 Hey everybody, welcome to episode number 11 of Patterson in Pursuit. This week is another breakdown episode, which I've been looking forward to for several weeks. I've been chopping at the bit, ready to dive into specifically one interview that I conducted a few weeks ago. Before we get into it though, if you guys enjoy this show, could you do me a favor? Go into iTunes, go into Stitcher, and leave a rating and a review. The show's not been around that long, but it's already getting some popularity and what's really going to help it grow in the future is having more ratings and reviews. So if you have a couple minutes and really want to help me out, I would sincerely appreciate it. Since the last interview breakdown, there have been four interviews. I'm going to quickly go through three of them and spend the majority of the time talking about the interview I had at Columbia University about logical contradictions, my favorite topic. I feel like now that I've got several interviews under my belt, I can start pushing the envelope a little bit more. My own analysis, I'll be honest, is a bit sharp. I very strongly disagree with some of the arguments that you're about to hear and I'm not afraid to talk about it. Now I want to emphasize this is nothing personal against anybody that I had interviewed or anybody that I will interview. It's just an analysis of the ideas. Big ideas have very big stakes. And when some foundational claims are fundamentally flawed, it's very important. So in this set of interviews, we talked about egoism, religion, and iron ran with Michael Malus. We talked about completed infinities with Dr. Gary McGuire. We talked about Christianity and a personal Christian experience with Dr. Bob Murphy. And then we talked about logic and epistemology with Dr. Justin Clark Done of Columbia University. So the first thing I want to highlight is how important foundational ideas are in our worldview. Many times there are essential premises which are nestled into our worldview that we've not even examined. We just assume they're true or assume their faults. However, when we actually examine them, things might not be so clear. One premise that most people take as a self-evident truth is the inherent value of human individuals. And Michael challenges this idea. No, I don't. I'm a huge, since I was a kid, when I was a kid, I wanted to be a zookeeper. So I'm a huge zoology person. So I don't regard human beings as special and awesome and every human like this magic. I reject that completely. That's also a function of growing up in a Soviet household. So that kind of thinking is just completely foreign to me. Really? Yeah. Now, whether or not individual human beings are valuable is not a self-evident question. It's something that everybody needs to examine for themselves. And the implications of that belief are quite large in terms of having an influence on other areas of our worldview. So the next two points that I want to highlight are essential in mathematics. As the series progresses, we're going to have more and more interviews with mathematicians talking about mathematics. The question that I had for Dr. Gary McGuire was about trying to understand infinities, trying to understand this idea of a completed infinity, which strikes me as logically contradictory. And in mathematics, there is what's called the axiom of infinity, which is an explicit assumption that there are such things as infinite sets, that there's at least one infinite set. And what I'm trying to get to the bottom of is whether or not that assumption is justified, if that even makes sense to say there could be such a thing as an infinite set. As we were saying earlier, you postulate the existence of the infinite set. We assume the existence of the positive integers. We just kind of assume they exist, and we assume that we can put them into a set that mathematics does. So this is the standard response in modern mathematics. It is an assumption that they don't necessarily examine, and they just go from there. This is also something you'll hear in the interview at Columbia about logic. They say, well, whether or not a square circle exists, that's an empirical question. Let's assume that one does and go from there and see what follows. I think this is a huge mistake. You can't just assume things that are potentially logically, conceptually contradictory. All right, the other critical point to take away from this interview is this idea right here. I'm trying to rephrase what Gary has said, and then he ends up agreeing with me. So are you saying that conceptually speaking, there's nothing that infinity adds to the equation that you just can't get from finite mathematics, but let's say the calculations and the formulations are a lot easier when you allow infinities? That's exactly right. In my opinion, that's a perfect way of putting it. That's right. There is nothing essential that infinity brings to the table that you can't accomplish with finiteist mathematics. It just makes the calculations a little bit more difficult. Which in my opinion, not being a mathematician is obviously a worthwhile trade-off. A little bit more work to have something that is conceptually coherent. Now in the same vein, I thought a really neat part of the interview I have with Dr. Bob Murphy about Christianity was a point that he brought up about death. It's very tempting and very intuitive to assume from our normal human standpoint that death is a bad thing, that murder is a tragedy, smallpox killing, 100 million people is a tragedy and so on. But Bob brought up a point that I really hadn't thought about before, that was kind of one of those fundamental assumptions that I had that I just hadn't examined. So yeah, I actually got telling Joshua to lead his army in and slaughter babies. That is like, what the heck is going on there? So let me just say this, if you think that the God of the Bible exists, it's not as if those pagan babies growing up and then dying of old age from a heart attack when they're 87, God still killed them. You see, he is the absolute sovereign in command of everything that happens. Every moment of existence is exactly what he wills it to be. It's not that, oh yeah, there's nature running its track over here. Then once in a while God comes in and intervenes and does something. I mean, no, everything is just a complete manifestation of his imagination or whatever you want to call it. And so at some level, anytime a human dies, it's because God killed him. And so to me, it's a kind of silly human convention to say, oh no, he's a murderer. If he tells somebody to stick a sword in somebody, or if he just kills them because the kid has a rock fall on him or because there's a tornado that goes through or he dies of a heart attack when he's 87, ultimately God is in charge of all that. I think there's some meat to this argument here. There's a lot of people are skeptical for good reason of the idea of a benevolent God or that God loves everybody and yet he causes all these bad things to happen. However, I think Bob makes a good point that actually, if it's the case that there is a God and God is in control of all of these things and orchestrating it all, that means every single death this God would be responsible for from the miscarriage to the infant death to the child death to the teenagers, tragic death and a car accident to somebody that dies when they're 105 of old age. Every single one the God would be responsible for. We humans would be drawing the lines between a tragic death and an okay death, a justified death and an unjustified death. When in reality, if this is all some kind of storyline that's being orchestrated and played out, then it does seem kind of silly to argue against the existence of some kind of God just because there is what appears to be tragic deaths from our perspective. So if you haven't had a chance to listen to those interviews, make sure you go back and listen to them. They're very insightful. I'm going to devote the rest of this podcast to breaking down the interview I had with a professor at Columbia University who was arguing for the existence of logical contradictions. He's a super nice guy and we got along very well, but I just agree with him in the most radical and fundamental way. All right, so this clip is kind of the central point that Justin is making here. We're talking about logic, we're talking about contradictions. Is it possible to have a true contradiction? 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 it can never hold. Sometimes I come to the table believing 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, we've got to make an amendment somewhere. So all I'm saying, I just want to be clear about the view. I mean, 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. I 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. OK, so he's essentially taking the position that, look, there's a lot of different logics out there. We can't be frivolous in choosing from them. However, he explicitly says, I'm not claiming just because there's a lot of logics out there that means we can't make any progress. It doesn't mean that none is essentially any better than the other. And then very shortly after that, he says this. 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 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. Isn't this an indigesting proposition to claim that because there are multiple competing logics out there, the claim that there is a correct logic doesn't even make sense. Now, my own personal beliefs are exactly exactly the opposite of this, where I would say that to claim logical pluralism is true, to claim that there is no logical basis for evaluating something as being true or false, that this is all just a cultural phenomena and we have to choose based on some normative framework to me is incomprehensible. The reason is because you can always come back as I do in this interview to the laws of non-contradiction and identity and very quickly discover that, yes, there are some inescapable groundwork rules in order to make sense of anything. 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. And it seems like you just can't get around that. Even if you claim you can, you really can't. Yeah, no, good. I mean, a way to sort of articulate what you're saying is, you know, so suppose I give a non-classical 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 non-classical 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, OK, this is actually just a formal trick. I mean, everybody agrees you can lay down rules that, you know, conflict with the rules. But what's interesting is that doesn't seem, you said in a scapegoat, 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 understanding. So to put this another way, my claim and the claim of perhaps the classical logicians is to say there's no way to sensibly contradict yourself, to include logical contradictions into your worldview or into your argument is making a catastrophic error. The response of the para-consistent logicians is to say, no, no, you're just using classical logic. Yes, I contradict myself. And yes, my proofs contradict themselves. And yes, even every feature of my arguments is contradictory. But that's OK because I allow contradictions into my worldview. My response would be to say, well, you don't understand what you're doing when you allow contradictions into your worldview. You are quite literally defeating your own argument. But that leads me to this question. 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 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 there has to be a perspective where one cannot act as if one is making sense. And then the other party pounds their fist and says, no, no, you aren't making sense. Now, this is what throughout this interview happens. It is taking the appearance of sensibility and saying, well, therefore it's sensible. And notice also the really interesting use of language, which says, what do we mean by sensibility? I think we have to choose something that's interesting. This reminds me of the interview I had with Dr. John Stur at Emory University, who's the American pragmatist who kept coming back as well. We have to have interesting notions that this is interesting. And I go, oh, well, the old, old use of classical logic is not, it's not really interesting. What do you mean interesting? I agree to some extremely superficial degree. Somebody claiming that they can sensibly contradict themselves is interesting, but that doesn't justify taking the arguments seriously or heaven forbid acting that just because somebody goes through the motions of making a sensible argument that somehow we think, oh, well, it's as if they've made a sensible argument. Therefore, classical logic isn't this impenetrable thing. As we keep talking, this argument keeps coming up the idea that you can assert a logical contradiction and act as if you're making sense of it. Therefore, we can't simply say contradictions don't exist. 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 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 looks from, you know, 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. Listen to this argument, the idea that from the outside, people who don't understand the field, people who don't understand what they're talking about, will overhear these arguments between philosophers and say, oh, well, that sounds just like any other claim. Therefore, there must be nothing intrinsically unique about it. But this is completely irrelevant. If you were to take somebody who was wearing a lampcoat and was talking about biology, for example, human biology, and they were to make up a bunch of gibberish words that didn't actually correlate to anything in the body, it was just your fruit of Fra Fra and the left ventricle of your, of your major pinard is now being blocked by some metal rabituaries in the grunt. People who don't know anything about the field will go, oh, yeah, well, that seems entirely plausible. Those, those sentences have a bunch of subjects and verbs and a bunch of nouns and words I don't understand. Oh, isn't that interesting? But therefore, what I just said, the gibberish I just spoke, should be somehow evaluated as that potentially that's true. It's like saying we have no principal position to discern gibberish from actual words, because to somebody who doesn't understand the language, they sound the same. 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 unintelligible 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 now I also don't think that it's coincidental that the example that he brings up comes to the axioms of math because specifically in mathematics, something that I keep hinting at, I've written a little bit about and some of my interviews talk about is the idea of the axioms of math actually being logically flawed, specifically the axiom of infinity, the idea that there is an infinite set. I would say when you unpack the concept of infinity and set, these two things are logically mutually exclusive. And therefore, yes, we can argue about them, but that doesn't somehow give the argument credibility when there is a conceptual contradiction with the terms involved in the axiom. And in fact, this is one of the reasons that I got interested in mathematics is precisely because a lot of people when they're arguing for the existence of logical contradictions will come back to mathematics. They'll say even more radical claims like, I overheard Lawrence Krause once in a lecture that 2 plus 2 equals 5 when you have extremely large magnitudes of 2. That's not a joke. You can Google it, there's a YouTube video of him saying that. Now how could it be that we get to such a point in our intellectual culture where somebody can seriously say 2 plus 2 sometimes equals 5? I think ultimately if you follow the trail of what I call irrational arguments, a lot of it leads back to mathematics. In set theory in particular, which throughout this interview, Justin keeps coming back to. Okay, so I asked him a question that takes away all the abstract. We're talking about concrete contradictions. If you all take a listen. So let's go to some concrete, something like, is there a way to make sense of a claim like in some circumstances there is a married bachelor. There's a married unmarried man. Yeah. Is that, 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. This is the other consistent thing that you see with intellectuals and academicians in general. With all due respect to Dr. Justin Clark Stone, this is jargonism. This is obscuring a crystal clear question to try to say, oh, well, actually this resembles some debate in some paper somewhere, and I can use all these jargonistic terms to try to act like I've answered the question when I actually haven't. Very crystal clear question. And there's a very clear reason in my mind why he's uncomfortable answering it. 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 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, it's not a first order logical truth that some bachelor is married. Did you catch that? Yes. So the question was, is there a way to make sense of something like a married bachelor? And the answer was a bunch of jargon. And I want to say, I do want to say one more thing on the subject. One of the nefarious things in academia, one of the reasons that I'm not in academia is because of this type of stuff, the way that many academics phrase arguments is the framing of issues is fundamentally mistaken because it comes from their profession. So there's a particular way of arguing a particular way of reasoning, a particular set of questions that people are dealing with in academic journals and in academic discussions. And if those fundamental questions are framed incorrectly, I think it's a gigantic waste of time to be talking about them so much. This is an excellent example. Only, only in the world of academia would such a simple question be met with such a complex and indirect answer. Only in the world of academia would such an answer satisfy somebody who asked the question. A lot of people's tendency is to run away when they ask a question like this and that's the response they get to go, oh, I just must not be smart enough to understand that answer. Surely it's not the case that that answer was actually completely vacuous and jargonistic and obfuscatory. So I'm just going to act like I understand what's going on and we'll move on. Fortunately, I'm not in that circumstance. I don't have anything to prove. Am I suspicion of the last several years has been confirmed that when you hear an answer like this, it's not a sign of you being unintelligent. It's not a sign of the question being a super difficult one to answer that, oh, this is the best we can do. No, it's a sign of somebody intentionally being obscure and trying to sound academic so that they can weasel out of an answer. So that's my internal experience. But of course, in the middle of an interview, I can't say that. And I don't want to be mean. I want to be respectful in all these interviews. So this is what I ask. 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 something is a logical truth that there's no assignment of the predicates 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 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. Yeah. This is also why if I may be so bold, the world of academia as I understand it has a population bias in it. Because in order to be an academician in order to be a professional philosopher, mathematician or in any social science field, and perhaps even in the hard sciences, you have to be able to put up with this. This kind of argument really gets under my skin, I'll be honest, I'm on the pursuit of truth. And there's supposed to be an institution out there, which is academia, which is filled with people who are intellectual truth seekers who care about critical reasoning more than they do their careers. What I think has happened is the only people that can make it in academia are the people who can stomach nonsensical and vacuous fluff. The question is clear. The answer is outrageous. So so you might say this is naive because 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 well, anyway, say now we have a clear answer. I'm asking, is there any way to make sense of the idea that you could have a married bachelor and the responses? Well, is the pope married? Maybe. This is an unsatisfactory answer. There is a very simple resolution to the question. It depends on what we mean by married, and it depends on what we mean by bachelor. If we're simply explicit about what we mean and we don't change the meaning of our terms, then no, the pope is not a married bachelor. What you also find when you're searching for the root cause of irrational ideas is a lot of stuff like this, that when you start asking simple questions and you try to get clear answers, you get a lot of jargon, you get a lot of references to other people's work and stuff that is supposed to be very complex and difficult to sort through. And then when you actually get an answer that is clear, a lot of times it's outrageous. So for example, in the world of quantum physics, something that I'm going to be having a couple of up cupping interviews talking about, when you actually sort through the jargon and you get to the central claims of what's called the Copenhagen interpretation of quantum physics, which people use to argue that logical contradictions can exist. The argument is preposterous and extremely easy to resolve. Or another example that somebody was arguing when we were talking about logical contradictions was is George Costanza bald? Or if you don't know who George Costanza is just Google George Costanza, he's a character on Seinfeld. And he's like he's half bald, right? He's just done that the edge was like, well, he's kind of bald, where he's not kind of bald, you can make both argument. And this is supposed to show how contradictions of paradoxes can exist. Well, he is bald and he's not bald at the same time. And then they go from there and develop all these wild jargony complex theories about how our minds can't know anything about how the world is a big paradox. And of course, the resolution to that is also very simple. Bald is a word that different people use to mean different things. So my conception of what bald is, when I use that term is different than when other people use that term. It's a subjective criteria. If we want to be precise, then we can talk about the objective surface area coverage of George Costanza's hair. He has a certain amount of hairs on his head. Whether you call that bald or not is entirely irrelevant. The metaphysical reality of George Costanza's hairline is not something that somehow justifies the existence of logical contradictions. And this is a similar circumstance. No, the Pope is not actually a case of some metaphysical logical contradiction existing. 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 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 getting 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 put it a different way. So suppose I say something like, suppose that some bachelor is married. 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. And there it is again. First of all, no, it is not even sensible to say imagine some world in where there's a bachelor, there's a property of being a bachelor and there's a property of being married together. Couldn't that be possible? No, not if we're precise about what we mean by the terms. And then there is the resorting to what I was talking about earlier. Well, let's assume that's the case. Let's assume that there's a square circle and we can talk about it in a similar way that we could talk about other things. Therefore, maybe it's possible the square circle exists. Here's what I would say 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 about it 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 dialecticism, 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, it's, 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. Again, no direct answer to the question. I'm talking specifically trying to talk about a metaphysical contradiction, my shoes being black and not black at the same time in the same way. And we're talking about the Pope, we're talking about the axioms of mathematics, we're talking about the liar's paradox. Now, in my worldview, it is absolutely crystal clear why there is not a response to such a simple question. And that's because the answer is obvious. What we mean by a logical contradiction is precisely that there hasn't been an error committed. When we make any given claim was that the shoes are on my feet. That claim also comes with an implicit premise. There's another proposition that you are claiming when you're claiming that the shoes are on your feet. And that is, it is false to say that the shoes are not on my feet. So every proposition that comes with this two fold claim, identity and non contradiction. So the shoes are on my feet means it would be false to claim that the shoes are not on my feet. Therefore, when you put these things together, it's a simple confusion about what we mean by assertion and what negation does. Every assertion implies that a negation is false. That's what we mean by the assertion. So the answer is very crystal clear. Well, is there any way to make sense of a contradiction? Well, no, not if we're clear about the concepts and understanding what we mean by any given proposition in all circumstances. Now, as far as the Liar's Paradox goes, I'm not going to play it here, but I have a perfectly satisfactory resolution to the Liar's Paradox. I talked about it in this interview I've written about it. I've done a video about it. And I'm going to have a big section on it in my upcoming book, Square One, The Foundations of Knowledge. All right, so here's another attempt at giving some kind of metaphysical possibility to the ideological contradiction. Yeah, there are other alleged counter-examples, right? So I think Grand Priest, for example, talks about, you know, laws are typically, you know, very often they involve implicit contradictions, right? Like, yeah, like constitutional documents, right? So you'll have a bunch of obligations, but if you actually unpack them all, you'll get a sentence of the form you're obligated to do this and it's not the case you're obligated to do that. Now, you know, I want to make like 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 possibility. Again, here we have a concrete claim that is very easily resolved. If you're playing Simon says, and the person who's Simon goes, all right everybody, stand on one leg and don't stand on one leg at the same time. It doesn't imply that logical contradictions exist. It implies that that thing can't be done. If some lawmakers write down a bunch of rules and say every Tuesday you have to wear a green hat and every Tuesday you must not wear a green hat. That does not imply, we have discovered a logical contradiction because the people have wrote it down on paper. No, that means that simply can't be done because of classical logic. We can know, oh look, you dumb lawmakers, you've made something which is an impossibility to execute because it contradicts the laws of identity and non-contradiction. What we mean by wearing a hat on Tuesday is precisely not not wearing a hat on Tuesday. So no, it cannot be done. It's as if we're talking about language and we're discussing is it possible to write down a sentence without using words? And somebody comes along and writes down a sentence that says, this sentence is not written using words. And somebody looks at it and goes, oh my gosh, we've just discovered a contradiction. It's a sentence that's written down in words, but it's not written down in words because it says it's not written down in words. That's a contradiction. No, of course, that's not a contradiction. That's just several layers of confusion about the relationship between language and metaphysical reality. All right, so this next clip, you have to listen to very carefully. It reminds me a bit of the conversation again I had with a pragmatist in Atlanta. All right, so this next clip you have to listen to very carefully. It reminds me a bit of the conversation again I had with a pragmatist in Atlanta. People have been appealing to like concepts just follows 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 with the concept of good and so on and so forth. It's not like anything really was resolved by making that additional claim. We're right that 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 action. Here's another way to put it. If you and I disagree about what's packed into the concept of good or packed into the concept 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 going to make much progress by saying, well, just think about the concept, though. It's obvious that every set is well fit. Well, if I don't think that the axiom of foundation is true, then, of course, I don't think that follows from the concept. So the first point I want to make is just this doesn't seem to me likely to advance the discussion much. OK, so before we go on, let me just clarify that for people who are unfamiliar. Again, we're talking about mathematics, but the idea is universal. We're talking about what is implied by a concept. So if we have a very clear conception of what a square is or what a cube is, is it the case that it is implied that that cube is not spherical? Does one imply the other? My position is, yes, certainly, of course. And his position is no. And then listen to what he does. So let's again take a cleaner case. Let's take the concept of set. Suppose that you were to, you know, we did like conceptual surgery on the concept of set and we just got super clear and it's just obvious that, you know, sets are things that are built at, you know, at different stages in this transfinite generation process and it just doesn't make sense to talk about a set, you know, that precedes itself. So no set can contain itself, for example. And there's no infinitely descending chains and stuff. Okay, fine. You know, here's something that we can introduce. We can introduce a concept of Schmitt. And Schmitts are exactly like sets, except some Schmitts 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 Schmitts? So there it comes up again. Instead of sets, let's talk about the cube versus the sphere. The discussion is whether or not you could have a spherical cube. Classical logicians like myself would say no, you absolutely certainly cannot. What we mean by the concept of cube is mutually exclusive with the concept of what we mean by a sphere. And so his response and the response of logical pluralists and American pragmatists is to say, well, assume that a spherical cube exists. And then what follows from there? Now the discussion is not whether or not the concept makes sense. It's whether or not such a thing exists. And they think they can get away with this by simply renaming it. So OK, yeah, cubes can't be spheres. Yes, spheres can't be cubes. But the question is whether or not there are cubeheres. And what a cube here is, is it has the property of being spherical and it has the property of being cubicle? Do such things exist? Is an empirical question? This, in my mind, is a gigantic, catastrophic sleight of hand. It is, again, instead of going into the concrete to examine what is packed into our concepts, it abstracts. It says, well, let's not deal with the concrete. Let's just assume that a logical contradiction exists or assume that two mutually exclusive things can be together and see what follows. And now it's an empirical question because we renamed that thing. OK, so this next question that I ask him is about whether or not things could have been different. So we're talking about the laws of physics might have been different, the laws of any given country might be different. Could the laws of logic be different? Now, his position so far has been, well, let's keep an open mind. Maybe these laws could have been different. And my question is very, very, very simple. And listen to the answer. 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, 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 map maps an object to itself and to four, right? It's talking about individuals, numbers. And it's 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 my question is about two plus two equals four. That is a logical relationship between the concepts of two and the concept of four. And he's trying to say, well, if there are no objects, then maybe that law doesn't hold, right? That response with all due respect is exactly what you would expect from an academic. From somebody that is has decided their career is going to be an academia making arguments like this, two plus two equals four. Is that always and everywhere true? Or is it possible that could be false, you know, and go and you are free to go back and play the response. So the last thing that I want to play for you is a question that I asked him that I've asked lots of people in my pursuits and in my own personal conversations, I've met lots of people that argue that logical contradictions exist. I've not really met anybody that claims they can make full conceptual sense of that. So I asked him earlier in this conversation, can you make sense of a logical contradiction? And the example that he gave of making sense of it is in set theory, not coincidentally in mathematics and in set theory, yes, in some way he can make sense of logical contradiction. So then I ask him this question. But I do think it's interesting and I guess we'll have to end it here and in some mystery and awe that you have a way of cleanly conceptualizing a contradiction in 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, you know, something being circular and being square at the same time. Can you have that ability as well? Because I view that as very incredible. And I'm like, I'm missing something. Yeah. There's something mental capacity that I just absolutely am a miles away from. Right. I mean, to be honest, I haven't thought about the cases I almost solely think about or the abstract sciences. Of course, you know, 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. I find this really interesting question. And I would ask my listeners, you know, why do you think that's the case? If it's if it's possible that people can make sense of logical contradictions in set theory and in mathematics, or at least they claim that they can, why is it that they can't seem to in metaphysics? In his case, I find it odd that this is not something he's thought about. And just in common sense, every day, metaphysical language, oh, I wonder if there's any way that a cat could exist and not exist at the same time. He just concerns himself with the higher abstract sciences. Again, I don't think that's coincidental, but I'll leave that to you to decide. So that's everything that I have for you today. I got some really awesome upcoming interviews, including an interview with a professor at Cambridge about quantum physics, which is simply directly related to the idea of contradictions. Everybody who's interested in philosophy seems to like to bring up quantum physics at all the wrong times. So I'm talking about the basics of quantum physics with a professor from Cambridge. Make sure to tune in. I think that's going to be next week's episode. If you like what you hear, make sure to leave a rating and a review. Make sure to subscribe. If you're a big fan, check out my Patreon page at patreon.com slash Steve Patterson. And you can support the creation of more shows like this. All right, everybody, I hope you enjoyed it. Have a great day.