Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas - 178 | Jody Azzouni on What Is and Isn't Real

Episode Date: January 3, 2022

Are numbers real? What does that even mean? You can't kick a number. But you can talk about numbers in useful ways, and we use numbers to talk about the real world. There's surely a kind of reality there. On the other hand, Luke Skywalker isn't a real person, but we talk about him all the time. Maybe we can talk about unreal things in useful ways. Jody Azzouni is one of the leading contemporary advocates of nominalism, the view that abstract objects are not "things," they are merely labels we use in talking about things. A deeply philosophical issue, but one that has implications for how we think about physics and the laws of nature. Support Mindscape on Patreon. Jody Azzouni received his Ph.D. in philosophy from the City University of New York. He is currently a professor of philosophy at Tufts University. In addition to his philosophical work, he is an active writer of fiction and poetry. Web site Tufts web page PhilPeople profile Amazon author page Wikipedia PoemHunter page

Free is great, but only if it's useful. Free credit scores from some apps can differ by as much as 100 points from your actual FICO score that 90% of top lenders use when you apply for a credit card, personal loan, car loan, or mortgage. That can mean a higher interest rate, a bigger monthly payment, or worse. Denied. My FICO gives you your actual FICO score, the score lenders use straight from the company that created it. For the moments that matter, get the score that matters, your FICO score. Visit MyFICO.com and get started for free today.

Aging is real, and so are the benefits of adding vital proteins collagen peptides to your daily routine. New vital proteins collagen sparkling water. Your daily glow-up now in three fresh flavors. Strawberry blossom, lemon, lime, and blood orange. Improved skin health in as little as 30 days thanks to collagen peptides? Cheers to that. Or go with our classic collagen peptides. So you can stay vital, stay you.

Visit vital proteins.com to learn more and where to buy. These statements have not been evaluated by the Food and Drug Administration. This product is not intended to diagnose, treat, cure. or prevent any disease. Hello, everyone. Welcome to the Mindscape podcast. I'm your host, Sean Carroll. Welcome to 2022, a whole new year.

I hope you're all excited for the new year. It's getting harder and harder to say, you know, very excited about the new year when previous years have been a bit of a downer with the pandemic and other things, but still, hoping things get better in this year. We're going to start the new year with a big one, the question of what is real, really?

We have talked about this question before, but interestingly, it's a question that, physicists don't like to talk about. You would think that physicists who care about the structure and reality of the physical world would care a lot about what is real and what is not, but they're much more operational. They're much more down to earth than that, most physicists. They want to know what they're going to see in their experiments. And, you know, at the boundaries when it comes to like virtual particles or the multiverse or something like that, there are some things they're not sure, whether it should qualify as real or not. And they don't like to talk about that. It sort of gets them

all discomfited, whereas philosophers love to talk about what is real. So that's what we're going to do today with philosopher Jodi Azuni. And Jody has a relatively extremist point of view on these questions. He is what is called a nominalist. So nominalism goes back, I think, to William of Akum, of Akum's Razor fame. And nominalism is the idea that abstract objects don't exist. So it's in contrast with something like Platonism, Platonism about math, for example, would say that mathematical structures and ideas exist. They're real in some sense. As previous podcast guest, Justin Clark Donne said, that doesn't mean that they're out there somewhere. There's not, what did he call it, plutonium or something like that, some place where you find perfect triangles, et cetera.

But there's a reality to these mathematical structures. For example, if it weren't true, why is it so useful to use math when discussing the real world. So a lot of mathematicians are Platonists. They think that mathematical structures have some reality to them. Nominalism is a relatively minority position, at least among philosophers of math. So Jodi Azuni is here to give you the epilogia for nominalism. So here's why this is an interesting question. You might say something like, look, if you don't believe numbers exist, then you don't believe prime numbers exist. So how could you say something like there are prime numbers between 10 and 20 if you don't think of there are any prime numbers at all?

Just talking about math, it would seem, so the argument goes, implies or takes for granted the existence of these actual things. And so what Jody's going to say is something like, I'll let him put it in his own words, But it's something like, look, Sherlock Holmes doesn't exist. It was not a real person named Sherlock Holmes, but we constantly talk about Sherlock Holmes, as Jody will say, we say that Sherlock Holmes is smarter than Mickey Mouse. We're comparing the relative smartness of two things that don't exist. So it is possible to talk about things that don't exist in a useful way.

Now, math is trickier than that. I myself am somewhat on the nominalist side. I'm sympathetic to it, but my understanding of the foundations of mathematics and the philosophy of mathematics is not nearly good enough for me to be very convinced in my own point of view. That's why I wanted to talk to one of the experts here. And we'll get into why it matters, right? I mean, who cares? What exists and not? As long as we can make predictions for what we're actually going to experience, well, I think it does matter.

And I think that our goal should be more than to just know what will happen next in the world. Our goal should be some understanding of what the world is and how it behaves, and that involves what parts of the world are real and what parts are kind of stories that we want to tell along the way that are helpful or entertaining to us, but are not latching on to any reality that is actually out there. So even though I have an opinion here, I'm still pretty open-minded about it. I want to explore this, and I think this podcast is a very good way of getting there. Also because Jody is very good at words. He is a published poet quite successfully, likes talking, likes writing.

He expresses himself in a very entertaining and also extremely clear way. So this is going to be a good way to start the new year. Let's go. Jody Azuni, welcome to the Modicay podcast. Glad to be here. Let's talk about what is real. Don't tell me yet what is real, but let's talk about the question, what is real. But let's talk about the question what is real

because it's interesting that as a physicist, I talk to my friends who are physicists, they don't care what is real. They get very nervous when you start asking questions about that. They think you're being too philosophical, which is fascinating to me, because if anyone should care what's real, I think it is a physicist.

So, I mean, maybe give the sales pitch for why we should care about what is real and what is not real. Well, I mean, my pitch for that, Because as you can gather, there are certainly philosophers who say, this is not an interesting question, or this is a bogus question, or this is a fake question. And for me, it's not a fake question because of, of course, in the background, what I think when you're asking, if something is real, what you're really asking. And I think, you know, we have a picture of things that are kind of, and I'm going to speak very roughly. things that are kind of independent of us and other things that aren't independent of us.

Okay. So my go-to example is always Sherlock Holmes, you know? Now, there's a sense in which the concept and the ideas and the stories and the material about Sherlock Holmes is independent of me anyway, right? I can get Sherlock Holmes wrong in certain respects, and people do. And you might uncover a notebook of Doyles in which you find out, okay, here's what was really going on with Sherlock Holmes. And then you can see the text is weirdly hermeneutical. And there's things, you know, that can happen. Nevertheless, it's not independent of Sherlock, of Doyle.

You know, Doyle, you know, pen and hands and, and, eh, I want to go this way. I want to go that way, blah, blah, blah. You don't get to do that with things that are real, okay? Even the things that are real that you can affect, for example, aspects and states to some extent of your own brain, you can't do it by just pen in hand, let me change that, you know? You got to put, there's a process. And to me, I call that sometimes mind and language independent. Okay. And I say that's a criterion for what's real.

There's a little bit of complexity here, but that's roughly the idea. Why do we care? Because we want to separate what we're making up from what we're not. Now, there are philosophers, almost all major philosophers up until, say, oh, the 1980s. and I'm thinking of people like Putnam, like Quine, you know, thought you can't drive a wedge between these things. You can't separate, you know, what you're making up and what you're not, what you're projecting onto the world and what's really there. I actually think that's wrong. I don't think it's easy.

A few books have been written. Well, you know, that's why I end up writing a lot of books. I mean, it's not just to make sure that I have a job. it's because it's kind of complicated. So just take what our senses present to us, what we see. A lot of what we see indicates what's really out there. But a lot of what we see is a projection of our biology, of our culture, all mixed up. So it's not an easy thing to do, but I think it's a real distinction.

And we care about it because when we get down to, You know, how is the world working? How are things happening? You know, how's, we want it. It's the real stuff that's telling us. That's the motor. So that's why we care. I think that makes sense. But, I mean, let's make, let people in on all the various ways in which it's a complicated question, right? Before getting to what the right answers are, we can bring up some edge cases. Like most of us agree that Sherlock Holmes is not real. Although even there, Conan Doyle wrote about him. there's a sense in which he's real, but he's a fictional character, okay, but what about things like, ultimately I want to get to like physics and math, but what about things like a country or a family? Do those count as real? Perfect examples, okay? Perfect examples. Look, for the time being, let's say that pretty much our description of human beings is real. You know, what a human being? And that's complicated, too, because our picture of a human being is a very complex notion that involves norms of various sorts and other things as well as just the sheer physical presence of a bunch of cells coordinated for a while, right?

But what's going on is that let's just go with that for the moment. What's a country? Well, it's really quite subtle. There are things that are real in a country or constituting a country, and there are things that aren't. So with something like a country, you've got to analyze it. You don't simply, you know, go a certain way. Now, look, something important is kicking in here with the words. Yeah.

Okay. When we start talking about banks, countries, borders, right? We, human beings, I don't, this doesn't happen in other species as far as I know, but human beings automatically think a thing. Yeah. A thing with properties, you know, and they go even further. I mean, here, you read the economist, for example, right? I read it.

And the economist, you know, tries to be pretty rigorous in its way. Nevertheless, you hear things, you read things all the time like China is not happy with the U.S. policy regarding such and such, okay? And I look at that and I say, okay, you know, there are two things going on. One of them is how else are they supposed to convey a certain aspect of Chinese policy? We don't have a different way of doing it. Second of all, doesn't really follow that there's this thing, China, that's, you know, has attitudes? No.

Well, maybe it's short-hand for the individuals in China that are ruling the place. That's not so straightforward. Okay? So again, it's a subtlety. But in point of fact, the borderline cases invariably turn out to be like this. They're not straightforward cases of something that exists. They are a complex blend of stuff that does exist. coupled with our ways of packaging and bundling how we think about it.

So you said something I think that makes perfect sense to me about our linguistic way of grasping these ideas. Like we have a way of talking about tables and chairs. Let's for the moment say the tables and chairs are real. And we have a way of talking about them, you know, moving them. They have an impact. They have causal powers, et cetera. And it just is natural for us to then use the same kind of linguistic. strategies when we talk about more abstract things like countries and families.

Right. But can I stop you just for a second? You're absolutely right. It's very natural for us. But don't think it's natural in some broader sense. It's just, this is an aspect of how the human mind works. All human minds. They go, yeah, I talk about tables and chairs this way.

I talk about people this way. I talk about countries this way. I talk about clouds this way. Yeah. Very natural. Yeah. Or fictional characters, for that matter, right? Or fictional characters or mathematical objects.

As we will get to in brain splitting detail, I'm sure. So, okay, but then, so where do you personally come down on the countries aspect? Before we get into details about how we draw the line, are countries real? Do they exist in your ontology? Not them. but what they're composed of elements of them for sure. Okay. Okay.

Same thing for institutions like, oh, I don't know, Microsoft. Right. And again, we implicitly do this when we really start to analyze these things and not just speak vaguely at a certain distance about, ooh, Microsoft has this attitude or is doing this. We start to look at the parts that are real. and ask what's going on with them. Oh, here's a policy that the CEO was pushing. Here's something that was going on. There was a dispute about this. Here are some regulations that are in place. Those end up helping us to predict how the so-called institution is going to move through space and time in certain respects. That's how I picture it. So, you know, at the end of the day, if someone says to me, are you committed to? Are you committed to? the existence of Microsoft, I'm going to say, no, but that doesn't mean I think it's like Sherlock Holmes.

When people turn to telehealth or weight loss, they're looking for real support. That's why more people are choosing orderly meds.com. Orderly meds connects you with real doctors and access to proven GLP1 medications like semaglutide and terseptatide. No guessing, just a more supportive experience, and all shift directly to your door in discrete packaging. Do your research, ask questions, then visit orderlymeds.com slash podcast for an exclusive offer. That's orderlymeds.com slash podcast. Individual results may vary now. Medical advice, eligibility required, C-Sight for details. My best skin ever at 45? Give me a theme song and a best skincare award, because it feels like this, right? Can you feel like there? That's farmhouse fresh skin, all right? I'm blowing,

and everyone asks how. The best skin care? is Farmhouse Fresh, and the award is you, your best you. Visit farmhousefresh skincare.com and use code radio for a free starter routine with any purchase. Well, that's why it's tricky. So one question is, are there different senses of the word exist? Is it possible to have like different levels of existence or something like that? I mean, one attitude might be the word Microsoft or even sentences like Microsoft wants to do the following thing. these are really useful sentences. These convey a lot of information.

They seem to latch on to something real about the world, and therefore we should attribute reality to what they're referring to. Okay, so again, this is complicated. The first thing to point out is, on my view, not every philosopher agrees with this, on my view, the question about the word exists or the phrase there is, or the word real?

Do they have different senses? Are there different senses of there is? Are there different senses of exist? Are these three words different from one another in what they mean? These are purely linguistic questions. These are not philosophical questions. These are questions to be answered by the lexical semanticist. In my view, the answer to the question, for example,

does exist have different meanings is no. Okay? And I claim there are kind of humdrum linguistic tests for that. Okay. Now, the other, so that's one thing. So I'm just going to say that about that bit. Now, here's the other thing. You say, look, you can make certain kinds of statements that are really informative.

Here's an informative statement. It's either true or false. I don't know which it is because I've never done a head count, as it were. there are as many Greek goddesses as Greek gods. Okay? Now, that's either true or false. Okay? I don't know which it is.

But if you ask, well, what's making it true or false? What's not making it true or false is some kind of correspondence? Right. Sure. Okay. If I say there are three chairs in my bedroom, that statement turns out, I'm looking around, that statement turns out to be false. And it's a correspondence question.

You know, there's a word chair. It refers to chairs. How many chairs are in here? None. Okay. So it's false. But there is many Greek gods as goddesses. You don't go around looking at the Greek gods and goddesses to figure out how many there are.

So, yes, the statement is informative and it corresponds in a broad way to a truth. It's a truth that corresponds to a way that the world is, but not because the words in it refer to specific things that exist that are certain ways. Sure. Okay. So I think I get that, but there is a multi-layered distinction here that I want to get right on. So in the case of the Greek gods, we could, if there were some definitive canonical list, answer that question by looking at the list.

And what you're saying is we're not looking at the gods and goddesses to do that. looking at someone's list that someone made up. That's right. And the list is a cultural product diffused from, yeah, yeah, exactly. That makes perfect sense. Yeah, go ahead. But I think that's different to me than the Microsoft question, because when I'm saying that, you know, Microsoft is acting aggressively, that tells me something about the world,

not just about someone's figments of their imagination. Correct. And that's because different kinds of sentences that, don't correspond directly to the world, their relationship to the world differs in different cases. In the case of the fictions, it really just refers to a kind of literary slash movie practice, let's say. In the case of Microsoft, it's going to correspond to something a bit more complicated, namely the actions and decisions and other facts and legal papers that are kicking around that we regard as part of Microsoft in some broad sense of part. Okay.

Okay. Again, it doesn't turn on the object, Microsoft being aggressive. It turns on series of actions carried out by individuals who in various ways are connected to, Microsoft as we understand it. Okay, so I'm just going to, you know, actually I should say that I'm broadly sympathetic to your, most of your points of view here, but it's my job, of course, as the, as the host to pretend to be skeptical at the appropriate times. So I think I buy that. I think I get that, that, you know, we're talking about Microsoft in a way that conveys useful information about the world, but really it's because it conveys useful information about the real things that make up

what we think of as Microsoft. But then wouldn't the same kind of logic, say the tables and chairs don't exist? All that exists is the atoms or the particles that make them up? Yeah, that would follow if you decided that here's a principle of what exists. You know, go for the smallest bits that make it up. And I'm going to say, no, that's not how it works. one of the reasons I'm going to say no that's not quite how it works is because there's nothing wrong with saying that you've got a thing in front of you if the bits are operating in a certain way with respect to each other and going on. Now, you're going to ask me, and you should, okay, what's the principal difference here between a human being made up of a lot of bits and Microsoft being made.

up of a lot of bits. Now, one of the things that's going to go on is that a lot of what's going on with Microsoft doesn't involve little bits that are really in Microsoft. Okay. You don't have. Microsoft isn't in that sense of physical object. It's kind of a stipulated object. And you'd make the same mistake with a bank if you said, well, where, you know, where's the bank physically? And then you say, okay, well, it's all these people and it's these locations in, you know, physical space, you know, the bank offices. And then you find out that HSBC, for example, is kind of, or there are other banks now that are entirely online. And then you go, okay, so where are they located? And you start to realize it's really not the location that's doing the work here.

Sure. It's a stipulated where constituting it out of these things. So what I want to say is that what kind of works in the case of a person where you can actually see, well, you don't see, but you know, you're thinking of the person as literally constituted of little bits that are operating causally in a way and that the causation actually sums up to, in certain respects, the causation that, the person manifests, I'm moving my hand, and now the story you're going to tell ultimately is going to be an anatomical slash molecular slash story about forces. That's not the kind of story you can tell about Microsoft. Okay. I think I actually get it now. Let me try to phrase it back and you can tell me whether I've gotten it. As you said from the beginning, we should attach reality or existence to things that exist independent of our minds in some sense. And if there were no human beings around, there would still be a fact of the matter about whether the coffee cup is sitting on the table.

But if there were no human beings around, there's no facts of the matter about what Microsoft is doing. Because it's entirely something that exists in human minds. Is that fair? That's right. Although there may still be a fact of a lot of the things that were moving around that we treated as part of Microsoft, right? So if you treat a country as geographically located, that geographical spread is real, even if there's no person. Okay. No people, right?

But nevertheless, making it a country, and by the way, of course, geographical spread is hardly all there is to making a country a country. That's important, right? That wouldn't be there, although these other things would be there. So if you treat London, for example, now I'm kind of borrowing an example that I've read dozens of times from Chomsky and quoted because I love it. You know, he talks about London and he says, oh, London is so polluted and dirty, et cetera, that it should be moved upstream 500 miles of the TEM and reap. Right? He talks a certain way. And what you're seeing is a cross conflict, almost, of different ways that we treat London as existing.

as a thing. And those facts could all be there without a London, without people. I mean, imagine it could still be polluted. I mean, pollution is us. But imagine it's still, you know, there's still the geographic location. Imagine, you know, et cetera. You see what I'm saying? Yeah, I do.

Okay. And just to be clear, because some people might have gotten the wrong idea, you're not attaching reality to any special features of spatiotemporal location. I'm not committing myself to that. Yeah. I'm just being illustrative. Sure, exactly. And then what about, I guess the obvious next question there is what about things that are not nouns?

Are properties and relations, do they have existence? I presume the answer is yes if they exist independent of our minds. Okay, so I'm going to describe myself as having gone through two phases. Okay. For a very long time, up until some point in 2017, I was what you might call a Hobbesian nominalist after Thomas Hobbs. And basically the idea was, there are objects, okay? They're careening around. There is also the way objects are, but those aren't things.

Those don't exist. Objects just are certain ways. and we're talking about properties and relations, we're really just talking about objects are in certain ways. Okay. My current view is weird enough and complicated enough that I almost don't want to describe it. But it's something like, look, there really aren't objects or properties

because in order to get your idea of an object, you have to kind of put a border around it in space and time. And you've got to circumvent it, circumscribe it in other ways as well, modally, as philosophers say. And I think all of that's arbitrary. In the sense of it's not in the world. Right. You know, like if you ask yourself, are these borders in the world, are they independent of it? No, there isn't anything like that.

So my current view is that the way reality is, is it's a kind of, all right, I'm going to go horribly metaphorical. I'm so sorry. You know, it's a kind of fabric that's spread out. Okay. And I call it, it's a feature fabric. So they're these features. They're not properties. They're not objects.

You know, it's just a spread of features. I think that's all I want to say about that because, you know, otherwise, I'm going to start sounding zen like or something mystical, weird, scary. I have a book on this, and I hope the book, you know, kind of conveys what I have in mind, but this is a tough one. I know. For our purposes, we might as well just leave me with the Hobbesian nominalism because that makes sense.

That's clear to people, I'm sure. Well, except that, you know, now you're, I can't let it go. because you're bumping right up against literally the research I'm doing right now in quantum mechanics. I just had a paper out earlier this year saying the reality is just a vector in Hilbert space. And what we do is we ask questions about the possible emergent patterns we can find in that single vector in some hugely high-dimensional vector space. And so following someone like Dan Dennett, your colleague, right, at Tufts and his idea of real patterns, if there are ways of describing the world, even if they're just approximate,

at some higher level of abstraction, they should still count as real. Otherwise, you're not going to be able to hold onto tables and chairs, right? Yeah. Now, the thing I want to say, I have not yet officially written about quantum mechanics and this kind of issue. I intend to.

All of this turns on my living long enough, and who knows? So much turns on that. You know. But my own view is, is the emergent patterns that you described, that's real. Yeah, okay. The Hilbert vector space, that's a mathematical formalism. Okay. Now, the reason I think this, in a nutshell, is because there's a strong tendency we have to think,

if I get a characterization of something and that characterization is empirically on the money, that's evidence that everything that characterization talks about mathematically and otherwise exists. I'm going to reject that. I'm going to say what exists is in a certain sense what we get, and now this is my own kind of language, epistemic access to, thick epistemic access to. We need instrumental access. We need manipulation. access, things like that. So I'm happy with the kind of middle-level description of objects they're jumping around, you know, or they're shifting, or they're a wave pattern. I like all that.

And I say, yeah, that is real. But the mathematical formalism that we use to enable us to describe it, even to unbelievably good accuracy, I'm not going to claim that's real. I think that's fine. I'm always sloppy because I am a physicist, not a philosopher. And when I say that reality is a vector in Hilver's face, what I mean is reality is reality. It's sui generis, but it is represented accurately by a very, very, very simple mathematical structure that doesn't a priori have any subpieces. Then we ask afterward, is it possible to describe it in terms of subpieces that have some, you know, real heft to them and find that the answer is yes, et cetera. So I don't think I'm that far away. But then just to be super clear that I'm on the right page, what about something like the velocity of an object?

If the object exists, does its velocity exist, or is that a mathematical abstraction we use to talk about it? It may prove to be a mathematical abstraction. It may not. I mean, again, it depends on the nature of the relations we're looking at, how we're get access to them, what kind of role the mathematical formalism is playing in kind of constituting them? Okay. So velocity in particular, right, seems to be something that we almost stipulate as opposed to accelerations. Yeah. Right. And that is an argument for saying, well, you know, velocity isn't real. Okay. But.

acceleration is. Right. Okay. And this, I kind of do the same thing in a different way when it comes to space time. So for example, in the Newtonian context, let's assume that was right. I would say something like, no, space time isn't real. Okay. It is a way of describing ways that objects are.

It's a relational kind of thing, not a substance. It's not substantial, but more or more. importantly, we don't have to be committed to it. Right. Okay. So the substance, the substantial relational distinction isn't quite mapping onto the distinction I've got in mind. It kind of, it's a cousin.

Okay. Okay. On the other hand, when you end up with space time playing a substantial physical role, containing energy, et cetera, et cetera, you may or may not be dealing with something you should be committed to. And again, it's going to turn on the details of how you get access to it and what role the mathematical formalism is playing, et cetera. So it seems like a disadvantage of this view is that something as basic as the velocity of a car with respect to the road beneath it is something which we don't know whether it's real at the present moment. It's going to depend on

future developments in physics and philosophy. Well, that I think, If somebody was hoping, you know, I want a nice, crisp, straightforward description of what's real that doesn't give any hostages to future science or future thinking, philosophical thinking. I would say, yeah, you're out of luck. You come to the wrong place, yeah. You've come to the wrong place. And I think it was an unreasonable demand. Okay. Okay.

I think the concept of what exists is not that esoteric. That's how we began the interview. But that doesn't mean that the result of discovering what falls under it is going to be straightforward. And I mean, this shows up straight easily in lots of ways. I mean, we're worrying about the subtlety of certain concepts. But, I mean, it comes up, is Bigfoot real or not? That's an empirical question. And I think the answer is no.

So do you, I suspect. But we have other examples that are more subtle, right? That it's not obvious. And yeah, we're beholden to the science to tell us the answer. And that says it should be. I mean, sure. If someone says, is our weekly interacting mass. particles as the dark matter, are they real? Yeah, science hasn't told us yet whether they're real.

That seems different than velocity to me. I like to think that's because you've lived with velocity so long. I mean, I'm going to switch to a mathematical example, which I think is the same thing, as it turns out. So the notion of a group, you're familiar with that. I am, but maybe the folks in the audience aren't. So you can explain. Okay, it's a mathematical. object of a certain sort, a very broad class of mathematical objects that obey certain properties, you can do simple arithmetic with them. That's basically the characterization of a group. You can do multiplication.

Not necessarily multiplication in addition. That would be a ring, but multiplication or addition, however you want to think about it. Now, our normal notion, intuitive notion of a group is it's a class of objects. And I said that to begin with all different kinds of groups, all with different kinds of structure. Our intuitive picture of the natural numbers, 0, 1, 2, 3, 4, 5 going on forever and no more, we have a different intuitive picture of that. Our intuitive picture of that is that's one kind of thing. That's one thing.

The numbers. The numbers, yeah. Turns out there are lots of things that can fit that structure. Okay. That was discovered along with what's called, you know, non-standard models. Okay. You characterize the numbers in piano arithmetic and then you discover, there are lots of things that fit that model. And it's not clear we can get the one we're really thinking of, which is what I just said. Zero, one, two, three, and no more. Because characterizing the and no more is non-trivial. Okay. So, so. So we, but we have a different picture. And the picture is intuitive that, you know, well, we have this intended model when we're talking about the numbers. Whereas we don't have an intended models when we're talking about groups.

I actually don't think there's a real distinction here. So it's the same thing. I think, yeah, lots of different kinds of piano numbers. Right. Okay. Yeah. I'm actually on board with that, but yeah, my friends are not always. So, I mean, maybe this is worth noting for the list.

that is it fair to describe your view as extreme within the world of philosophers? Again, that's something you have to ask other philosophers, but I believe the answer is yes. I just gave a little talk at a workshop the day before yesterday where I talked a little bit about how a certain very natural model of mathematical proof that arose among the ancient Greeks was misleading because it became our notion of justification as well. And then we had a very narrow picture of how we justified that really didn't handle all sorts of other ways that we justify things that we know. For example, by looking at them. Okay.

And I thought, oh, this isn't going to be an interesting talk because I'm just kind of, you know, just mentioning a whole bunch of trees. And it turns out it was described in the Q&A as, oh, you're very provocative, shocking. And so I guess the answer is, yeah, I'm kind of an extreme view. But, you know, as people sometimes say who end up with extreme view, I really didn't plan to end up here. That makes perfect sense. And believe me, I'll move to the center if I can figure out how. My best skin ever at 45? Give me a theme song and a best skin care award

because it feels like this, right? That's farmhouse fresh skin, all right? I'm glowing and everyone asks how. The best skincare is farmhouse fresh and the award is you, your best you. Visit farmhousefresh skincare.com and use code radio for a free starter routine with any purchase. And is it, so also let me lay some jargon on the audience too. You've already used the word

nominalism. I'm only catching up in the last couple years with what that even mean. So the nominalist aspect of your thought is a denial of reality for a whole bunch of abstractions that other people might think are real. Is that safe to say? Exactly. The nominalist says there are no numbers, there are no mathematical objects that don't exist in any sense at all. There's only one one sense of exist, according to me. That's important. There are no properties. There are no relations. We talked about this. And there's a whole bunch of other things that they don't exist, although we talk about them like corporations, like. So yeah, I'm a wide ranging nominalists. But this is key, right? And this came up also

in what we were talking about. Certain kinds of nominalists think, if you're going to deny that something exists, you can't say, you know, there are blas. You can't really even talk about them. I'm not that kind of nominalist. I think you can talk about them. That's why I'm telling that funny story about truth. Right. So a classic example would be something like, there are prime numbers between 10 and 20. And you want to be able to say both, there are prime numbers between 10 and 20, and there are no numbers. Right, and you can do it. We do do it.

You can say there are several, let's say, prime numbers between 10 and 20. That's not quite to count them in real time. But that is not to say that prime numbers exist. Right. And now what you're doing there is you're doing a kind of contrast move. Again, it's linguistics here. You're now using the word exist. to implicate really exist, and you're not using There Is that way.

Right. And so there's a very kind of subtle interplay in the language. And it's part of the reason why we have distinct words like Exist Real and There Is. All of those words can be used at times in a lightweight way. We're not really talking about what's real. But then sometimes when we want to indicate what's real, we use them contrastively. Good. And that's an illustration.

So your kind of nominalist is going to want to be able to make statements that are true or false have a truth value, but don't refer to anything real in the world. That's right. For example, Sherlock Holmes is a lot smarter than Mickey Meadow. house. Right. You know? Or Sherlock Holmes is more famous than any detective, real or not. Uh-oh. Okay. I think that's true. Yeah. Can you think of a real... I bet you can't even think of the name of a real detective, let alone a famous one. Right. You know, I once said this. I once said, this is a sad sociological fact, and I still believe it, so I'm going to keep repeating it. Fictional objects, fictional characters, are more famous than any real people.

And I think that's something weird about us that, you know, that that's true. So, yeah, but it's an interesting point because you're saying that we can actually compare fictional and non-fictional things, real and non-real things. We do all the time. I can say something like this imaginary woman I dream of every night. looks just like, and then I don't know, Greta Garbo, whatever. Or somebody who's alive at the moment. So that's nominalism.

Is it worth helping out our audience or torturing them a little bit by talking about Quine's view of what is real? I mean, famously, maybe this is the most favorite thing for philosophers to say about what is real. Quine had this inscrutable sentence about bound variables. Yes. Basically what that comes down to in natural language, what's happening here, and it's always important with 20th century analytic philosophy, is you've always got to keep in mind that they are thinking about one way or another, the importance of the invention of logic. And I call it the invention of logic at the hands of Frege. And really, what it was the invention of was the first artificial language. sophisticated artificial language sufficient for doing all of mathematics in all

in a formalism okay so that was an invention and they worry about this so the bit about the bound variables has to do with quine's favorite formalism but let's just put the point in natural language which he felt he could actually because what he was doing is he was transliterating statements from natural language into his favorite formalism. Okay? And the statement is simply that if you have to say there are blas, then you are committed to the reality of blas. That's called his criterion.

Again, bells and whistles about first order logic, which I'm going to skip. Sure. But the point is, if you can't get out from saying there are blas, you're committed to the blas. And it's really that you have to be able to say things about them, not that you could say things about them. It's that you have to. So the reason why Quine found himself being a platonist,

as he called it, which meant he was committed to mathematical objects, was because he took physics seriously. And for much of his life, that was the only science he took seriously. It was a bit restrictive. It good taste. But let's not worry about that, okay?

The point is he takes physics seriously. Well, unfortunately, for him, as a philosopher ontologist, if you're going to take physics seriously, then you've got to take mathematics seriously. Then you've got to take statements. There are statements where what follows there are are claims about numbers, functions, etc. Hilbert spaces. Conclusion, you're committed to these things. They exist. So any project like mine, which says, I'm going to look at your physical theory and I'm going to try to factor out the mathematics because you're not committed to the mathematical objects.

You're only committed to the physical objects. That project for Quine is off the table. Right. Because you said there are. We're done. You're stuck. And you don't agree. So what is your, I mean, this is still a pretty popular view.

view as far as I can tell among many philosophers. But it's still a very popular view. It is the go-to view. It is one of the reasons that Quine will be on the philosophical map now and forever. Because this is kind of the view where you have to start. My answer is twofold, depending on whether Quine is going to take refuge in natural language or whether he's going to work in a formalism. If he's going to take refuge in natural language, I say natural language.

doesn't work that way. You're just wrong. Okay? There are as many Greek gods as goddesses. Perfectly good statements. True. No one's committed. Right. We have to understand when we introduce commitment in natural language, it turns out to be subtle. And again, a matter of linguistics. Yeah. That makes sense. Right. If on the other hand, Quine says, no, no, never mind natural language, that botch, that mess, that thing that evolved horribly. Look at it, look at it. Oh, I've hurt my eyes. Let's look at the formalisms.

Then the response is, a formalism only commits you to what you stipulate in the formulism does commit you. There's nothing about any formalistic little object, a quantify or anything else that yells out, I'm committing. Okay? And that's true, even when you take that. that formalism, and now I'm going to throw more jargon out, which hopefully you won't demand I explain, you give that formalism an interpretation, a semantic interpretation. It's not just

a formalism. It means something. Again, you have to build into the meaning, the commitments. They don't just show up. So there's no argument here. And there's no argument that anyone has. that we have to read any of the languages we use, natural language or formalisms, mathematics, etc., in a way that requires us by virtue of there are, followed by noun phrase, has to commit us. So, for example, a common thing that philosophers will say is that you've already alluded to this fact, science physics in particular uses math all the time you can't get you can't state the standard model of particle physics without using math in any way that we know therefore that involves there is statements right right so i mean i'm stating the what i take to be the conventional philosophers view which i don't think either you or i share but it's that since you are committed to making use of those ideas those mathematical ideas to be a good physicist you have to believe in these abstract entities that as real. That's right. And I'm simply denying that. Yeah. And if I can try to rephrase your

denial, it's that, no, that's your denial. You can talk about these things and use them and committing to their existence is a separate independent step. Exactly. Exactly. And I claim that's licensed by how natural language actually works, how these words exist, there is, actually work and or it's licensed by the options we have when we're using a formalism and how we interpret it. So one thing that this raises as a question that needs answering then is, why is mathematics so good? Why is it so reliable?

If it's not real, but it's objectively true but not real, should that worry us? I think, yes, it calls it. for an explanation. I have spilt much ink, as they say. Although it hasn't been ink. Electrons, yeah? The kind of resources that Bitcoin choose up, right?

In answering this question, and I actually think it's a case-by-case answer. I mean, one of the things you can do to make the question look far more forbidding and frightening is to say something like mathematics, the whole thing.

is reliable in the sciences, the whole thing. But that's not the right picture. The right picture is specific branches of mathematics and specific branches of the sciences, and specific branches of physics. And then it becomes much more manageable how to tell a story. Okay? For example, the vast majority of 20th,

century mathematics has no applications whatsoever. It's wonderful stuff. It's beautiful stuff and it may have applications. This is by no means an argument for trimming mathematics departments. Okay. But, you know, there are lots of stories. The stories about how, you know, Riemann's developments in non-Euclidean geon. took a bunch of years before they found an application. Lots of mathematics has no application. So you have to focus in on the stuff that does. And then when it has applications, again, you don't want to be too broadly in your picture about this.

Often the applications are specific. And sometimes you end up telling a very specific story based on the underlying physical reality that tells you why that mathematics. works. Now, here's a kind of simple-minded example. I have a chalkboard. Once upon a time, people did, and you draw geometrical objects on the chalkboard, and you notice that Euclidean geometry more or less works for those figures. And if somebody says, why does it work? There's no deep mystery here, although a lot of it is going to end up involving physics that we don't entirely understand, right?

Why the chalk adheres the way it does to the board, et cetera, et cetera. Right, frictional effects. We all know how hard it is to make sense of them, et cetera, et cetera. Nevertheless, the story that will emerge literally tells us why Euclidean geometry is going to be up to maybe very high approximation the right mathematics to use on those figures. Now, when you're dealing with a fundamental physical science, let's say particle physics at a certain stage, here are the particles and here are the brute facts about them. And notice we can now use a certain algebraic formulation, maybe something invented by Hamilton, William Hamilton in the 19th century. And we go, yeah, yeah, yeah.

We can use that. And somebody says, why does it work? And now you're at a brute level. We don't know why it works, no more than we know why the particles act the way they do. At a certain point, a new theory may emerge. That's more fundamental. Oh, I don't know, string theory. And then the string theory will have its own distinctive geometry.

And in terms of that, we may be able to say, here's why this works, appear. That's how it always goes. When people turn to telehealth or weight loss, they're looking for real support. That's why more people are choosing orderly meds.com. Orderly meds connects you with real doctors and access to proven GLP1 medications like semaglutide and terseptatide. No guessing, just a more supportive experience. And all shift directly to your door in discrete packaging.

Do your research. Ask questions. Then visit orderlymeds.com slash podcast for an exclusive offer. That's orderlymeds.com slash podcast. Individual results may vary not. Medical advice. Eligibility required, C-Sight for details. My best skin ever at 45.

Give me a theme song and a best skincare award, because it feels like this. Right? There. That's Farmhouse Fresh Skin, all right? I'm blowing, and everyone asks how. The best skincare is Farmhouse Fresh, and the award is you, your best you. Visit Farmhousefreshskincare.com and use code radio for a free starter routine with any purchase. So I like this.

So, again, I'm going to try to rephrase to make sure that I understand. people will say, look at all this math that is so useful in physics. Clearly, the math must be real. It must have some abstract independence and therefore reality that doesn't depend on the physical world. But you're saying, well, no, it's not math as such that has used. It's certain pieces of math, and those pieces of math have used because they're representing the physical world. What exists is the physical world, and we abstract a little bit from that for our purposes, but that doesn't mean we need to attribute reality to our abstractions.

That's right. And here's how I would put it even a little slightly differently, but really it's what you just said. I would say we can use a certain branch of mathematics and we can take certain terms of the mathematics. And yes, we can have them represent aspects of the physical world. Okay. And sometimes we can tell a story in terms of more fundamental. mental facts, why we can do that, and sometimes we can't. Right. Okay.

And now, you know, there's nothing surprising here, really. Well, one potentially surprising thing, or one of those things which we need to decide whether it's surprising or not, is the existence of the laws of physics themselves, right? So we've been talking about math, but there is an ongoing debate about the status of the laws of physics. There are humeons, which would say laws of physics, just a convenient. way of summarizing what happens in the world, and they're anti-humians who I've made fun of because they don't have a person to attach their position to. They just are anti-hum. But they're going to say

that the physical laws have some oomph, have some separate existence. And one of the most casual but obvious arguments in favor of that is, why would they keep working if they didn't have some separate existence? Should we be surprised that the laws of physics work just as well today as they did yesterday if all they are is a summary of the world doing its thing? Well, again, my response and it may not satisfy everybody is what's in back of this issue is a certain picture that we have of how we explain things. And sometimes we have this real belief, it gets more formalized in philosophy, but I think it's operative all over the place, that, you know, everything can be explained or should be explainable.

And we don't like the idea that sometimes something is brute, and all I mean by brute is explanatorially brute. Right. There it is. There's nothing that tells me, and I don't see any kind of philosophical argument or any other kind of argument for that matter that's going to establish the fact that

if I can write down a certain generalization about how the world works that there has to be an explanation for why that generalization works. I'm like, why? Maybe there is.

But notice if there is, it's going to be in terms of something else. that also isn't going to be, that itself might not be explainable. There's nothing that tells me that everything is either explainable or self-explainable. Here we're like bordering on theological notions. You know, well, no, God, but it's self-explainable. I don't know what that means. What I do know is that if you have a generalization, you may be able to explain.

it in terms of something else, other generalizations, or you may not. And if you're not, you're not. Period. And nothing more to say. Be humble. I'm very much in favor of being humble. I like that. And again, you're expressing exactly what I want my view to be. But I will confess to a sliver of sympathy for the idea that I'd be happier if there were some principled reason why. I should expect the laws of physics to be just as good tomorrow as they were yesterday. I think that it's a feature. Like you say, it's a way of talking about the world that that has been working so far. The zeroth order thing is to expect it to keep working.

But I get why people want more than that, even though I don't think it exists. Yeah, I almost feel that this is a hankering for, as I would put it, solving the problem of induction. How are those related? Yeah. Life has been good so far. Can't we get a guarantee here? Right. And I'd like to say, yeah, I understand why you want a guarantee, you know.

But no, you can't. Period. We're done. Okay. I mean, that's what I would say to that. I get it. Again, I'm very sympathetic there. Let me, let me.

Tough love, right? Yeah, exactly. You know? No one never promised you a Rose Garden. So let me, let's just come close to finishing up here by pushing on what I've heard from my philosopher friends as their best arguments in favor of Platonism, in favor of some attributing some reality to mathematical entities. Okay. One of them goes back to what you already alluded to, the existence of these non-standard models of arithmetic. So when you have a formal system, mathematical system that is as powerful as arithmetic, we know,

I'm not going to get this right because I'm very terrible at mathematical logic, but we certainly know that you can't prove that they're consistent internally, right? That's right. A girl will prove that. We also know that there will be statements you can formulate in the language of that system, which are either unprovable or the same. system is inconsistent, right? And somehow it follows that there are these inevitably multiple models from the same set of axioms. So this is a very long-meted way of saying, one might have

thought, because I know because I did use to think this, that all of math was kind of like geometry, right? Geometry, you have the parallel postulate, you can have different versions of it, and you get different geometries. And so you just say, you pick different axioms and what math is about is figuring out what follows from the axioms. But I've been corrected in that because when your axioms are powerful enough to include arithmetic, what follows from the axioms is not the whole story because of these different models. So I think I follow that much, but then there's this extra leap that comes at the end, therefore the fact that one plus one equals two need some extra truth over and above just sticking with some axioms.

Well, the actual picture is something like this. What's happening is, right? I mean, you're right. The idea is, though, it's not the whole story. That means there are more truths that are not being captured by the axiom system. So in some sense, syntactic deducability is transcended by truth. In what sense? Okay.

What? In what sense? That's roughly the idea. There's more to say that we can't get access to if the system is consistent. Unless we supplement the axioms. Now, that's, to me, is the key phrase. So what's going on here is it's incompleteness. An axiom system worth its salt, least arithmetic, is incomplete.

which means all that incompleteness is is that there are statements P where you cannot show P and you cannot show not P. Not with those axioms. You can find other axioms that more powerfully will dictate P or not P. Now, there's another piece to the puzzle. We can introduce a formal notion of truth okay using the

what are called the Tarski biconditionals a set of them things like that as to characterize it we can now supplement the axiom system in a certain way by introducing that notion

into it and we will get new results that we couldn't show otherwise it's still incomplete, but it's strictly bigger than what we had before. But it will never be complete. You're never going to add enough to make it complete.

Not if you're going to write down a set of axioms that you can actually survey that are recursively innumerable. No, that's the key. That's the key point. Okay. Now, what is this show? Does this show that there are truths out there that we don't have access to? subject to the interpretation of how we're reading the truth predicate we just introduced, yes. Otherwise, no. So my response is, I've just said it. Yeah, yeah, yeah. Rig it a certain way.

Interpret that predicate a certain way? And sure, there are truths that you cannot show. Otherwise, the only result is it's incomplete. But you're not going to let them go from there are truths you cannot show to, therefore, there must be abstractly real things out there. I'm actually not even going to let them go to their truths you cannot show. Oh, I thought you just did let them go there. Sorry. Yeah, I don't want to do that. I want to say there are statements, neither of which you can show P or not P. Okay.

It's an additional move to say, well, one of those, P or not P is true. at that point, you have a substantial notion of a standard model that you're bringing to bear, or you're interpreting the predicate that you introduced in a very specific way. That's how you get truths. Otherwise, you don't get it. So what I'm claiming here is that, yeah, there's still a stipulation going on. That's how you do this. Otherwise, it's just an axiom system and a nashem.

nice bigger axiom system. Well, is it also useful to note, and I honestly don't know the answer to this one, that these statements such that you can prove neither P nor not P in your system of arithmetic, these are pretty way-out statements. None of these statements are really relevant to doing physics or anything like that, and therefore can you just take the attitude, who cares? Not necessarily, because the statements that we've managed to show, that are of this sort,

your right are pretty far out. They end up, you know, they're established by very technical, sophisticated means, and they don't have a nice or obvious mathematical content. But there are

some that look closer to having a nice mathematical content, and there's nothing that's stopping this. Right, okay. Okay. So in completeness, you can't You cannot say, we do not know, as far as I can tell.

Oh, yeah, the statements that can't be shown in a nice axiom system like piano arithmetic are ones you don't care about anyway. That, that we cannot show. Not there yet. Okay. Maybe we'll never get there. No, we'll never be there. Never get there. Because I actually think there probably are some we can use.

That'd be interesting. It'd be interesting to see such a thing. Well, one of the ways to get there is to introduce new and strange mathematical concepts. This is happening the most in set theory, contemporary set theory. And when you introduce those, that may be a way of getting a grip on a genuine supplementation of your previous mathematics that has content that you really can see is going to have. have an effect, for example, on the continuum, on the real number system, and therefore, in principle, at least on your physics. In principle, I'm not so sure about that, but we don't know.

Like you said, we don't know. We don't know. We don't know. That's why I said in principle. Isn't in principle a nice, cautious phrase? It really is. I was hoping it was. I was trying to be cautious here.

Let me phrase sort of what might be another version of the same point, but in different words. And this comes from Justin Clark Done, who is a philosopher who I had on the podcast earlier to talk about mathematics and morality. And he emphasizes the bit about consistency in these axiomatic systems. The postulates of arithmetic, piano arithmetic, etc., have implications. for the consistency of the theory itself, right? Like, you can't prove it within the system. And so he would argue that if you think that there's an objective claim that arithmetic is consistent,

in other words, that you can not imagine building a touring machine that would eventually prove zero equals one, then you must think that these arithmetic claims are objectively true independent, in a way that doesn't just come down to the axioms. So that's his argument for needing something else other than just saying, well, there's different axioms and they're all equally good for describing different things. I'm going to disagree. I'm going to say, look, the interesting notion ultimately, he's building into his notion of consistency,

a semantic component. I'm thinking consistency just means syntactic consistency, which means, yes, Turing machine. and you get zero equals one at the end. That's syntactic inconsistency. The sad fact is we never get to show that. We don't, if, you know, basically, as long as you've been churning out results, as long as you haven't shown an inconsistency, as far as you know, there isn't one. But that's not, there's no decision procedure here.

And if you embed it in a bigger system and prove with respect to the bigger system, system that it's consistent. Well, you've essentially spun your wheels because you don't know that the bigger system is consistent. Right. And again, I mean syntactically deriving some suitable contradiction in the bigger system. So to me, that's it. There's nothing more to the notion of consistency than that.

And there's nothing more to say here to cheer ourselves up. There's a fact of the matter. And the fact of the matter is whether you can derive zero equals one in piano arithmetic. But this is a fact that we cannot, this is a syntactic fact, but we can't show it. Well, it's tricky because if we built a touring machine that did prove it, then we would have shown it. Oh, absolutely. Absolutely. That's how showing something as consistent works, by the way.

You build a model. But then, of course, that's relative to the stronger system you're in. So your attitude is that we should just be happy not being sure that arithmetic is consistent. That's right. We should just accept that and not worry about it because, again, life doesn't give us anything else. Yeah, okay. Harsh lessons we're getting here from you, Jody. This is, you know, you have to bite a lot of bullets.

But I think these are bullets that, you know, I don't know. We're stuck with. Yeah, I agree. Okay. So then the final question is, you know, we talked about what is real, what is not real. We focused on things like tables and chairs, laws of physics, numbers and axioms. What about good and evil or beautiful and ugly? Are there implications for your way of thinking?

for moral realism, aesthetic realism, other kinds of realisms. I mean, I'm going to guess that since you don't think numbers are real, you probably don't think that morals are real either. Well, in one sense, I certainly don't. I don't think there's any sort of entities or commitments or anything like that going on. I guess I haven't written about this, so, you know, I always have to be careful because I end up writing things that are a little different. from what I sometimes anticipate.

But my view is I'm a kind of naturalist about this. Okay. And broadly speaking, when I think about morality, I think about our evolution to find certain things repulsive or appealing. And our practice of making agreements with one another. And that's kind of how I say. this working. Okay. And I mean, there are people thinking, well, if we evolve differently in a more reptilian way to be insulting to the reptiles, we might then would that mean it was perfectly okay to eat each other under certain circumstances or something like that,

do horrific things? And if we were those reptiles, I think, the answer would probably be yes, but we're not. We're not those guys. Okay, I'm on board with that too. I guess I will have one final question, which is it would be a shame to let people go without noting that in addition to writing a whole bunch of books about what exists and what doesn't exist, you also write fiction and poetry. So I'll just advertise that, but also, is there a connection that is either explicit or implicit between your poetry and your philosophy? Is this something that people should be more aware of? I don't think so. Although there are friends of mine who disagree. Some of the poems are infused with philosophical themes, and maybe in some of my philosophical writing,

I wax a little more poetic than I should. But at the end of the day, I'm a kind of words. myth. That's what I do. I work with language and I care about language and I deal with all aspects of it. And that includes the creative aspects as well as the, you know, aspects of how we use language to understand the world. And I'm equally committed to all those projects. But that doesn't mean that they need have much overlap. I mean, sometimes I use this analogy. Imagine someone who's a really good swimmer and a good basketball player. They use their arms in both cases. They just don't quite use them the same way. I think it's perfectly fair. And I think you've given us some good words to think about. Again, with the caveat that words that we say here extemporaneously are not always

as careful as the words we would write down after careful thought. But I think you're giving us a lot to think about. So Jody Azuni, thanks so much for being on the Mindscape podcast. Thank you.