 Hello, I'm J.J. Joachim and welcome to Philosophy and What Matters, where we discuss things that matter from a philosophical point of view. Our topic for today is truth and paradox. For some philosophers, truth is a substantial property. When I say that it is true that Paris is in France, it is true part add something to the sentence Paris is in France. Now this added feature might be the sentence corresponding to facts, or cohering to other beliefs, or being empirically or formally provable, or even being a useful belief to have. Now other philosophers deny this. For this latter group of philosophers, truth is transparent and does not add anything to the sentence. They argue that in non-abate context, there's nothing substantially different in uttering the sentence, it is true that Paris is in France, from simply stating that Paris is in France. So who is right here? What is the nature of truth? Now whatever the right theory may turn out to be, however, it would have to come to terms with a liar paradox. The problem of ascertaining the truth of the sentence, this very sentence I'm uttering now, is false. Now to guide us through the philosophical spandrels of truth and why it matters, we have J.C. Dio, a new family professor of philosophy at the University of Notre Dame. So hello J.C., welcome to philosophy and what matters. Thank you, it's good to be here. Okay, so let's start with the question, what do philosophers mean by saying truth is a substantial property? And what is it a property of in the first place? So let me take this one at a time. The last question, what are the truth bearers? What are the things that truth is a property of? This is debated widely. They can be propositions, they can be mental states, beliefs, thoughts. I myself think that no matter what the truth of the bearer question may be, many of the important issues still exist. So I myself have never gotten too worked up about that debate. Not to say there aren't hard and important questions there, but I tend to take the view that we use declarative sentences to say something, to declare something about the world. We try to describe the world using declarative sentences. We assert declarative sentences. And I tend to leave the bearer question right there. So truth is a property of declarative sentences. The philosophical debate over truth bearers is really the question of whether declarative sentences are the primary truth bearers or whether there's something language independent that's the bearer. And I myself am going to just sort of let others figure that out because I think many of the issues about truth still apply no matter how that debate goes. So I've gestured at your, your second question about the truth bearers. Let me now answer the first question you had, which was what philosophers mean when they say that truth is a substantial property. Of course, as with many things, different philosophers can mean different things. But I think that the most useful answer to this question, at least in the context of this discussion, and in many philosophical contexts, but the most useful answer points to the idea of an explanatory property. So when people say that truth is a substantial property, I take them to be saying that truth itself is doing a lot of explanatory work in our theories of reality. So the property of truth is comparable to other important explanatory properties. So, you know, in a sort of ordinary fashion, the property of being human, and the property of being a tree, and the property of being a peanut. These things, forget about whether these can be reduced to more fundamental properties. But in general, these things do explanatory work, right? They really characterize parts of the world in a way that explains the difference between this object and that object. And why this object, say, the object that bears the property of being human puts one of these objects that bears the property of being a peanut in its mouth or something. You know, you have all these, you have all these sort of explanatory properties, and then as theorists, we might say, yeah, but is being human. Is that really the fundamental question and then you can have debates about whether that should be reduced to more fundamentally explanatory properties and so on. Okay. So I didn't define what it is to be an explanatory property, but I hope I've gestured at what I'm talking about. Now, when philosophers say that truth is a substantial property, I take them just to be saying that truth is also explanatory. There's something out there in the world, or if we were to fully describe the world, we would have to describe this property truth. We would have to, our explanation would be lacking somewhere if we didn't have this property truth involved in a critical way. Yeah. And as you said in your intro, some people who think the truth is explanatory, they think the explanatory work it does is, it's the relation between a true sentence in the world. It's correspondence between this sentence and the way the world is. So they think in order to characterize that part of reality, the sentence world part, you have to talk about this important property of truth. Or others, as you said, coherence or a sort of pragmatic view where most useful, I mean, all these things you can imagine truth playing an important explanatory role, it's answering an important theoretical question. Okay. That's what it is to say the truth is a substantial property, at least on clear accounts of what it is for truth to be a substantial property. It's basically, it's doing important explanatory work. So that's the answer I would give. Thanks very much. So the idea is that truth as a concept might be an explanatory in the sense that it gives you a correspondence relation or a coherence relation or a pragmatic relation or even a probability relation if you're an anti-realist. But truth relates to other concepts as well, like beliefs, facts and logical consequence. So could you picture how the concept of truth relates to these other concepts? Well, of course it depends a little bit on your view of what truth is. But in general, people think that beliefs can be true. And that beliefs, some people say things like one difference between beliefs and desires is that beliefs can be true. So, and that in some sense, other things being equal, they sort of aim at truth. Whereas desires, they don't aim at truth. So notice here, something like that is trying to invoke truth as an important explanatory difference between these mental states. Concepts, let me set that aside a little bit. I mean, people can say, I mean, concepts I think actually is related to truth indirectly through a different sort of notion, which is true of. So, a concept may be true of something, but concepts themselves aren't true or false. They're not, let me say propositional or sentential or something. And logical consequence, that's an interesting one. Many philosophers have said that logical consequence is necessarily truth preserving. And, you know, a key to logical consequences is that it preserves truth. If all of these premises are true, then so too is any logical consequence of them. So, and this is supposed to be a necessary preservation of truth relation. So, you know, you can, you can see how truth is related to consequence. It turns out that there are some sort of complications with that, with that tie in between truth and logical consequence. But, but maybe it's best not to get into those. I mean, but that's the general sort of way in which truth is related to consequence is the way that I said, even though, in fact, I think there are problems with saying that but that's that it's more technical and probably we can talk about that another time. Okay, so yeah, so I'm trying to understand the issue here. So when philosophers think about truth, they're thinking about it in terms of whether it's a substantial property or not. It's substantial in your sense, if it gives or provides an explanation, it has explanatory power and it relates to beliefs because beliefs are true as opposed to desires which are not. Concepts will be something like you can satisfy a concept. So if you satisfy a concept then you, it's true of you that you satisfy this. And the logical consequence relation will be kind of truth preservation according to some theory. However, here's the thing. In a field paper survey, majority of professional philosophers, more than 50% as you can see here, accept or lean toward a substantial view of truth, something like a correspondence view and only 24% are going for the negative view. This is known as the deflationary theory. You're part of the minority by reading your work. So you think the truth is not really a substantial property, that it is something transparent. So what does it mean for this view? What does transparent to mean here? And how is it motivated? Right. Well, let me just say that I, on the side, I've never understood just how much weight and what information we're getting from the survey. Partly because, you know, people who have thought hard about truth, they've, you know, done a lot of work on it and all that, know that there are a lot of distinctions. So when people talk about deflationary truth, right, I mean that can mean a lot of different things. When they talk about correspondence, that can mean a lot of different things. So for sort of no doubt, very good philosophers who know of these debates, but they just sort of say, well, I sit with the correspondence. It's not clear to me whether that means what it indicates exactly. But having said that, I am convinced from years ago, years giving, you know, talks and engaging with students and colleagues all over that you're right about one thing that I and other so-called deflationists really are in the minority. Yeah. But I think that the explanation for that is that when people say, I'm definitely not a deflationist, they're rejecting something that probably is not really part of the view or something. And again, just to be clear, deflationism is not actually a view. It's sort of a family of views that are united on one point. Namely, that truth is not a substantial property in the way that we were talking. So the property of truth does not answer any explanatory questions. So deflationists are so-called because they're united around that commitment. Now, a transparent truth theorist such as myself or Hartree Field is another person who's done a lot of work in the area. This is the idea that not only is truth not explanatory, but it really is sort of completely see-through. So an inscription of transparent truth to a sentence is equivalent, absolutely equivalent in its consequences to the original sentence. So sometimes this is put as to say a sentence P is true for transparent truth. That truth description to P is intersubstitutable with P itself. Everywhere except of course in so-called intentional context like inside quotation marks and all that stuff. So transparent truth is really that there is a property of truth, but it's completely see-through. So I put this in some of my work in the past. I've put it this way that God could completely describe the world entirely, lead nothing out without ever mentioning truth or without ever using the truth predicate. So it's not adding anything. Now, of course, you might ask, well, why do we have it in the language then? I have my own answer, but I'll gesture an answer that's common among deflationists as I defined it. I defined it negatively. We have it in the language because it allows us to make certain claims that we couldn't otherwise make. I think the philosopher made the clearest was Stephen Leeds, and then Klein said something similar, but the point is right. So you ask, well, why would we have a predicate that doesn't add any consequences to what we say? It sort of adds sort of bells and whistles like you just saying true, but you could have had all the consequences without that. Well, the reason is that there not being God, not having all the infinite capabilities being stuck in our finite situation, there are many things that we cannot express without this device. So let me give you a common example. Suppose that let me let me do it in two steps. That one, right? Let's say that your favorite, your favorite set of numbers. No, no, sorry. Sorry, let me not do it that way. Let me do it this way. Your favorite set of claims or assertions are the following three. Okay, so your favorite ones are exhausted by the following three. The number one comes before the number two, the number two comes before the number three, and the number three comes after the number two. Those are three claims, and that set of claims, that's what you believe, and those are your favorite true beliefs. Now, if I were to say, well, JJ's favorite theory is, and then I point to this set of three sentences, I can say, his favorite theory is this set, he thinks all of these are true. Well, I could have more informatively said JJ thinks that the statement one comes before two is true, he thinks two comes before three is true, and he thinks that three comes after two is true. But notice, I don't even have to say true there. I can just say, here's what JJ believes. He believes one comes before two, two comes before three, and three comes after two. And that's all he believes. Or at least those are his favorite beliefs, and he believes them. That's what he believes. So I don't need to use truth at all in that position. But now, suppose that what you really believe is sort of the generalization all the way up through, you know, infinity, for all the natural numbers, right? JJ believes one comes before two, and two comes before three, and I'm going to now change what I said before just to make the example. Three comes before four, four comes before five, and so on. Notice that I can never communicate what you believe in a finite amount of time. Right. Unless I have some device that allows me to say exactly what we want to say, but do it without needing to find an infinite amount of time. Here's how I just say, take the set of all claims of the form n comes before n plus one. JJ believes that all of those are true. That claim that JJ believes all of them are true is absolutely equivalent to saying JJ believes one comes before two, two comes before three, three comes before four. So that's why I say God, of course, could just zip through all your infinitely many beliefs. Never needs to say true or anything like that. JJ believes this, believes that, and so on. We can't do that. So we have this device in the language that allows us to technically, it's called quantifying into the subject position there where you have sentences. And we say, you know, for any X of X is in that set, then JJ believes X is true. Okay. So for those who have never heard that before that might be a little complicated, but remember the question that that's supposed to answer is, if, if ascribing truth to a sentence adds no new consequences to the to what the sentence would have had. Why on earth do we have it? Well, the reason we have it is just for practical reasons. It allows us to say true things in our finite situation. So it's like truth is, it's like a shortcut here because you have a generalization. Yeah, so you use the two concept as a shortcut for that. That's exactly right. It's a shortcut, but that's exactly why I say God could describe all of reality without ever using the truth predicate. And he'd leave nothing out. He'd describe all of reality and leave nothing out without ever using the truth predicate. We have to use it because we're, you know, we have no other option. We can't go through the claims and so on. Yeah, so I like that motivation. So because we are finite teachers and we're talking about some something infinite, we need some kind of shortcut, perhaps a heuristic device for this one. Now, in your work, you use the metaphor of spandrels to describe transparent truth. So, by the way, JC's work is this book, Spandrels of Truth. So what do you mean by this spandles of truth idea? Well, the evolutionary biologists, Gould and Lou Wanton, they took an architectural term, spandrels, which applied to certain inevitable features of an architectural structure. And that's what it was, an architecture. And they applied it more generally to evolution. And they said, for example, okay, they didn't say this, but here's a way of seeing the idea. Somebody might say, you know, why did Mother Nature select the trait of having fingers on human hands, right? And the answer, of course, as well, that made humans better able to survive and thrive because you can grip things and so on. Okay, fine. Now, why did Mother Nature select to have a V shape between the fingers? And so you can imagine one way of doing biology is to think, yeah, there must be, there must be an answer, there must be an answer. And trying to figure out, well, why pick that shape, you know. And the other way is to treat it as a spandrel of the selection of fingers. So if you select having four fingers just so, you inevitably have a V shape between them. So it's an inevitable, often unintended side effect of selecting this feature, okay? So you bring these things into an environment just so you cannot but bring these shapes into the environment. So those are spandrels. And in the end, you don't need to ask, why did Mother Nature select those? That's the wrong question. Those are just spandrels of Mother Nature selecting having four fingers just so. Okay. So I took that idea and thought, well, that's very much like truth, transparent truth. So we spoke a language where, as I said, there's no property of truth in the world where we need a predicate to name it. Like there are trees, so we need is a tree. There's this, there's that. But we don't need, there's no property of truth in the world that we need to bring in a predicate and name the thing. But for reasons we went through, and I wasn't very clear in my account of it, but for reasons we went through, remember trying to describe the infinite theory that JJ endorses ones below two and so on and so on and so on. We needed a device that allows us to make those claims. So we brought the truth predicate into the language that we have, and in that linguistic environment, and bringing that in is going to have inevitable and often unintended side effects. And one of the side effects is that you have sentences, new sentences of the language that you would never have had before bringing that thing in. And these are, so when you bring in a transparent truth predicate or a transparent falsity predicate, you're going to have new sentences that in absolutely no way would exist until you brought that those predicates into the language. So, and these of course are the famous paradoxes. Okay, so let's get into that. So one of the biggest problem about the notion of truth is the liar paradox. So this is one of the unintended consequences. So putting in that predicate, right. So any theory of truth should come to terms with it. So can you tell us something about this problem. Yeah. So the So as I said before, let's let's say that we've for the generalizing purposes at hand remember God didn't need to use a truth predicate or a falsity predicate God can describe everything without using we bring them in for our own practical purposes. If I want to say everything in JJ's theory is false. Just using, you know, the generalizing falsity predicate. I'm not pointing to some important property in the world falsity or anything like that. I'm just saying that it's transparently false. Not in the nebistemic way, but in this transparent truth. Yeah, yeah. Okay. So, so we bring in the predicate false for these practical purposes only. But once we do the grammar of the language into which we introduce these things automatically generates sentences that you didn't have before, such as you know, as a sentence like this. I don't know if you can see it. Is that Yes, it's a red sentence. The red sentence is false. Yeah. Yeah. So there's no way you'd ever be able to formulate that it would never count as a sentence in the language until you introduce this this falsity predicate. But not only do you have these weird sentences coming about. But they're actually they're called paradoxes because they they challenge a number of the challenge our theories in a number of different ways. So if you take the sentence I gave you the red sentence is false. Is that showing up I can't really see. Yeah, I could read it the red sentence is false and it's in color red. Yeah, yeah, yeah. So if you look at if you take that sentence right. The standard argument or the standard account of logic tells us that every sentence is true or false. So that sentence has to be true or false. If it's true, then of course, well what it says is correct. So the red sentence is false. So if it's true, then it's false. But of course, so you might say well that's not right. So now go to the other side. If it's false, well then of course what it's saying is true. It's saying it itself is false and it's truly describing that. So on the standard account of logic this thing this new sentence has to be either true or false. And but in either case, given the rules of truth and falsity that the rules that are definitive of this device. If it's either true or false, it's going to be both true and false as we saw. If it is true, then it has to be false. So it's true and false. If it's false, it has to be true. So again, it's false and true. Okay, so I'm trying to make sense of the liar paradox is one of the oldest paradoxes we have in philosophy. So we start with a sentence something like this one, the statement is false or the red sentence is false. Okay, and so on. So you have those sentences. It's generated because you have the truth and falsity predicate in your language. So you could use those things to talk about well sentences themselves. But there's another feature that you're talking about the principle that a sentence at least common sense would tell us is either true or false. So I think this is known as the law of excluded middle. Correct. Correct. Yeah. So, yeah, when I said the standard account of logic tells us it gives us, as you say, the so-called law of excluded middle, which says every sentence is true or it's false. I mean, that can be represented sort of as a form, either a or not a for all sentences a. But that given transparent truth and transparent falsity that form will just be equivalent to saying every sentence is true or false. And moreover, the standard account of logic gives us the so-called dual of excluded middle, which is that no statement is both true and false. But this kind of statement, this liar, if the standard account of logic is correct, we have excluded middle and it's dual. Excluded middle tells us that this statement is either true or it's false and given the way truth and falsity work, if it's true, then it's false. And if it's false, then it's true. Either way, it's true and false. But again, from standard logic, if a statement is true and false, then, you know, absurdity follows like your worst nightmare. So one thing that these statements challenge and the reason the liar paradox is so, yeah, as you said, it's a very difficult thing. It challenges our very concept or the very account of logic. Now, some people say it challenges our very concept of truth. Well, that may be so. In fact, a colleague of mine, Michael Glansberg, he's a real believer in this kind of thing that it challenges not our account of logic, but it challenges our concept of truth. Maybe so, but it's not, I mean, if you think that truth is transparent, then what's there to challenge? I mean, you've just had those rules that you can substitute true P for P and false P for not P and anywhere. And so it's, there's not like some concept that's being challenged here. It's just a device that we introduced. So you'd have to, you'd have to reject that there's any such device. And someone like Glansberg would, but I find that, I find that a bit difficult to, to accept. Yeah. Yeah, so let's go to the solutions to the liar paradox. So there are so-called standard or classical solutions and there are non classical or non standard solutions. The classical solutions abide by the laws of classical logic. So, yeah, we talked about the law of excluded middle in its jewel, the law of non contradiction. So you have those things. So for classical theorists, they'll say, well, we need to abide by the laws of logic. So there's something wrong with the sentence itself. Yes, correct. Yeah. So on the other hand, the non classical solutions would say, well, there's something wrong with the logic, perhaps. So they will deny one of those laws that we have talked about. That's correct. Yeah. So how do these solutions work? Let's start with the classical solutions first. So, So let me talk about So under that description, let me talk about three general approaches. And there are many that fall under these various approaches and none of the approaches may fit exactly what I'm going to say, but, but given your characterization, which is pretty good for just a general characterization. There are basically three approaches. One is often called Tarskian, which I'll mention, and then one is I'm going to call it sort of propositional or non Tarskian but hierarchical and oftentimes these get to be called contextual. So the way Michael Glansberg or Charles Parsons or Tyler Burge, they, they instead of hierarchy of languages, they talk about a bunch of different contexts. So Tarskian, I'm going to call it propositional, even though none of them would like that. And then there's the revision theory of Gupta and Gupta and Belknap. And I need to note though that Gupta and Belknap's account is compatible with classical logic, but it's also they pride themselves in their account being compatible with no matter what logic you pick. Their account is going to be fine with that. I mean, there's some restrictions on that, but so their account is really special in that way, but I'm not going to say a lot about it only because it falls out of a more general account of circular concepts, and you have to accept that truth is circular in their sense. It's a powerful research program, an interesting solution to liar paradox. But let me just focus on the Tarskian and propositional. Okay. The Tarskian one is so called because it traces back to upper Tarski. Tarski though was clear that he didn't see a solution to the liar paradox as it emerges in natural language. So he was talking about how could you have a formal theory so very precise and and and so on. That's not really natural language. He said natural language. The thing about it is it can wiggle around and do whatever you want to and that's its strength and its weakness is you can't sort of bind it. in the way you can a formal language. So Tarski was just showing that there are ways of avoiding the liar in a formal setting. And I'll tell you about it in one moment, but many people and they talk about a Tarski and solution actually sort of think of it as applying to natural language. And the idea is just this anytime you have a liar sentence, that's a sentence that appears to arise within a given language. But imagine that the true description of linguistic reality is like this. You have a base language that does not contain its own true falsity predicate. So that's a sort of very elementary one that cannot in any way have a liar sentence because there's no falsity predicate there's no truth predicate. Okay, now step up one level to language to the to the first language up that language also doesn't have its own truth or falsity predicate, but it has a truth and falsity predicate. It's just that that one is restricted to the language below. So when you say a sentence is true what you're really saying is a sentence in the language below is true, or a sentence in the language below is false, and so on and so on. So you get this Tarski and hierarchy of languages with truth predicates, but no language in that hierarchy has a truth predicate for itself. Okay. So basically you're just saying that liar sentences don't arise they're just not really there. And you're trying to explain how that's that struck many I think including Tarski although I'm not a historian, but it strikes many as completely. It's just nearly impossible to believe that natural language doesn't have a truth and falsity predicate that can apply to sentences within the same language. Okay, so that's one approach a classical, then there's the what I'm calling the note that the propositional often these get cast out as contextual solutions, and basically the idea is this, when you look at the red sentence, you know the red sentence is false. Basically, this thing gets evaluated as as neither true nor false. It doesn't express a proposition to use the technical machinery that they wanted to use. Okay. But now, because language is so resourceful. A new sort of thing springs up. Can you see this. I wish I could see it's not complete. Can you. Yeah. Okay, so either the blue sentences falls or it is neither true nor false. Yeah, so this is a different one. Remember the solution to the red sentence was that it didn't express a proposition. So it's it's And they say classical logic is correct, but it applies only to sentences that express proposition. So they're relying on this machinery of propositions but So the this original liar this this sentence is false. That is neither true nor false because it doesn't express a proposition and because it doesn't express proposition excluded middle and the rest doesn't even apply to it. Okay. Okay, but now think about the blue sentence that as I said, it's the sentence says of itself only that either it is false or it's neither true nor false. Well, if you say it's neither true nor false, then the sentence has at least one true disjunct. So what they want to say is that in effect, a sentence like this to it's not going to express a proposition, but there's going to be a context in which this is true. But it's going to be speaking of a sentence in a prior context. So where Tarski sort of went up a series of languages and said that no language has its own truth predicate the proposition no proposition or contextualist accounts say, No, no, he's wrong about that language English, for example, any natural language has its own truth of falsity predicate. But it's tied to context. So when we say, we can say truly that the blue sentence is either false or it's neither true or false. It's just that we're in a context that expresses a proposition about the sentence before and in different contexts. So anyway, yeah, yeah, yeah. So that's the classical and it's way too fast and and I'll try to be less complicated but I fear, like, if I say less than I'm being even more misleading than I already have. Yeah, that's all right. So I'm trying to grasp the classical solution. So the classical solutions want to preserve the loss of logic that we have discussed so log the school in the middle law of non contradiction. So one way of preserving those things is by saying like Tarski you have a hierarchy of sentences and each sentence is a truth predicate but it can't refer to itself so it's not a referential to predicate. So the higher you go up, the lower you go down in truth predicate. So for example, you have a meta language. So the meta language talks about the object language below and the truth predicate for the meta language in the meta language is attributed to the object language. So that's what's going on there. And until you have the whole series of the hierarchy, the other theory is you're calling it propositional. So, yeah, contextual. So the original liar sentence is not a proposition does not express a proposition. So it does not really, it's not a true nor false because it's not expressing any proposition. However, the revenge puzzle that you have given the blue one, it's a disjunction. So, yeah, it should express some proposition because one part would be true. The neither true nor false part would be true. So one way that this contextual is or the proposition people will will solve this one is to say that well it's the given context that gives the truth value for this. Am I getting the two solutions? That's correct. Yeah, yeah, yeah. No, that's exactly right. Yeah. Okay, so let's go now to the non classical solutions, which show the non that you prefer. Right. Yeah, yeah, yeah, I was going to say the non classical ones are very easy to describe. We can basically just say that they're correct. Okay. Now so whereas the classical ones as you put it well they want to say look, our account of logic is correct. But we have to but our account of truth. As it applies to sentences is more complicated than we thought. For a transparent truth theories that's just not an option, because transparent truth is really easy to describe it's just, you know, you bring this device in and applying it to us to to a sentence is inter substitutable with the sentence. So that there's no, there's no more complication that's just the device that's what it is. So non classical solutions tend to think okay well it's not truth that's complicated that we need to figure out we know what that is. Rather there's some problem with logic and here you're either going to just to keep things simple you're just going to reject either excluded middle. Here you're going to think that logic does not demand that every sentence be true or false, or you're going to reject a non contradiction logic does not say that no sentence can be true and false. So the view that I actually hold is that the right account of logic is one where both of those principles fall away. And once you get away from those then of course you don't have so much of a problem from these liar type sentences as an interesting phenomenon that you know that's sort of rare entity where there are these true and false things or these neither true nor false things. These, to me, seem like mirror images of each other or so, you know to say that neither true nor false or both and so on. There might not be a lot of statements in the world like that, but here, here are a couple weird ones. I tend to think of this nonclassicality as fairly tame, because the accounts of logic that tend to be a part of this in this context tend to be what are called sub classical logics, and these are just slightly weaker than classical but if, if, so if a sentence is, or sorry, if, let me say argument of an argument is valid according to this weaker thing. Then it's valid classically. And so the one is a sort of sub relation from the other. And the picture here is just that what we learned from the paradoxes is that the standard mainstream account of logic so called classical logic just overshot the mark. It classified too many things as valid. And that's it's real. That's it's only problem. There are more in my eyes, but this is completely a contentious way of putting it. There are some more non classical solutions that are much more radically non classical. And there's a lot of activity right now. A lot of activity around so called substructural approaches to paradox and very fascinating work, important work, but probably best that that I leave that to your listeners to look up. Okay, so yeah, so the non classical solutions just to review, you have either you deny the law of non contradiction or the law of excluded middle or both, right. So yeah, the ones where we talked about yes. So either way, you'll you'll still get your transparent to but you have to let go of one of those principles and larger. So that's basically the idea. So where does the gap do you and the glut view come in here. So, so a gap is a sentence that's neither true nor false. It's it falls in the gap between truth and falsity. And a glut is the dual it's it's it's a glut of truth and falsity it's a sentence that's both true and false. So you have both true and false to be applying at the same time to the sentence, whereas a gap is the sentence that falls in between the two. That's the picture the metaphor. And gluts are our sentences that serve as counter examples to non contradiction and gaps are counter examples to excluded middle. And, you know, I tend to think that the truth truth maker sentence or sorry truth teller sentence a sentence that says I'm true. Right. Well, if it's true it's true. It's false. It's false. Okay, but looks like there's not a whole lot. This one looks sort of like you might want to say naturally, it's gappy. It's neither true nor false. But something that says I'm false. If it's true, it's false. If it's false, it's true. Now without excluded middle you can't deduce that it's both. But in other work I've pointed out that we are never led in our systematic theorizing by logic alone were led also by a methodological drive to classify all sentences as either true or false and do so by principles of natural mess and so on. So if you look at the statement on the statement on the screen right this statement is false. We want to classify it as either true or false because we're driven by the quest for completeness. Well, if we say it's true. Okay, it's also false. If you say it's false. Okay, it's also true. So if we if we classify one way or the other. We've got to classify as both and now you have to ask, would classifying it as both be a natural account of it. And I say, of course it would this thing all it says of the only thing it says is I'm false. And given the way falsity and truth work. That's crying out to be classified as as a glut as a lot of truth and falsity is both true and false. Okay, but it's a glut because of how natural language works and how the truth predicate works right. That's correct. That's correct. Yeah, yeah, yeah, yeah. That's why your view was labeled as semantic, merely semantic. Yeah, yeah, yeah, that's correct. That's correct. Yeah, so in the spandrels book. I was working out a position where there are no gluts except for the spandrels of truth. So in that and remember the metaphor of God, not God being able to describe all of reality without truth and falsity. Nonetheless, we have these sentences. But they're sort of like, in some way, like, merely semantic or you might even say, although I don't say this, but you might even say something like they're almost like epiphenomenal, right there. But nonetheless, so the simply semantic glut theory that that I was advancing there was that everything else is perfectly classical, and only the spandrels of truth are the gluts. I've since matured a little bit, and I think actually, reality is more, more involved. I think that there are other sorts of gluts and certainly gaps and so on. But that will take us off topic. So I'll leave that there. Okay, so you and Greg Restall have advocated logical pluralism. You have a whole book on this one. So what does this view all about? Logical pluralism. Well, I should warn you that because of some of my recent views, my, my collaborator and one of my all time closest friends, Greg Restall, he's accused me of no longer being a logical pluralist. So, so take what I'm about to say, you may have to do a follow up interview with Greg. But I'm going to. So, so I'll give you sort of the way the view given in the book, which is just we say that that the concept of logical consequence is, is sort of precise only up to a certain point. And we, we, we talk of that point being a certain recipe. Basically, it's, it's, it's like a schema. Okay, it's, it's basically the argument from this sentence to this or this set of sentences to this sentence is valid. Sub X, if and only if there's no case sub X, in which all the premises are true, and the conclusion isn't now what what's with the sub X stuff. Well, we point out that depending on what you say about cases and counter examples, you get a different relation of logical consequence. So again, we said that the concept of logical consequence is settled down to that recipe, namely that this is a logical consequence of that if and only if there's no case in which all of this is true. And the other, the conclusion is not. But what do we mean by case here why you can mean possible world you can mean impossible world you can mean situation you could mean a whole slew of things that construction as in constructivist mathematics. And depending on what you say there, you get different relations of logical consequence. Now, one person a monist might say yeah but only one of them gets things right. And we said, well, no, I mean, what exactly would it be to get things right here I mean, if the notion of logical consequences only settled up to the point that we say it is, then you get lots of relations of logical consequence out of that settled poor. There's a bit more to it than that we say that any such relation to count as an admissible instance of that recipe has to have various features necessity formality normativity, but then many, many, many instances have those. So that's the basic idea, and of logical pluralism, I guess, one thing that's key and this is partly where Greg accuses me of not being a pluralist anymore and he's joined by a colleague of his Sean Standifer who also accuses me of not being a Noticed that if you look at the book, Greg and I do not demand that logical consequence, no matter which relation logical consequence you may be talking about, we do not demand that to be an admissible instance of that recipe, you have to play a particular role. Okay, that means that how one of these relations winds up being used in our pursuit of truth or theorizing or whatever just doesn't matter, you're still a relation logical consequence you are, you are logic. Okay, I've, I completely agree with that so I'm a pluralist on in that way, but you might think that there's a strong tradition. According to which the role of logical consequence is to be the sort of fundamental universal consequence relation in all of our true theories. So people talked in the in the old days, and they still do but logical vocabulary being topic neutral doesn't matter. It doesn't matter what your theory is about what topic logical vocabulary, the logical vocabulary is part of the language of your theory, if your theories to be aiming to be as complete as possible with respect to the phenomenon. Under discussion. So if you take logical if you say sure there are all these logical consequence relations per the bill rest rest all accounts no problem but if we're going to debate whether logic is non classical, or logic is classical. We have to demand more of what counts as logic. And I've said, look, a good way of doing that is to point to this role, the sort of universal consequence relation at the bottom of all of our true theories governing the topic neutral vocabulary. And, and so when you ask me what relation is that I'm a monist about that. Yeah, yeah, and I think Greg is actually he told me once that he he's a pluralist about that but we, we, we're in the middle of his family room and he was also very kindly making dinner and so I can't. I'm not sure like how how that went but I think Greg's a pluralist about even that, and I don't understand that. But it's a I mean I find it fascinating I would like I need to follow up with him. Yeah, so I said I understand your, your view now you're more mature view is that there's some minimum base of logical relations that you could accept logical consequence relation and for you that's the kind of first degree entailment. And for every phenomenon or for the next phenomenon that you will describe perhaps you add another bit of logic there so. Yeah, yeah, yeah, that's exactly right. So that's a picture that you're coming up with now. Correct. Correct. So, finally, on a more personal note, you got a you got a pretty dynamic philosophical career with all your published books and papers and all the teaching posts you got over the years so you're there from Yukon now you're in Notre Dame. But how did you get into philosophy in the first place what drove you to a career in academic philosophy. I grew up in a sort of and discussing theology and that and, you know, sort of systematic theology kind of things was common. And so I was exposed to that and that in the end is very philosophical. I went to a small liberal arts college for my undergrad college it's a university level, but in the US liberal arts college is a common term. And this is a sort of, you know, you do some mathematics you do some philosophy just history and that kind of thing, and some religious studies at the place. And I, you know, I was, I had some talent mathematically, and I had some talent, philosophically, but when I was at college as an undergrad I didn't. I didn't really understand what sort of analytic philosophy was I don't think I was ever exposed to that. But I went on to work in philosophical theology I went to do a master's in that thinking that's really what I like. And then I got exposed to analytic philosophy in a completely indirect way. And then I just sort of, it just all came naturally, my enjoyment of it, my fascination with, and the way it's done, you know, it's, it's, so if you're, if you find sort of logic and mathematical sort of things very natural. And that philosophy is very, it's very, it too is very natural. So I guess I just fell into it, and I got very lucky, you know, that I, I had the opportunity to pursue certain ideas and yeah, so yeah, I just fell into it naturally, I guess. So what's your advice to beginning philosophers, how can they keep the dynamism that you have. Well, I think an important thing. So I've learned this over the years. I mean, you know, when I was, when I was earlier, before I had my first job. Right. I was doing philosophy. I just loved it. You know, you think about children, little children, they go around the world. And they're just like, fascinated with everything. Right. You know, they see a little window latch, and they're fascinated. You know, it's in everything was just fascinating to them. And I think when I was before I had my first job. I couldn't get enough sort of ideas and I was I was fascinated with them. In fact, my problem was I would never stay with one idea long enough to actually, you know, I was just, I, there were so many things that were exciting. And then I got my first job and I had to work hard to really commit to a sort of discipline program of making sure that, you know, when I have ideas to write them down enough that I can then, you know, write out a paper and get that done. But also, you know, you sort of, you get to a point where you feel like there's not a lot more that surprising, like you sort of predict what so and so will say and this and that. And you can get into a rut. And so I set all that background, because I think one important thing to say to younger people in philosophy is, don't lose the sort of eye of the child like, yeah, it's a job, you know, if you, you know, if you're successful at landing a job and and it's not easy, you know, and it takes patience and hard work, but, and a lot of luck. But, you know, you land the job. Try to avoid. No, try to cling to that to the sort of eye of a child don't allow yourself to think that you know what's coming like always try to see something new in in things in philosophical claims in non philosophical claims. And, and so that's the first thing I have a child. And that's something I constantly trying to do myself. But, and that just keeps your brain alert and it keeps you sort of humble and it keeps you listening to other philosophers, because, you know, if you think that you know what they're going to say, or you think you know, you know, you'd stop listening, but if you actually listen to them in a genuine way because you're, you know, you want to hear what they have to say. And you just want to hear you want to sort of figure out what they're talking about. That's a really good state to be in. That's the number one I have a child number two, make sure that you write down your ideas. So most of my career, I've always carried around notebooks. A good friend and former student and now colleague in the field Dave Ripley. When he was a student, he used to carry around three by five cards. And I must say he was probably smarter than I was because I always carried around notebooks that I couldn't fit in my pocket. And sometimes I'd forget I'd leave it in a room and Dave would always have his three by five cards. Don't ever leave home without them. Like you must always have these cards and be disciplined about writing down an idea. Many of the ideas won't pan out, but some of them will. And yeah, and then so those are the two top tips I would give to budding philosophers. Yeah, and then just keep at it, I guess. Is the career worth it being an academic philosopher. I think it is. I mean, I, I, I love what I do. That's not to say I love everything I do. There's, you know, there's some administrative things and and that can be hard, because sometimes you're not clear why you're even doing this. But look, I mean, there are lots of, you know, every job is going to have that that aspect of it. I don't care what the job is, they're going to be some things that you're doing and you're not sure whether you should but you know you need to do it. And, but I think a career and academic philosophy is very much worth it. Do I think that everyone who does a PhD in philosophy or a bachelor's of arts in philosophy or a master's of arts in philosophy, any degree in academic philosophy, do I think that the goal should be to be an academic philosopher? No, I do not. I think that I think that people should, people will benefit from doing academic philosophy, but whether you should do it as a job depends on depends on your other talents, your desires and your situation. And, but for me, yes, it works. And I'm, I'm very grateful to have the job I do. But I can imagine somebody with the same interests as my as me. And same degrees, same everything. And, you know, they do something else entirely like the other job I would love, by the way, is being a farmer, but I know that I wouldn't, I wouldn't do it. I love being on farms. I love that sort of thing because it's so different from what I do for a living. But it's also extremely difficult to make a living as a farmer. But anyway. Okay, so thanks for that, JC. Thanks for sharing your time with us. So join me again for another episode of philosophy and what matters where we talk about things that matter from a philosophical point of view. Thanks. Thank you.