 Hello my friends and welcome to the 83rd episode of Patterson in Pursuit, talking this week again about my very favorite topic and what I consider to be the most important topic in the entire world, logic, and in particular its relationship with metaphysics. If you guys have read my first book of philosophy, Square One, The Foundations of Knowledge, it's essentially an explanation for why there are no contradictions in the world. I claim that everything is the way that it is and I make the claim that logic and existence are inseparable, kind of the central claims of the book, and I am very explicitly rejecting the notion of the possibility of the existence of any kind of contradiction either in our mind or in the world. However, the guest for this week is the man on the exact opposite end of the philipsophic spectrum. His name is Dr. Graham Priest and he's made a name for himself over the course of several decades making the case for the existence of logical contradiction and true contradictions in the world. Dr. Priest has written a myriad of books on this very topic, including logic, a very short introduction in contradiction beyond the limits of thought, towards non-being among several others. And in the course of Patterson in Pursuit I've interviewed a few other people who take the position that contradictions exist like Dr. Patrick Girard in New Zealand and I think Dr. Justin Clark Doan at NYU was sympathetic to the idea. And both of them draw from the work of Dr. Priest. So I'm very excited to have him on the show. We had an excellent conversation. And one of the topics that I cover in my book and comes up almost universally when talking about the existence of contradiction is the liar paradox in particular. So we spend a good maybe hour and 20 minutes in over the course of the conversation talking about logic and contradiction, a large chunk of which is specifically on the logic of the liar paradox. So if that sounds interesting to you, oh man, this is going to be an episode you don't want to miss. This episode is broken up into two parts. We have a great conversation about logic and metaphysics and the existence of paradoxes and contradictions. And then part two is a conversation about the history of mathematical logic or logic and mathematics and its history, especially what happened around the turn of the 20th century. Something that might not sound interesting unless you're a specialist in the field, but believe it or not, quite a lot of shifts in thought happened around the turn of the 20th century in these areas. They've been massively influential in the 20th century. And so if you are interested in this field, it is something that you must learn about. And so Dr. Priest teaches me a bunch of historical facts I didn't know. And if that's something that you're interested in, you're going to enjoy part two, which will be also released next week. All right, Dr. Grand Priest, thanks very much for coming on Patterson in Pursuit. It's a pleasure to have you on the show. Thank you for inviting me, Steve. It's a great pleasure to be here. So I'm really excited to get to talk to you because there's not too many people I find that see how profoundly important logic is. Many years ago, maybe about a decade ago now, I was in Florida and I was kind of writing notes to myself. And I was thinking about, you know, how do I know things? I think I know things, but how do I know them? And I ended up stumbling into, let's say, like the law of identity. Well, things have to be themselves, like A is A, a thing is a thing. I thought, oh man, this is a really good deal. Turns out this is, you know, not an original insight has been talked about for a long time, but I realized that was kind of one of the first seeds that sucked me into philosophy and sucked me into analyzing logic because it's one of those things that is absolutely fundamental really to everybody's entire thought system, whether they realize it or not. The history of the role of logic in philosophy in the 20th century is kind of interesting because as you probably know, there's a big revolution in logic at the end of the 19th century when philosophers and mathematicians really applied mathematical techniques to logic for the first time. And this was an enormous advance, and so people started to see the new tools that logic gave them as a way of investigating all kinds of things. So in the first half of the century, logic sort of took center stage in philosophy. You think of the logical phosphorus, the logical empiricists, and so on. Those days have now gone. Logic is not seeing that way anymore. And logic is often seen in philosophy departments as a fairly esoteric subject. You don't need it to do political philosophy or science, history of philosophy. But the pendulum is sort of swinging again because metaphysics is now making a comeback. Metaphysics is out of fashion for a lot of the 20th century, okay, whether you're Heidegger or Carnap or Derrida. People just thought we were doing stuff about language, okay, metaphysics went out of fashion. Metaphysics is now making a comeback. So people are really starting to worry about both old and new metaphysical issues. And the entanglement between logic and metaphysics is enormous. Yes. So it's throwing logic into prominence again in this very core area of philosophy. Yes, I think that really is fundamental to any analysis of any topic. Even if it's something like biology or it's something like just pure mathematics, you're going to be presupposing a metaphysics, which means you're implicitly presupposing a logic. You're kind of constrained by whatever logic that you're using. That's why I think it's something that's so fundamental. And as you mentioned, it's seen as kind of esoteric. I think that's kind of a tragedy because what could be more important if we're wrong about logic, then that means kind of the most fundamental structure of our entire belief system has the potential to be flawed. Yeah. Well, there was an old view about logic, which is that it's kind of completely neutral as to anything. So it's not hostage. You're just talking about words, what words mean. So you're not hostage to the real world at all. But that view is hard to maintain once you look at the history of philosophy and how logic has been entangled with metaphysical views. We can talk a bit about that if you'd like. But you're right that if you subscribe to various metaphysical pictures of nature in the world, you are going to presuppose some kind of logical picture, whether you like it or not. Exactly. And that's specifically why I'm so happy to have you on the show because though we are going to agree on the importance of logic, that picture that we presuppose I think is going to be completely different. So it'll be good to see exactly where logical disagreements are going to result in profound metaphysical disagreements. I think a good place to start would be talking about the status of paradox. This is something that you're known for. You've been writing about and thinking about paradox and inconsistency for a long time in your professional career. But there's a kind of common sense general idea that people have that if you ever encounter a paradox, there's some kind of funny business going on. Like there's some, there's a mistake that's been made. If you see a contradiction, you think about a contradiction, you've demonstrated that you're thinking in an incorrect way. Another way you could phrase it is paradoxes can't be true. Contradictions can't be true in the world or they're like a demonstration of error. I'm very persuaded by that idea. I think most people have no exposure to any other real way of thinking. So kind of in a nutshell, what is your thought on paradox? Is it everywhere and always something that's necessarily false or is there room for maybe paradoxes and contradictions, even existing in the world? Okay, there are several questions entangled there. Let's walk through them slowly. What you're calling a paradox is something like where you have an argument with premises that appear to be true and steps of inference that appear to be valid, which ends in a contradiction. Now, if the argument is vertical, you have a true contradiction. But normally when people meet a paradox like this, there is a sort of standard assumption that something has gone wrong and you backtrack and you explain which premise is not right, which step of inference is not correct, and then you have to explain why. Otherwise, it's too easy to say the problem's here, why here, okay? Now, if you think that some contradictions are true, this does not gain, say, the importance of this move. So every time you'd apparently don't have to say, oh, well, there goes another true contradiction. What the belief that some contradictions might be true opens for you is another move in metaphysical space as well. It says, hey, there is another option. Maybe you should just accept the contradiction. So you now have a choice, which was kind of ruled out in the old book. So you just have a new option. And then the question becomes, hey, which of these many options should I take? And I don't think many dilutes are such a much. A dilute is a person who believes that some contradictions are true. And I don't think that many dilutes are this. I think the most dilutes would say, yeah, when you find this sort of paradox of contradiction, it isn't like something's gone wrong and you see something about it. But sometimes this is not the right move. OK, for example, when? Now, you mentioned paradox and the most famous paradox is the liar paradox, which goes back 2,500 years. Some of your readers, listeners, sorry, will know what it is. But for those who don't, let me just say, suppose I say to you, this very thing I'm saying is false. OK, is it true? Is it false? Well, if it's true, it says it's false, so it's false. If it's true, it's false. But if it's false, well, that's what it says, so it's true. OK, this is the liar paradox, the simplest possible form. And it's reputed to be invented by eubulities 2,500 years ago. Now, the liar paradox has been subject to intense investigation by logicians in the great periods of logic. Ancient Greece, the Middle Ages, modern period. And there is no solution to it if consensus is to be the mark of a solution. Because after 2,500 years of trying to explain what's gone wrong with the argument, there's no solution that really stands up to inspection, at least as far as most people are concerned. So let's suggest that maybe we've been bar-kept the wrong tree, as far as, at least as far as this paradox goes, that we've got this apparently veridical article. We've kind of failed historically to show what's wrong with it. So maybe we should just accept what's staring us in the face and say, well, it is a veridical argument. And that connection is true. So I definitely would have come back to the liar paradox. I think that's a huge one. I've got, I want to run an idea by you about a potential resolution that I'm not extremely well read on that particular one, but I haven't come across this resolution anywhere. And so I'd like to hear your thoughts on it. But are there any other ones that aren't like about language? That one seems like it's kind of, what is it telling you? It's telling you anything about the world. It's referring to itself maybe, but it's a sentence. Is there anything that's like more concrete, like clear, metaphysical, like Schrodinger's cat is alive and not alive at the same time type a deal? OK, well, paradoxes in the class of the liar arose in the 20th century in the foundation of mathematics. So we're dealing there with fairly abstract entities. And your question is, well, hey, what about the concrete world? Some people have suggested that quantum mechanics should be diluted because the cat is alive and dead. I mean, I'm not a quantum mechanist, but I think that's just a misunderstanding of quantum mechanics. Me too. A superimposed state is not a conflict-free state. Right, kind of by definition, as far as I understand. Yeah, well, by the nature of the mathematics involved. OK, now, if we're looking for examples of true contradictions in concrete reality, this is going to be much more contentious. But certainly, there are some people who subscribe to contradictions in reality in the sense we're talking about, and I'm one of them. And one of the places where I think this is very plausible is in the counts of motion. Now, we're not a million miles away from paradoxes here. So let me just give you a little bit of history. Zoom out. About the same time as Ubiulides, constructed number of paradoxes in motion. And for most of them, at least, there's consensus over how you solve them. The one I think that's hardest is the paradox of the arrow. OK, so in the paradox of the arrow, you've got to imagine an arrow, at least its tip, and it's fired from the bow to the target. Now, take an instant of its motion. How much progress does the arrow make in that one instant? Answer, zero. OK, because it's an instant. But the temporal duration from the firing of the arrow to its hitting the target is made up of instance, at least according to modern mathematics. And if progress made equals zero at each of these instance, progress made over the sum total is still zero. If you add zero to zero, even infinitely many times, uncountably infinitely many times, it's still zero, right? So how does it do it? Now, this is in those paradoxes of the arrow. And if you read Hegel, who is one of my sort of favorite historical philosophers, Hegel says, look, you've got to understand that these ancient dialecticians are onto something here. To be in motion is not simply to be here at one moment at a time, an ear to another, because after all, that's compatible with it being at rest at both those times and places. What he says is, look, to be in motion is to be here and not here, same place, at one and the same time. So that's a contradiction, right? Now, what's driving this? Come back to Zeno's arrow paradox. The difference between something that's in motion and something that's stationary is that something that's in motion is kind of in a little dynamic state. It's kind of, you know, it's got a bit of impetus. And what that means is at the instant, if the thing's in motion, then it's already gone a little bit further or maybe hasn't even quite got there yet. So if it's stationary, it's there and just there, but if it's in motion, it's already gone a little bit further and maybe not quite reached there yet. So how does this solve the lie paradox? Well, sorry, how does it solve the arrow paradox? Well, because progress made by the tip of the arrow at an instant, it's actually not zero because it's already gone a little bit further. So it's made a little bit of progress in that instant. So this was Hegel's solution to the arrow paradox and he interpreted the arrow paradox as implying that motion actually realizes contradictions in reality. Now, this is hardly the orthodox view, which is that motion is consistent. Go on, I rather like Hegel's view. It's interesting you bring up Zito in this circumstance because when I also am kind of a fan of Zino in some respects, because I'm sure you're aware of this, that the standard resolution to some of Zino's paradoxes are that calculus can solve, for example, Achilles in the tortoise, calculus solves it. I actually don't find that one particularly persuasive. If it's the case that you agree with Zino's premises about the infinite divisibility of space, I think calculus will get you to explain how Achilles gets arbitrarily close to the tortoise with the concept of the limit, but I don't think it actually fully explains how Achilles can overtake the tortoise. So my resolution though to that would be to say, oh, I think therefore one of the premises that is wrong is that space is infinitely divisible. I think if it's the case that motion is happening, then it must be the case that there's a kind of fundamental, like a geometric atom or something like that of space that you just can't get any smaller than that. And it's interesting that in the circumstance you bring up with the paradox of the arrow, instead of trying to resolve it or resolve the tension, you think that it's even more of a relief of the tension to accept contradiction. Yeah, well, I mean, the thought that space and time are discrete is, it's certainly on the cards, especially if space and time are quantized, some physicists now think. But the standard resolution of the Achilles and the dichotomy and stuff like that, I don't think the calculus gives you a solution because you can spell out what's going on in non-calculus terms, all right? And when you do that, what you see is that there is an assumption that's being made in the Achilles and the division and so on. And the assumption is this, you can't do an infinite number of things in a finite time, that would have seen a pretty natural disunction to Zeno. But in a certain sense, what we've learned from modern mathematics is there's nothing essentially problematic about doing an infinite number of things in a finite time, provided they can get short and solve it, so you do the first one in half a second, the next one in quarter a second, the next one in eighth a second, and so on. Now there's some discussion of this in the literature on the subject called hypertasks, which is whether if you do this infinite number of things in a finite time, you get another paradox, but most people don't find that very convincing. But the standard solution to most of the Zeno's paradoxes is precisely that this assumption that you can't do an infinite number of things in a finite time is just false. The reason I come up with the arrow paradox is that whatever's going on there, it's not that, because that premise, that assumption is not made. The assumption that is made is that if you add zero to itself infinitely many times, you're gonna get zero. One can test all these, it's not what's going on in the dichotomy and the accolades. So do you see other paradoxes? So that would be a paradox, if that's a real contradiction in nature, that's something that's ever present. That's at every moment, there would be quite a lot of contradictions taking place. Do you see other paradoxes that are also out there in nature as regularly as we see something like motion? Well, it depends what you buy in nature. But if you count social society as part of nature, yeah. So for example, let's talk about the law and let's talk about claims and rights in law, Tom. And you can imagine, the real law is completely messy, okay, but let me give you a toy example. Let's suppose you've got a duly constituted legislature and they pass each of them piece of legislation of the following form. All property holders shall have the right to vote and clause number two, no women shall have the right to vote. Now, you can imagine that at the time when this legislation was passed, no women held property and it was kind of inconceivable in the social culture of the day that women should hold property. So given that context, these laws are quite consistent. Okay, however, time's changed and you can imagine that as you tell the story, women do come to hold property. You may be first de facto and then de jure. And you can imagine that at some stage, a woman, let's call her Hillary, rocks up to the polling booth and she says, hey, I hold property, here are my share certificates, okay? So I have the right to vote. And the polling booth officer says, no, you're a woman, you haven't. So now we have a contradiction. It wasn't that the law was originally a contradiction, but when you add in this extra sort of empirical premises that this woman holds property, then you have a contrary situation. Now, the law, the point of the law is very practical one and if the situation were ever to arise, the law would be changed, okay? So a judge would make a ruling or the legislature would change the law or something like this to get rid of the contradiction. However, the reason that change was necessary was precisely because before the change, you weren't, it was a contradictory situation. Hillary both had and did not have the right to vote. Now, this is not exactly physical reality, but it's kind of social reality. So with that example, could you say something like, because it's the case that the law was contradictory, it couldn't be the case that Hillary was in a position of not violating the law or something like because the premises, if you will, are contradictory, you can't have a consistent conclusion. So versus reality as contradictory, it would be something like because reality isn't contradictory, you can't have that legal tension resolved in a coherent way without changing one of the fundamental premises or laws. Yeah, I think that's right. I mean, it's not Hillary's in the bind, it's the polling booth officer. Right, right, right. Because given the legal status of Hillary, I mean, she hasn't gotten the right to vote. So this guy or girl, whoever it is, has an immediate problem, right? Do you let Hillary come in to cast her vote? And you don't really want your voting procedures to throw this sort of issue up. So then you would have to change the law to make the law practical. Now, the Lie Paradox and Motion and so on, not like this because they're not concerned with practicalities in quite the same way. Okay. Okay, so I do want to cover both of the ones, the Air Paradox and the Liar, but before we do kind of as a preface to that, I want to talk to you about like a theory of truth or a theory of reality or how you can concretely make sense and wrap your head around a contradiction. So what does it mean to say that reality is in mutually exclusive states at the same time? It seems like by definition, if two things are mutually exclusive, they can't be realized together. So if I were to say something like that, where would you say I'm making a mistake? Like I would say, oh, you can't have a contradiction in nature because what we mean by something is some way and something is not some way is precisely that they're mutually exclusive. Yeah, but it's exactly the last claim that someone like me is going to jack up at because if for some claim, A in its negation can both be true, then in a very clear sense, they're not mutually exclusive. Now, when you bring truth into the picture, of course, there are so many different theories of truth. And I don't think dialythism presupposes any particular theory of truth as such. If you think that truth is verification, then it means some contradiction to be verified. If you're coherentist, it means that some of our inconsistent theories are more coherent than consistent theories. If you're a kind of correspondence theorist and you think that what makes something true is a kind of fact out there in reality, I think that probably puts up the stiffest kind of resistance. And I think that's what you're sort of gesturing at here. So suppose that what makes something true is a fact in reality. Okay, let's run with that thought for a moment. So suppose A and not A are both true. Okay, then by the correspondence theory of truth, there's got to be a fact that A and a fact that not A. Yes. Now, the fact that not A is clearly not the mere absence of a fact that A. So there can be a fact that not A, even though there is a fact that A. So if you like, there've got to be negative facts, a fact that not A, negative in the sense that they're the kind of thing which make negative sense is true. But they're positive in exactly the same way that any fact is positive. Okay, it's kind of out there in reality. So I guess this also gets into the meaning of what negation is, because what do we mean when we say not? What does that actually mean? So when I think, so I've got a pin here, when I think to myself, there is a pin out here or let's say, there are colors in my visual field if we want to reduce it to my phenomenological experience, but let's just say there's a pin here. It seems like when, if I were to say, there is not a pin here, that is like an explicit negation of what is being affirmed. Like we have this kind of conceptual technique to say, whatever it is that you're affirming, that is not the case. Or like there is no fact in reality that that corresponds to. So if that's true, then I'm not seeing how the, to affirm and to negate seems like to kind of destroy the meaning of what you were saying. Like the meaning of affirmation is not negation and the meaning of negation would be not affirmation. Okay, so you raise a very, very good point. And the question is, what is negation? How does it function? Yeah. And over the last two and a half thousand years of logic, lots of different theories have been put forward about how negation works. So it's not exactly in a settled matter historically, even though there's currently an orthodox view. Now, something that's a relatively uncontentious characterization of negation is this. If something is true, it's negation is false. And if something is false, it's negation is true. Most people would be happy with that definition of negation. But of course, you're defining negation in terms of falsity. So the question then becomes, well, how does falsity work? Now, the standard view is that falsity is the kind of conglomerate of truth. So the truth and the forces are exclusive and exhaustive. That's the kind of a counter truth that you were gesturing at. And if you accept that, then it's not possible for a contradiction to be true just because one or other is not true. Okay. Now, in the various theories which allow for true contradictions and the kind of flip side of that, which is truth value gaps, you cannot subscribe to that principle. If you are a dialysis, you're going to have to hold that truth and falsity can actually overlap. And if you believe in the sort of dual view, that there could be things which are neither true nor false, which is much more common view in contemporary logic, then truth and falsity actually underlap. So there's a gap between them as it were. But whether you hold the view that they're, so dialysis is sometimes called gluts. It's not a great word, but it is sort of a rule of gaps. If you're holding there a gaps or gluts, you cannot hold the thought that truth and falsity are exclusive and exhaustive, okay? In one case, they overlap, and in one case, they underlap. Now, so the crucial question becomes, what are we to say about truth and falsity and their underlap and their overlap? Now, this brings us back to a place we were at earlier in the discussion about metaphysics, because here you are hostage to metaphysics. So let me give you an example of that for gaps because it's kind of historically interesting. So the thought that there are no gaps is usually expressed in the principle of excluded middle, okay, everything is true, or false, no, tertium non-data, and you find that slated and defended by Aristotle in the metaphysics. But there is a very strange chapter of Dane Tertiani where he says something different, and this is usually called the seba. And what he says is this, if you take things about the future which are not yet determined, then they're neither true nor false. So he's sitting up on the Parthenum, he's looking at over the Aegean, there's the Spartan fleet, there's the Athenian fleet. Are they gonna fight tomorrow? Are they not gonna fight tomorrow? Dunno. And Aristotle says, well, claims like that about the future are at the moment neither true nor false. Now, tomorrow they will be. Tomorrow, they will fight or they will not. So tomorrow, these things will have a truth, right? But now they don't. Can I interrupt you just there first? So, because I wouldn't claim to be that it's still either true or false that they will or they won't fight. So either they will, so if we were to take the law of the excluded middle and apply it to that circumstance, wouldn't we say it is either the case that they will fight or it's not the case that they'll fight and there's no third option? Yeah. In interpreting that chapter of day in terms of how DNA is difficult and in some places, Aristotle does seem to suggest that. And in some cases, he suggests that the future things are neither true nor false. And if A is not true and not false and not A is not true and not false, then unless something very strange is happening to disjunction or then A and not A is not true and not false, okay? All right, so how you interpret this part of Aristotle and how you make it compatible with what he says in the metaphysics is something that scholars argue about. But he actually gives an argument that contingent claims of the future are neither true nor false because the argument goes, if they were, fatalism would follow or fatalism is crazy, okay? Now, most of what is now don't like Aristotle's argument. They don't think that screwing middle entails fatalism. However, there's something, even if that argument doesn't work, there's something kind of tempting, attractive about Aristotle's view about the nature of time because we're all sort of tempted by the picture that things past and present are fixed. Now, there's nothing that you can do about in these things where the future is, in some sense, indeterminate and it's only gonna get made determinate in the course of events. So sometimes it's beautiful, the open future and there's something very attractive about the open future. I'm not saying I subscribe to it, but whether or not the view of the open future is correct is obviously a really interesting metaphysical question about the nature of time itself. So what this shows is that something like the principle of excluded middle is gonna be a hostage to certain views in metaphysics, such as views about the nature of time. Okay, let me ask you, that's a good point. So with the law of the excluded middle, where I see difficulty is not necessarily with the logical principles. So much as there are linguistic circumstances in which it doesn't really apply. So the present king of France is bald. Is that true or is it false? Well, in one sense it's false because it's not the case that there's a present king of France, but in another sense, it doesn't really apply. It's not really the right way to frame the question. So if we talk about future events, I guess my, I haven't really thought too much about it, but my intuitive thought is that it's not, it wouldn't be a tension to say that things in the future will either be some way or they won't be that way. And whether or not they are that way or not that way is still open. So I don't see where that would lead to a kind of fatalism to say that the future is unknown, but it's still gonna either be the case or not be the case. Yeah. Okay, so several things. First of all, I mean, Aristotle's argument that excluded middle entails fatalism is, I don't think anyone agrees with that. So what's at issue here is this picture of the open future. Now, it's quite possible that someone who holds this view can say, well, it will be true or it will be false. That's okay. That doesn't commit to the claim that it is now true or it is now false. I see, I see. The view is short. It ain't now true or false, but it will become so. Okay, but that seems like to me, it's still something that language could easily resolve if we're just careful on what we mean, you know. Well, I mean, this raises, again, a number of interesting questions. I mean, you raised the question of the, I'd be loved, King of France. And so we're dealing here with reference failure. Reference to things that don't exist or like the present King of France. Famous example from Russia. How you handle this is a contentious matter in logic, because orthodox logic kind of assumes that every name refers to something. Yeah. And that doesn't seem kind of right. So you've got to bend logic a bit to handle this kind. Now, you've got various options about how to do this. Russell's option was to say, well, okay, let me keep it simple and cut through some of the Russellian niceties. The present King of France, that name does not refer. So the present King of France exists or is bald is just plain false. And so it's true. Present King of France is not bald. The present King of France doesn't exist. Present King of France isn't a king. Doesn't it be France? Okay. That's one possibility. And it's essentially the one that Russell favored. But 30 years before that, the founder of modern logic, Gottlieb Fager, gave a different answer. He said that if you take a sentence with a name that doesn't refer, it has no truth value. So it wasn't the King of France. For him, it was Odysseus. So Odysseus is a character from Greek mythology and says, Fraga, well, Odysseus doesn't refer to anyone. So the claim that Odysseus was, what was it, set ashore or sleep on the coast of Ithica? Something like that. Fraga says, this is not true. It's not false. Just because to be true, it would have to have a predicate either applying to an object or not. And there's no such object. So this is another view that endorses the existence of truth value gaps. Yeah, yeah. So in that circumstance, I've never heard that one with Fraga. It seems like there's a pretty simple resolution or potential resolution, which is these things refer, but they refer directly to ideas in our mind. The ideas don't have any kind of external reference. So if I'm talking about Odysseus, I have a very clear concept of what I mean. I could talk about the properties of the character, the history, but it doesn't refer to some mind-independent phenomenon. Okay, good. So we're back in heavy metaphysics here. And another issue that's on the cards is the thought that these things can refer, but they refer to non-existent objects. So you've got three possibilities. They don't refer. They refer to non-existent objects or they refer to existing objects, but they can't refer to existing objects that you can, that the kind you think they do. They've got to refer to something else, and not suggest them with ideas in the mind. And these are sort of contemporary issues in metaphysics, as you might know. There are pros and cons for all of them. Let's just talk about one of the cons for yours. Suggestion, if I'm talking about Paris, I'm talking about an object. And it's a quite different object from my idea of Paris. Okay, Paris is in France. My idea of Paris is not in France. So when you say Paris is in France, though, you have an idea. Indeed, yeah. And when I talk about Odysseus, let's agree that Odysseus doesn't exist, I'm not talking about the idea of Odysseus. I'm talking about, if anything, a non-existent object or, again, in the case of existing objects, it's clear that the object and the concept of it are distinct things. And you can talk about the one or you can talk about the other. And at exactly the same point holds when you're talking about potentially non-existent objects. The object is one thing, the idea of it is another. Well, we could talk about, we could say something like, the idea of it is one thing and the assumed external referent is another. So with the Paris example, I think if we're being strict, we could say that when I talk about Paris, I am actually talking about an idea in my head that I assume has an external referent with a bunch of properties that my idea of it doesn't have. Yeah, okay. I mean, look at the standard truth conditions of Paris is in France. I mean, what most logicians are gonna tell you is what makes that, what was it for that to be true? Well, it's true if the object referred to by Paris is in the country of Paris, is in the country referred to by France, okay? And know that you're talking about the objects. Yeah, I think so I think that's the thing with the general language. So to go back to the pen, I think actually that's kind of a, that's like a shorthand thing that language does. When I'm talking about the pen, I don't actually think there's, so there's a, I'm assuming that there's a bunch of matter out there in space, but I don't have access to that world. I have access to kind of the world of my sensory experiences. And so I have an idea of the pen. And when I'm referring to it, I'm really talking about like experiences in my visual field, for example, I've been really concrete. But that's just because, I mean, that's just shorthand. So our whole theory of physics and like the standard idea of how we think the world works is that there's a whole world that, that my ideas refer to, but I'm not sure about the state of that world. So if I were to say, I have a pen in my hand, I think that's a true statement, even if it's the case that I'm hallucinating. It might be the case that my experience doesn't correlate to the world as I thought it did, but I say, I have a pen in my hand is still, would still be true. Okay, now we really are in deep metaphysical. Yeah. I'm sure you probably realize what world is and is the question of realism versus idealism. Yeah. External world. And whether one can be a realist about external reality, even though let's agree, we don't have a direct acquaintance with it. Whether this justifies a skepticism, whether you should be an idealist, whether they sing, so it's all in the head. These views are well-known historically and I don't know that there are any knockdown arguments one way or the other. But I suspect if we pursue this path, we're gonna drift off. Yes. Really talking about was, you know, the possibility of logical gaps and gluts and what the discussion has sort of showed us in many ways is that you're not gonna be able to disentangle questions such as this from serious and deep metaphysical questions. Yes, absolutely. And it's a lot of the philosophy of language too. What do words mean and how do they work? So you gave the example, I like the example of the underlapping truth and I think that makes sense that I would say we could phrase things in a way in which it's not immediately clear whether something is true or false or if it even has a truth value. So there's a kind of, I have a loose way of understanding that. What about the overlapping circumstances, the overlapping truth values? So you gave the example of the liar paradox. But if we're talking about the arrow, we're talking about any other contradictory phenomena, I still have a much harder time saying or like clearly conceiving of the state of the overlapping true and not true. Cause when I think, if I were to say something like, it is true that X and I were to say something like it is not true that X at the same time, to me that would be the definition of internal incoherence. Like there's- Be careful. Okay. Yeah. If something is false, it's not to say that it's not true. If you identify falsity with the absence of negation, that's exactly right. But if you hold there a gaps or gluts, then for something to be false is certainly not for it, not to be true. Cause if you believe in gaps, something can be not true and that doesn't make it false. And if you believe in gluts, something can be false and that doesn't make it not true. Okay. So the overlap and the underlap. Okay. It's important to distinguish between something not being true and something having a true negation, i.e. being false. Okay. So when you say, when you're talking about contradictions though, are you saying then that a contradiction is something that is true and not true or are you saying that something is true and false? There may be contradictions of that kind. That takes us into questions about various kinds of paradox. Okay. But in general, I believe this is simply the view that there are some a's which are both true and false, i.e. such that both they and their negations are true. Okay. So that's the harder one. That would be the harder one than to wrap your mind around versus just saying they're true and it might not be the case that they're true. Well, to say they're true and not true is a very particular kind of contradiction and it involves the notion of truth. So we're back in the question of how truth behaves, right? But to say that some things are true and have true negations. Okay. I guess that involves truth as well. But you can claim that something can be both true and false without claiming that something is both true and not true because that smoke is in this kind of tendentious and accounts of negation. Okay. So let's take the circumstance of the arrow. Is that something that you're saying, you know, the arrow, it is the case that the arrow is in motion and it is not the case that the arrow is in motion? No, the example was the thing's in motion and if it's in motion at this point of time it's here and not here because it's already gone a little bit further. So the contradiction is it's here and not here. It's here and not here. And that would be different from saying it's here and it's not the case that it is here. If it's not the case means it's not true, yes. Okay, so are there any. Not the case is kind of ambiguous. Okay. So are there any then cases of the explicit, I'm trying to get this straight to make the distinction because the way that I use true and false is to say what is the case is true. If something isn't the case it's false and if something isn't the case it's negation is true. I do make them kind of mutually exclusive but if we open that up though, are you saying that, is there any circumstance in which we can make the explicit affirmation as being true and then the negation of the affirmation as being true also? If you buy a certain view about the paradox itself reference, yes. Okay. But let me just sort of point out that dilithism is not a view specifically about the paradox of self-reference. It's simply the claim that some contradictions are true and you might apply this thought to a variety of theories such as motion or the law or whatever. And the sort of scenario that you're raising is something that arises when you apply dilithism to the paradox of self-reference. Take, come back to the lie of Parox. So before I get you in the form, this sentence is false. What I'm saying is false, juggle that a bit. So as I'm saying this, what I'm now saying is not true. Now, is it true or is it not? Well, if it's true it's not true and if it's not true, well it's true. So simply that it's either true or not true, you're in this situation where something is both true and not true. And that's the contradiction and it's a contradiction that concerns explicit truth predicate. So it's something in the form, okay. This object is here, this object is not here. Doesn't concern truth explicitly, right? But this is true and this is not true, does. So we're dealing with the behavior of the truth predicate here. And yeah, you know, this can happen. So before we talk, it's a perfect segue to get into the liar paradox and issues with self-reference. Are there any examples of that phenomenon with the affirmation being true and the negation of the affirmation being true when they aren't self-referential? None that I know. Do you think that it's possible, like theoretically? Certainly wouldn't want to deny it. But if you want something that's true and not true, I mean, it's gonna have to be, the argument is gonna have to evolve truth somehow. So your theory of truth is gonna have to get into the act. Are you saying that this is your strong suspicion or do you think that there's a kind of theoretical necessity that if you're claiming something is true and not true, that unless you're talking about self-reference, you have made an error or something. Well, let me just put it this way. I mean, I know of no argument that something can be both true and not true once you're outside the domain of self-reference. I'm sort of bold enough to say it's impossible. But I haven't had any. Okay, okay, that's interesting. But so that then, so that kind of frames the issue. Let me try to rephrase something. I kind of give it some perspective. And if I misspeak, then this would be an opportunity to correct me and see if I've made an error in what you're saying. So I think you're saying is in some circumstances, you can have something that is both true and false. If it's the case that we say that it is not necessarily the case that true and false are like the opposite, the mirror opposites of one another. So would you, and you would also say that it is only in the circumstance that we have that view of truth and falsehood that you get something being true and false, right? Kind of a definition. So in other words, if you want to accept the idea that there's true and false, you have to take the position that true and false are not these mirror opposites. That's the standard way that the logical theory goes. Okay, I mean, just let me draw your picture, okay? If you look at semantics of logic, and look at the situation, it's going to divide the statements up into the truths and the falses, and those are exclusive and exhaustive. Now, if you think for metaphysical reasons that there can be an underlab, that this is going to happen. If you think that for metaphysical reasons there can be an overlap, this is going to happen. And if you think that both can happen, this is going to happen, right? Now, as a matter of fact, these pictures are well-known and well-understood in contemporary non-classical logic. So there's nothing mathematically outrageous about these things. We know that the properties of these logics have, you know, how to actualize them and algebraicize them. So their mathematics is well understood. So it's not in the technological details for these to stand or fall. It's really, back to the metaphysical question of which of these pictures is right. So, and in order for the overlapping picture to be possible, your position is also that you have to take the claim that what is not true is different than what is false. Is that correct? Correct. Okay. If you, in terms of how the gaps are glass, that's got to go. Because to say that it's false, if it's not true, is just to say that its negation is true, if it's not true, and that's to say, hey, it's like that. Right, correct. Things are exclusive and exhaustive. Okay. And that's exactly what's at issue. Okay, so then a lot of this, it seems like comes down to the Lyres paradox in terms of the hardest of cases. We have something being true and not true, not just true and false. So even if you grant there's a difference between true and false and true and not true, this is kind of the big one. This is the one that gets to the heart of everything that you might have at least one circumstance in which you have something which is true and not true at the same time. Well, I mean, you might find that hard as course. I mean, for me, look, I mean, if you believe that contradictions can arise, you're gonna have to hold that some predicates can behave inconsistently. They can have an overlap. So, you know, is in this position, is not in this position. Okay, predicate and its negation, if you're haggling about motion, you're gonna have to say these two predicates can have an overlap, something can satisfy both of them. Now, what we're exploring is another very particular predicate, namely it is true. So, to say that the sort of contradiction we're talking about now can arise is to say that essentially the predicate is true and is not true, can have an overlap. And in that sense, it's not that different from any other predicates, except maybe in the role that truth itself plays in our thinking. Well, yeah, so that's why I would say it would be a kind of a category difference is because literally any other thing that you're talking about kind of presupposes your truth, your perspective on truth, and is implicit in like any claims that you're making. But in this one circumstance, you're talking about truth itself, right? So it does seem like there's like a huge category distinction there. But I guess that's a distinction without a difference. The main point that I wanna talk about is now self-reference because this is clearly something that if it's the case, at the fundamentals of logic, you have something which is like an inescapable contradiction, you really have to, as far as I'm concerned, you have to radically revise your worldview. I think a worldview that is tolerant of contradiction and a worldview that isn't tolerant of contradiction, to me, look very, very different. So let's explore that. Anything, you look like I interrupted you when I said anything, any other things on that topic? I was waiting to see where you're going. Okay. All right, so this sentence is false. Here's a potential resolution that I wanna know your thoughts on because I find this persuasive and if it's persuasive, I like the idea of keeping my worldview consistent and free from contradiction. If it's not persuasive, then obviously I need to expand my worldview if I can't escape contradiction. So I think a good way to phrase it is this sentence is false. The way that I think language is working in that circumstance is there's one of two possibilities. One of two possibilities that are highlighted by the question, which sentence are we talking about? Exactly, what sentence exactly is false? And I think the sentence either refers to one of two things. This sentence is false is either talking about the words, this sentence, and saying that it is false, or it's the case that it is talking about itself or the whole sentence. So this sentence is really saying this sentence is false is false. That's the way that I see this kind of one of two options. And in either of those circumstances, you have a kind of grammatical error or linguistic error. And the first circumstance is fairly easy to see. Two words, this sentence can't be true or false. It's not a proposition, it's not a claim, it's just kind of two arbitrary words. I could say this cloud is false, it's not really a proposition. The interesting case is, if it's true that this sentence is false references this sentence is false, then it seems like to me the Liar's Paradox generates an infinite regress, that what it's really saying is this sentence is false is false. And if we're careful, we were to say, okay, well what exactly is false? So it's this sentence is false is false. Then we kind of plug it back into itself and we're left with this sentence is false is false is false. And we say, well what sentence exactly? So this sentence is false is false is false is false. And it just kind of generates this infinite regress that there's never some meat that you can actually identify as true or false that either generates the infinity or kind of collapses to just two words. And the actual? If that's the case, then it would be the case that this sentence is false is not a case of a true contradiction. It would be no more than saying this pan is false. That's in your first case. What about the second case? What do you want to say about this sentence is false? If this sentence refers to the whole sentence? Oh, that's what I'm saying. That is the case in which it generates the infinite regress. So if this sentence is false is false, then you're looking at this sentence is false is false. So I like to do it with parentheses. You have like this sentence is false in parentheses. So what are we to say about this sentence? This sentence is false. So what I'm saying is if we are looking for a concrete referent for the words this sentence, if it refers to only this sentence, that's a non sequitur. If it's not relevant, it's not relevant. Right, right. So if this sentence really is talking about this sentence is false, then you get the infinite regress and you get like a nesting error. So it's this sentence is false is false is false. And what follows from this? I'm sorry? What follows from this? Okay, so I guess another claim I'm smuggling in here is if it's the case that you get an infinite regress, it's not the case that you can evaluate an infinite regress as being true or false. It's like a mistake of a language. So it's neither true nor false. It's neither true nor false in the sense that it's a bad sentence or like it's a tricky sentence. All right, sure. Okay, so there are many well-known solutions or proposed solutions to liar programs. And certainly what you're articulating is one. And... Have you heard that one before, by the way, for my own sake, because I have never come across that one anywhere. And I feel like surely somebody else has thought of that. Look, it has many varieties depending on how you articulate the regress to you, okay? But at least in one way of looking at it, it's the core of a solution posed by Saul Kripke. Okay, this is an outline of the theory of truth in 1975. But the thought that when you get a regress, something goes symmetrically wrong is older than Kripke. And it's pulled by people in the 50s. Okay, now, let's try and keep this simple. In the lie paradox, the noun phrase, the subject term, this sentence refers to the whole thing. Okay, the other option is not really an issue. But you're actually right, you're going to get a regress. Okay, it's not clear that this is vicious. Okay. Consider this sentence I was speaking is in English. What sentence? Well, the sentence I was speaking is in English, is in English. So self-reference is going to give you a regress. About the regress as such, which is problematic. So let me try to answer that one and see if you find this compelling or not. So it is not the case that self-reference in practice needs to be vicious. But there's a difference in terms of what's being claimed. So the claim is in English is very much different than is false. So if you were to look at the sentence, this sentence is in English, what it's doing in your mind is it's saying, it's like pointing to itself or it's saying, in this sentence you have English words. So then your mind looks at what the words are if they're in English and says, ah, that's true. So it gets away with self-reference. But you can't do that with the false claim because there's not the truth claim being made. Sure. So you're applying something like this. The fact that the self-reference holds the truth crooked means that if you try to evaluate the truth that they've seen, you get into this infinite regress. So the regress is there. But it's sort of vicious in the sense that it prevents you assigning a determined truth value or meaning or something to this claim. I'm saying that if we were going to analyze the claim, this sentence is in English and be really dogmatic about it, then we would generate an infinite regress and say, it's a mistake. Like you can't do that. You don't want to go that way. It's just plain truth. There's nothing dogmatic about it. What I'm saying is that's the correct position, but there's a different explanation. So the explanation is in that circumstance, when you write down those words or you see those words anywhere, the sentence is in English, all that it's doing is it's kind of popping out those words and then your brain is evaluating them and saying, the words in these parentheses have a certain property. It could be the words are red, the words are blue, the words are in English. And then you go through and you evaluate, is it the case that these individual words meet this criteria and therefore it gets the truth value? I mean, the regress is there. Whether it's true or red. But that's not an infinite regress. Sure it is. It's exactly the same. This sentence is in English. What sentence? This sentence in English is in English. What sentence is that? This sentence in English is in English is in English. The regress is exactly the same because all you're doing is replacing a noun phrase with a quoted whole sentence. And you can play that game indefinitely. But I do think there's a category distinction here between saying it's false and it's in English, but here's why with the reference it actually does end. You can very much make sense of the claim. If you think of it in terms of parentheses, this sentence is in English, is in English. That doesn't need to progress anymore. The self-reference does not end. What you're playing with is the thought that even though you've got the self-reference, you've got infinite regress in the case about speaking English, you can still assign the thing a determinant truth value by looking at the rules of grammar. Whereas in the truth regress, the fact that you've got a regress is going to prevent you assigning a determinant. Now either it's either truth value or a meaning or something like this. So it's not the regress. And it's why I asked you what hangs on this regress. And the thought was, hey, if it's the regress and truth is an issue, there's something which makes this a bad sentence, as you put it, right? Yeah. Okay. And how you diagnose the badness is, you could go different ways, but the most common thought is, because you've got this infinite regress, it makes it possible to assign this thing any determinant truth value. That's the creepy version. So there's the modified creepy version. We're going to call the Patersonian version, which is obviously less sophisticated. But I still feel like there's an objection here that is valid, which is, if you think of the one generative process, so we're looking at this sentence as an English is an English, is that something that's going to necessarily generate a regress? I don't think so, because the nature of the claim is in English is another way of saying, look within the parentheses and see if the elements in that parentheses are of a certain type. So in other words, what this sentence is in English means is observe this set and see if the elements of this set are in English. That's all it means. But you can't do that with is false because it implies that there's a proposition within the parentheses. It's not just the elements in the parentheses are of a certain type. It's that there's an actual truth claim there to evaluate as false. The syntactic regress is there for both cases. What you're actually gesturing at is the fact that in the case of the truth and the lie paradox, there's something about the regress that prevents you from making a determined resolution of its truth value or maybe to give it a determinant meaning that doesn't express a proposition. It is by the nature of saying... So imagine I would say this sentence is tall. So that's kind of a... the claim is tall is kind of a misapplied... That sounds like a category mistake. Yeah, it sounds like a category mistake. That's a good way of putting it. So I guess maybe that's a better way of putting it that to say this sentence is false is a category mistake. But to say this sentence is in English is not a category mistake. That's wrong because sentences aren't the kind of thing that can be tall or short whereas sentences are the kind of thing that can be true or false. So what is going on here is not a simple category mistake. So I will choose to beat the dead horse here. I'm sure my audience is saying, Steve, you've got to get it here. But I'm doing this for my own sake too. So I have no difficulty with the sentence. The sentence is in English because I'm just analyzing... I'm reflecting on the nature of what my mind is doing. I'm saying what is actually taking place when I see the words this sentence is in English? Oh, I'm generating a new sentence. I'm saying the sentence is in English is... The contents of that are English words. Just like the words in the sentence are red. It's like a claim about the actual individual objects in a set of parentheses. I think no problem. I could say the sentence is in French. We could have all kinds of really acceptable, valid sentences which would include self-reference. But we could also have sentences which wouldn't include self-reference and one of which would be to say that this sentence is false because you're not talking about the words. You're not talking about the elements in the set. You're talking about it as if it expresses some... as if it's a proposition. As if it's a claim, that can be true or false. So that seems like a pretty clear example of where it gives the illusion of having a structure that makes sense, but it's actually this kind of subtle linguistic mistake. What you're actually talking about is kind of truth evaluation. So with this sentence in English, even though there's a syntactic infinite regress, it doesn't affect the way we can evaluate its truth. Whereas the thought is with the truth predicate there, it does affect... Ah, OK. It follows from that. It's not clear. You might want to say the thing has no determinant. Truth value, you might want to say it's meaningless. You can push it a number of ways. OK. OK. That's the movie I'm making. OK. So I think this is what it comes down to. I'm sorry. Go ahead. Go ahead. No, no, no. We've only just started. Because there is a very standard problem for this kind of solution, OK? Which is why I asked you what you want to say about this sentence, OK? And you said, well, let's just call it a bad sentence. OK. Let's leave it, right? I'm going to worry about what that means. Now, there's a phenomenon in logic or paradox of self-reference called extended paradoxes or strengthened paradoxes. OK. So let's... I want you to consider this. This sentence is either false or bad. OK. Now, if it's true, it's either false or bad. And that sounds like a contradiction. If it's false, well, if it's false, it's either false or bad. So it's true. Now we've got the third possibility. It's a bad sentence. OK. Well, if it's a bad sentence, it's either false or bad. So it's true. OK. This is a typical revenge problem. So when you were saying it kind of popped in my head, here's what I think the actual disagreement lies is I am actually claiming that in one circumstance you generated an infinite regress, which is a problem. And in the other circumstance, there is no infinite regress generated. I can make full, complete, coherent sense of this sentence is in English as in English. I cannot make full, complete sense of this sentence is false is false. OK. So we've gone back to the first topic now. I mean, you want to, you explain what bad means. Well, but so if I were to say, it's not the case that the infinite regress or it is not the case that you can evaluate any sentence with an infinite regress. Why do you think that's incorrect? Why do you think infinite regresses are OK? Well, it's you that thinks they're not. OK. Well, I don't think they are because I don't think you can make, I don't think you can really comprehend an infinite process. I don't think that really makes sense. OK. We're back to Zeno. OK. Let's not follow that up. Look, what are you going to say about the extended paradox? This sentence is either false or bad. The exact same thing. If it's the case that you're talking about. Well, I'm going to say it's, if it's the case. Well, so if it's the case. OK. No, you're in a self-referential point. OK. Because you want to say it's bad, but you don't want to say that what you said is true. What I'm saying is it's either the case that in order to make sense of that, it's either the case that you're saying the words this sentence is good or is true or bad, which of course doesn't make any sense. Or you are trying to do something. If it's the case that this sentence refers to itself, you're going to generate an infinite regress that can't be resolved. So what are we going to say about this? I asked you if you want to say about the liar. You said it's a bad sentence. I'm going to throw the words back in your face. I'm going to say what do you want to say about this sentence? It's either false or bad. Using your word bad, whatever you mean by it. OK, that's fine. I just want to know what you want to say about this, but extended sentence. But here's the thing. Here's the thing we're actually disagreeing on is on the infinite thing. That actually really is the... I'll give you the word bad. It can mean anything you want, because the extended paradox says it doesn't really hang on the meaning of the word bad. All it hangs on is the thought that you want to call these guys bad. OK. I'm saying that there is a grammatical error present whenever somebody... So call it ungrammatical. This sentence is false or ungrammatical. It doesn't matter what bad means. But that would be a syntax error. That would just be... That would be like... I mean, that's just like saying... like a non sequitur. So I could say, you know, the pin, the lamp green. I mean, I can say those words, but that doesn't necessarily mean that I'm saying something that's coherent, that I can evaluate as true or false. Is NFS being not ungrammatical by the canons of English? OK. What you've got to claim is that it's semantically defective in some sense. Yes. OK. Now let's consider the sentence. This sentence is either false or semantically defective. What do you want to say about it? I'm claiming that the words that you've just spoken... are a non sequitur that have the illusion of being sensible. OK. You've claimed that it's semantically defective. I'm saying that that as semblance of words is not coherent. OK. All right. So this sentence is either false or not coherent. You tell me it's not coherent. It's either false or not coherent. So what you said is true. So you're talking about semantically coherent being true. You're treating it as something that's coherent. No. I'm respecting what you say. Because you tell me it's semantically incoherent. And I believe you. OK. Because that's diagnosed. But I'm not. Because I'm not even... See, you're saying it is semantically coherent. As if it's... No. And I'm saying that... Yes. That's it. Semantically coherent is your term. Right? You say this is semantically... not semantically coherent. I'll give you that. But you're also claiming that it's not semantically coherent but there seems to be an argument which says, look, that better be true unless your theory is self-refuting. And if what you say is true, then it's true that it's either false or semantically coherent. So damn me, it looks as though it's true. OK. This is the extended paradox. OK. So I'm going to try one more time to see if I can phrase this in a correct way and then we can keep moving on here. So there's something... What I'd say there's fish... fishy business going on here, which is your... it seems like you're giving a kind of structure to words that I'm not. So I'm saying there are certain ways you can violate maybe the laws of grammar or the rules of logic or something like that where you can violate them in a really tricky way so that it's not immediately self-evident where the error is. It's kind of a nestled linguistic error. So I'm trying to say... I'm trying to take one step back and I'm saying in circumstances in which you have a sentence that when you try to flesh it out and see what it's really claiming, it generates an infinite regress when you're really trying to flesh it out. It is not the case that that is something you can evaluate as true or false. So in all circumstances where you have an actual infinite regress, you have made a grammatical error. Now it just so happens that there's a sentence this sentence is in English that I am saying doesn't generate the infinite regress because if it did generate the infinite regress it wouldn't be able to be comprehended. And so I say, well is there some way we can make sense of this sentence is in English? Yes. The sentence is in English is in English. No problem. We can make sense of it. But I'm saying the other claims whether they were the basic, the sentence is false or they're the strengthened version the sentence is either false or it's bad sentence or whatever you want to say. Those you can't make sense of those necessarily in order to try to put meat on them to try to evaluate them as either true or false you have to generate that infinite regress. And so my objection is actually to this idea of the infinite regress rather than what you're saying you're trying to like it seems like you're kind of putting me into the category of already accepting that this sentence is false is something that's meaningful and I'm saying well that one actually might not be. No, no. Look, I don't think I've got anything much more to say on this. What you've just done is describe what it means to be bad. Your thoughts. Now, the extended paragraphs I gave you doesn't really hinge on what bad means. It just depends on the fact that you want to say it's bad and presumably you take yourself to be telling me something true. That's all the extended argument depends on, right? So do you think that all assymblances of words are necessarily coherent in some way? No, I'll accept that there are some things which are bad. I mean the extended live paradox does not depend on the meaning of a bad how you analyze bad. It just depends on the fact that you want to say this guy's bad and in doing that you're telling me something you take to be true. Look, virtually all consistent solutions to live paradox have these extended paradoxes where you take the concepts deployed by the paradox solver and you rejig the argument. Even when it's about kind of rejecting this idea of self-reference add-in fun item fundamentally? Absolutely. This kind of extended paradox is a standard objection to most theories that try to give consistent solutions to the live paradox. Okay, so you'd say that one way or another this is not a language problem. This is something that points to the fundamental structure of logic rather than saying maybe our language is a little funky here. This is something that gets to logical contradictions existing. Well, we go back to this point we had some time ago now. You've got this prima facie vertical argument for contradiction. How do you respond to it? Okay, now my response is to it is, okay, it's a vertical argument, end of story. Okay, most people have not gone down this path. Most people have said, well, there's something wrong with it and they've tried to diagnose what's wrong with it and they produce theories of the kind you suggested or other theories, but they've all got these problems and extended paradoxes are one of the big problems for all these things. You just take the vocabulary or the machinery that's put forward by the solver and you just tweak the example, deploying that very vocabulary. Okay, so would you say then the argument that the liar is this case of kind of inescapable self-contradiction is actually only applicable to the extended liar because it seems like maybe the other ones have like the standard liar's paradox can have resolutions but the one that you really think is inescapable is the extended liar? No, I think the ordinary liar is both true and false and I think that's a contradiction because to be false is to have a true negation. Okay. So if L is the liar, L and not L. So you're persuaded by none of the resolutions to the non-strengthened liar? I'm persuaded by none of the consistent solutions to the liar paradox and I'm not alone with that. Okay. Because there's no consensus on the matter in contemporary logic nor has there been in the history of logic. All right, that was my conversation with Dr. Graham Priest about logic and metaphysics and paradoxes and the liar's paradox. Lots more to say on the topic. I really can't wait to do an interview breakdown of this discussion. And like I said at the beginning of the show, next week is part two with Dr. Graham Priest talking about the history of mathematics and logic and what exactly happened around the turn of the 20th century in those fields. So stay tuned. There's a lot more to talk about.