Theories of Everything with Curt Jaimungal - Graham Priest: Logic, Nothingness, Paradoxes, Truth, Eastern Philosophy, Metaphysics

Episode Date: April 15, 2024

Curt Jaimungal and Graham Priest sit down to discuss various philosophical themes including the nature of truth, logic and paradoxes, the philosophy of mathematics, concepts of nothingness and existence, and the influence of Eastern philosophy on Western logical traditions.Please consider signing up for TOEmail at https://www.curtjaimungal.org  Support TOE: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - TOE Merch: https://tinyurl.com/TOEmerch  Follow TOE: - *NEW* Get my 'Top 10 TOEs' PDF + Weekly Personal Updates: https://www.curtjaimungal.org - Instagram: https://www.instagram.com/theoriesofeverythingpod - TikTok: https://www.tiktok.com/@theoriesofeverything_ - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything  Links Mentioned: BOOK - "Logic: A Very Short Introduction" - https://a.co/d/cyGwXCK BOOK - "Everything And Nothing" - https://a.co/d/hUHGGM0

What is true is not something that corresponds to some kind of reality, but something for which there is appropriate verification or evidence or something like that. Sometimes this kind of notion of truth is said to be epistemically loaded. Nothing is what you get when you fuse no things, when you put no things together. Nothing is both something and nothing. There's a paradox concerning nothingness, because nothingness is something. You can talk about it, you can think about it, you can wonder whether there is such a thing, you all know. Graham Priest is a philosopher known for his work in logic and philosophy of math.

His book, Logic, a Very Short Introduction, is considered the quintessential book, the philosopher's stone, if you will, of logic. If you've ever taken a logic course in university, this is the beacon that's assigned. Today we talk about logic, paradoxes, how can contradictions be true, or more accurately, how can contradictions be the case, which is a different statement. Furthermore, what is nothingness, what does everything mean in a technical sense, what is dialectical logic and paraconsistent logic. Graham Priest holds the title of Distinguished Professor of Philosophy at the City University of New York. Professor Priest's contributions also

extend to Eastern philosophy where he examines non-classical logics found in Buddhist thought drawing parallels with Western logical traditions rather than the mere contrastive approach that most others take. This is a fantastic episode. I've been waiting to speak to Graham Priests for literally years. My name is Kurt Jaimungal and I have this podcast here called Theories of Everything, which is about exploring theories of everything, usually in the physics sense from my background in mathematical physics.

But more and more, I've become interested in philosophy and the largest questions that we have such as what is consciousness? What is everything? Which is explored here. What is nothing? What is existence? What is real? This podcast is like wine. The longer you listen into it, the better it gets, especially the last half hour. And that's saying something because man, Graham starts off strong and technical. Enjoy this podcast with Graham Priest. So Professor, there are various Zenos paradoxes. Many people just know about the one about the tortoise and you just go half and half. You can't overtake the tortoise.

But there's another one that you like called Zeno's Arrow. Can you please outline that for the audience? So as you say, the four paradoxes from Zeno have come down to us. The ones that most people are aware of are the ones that depend on the thought that you can't do an infinite number of things in a finite time. So if I'm going from here to Toronto i gotta get half way first and then. Halfway again and half again and so on so forgets toronto i've done an infinite number of things and the paradox. Depends on the thought you can't do that in a finite time and no one would now think that's true although it might have been a plausible assumption for zeno.

would now think that's true although it might have been a plausible assumption for Zeno. However the one that you mentioned the arrow is rather different and it goes like this. Let's take the arrow. Suppose I fire it from my bow and it makes its way to the target. Now, take some instant of the motion. At an instant, the arrow makes zero progress on its journey. Because it is an instant and it cannot occupy more than a single place at that instant. So it makes zero progress doesn't get any further. Okay, so progress at any instant is zero now at least going to sort of standard mathematics and physics the time

Between my firing the arrow and hitting the target is made up of those instance so at each instant it makes zero progress so if at each instant it makes zero progress it can't make any progress over the whole period because you can add zero to zero as many times as you'd like, even uncountably many infinitely times and you still get zero. So, uh, the argument goes, the argument cannot move. It cannot get from the bow to the target. That that's the, that's the Zeno's arrow paradox. So why can't measures theory overcome this?

Well, yeah, look, it can in a certain sense. So if you try and apply standard measure theory to this, it depends on the thought that if you have a bunch of intervals with non-zero measure, or with zero measure rather, and you add them all together and consider the measure of the sum, then this can have non-zero measure, provided there's enough of these things. And you need an uncountable number to do it, but that's okay. So that's some mathematics, but the problem is not about mathematics. The problem is about how the arrow manages to actually move. And that's not going to be solved by mathematics. You need to tell a story of something else,

something that relates to the real world to do this. So just so, I mean, if you assume that you can add an uncountable number of intervals with zero measure together and you get something with non-zero measure. That's true but how is it that reality answers to that bit of mathematics? There can be other bits of mathematics you could use. You could have a different kind of measure theory. Why choose that one? Well because the one you choose has got to apply to reality in some sense. So what is it in reality that makes that the appropriate bit of mathematics? And that's the real problem, I think.

So this is seen as a paradox, and there are various types of paradoxes. Most people think of paradoxes the same as contradiction, but there are at least three. Can you please delineate them? Um, the reason being that paradox is going to come up again and again in this entire interview. So we may as well be specific as to what we're speaking about. So normally I think there are two, the vertical and the false vertical. Um, I'm not quite sure what you're thinking of as the third, but you can tell me.

Antinomy, so self-contradictory. So a vertical would contradict our intuition, and a false-sydical seems true, but there's some fallacy in it. Okay, so let's take a step back. What is a paradox? Okay, and the standard definition of a paradox, everything in philosophy is contentious, but what most people are saying, I think it's right, is that a paradox is an argument for a start. It's an argument that proceeds from premises that appear to be true, with steps of inference that appear to be valid and yet the conclusion you deduce something which isn't true, maybe can't be true but certainly isn't true, right? So you're starting off with these things which appear to be true to you, making inferential steps that appear to be right, you end up with something you can't accept.

That's the paradox. Now if you take that as your definition of a paradox, you've got two choices. Either there's something wrong with the argument or the argument's fine and you have to accept the conclusion. Okay. And usually the ones where you accept the conclusion on reflection are called veridical So you might have thought you couldn't accept the paradox, but you can a paradoxical conclusion but you can and The for cynical ones is where something has gone wrong with the with the argument

And then of course we worry about what the argument is and there are both kinds in the history of philosophy is. And there are both kinds in the history of philosophy. So, for example, the liar paradox, which we can come back and talk about if you want to, is usually taken to be a false, cynical paradox. People think there's something wrong with the argument. And the name of the game for two and a half thousand years has been, find out what it is. But there are other paradoxical arguments which are now thought to be veridical. So a very standard paradox until the late 19th century was, it's sometimes called Galileo's paradox but it was known a long time before him that if you take the natural numbers 0 1 2 3 4 5 6 etc and you take the even numbers 0 2 4 6 8 and so on then you can put those into one-to-one

correspondence you pair off 0 with zero, two with one, four with two, six with three, and so on. So there's a one to one correspondence between the even numbers and the natural numbers, okay? Yeah, and so it seems that there's the same number of each because they can be put into one to one correspondence, but it seems plausible that there's got to be more natural numbers than even numbers,

because you've thrown away all the old ones. OK, so this was a standard paradox until the end of the 19th century in the work of a mathematician called Cantor on the infinite. And now the standard response in mathematics is, well, you thought that the naturals and the evens have a different number of numbers, but you're wrong. They actually do have the same. They're actually the same number of natural numbers

and even natural numbers. And puzzling as that may seem at first, that is now thought to be true. So there's a paradox which has turned out to be veridical in modern mathematics. You thought you couldn't accept the conclusion. It's counterintuitive for sure. But okay, it is true. And that's the way that things work. And then you tell a story about set theory to explain why. Additionally, because we're going to be speaking about logic, it would be great to get a definition

of logic. Look, that's a hard question and it's hammered around in the philosophical literature by philosophers and logicians. Well, just for the people who are watching and maybe they skipped the introduction and they're not aware of who you are, you're a preeminent philosopher. In fact, you have the title of distinguished philosopher at the City University of New York. And furthermore, you've written what's considered to be the go-to text in logic, which is the very short introduction to logic. So you know what you're talking about. And when you laugh, you're laughing for a particular reason.

This isn't just someone who hasn't studied logic or studied it at the surface level, you're deep in it. You're the source of it in a sense. So please explain. But I'm certainly a logician, okay? So I laughed because you're asking a contentious question because people disagree about that. And the word has been used in many different ways in many traditions over the last two and a half thousand years.

So let me just tell you how contemporary logicians tend to understand the nature of logic. But even that's contentious, but as a first cut, it's something like this. We argue, that is, we give reasons. And reasons start from premises, that is things that you assume for the sake of the argument, and then steps in the argument which take you to your conclusion. OK. Now, whether or not the premises are true will in general be someone else's business.

So if we're talking about something in geography, whether something's a geographical fact is going to be the business of the geographer. Simileaf history or psychology or whatever. But what a logician is interested in is given the places you start, what are the legitimate steps that you can use thereafter? So what are the legitimate forms of inference? And logic is the study of answers to that question.

So if I'm arguing with you about something, you may use a form of inference, and then it's up to the logician to tell you whether or not it's valid you whether or not it's valid, whether or not it's a really good, it is a good step in the argument. So in a nutshell, most modern logicians would tell you that logic is the study of what follows from what and of course why because Saying yes or no is bit boring. You gotta have understand why

Okay, so it's akin to Following the rules of the game and then sometimes you can argue about why some rules are more applicable to this universe than others And what's making an argument? It's about what what the right rules of the game are. So an analogy not to be pushed too far is with grammar. So we speak a natural language. Let's take English since we're both speaking English now. What grammarians do is try to figure out the rules of the grammar of that language. What are the rules which determine whether a sentence or string is grammatical, the cassette

on the map, or ungrammatical, like the cassette is met on? So logicians, sorry, grammarians or linguists in general, try to figure out what the rules of that game is, if you want to call it a game. And what logicians do is try to figure out similar rules, not about grammaticality, but about validity, about when things follow from other things. Now you mentioned that we are given a set of axioms or a set of statements we believe are true and then you say, okay, well, what follows from this? When we say that rules of inference are there to then bring you to someplace, but you mentioned the starting places is not the place of logic. Is that always the case?

Or is there a form of logic that tries to bootstrap itself up? Well, if your premises are about logic itself, then of course the truth of the premises is the logician's concern. But most arguments are not about logic, they're about something else. But yes, you're right. I mean, in unusual cases, the premises could be about logic as well. In unusual cases, the premises could be about logic as well. The reason I'm asking is that there's a philosopher named Christopher Langen. I'm not sure if you've heard of him, but he's known for the cognitive theoretic model of the universe, which is an attempt to build a language or a meta language that describes the universe.

But anyhow, what I would like to talk about is this conversation, again, we're going to get more deep into the weeds. This whole conversation will stand on three legs, logic, truth, and then reference, because we're going to be speaking about the liar's paradox and other forms of paradoxes and even nothingness and everything. So what are the different theories of truth and where do you stand on it? Obviously there are too many to name but let's say the predominant ones. Yeah, okay. So the nature of truth has been hotly contested in philosophy east and west for two and a half thousand years Okay And there's no consensus on the matter

So there are many different theories as A first cut you can So there are many different theories. As a first cut, you can distinguish between those that are realist in some sense and those that are non-realist. So the realist ones, I'll tell you, something's true if it corresponds to reality. There's some stuff out there we call reality, and the true statements are the ones that have the appropriate kind of correspondence. And what that is, of course, highly contentious.

But those are sort of realist theories. Then the anti-realist theories are ones which do not like to talk about this kind of metaphysical notion of reality, and so they give some other kind of answer. And then there can be various kinds of answers. So a very standard kind of answer is that what is true is not something that corresponds to some kind of reality, but something for which there is appropriate verification or evidence or something like that. So sometimes this kind of notion of truth is said to be epistemically loaded

because what makes something true is precisely its verifiability or the grounds for knowing that it's true or something like that. So there are a number of different theories which fall into those two categories, but as a first cut, that's a sort of rough distinction. And some theories of truth, they're kind of hard to sort of fit into that dichotomy, so it's complicated. I don't really have a horse in this game. I suppose I have a kind of temperamental disposition towards some kind of realism, but I think the matter is contentious.

Why do you say that? Oh, that's just a comment on me. It's not a comment on the truth. That's just, you know, the way I'm disposed to favour things. But that's a comment about me, not a comment about the subject. I mean, everybody has various dispositions in philosophy, as you know, in everywhere else. Some people do have realist dispositions, you know. If something's true, there's gotta be a ground for it. What could that be? Well, it must be some kind of reality, okay?

And that's kind of an intuition that appeals to many people, including me. And some people think, no, you know, talk of what's true in abstraction is sort of vacuous misleading. I mean, truth is just what we've got evidence for. And some people find this kind of intuition persuasive. I find that less persuasive, but I can see that there are arguments for it.

So sorry, that's a rather evasive answer to your question, but that, I mean, you can ask a dozen philosophers that question, you're going to get a dozen different answers. Well, what I meant was more psychological. How is it that you even identified that this is your predilection or your affinity? You have an affinity toward a realist position. Is it because you noticed when someone is speaking from a realist point of view, you have an affinity toward a realist position, is it because you noticed when someone is speaking from a realist point of view, you jive with them or you're less anxious like how is it that you even came to the realization?

The realist intuition is that truth does not float in mid-air. If something is true, there must be something that makes it so. Okay? And then what could that be? Well, you know, look, here's something that's true. Melbourne is in Australia. What makes that true? Well, I mean, it's partly the meanings of the words, like the meaning of the word Australia, the meaning of the word Melbourne. But in the last instance, what makes that true is a bit of geography about, you know, a continent in the Southern

Hemisphere of our planet. So, would that be the case always? Because even an idealist, at least many idealists would say that what makes something true is that it corresponds to mind. Now they may just not say it's reality, they may say it's mind, but they would also say that there does exist illusory concepts or illusory facts or illusory experiences and it's because they don't correspond in some way to the ground of reality, which itself is mind. It's just they have a different ground. Um, okay. So that there are plenty of real idealists and those are usually, um, so, so you raise the question of idealism, uh, and idealism is that there are many different kinds. Okay, but standardly at least,

most idealisms are taken to be some form of anti-realism. So there's no reality external to your mind, it's all in your mind. I guess I've never been disposed to that. Why? Because it seems to me that what makes it true that Melbourne is in Australia? It's not something in my mind. I mean I can't make Melbourne somewhere else by just changing my mind about it. If I did, I'd just be mistaken. And you know, the same is true for the whole human race.

If everyone was kind of befuddled by some kind of social media and started to think that Melbourne was in New Zealand, they'd just be wrong. So I mean, it does seem to me that in some sense, facts about the world, at least some of them, not all of them, but some of them have to be mind independent. I believe there's a difference here between solipsism, so it's all in your mind, versus it's all in mind. Correct. So mind is the ground of reality.

Well, yeah, no, you're right. I mean, solism, Ptolepsism is the view that there's only one mind in the world. And if you hold that view, you could, I guess, be a realist as well. There's only one world. But most people who are solipsists will probably be some kind of idealist as well. That's true. Earlier, you used the word intuition and there's a strand of logic called intuitionist logic. Again that's something that many people don't know about. There are different forms of logic. They would just think there's classical logic.

So please outline what intuitionist logic is and then this is a great time to talk about para-consistent logic and Your particular brand of logic Okay, so look there are lots of things there You mentioned intuitionism I'll come back to that in a second But that that use of the word intuition has nothing to do with the way that I was using the word. I mean these It actually derives back to a view of Kant who used the word intuition from to mean something like sensation and intuitionistic logic is supposed to be derived from Kant's view of time which informs our sensations. Okay let's

not get into the weeds I just wanted to make sure that this this thing intuitionist logic is a is a very technical reference to Kant although the philosophy of intuitionism doesn't necessarily go back to Kant. Okay so Okay, so let's put that aside. Look, I said that a modern logician will tell you something like logic is the study of what follows from what and why. And the views about what follows from what and why have been changing over the last two and a half thousand in the West, let alone the East. Let's just stick to the west to keep things simple. So the first person to produce some kind of theory about what follows modern why was Aristotle. Okay, no

one believes Aristotle's view now. The medieval Christians and the Arabs had different views, building on Aristotle's views about what follows from what and why. Then in the 19th century, you get all sorts of new views about what follows from what and why. And one that's been very influential was produced by the German logician Gottlob Freger and the English mathematician Bertrand Russell. And that was much better than anything that had gone before, so it quickly became orthodox. And that's now what's referred to as classical logic usually.

So classical logic has nothing to do with the classical civilizations of anywhere. Okay. It's completely different from Aristotle's view. In fact, it's inconsistent with it. But it became kind of orthodox early in the 20th century. But since then, logicians have invented many other possible answers to the story of what follows from what and why. And these are now usually called non-classical logics in contrast to the logic of Frager and Russell. Okay, to a bit of terminology. Now, intuitionistic logic is a non-classical logic.

It was invented by, well, it's mainly a product of the Netherlands. So intuitionist philosophy as such was produced by a Dutch logician, just mathematician, Bra, and he's working around the same time as Russell, and he has a critique of orthodox mathematicists of his day, and he says, well, you know, it actually, standard mathematics uses principles of inference that are wrong. And he tries to develop a different kind of mathematics which doesn't use these principles he thought were invalid. So he was not a logician, he was a mathematician and he didn't think much of formalizing logic. But about 20 years later there was another Dutch mathematician called, whose name is Heiting, and he formalized the sorts of reasoning that

he thought that Braille was using. And it's that that's called intuitionistic logic. Okay. And it differs from so-called classical logic in a number of ways. Probably the most famous, although actually it's not the most fundamental, is something called the principle of excluded middle. So we're inclined to assume, and it's certainly assumed in the mathematics, orthodox mathematics, that if I say something, either true or false okay 10 to the 10 to the 10 is either a prime number or it isn't 10 to the 10 plus 1 is either a prime number although it already isn't okay we might not know the answer we

have to say something well-founded well if it's not well founded, would you just say it's false or you would just know that that according to these guys, if there's some kind of procedure for determining the falsity, then it's false. Otherwise, it's kind of neither. You've got to be very careful about how you formulate these views, but that will do for this very rough and ready forum. So Brauer thought this was crazy because he was one of these people who thought that truth had to be determined by evidence. And if you have no evidence for claiming mathematics, either that is so or it's not so, then he

thinks you can't apply the law of excluded middle to it. So let me give you an example. Take the decimal expansion of pi. So pi is an irrational number. So it's the form three point something, something, something, something, something, which goes on forever without repeating. And we know what the decimal expansion of pi is to some enormous number of decimal places because there are computers that try to figure this out,

but they only know a finite part of it and it goes on forever. So question, in the decimal expansion of pi, is there a sequence of 100 consecutive sevens? We don't know. Maybe there is, maybe there isn't. And Brauer said, well, out with the proof of the fact there is, there isn't. This is just something that's indeterminate, it's neither true nor false. Okay, so there's a kind of principle of standard logic, classical logic, if you like, that things are either true or false. And Braille wasn't persuaded by this at all. So he rejected the law of excluded middle. It's either so or not.

So, um, and so that principle is not valid in intuitionistic logic. Okay. Uh, intuitionistic logic is just one of many kinds of non-classical logic. Now, you use the word paraconsistent logic and that has a kind of technical definition, but let me try and keep this simple. Roughly speaking it plays the other side of the street to intuitionist logic. So there's this principle called excluded middle it's either so or it's not so and that goes out of the window in intuitionist logic. There's a kind of flip side of that, which is called the principle of non-contradiction,

which said nothing could be both so and not so. Okay, so ones are neither and ones are not both. And these are not exactly the same, although they often get run together. And a paraconsistent logic is roughly one that ditches the principle of non-contradiction rather than the principle of excluded middle, although there are logics that ditch both. So a paraconsistent logic will allow for the possibility that some things can be both so and not so.

So in some sense, you know, intuitionistic logic and a paraconsistent logic play the opposite sides of the street. Yes. Now there are important differences that I'm sliding over. But roughly speaking, that's a kind of big picture story. So one way to understand this that I find helpful is to imagine a sheet of paper and that the standard logic is that this paper is just even, well, not evenly divided, but can be divided into just being colored red and then colored blue and all of the paper is colored red or blue.

So you pick any point, you look at it, it will either be red or blue. So that's classical logic. The other way when people say exclude a middle, it's quite a funny phrase until it's thought of like this. It's only the border of red and blue. When you have a middle, so now you have white, you have some blankness. So you can have red, then you can have blue, and there could be some blankness here. That's pair of consistent. And what's interesting about paraconsistence is that this image changes through time. So more and more of this map gets filled out

with red and blue. So Fermat's last theorem apparently to the intuitionist would be like, it wasn't true until Andrew Wiles came along and proved it to be true, or some alien civilization in the past proved it to be true, something like that, at least in one form. And then paraconsistent would be if you had the red and blue, you're allowed to overlap with red and blue.

Yeah. You can also think of coloring this in not with markers, but with something like pencil crayon and the more intense colors are more truthful and the less intense are less and that's actually fuzzy logic. I like this analogy. It's a way to not just memorize but to understand the litany of logics. So another example would be that if you have a bumpy terrain and there are different points of density inside of red and blue, well that's contextual logic

or modal logic because it depends on the altitude. What's great about this is that you can formulate the other forms of logic in this analogy. So ternary logic is if you then take a third color and you color it green or Kripke's logic is like if you color it red and blue but not on the paper itself on tracing paper and then the next time you draw it on the next tracing paper. Okay look I like this I like this metaphor.. Let me just say that I don't think that that Wilde's proof of thermos-slot theorem is intuitionistically valid. I think it uses plenty of principles of inference which are suspect but then I've never studied Wilde's proof in detail so I could be wrong but I don't think I am.

Okay so but let's come back to your metaphor of how to understand these things which is a nice metaphor. So you've got this piece of paper let's suppose that there's a line down the middle it's red on one side blue on the And you ask, what color is the line? Okay. So you can think of classical logic, intuitionist logic and power consistent logic like this. The classical logician says, hey, well, it's either red or blue. Maybe we don't know which, but it's one or the other. It ain't, you know, yellow, it's either red or blue. Maybe we don't know which, but it's one or the other. It ain't, you know, yellow, for example. Okay. Yes. Yes. And someone might say, well, hey, no, it's just neither red nor blue. It's something else. And that's the person who is kind of ditching. Okay. It's not quite excluded middle. It would have been better had I started with red and not red. Maybe. So someone who says, well, this line in the middle is neither red

nor not red. That's exactly ditching excluded middle. Yes. Okay. And if someone says, Hey, this line in the middle is both red and not red. So red and blue, then that's the kind of paraconsistent move. Okay. Um, and for the purpose of this discussion, you can think of, um, classical logic is too valued. You know, uh, it's either true or false. Intuitionistic logic as three-valued, true, false and neither. I'm sliding over technical sophistication here, but this will do for the present.

So the intuitionist is someone who says, there are things which are neither true nor false. Okay, that's the third value. And the paraconsistent logician is someone who says, yeah, it's both true and false. And that's the third value. So true only false only in both. So in some sense, you can think of these two things as a three-valued logic So classical logic is true and false, that's it a logic with truth value gaps is True false and neither the power consistent logic is true false and both So the intuitionist and the power consistent audition are going to disagree about what the third value is, either both or neither. But as you can probably imagine, you can have a logic with four values, true, false, both and neither. We know those. And in principle, you can have an indefinite number

of values, true, false, both, neither, and take your pick. And in principle, you can have any number of values, including an infant number. So it's hard to sort of demonstrate these with the metaphor of the piece of paper. But yeah, I mean, logical techniques go a long way beyond that. But it just thinking about how to react to true, false, both and neither. I mean, the image of a piece of paper with a line down the middle and you argue about the color of the line is a nice way of visualizing things. Now, I misspoke when I said that paraconsistent is allowing some overlap. It's not just that it allows an overlap. It's that it allows the overlap to not explode. So technically, in classical logic, if there was even the

tiniest bit of overlap, then it poisons the well and everything becomes red. Correct. Correct. Okay. So paraconsistent just allows the overlap to not poison the well. Correct. So I said there was a technical definition of paraconsistency and I didn't give you that because I was trying to avoid some, just give people the basic idea rather than go into the technical details. But since you've raised it, let me go into the technical details. So in classical logic and intuitionist logic, there's this principle of inference that says that from a contradiction, everything follows.

So here's an inference, Donald Trump is corrupt, Donald Trump is not corrupt, so therefore the Earth has 17 moons. Now prima facie, that doesn't sound a very good inference. I mean, the number of moons seems to have absolutely nothing to do with Donald Trump corrupt or otherwise. to otherwise. So, prima facie, you can think that's not a very plausible valid inference, but it's said to be valid in both classical and intuitionistic logic. And it's not stupid. The story that you'll get told to justify this slightly implausible thought is this. Yeah, but you know, this premise that Donald Trump is corrupt and not corrupt just can't possibly be true because the contradiction can't be true. And so explosion will never take you from truth to falsehood because the premise can

never be true. So explosion is kind of vacuously valid. That's why this principle of inference gets to be valid in both classical logic and intuitionist logic. Okay, now, if you move to a paraconsistent logic, it's going to allow for the possibility that some contradictions are true. You know, the line down the middle of your piece of paper is both red and not red. Okay.

But you don't want to say, well, it's neither red nor not red, so the earth has 17 moons. I mean, that would be silly now. And now you can't say, well, it can't be the case that the premise is true because we're allowing for that possibility. So explosion has to be invalid. And that is the technical definition of a paraconsistent logic, the invalidity of the principle of explosion. And you can make the thing more complex, but you might have a logic with neither and both

and some other values as well. So Professor, why don't we talk about the liar's paradox, your views on why contradictions just exist, they do correspond to something in reality. So let's start off with the liar paradox. Okay. Many of your listeners will know this, I guess, but many of them will not. This is a very old paradox in Western philosophy, Western logic. We think it goes back to the ancient Greek thinker eubelides, a rough contemporary of

Aristotle, maybe fourth century BC. Um, and the paradox essentially goes as follows. Um, suppose I tell you that Melbourne is in Australia. Is that true? Yeah, sure. Suppose I tell you that, um, Melbourne is in China. Is that true? Well, no. Now pay attention.

Is that true? Well, no. Now pay attention. Suppose I say, look, this very sentence that I'm uttering now is not true. Is that true or false? Well, it's kind of hard to answer that question. Suppose it's true. Well, if it's true, it says that it's not true. So it's not true. So if it's true, it's not true. All right. Is it false? Well, if it's false, it's not true. And the very

claim it's making is it's not true. So it seems to be true. So if it's false, it's true. So you seem to be in this very strange situation where if it's true, it's false. And if it's false, it's true. So you seem to be in this very strange situation where if it's true, it's false. And if it's false, it's true. And the standard para-consistent thought is that it's both true and false. So that explains why if it's true, it's false. If it's true because it's both. Now this is not the most popular account of the paradox certainly historically because coming back to the distinction we drew between verical and false radical paradoxes the standard reaction in the history of western logic has been that this is a false radical paradox you can't accept the conclusion because it's a contradiction. reaction in the history of Western logic has been that this is a false, cynical paradox. You can't accept the conclusion because it's a contradiction. So the game in town has been

to explain what goes wrong with the argument. And logicians have not been very successful if consensus is a mark of success because two and a half thousand years after you be ill at ease, there's still no consensus on what's wrong with that argument. The paraconsistent move is, this is not a false-idical paradox, it's a veridical paradox. Namely, you accept the conclusion. The conclusion is that that sentence is true and false. Is that a contradiction? Yes.

So some contradictions are true. That's the argument. Okay. Now where the discussion goes, the discussion going many ways at this point. How do you want to, how do you want to proceed from here? In math, there's a concept called proof by contradiction, which is exceedingly powerful. And I've never heard an argument from an intuitionist. So I'm currently speaking to a paraconsistentist,

but I've spoken to intuitionists before, and I've never heard an argument for why is it that? The proofs by contradictions seem to prove results you get to results that you could also get to constructively like later on you get to them Constructively so there seems to be something true about this whole proof by contradiction. No, let's go down the other path Like there are two paths. Let's follow one. That's a contradiction Therefore it's the other path. Now in this sentence about the liar, it's interesting because you go down one path and you say, there's a contradiction. Okay, so let's explore this other one. We also get to a contradiction. In math, it's not like that. You explore one path, if there's only two, it leads to a contradiction,

it's a contradiction, great. So then you accept the other path as true. Yeah. This leads to miracles of engineering and we're here and there's running water and so on and so physics has its applications and math has applications in physics, so it seems to have something to do with reality. So why do you think that is? Why do you think proofs by contradiction work? Okay.

So there are many things there. There's a standard of, there's a form of proof called reductio ad absurdum. Actually it'll be better called reductio ad contradictionum. And it's valid in classical logic, it's valid in intuitionistic logic. Okay. And the form of proof says assume P, deduce a contradiction, and then infer that not P and get rid of your assumption. Okay. In that form it's valid in classical logic

and intuitionist logic. Whether or not you can always turn that into constructive proof depends. You can't always in classical logic. You can in intuitionistic logic. So that's the difference. But it's valid in both forms of logic. Is it valid in a paraconsistent logic? Well, it's complicated because there are many versions of paraconsistent logic. There's really only one intuitionistic logic, but paraconsistent logic comes in many different kinds. So in that sense, intuition is logic and

paraconsistent logic aren't kind of playing different sides of the street. And if you look at that kind of argument in paraconsistent logics, it's going to be valid in some of them, but not others. Because you're not... If I look at what kind of argument? Because you're not... If I look at what kind of argument? Reductive argument. I see.

So assume P deduce contradiction and infer not P. Okay? Right. And a lot hangs on how you infer in fact. What is the sort of ballpark statement it's not gonna work in a lot of power consistent logic. So. I'm. How come we can apply logics where it is valid and things go right? That was your question, right? Well, there are several relevant things here.

But the first thing you should notice is this. It hasn't always been the case that people reasoned in this way and got results that were useful. So for example, in the 17th, 18th century, mathematicians invented the infinitesimal calculus. Now, a feature of the infinitesimal calculus is you're dealing with things, infinitesimals, which at one point in the computation of derivatives, integrals, and so on, had to be assumed to be non-zero, and another point, they had to seem to be zero. So at different points in the computation you assume that infinitesimals are having consistent properties and this was well

known. It was sort of satirized by Berkeley who called infinitesimals the ghosts of departed quantities. And you know the people knew, the mathematicians knew this, but they reasoned in a certain way using infinitesimals and they got the right answer. I mean, the infinitesimal calculus was the basis of Newtonian dynamics and other things as the centuries went on. Okay, now it's true that about 200 years later, it was figured out how to do these computations without using infinitesimals. So infinitesimals disappeared from the mathematical menagerie. But for 200

years, mathematics assumed that infinitesimals had different, had contradictory properties at different points in their computation. So, obviously they weren't using reductio ad absurdum, otherwise they could have proved anything, which they didn't do. So, would people still argue about what forms of reasoning they were using. That's a contentious question. But certainly they weren't using an unbridled form of reductive pseudon. But they were getting the right results. We inferred how things moved, we inferred how to send rockets around the world and so on.

So it's actually not true that mathematics has always used reasoning successfully which used the redactio principle. I think people tend to forget that. There are other cases of this in the history of science, but that's the most striking, I think. There's a question that you then raised about how is it that if you do reason in a way that uses reductio, you get the right answer? Well, that raises a much bigger question. Namely, how do you know what the right bit of mathematics to use is?

Because people have applied different bits of mathematics for different reasons. So for example, in particle physics, there were two kinds of particles, bosons and fermions I think they're called and they satisfy different probabilities distributions. So you reason about bosons and fermions differently in probability theory because they have different probability distributions. How do you know which is the right bit of mathematics to use? And the answer is, well, you get the right results. Now, so there's always a question of how you, what bit of mathematics you use. We know that

you can be wrong about this. Another example is this. Until at least the end of the 19th century, maybe the early 20th century, people thought that if you want to reason about the space of the cosmos, or at least the space-time of the cosmos, use Euclidean geometry. That was what it was designed for, you know, 200-1000 years ago. We now think that's wrong. We think that's the wrong bit of mathematics because the geometry of space or space-time of the cosmos is not Euclidean.

So we just got the wrong bit of mathematics. And how do we know? Well, because a different bit gave the right results. So how do you know whether something is the right bit of mathematics to apply? Well in the end it's going to be that gives you the right results. Now bits of mathematics which use redactio do seem to give you the right results sometimes. Other times they may not if you use them in the 18th century for doing the calculus that have given you the wrong results. And in fact mathematics is a much bigger game than people who only learn contemporary mathematics think and we now know that

there is mathematics based on classical logic, there's mathematics based on intuitionistic logic, there's mathematics based on paraconsistent logic. You've always got a choice about what you're going to use and you use the one which gives you the right results for the application. In the end that's going to be an empirical matter if you're applying mathematics to the empirical. So, I think that answers your question. Tell me if you want to come back to it. Yeah. My issue is that if you start off with some axioms, and let's just say ZFC to be clear, if you start off with that, one way of looking at that is that it then branches out the whole theory of math that comes from

ZFC is like a tree So you start with the seeds of the eight or so or ten or so axioms of ZFC and then out from that populates this tree of statements and then some of these statements you want to get to you try to get to and you find that it will lead you to Contradiction so then you prune off that branch and go into other branches and you form this Baroque tree. You can also form a tree with Z of C at the bottom and then say, well, you have to minus the C part, or the axiom of choice for the intuitionists. And then you formulate a tree as well. And this tree overlaps and

it overlaps so prevalently. Now, not all and it overlaps so...prevalently. Now, not all of it overlaps. Like there's Zorn's Lemma and whatever else comes from the Axiom of Choice. But it's just odd to me that if you allow proofs by contradiction, then any point that the person who doesn't allow a proof by contradiction can get to, I can also get to. And then what you're saying about the physical reality only corresponding to one branch or some subset of this branch, that's fine. That doesn't impact what I'm saying. I'm just saying that I wonder why. Because in the Boson and the Fermion case, there's nothing contradictory about the math

itself. Correct. Now which math itself we choose, we don't choose a contradictory math. That's what I'm saying. Not in that case. Not in that case. But of course, in the case of the theory of infinitesimals, if you'd chosen to use a logic with explosion, you'd have got the wrong answers. There are a lot of things going on here.

The first is that you talked about Zemile-Frankel set theory and a very standard view, at least until relatively recent times, post-1920, is that all mathematics could be developed on the basis of Zemile-Frankel set theory with choice. Okay? Uh-huh. You can drop choice. If you drop choice, you prove fewer things, that's true. But anything whose proof doesn't depend on choice is gonna follow in the theory without choice. So that you've got an overlap is not surprising.

But even though it was kind of an orthodoxy that all mathematics can be captured in Zemilo-Franco set theory, that's highly dubious. And we've known that for a long time. Category theory doesn't really fit into it, for example, because category theories at least prima facie deals with enormous totalities which don't exist in Zemile-Franc Alcert theory. So at least since the emergence of category theory

the orthodoxy that Zemile-Franc Alcert theory grounds all classical grounds all mathematics is just not right. What's fair is that it seems to be able to ground all mathematics at least as it was in the 1920s to maybe the 1960s. And we now know that mathematics does not have to be restricted to being based on classical logic. There's intuitionistic mathematics, intuitionistic paraconsistent mathematics. You can prove different things. For example, you can't prove the same things in intuitionistic mathematics as you can in classical mathematics. In fact, you can prove things in intuitionistic mathematics which are contradictory to things

in classical mathematics. But, nonetheless, they're perfectly good, pure mathematical structures. You can determine rules and you can investigate them and prove things. Like what? What would be an example of something you can prove in intuitionist math that contradicts classical math? That all real valued functions are continuous.

Uh-huh. So that one would be in classical? No, that's demonstrably false in classical real number theory, but it's demonstrably true in intuitionistic real number theory. Why can't you make a real valued function that's not continuous in classical? Because you've got to jump, okay? Just consider the function which is zero, function fx, which is zero if x is less than zero, and one if x is greater than or equal to zero. That's got a discontinuity at x equals zero.

But in intuitionistic real number theory, you can prove that all real valued functions are continuous. Oh, sorry. I thought you were saying that in classical math, real valued functions are continuous. No, other way around. Because I'm like, yeah, you can have step functions. Sure. Okay. Understood. Understood. Okay. So let's move a bit, but still staying within intuitionist

logic in theme. I was speaking with a quantum physicist named Nicholas Gisson. He's an intuitionist and he suggested that intuitionist logic is intrinsically tied to time Why because something remains undefined until a certain time? So the classic example is will it rain tomorrow? Well, it's not truthful. It's not false But it's undetermined until it's tomorrow. At which point it then becomes true or false. Okay. Per consistent logic. Does that have anything to do with time?

Um, look, it's, it's true that, um, Look, it's true that on most understandings of intuitionistic mathematics, things can achieve a truth value they didn't have before because you've got a new proof. That's absolutely right. But you can have that in different non-classical, other non-classical logics as well. I mean the example you're using about future contingents they're called is usually taken to validate not intuitionistic logic but a three-valued non-intuitionistic logic. So this thing about time is not specific to what your person was pointing to, is true, but it's not specific to intuitionistic logic.

It works in a number of other logics as well. Um, whereas if you're a classical logic, um, you're not going to accept either of those because even if you don't know what's going to happen in the future, it's either true or it ain't now. Okay. So now the question is, what's interesting is look, some logics have some metaphysical implications with regard to time now does pair of consistent have something similar. Maybe it's not just with time.

Maybe it's with something else. Could be space could be something else. Well, time is a tricky subject. Um, and a number of problems with time are highly contentious. Not the stuff you do in relativity theory. That's pretty standard, but there's lots more to time than just special relativity or general relativity. I mean, there's a sort of phenomenology of time.

There's the flow of time. There's all kinds of problems with time which are addressed by special relativity. And some of those problems maybe can be addressed with a paraconsistent logic, it's going to be contentious. But you know, there are some problems about time philosophical problems about time which are contentious now look. Let me give you one example. Think of the flow of time. Naively we all think that you know the stuff now and then it goes into the past and then new stuff happens and you know. and then it goes into the past and then new stuff happens and you know

But this is sort of partly to do with the open future that you were describing But time seems to flow in some sense, you know things start off with the future Come present then become past. This is usually called the flow of time There's no such thing as special relativity, but certainly that's the way that time appears to us. It's part of the aphanomenology of time. Now how do you account for that? Okay, as I say, there's no consensus on this, but the flow of time certainly does seem to lead you into contradictions, some very famous ones, in fact.

One is one suggested by a British, actually Scottish philosopher, MacTaggart, at the beginning of the 20th century. And MacTaggart argued that flow of time is real and that means that time is contradictory because nothing can be past, present and future, but everything is past, present and future. Okay, now there are various ways of replying to this and Mactaggart had various counter-replies and so on, but we don't go into that, we don't need to go into that here. All I'm pointing out is a number of people have thought that aspects of the nature of time generate contradictions.

Now you might disagree with the arguments of course, but if you think those arguments are right and you don't think that time is illusory and so you just throw up your hands in horror, then if time is contradictory, when we reason about time, we're going to need a power of consistent logic. So it could well be that various aspects of time will require a power of consistent logic if you're going to reason about them sensibly. And this is very contentious, but everything about this area of time once you get beyond special relativity is contentious. I'm afraid. So the tricky part here is that often in philosophy you find that some statement is contradictory or some concept is contradictory and That leads you to investigate it further and find that you were using ambiguous terms or you need to explicate further You get the idea and it leads you to some further insight

the You get the idea and it leads you to some further insight. The issue with pair of consistency that I'm sure you've thought of is that if we're going to accept contradictions, then how do we know we're not prematurely accepting a contradiction? How do you know? I mean, how do you ever know you're not accepting something prematurely? Look, our views all change all the time. Okay. They can always, you know, we can always find that we're wrong. That's a hard fact of, you know, adult life. But sometimes when you've got a theory and it generates a contradiction, then you want

to change the theory and that's the right thing to do. Sometimes it may not be. So look, when you apply, when we're doing most things of any substance, physics, philosophy, moral philosophy, history, politics, we're dealing with things about which we have to theorise. And there are different theories. There's virtually no theoretical enterprise in which there aren't, at least haven't been competing theories. Now if you subscribe to classical logic, if your theory turns out to be inconsistent, you say, hey, it's wrong. We've got to look for a consistent theory, right? If you're a power consistent logic and you get to an inconsistent theory you can say the same maybe there's something wrong and

Let's look for another theory, but something you might say is well, maybe the phenomenon. We're dealing with really is inconsistent So it puts another possibility onto the table. So you're not losing anything. You're gaining extra possibilities So you already had a bunch of different theories to choose from. Some have now gone because you've written them off a priori. But you're still going to have a bunch of theories. Some of them are consistent, some of them are inconsistent, and you choose the best theory. Okay, how do you choose the best theory? Well, that's the sort of standard problem in the philosophy of science.

You choose the theory which answers best to the data, which is simplest, most unifying. These are standard criteria in the philosophy of science. And sometimes it may well be that the inconsistent theory fairs badly than some of the consistent theories. Maybe that's often going to be the case, but maybe it's not. So, I mean, just come back to the liar paradox. We've been

constructing theories, most of which have been consistent, for two and a half thousand years. None of them seems to work, at least if consensus is a mark of working. So now we've got another possibility on the table. The theory of truth is inconsistent. Let's compare that theory with all the other theories and see which fairs best. When talking about paradoxes, something I wondered is, is paradox exclusively a property of self-referential systems? So the liar's paradox is self referential. But that you just

outlined the mick taggart time paradox. So that doesn't seem to be referring to it. Philosophers disagree about this. Some philosophers have argued that all dialects, all true contradictions were generated by self-reference. So there's an American logician, J.C. Beale, who argued this at one time. I'm laughing because he's recently changed his mind, and he now thinks that's false, and he thinks that God can be inconsistent too. Okay. now thinks that's false and he thinks that God can be inconsistent too. Okay, I'm not

going to go down that path. But you know, at least 30 years ago or 20 years ago, that was his view that all dialysis were generated by self-reference. But I've never held that this is the case. I mean, maybe the paradoxes self-reference the most striking But I think there are other very plausible examples, and you know, we've talked about motion That's another one and there are others that I find very plausible Now professor something that is extremely interesting is you have a talk which again will be linked in the description And I believe I referenced it in the introduction. It is everything and nothing. Yes, this is a wonderful talk. So the reason I say that

is that I just watched it recently. I can tell when I watch something whether it will stay with me for a while and this is one of those that I'll be thinking about for some time. It also is extremely accessible to the public. Like there's not much background knowledge. In fact, some background knowledge will hinder you from understanding it. I say that because there's a lowercase sigma for sums. And I'm like, oh, just use the uppercase sigma, because then I could read it like that. But now I have to apply some second order thinking to it. But anyhow, in it, you argue that not only is nothing or

nothingness, which we can talk about, not only is nothingness contradictory, but it is the ground of reality. And you explain that as either as ontological dependence, which I don't know if that's the same as supervenience. So I would like to know what is the difference between ontological dependence and supervenience before we go on. Well I'm just trying to think how to put this in simple terms. Okay. Let's take supervenience first. Supervenience occurs when you've got two levels of reality, so to speak, and you can't have a change in the more superficial level without a change in the more fundamental level. So one context in which that's often appealed to is the philosophy of mind. So we have mental states.

Some people think those are completely different from physical states of our body and our brain. Some people have held that you can reduce mental states to physical states, so you can define a mental state in terms of physical states. Both those views face steep problems. Another view is that the mental supervenes on the physical. So you can't actually define the mental in terms of the physical. But what you can say is that in some sense, there's a sort of dependence relation that you can't have two different mental states without some different physical states.

And that's supervenience. You know, the supervening phenomenon, you can't have a change in the supervening phenomenon without a change in the subvenient phenomenon. That's supervenience. Okay. Ontological dependence is this, that, okay, and it comes in various different forms, so let me try and keep this simple. One very common form is that the nature of something depends on something else. So for example, it might be said that your being a human depends upon your genetic

structure. Actually, let me give you a better example that can be appealed to. Suppose you've got a tree and the sun's out and you've got a shadow of a tree. The shadow of the tree depends on being a shadow of a tree on the tree. But the tree doesn't depend on being a tree on the shadow of a tree. Okay. Understood. Now, this is not the same as the super-invenient picture. I mean, you don't have two levels of reality for a star because shadows, trees are part of the same reality

So this is not a relation of supervenience it's but it is taken to be a relation of ontological dependence Okay, so now let's explore. What is the difference between nothing and nothingness? Okay, the word nothing in English and cognate words in other languages is ambiguous explore what is the difference between nothing and nothingness? Okay. The word nothing in English and cognate words in other languages is ambiguous. The word nothing can be a quantifier, which means that it's not a referring term. Um, quantifier phrases tell you that quantifier phrase things like something, everything, few, many, most, and it tells you whether something, everything, few, many, most things satisfy some condition. These are not, quantifier phrase are not referring phrases. And if I say, she opened the fridge and there was nothing there inside, that's a quantifier. It's saying for no x was x inside the fridge it was empty right

so often when we use the word nothing it's a quantifier phrase but nothing can also be a noun phrase so it does refer to something well if it refers at all that's contentious but if it refers at all, that's contentious. But if it refers, it's the kind of phrase that refers to something. That's what a noun phrase is. So if I say, Hagel and Heidegger wrote about nothing but said different things about it. The word nothing there is a noun phrase. How do you tell? Well there's this anaphora pronoun it. I need first back to whatever nothing is referring to so nothing must refer to something.

Okay. So when we're talking about nothing and we're not talking about the quantifier we usually mean it as a noun phrase something that refers. We usually mean it as a noun phrase something that refers. And in English we often put the word the suffix the post fix ness on the end nothing ness to make it clear that's a noun. In German and other languages you would put a definite. I'm description in front of it that's next which you don't do in English right we don't talk about the nothingness in English. I'm that we have various devices which we use in most languages to tell you you're talking about the noun phrase and not the quantifier. And somebody in that lecture you mentioned I was talking about nothingness that is is nothing qua noun phrase, not qua quantify, which is quite different.

So again, the lecture will be on screen here. I'll show an image of it and the link will be in the description. I recommend you watch that because there's a formal proof that the notion of nothingness given some assumptions and which are reasonable assumptions given what we think the properties of nothing should be lead to nothing being contradictory, but also that every object is dependent on nothing. So this is metaphysically interesting. Uncontentious. interesting. Right, contentious. Right. Now I want to leave that as a teaser, which will come back to and there's a flip side

to nothing, or nothingness, which is everything. So please define what everything is and talk about whether it itself is a well defined notion. Okay, look, all this stuff is contentious. I think both nothingness and everythingness, if I can use a kind of very strange way of putting it, are both fine. Now, I gave that lecture that you're referring to in Bonn, and I was invited by a philosopher there called Marcus Gabriel, who has made quite a name for himself, arguing that there's no such thing as everything.

There's no totality of everything. Right? Oh, okay. So when you were saying in the lecture that Marcus said so and so, it wasn't Marx, you weren't speaking about Karl Marx. Okay. Because I was wondering, I thought, has Karl Marx spoken about everything? No.

Because it sounded every time he said, Marcus said, I thought you has Karl Marx spoken about everything? Because it sounded every time he said Marcus said, I thought you said Marx has said so and so. My poor pronunciation. No, I was talking about Marcus Gaffigan, who was in the audience. Yes, okay. And in fact, Marcus and I have since written a book called Everything and Nothing. Well, that's wonderful. Marcus does not think there's such a thing as everything, and I do. I think there's also such a thing as nothingness. Marcus was a bit dubious about that, but that's a different matter. So the question is, how do you define these things? And in the case of everything, there's a standard definition in the branch of metaphysics or logic called

Mariology. Mariology is the theory of parts and wholes. And everything is just the object you get when you put together every thing. So it's a noun phrase, it's the merriological sum of everything and every thing there is a quantifier. So you take all the things there are you squish them together to get one single object and that's everything. So in merriology you got this operation of fusion. Which means if you take the parts of something and squish them all together, you get the thing in question. I have parts, I've got two arms, two legs, a head, a torso, etc. If you put all those things together, you get me. If you take Beethoven's Fifth Symphony, it's got four movements. if you put all those things together you get the symphony.

I'm the thought is everything is you take every thing and squish more together you get this thing everything. No phrase. Mark doesn't like that argument for various reasons but i do. I'm. for various reasons, but I do. So that's everything. It is a standard creature in orthodox Mariology. Now if that's everything, what's nothing? Well it's the flip side.

It's what you get when you put no things together, right? Everything is what you get when you put everything together. When you fuse all things, nothing is what you get when you fuse no things, when you put no things together. And it must be said that nothingness, that the empty fusion is not a standard part of Mariology. But one of the things I did in that lecture was show that you could construct a Mariology based on very natural ideas, which gives you an empty fusion,

a fusion of no things, and you can use that to prove that nothing is both something and nothing, both an object and not an object. And if you think about it, there's a paradox concerning nothingness. Because nothingness is something. You can talk about it, you can think about it, you can wonder whether there is such a thing you are now so nothing this is something but nothing this is well.

Nothing nothing there's nothing there so this is something i recently been calling the paradox of nothingness is not not a famous paradox like the zeno paradoxes of the paradox of self reference. paradoxes or the paradox of self-reference. But I think it's a really interesting paradox. And for me it ranks right up there with those paradoxes. Does the sort of paradox that's associated with nothingness characterise everything as well? No. There isn't a corresponding paradox. Because if you think there's everything, it's clearly something. There isn't a corresponding argument that it's nothing. That only arises in the case of nothingness. Okay. Is there a paradox of everything of a different sort then? Outlined by your friend, the co-author, Marcus. In the lecture, it seemed like there was,

and then it seemed like you just accepted that as intrinsic, looping back on itself. Of course, there are various arguments about everything. Ness, okay? Yes, yes, yes. And Marcus does use arguments to try to establish that there's no such thing because it leads you to contradictions. For example, he thinks that everything has got to be part of something different, bigger.

Though there can't be a totality of everything because it would have to be part of something bigger, and there's nothing bigger for there to be. That's an argument he uses. I think that's a fallacious argument because that assumes that nothing can be part of itself which is a kind of standard, merriological principle but it's one that's been very- You mean everything can be part of itself?

He thinks that nothing can be part of itself. Ah. Okay. Which is a standard principle of Mariology. And I think that principle is, I mean that principle has been questioned by a number of people and I actually think that principle is incorrect. So he doesn't accept that there's such a thing as everything because he thinks that that's a good argument and I don't. Whether you want to call it a paradox, I'm not sure. Okay now another question is given you have such disagreements with this colleague of yours, how is it that you could

write a book together? What was that like? Because it was a dialogue. I put my side of the case, he put his side of the case, and then we sort of discussed these things and recorded it and transcribed the recordings and put them in the book. Did we reach consensus? Of course not. This is philosophy.

So it wasn't the sort of book where you write and there's chapters and it's an ordinary book that's not in the form of dialogue. Correct. It was definitely a dialogue between Marcus and myself. Okay. Now, what's interesting to me is that nothingness is contradictory. Contradictory seems to be a property of nothingness. But that would imply that nothingness has properties.

Sure. So that's not a problem for you? Nope. That's interesting to me. Because to me, I would think that nothingness would be that which has no properties. Or at least that a property of nothingness, I know this contradictory, maybe this is, you're allowed to accept this, but a property of nothingness is that it has no properties. Not only does it contain nothing, no thing, but it also has no properties.

But I would like to hear your thoughts on this please. Well, look. Well, look, if you define nothing as a thing which has no properties, then of course, well, not of course, but you might think that is true by definition. I don't think that's the right definition of nothing. Nothing is what you get when you put no things together, which is kind of different. But anything, and that's the quantifier, has some properties. For example, it's self-identical, or it's something, or I'm talking about it, or lots of things have properties.

I mean, sorry, everything has properties. And even if you claim that nothing has no properties, well, yeah, maybe so, but then that's a property, the property of having no properties. I mean, you can't get out of it. Are there any contemporary philosophers who don't agree with the, I don't know if it's a law, but self identity that X equals X. Yes, there are. Um, you can construct systems of logic where that fails.

Um, uh, one thing we've learned because of the tools of modern logic, they're so powerful, so versatile that you can construct a system of logic where anything fails. Let me just say a little bit more about that. There was a revolution in logic around the beginning of the 20th century associated with Frege and Russell and various other people where they showed for the first time really in the history of logic how you can apply very powerful tools of mathematics to the subject. It was the birth of mathematical logic and they used the tools to construct classical

logic and for a while it was taken that this had to be the right logic because it was a result of applying the tools. But we now know that these tools are really very powerful. Axiomatics, combinatorics, model theory, proof theory. And you can use these tools to construct so many different non-classical logics. That's not contentious. And they're so powerful that you give me any principle and I can construct a logic where that principle fails. That's how powerful the tools are. So just applying the tools is not going to get you in itself anywhere. You then got to worry about, you know, you've got all these systems of logic.

How do you know which one is right to use? And we're back with the question of, you know, applied mathematics. How do you know that it's the right bit of applied mathematics to use for the job? We're in that ballpark. But, uh, yeah. So sort of, I, I sort of digressed a bit, but I thought it was maybe an interesting digression. Yeah.

There are logics where the principal identity does not hold. What are those called and who is a proponent of them? Like a serious proponent of them and not just as an intellectually curious endeavor. Uh, let me see. There are probably a few people, but I heard. just as an intellectually curious endeavor. Let me see. There are probably a few people, but I heard, I'm just reading a paper by an Italian, sorry, a Japanese colleague of mine, Naoya Fujikawa,

where he discusses these systems. I heard a talk by a Brazilian logician, Octavio Bueno, who works in Miami two weeks ago, where he was talking about logics about these things. So, I mean, there are certainly philosophers and logicians who play with these ideas and talk about possible applications. So that's two, right?

One's Japanese and works in Japan, one's Brazilian and works in the US. And there are others too, I'm sure. Speaking of an interesting digression. Actually it's not a digression. What would you say is the difference between no-thingness, so nothingness, but I'm going to call it non-thingness to make it congruent with the following. So what's the difference between non-thingness, non-existence, and non-beingness? Disembroil those for me if you don't mind.

Okay. Look, for start the word being is ambiguous. So being is the abstract noun derived from the verb to be in English. And any logician will tell you that's ambiguous. There's the B of predication. John is happy. There's the B of identity. The current president of the United States is Joe Biden.

There's the B of quantification. There are people who think the contradictions are true. Now, those are different. Why are any of those even being? Because I didn't hear the word being in there. There are? Look, being is the abstract noun derived from the verb to be. And there are or there is uses the verb to be. No? Explain this for me. So the sentence, if I was to write it out, I don't see the word to be in it. No, but you see the word.

Sorry, you're saying it's implicit in. No, no, you see the word is and is is the third person singular of the verb to be. Okay. The reason why I have a sticking point with that is because of you, because you made an interesting, I've never seen this done, you've made an interesting distinction between is and existence. Yeah, that's a different matter. But I'm just pointing out that the verb is, be, is itself ambiguous.

I see, I see. Okay. Okay. For me now, the word is is no longer so clear cut. So that's why I didn't make it equivalent to be. Okay, okay for me now the word is is no longer So clear cut so that's why I didn't make it equivalent to be okay now because before I would have made it equivalent to existence and now since that's Okay in the air well, so that that's right now one of those meanings

namely the meaning of quantification there is Has been held by some famous philosophers including Van Orme McQuine, to be equivalent to exists. So he held that when you say there is something, that means kind of, he made that an orthodox view in Anglo-philosophy. It's a very dubious view and it's well his arguments because I can say things like, oh, there's something, there is something I wanted to get you for your birthday, but I couldn't get it because it doesn't exist. It was an actual picture of Sherlock Holmes. Now, if there is means there exists, what have I just said? I've said there exists something I wanted to do to buy you for your birthday, but I couldn't buy it because it doesn't exist. I've just

contradicted myself. And dialetheism aside, that's not a very tempting contradiction. Okay. So, the reason I was pausing is because the question you raised is kind of tricky for several reasons. The first is that the verb to be is ambiguous. The second is that in one of those meanings, some people identified it with existence, oh, I don't think that's a good idea But then there's another part of your question about nothingness and no thingness Now that raises different issues again, okay So If I'm right about nothingness

It is no thing. It's something as well. There but it's nothing that's part of the paradox right but. Other other things which are no thing. That be paradoxical but i mean is nothing is the only kind of thing like this are there other things. So are there other things? Well, there are certainly things that don't exist. I mean, Quine didn't think so, but you know, Sherlock Holmes doesn't exist. Maybe you believe in some God or other, but you know, you don't believe in all of them. So whichever ones you don't believe in, that God doesn't exist. You know, lots of I don't mean by are, exist, I

mean just a being, right? Not an existent being. And a lot of people think the answer to that is no. The only thing that is no, the only thing. That is no thing is nothingness. That's not actually my view, but a lot of people hold that view. So, okay. I've taken you through some weeds there and I apologize, but the weeds are fine.

I like the Sapporo. We live for the technicality. The question you asked at the chaperon. We live for the technicality. The question you asked had many different aspects and it's hard to answer without teasing some of these aspects apart. So apologies for taking you through these various distinctions. What came first, your love for paraconsistent logic or your fondness for Buddhism slash Taoism? Um, the former. Um, so you may or may not know that my doctorate is in mathematics, uh, and

it was in classical logic, so I was trained as a classical logician. logic. So I was trained as a classical logician. But soon after that I started to realize there are problems. And everybody knows there are problems, but I thought these problems were serious, right? So that's when I started to work on power of consistency. At that time I knew absolutely nothing, actually I knew nothing much about philosophy because I was trained in mathematics, but I certainly knew nothing about the Asian philosophical traditions and I didn't know anything about those until 25 years later, at least 20 years later, by which time I've been a professional philosopher for 20 years. Okay, so professor you've traveled to many places in the East and you've lived there

and you've mentioned your affinity to Daoism and Buddhism, maybe even their practices, I'm unsure, but I'd like to know how has that point of view influenced your philosophy in the analytic sense? Okay, well, for a start, I'm not a Buddhist. I don't have any religion. Okay? I don't practice meditation. So what I've learned from the Asian philosophical traditions has nothing to do with religion specifically. Of course, I am sympathetic to various views, both ethical and metaphysical, that you find in Eastern traditions, maybe especially Buddhism, but then I'm sympathetic to many views you find in

various Western traditions, some of them are religious too. So, as I say, you know, this has nothing to do with religion, but that doesn't mean that I disbelieve everything that any of these things says. Okay, so what effect has learning about the Asian traditions had on me? Well, very simply, it's made my understanding of philosophy much richer. So in all the world's religious traditions, there are some questions which crop up everywhere. What's the nature of reality? How should I live? How do you run the state, how do you know these things? Okay? They all address these in one way or another.

Sometimes you find questions in one tradition you don't find in another, that's fine too. Sometimes when they are dealing with the same questions, they will give similar answers, sometimes they give very different answers. But you want to know these things, you get a much broader, richer canvas of philosophy. So when I do philosophy nowadays, I'm able to draw on a sort of a wealth of ideas from many of the world's philosophical traditions that I wasn't able to do, say, 30 years ago. So my understanding is richer, the tools I have are richer. Hopefully my

philosophy is richer. We haven't talked about why nothingness is the ground of reality. I understand that there's an hour-long lecture, which I'm recommending people watch where that argument is laid out. However, can you recapitulate that in a succinct form? Look, it's difficult to do that. Um, but let me at least hint at the reason. Um, Let me at least hint at the reason.

Um, how about just the idea of ontological dependence on nothing? Yeah. Okay. Um, look, let me, ontological dependence is often couched in terms of certain conditionals, which logicians call counterfactuals. What I mean is this, this, the shadow of the tree depends for being the shadow of a tree on the tree.

If it weren't a tree, it wouldn't be the shadow of a tree. Okay, that's a conditional, it's called a counterfactual. If this thing weren't a tree, it wouldn't be the shadow of a tree. So that dependence is often couched in terms of these counterfactual conditionals. Okay, but counterfactual conditionals or at least dependence conditionals can be negative ones as well. So take a hill. negative ones as well. So take a hill. If that weren't distinct from the surrounding plane, it wouldn't be a hill. Okay, so there's a counterfactual. If it weren't, that's the

counterfactual, distinct from the plane, it wouldn't be a hill. It would be part of the plane or it would be a ravine. No, if it were a ravine, it would still be distinct. Let's just leave it at that. Okay? It's being a hill depends on it being distinct from the plane. Okay, leave it at that. Now, something being an object depends on it being distinct from nothingness. If it were nothingness, it wouldn't be an object because nothingness isn't an object. So it's a bit like the hill in the plane. What makes it a plane, what makes it a hill is that it stands out from the plane. And in an analogous way, what makes something an object is that it stands out from nothingness. Okay, that's the basic form of the argument.

And I stole that from Heidegger. Now, did he steal it from Spinoza or is that a different argument? Not as far as I know. So the reason I'm saying that is this idea that in order for you to specify an object, you have to write about its negation or speak about what it isn't. No, that's, that's every determination is a negation. That's spinosa. That I think that use a negation. Um, but I don't think, but it's a special kind of conditional, which has

to do with the nature of something. Um, what's, you know, I was talking about was simply a way of, if you want to characterize anything in any way, there's got to be a was talking about was simply a way of, if you want to characterize anything in any way, there's got to be a contrast with something that's not that. Okay. And you know, that's a different point. There's a professor of philosophy. You may know him.

His name is Anand Vaidya. Yeah, I know him. There's an interview for people who don't know with Anand Vaidya on analytic philosophy, epistemology, Vedism. It's in the description. It's a fascinating gem of an episode. There are several insights there into non-dualism, dualism, truth and falsity. He knows I'm interviewing you and he said a question.

He said, can we understand the Madhyamaka claim that the ultimate truth is that there is no ultimate truth through paraconsistent logic? Well, the straight answer, the simple answer is yes. Okay. Now, of course, the simple answer is not very interesting because we want to know why. And let me say first of all that this is contentious. Even amongst scholars of Madhyamaka, this is contentious. But many years ago I wrote an old paper, I wrote a paper with an old friend of mine, Jay Garfield, on this question. And prima facie, the ultimate truth is there is no ultimate truth, is contradictory because

it implies that there is something that's ultimately true and there isn't. And Jay and I argued that that's exactly how it should be understood. Now a lot of Buddhist scholars disagree with this, but at this point we have to go into all the reasons there are for what Buddhists, what the Madhyamaka thought about ultimate truth and its properties and its nature and so on. And I can't do that in this context. Now Anand does have another question. Can you outline your views on the debate over logical pluralism and monism and where you see para-consistent logic in that debate? Look, the word logical pluralism is highly ambiguous.

I'm sorry to have to keep saying this to you, but lots of these words get thrown around and they're ambiguous. And if you don't get clear about the differences, you're gonna get confused. So this is why I keep coming back to things like saying, well, it depends what you mean, right? But what is not contentious is that there are many, many different kinds of pure logics,

classical logic, paraconsistent logic, intuitionistic logic and all the others, right? And as pure mathematical structures, they're all equally good. That's not contentious. They're just bits of pure mathematics. But when you apply a bit of pure mathematics, you want to know, you want to get the right one. We've been over this. And when we apply pure logic, it can have many applications. They're not all to do with reasoning by any means. But there's a sort of canonical application of pure logic, which is precisely about reasoning.

Comes back to where we started, figuring out what follows from what that's the canonical application of a pure logic and logical pluralism in the only interesting sense there is is that when you apply a pure mathematics for that application there are different logics which are equally good. Some people are logical pluralists in that sense. I'm not. It's a kind of fairly hot topic in the literature at the moment. Traditionally, logic has been modest, not pluralist. Logical pluralism doesn't really appear on the philosophical scene until about the last thirty years, I think, in the history of logic. So I'm sort of in good historical company here.

Of course, that doesn't mean anything really. But I've never been persuaded by the people who put forward cases for logical pluralism in that sense. It's clear that paraconsistent logic is one of the plurality of pure logics. In that sense, it's one of the one of that plurality. I happen to think that when you apply it for the this canonical application of pure logics, there's one correct logic and it's paraconsistent. Even given that, is there still a contradiction or a paradox that you find to be most challenging? We imagine that we've solved or that you in your mind are settled on the liar's paradox, but is there another paradox like Newcombe's paradox or something else that sticks in your crowd, nettles at you.

Okay. The history of logic is full of paradoxes. Um, I guess to the extent that I thought about any of them, I've found solutions which satisfy me. Sometimes it's a paraconsistent solution, sometimes it's not. I can't think offhand of a paradox that I don't feel comfortable with a certain solution to, but maybe I'm just misremembering. Well, then can you describe an epiphany moment where you were struggling with something and then an insight came to you? What was that like? Yeah.

What was it? Um, well, here's one. Um, there's another kind of paradox, which is very frequently discussed now. It wasn't so frequently discussed in the history of logic, called the Soraites paradox. So the Soraites paradox is when things happen by degrees. So you know, if I can be totally sober, if I drink 1cc of alcohol, I'm not drunk. If I drink 2ccs, I'm not drunk. And generally speaking, if I'm not drunk after nccs, I'm not drunk after n I drink two cc's I'm not drunk. And generally speaking, if I'm not

drunk after n cc's, I'm not drunk after n plus 1 cc's because 1 cc doesn't make a difference. But of course, if you drink a whole couple of litres of alcohol, I don't know how many drops that is, but it's a lot, right? Yes, yes. Okay. So this is called the psoriasis parerox. And I did struggle with the Soraytius Paradox for a long time. I didn't really find a solution that I was satisfied with until in arguing with some or discussing with some friends, they pointed out that there's actually a way of seeing it as a paradox with the same structure of the paradox of self-reference. And once I saw that, then

I became sympathetic towards a dialectic solution, because if the paradox of self-reference have a dialectic solution, then so should the Soraytis paradox. And so that was sort of a moment of epiphany. Well, you'll have to explain how it's similar in structure. It's hard to do that without a piece of paper and a chalk, or a blackboard. The structure is called the enclosure schema. That's I N C L O S U I. Right, right. Way back, I suggested that all the paradoxes of reference are enclosure paradoxes. They fit this general schema. And it was only when talking to friends, we realized that the Sorority's paradox fits the enclosure schema.

I thought, okay, well, that's the best solution. So, Professor, many people have been watching maybe for two hours now. I'm sorry, they haven't got better things to do with their time. And throughout all of this, we've talked about contradictions and dialecthisms and different forms of logic, nothingness and everything in a technical sense. But a looming, maybe the looming question is, okay, so what? Like you're speaking to the person now who's been listening again for a couple hours, how are they supposed to act differently now as a

result of these newfound theoretic insights? And why should they act differently as a result? I mean, when we theorize we're interested in problems and we're trying to get to the truth and when we finally get to the truth, we understand the world better. Does this necessarily affect how we live? No, not necessarily. Insights in physics don't necessarily affect how we live. Insights in chess don't necessarily affect how we live. And it may well be that insights about the paradoxes of reference don't necessarily affect how we live. You know, how we live is important, but it's not the only important thing in life. I think truth is important.

So maybe the answer is nothing much, but maybe there's a sort of meta lesson. And the meta lesson is this. The principle of non-contradiction has been high orthodoxy in Western philosophy, much less so in the Asian traditions. And so, often when people are struggling to solve a problem, whether it's a practical problem or theoretical problem, if they think that you can't accept an inconsistent or a contradictory theory, there are going to be certain approaches to the problem that you're going to write off just without thinking. And the main meta solution or the main meta takeaway lesson is don't be so narrow-minded. There's more

to the possible theories in heaven and earth than I thought of or that I dreamt of in your philosophy, her ratio. So keep an open mind. Think of all the possible solutions to your problem. Some of them may be contradictory. And once you've got a clear view of all the possibilities that lie before you, then make a sensible choice. Professor, thank you. You're welcome, Kurt. I appreciate it. Okay. Well, sometimes we've got a bit deeper into the weeds than it is easy for people to follow.

I apologize, that's okay. I did try and keep things as simple as I can. Sometimes perhaps over simple. Like I said, I live in the chaparral and same with the audience. So we like the technicality. Okay. All right. Well, thanks for the interview, Kurt.

It's been a pleasure, Shan. Firstly, thank you for watching, thank you for listening. There's now a website, kurtjymungle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service. Now a direct mailing list ensures that I have an untrammeled communication with you. Plus soon I'll be releasing a one page PDF of my top 10 toes.

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