 Hi everybody, welcome to episode number 9 of Patterson in Pursuit, also known as my very favorite episode so far. The reason is because of this week's topic, which is logic and epistemology. Is there any way that we can make sense of logical contradictions? Is there any alternative to classical logic? Is it possible for some things to be true and false at the same time? I'm joined today by Professor Justin Clark Done, who is a philosophy professor at Columbia University. His focus is in epistemology and in logic. What's funny about this interview is that I saw on the Columbia website that he has an interest in a priori reasoning, which is something I have a very strong interest in. I thought at the beginning that this was going to be an interview about a priori reasoning and it took all of two minutes for it to turn into an absolutely fantastic discussion about logic. This is one of those conversations that's really essential. We're talking about the foundations really of philosophy itself. Don't be intimidated about the terminology or some of the advanced concepts in this. If you don't get everything we're talking about in one go around, it's really not that big a deal. Now this conversation is so good and there's so much meat here that two episodes from now in episode 11, I'm going to be doing a breakdown episode where I'm going to be giving my own analysis of the ideas that we're talking about here and I'm going to give special attention to this particular interview. If you're interested in this topic, then I have to give a plug for my upcoming book, Square One, The Foundations of Knowledge. It is specifically written about logic, epistemology, and a ton of the ideas that you're about to listen to. I hope you enjoy my interview with Dr. Justin Clark-Done that took place on the absolutely beautiful campus of Columbia University in Manhattan. So first of all, thank you Dr. Justin Clark-Done for sitting down and speaking with me today. Thanks for helping me. So a lot of your work focuses on the world of a priorism and I think this is a really interesting area specifically in my background. I have a soft spot in my heart for a priorism and so I saw your bio online and I thought, oh, I got to talk to this guy about a priorism. So I was hoping we could start with the very basics that what do you think the definition of a prior, a prior reasoning is and perhaps how it's contrasted to other forms of reasoning? Yes, I mean, I guess like, you know, the traditional cartoon definition is that a prior knowledge is knowledge that's independent of experience. But of course, that doesn't make a lot of sense because you can't have knowledge independent of experience presumably. So I mean, you know, the real content of that is presumably knowledge that is independent of any particular kind of experience. It's knowledge you can have without having any particular kind of experience. And you know that contrast with knowledge that say it's raining outside where it seems like you need to have one of a particular variety of experiences to know that. So in that sense of a priori, which so far isn't so demanding, depending on your views of like what it takes to have justified belief, you know, in that sense of a priori, I think it's pretty clear that we have a fair amount of a priori knowledge. You know, I think that you can know without having any particular kind of experience that if there are dogs, then there are dogs, you know, that that two plus two is four that you shouldn't torture people just for the fun of it and so on and so forth. On the other hand, though, you know, some people have tried to strengthen this definition by requiring also that the knowledge is indefeasible, that it can't be defeated by additional evidence. And when it comes to that stronger notion of a priori knowledge, I'm inclined to agree with Quine in a famous paper in the mid 20th century called Two Dogmas of Empiricism. He wasn't actually talking about the a priori, he was talking about analyticity, but I think that the point applies to the notion of the a priori. I'm inclined to think with him that it's really doubtful that we have any indefeasible knowledge. So these are two quite different notions that we have knowledge that you don't need to, you know, that you can be justified, knowledge that you can have independent of, you know, doing an experiment or making a particular observation. I think there's a lot of that. On the other hand, I think there's maybe not any knowledge that we can't imagine getting defeated. So can I pursue that a bit? So I think those examples were, you know, if there's a dog, there's a dog. Right. There are two questions. One, is that not completely independent of experience? Or if it's not, where's the experience in that example? And two, wouldn't that qualify a certain knowledge? If there are dogs, will there are dogs? Yeah. On the first question, I mean, one difficulty that you're kind of pointing to is, you know, I need to have some kind of experience to get the concept of dog. So this is another sort of complication to even whether you can really, you know, persistify this idea of knowledge independent of any particular kind of experience. Because we at least need certain kinds of experiences to acquire the relevant concepts. Even if it's like a secondhand experience, so if somebody tells me about a concept that still qualifies as experience. Yeah, yeah, yeah. And I mean, some people have sort of been moved by this kind of obscurity to believe that actually there's just no real clear distinction even, you know, when we're limiting ourselves to this pretty mild notion of a priori, assuming that we can make a distinction between the experience needed to acquire concepts and the experience needed to justify their application, then I think that we at least can make sense of this weak notion of a priori. When it comes to something like, you know, some banal claim, like if there are dogs, then there are dogs, under what conditions could I feel to be certain that if there are dogs, then there are dogs? Well, I mean, you know, here's a simple kind of example, a simple kind of example is that I can imagine, you know, the logicians to grand priests, you know, one of these somebody who knows more about, you know, alternative logics than I do telling me that actually here is a, you know, theoretical reason to think that this law fails sometimes. And so, you know, it's not clear whether we should accept this particular instance of the law. Now, you might say I should still maintain it. I should say that guy, you know, has taken too much logic. But it seems like my credence should be somehow affected, you know. It seems like when people, you know, I mean, Quine made essentially this point when he talked about, you know, amending logic, you know, in response to quantum anomalies, right? So even in circumstances where it's a strict logical contradiction, he's saying A and not A, you're saying that if somebody presents an argument, regardless of the content of the argument, it should sway us a little bit to think, well, maybe I'm, maybe I could be wrong about the strength of my belief in this? Well, you know, I wouldn't want to say regardless of the content of the argument. I mean, what I think is that we know that in one boring sense, there are lots of different logics ranging, you know, going very far in the direction, in the radical direction on the spectrum. It's not like that alone establishes anything about what follows from what. But it's also not like you can just pound your fist and say, well, you know, the claim is true in all models, because your notion of models, a classical notion of model, and the question is precisely which models should we be looking at? Well, doesn't that kind of frame the issue in terms of models? So what if, what if somebody's claim isn't, this is true in my model, but this is true. This certainly corresponds to reality. It doesn't matter how you, it's almost like a taxonomic distinction to say, you have this model, you have that model, this is this, I'm just saying, this is certainly true. Yeah, so first of all, just to be clear, but what I meant by models is the semantic sense of model, like there's a proof theoretic definition of the model theoretic, so, but right, so even if you didn't want to use a model theoretic analysis of logical consequence, my point is kind of the same. It's that we know that there are different views as to what follows from what. You can't just pound your fist and say, well, you know, it's just contradictory to say P and not P because in another logic, it is not contradictory in the sense that, you know, it can never hold. What about if somebody were to say that in my world view, I am absolutely certain that you don't have a conscious existence? Is that something you can say that? It doesn't really matter how strongly you believe that, Steve, you're wrong. You know, again, I'd want to distinguish two things. One is like, you know, the mere existence of other views, presumably every single view under the sun, there's somebody who has the alternative view, even that I exist, but from the reasoned, you know, defense of another view. Now, of course, reasoning assumes a logic. And if there is no overlap between the logic used in defense of the view and a logic that I agree with, then it might, we might get stuck in a situation where there's really like, there's nothing to say to one another. But that's not what's interesting as a sociological fact is that's not how it actually goes. What's interesting as a sociological fact is that sometimes people change their views about what follows from what, not just about what is actually happening in the world, but sometimes I come to the table believing, you know, the standard classical logic. And then I take a bunch of philosophy. I have a lot of discussions. I think about the semantic paradoxes or whatever. And I say, actually, you know, we've got to make an amendment somewhere. So all I'm saying, I just want to be clear about like the view. I mean, like one view, which I definitely don't agree with is just like because there's a bunch of different formal systems, there's no correct logic or it must be the weakest one or whatever. Definitely don't think that what I'm saying is because there's all these logics, one can't just pound one's fist and assume that the logic one happens to adopt the one that one is inherited is the correct one. Perhaps the word assume is the one that that we're getting or I'm getting a little bit confused on because I would say it seems like for any field of thought or inquiry, you can, you should evaluate all the different mutually exclusive claims and it may be that there is a strictly logical reason to say, oh, this is the correct logical framework or this is actually the solid foundation. And if you start from this standpoint, all the other ones are just simply wrong. Are you uncomfortable saying something like that? Let's say classical logic is, you know, pound your fist on the table. This is the one that's right. And all the other ones must be wrong because this is right. So right. So there's two issues. One issue is can we be certain or confident of a particular or logics being correct? And I'm saying that, well, we can probably be confident. I don't think we can be certain or dogmatic about it. Another question is it doesn't even make sense to say that one logic is correct. Right. So there's another issue, which is known as the issue of logical pluralism according to which, well, I mean, there's different formulations, but one formulation would just say, OK, well, we know there are different logics in the sense of formal systems. What more, what more, you know, what other question might you have? And one, one view would be, well, the remaining question is essentially a normative question. How ought I reason? And just as there's, you know, relativism about ethics, there's relativism about reasoning, good reasoning. You know, you and I might have different standards about and what would it be relative to? You might say, well, it might be relative to goals, right? I mean, so certain logics are essentially more conservative than others and maybe you care more about not believing falsehoods than, you know, than I do. So there's another issue, which is not about degree of confidence in the logic we adopt. It's about does the notion of correct logic make any sense to begin with? Yeah. Yeah. And so, you know, I personally have sympathy for the view. It doesn't make a lot of sense. But what I was saying previously is that even if you think that there is a correct logic, I don't think that logic is different than any other theory about the world in that we can somehow be dogmatic or just, you know, the alternative views are just somehow immediately dismissible as being unintelligible or something. OK, so let me ask you, I want to I want to pursue this because this is excellent. What would you say to somebody I think like myself who would say that in all claims to knowledge and all methods for reasoning, there is an implicit presupposition of classical logic that even when somebody is trying to make the case, let's say, for a grand priest logic that even in the construction of his arguments, he's presupposing what he's trying to defeat. It's there's what you might call this notion of inescapability to, you know, if you're claiming a, well, then you're claiming a. Yeah. And it seems like you just can't get around that, even if you claim you can, you really can. Yeah, no good. I mean, a way to sort of articulate what you're saying is, you know, so suppose I give a nonclassical logic, I have to then give like a semantics and a syntax and stuff for the logic rules, you know, rules for evaluation, rules for for proof. And you might think I'm going to use classical logic in, you know, developing that meta theory. And this is, in fact, an objection people have made sometimes to the way nonclassical logicians have often pursued their craft. They've, you know, they've said, here's the rules for correct reasoning. But then when they, you know, explored the meta theory, they're just using the rules that they say you're not supposed to use. So it seems like, okay, this is actually just a formal trick. I mean, everybody agrees you can lay down rules that, you know, conflict with the rules. But, but what's interesting is, is that doesn't seem, you said in a stable, it doesn't seem inescapable. There are people, para consistent logicians who use para consistent logic in the meta theory. And even if you think they're wrong, even if you think like you're using that, you can make sense of it. You can evaluate it. It doesn't seem on. But do you think it's possible then to make sense of a logical contradiction? Yeah. I mean, so a key question is what do you mean by make sense of, right? And this is another case where I think like, you know, we just kind of have to choose an interesting notion for, for me, an interesting notion to make sense of can't be one where there's no sort of third person perspective that we can agree to where we can figure out in a principled way, whether, whether something can be made sense of. In other words, it shouldn't be the case that sort of you perform just as though somebody would who were making sense, but I pound my fist and say, it doesn't make sense. It has to be that there's some sort of perspective you can, you and I can both occupy that will decide the matter or give us reason, not, not a criterion, but, but evidence. So here's a simple example. I mean, I, you know, one of the things I keep coming back to is it's striking that in these debates about different logics and stuff, from the outside, it looks just like a debate about any other philosophical issue. People write journal articles, people respond, people, you know, they get into, to, to details and sometimes work out, you know, their differences. Most of the time they don't, but it's not at all like people speaking different languages. Like really, there's just no contact. Like I can't understand what you're saying. You might as well have just written random letters. It's, it looks from, you know, here's a great, here's a good analogy. You know, people also disagree about the axioms of math and set theory, right? Now that is almost all against the backdrop of classical logic, you know, almost everyone in those debates agrees to the principles of reasoning, but they're disagreeing about, you know, whether every set is well founded or, you know, the axiom of replacement or the axiom of choice or whatever. Now what's striking is someone who doesn't really, hasn't taken a bunch of philosophy and doesn't know the difference between logic and math. Many people I think would regard them as essentially the same thing. If you look at these debates from the outside, they look essentially identical. Now here's a question. Is there a principled reason to say that the second, the debate over the axioms of math is an intelligible, sensible debate that we can, you know, get involved with and potentially make progress on and the debate about logic is not. Maybe, but I'm inclined to say there's not. So you have two choices. You can either say, well, it doesn't even make sense to question the axiom of replacement or the axiom of choice or something. That's just an intelligible debate. It's the axioms of math. Pound your fist. Or you got to say, actually, the logic case is not different. We might not make progress. It might be very difficult, but okay, so I want to ask you a couple of questions on that topic. So that's a very, that's a very meta analysis. So let's go to some concrete. Something like, is there a way to make sense of a claim like they're, in some circumstances, there is a married bachelor. There's a married unmarried man. Is that intelligible? Yeah, well, I mean, okay, so again, like, you know, what do you mean by intelligible? So let's just start from, you know, a sort of argument that you'll probably think is naive, but but we'll get us into it. So first of all, what we're talking about the moment is not certainty, degrees of certainty, we're talking about possibility. So I just, you know, getting back to that distinction between, you know, modality and credence. So the question is, is it possible that some bachelor is married? Okay, well, okay, so what do you mean by possible, right? Well, you say I don't mean epistemically possible, because that's just another way of talking about credence, right? I don't mean, you know, Ken, you know, are you justified in believing it or something? I mean, is there a world even if it's not the actual one where that that obtains? Well, I, you know, I say, well, there's a, there's a classical first order logically possible world where that obtains, because there's an assignment of the predicate, you know, bachelor and married, such that some, you know, there's something in the intersection, right? I mean, it's some it's not a first order logical truth that some bachelor is married. I don't understand that. I don't understand the idea that they intersect in some way. Can you explain what that means? Yeah, so I just mean, you know, so first standard classical first order logic, right? You know, what, um, you know, something is a logical truth that there's no assignment of the predicate to semantic values, and, you know, a specification of a domain such that the thing comes out false. And the point is, there is an assignment of pred, of predicates to semantic values in this case, and a specification of a domain such that the thing comes out false. But isn't that, isn't that still taking the meta analytical approach that you're looking at, like just purely the structure and not the actual context of it's being claimed? Okay, right. So, so you might say this is naive, because if you're talking about language, I'm talking about, you know, bachelors, and I'm interested in whether, well, okay, I mean, but you know, people have people have brought up already sort of cases where it's dubious that, you know, somebody falls clearly into one or the other category, like the Pope, right? I mean, is the Pope a bachelor or is he, you know, I mean, maybe and, and, um, well, anyway, but the point is that, um, let's, let's take the claim that it's not the case that all bachelors are unmarried. It is not the case that all bachelors are unmarried. Right. Well, okay. So how would you argue that? Well, I mean, one way, um, is like, imagine that you can get convinced of some theoretical view in metaphysics where, you know, some properties exist and others don't, right? So I mean, people do this all the time when they talk about supervenient properties and fundamental properties, maybe there's only physical properties or something. I mean, couldn't, isn't it an entertainable view that, for example, there's the property of being a bachelor, but not the property of being unmarried? No, not given, not given the terms involved. I mean, that's what, isn't that what we mean by bachelors not married? What we mean. I mean, um, yeah, I mean, you know, I'm inclined to think that, you know, there's not a clear, this is essentially the content of the, the coin paper I mentioned before. I'm inclined to think there's not a clear division between questions of meaning and just theory, right? And it seems to me like, you know, so here's another, let me, let me put it a different way. So suppose I say something like, suppose that some bachelor is married. Um, now let's start working out what, what else would be the case? You know, you might say that that's an absurdity, that's a violation of the rules of language or something, but what's striking is you'll be able to pursue that counterfactual basically exactly like you pursue any other counterfactual. Yeah, but I mean, it's assuming that a logical contradiction is true means that anything follows, right? In classical logic. Yeah. So if we say, assume X is true and X entails a logical contradiction, what my question is, is there a way to intelligibly understand what that logical contradiction means? Like if we're talking about how the claim relates to reality, if we're saying, you know, if you take it, if you do take it one step, one step abstract and we say, um, you know, X has the property of a and not a, right? It is tall and it is not the case that it is taller is big and it is not the case that it is in the same way. Is there, to me, what I would say is, well, that I can't even make sense of it. It's not even that maybe it does, maybe it doesn't. It's that it's because it's self contradictory. You can't even make sense of it. So I mean, I feel like I just want to keep going back to the kind of draw the line argument I was making. So, you know, can you make sense of instances of the axiom of mathematical induction failing? You might say, well, it's just, it's constitutive of the natural numbers. Here's what I would say, though, that all non-self contradictory claims presuppose classical logic. So we can talk about, you know, different axioms that are just asserted and then we go from there in mathematics. But what I'm saying is any sensible proposition at all, any axiomatic claim, any claim whatsoever, presupposes that there's no self contradiction of all. That presupposes the law of identity and the law of non-contradiction. And I'm fine exploring the idea of, well, maybe that's incorrect. But what I'm saying is, is there any way to make it intelligible? So something just like it is the case that, you know, my shoes are black and it is not the case that my shoes are black at the same time in the same way. Is there any conceivable way to think, oh, I understand what that means? Well, I mean, you know, so advocates of dialytheism, you know, do claim to do this. If you take the liar sentence, you know, this sentence is false, you know, some people think that sentence is both, you know, it's both the case that it's true and it's also the case that it's not the case that it's true. However, I think the liar's paradox and other self-referential paradoxes all can be relatively easily resolved. It's just a mistake of language. Mistake of language. But I mean, so let's, let's, let's talk about this from it. So there's a tradition and, and I mean, maybe you're sympathetic to it that there's some relatively clear just rules of how we're supposed to talk and some mistakes can be sort of labeled just ungrammatical in some sort of philosophically substantive way, right? I mean, this was the ordinary language tradition. This is, you know, there's strains of this and logical positivism, but I mean, when you make a claim about the world, you're talking about the world, you're not talking about language and it's not like the world can be, you know, made one way or another because of facts about language just on their own. I'll give you an example, I guess, of what I was, what I was trying to get out. Say I were to make the claim, I'm standing halfway in the doorway. Yeah. Say it is the case that I am halfway in the doorway and it is not the case that I'm halfway in the doorway because I have the other half outside the door. Well, what I would just say is, well, that's just, that's just clunky language. That could be very clearly resolved if we want to be linguistically precise and say, what, what do you actually mean? There's no contradiction there. If somebody's going to try to say, ah, this is a true contradiction. Well, I think it's just a confusion about language. I would say the same thing about the Liar's Paradox that it seems sensible superficially, but when you kind of dive into it, it's not, it's just an error in language in the same way. An error in language, but I mean, so in the case of the, the example you used, I mean, it's not like, I mean, the error in language is essentially that you didn't really mean what it looked like you meant. Right. In what sense, in what sense does this sentence is false, not mean what it looks like it means? Because, well, specifically it has to do with the words this sentence. So the question is what sentence are you referencing? Are you referencing this sentence is false or are you referencing just the words this sentence? Are you saying the two words of this sentence is false or are you saying this sentence is false is false? Right? I mean, presumably this sentence, the two words can't be false. So I have to be talking about the sentence that that refers to. So what I'm saying is if it's the case that this sentence refers to this sentence is false, then you're stuck with an infinite regress. Because when you say, oh, the actual liar's paradox is this sentence is false is false. You say, okay, well, hang out, what sentence? And you say, well, this sentence is false is false is false is false. And you never actually get to a sentence because you just keep saying is false is false. It's like, it's like a nesting problem. I don't see that. I mean, it's because the, the referent is not the subject, the sentence, the referent is this sentence is false. Well, that's what I'm saying. So if we were to put this sentence is false with parentheses and say, this sentence equals this sentence is false, right? Well, it doesn't equals. I mean, it refers to, it's not, these are not the same objects. Well, so if you were to draw it out, it would be this sentence is false is false. And then if you would say, okay, well, what sentence are we evaluating? It would be this sentence is false. So you would have another, another nesting in the parentheses. It would be this sentence is false is false is false. And so what I'm saying, you can keep doing that. And if I don't, you don't actually get anything to evaluate as true or false. So I don't really get that. So I mean, do you think in general self-reference doesn't make any sense? I mean, let's take a simple example. Like, you know, the set of all sets. Now in standard set theory, there's no such thing, but there are set theories with a universal set. Does it contain itself? Yes. Well, the reason, so it depends on what you mean by self-reference. And that circumstance, I think that presupposes a kind of mathematical Platonism. Like when people say the set of all positive integers, I don't really think such a set exists because there aren't integers out there in the world. There's sets that we create. So we can talk about sets that we create and then it resolves any kind of issues of infinity and any kinds of issues of self-reference because they're not out there and there's no set of all sets. So you reject impredicative definitions at some point? I don't know what it means. So definitions that make crucial reference to the thing to be defined. Well, certainly, yeah. Okay, so do you? It results in an infinite regress, right? Because there's nothing that you can actually value. You're saying X means something and then what that something is has X in it as a definition. So that never actually means anything. It's never fully defined. Okay, so what if I say something like the tallest person in the room? I mean, so now I'm defining a person, an object in terms of a class to which it belongs. So that's an impredicative definition. Do you think that's intelligible? By itself, no. I mean, you'd have to have the context of what things you're referring to, but yeah, I would say that there's no problem there. It's like saying that the person with the darkest eyes. Yeah. Yeah, but so I just don't understand why some of these cases are okay and others aren't because they all involve a certain kind of circularity. Now. Where's the circularity in saying the tallest person in the room? Because you're defining a person in terms of a collection where you've already helped yourself to, you know, he's already in the collection. You're helping yourself to a collection that he's in. Maybe we're talking, maybe we're not talking about the same thing. In that circumstance, I'm not saying that what we mean by the tallest person in the room is something that has to be defined before you get the definition, but something like, you know, X is false or this sentence is false. When you try to say, well, what is this sentence? It has itself within the definition. So it's like you can actually, you can never get to what you're talking about because it has to be defined before you can make sense of it. But I just don't think that's the case when you're talking about the tallest person in the room or anything like that. Okay, so you're thinking in the case of the tallest person in the room, we assume a kind of world out there of people. All we're doing is picking somebody out. In this other case, we're somehow creating or something. Well, one has a, one is an independent, like it has an independent definition or an independent existence. The tallest person in the room is another way in a concrete of referencing me, I'm six foot four, so that would be referencing me. But that's not the case with these other things. They don't have a clear, there's no reference. There is, almost by definition, no reference because you have this infinite regress. Okay, so I mean, so part of our disagreement then is just about, I mean, the debate about in predicate of definitions. I mean, you know, I'm not, I think that position is an interesting position. I mean, that's a radical position. So I mean, I'm not exactly sure how you, for example, understand classical analysis and use that's used in modern science that involves infinite totalities. It doesn't just involve. Yeah, I mean, I'm a totally a funitist. I reject, so I think what I would say is the idea of a completed infinity or a completed, an infinity that is and no more than itself is a logical contradiction. It's like saying, it's like talking about a square circle. And it's funny, because I was talking to you a little bit before this, that I just had an interview with a mathematician in Ireland who is saying that, well, there may be, he is also persuaded by this idea of finitism. And what he was saying is in modern mathematics, it's just asserted as an axiom that assume the existence of one infinite set rather than challenge it and see if that even makes sense. That's just the axiom, that was just the assumption, which I think is inaccurate. In my worldview, it's exactly saying, well, assume that there's a Mary bachelor, assume that there's a square circle, and then we'll go from there. And it's like, well, I don't think you could do that. I don't think that concept makes sense. Yeah, so I think that's a super interesting idea, but it's just we presuppose, at least on its face, that all the time when we use real analysis and set theory and stuff, so how do you understand those applications? How do you understand the use of analysis in physics, for example? Well, so I have a, this is a little bit up top, but I can't resist talking about it. So I have kind of a resolution to all circumstances that where mathematics invokes infinities, specifically in regards to calculus, but you can kind of take the concept there and apply it globally. People are talking about convergence, and specifically the resolution of like Zeno's paradoxes. Calculus solves Zeno's paradoxes. I don't think that's the case. I think that ultimately reality, physical reality, has a base unit and an indivisible base unit, and therefore all the calculations ultimately terminate. So like when we're talking about Zeno's paradox getting from A to B and going through an infinite amount of points, I reject that idea. It's just the reason calculus works is because the calculations terminate because reality is finite. So that's interesting. So do you actually have like an alternative formalism or? No, I mean, this is something that I mean, I guess the closest thing I would be called is a finiteist, but I realize that in the world of mathematics, being a finiteist is very clunky. It's a lot easier to just assume infinities and you can work with them, but that may be the case that making this little assumption allows for cool applications of mathematics. I'm not denying that at all. I'm just saying that it certainly is not because of strictly, because of the assumption of what I would say is a logical contradiction. So somebody could develop a worldview and one part of it, there's this assumption that there's a square circle and they might be able to make all kinds of cool claims, but I would say it's not because of the assumption of a square circle, that's just an error. So can I ask you about this logical contradiction thing? Sure, yeah, yeah. So I mean, there's two different kinds of skepticism you might have. So here's one kind of skepticism. Look, it just follows from the notion of infinity that it can't be completed. Sure. And somebody might say, okay, fine, have the word infinity. Let's use schfinity, you know? And schfinity is just like infinity, except it can be completed. And the question is, are there schfinfinites? But that's like saying, okay, I understand there's, squares can't be circles, but let's call them schmerkles. And let's say there is this schmerkle and it has the property of being a square in a circle. Yes, there is none. Okay, okay, so I mean, so I'm inclined to think that in these cases, like this gets back to our discussion about possibilities and bachelors and all that stuff. I mean, I'm inclined to think that there's actually not an interesting difference between these alleged absurdities and the things that are supposed to be sensible. The difference is just in whether we think they're actual. And if we wanna talk about, if we wanna talk about possibilities and orderings on them, well, we could put it in the following way. Some people talk about impossible worlds along with possible worlds. And many people think there are impossible worlds who don't think it's possible there's a square circle because they realize that, well, but there does seem to be certain things we can say about square circles. For example, we can say that square circles are square. That seems true and it seems false that they're triangle. It seems like we can say that if Hobbes had squared the circle, nobody would have cared in South America. All these things. So what's interesting is a lot of people say, well, okay, so you have to make a distinction between possible worlds and impossible worlds. What I'm saying essentially is, I don't think there's any interesting distinction, but I accept that we should make sense of impossible worlds what other people call impossible worlds. So what we're left with is just this, you can put words together basically at will. Now, there might be some limitations to what we can make sense of. For example, the following sentence might be a sentence that we just are not in a position to get our heads around. Every proposition is true. What would it be like for that to be so? Maybe I just can't get my head around that, but, you know, to, when- That's possible at least, right? You can imagine a world, at least imagine a world where nobody has spoken a false sentence. Okay, I don't mean token sentence. I mean every proposition. Okay, yeah, yeah. But, you know, when we can put these words together and say, and basically, again, from the third person perspective, do everything that it seems like we do with the alleged possibilities, the alleged reasonable claims, why think that, you know, what's the point of calling those just impossible? So it seems like this has to do with language that would you agree that words have reference? Words, sometimes they reference concepts, sometimes they reference objects in the world, words have reference. So what I would say is, when people use language in such a way where you get us what you could call a self-contradiction, it's not that there isn't a reference, it's that there can't be a reference, that what we mean by, you know, A and not A is a negation. If we're claiming A, there's this other thing we have in language which is called the negation, which says not A. What we mean by everything is mutually exclusive. They cannot be, that's the whole point of the negation, is to say the opposite of this. And what we mean by opposite or negation is they can't be put together. So what I would say is, if you do that, if we say A and not A, it's not like an empirical hypothesis whether you could have some possible world A and not A, it's that it's not even sensible. It's not that it could exist in the world, maybe it doesn't, it's that it's not even a sensible claim in the first place. Now you can talk about it superficially, you could say, oh, well we could talk about the properties of a square circle, but it's not true. What I would say is you can take some of the properties of squares, which has a reference, and you can describe them. You can type some properties of circles, and you can describe them. And you can act like you're just talking about a square circle, but it's not actually a square circle. You talk about the squareness of something and its properties of the circularity of something, but not together, that there's no way to make sense of it, because one implies a negation of the other. So, let me try this way. So as I said, a lot of people who sound just like you would say that there are impossible worlds where we can talk about impossibilities just like we can talk about possibilities. And they say, but they're impossible. But they're impossible, it's not like, I don't think it's possible. But I'm not saying they're impossible, I'm saying they're not even sensible. They're not even comprehensible. They're not even comprehensible, but what, okay. So let's then go back to this issue of what do you make comprehensible and is there a principled way to figure out whether something's comprehensible? I say a notion of comprehensibility isn't that interesting if it's not something you and I can get in a third person perspective on and sort of settle the matter. If comprehensibility is in the eye of the beholder, well, let's find a notion that we can actually resolve disagreements with. And what I'm saying is, you claim that things are not comprehensible, but what is the evidence that's not just questionable, that's not just like, I don't get it? That's an excellent question. And it's such a good segue too. Cause this gets into logic, which is one of the things I wanna talk to you about. What I would say is this is the subject of the book that I'm hopefully gonna release very shortly. Is that I'm not appealing to evidence. I don't have to appeal to evidence. I'm simply appealing to the meaning of our concepts. That we have concepts that, you know, we use words to sometimes reference concepts that reference things in the outside world. And, or maybe the inside world, you talk about your feelings. And in some circumstances, we have this unique tool of the negation. And what we're saying is when we say negation, like there, what I could say a sentence like, you know, I have shoes on my feet. And there's this other sentence I could say, I do not have shoes on my feet. And if we really unpack what we mean by all of those concepts, one is precisely the negation of the other. It's saying X, the other's saying not X. And if you understand what negation means, what assertion and negation means, that it's not a matter of empirical possibility or evidence to say that logical contradictions don't exist, it's because they can't exist because these things are mutually exclusive. And so that's one of the reasons that I'm so humbled by this idea of logic is because it's so powerful. You can make claims about the world, about all possible universes. You can say, well, I know a limited number of things about them, that there can't be things which are mutually exclusive by what we mean by the term mutually exclusive. So first of all, just to understand your view a little better, let's take the law of the excluded middle. Do you think it just follows from what we mean by or? I don't, I don't actually have, yeah, I don't, my laws of logic are identity and non-contradiction. There are some sentences which aren't logically contradictory. They're sensible in a sense, but they don't follow, that third law, they can kind of mush around. Yeah. Okay, but I mean, I must sound obnoxious and rationality, but I'm just trying to like, I mean, you can see, so from an outsider's point of view, it's like, okay, well, hold on. So there's all these different views about which logical laws are valid. And here's this guy pounding his fist and saying, well, the law of non-contradiction is an absolute boundary, but the law of non-contradiction middle is- Let me give you an example. Right, the king of France is bald. Yeah. Is that true or that false? So I think it's truth-valueless, but yeah. So that's what I'm saying. So that kind of circumstance is where I would say, if somebody were to try to be a stickler about the law of contradiction, non-contradiction, I would say, well, if we wanted to be precise, we can clear up everything and not violate any laws of logic by just saying there is no king of France, problem solved. But if somebody were to just try to analyze and say, it's not true, it's not false, it's like, okay, I can accept things like that. Things which are truth-valueless. Right. But what I would say is it's a poorly constructed sentence or it's very easily cleared up. So that's the only exception I'm giving. Okay, but so in the case of the law of non-contradiction, so you were impressed by the lawyer's sentence, that gets us into all the stuff that we're not gonna resolve today about self-referential definitions, but there are other alleged counter-examples, right? So I think Grand Priest, for example, talks about laws are typically, very often they involve implicit contradictions, right? Like constitutional documents. Oh, sure, sure. So you'll have a bunch of obligations, but if you actually unpack them all, you'll get a sentence the form you're obligated to do this and it's not the case that you're obligated to do that. Now, I wanna make two observations. The first is, that's not, you know, maybe that's true. I don't know, I haven't thought about it enough. But the second is, even if it's not, like I can make sense of that and if I can make sense of that, then why can't I claim that there is a scenario where the law of non-contradiction holds? It might be extremely distant, you can call it impossible if you want, but for all practical purposes, it's just like any other possibilities. For that example, I have a simple resolution would be that people can write logical contradictions. It's not that logical contradictions don't exist linguistically, it's just that they don't exist metaphysically and you can't make sense of them in the sense that if somebody were to claim the responsibility of a citizen is to act in accordance with the law and the law contains a written contradiction, then it must be the case that this is and cannot act in accordance with the law, is what I would say. Right, he cannot act in accordance with the law. But there's no way to do it. It doesn't even make sense to say act and do something and don't do it at the same time, that's impossible. Okay, so I mean, but the claim is that, you know, if you live in a community and there's a constitution passed and all of the cases that you've ever considered are ones where you can follow the law and it turns out that there's this implicit contradiction and of course, therefore, you cannot both follow it and not follow it, the view is that you're still obligated to follow the law because the local constitution is binding. Now, just to repeat, as I say that, I mean, I haven't read Graham's stuff on this, but it doesn't strike me as especially compelling, but you want to say something stronger. You don't just want, I mean, this is the point I want to just keep coming back to. It's not, so I think our main disagreement is this, what is the status of disagreement over logical laws? I claim it's basically like disagreement over anything else. Right, and I'm saying that if somebody disagrees over the status of the law of non-contradiction or a law of identity, they're simply confused. Right. That's what I would say. Right, which sounds presumptuous, I know. I mean, it's not like my response to you is how dare you say that, my response is that how are we supposed to resolve this, right? I have an answer. It would be to, read my upcoming book. Buy my book, yeah. It would be to really unpack what we mean by identity. When we're claiming A, regardless of what A is, it is also the case that we are claiming not A is false, we're saying A is true. We are also saying inescapably so that the denial of this truth is false. That's what we mean by true and false and that's what we mean by assertion and negation. And if that's true, you simply, not only can you not have a contradiction, it's that you understand that self-contradictions don't make sense. There's no way to make sense of them. Right, okay. So, I mean, I have two responses. The first is I'm getting back to sort of the bit about Quine that I agree with. I'm just highly suspicious that we're, I mean, here's a way to put the first point. The first point is, you know, people have been appealing to concepts that just fall as from the concept since the beginning of philosophy, right? And what's striking is, none of the questions have gone away. I mean, Plato tells us, you know, about what's packed into the concept of good and so on and so forth. It's not like anything really was resolved by making that additional claim. We might as well have set aside concepts and just had the first order disagreement about whether contradictions are possible. Because it doesn't seem like any actual, here's another way to put it. If you and I disagree about what's packed in to the concept of good or packed into the concept of set, let's take the set case. If you and I disagree about, say, the axiom of foundation, if every set is well-founded, we're of course going to disagree about what's packed into the concept of set, right? It's not like we're gonna make much progress by saying, well, just think about the concept, though. It's obvious that every set is well-fed. Well, if I don't think that the axiom of foundation is true, then, of course, I don't think that falls from the concept. The first point I wanna make is just, this doesn't seem, to me, likely to advance the discussion much. Second point is I'm inclined to think that not much can turn, even if we could advance the discussion much, on what follows from a concept. Let's, again, take a cleaner case. Let's take the concept of set. Suppose that we did conceptual surgery on the concept of set, and we just got super clear, and it's just obvious that sets are things that are built at different stages in this transfinite generation process, and it just doesn't make sense to talk about a set that precedes itself. So no set can contain itself, for example, and there's no infinitely descending chains and stuff. Okay, fine. Here's something that we can introduce. We can introduce the concept of schmet. And schmets are exactly like sets, except some schmets can contain themselves. Now, what metaphysical question could be resolved by just figuring out what's packed into the concept of set? Because now the question is, are there sets or are there schmets? Unless, that is true, if we're talking about something like animals and biology or other areas of thought, that is true, and I agree with almost everything you said, except with logical things. Because what I'm saying is underlying all propositions, all concepts, you have the same logic. You have the same logical rules. So when you're talking about are there schmets or are there sets? Well, if we're saying are there X, are there Y, we're also, we're presupposing the laws of identity. We're saying that schmets are schmets and they're not not schmets. So regardless of whatever kind of counter argument or skepticism or open mindedness you have, well, it might be the case that X, it might be the case that Y. In all, every single one of those circumstances without exception, you're still saying, well, this might exist as itself. That might exist as itself. And in saying so, we're also saying, however it is as itself, it is certainly not itself, right? So okay, so I mean, the big picture is you and I both wanna be very open minded, but you wanna draw a line somewhere. You wanna say there's a difference in kind between all these different kinds of disagreements we could have about all these apparently logical mathematical things. And then we reached this kind of privileged point where somehow we're just unable to even have the conversation. Well, we can have the conversation. It's just that there's at some point when you reach the laws of logic, you discover this is the bedrock foundation on which all other sensible propositions presuppose. But I mean, of course, somebody like Grand Priest thinks he's also using the laws of logic. Well, so this is the perfect segue. This is the perfect segue. So let's entertain a possible world where people are making illogical arguments. And by illogical, you mean? Violating classical logic. Okay, but you don't just mean classical logic because you accept violations of the law of the excluded middle. Well, it's not that I accept laws. That's why it was kind of a qualified statement. It's that there are some sentences like the King of France's ball in which if somebody wanted to be a stickler, they would say, well, the law of the excluded middle doesn't apply. So I wouldn't consider that violation it's just that some sentences are poorly formed. And so they contain hidden premises that if you just take them for face value, the law of the excluded middle doesn't really apply. Okay, so I mean, maybe for simplicity we can just talk about the laws of intuitionist logic and you think that maybe gives an absolute boundary. I'm not sure what you mean by intuitionist logic. Okay, it doesn't matter. We'll just say a world in which we have the grand priest arguing A and not A. Okay. What I'm saying is to what does grand priest appeal to make his arguments? What I'm claiming is every argument appeals to logic, to classical logic in terms of the law of identity and adjudication in order to be sensible. What are you or what would if somebody believes in grand priests, what are they appealing to? Okay, so I think this is actually an important point. So one way of putting your question is, I mean, maybe like the key issue is the distinction between a logical law and an instance of it, right? Now grand priest is perfectly within his rights to use instances of logical laws that he thinks can be violated, right? It's not like because he thinks that the liar sentence is both true and false. He thinks every sentence is both true and false, right? So it's not like he can't lay down a claim without asserting its negation. That's certainly not the view. Well, but in that instant, when he's saying there are like the liars paradox, what is he appealing to if not identity? What is he appealing to if not identity? I mean. And non-handrediction, of course. If not logic, what is he appealing to? Well, so I mean, so I don't really get it. I mean, so, okay. So in the case of the liar sentence, it sounded like your objection was not that there was some incoherence in principle in the logic invoke. It's that there's some incoherence in principle of the self-reference involved. It's a poorly constructed sentence. It gives the superficiality of sensibility, but when you actually analyze it, there's no referent. Okay, so I mean, you know, I mean, so, okay. First of all, in response to your question, what logic is he using? I mean, he might be using the logic of parallel. No, I'm not saying what logic is he using. I'm saying, what is he appealing to? What is his, like, for me, if I were to say, you know, there are no square circles, I would say, why do you believe that? I would say, well, I am appealing to logic. I'm appealing to what I would make the further claim in my upcoming book that logic is actually the rules of existence. This is the way things must be, inescapable rules of existence. That's what I'm appealing to. It's not a construction. It's not, oh, we have these, like a chess rules or negotiable. I'm saying is there are rules of existence which you can't get outside of. I'm gonna call them logic and that is what I'm appealing to. What would a grand priest say he's appealing to you to make his arguments? So, I think he would say exactly the same thing. These are all, he thinks you're just wrong about the rules of existence. Right? I mean, in other words, I mean, right. So there's like different, okay. So there's kind of boring and interesting debates about logic, right? One kind, a boring debate would be like, I think logic isn't a different business. It's like a relevant logician. Might just have a sort of different conception of the role of logic. Now, you've told us your conception of the role of logic and then the question is, can we have a disagreement about, as you put it, kind of the laws of existence or something? I mean, I take it that from what you're saying, you sort of understand logic in modal terms. So, if a law is a law of logic, then it's not just that, you know, I mean, I'm not totally clear where you have packed into the notion, but you might have the following. Maybe I can be certain of it, though I would probably not want, I think you probably don't want to say that because there are lots of laws of logic, right? Validities that are, you know, have more logical particles and there are particles in the universe. I certainly wouldn't be certain of one of those. It would take me forever to compute it, so. Yeah, I wouldn't say on principle. I mean, well, I guess what I would say is something like this. The inescapable laws of logic can sometimes be symbolized with like propositional logic, for example. And if you follow those rules, which we can write down and notate in categories, then yes, you can have certainty, right? So there are some circumstances in which you can have certainty just following the rules of existence. Right, okay, so maybe the basic logical rules are certain and maybe certain of the basic principles are certain. Okay, but the other thing is that I think you were saying, and I think this is the really important thing you're saying is that set certainty aside. The point is that if you have a validity, it cannot fail to hold. That's part of what it is to be a validity. In other words, a validity isn't just a truth. It's not just like a truth that we're certain of. It has this additional feature that it could not fail to be otherwise. And maybe even we might add something like it couldn't fail to be otherwise because of the meaning of the logical constants. Now, that last part, I don't really know what that means because presumably the world is as it is and it doesn't depend at all on my concepts, right? It's not like if I had different concepts, the world would be different. So I think that this idea of the logical truth holding in virtue of the concepts doesn't make much sense. It might be that the way I know that it holds is thanks to my concepts or something, but it holds that even if there were nobody around and no concepts to be used, it seems to me. But the modal claim I think is the really sort of meat and potatoes of your view and this is where I would want to get off the boat. And so basically, let me give you a different picture. Maybe that's the best way to sort of approach the debate. Here's just a very different picture. This is the picture I actually happen to believe. So the picture I believe is that, let me start from a view that's much more conservative than yours and it's actually the standard view in analytic philosophy. The standard view in analytic philosophy is that when you consider non-epistemic modality, so possibility and necessity not understood as like claims about credence, like it's possible Obama's in the White House, not like that, but even if he is in the White House he could have failed to be that kind. Okay, most analytic philosophers think that we've got things like biological necessity, we've got things like physical necessity, but of course there's some sense in which the laws of physics could have been different. But nevertheless, you reach this boundary and the boundary includes things like the mathematical truths and it includes things like identity truths, like Hesse versus phosphorus and it includes things like waters necessarily H2O and maybe it includes things like you have the parents that you have and all this time. I mean these are controversial but the point is you reach a substantive point where any other possibilities, any possibilities that lie outside that space are nearly epistemic. You can talk about it, you can pretend as though there's some counterfactual scenario where that obtains but that's not non-epistemic possibility, right? That's just talking about maybe your credences or maybe your imagination. But anyway, so my view about that is there's no principle place to draw the line. I mean, so the- Isn't that a principle place though? Okay, well so what would it take to have a principle place to draw the line? Well, here's one way to figure it out. Let's look at the reasons we give for judging that something is possible, right? And let's see if we can then apply those equally to the claims that are supposed to be necessary, I mean to their negations. So take something like a paradigm case of a metaphysical possibility are the laws of mathematics. Now it seems to me that there's just no, all the reasons we give for claiming that, you know, you could have failed to come today to this interview, are reasons equally to give for, you know, that the law, the axiom of choice could have failed. I would just say an excellent example in terms of what you're talking about is something like two plus two equals four. Right. Is that something where you still have the same position? Right, so good, so you might say like, well maybe it's like vague the boundary, but aren't there, I mean, here I'm inclined to think let's be very clear about what we're talking about. So two plus two is four on a standard analysis is like the present king of France is bald, right? It's a claim that involves reference to things. It says the plus function maps an object to itself and to four, right? It's talking about individuals, numbers. And it fails to hold if there are no such numbers. But as Russell pointed out already, you know, in his work on the foundations of math, it seems like we can make sense of a world without anything. It seems intelligible to imagine an empty world. So I guess I didn't quite understand your claim about two plus two equals four. It's, this is something you're saying, I don't actually disagree that these things have reference. I think that ultimately numbers are conceptual and they're not out there in the world. And therefore, the numbers need a unit, right? Two isn't floating out by itself, it's two x, it's two something, they have to have something concrete that they're referencing. But my intuition is the thing, I think a lot of people's intuition is the thing, that what mathematics is, is it like a description of logical relations between things. So it seems to be certainly the case that if you have one unit of x and you add another unit together, conceptually, that is two, that's what we call two. Okay, right. So there's another, when it comes to very elementary arithmetic, there are other claims in the neighborhood which are not strictly what the mathematical claims say, but they are their first order logical trees essentially. So, you know, if there's exactly one, so yeah, there's exactly one book on the left side of the table and there's exactly one book on the right side of the table and no book on the left side of the table is a book on the right side of the table then there are exactly two books on the left or the right side of the table. We are exactly one and exactly two. There are really just abbreviations for expressions involving just quantifiers and identity, so those are just logical truths. But do you have the same kind of epistemic open-mindedness towards whether or not they could be false? I want to get to that. For the moment I'm just trying to say that the metaphysical possibilities do not give an absolute boundary. So the standard view is not just that those very sort of elementary claims that are logical truths can't be false. It's the claim that there are infinitely many prime numbers can't be false. You could prove that. How could that possibly be false? My view is there's no reason to draw the line there. So then the question arises. Let's suppose you agree with me on that. I don't know if you do, but let's suppose you do. So then the question arises, can we find a place to draw the line? So maybe the philosophers are wrong about where to draw the line, but is there a place to draw the line? Essentially my view is that the notion of absolute possibility is an indefinitely extensible notion. We cannot once and for all say this is the boundary of intelligibility. Is that itself a claim, though, about boundaries that there are none? Isn't that kind of your boundary is to say my boundary is that? Good. So let me distinguish my claim from another claim. Here's another claim. There are no claims which are absolutely necessary. I don't accept that. So for example, maybe the claim that every proposition is true is absolutely necessarily false. What I claim is you cannot collect all such claims once and for all and include all and only the absolute possibilities. In other words, if you do that, if you try to do that, what's going to happen is one of two things. Either there will be some claims that you realize by your own lights you should have included. If I can make sense of this law, I can make sense of it failing in this one case. So I have to include a few more possibilities. Or the notion will not be a non-epistemic notion because you'll include things that are not possible by your own lights. It seems like that takes some prescience to say. It sounds like, from my perspective, at least as I understood it, it's essentially kind of like saying there are no absolute truths, roughly speaking, in a sense that isn't that itself an absolute truth. It's precisely not like that because of this distinction I was just drawing. I guess the distinction I didn't quite, I must not top that. Okay, so actually there's three distinctions. So one distinction is whether there are any absolute truths in the sense of truths that are necessary in every non-epistemic sense. I do think that. I think that. Let me be super clear about that. Suppose I thought there weren't, well, then there would be an absolute notion of possibility and it would be the trivial notion. Everything would be possible. Every single claim. I don't think that because I don't think, for example, that- But that is a boundary, right? Aren't you saying that, so why do you draw that boundary? I guess maybe that's where I'm getting, based on what we said earlier, what are you appealing to, why do you object to that claim? The reason I object to that claim is that the reasons we give for judging that paradigmatic possibilities are in fact possible do not seem to generalize for every claim whatever. So let me give you a simple example. What are you appealing to when you make that claim? So isn't that also, aren't you also presupposing the same laws of logic that I'm presupposing when you make that claim? I don't see that. You don't think so? I don't think so. But I mean, so on what ground, you're asking me why don't you think anything literally is possible? It sounds like you have no place to draw the line. What I want to say is the notion of absolute possibility is essentially like a vague notion. It's like heap, right? So if you give me something that is definitely not a heap and you add one thing, I'm committed okay to that thing not being a heap too. But there are definite cases of non-heaps and definite cases of heaps. I think there are definite cases of possibilities and definite cases of impossibilities. The problem is you cannot draw the line. Now why do I think that there are definite cases of impossibilities? The reason is that if you look at the grounds that we give for judging that something is possible, they don't actually generalize to any claim whatever. So here's a simple, what's the most familiar ground we give for judging that something's possible? Conceivability, right? Descartes tells us that if we can clearly and vividly conceive of something then we can think that God could have created it to be so. If that notion has any content, then we can't conceive of literally everything, right? It can't be that literally any set of propositions put them together whether they're closed under logical consequence or not is conceivable. But in the concrete wouldn't that mean any actual one as you heard it he would entertain as possible, right? So it's not like all in the abstract to put them all together and you can't conceive of all of them at once. Isn't that what you're saying? Well, no, but possibilities can be represented as collections of true propositions that hold at the world. Yeah, but you're not evaluating the collections. You can't evaluate the collection. The collection is just like an abstract boundary that you're putting around it. You're evaluating all the individual claims, right? Right. So let's take again a case that I think is absolutely necessary. It's not the case that every proposition is true. It's not the case that every proposition is true. I'm saying why do you believe that? Because our paradigm ground for judging that something is possible does not seem to work as a ground for judging that it's possible that every proposition is true. So why do you find that compelling though? That seems like that would be like the grand priest I think if we were to go back to that example. Don't you think that would imply that really that's every possibility because you don't even have the laws of classical logic preventing anything from being impossible in principle? Well, no, I mean, so two issues. One is that as a matter of fact, I think basically grand priest does think anything is possible. He doesn't put it that way. He's one of these guys who thinks there's impossible worlds and possible worlds. My own view is that there's no interesting difference between the notion of possibility and impossibility because they do the same work. But it doesn't follow from the logic, right? The whole point of his logic is that you cannot infer everything from a contradiction, right? So here's another way to put it. If you think contradictions can be true, then you better not think a lot of explosion holds, right? You better not think that you can infer anything from it. And so they don't. That, you know, their logic is one that does not validate the inference from P and not P to anything. So I want to be clear. You think that grand priest is actually saying that everything is possible. I think basically that's what he's committed to, not by his logic. This is a different commitment. But you are saying that you don't think everything is possible. Correct. And what I'm saying is, from a philosophy like my own, the reason I don't think things are possible is I'm appealing to logic to make that claim, what I consider to be the rules of existence which determine possibility and impossibility. What are you appealing to? Well, I mean, again, I'm not sure what you mean by appealing to. The grounds I'm appealing to are conceivability grounds. And my claim is that while we can conceive of the laws of physics being different, while we can conceive the laws of mathematics being different, while we can even conceive of different logics holding because it seems like we can give semantics for them and understand what it would be like to live in such a world. Like, you know, you redumb it on intuitionistic logic. It's not like he's just talking about a formal system. He's giving you an overall worldview, what it would be like to live in a world where, you know, the lobby excluded middle didn't hold. And you can think it's false, but to say that it's just unintelligible seems like a pretty strong claim. And anyway, doesn't seem to advance the discussion much. But if you say, but, you know, beyond conceivability, I mean, you must be appealing to something. Of course, I'm using a logic, right? I'm using a logic to figure out, for example, what would hold in a certain circumstance. What do you mean by you're using a logic? What do you mean by that term logic? Because for me, I can say when I am using logic, it's not this logic or that logic. It's the inescapable rules of existence. Okay, good. So this gets us back to the pluralism debate, right? I mean, so one, you know, again, like one question, the question we've been debating so far has sort of assumed that there's a correct logic. And we've been asking whether we can rule out from the start that a logic that doesn't, you know, that violates the law of non-contradiction could be that one. I mean, maybe this is a good time to say that once you make the distinction between logic as norms of reasoning and logic as a set of validity, say, I think it's very hard to talk about the correct logic, just like it's very hard to talk about the correct manners or the correct, you know, taste and art or arguably the correct ethical views. I think it's hard to talk about the correct rules of reasoning because goals for reasoning can differ. And if goals of reasoning can differ, there's no obvious reason why there should be an objective fact as to whether you ought to believe P, you know, whether you ought to believe Q for any Q, if you believe P and not P. So I guess what I was trying to articulate more clearly when I was saying what are you appealing to is you're saying that you're using a logic and I think you're saying that logic is your rules for reasoning. I'm saying in your construction of your rules for reasoning, are you just appealing to what you find personally persuasive or what you find aesthetically pleasing? Because for me, I can always come back to I'm appealing to metaphysics, the inescapable rules of existence. What is it that you are appealing to if not the same thing? Like the law of identity and non-contradiction. Yeah, so I mean, of course, of course. So here's maybe one way of putting what you're saying, if I understand you correctly. Suppose that we look at some alternative logical world that I claim is possible, right? So I claim, for example, that it's non-epistemically possible that some other logic held. Now you're gonna say, okay, let's look at that world and let's ask what happens in that world. Now how am I gonna figure it out? You're gonna say I'm gonna use the laws of logic. But hold on, this is the whole point of this world. There's a world where a different logic holds so you're gonna end up actually saying that in some world where another logic holds the same old kinds of things happen. But I don't think that. I think when you go to the different logical world you gotta use the logic of the world. What I would say is you can try to do that but you'll end up thinking that you might be making sense of things by talking about the squareness of a square circle. But in reality you actually can't make sense of it. It's kind of like the Liar's Paradox. It gives the illusion of sensibility but it's actually impossible to make sense of. Now you can say, oh well we can half make sense of it but at no point when you have this idea of mutual exclusivity I don't think you can just say, well imagine a world where what we mean by mutually exclusive is actually that they can be together. Well you can state that and you can act in some ways as if it's the case. But you can't have a clear conception of that kind of world because such a world isn't possible. Yeah, I mean so one of the issues that I guess you're bringing up again and again which is a real issue people debate but I would claim that that's just more evidence from my view that you can't do something out of hand is what is packed into the notion of negation. When are you just changing the subject? And this is definitely something that is central to the literature on paraconsistent logic and stuff. My own view is that you don't have to take a stand on that debate to agree that it's like an intelligible debate. But if it's an intelligible debate then the alternative views are intelligible. That's not the case. It is an intelligible debate and one side is making unintelligible claims. Superficially intelligible claims. This is what I would say. Yes of course the debate is happening but that's because one side is wrong and the other is right and it just so happens that the nature of the inaccuracy of one side of the debate is that they're contradicting themselves which means their concepts are mutually exclusive which means that they can't even make sense of it. If they think they're making sense of it they're just confused about it. I was using intelligible debate to mean that if you and I have an intelligible debate then each position is intelligible. I would be denying that. We could argue forever about whether or not this is intelligible. It seems to me like the more productive thing because that's not likely to make a lot of the more productive thing to argue about is what should we mean by intelligible such that we can make some progress on this issue. It seems to me like you don't want to mean by intelligible something where it's like you and I can have all the same evidence. You and I can talk ad nauseum about the issue but still you know that the thing is not intelligible and I don't. Another way to put that is we're discussing whether Picasso is a better painter than Matisse and we study their art at great length. We talk amongst each other to figure out why do we believe this why do we believe that. We know all the same evidence that might be relevant. We know their biographies, everything about the context and stuff. There's no outstanding information that we're waiting on but one of them strikes you as better and one of them strikes me as better. Now one view we could have is that one of us has seen the light and the other one hasn't. It seems more natural though to say to sort of do away with whatever notion would be that private and make use of notions where there's some independent criterion of deciding debates. Yeah I think in that circumstance it would be if somebody were to try to claim one particular painter is objectively better than the other I think that's just a confusion of objectivity versus subjectivity. Subjective preference is not something that correlates to you know when I say vanilla is my favorite flavor of ice cream it's a very different claim of everything objectively vanilla is the best flavor of ice cream but I have already taken a lot of your time but I have to ask you this question because it's so centrally important to what you were saying. You use the term you know you have seen the light and that you know we're when we have this kind of foundational disagreement it's very difficult to make a lot of progress especially when one side is saying this is an unintelligible claim versus an intangible one. So for you then you think that paraconsistent logic is intelligible that there could be a way in which square could be a circular that that is intelligible in principle. Yeah I think you can't rule it out from the start. Do you have any experience of fully integrating a logical contradiction in your head so like a way where you can say like I would have a clear and distinct understanding of identity that a thing is however it is. I get it. Fully. Would you make the claim because I would also make the claim I do not have a clear and distinct conception of how mutually exclusive things could be together. Do you can you integrate those things satisfactorily? I mean I'm worried that you know the question is loaded because what you mean by clear and distinct will already assume like classical logic you know criteria. So by any criteria that you choose so I'll try to get out of my own classical presuppositions here from your perspective is there a way to make sense of it. Here's what I think. I think that we can make sense of that stuff my experience is that I can make sense of that stuff as well as I can make sense of for example different views about the axioms of set theory. That's what I think. And there's a further question as to the big picture is I don't see a principal place to draw the line. There are people just like you who draw lots of other places. We would be having exactly the same debate but they would say the same thing about you know the lobby of excluded middle. Or they would say the same thing about the axiom of choice or they would say some would even say the same about for example basic moral principles. My big picture position is you can either go all the way to the extreme conservative end and say tons of what we say every day is just unintelligible. Or you can say actually there's a quine was right. And there's really no boundary of intelligibility. We can always push it a little further. So when you said specifically you view the question similarly as you view the axioms of set theory. Now is that a very particular example specifically in set theory because what comes to my mind is the same way of reasoning in the sense that we're just going to assert x as an axiom and see what follows. So that's kind of the reasoning in set theory. Or are you saying in principle you can make sense of the idea of a cat being dead and alive at the same time or a square being circular. Because in one circumstance you're saying you know assume that a square is circular and we'll see what follows. And the other is is there a way to make sense of the assumption that a square is circular. Do you see what I'm saying? Not really. I mean it sounds like you're thinking that I'm seeing debates about the axioms of set theory as just kind of debates about what follows from them or something. I'm talking about debates about which axioms of set theory are true. Because set theory can be seen as a foundation for math and there's a question of what existence assertions and stuff. So for example I'll just say what this gentleman I spoke with the other day who I think phrased it very well. He was saying that there's some in set theory you can analyze the concept of something like an infinite set and see whether or not there's a way to intelligibly make this sensible this concept of an infinite set. There's another question which is to say let's just assume that's the case and see what follows. Right. So what I'm saying is in circumstances like para-consistent logic or strict logical contradictions are you saying what you can do is just assume that they're true or possible and see what follows or are you saying that I can actually clearly make sense of a logical contradiction. Yeah I mean it's a little tricky here right because in the case of imagining different logics you're imagining different things falling from different things right. So the subject is what follows from what. But the short answer is I'm imagining the analog to the actual axioms being different. I'm imagining in other words I think that we can make sense of the actual basic principles of the logic being different and of course logic doesn't tell you anything about cats and dogs per se it just tells you you know it gives certain boundaries on the way the world could be. So can you do you have any clear conception of like a metaphysical contradiction being in existence. So we have the logic that says you know okay in principle this thing could be mutual this thing could have mutually exclusive properties for example and I'm saying I don't have maybe I'm missing something but I can't even conceive of it can you. Yeah I think that for example like so okay so you know let's get back to the set theory case but so I've been talking about set theory the way most people talk about it which is you assume classical logic and then we can have debates about the axioms. There is another approach right to Russell's paradox and the paradox is at the turn of the 20th century that maintains the naive picture that Frege had and changes the logic. So you know there are I don't think my listeners will exactly understand those references or me either. I thought Frege and Russell had a lot in common in regards to set theory. Right okay so Frege had this set theory which is very intuitive which basically says that when you have a sort of predicate when you have a condition there's a set of things that satisfy the condition maybe it's empty right so like the condition you know being 10 feet tall and not being 10 feet tall that's satisfied with something that's the empty set but take any condition and there should be a set of things that satisfy you know there's a lot of nice features of this view it seems very principled it's very natural it's arguably how we think about sets unfortunately you know it's inconsistent because if you consider the set of all sets that don't contain themselves oh right right right and this is what Russell discovered in simple letter to Frege you know you get the answer that it contains itself just in case it doesn't contain itself so the standard approach to that is to in ZFC set theory is to limit the comprehension scheme so if you already have a set then you can take all elements of it that satisfy some condition you can take a subset of the set already given but there's another approach to it which is definitely not mainstream in math but some philosophers take it seriously which is actually that picture is basically right it's a principled picture what we were wrong to think of is that we were wrong to think that we have to assume classical logic and in these views you know you might have for example the Russell set both contains and doesn't contain itself you know and you're saying you have a way to make sense and I feel like yeah I can make sense of that as well as or basically as well as the alternative approaches to paradoxes you know I might think it's wrong I might think a better approach is to stick with classical logic and you know develop a cumulative hierarchical picture but the point is that you know it seems to me like you know I hate to always be getting back to the slippery slope argument but I think that's really where I'm coming from if just some outsider maybe you might be listening to this we're just watching people debate the foundations of math what's remarkable is even if they were following the reasoning and stuff I don't think they would see a principal difference between arguing about the ZFC axioms and arguing about the axioms of the logic it would basically be it's just the same basic enterprise and it's very abstract and very foundational but it's not different in kind from any other metaphysical debate it seems to me it's very interesting talking to you that you really feel like there is this bright line kind of it's very interesting to me and it's not like I want to deny that fact about your phenomenology the question I guess I wonder about is that fact about your phenomenology is so pervasive in philosophy it's almost the most pervasive thing everybody has their bright line but they differ where it goes over all different subjects there's a bright line space and time the nature of space must be Euclidean that's a bright line anybody who says not is just changing the subject or talking nonsense it was a bright line that people but for me I think that the notion of a bright line is not a useful notion we have to figure out how to do philosophy without bright lines and I can see how that would be extremely frustrating because everybody who's got it's not like I too have had things like bright lines that I ended up deciding weren't bright lines but at the moment I'm not even trying to say regarding things things you shouldn't give up but just as a methodological matter appealing to bright line this I don't think is like a way to make progress the only lines that I think are bright are the ones which I would consider inescapable that everybody presupposes but I do think it's interesting and I guess we'll have to end it here in some mystery and awe that you have a way of cleanly conceptualizing a contradiction and whether it's in I think the example you gave is in set theory would you feel comfortable claiming that kind of understanding outside of mathematics like for example I've been talking about things having properties that contradict something being circular and being square at the same time do you have that ability as well because I view that as very incredible I'm missing something there's some little capacity that I just absolutely am miles away from to be honest I haven't thought about the cases I almost solely think about are the abstract sciences of course people often talk about physics in this connection I haven't thought about that case enough to know what I think about that and also I don't get the sense that a lot of people know what they think about that even though there's different theories on the table but maybe one last thing to just say which I think is interesting is that I think our discussion might bottom out in two different conceptions of how you make progress in philosophy and the conception that I think you have has like a distinguished tradition and there's lots of people who still hold it and it's that sometimes philosophy can trump like science for example and people used to have a much more ambitious views maybe as to how it can do that and what circumstances it can do that it sounds like your view is pretty modest you don't think that for example we can dismiss fundamental physics because we know that this is mostly solid or something that's a Morian datum but you do think that some I assume that you would want to apply your theory in such a way that sometimes if a scientist comes forward with what looks to be a well confirmed theory that a lot of people agree to but it violates the law of non-contradiction as formulated in this example there's one interpretation of quantum physics which implies a logical contradiction which historically has been believed by the majority of the physicists I reject the Copenhagen interpretation and it just so happens that within the last 20 or 30 years the Copenhagen interpretation is now I don't know if I consider a minority but it's not the standard interpretation you have the many worlds hypothesis and you have my preferred interpretation which is called pilot wave theory which doesn't apply any kind of logical contradictions everything is deterministic and everything but yes I certainly apply this principle universally because I'm not claiming this is just about philosophy these rules are for all existence in all possible universes including physics that's really interesting I love these metaphilosophical debates this is in a way my fundamental interest in philosophy is meta-philosophy how are we supposed to do it how do we make progress, what's interesting all that kind of stuff it's a super interesting position one way of defending it is to go back to the quine example that I used to say famously at the end of two dogmas of empiricism that you know in principle math and logic are not different in kind from high level physics it's just a very abstract empirical theory that we can imagine of returning and you can't say ahead of time what's off limits and some people said well yeah but you need rules to figure out how to change your beliefs in light of the observation won't those be off limits those will essentially be some logical rules won't those be off limits and in a way maybe the way to sort of get at what we're talking about is are there such rules are there such rules that you know even if quine was basically right he was wrong about some privileged subset of beliefs some little bright line and you know I tend toward the view that not but I'm very interested in the idea that there has to be a bright line there yeah well on that note I want to thank you so much for talking with me today this has been fantastic thanks a lot so that was my interview with Dr. Justin Clark Done I know these ideas are abstract and certainly some people they're very boring but they are of the utmost importance when we're talking about this level of philosophy the very basics of critical reasoning if we make mistakes here it will affect our entire world view and so we have to have the utmost caution when we're talking about epistemology which is why I love the area of thought so much so as always if you want to help support the show please check out patreon.com slash Steve Patterson and you can support the creation of content like this by pledging just one dollar per episode that I release and if you do so you also get a copy of all the books that I've written and all the books I will write in the future including square one the foundations of knowledge thanks so much for listening guys I'll see you next week