes.
GP: Absolutely. So what some logicians have suggested that category mistakes require a non-classical logic where you have the value true, the value false, and then some value meaning a category mistake or something like this. What many classical logicians will tell you about that is, well, we're assuming that we're using a language where all the category mistakes have been factored out in the first place. I mean, just ignore those. So I don't think that's been a particularly tough challenge for classical logic. There are many tougher challenges. So one of the earliest challenges was intuitionism. And this was driven by developments in the philosophy of mathematics. So Brower said, Look, what's truth in mathematics? So truth in physics is kind of well, you know, there's a real world out there. What's true and what's false? It doesn't really depend on us. That's contentious view, of course, but certainly truth about the natural world is fixed because, hey, the natural world is out there. What about mathematics? Okay, you can think that the mathematical world is out there like the natural world. And some philosophers do, but some think that, hey, that's just a kind of mysticism. Okay. So if mathematical truth is not sort of constituted by reality, it is out there. What does constitute mathematical truth? And Brower said, Well, you know, what constitutes mathematical truth is provability. So to be true in mathematics is to be provable. Right? Now, there are lots of places in mathematics where you can't prove something. You can't prove a for example, and you can't prove it's negation. You can't prove that it's true, you can't prove that it's false. And in these cases. said Brower, okay, you cannot apply the principle of excluding the middle, at least until you got a proof of one of these guys.
PA: Can't you even sometimes prove that you can't prove either a or it's converse.
GP: You can certainly prove that there are certain systems of logic, where some things can either be proved or refuted. So this is a standard interpretation of one of the great theorems of Gödel, or the theorems of great Gödel. But Brower was talking about not provability with respect to some system or other, he was talking about provability, period. And Brower himself had a very jaundiced view of formal systems. He thought that proof is about mental constructions, which may not be able to be captured in any one given formal system. So this is one of the early challenges to classical logic. And it's, it depends on a sort of verificationist theory of truth. And of course, there's a lot to argue about there. But it's an illustration of one of the reasons that logicians have come to challenge classical logic. I mean, classical logic was pretty very much orthodox in the up to about the 1960s, then a number of people started to worry about it. I think it's probably fair to say that it's still the orthodox view, especially in philosophy. But I think that logic's in a very exciting state of the moment, because a lot of logicians have come to realise, there are all kinds of ways in which we may not have got it right. And we really need to think about these things very carefully. So even if there is an orthodoxy, then we're not as sure that we that the orthodoxy is right, as we were say, 50 years ago, there's a very exciting time.
PA: Maybe now we can turn to the Buddhists, which obviously is the most interesting thing from the point of view of this podcast series. And I mean, from what you've said, it's obvious that the Buddhists weren't operating with classical logic, surely least unless they independently discovered Fregean logic, which is unlikely.
GP: Which they didn't.
PA: Yeah. And I guess maybe one question that arises before I ask you about parallels between contemporary work and non-classical logic, and Buddhist, ancient Buddhist logic. To what extent do you think it's fair to ascribe to ancient Buddhist thinkers logic? Because clearly they weren't doing the same kinds of things that say Russell is doing in the Principia.
GP: That's a good question. They certainly weren't doing anything that you might recognise as contemporary formal logic. Things are much more complicated and nuanced than that. First of all, when we talk about the great Buddhist logicians like Dignāga and Dharmakīrti, you wouldn't really want to call them logicians in the modern sense. They used the word ‘logic’ to mean something like epistemology. So these guys are particularly concerned with epistemology. Epistemology is concerned with sources of knowledge. So what are the source of knowledge? Perception, testimony, inference. So you need to have a story to tell about those things. And so they do engage with inference. That's something that is part of contemporary logic, but they didn't have particularly sophisticated theories. So Dignāga, Dharmakīrti, formate, sort of a formal logic, which is a bit like Aristotelian syllogistic, but it's different. But it's about that kind of level of power, maybe less powerful. So I don't think that's really where the interest lies. Epistemology is really interesting, but I don't think that if you look at their theories of inference, they're going to be particularly exciting for a contemporary logician. I think that's where the interest lies. The interest lies elsewhere and it's back a lot further. It's very hard to draw the line between logic and metaphysics in some sense, especially in the old positivist era. People thought that logic was metaphysically neutral. That I think is almost, well that's certainly false. And I think most philosophers would now agree with that. I mean, just think for a moment about my description about intuitionist logic. That's obviously not metaphysically neutral because it's to do with reality, physical and mathematical. And you don't have to sort and probe most systems of logic very hard to see that they've got metaphysical underpinnings. So one of the things about the people who worried about things which you might want to call logic are interesting because they just have very, very different metaphysical underpinnings. So it's not in the epistemology that you find things which are interesting for modern logicians; it's in the metaphysics. Okay, so there are thinkers in ancient India who have metaphysical pictures which are very different from most contemporary Western metaphysical pictures. The Buddhists and the Jains do. And in Buddhism, you get a view called the Catuṣkoṭi literally means four corners. What the four corners are, are possible answers to a question. So for example, at one point, someone asks the Buddha, well, you know, what happens to someone who's enlightened after they die? Do you think they exist? Do you think they don't exist? Do you think they both do and don't exist? Do you think they neither exist nor don't exist?
PA: By the way, we were calling the Tetralemma in earlier episodes.
GP: That's exactly the Tetralemma. Okay. Now the Buddha refuses to answer yes to any of these questions. That's another story. What's clear is that these guys think that those four answers are all on the cards. Now, their picture of reality allows for those four possibilities, as it were. Now in the West, at least until recent times, only two of those are on the cards. Yes and no. You can't have both. You can't have neither. Well, it's actually a bit more complicated than that because sometimes Aristotle does suggest neither, about the future. But generally speaking, the only two main answers that have been on the cards are yes and no. Whereas at least for the Catuṣkoṭi, the Tetra lemma, you've got four answers on the cards. Now these guys never work that up into the rigor of modern logical system. We know exactly how to do that now because of developments in contemporary non-classical logic, where there are logics where you have exactly these four possibilities and we know how exactly to handle these things. So that's the Buddhists. Now the Jains as well. The Jains are even cooler because for the Buddhists, at least the Buddhists at that time, there are four possibilities. The Jains had seven. Why seven? I hear you asking. Well, it's because it's two to the three minus one. Okay. We can, I'll talk about that if you want, but we don't need to. So, but the Jains had this Saptabhaṅgī, the seven answers and that's wrapped up with a metaphysics of aspects. So the Jains think that reality has many different aspects and things can have be, you know, holding one aspect and not another. So you have to take into account all these aspects and okay, it's a long story, but that's how you get seven.
PA: Can I actually go back to the, what you said about the Tetralemma? Because I think maybe the easiest way to get us to see why this might be a different way of thinking about logic would be to focus on the third answer because we already talked before about the neither answer, right? So it's like, it could be a category mistake. Maybe it's neither provable that it's true nor that it's false. And if truth is provability, then hey, you have your neither answer. And so it's not that hard, I think, to get your mind around how a meaningful proposition could be neither true nor false. You gave another example just now Aristotle says, well, maybe things in the future that aren't yet decided. If you say something will happen, that might be neither true nor false. I guess a battle will happen tomorrow. But what about both? So can you give me an example of why it would be useful to think about that? A meaningful proposition could be both true and false.
GP: Okay. So a little bit of history again. What we're talking about is the principle of non-contradiction, which says essentially it rules out the third koṭi. Okay. So something can't be both true and false. And this has been high orthodoxy in Western logic philosophy since Aristotle, much more so than the principle of excluded middle, which is the other thing we talked about. Aristotle defends the principle of non-contradiction in the Metaphysics. And he has a long string of arguments in defense of the principle. And most modern commentators think these arguments really don't work. But for a start, they're not very clear. Most of them, well, a number of them clearly beg the question. But Aristotle is attacking certain people. He tells us who they are. He tells these attacking Heraclitus, Anaxagoras. So he thinks that there's an issue to be fought here. And so he fights it. And even though the arguments actually not very good, they kind of secured the principle of non-contradiction a place of high orthodoxy in the history of Western philosophy. So much so that virtually nobody has even bothered to defend the view at any length since Aristotle, as far as I know. So virtually every philosopher in the West has accepted the principle of non-contradiction, at least until recent times. Now, there is an important exception. That's Hegel. So interpreting Hegel is a dangerous business. You haven't probably got Hegel yet in the series.
PA: It's something I'm looking forward to in some trepidation, actually.
GP: Look, there are certainly attempts to consistentize Hegel. But if you read the guy, he is, all right, the view that some contradictions are true, the modern name for that is dialetheism. And a dialethe is something that's true and false. If you read Hegel with an open mind, this guy is a dialetheist. There's absolutely no doubt about that. For example, when in the logic he discusses motion, he says, what is it to be in motion? Well, it's not to be here over on my right at one point of time and here over on my left at another point of time. But it's to be here and not here in one and the same place at one and the same time. That's almost his exact words, but yes, we're translating to English. So he says motion itself realizes contradictory states for affairs. He then draws on paradoxes like Zeno's paradoxes of the arrow and so on. So he's a big exception in the history of Western philosophy because he's a really important philosopher in history of Western philosophy. But what I mean, the fact that he's an exception just tells you how orthodox his principle has been because there aren't many others. All right. Now, I haven't forgotten your question, but I was just putting it in some historical context. One thing that happened around the 1960s in contemporary logic is the development of systems of logic where what fails is not the principal excluded middle, but the principle of non contradiction. So these are logics which are now called power consistent logics. These are systems which are which are logic tolerant in a certain sense. So in classical logic, once you've got a contradiction, all hell breaks loose because it's a principle of classical logic that a contradiction implies everything. So once you've got one contradiction, you've got everything. The defining feature of power consistent logic is that this is not the case. So you can have a contradiction and it's kind of constrained, it's limited. And these are power consistent logics started to be developed in the 1960s, 1970s. And we now have a pretty good understanding of how they work. There are many of them. All right. So if you can have a logic that tolerates contradictions, then you start to wonder, well, could some contradictions really be true? I finally get around to your question, which is, well, give me some examples. Now, there are many examples. Maybe when you get around to 20th century logic, we can talk some more about this, but probably everyone's favorites are the paradox of self-reference. So there's a whole family of paradoxes of self-reference, which became really, really important in the foundations of mathematics around the turn of the century, because they turned up in the foundations of mathematics. Russell discovered one of the most famous paradoxes, somebody called Russell's paradox that crashed Frege's program. So, you know, we're not playing games here, but the oldest paradox of this kind go back to the fifth century BCE. There's a paradox called the liar paradox. It was invented by or discovered by the Greek thinker, Eubulides, and it might sound like a party game, but it isn't because it's closely connected with all this stuff that turned up in the foundations of mathematics in the early 20th century. So the liar paradox is this. Suppose I say to you, what I'm now telling you is false and you ask yourself, well, is it true or is it false? Well, if it's true, well, it says it's true. It says what I'm telling is false. So if it's true, it's false. Oh, okay. So suppose it's false. Well, it says that it's false. So it's true. So prima facie, the liar sentence, this sentence is false is both true and false. So your question originally asked for an example. So this is one example that modern dialetheism often give us a possible example. So paradox like this have been discussed at length at nauseam in the three great periods of modern, the two great periods of logic, ancient, medieval and modern. And as far as that paradox goes, there is still no consensus. Most people have thought there's something wrong with the argument. They've tried to explain what goes wrong with the argument. At least if you judge by consensus, there have yet been no success because amongst modern logicians, there's still no consensus about how you handle this. So the dialetheism sort this: Hey, take something like the liar paradox. Why suppose that there's something wrong with the argument, especially since we've had, it's been so difficult to explain what is wrong with it. Maybe it's what it appears to be, namely a ridicule argument for something that's true. And the truth is a contradiction. So this is a contentious view, but this is one example that frequently gets appealed to, to explain some examples of dialetheism.
PA: You know, I find it interesting that the Buddhists, we originally started talking about this in the context of the Tetralemma, and the great expert in the Tetra lemma and how to wield it is of course Nāgārjuna. And he usually uses it to give four options, all of which he's going to refute. Right? So for example, he'll says, well, here's four things you could think about motion or causation, right? So something is self-cause it's caused by another, it's caused by itself. And the interesting thing is that when he gets to the third option, he doesn't say, well, this is obviously silly because it's a contradiction. He actually gives you a detailed argument against it. Right? So he seems to have thought, I mean, there's obvious, as we talked about in the episode on Nāgārjuna's Tetralemma, there's different ways of interpreting what he was up to there, but at least they seem to lack what apparently classical logicians and a lot of other people have as a very strong intuition, which is that you can immediately rule contradictions out of court.
GP: And that's because Nāgārjuna is picking up on the history of Buddhist philosophy, which by that time is 700 years old. Now the Tetralemma is canonical Buddhism. It's in the sutras. So Nāgārjuna is, you know, a good Buddhist. He's not going to turn around and say: hey, the Buddha was crazy. Okay. So the Buddha in the sort of context we just talked about, it's true that he refused to answer. Now that's going to be important for Nāgārjuna as well. But the Buddha didn't… when the disciple says to Buddha, well, do you think the enlightened person after death might both exist and not exist? The Buddha doesn't say, Oh, don't be silly, my dear, you know, the principle of non-contradiction rules that out. The Buddha is prepared to countenances and Nāgārjuna is just, you know, paying, he's being faithful to the tradition. Nāgārjuna deploys the Catuṣkoṭi in a very novel way. You summarized the use that Nāgārjuna makes of this just now. I don't think that's quite the right way to look at it. Okay. Interrupting Nāgārjuna is hard. Okay. But I think this is the right way to look at it. And I think many of my colleagues agree with this. Nāgārjuna is the foundational philosopher of Mādhyamaka, which is one of the two kinds of Indian Mahāyāna philosophy, Buddhist philosophy. And the central thought, the central metaphysical idea of Mādhyamaka philosophy is that everything is empty. Now, what does that mean? It most certainly does not mean non-existent. If something is empty, it's empty of something like the glass is empty of beer. So if things are empty, what are they empty of? And the answer is, they are empty of the Sanskrit term, the term is Svabhava, literally means self-being. You can translate it if you like as intrinsic nature. So the metaphysics of early Buddhism first 500 years held that ultimately reality is composed of call them atoms, if you like, they're not atoms in the modern sense, but they're kind of the building blocks of reality. The word is dharmas. And these dharmas have intrinsic nature. Okay. And what happens when you get the rise of Mādhyamaka is Nāgārjuna launches a severe attack on the older metaphysics. So Buddhism is not what I think Buddhism evolves over two and a half thousand years. And this is, this is one of the turning points in Buddhist philosophy, where Nāgārjuna attacks the old metaphysical picture. How does the Catuṣkoṭi feature into his attack? Well, what many of the chapters of the Mūlamadhyamakakārikā do is perform a reductio on the claim that something or rather has Svabhava. So he runs through all the things you might think has Svabhava and reduces those views to absurdity. So the chapter you mentioned on the causations is the first chapter of the MMK. There's a tacit assumption that causation is Svabhavik. It has an intrinsic nature of its own. Now, that's not explicit in the text, but that's really what's going on. You start with this unspoken assumption that there is, in this case causation has Svabhava. Okay. So if there is Svabhava, there are four possibilities that something about it is either true, false, both or neither. And that's what Nāgārjuna reduces to absurdity by going through the four cases. It's actually a pretty standard reductio argument. You make an assumption and you show that there are various possible cases and none of those works. Now, if you do this in the West, there are only two cases to consider true false, but Nāgārjuna is working in the context of the Catuṣkoṭi. So he's got four cases to consider. So that's why he runs through the four cases and has to take account of all of them, as you pointed out. But the ultimate aim of this is to produce a reductio on the assumption that something or rather has Svabhava. That's what's going on in many of the chapters of the Mūlamadhyamakakārikā.
PA: So we've seen with the Tetralemma that he at least considers as a viable option this both case. So it's both true and false, let's say, or both self-caused and not self-caused in the case we were just talking about. But of course he rejects that. Are there other cases in ancient Buddhism where they are thinking like dialetheic logicians and asserting something that's a contradiction?
GP: Okay. So in the Mūlamadhyamakakārikā, Nāgārjuna often runs through these four cases and he rejects all four. But what he's rejecting is actually the initial assumption made for reductio. So that in itself doesn't show there's a fifth possibility. However, there are other places in the Mūlamadhyamakakārikā where he does suggest there's a fifth possibility, where he actually says that there are cases where none of these four applies. So this is not in a reductio context. It's not just a knockdown argument. This is where he's putting forward a view that there is a fifth possibility. This is where interpretations of Nāgārjuna get much more contentious amongst scholars. However, the natural reading, at least for me, of the Mūlamadhyamakakārikā in these passages as far as it's standard in Buddhism that there are two kinds of reality. There's a kind of ultimate reality and then there's a kind of, which we're not really aware of, there's a conventional reality which are Lebenswelt, which we are aware of. And in the older Buddhist tradition, the ultimate reality was composed by these things called dharmas. And you might well think, well, Nāgārjuna attacked the views about the dharmas, so he might have done away with this view that there's an ultimate reality, but he doesn't because he's got to be faithful to a number of the texts and a number of the sutras by this time are talking about ultimate reality. So what is ultimate reality for him? Well, he doesn't spread it out much, but the view that kind of evolves over the next, certainly over the next couple of hundred years, is that reality, ultimate reality is what you get when you strip away the conceptual overlay from things. So if we take a chair, for example, and we strip off its blueness, its four-leggedness, its chair-ness, these are all sort of concepts we apply to it. Suppose you peel these off in a certain sense, then what remains is what was there before any conceptual overlay. It's that that Nāgārjuna thinks is ultimate reality. All right. So what's ultimate reality like? Well, obviously you can't answer it because any answer you give is going to have to apply concepts.
PA: Can't you say it's empty?
GP: Well, that is applying a concept because emptiness is a concept. You just cannot answer the question. Ultimate reality is ineffable. And the fifth possibility is true, false, both, neither ineffable. That's the fifth possibility. Now we're facing some real problems because ineffable, yeah, but aren't you just talking about it? Yes. So you can talk about the ineffable. Yes. Isn't that a bit paradoxical? Yes. All right. So Mādhyamaka philosophy seems to have a problem with this paradox. Buddhists, Buddhist scholars, Buddhist philosophers respond in different ways to this paradox in exactly the same way that Western logicians have responded to the Liar Paradox. But prima facie is a real problem. Talking about the ineffable, I'm inclined to think that the best way to understand what's going on is to suppose that you really have a contradiction here, that you have to accept that at least some of the things that are ineffable you can talk about, which takes us back to my meeting with Jay. Because once we started to discuss this, we realized that one interest we both had was in this kind of situation. He was coming at it from his translation of Nāgārjuna. I was coming at it from the direction of contemporary logic. But it was a phenomenon that we both thought was very important. So, I mean, the Liar Paradox is not about ineffability. But there are paradoxes in the same family as the Liar, which are very, very close, where it does look as though you start to talk about things that are ineffable. These arise in connection with large infinities, where some things are so large that you can't describe them. There are more things in infinity than you can possibly describe. So, there are things in infinity, in the infinite world of set theory that you can't describe. Yet, I can tell you what some of these things are. Like, you know, standard set theoretic construction. This is sometimes called König's Paradox. Julius König was a, I think it was a Hungarian logician, mathematician working around the 1920s, maybe 1910. So, I don't expect your listeners to follow all those details. But the point I'm making is that they look as though there are paradoxes and ineffability in modern logic as well. So, I had some paradox ineffability. Jay had what looked like paradox ineffability. And we thought, well, okay, maybe we should start thinking about these together. So, that's where we've written a number of papers together over the years. But that was the starting point of our cooperation.
PA: And just as a last question about this, I mean, do you see this more as using the ancient Buddhist tradition to find resources that could be used in contemporary logic, for example, work on non-classical logic? Or do you think of it more as using the tools of non-classical logic to understand Nāgārjuna, say, which actually is what you do in some of these papers?
PA: So, you have papers where you're talking about the Svabhava theory, and then you turn the page and there's lots of symbols and sort of mathematical logic. Or do you just see sync the two kind of go both ways? So, you can use contemporary logical tools to understand ancient Buddhism, and you can use ancient Buddhism to inspire work now?
GP: I think it goes both ways. The history of philosophy is really important for contemporary philosophy because there have been lots of great philosophers. Most of them are wrong about most things. That's philosophy after all. But they're important points of understanding that all great philosophers have, whether they're right or wrong about everything. Nonetheless, there's so much you can learn from the great philosophers of history because they're smart people and they all had fantastic points of insight. So, we can, in a sense, kind of mine the history of philosophy for insights which we can learn anew. So, how many times in the history of Western philosophy have we mined Plato or Kant or Hegel or whatever? These are rich sources which we can apply. And exactly the same goes for the Asian traditions. Metaphysical insights of Mādhyamaka are really, I think, profound. And if you apply these, then you naturally come up with something like a four-valued logic, maybe even a five-valued logic. And what this shows is that when modern logicians have started to examine these systems, you might think that they were just playing games. You know, you squiggle a few symbols and it's a bit like chess. Okay. Some logicians do that. That's fine. But what these sort of metaphysical insights do is show you that you can think of these systems of logic that modern logicians have come up with as anything but playing games. They're really, I mean, I said that any logic has metaphysical underpinnings. Okay. What the Buddhists are doing are actually showing us some of the things that could well be metaphysical underpinnings and modern logical systems. So if you want to understand the connection between modern logic or some modern logics and metaphysics, hey, you know, the Buddhists and the Jains actually have something very important to teach us about what's going on in the sort of metaphysical underpinnings of these logical systems. So that's the influence one way. Now, the influence goes back the other way because it'll be silly to suppose that Nāgārjuna had the tools of modern formal logic. It'll be silly to suppose that Plato did. But one thing you can do with modern formal logic is articulate views in a much more careful way than the thinkers of the time had the ability to do. And it was not that they were stupid, far from it. They just didn't have the tools. So it's not a criticism of Aristotle. They didn't have a microscope. If he had a microscope, he'd have made great use of it. Right. But we can now know a lot more about biology because we have a microscope in the same way we can now understand the views of Plato, of Nāgārjuna, much better than they themselves could have done. And that's not because we're smarter than they were. They were probably much smarter than we are. Okay. But it's because we have the appropriate tools like the kind of logical equivalent to the microscope. So we can go back and we say, okay, so this is what's going on in the Mūlamadhyamakakārikā. Let us formulate it with all the clarity and the precision of modern logic. Let us see what the import of this idea is. So now we formulate it more precisely. We can see what follows. We can look at its logical consequences. We can examine the arguments that get put forward for this view to see how good they are. So often we apply modern logic to analyze the Western arguments for the existence of God. Okay. And that's fine. And Anselm, Descartes didn't know anything about modern logic, but we understand their arguments much better because we've got the tools, same for Nāgārjuna. So I do think that the enlightenment goes both ways. I'm a great fan of modern philosophy. I'm a great fan of the history of philosophy, East and West. And one thing I love is trying to take insights from both to help me understand the other better.