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.
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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.
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0:00:00.3 Sean Carroll: 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, '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 gonna 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 wanna know what they're gonna see in their experiments.
0:00:46.9 SC: And at the boundaries, when it comes to 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 gets them all discomfited, whereas philosophers love to talk about what is real, so that's what we're gonna do today with philosopher Jody Azzouni and Jody has a relatively extremist point of view on these questions. He is what is called a nominalist. So nominalism goes back to William of Ockham, of Occam'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 Clarke-Doane said, that doesn't mean that they're out there somewhere. There's not... What did he call it? Platonium or something like that, some place where you find perfect triangles, etcetera but there's a reality to these mathematical structures.
0:01:52.4 SC: 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 Jody Azzouni is here to give you the apologia for nominalism and 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 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.
0:02:47.0 SC: And so what Jody is gonna 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. He 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. Who cares what exists and not, as long as we can make predictions for what we're actually gonna experience?
0:03:42.7 SC: 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 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 gonna be a good way to start the new year. Let's go.
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0:04:50.6 SC: Jody Azzouni, welcome to the Mindscape Podcast.
0:04:52.8 Jody Azzouni: Glad to be here.
0:04:54.5 SC: 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?' Because it's interesting that as a physicist, I talk to my friends who are physicists, they don't care what is real. Like, 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's a physicist. So maybe give the sales pitch for why we should care about what is real and what is not real.
0:05:23.9 JA: Well, 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 course, in the background, what I think when you're asking if something is real, what you're really asking. And I think... We have a picture of things that are... And I'm gonna speak very roughly.
0:05:58.4 SC: Yeah.
0:05:58.9 JA: Things that are independent of us and other things that aren't independent of us. So my go-to example is always Sherlock Holmes. 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. I can get Sherlock Holmes wrong in certain respects, and people do, and you might uncover a notebook of Doyle's 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 that can happen. Nevertheless, it's not independent of Doyle.
0:06:47.7 SC: Right.
0:06:49.8 JA: Doyle, pen in hand said, 'I wanna go this way, I wanna go that way', blah, blah, blah. You don't get to do that with things that are real. 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 gotta put... There's a process, and to me, I call that sometimes mind and language independent.
0:07:25.7 SC: Okay.
0:07:26.2 JA: 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 wanna 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, thought you can't drive a wedge between these things. You can't separate 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.
0:08:11.6 SC: A few books have been written.
0:08:12.0 JA: Well, and that's why I ended up writing a lot of books. It's not just to make sure that I have a job. It's because it's 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, how is the world working? How are things happening? It's the real stuff that's telling us, that's the motor. So that's why we care.
0:09:00.5 SC: I think that makes sense, but let's let people in on all the various ways in which it's a complicated question. 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, so there's a sense in which he's real, but he's a fictional character, okay, but what about things like... Ultimately, I wanna get to physics and math, but what about things like a country or a family, do those count as well?
0:09:28.4 JA: Good. Perfect examples. Perfect examples. Look, for the time being, let's say that pretty much our description of human beings is real. 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 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 gotta analyse it. You don't simply, go a certain way. Now look, something important is kicking in here with the words.
0:10:30.7 SC: Yeah.
0:10:32.4 JA: When we start talking about banks, countries, borders, we human beings, this doesn't happen in other species as far as I know, but human beings automatically think, 'A thing. A thing with properties.' And they go even further. Here, you read The Economist, for example. I read it, and The Economist, 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 US policy regarding such and such.' And I look at that and I say, 'Okay, that's... ' 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.
0:11:33.3 SC: Right.
0:11:33.4 JA: Second of all, does it really follow that there's this thing China that has attitudes? No. Well, maybe it's shorthand for the individuals in China that are ruling the place. That's not so straightforward. 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.
0:12:17.1 SC: So you said something 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 that tables and chairs are real, and we have a way of talking about them, moving them, they have an impact, they have causal powers, etcetera, 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, but...
0:12:44.5 JA: Right, but can I stop you just for a second?
0:12:46.8 SC: Please, yeah.
0:12:47.3 JA: You're absolutely right. It's very natural for us, but don't think it's natural in some broader sense, 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.'
0:13:14.9 SC: Yeah.
0:13:14.9 JA: Very natural, yeah, for us.
0:13:17.7 SC: Or fictional characters, for that matter.
0:13:17.8 JA: Or fictional characters, or mathematical objects.
0:13:24.1 SC: Right. 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?
0:13:38.7 JA: Not them but what they're composed of, elements of them, for sure.
0:13:43.7 SC: Okay. Okay.
0:13:45.7 JA: Same thing for institutions, like, oh, I don't know, Microsoft. And again, we implicitly do this when we really start to analyse 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 gonna move through space and time in certain respects. That's how I picture it. So at the end of the day, if someone says to me, 'Are you committed to the existence of Microsoft?' I'm gonna say, 'No, but that doesn't mean I think it's like Sherlock Holmes.'
0:14:48.2 SC: Well, that's why it's tricky. So one question is, are there different senses of the word 'exist'? Is it possible to have different levels of existence or something like that? 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.
0:15:17.7 JA: 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 'exist' or the phrase 'there is' or the word 'real', do they have different senses? Like, 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.
0:16:01.6 JA: In my view, the answer to the question, for example, 'Does exist have different meanings?' Is no. And I claim there are humdrum linguistic tests for that. Now, the other... So that's one thing. So I'm just gonna 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 'cause I've never done a head count, as it were. 'There are as many Greek goddesses as Greek gods.' Now that's either true or false. 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 kinda correspondence.
0:16:51.3 SC: Right, sure.
0:16:52.3 JA: 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. There's a word 'chair', it refers to chairs. How many chairs are in here? None. Okay, so it's false. But, 'There are as 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 true... 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.
0:17:41.1 SC: Sure, okay, so I think I get that, but there is... There's a multilayered distinction here that I wanna get right on.
0:17:49.0 JA: Sure.
0:17:49.4 SC: 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, we're looking at someone's list that someone made up, and so...
0:18:02.2 JA: That's right, and the list is a cultural product diffused from... Yeah, yeah, exactly.
0:18:08.2 SC: That makes perfect sense.
0:18:08.9 JA: Now, when it comes... Yeah, go ahead.
0:18:10.3 SC: But I think that's different to me than the Microsoft question, because when I'm saying that Microsoft is acting aggressively, that tells me something about the world, not just about someone's figments of their imagination.
0:18:25.0 JA: 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.
0:18:36.7 SC: Okay.
0:18:37.2 JA: In the case of the fictions, it really just refers to a kind of literary/movie practice, let's say. In the case of Microsoft, it's gonna 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.
0:19:11.6 SC: Okay. Got it.
0:19:12.6 JA: Again, it doesn't turn on the object, Microsoft being aggressive. It turns on a series of actions carried out by individuals who in various ways are connected to Microsoft as we understand it.
0:19:32.4 SC: Okay, so I'm just gonna... Actually, I should say that I'm broadly sympathetic to most of your points of view here, but it's my job, of course, as the host, to pretend to be skeptical at appropriate times, so I think I buy that, I think get that 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 logic say that tables and chairs don't exist, all that exists is the atoms or the particles that make them up?
0:20:09.1 JA: Yeah, that would follow, if you decided that here's a principle of what exists. Go for the smallest bits that make it up, and I'm gonna say, 'No, that's not how it works.' One of the reasons I'm gonna 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 gonna ask me, and you should. 'Okay, what's the principal difference here between a human being made up of a lotta bits and Microsoft being made up of a lotta bits?' Now, one of the things that's gonna go on is that a lot of what's going on with Microsoft doesn't involve little bits that are really in Microsoft.
0:21:06.4 SC: Okay.
0:21:08.4 JA: You don't have... Microsoft isn't in that sense a physical object, it's a stipulated object. And you'd make the same mistake with a bank if you said, 'Well, where is the bank physically?' And then you say, 'Okay, well, it's all these people, and it's these locations in... Physical space, the bank offices.' And then you find out that HSBC, for example, is, or there are other banks now that are all entirely online, and then you go, 'Okay, so where are they located?' And you start to realise, it's really not the location that's doing the work here.
0:21:49.4 SC: Sure, good.
0:21:50.4 JA: It's a stipulated... We're constituting it out of these things. So what I wanna say is that what works in the case of a person, where you can actually see... Well, you don't see, but 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 gonna tell ultimately is gonna be an anatomical/molecular/story about forces. That's not the kinda story you can tell about Microsoft.
0:22:35.6 SC: 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 'cause it's entirely something that exists in human minds. Is that fair?
0:23:03.3 JA: 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. So if you treat a country as geographically located, that geographical spread is real, even if there's no person, no people...
0:23:23.3 SC: Okay, yeah.
0:23:25.1 JA: 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. That wouldn't be there, although these other things would be there. So if you treat London, for example, now I'm borrowing an example that I've read dozens of times from Chomsky and quoted 'cause I love it. He talks about London and he says, 'Oh, London is so polluted and dirty', etcetera, that it should be moved upstream, 500 miles up the [0:24:01.6] ____. And 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 imagine it could still be polluted, pollution is us, but imagine there's still the geographic location, imagine, etcetera. You see what I'm saying?
0:24:30.8 SC: Yeah, I do, okay, and I think... 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. That might be...
0:24:43.1 JA: I'm not committing myself to that, yeah. I'm just being illustrative.
0:24:47.9 SC: 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.
0:25:04.6 JA: Okay, so I'm gonna describe myself as having gone through two phases. For a very long time, up until some point in 2017, I was what you might call a Hobbesian nominalist, after Thomas Hobbes. And basically, the idea was, there are objects. 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.
0:25:45.6 SC: Okay.
0:25:47.2 JA: My current view is weird enough and complicated enough that I almost don't wanna describe it, but it's something like, look, there're really aren't objects or properties, because in order to get your idea of an object, you have to put a border around it in space and time and you gotta 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.
0:26:22.4 SC: Right.
0:26:22.5 JA: Like if you ask yourself, 'Are these borders in the world, are they independent of it?' Then you say 'No, there isn't anything like that.' So my current view is that... The way reality is is it's a kind of... Alright, I'm gonna go horribly metaphorical, I'm so sorry. It's a kind of fabric that's spread out, and I call... It's a feature fabric, so there are these features. They're not properties, they're not objects. It's just a spread of features. I think that's all I wanna say about that because...
0:27:04.2 SC: No, I'm sorry. You're not...
0:27:05.7 JA: Otherwise I'm gonna start sounding Zen-like or something mystical, weird, scary. I have a book on this, and I hope the book conveys what I have in mind, but this is a tough one.
0:27:19.2 SC: I know.
0:27:19.6 JA: 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.
0:27:27.5 SC: Well. Except that 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 that 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 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 gonna be able to hold on to tables and chairs.
0:28:12.7 JA: Yeah. Now, the thing I wanna 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?
0:28:26.6 SC: So much turnings on that.
0:28:29.0 JA: But my own view is, is the emergent patterns that you described, that's real.
0:28:35.9 SC: Yeah, okay.
0:28:36.8 JA: The Hilbert vector space, that's a mathematical formalism.
0:28:42.4 SC: Okay. That's fine.
0:28:42.9 JA: Now, the reason I think this in a nutshell is because there's a strong tendency we have to think, 'If I get a characterisation of something and that characterisation is empirically on the money, that's evidence that everything that characterisation talks about, mathematically and otherwise, exists.' I'm gonna reject that. I'm gonna say, 'What exists is, in a certain sense, what we get', and now, this is my own 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, or they're shifting, or they're a wave pattern. I like all of 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 gonna claim that's real.
0:29:58.6 SC: I think that's fine, but I'm always sloppy 'cause I am a physicist, not a philosopher, and when I say that reality is a vector in Hilbert space, 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 sub pieces. Then we ask afterward, "Is it possible to describe it in terms of sub pieces that have some real heft to them, and find that the answer is yes, etcetera?" 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?
0:30:42.4 JA: It may prove to be a mathematical abstraction. It may not. Again, it depends on the nature of the relations we're looking at, how we get access to them, what kind of role the mathematical formalism is playing in constituting them. So velocity in particular, right, seems to be something that we almost stipulate, as opposed to accelerations. And that is an argument for saying, 'Well, velocity isn't real.' Okay, but acceleration is.
0:31:29.3 SC: Right.
0:31:30.6 JA: Okay, and I do the same thing in a different way when it comes to spacetime. So for example, in the Newtonian context, let's assume that was right. I would say something like, 'No, spacetime isn't real.' It is a way of describing ways that objects are.
0:31:53.3 SC: It's a relational thing, not a substance.
0:31:56.1 JA: It's not substantial, but more importantly, we don't have to be committed to it.
0:32:00.9 SC: Right.
0:32:01.9 JA: So the substantial-relational distinction isn't quite mapping onto the distinction I've got in mind. It's a cousin.
0:32:13.5 SC: Okay, okay.
0:32:16.9 JA: On the other hand, when you end up with spacetime playing a substantial physical role, containing energy, etcetera, etcetera, you may or may not be dealing with something you should be committed to. And again, it's gonna turn on the details of how you get access to it, and what role the mathematical formalism is playing, etcetera.
0:32:39.6 SC: 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 gonna depend on future developments in physics and philosophy.
0:32:55.5 JA: Well, that, I think... If somebody was hoping, '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 outta luck.'
0:33:15.4 SC: You've come to the wrong place, yeah.
0:33:16.9 JA: 'You've come to the wrong place, and I think it was an unreasonable demand.'
0:33:20.5 SC: Okay.
0:33:23.4 JA: I think the concept of what exists is not that esoteric, as I... That's how we began the interview but that doesn't mean that the result of discovering what falls under it is gonna be straightforward, and this shows up straight... Easily, in lots of ways. We're worrying about the subtlety of certain concepts, but it comes up like, is Bigfoot real or not? That's an empirical question, and I think the answer's no. So do you, I suspect. But we have better... We have other examples that are more subtle, that it's not obvious, and yeah, we're beholden to the science to tell us the answer, and that's as it should be.
0:34:15.1 SC: Sure, if someone says, 'Are weakly interacting massive 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.
0:34:30.8 JA: I'd like to think that's because you've lived with velocity so long. I'm gonna 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?
0:34:46.0 SC: I am, but maybe the folks in the audience aren't, so you can explain.
0:34:48.8 JA: 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.
0:35:01.0 SC: Right, you can multiply 'em together, yeah.
0:35:01.4 JA: That's basically the characterisation of a group. You can do multiplication. Not necessarily multiplication and addition, that would be a ring, but multiplication or addition, however you wanna 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 kinda thing, that's one thing, the numbers.
0:35:43.2 SC: The numbers, yeah.
0:35:44.5 JA: Turns out, there are lots of things that can fit that structure. That was discovered along with what's called, non-standard models. You characterise the numbers in Peano Arithmetic, and then you discover, 'Hmm, 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, 0, 1, 2, 3, and no more, because characterising the 'and no more' is nontrivial, but we have a different picture, and the picture is intuitive, that we have this intended model when we're talking about the numbers, whereas we don't have 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, there are lots of different kinds of Peano numbers.
0:36:40.5 SC: Right, okay, yeah. I'm actually on board with that, but yeah, my friends are not always, and so maybe this is worth noting for the listeners, that, is it fair to describe your view as extreme within the world of philosophers?
0:37:00.0 JA: 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 justify, that really didn't handle all sorts of other ways that we justify things that we know, for example, by looking at them. And I thought, 'Oh, this isn't going to be an interesting talk 'cause I'm just just mentioning a whole bunch of truisms.' 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 an extreme view, but as people sometimes say who end up with an extreme view, I really didn't plan to end up here.
0:38:10.5 SC: Yeah. That makes perfect sense.
0:38:12.5 JA: And believe me, I'll move to the center if I can figure out how.
0:38:16.6 SC: And is it... So also, let met lay some jargon on the audience too. You've already used the word nominalism. I'm only catching up in the last couple of years with what that even means, 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?
0:38:36.6 JA: Exactly. The nominalist says, there are no numbers, there are no mathematical objects, they don't exist in any sense at all. There's only one sense of 'exist' according to me, that's important.
0:38:48.2 SC: Yep.
0:38:50.5 JA: There are no properties, there are no relations, we talked about this, and there's a whole bunch of other things that don't exist, although we talk about them, like corporations, like... So yeah, I'm a wide-ranging nominalist but, this is key, right, and this came up also in what we were talking about, certain kinds of nominalists think if you're gonna deny that something exists, you can't say, 'There are blahs. You can't really even talk about them.' I'm not that kinda nominalist. I think you can talk about them. That's why I'm telling that funny story about truth.
0:39:34.0 SC: 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.'
0:39:48.6 JA: 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.
0:39:57.2 SC: Yeah. Let's not try to count them in real time.
0:40:00.8 JA: But that is not to say that prime numbers exist.
0:40:05.2 SC: Right.
0:40:05.7 JA: And now what you're doing there is you're doing a 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.
0:40:25.4 SC: Right.
0:40:25.9 JA: And so there's a very 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 to... In a lightweight way. We're not really talking about what's real but then, sometimes when we wanna indicate what's real, we use them contrastively...
0:40:54.2 SC: Good.
0:40:54.7 JA: And that's an illustration.
0:40:56.4 SC: So your kind of nominalist is gonna be able to... Is gonna 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.
0:41:09.2 JA: That's right. For example, 'Sherlock Holmes is a lot smarter than Mickey Mouse.' Or 'Sherlock Holmes is more famous than any detective, real or not.'
0:41:26.1 SC: Uh-oh, okay.
0:41:27.9 JA: I think that's true.
0:41:29.1 SC: Yeah.
0:41:29.2 JA: 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.
0:41:36.3 SC: Right.
0:41:36.9 JA: I once said this, I once said this is a sad sociological fact, and I still believe it, so I'm gonna keep repeating it. Fictional objects, fictional characters are more famous than any real people. And I think that's something weird about us, that that's true.
0:42:00.0 SC: So that... 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.
0:42:07.7 JA: We do all the time.
0:42:08.5 SC: We do all the time, yeah.
0:42:08.9 JA: 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.
0:42:23.6 SC: 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? Famously, maybe this is the most favourite thing for philosophers to say about what is real. Quine had this inscrutable sentence about bound variables.
0:42:43.3 JA: 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 gotta keep in mind that they are thinking about, one way or another, the importance of the invention of logic.
0:43:03.6 SC: Okay.
0:43:04.2 JA: 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 and all, and a formalism. 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 favourite formalism. And the statement is simply that if you have to say there are blahs, then you are committed to the reality of blahs. That's called his criterion. Again, bells and whistles about first-order logic, which I'm gonna skip.
0:44:07.0 SC: Sure.
0:44:07.6 JA: But the point is, if you can't get out from saying there are blahs, you're committed to the blahs.
0:44:13.2 SC: And it's really that you have to be able to say things about them, not that you could say things about them.
0:44:18.4 JA: 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.
0:44:37.3 SC: He had good taste.
0:44:37.9 JA: But let's not worry about that. The point is, he takes physics seriously. Well, unfortunately for him, as a philosopher-ontologist, if you're gonna take physics seriously, then you gotta take mathematics seriously. Then you gotta take statements... There are statements where what follows there are claims about numbers, functions, etcetera, Hilbert spaces. Conclusion. You're committed to these things, they exist. So any project like mine which says, 'I'm gonna look at your physical theory and I'm gonna try to factor out the mathematics, 'cause you're not committed to the mathematical objects, you're only committed to the physical objects.' That project for Quine is off the table because you said 'there are', we're done. You're stuck.
0:45:35.2 SC: And you don't agree. So what is your... This is still a pretty popular view, as far as I can tell among many philosophers, but...
0:45:43.3 JA: 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 the view where you have to start. My answer is two-fold, depending on whether Quine is gonna take refuge in natural language, or whether he's gonna work in a formalism. If he's gonna take refuge in natural language, I say natural language doesn't work that way. You're just wrong. 'There are as many Greek gods as goddesses.' Perfectly good statements, true. No one's committed.
0:46:20.2 SC: Right.
0:46:20.8 JA: We have to understand, when we introduce commitment in natural language, it turns out to be subtle, and again, a matter of linguistics.
0:46:29.9 SC: Yeah. That makes sense.
0:46:31.8 JA: Right. If, on the other hand, Quine says, '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 formalism does commit you. There's nothing about any formalistic little object to quantify or anything else that yells out, 'I'm committing.' And that's true, even when you take that formalism, and now I'm gonna throw more jargon out, which hopefully you won't demand I explain, you give that formalism an interpretation, a semantic interpretation. You don't... 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, mathematic, etcetera, in a way that requires us, by virtue of 'there are' followed by noun phrase, has to commit us.
0:47:56.2 SC: 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...
0:48:14.9 JA: In a way that involves 'there is' statements. That's right.
0:48:18.2 SC: Right, right. So I'm stating what I take to be the conventional philosopher's 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 as real.
0:48:35.4 JA: That's right, and I'm simply denying that.
0:48:38.8 SC: Yeah, and if I can try to rephrase your denial, it's that, no, that's your denial. That said, you can talk about these things and use them, and committing to their existence is a separate, independent step.
0:48:51.8 JA: 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 them.
0:49:11.2 SC: 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 there's still... It's objectively true, but not real. Should that worry us?
0:49:30.5 JA: I think, yes, it calls for an explanation. I have spilt much ink, as they say, although it hasn't been ink, it's more like...
0:49:39.8 SC: Electrons, yeah?
0:49:40.6 JA: The kind of resources that BitCon chews up. In answering this question, and I actually think it's a case-by-case answer. 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. For example, the vast majority of 20th century mathematics has no applications, whatsoever.
0:50:39.3 SC: True.
0:50:39.4 JA: It's wonderful stuff, it's beautiful stuff, and it may have applications. This is by no means an argument for trimming mathematics departments but there are lots of stories, the stories about how Riemann's developments in non-Euclidean geometry 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 wanna 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 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.
0:51:51.5 SC: Yeah.
0:51:53.3 JA: And if somebody says, 'Why does it work?' There's no deep mystery here, although a lot of it is gonna end up involving physics that we don't entirely understand. Why the chalk a dheres the way it does to the board, etcetera, etcetera.
0:52:07.0 SC: I don't understand it, yeah.
0:52:10.1 JA: Right. Frictional effects, we all know how hard it is to make sense of them, etcetera, etcetera. Nevertheless, the story that'll 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.
0:53:00.4 SC: Right.
0:53:02.2 JA: 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, up here.' That's how it always goes.
0:53:21.2 SC: So I like this. So again, I'm gonna 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 use, it's certain pieces of math, and those pieces of math have use 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.'
0:53:54.7 JA: 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. And sometimes, we can tell a story in terms of more fundamental facts, why we can do that, and sometimes we can't.
0:54:29.5 SC: Right, okay, but let's...
0:54:31.0 JA: And now, there's nothing surprising here, really.
0:54:34.4 SC: 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. So we've been talking about math but there is an ongoing debate about the status of the laws of physics. There are Humeans, which would say, 'The laws of physics are just a convenient way of summarising what happens in the world', and there are anti-Humeans, who I've made fun of 'cause they don't have a person to attach their position to, they just are anti-Hume, but they're gonna 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?
0:55:28.8 JA: 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 formalised in philosophy, but I think it's operative all over the place, that 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 explanatorily brute. There it is. There's nothing that tells me, and I don't see any kinda philosophical argument, or any other kind of argument, for that matter, that's gonna establish the fact that if I can write down a certain generalisation about how the world works, that there has to be an explanation for why that generalisation works. I'm like, 'Why?' Maybe there is, but notice if there is, it's gonna 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 bordering on theological notions, well no, but it's self-explainable. I don't know what that means. What I do know is that if you have a generalisation, you may be able to explain it in terms of something else, other generalisations, or you may not and if you're not, you're not, period, end, nothing more to say. Be humble.
0:57:31.7 SC: 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 was 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 has been working so far, the zeroth-order of things, to expect it to keep working, but I get why people want more than that, even though I don't think it exists.
0:58:08.4 JA: Yeah, I almost feel that this is a hankering for, as I would put it, solving the problem of induction.
0:58:18.9 SC: How are those related? Yeah.
0:58:19.2 JA: 'Hey, life has been good so far. Can't we get a guarantee here?' And I'd like to say, 'Yeah, I understand why you want a guarantee but no, you can't. Period. We're done. That's what I would say to that.
0:58:38.9 SC: I get it, and again, I'm very sympathetic there. Let me...
0:58:42.4 JA: Tough love.
0:58:43.3 SC: Yeah, exactly.
0:58:43.8 JA: Inductive tough love.
0:58:44.9 SC: No one ever promised you a rose garden. So 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 favour of Platonism, in favor of attributing some reality to mathematical entities. 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 gonna get this right, 'cause I'm very terrible at mathematical logic, but we certainly know that you can't prove that they're consistent internally. Gödel proved that. We also know that there will be statements you can formulate in the language of that system which are either unprovable, or the system is inconsistent.
0:59:46.5 SC: And somehow, it follows that there are these inevitably multiple models from the same set of axioms. So this is a very long-winded way of saying, 'One might have thought', 'cause I know, 'cause I did use to think this, 'that all of math was like geometry.' 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 as 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 1 + 1 = 2 needs some extra truth over and above just sticking with some axioms.
1:00:40.8 JA: Well, the actual picture is something like this. What's happening is, 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 deductibility is transcended by truth.
1:01:07.9 SC: In what sense?
1:01:08.4 JA: Okay. What?
1:01:10.4 SC: In what sense?
1:01:10.7 JA: I think 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, the key phrase. So what's going on here is, it's incompleteness. An axiom system worth its salt in at 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 using what are called the Tarski biconditionals, a set of them, things like that, as to characterise 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.
1:02:40.4 SC: But it will never be complete. You're never gonna add enough to make it complete.
1:02:44.0 JA: Not if you're gonna 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. Now, what does 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 that 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.
1:03:32.2 SC: But you're not gonna let them go from 'there are truths you cannot show' to 'therefore, there must be abstractly real things out there.'
1:03:39.9 JA: I'm actually not even gonna let them go to 'there are truths you cannot show.'
1:03:43.8 SC: Oh, I thought you just did let them go there, sorry.
1:03:46.5 JA: I don't wanna do that. I wanna say, there are statements, neither of which you can show P or not P. 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 in a nice, bigger axiom system.
1:04:30.9 SC: 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, therefore, can you just take the attitude, 'Who cares'?
1:04:52.4 JA: Not necessarily, because the statements that we've managed to show that are of this sort, you're right, are pretty far out, they end up... 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.
1:05:23.6 SC: Right, okay.
1:05:25.6 JA: So in completeness, you cannot say, 'We do not know', as far as I can tell, 'Oh yeah, the statements that can't be shown by a nice... In a nice axiom system like Peano arithmetic are ones you don't care about anyway', that we cannot show.
1:05:43.4 SC: Not there yet. Okay. Maybe we'll never get there.
1:05:46.5 JA: I don't think... No, we'll never be there.
1:05:48.1 SC: Never get there, okay.
1:05:48.4 JA: Because I actually think there probably are some we can use.
1:05:53.4 SC: That would be interesting. It'd be interesting to see such a thing.
1:05:56.2 JA: 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 gonna have an effect, for example, on the continuum, on the real number system, and therefore in principle, at least, on your physics.
1:06:37.7 SC: In principle? I'm not so sure about that, but we don't know. Like you said, we don't know, so we don't wanna hang...
1:06:42.3 JA: We don't know, we don't know. That's why I said in principle, isn't 'in principle' a nice, cautious phrase?
1:06:48.1 SC: It really is.
1:06:49.0 JA: I was hoping it was, I was trying to be cautious here.
1:06:52.8 SC: Let me phrase what might be another version of the same point, but in different words, and this comes from Justin Clark-Doane, who is a philosopher who I had on the podcast earlier to talk about mathematics and morality, and he emphasises the bit about consistency in these axiomatic systems. The postulates of arithmetic, Peano arithmetic, etcetera, have implications for the consistency of the theory itself, you can prove it within the system. And so he would argue that if you think that there is an objective claim that arithmetic is consistent, in other words, that you cannot imagine building a Turing machine that would eventually prove 0 = 1, 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.'
1:08:00.4 JA: I'm gonna disagree.
1:08:01.9 SC: Okay.
1:08:02.6 JA: 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, you get 0 = 1 at the end. That's syntactic inconsistency. The sad fact is we never get to show that. Basically, as long as you've been churning out results, as long as you haven't shown an inconsistency, as far as 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 that it's consistent, well you've essentially spun your wheels because you don't know that the bigger system is consistent.
1:09:01.2 SC: Right.
1:09:02.1 JA: And again, 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 is a fact of the matter, and the fact of the matter is whether you can derive 0 = 1 in Peano arithmetic, but this is a fact that we cannot... This is a syntactic fact, but we can't show it.
1:09:33.9 SC: Well, it's tricky because if we built a Turing machine that did prove it, then we would have shown it.
1:09:40.1 JA: Oh absolutely, absolutely. That's how showing something is consistent works, by the way, you build a model, but then of course that's relative to the stronger system you're in.
1:09:55.3 SC: So your attitude is that we should just be happy not being sure that arithmetic is consistent?
1:10:01.3 JA: That's right. We should just accept that, and not worry about it because, again, life doesn't give us anything else.
1:10:09.6 SC: Yeah, harsh lessons we're getting here from you, Jody, this is... You have to bite a lot of bullets.
1:10:18.6 JA: Well, but I think these are bullets that, I don't know, we're stuck with.
1:10:25.1 SC: I agree. Okay, so then the final question is, we talked about what is real, what is not real, and 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'm gonna guess that since you don't think numbers are real, you probably don't think that morals are real either.
1:10:58.6 JA: Well, in one sense, I certainly don't. I don't think there's any entities or commitments or anything like that going on. I guess I haven't written about this, so 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 naturalist about this, 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 see this working. And 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 in certain... 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.
1:12:22.6 SC: 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?
1:12:50.3 JA: 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 wordsmith, 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 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. 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.
1:13:48.9 SC: 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've given us a lot to think about, so Jody Azzouni thank you so much for being on the Mindscape Podcast.
1:14:06.3 JA: Thank you.
Love the topic, perfect venue for a podcast: goldilocks- not too dense or too vague for a podcast, and an invitation to more.
Irhad Kimhi, Thinking and Being, a great book on first order logic, extends some of what was said today, post Russell and Frege..
“…we should attach reality or existence to things that exist independent of our minds in some sense…”
Fair enough, but since we only have epistemic access (Azzouni’s requirement) to what’s mind-independent via mind-dependent representations, perhaps we need to grant the reality of the contents of such representations. Without them, the world wouldn’t appear at all, either via one’s individual consciousness (qualia) or via collective science (quantities, concepts).
In a primal sense
Language serves understanding
Reality hides
Why can’t numbers be real to the extent the mathematical realm is real–in the world of abstract objects? Also, how would you counter Penrose’s taxonomy and arguments? And, for that matter, Tegmark’s (ancient) proposal? This should also have been a discussion informed by Kuhn’s Levels of Nothing.
This is one of the best philosophical discussions I’ve heard — it probably helps that he is a colleague of Dennett’s.
It brought me to this conclusion: if Space exists as a real thing (perhaps using Maxwell’s description of aether in Whittaker’s book on the subject) then neither nothing nor infinity can exist.
Are consciousness and reality so intertwined that one cannot exist without the other?
The subject of this podcast is “What is real and what is not real?” The guest philosopher Jody skips over, or dances around the definition of “real” … or, more accurately, he stumbles badly trying to define the term “real”. At the very beginning he explains that real and unreal are “what you are making up and what you are NOT making up.” Hardly precise. Off to a very bad start. [That’s like saying that death is the absence of life, and life is the absence of death. Hardly helpful.] Then Sean C. says that “real” means that it “exists”, and ‘not real’ means that “it does “not exist”. Then they address the question … “Is there a difference between the following terms — “it is “real” versus it “exists” versus “this-is-something-that-you’re-making-up” versus “this-is-something-that-you’re-not-making-up”, etc. Jody then says that “velocity” is not real, [does not exist] but “acceleration” IS real” [it does exist]. What? Th guest doesn’t even define the philosophical problem very well, and leaves so many loose ends. IMHO language describes what is real; so does math. End of story. End of discussion. Let’s move on to more important questions … like how many angels on the head of a pin. 🙂 IMHO this conversation was a sophists’ circle fest with one who is not “one of the world’s most interesting thinkers” … maybe an interesting novelist or poet, but a maddenly imprecise philosopher discussant.
Thanks to Rene Descartes (1596-1650) it can be said ‘The only thing we can be certain of is our own existence’. Therefore, except for our own existence, we can never be certain what is and isn’t real.
When it comes to understanding the world outside our own mind (if indeed there is such a world), it would seem the best we can hope for, at least as far as theoretical science is concerned, is to describe it using models constructed in mathematical terns (the language of science). Then using the so-called ‘Scientific Method’ compare those models with observational evidence. Are those mathematical terms (numbers, geometries, and formulas) entities that are real and exist outside the mind, and we just ‘discover’ them, or are they just ‘inventions of the human mind, that have no real existence on their own? Most likely we will never know the answer. As much as we would like to believe that given enough time and thought everything is knowable, it seems more realistically not to be the case.
“Problems that remain persistently insoluble should always be suspected as questions asked in the wrong way.” Alan Watts
Is the company that pays his salary real? 🙂
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Concordo com Jody Azzouni relativamente a:
– o que existe é o mundo físico. Abstrações que justifiquem nossos propósitos, em nada implica que essas abstrações sejam reais.
Utilização de certos termos de matemática que representem aspetos do mundo físico.
– Muitas divergências, são apenas puramente linguisticas.
Mente e linguagem independentes.
Gostei “Coisas que são indepententes de nós, e, outras coisas que não são independente de nós”.
Obrigada por este bom episódio
Jody Azzouni thinks “reality” consists only of physical, mind-independent objects. But since everything we experience, sense, think and feel is experienced in our own minds from which we can never escape, that would leave reality as a very narrow sphere indeed. Azzouni’s concept of reality is actually a mere semantic one that
has little practical use or importance. Trying to distinguish “things” that can be classified as mind-independent from those that are creations of our mind is a relatively useless enterprise. Many of us, including Azzouni, work in fields that involve things that in Azzouni’s world don’t exist. Yet we are well paid for doing so. Azzouni himself works as a philosopher involved in philosophy of mathematics, a subject he insists doesn’t exist. And those who work or act based on religious beliefs or morality are actually wasting their time since neither any god nor its moral principles exist either. String theory, the equations of physics and indeed all mathematical formulas are for Azzouni mere fictions. One therefore wonders how he feels about cashing his paycheck for teaching, studying and writing about his non-existent fields of endeavor.
The problem here is that “reality” and “existence” are short hand intuitive concepts that allow us to distinguish things that can function for us in practical aspects of day to day life and things that are “made up,” like ghost stories, ideas, ideologies, values, ethics, fiction, myths, all of which lack corporeal physical existence but which affect the physical world in very profound ways. It just isn’t useful to say that communism or fascism or racism don’t exist, because those belief systems move people to act in very profound ways.
Such ideas and feelings exist as much as a table or chair (which are mind-dependent concepts themself) and have far more profound effects in the physical world. We spend our lives interacting with ideas, relationships and concepts as much as we do with physical objects. Such very real events as World War II arose out of a struggle of ideas and belief systems. So Azzouni has constructed a nominalist philosophy that does little for us. It can’t explain our behavior or help guide it. His theory of existence is just a semantic argument over the meaning of a word (reality) that we all understand perfectly well enough based on our own intuitions.
The arguments for nominalism are nominalistic too, they don’ t exist as well since they are not ‘physical, mind-independent objects’ ;you can enjoy them as you enjoy Sherlock Holmes.They are not about reality and actually they don’t have to be about reality- and even they shouldn’t -for selfconsistency reasons(but fiction doesn t need to be selfconsistent-just entertaining and Jody Azzouni is as good as a fiction writer at this)
Mildly off-topic or at best tangential to this episode:
The mathematically inclined might find Michael Rathjen’s survey paper about “ The art of ordinal analysis” entertaining; contains an outline of (an infinitary variant) of Gentzen’s proof of the consistency of Peano Arithmetic based on Primitive Recursive Arithmetic + transfinite induction up to a fairly large countable ordinal.
Further off: the late Edward Nelson’s book Elements, a nearly successful attempt at proving Peano Arithmetic inconsistent.
“At the end of the day I am a kind of wordsmith” — states Azzouni. Nominalism is very good at deconstructing the perceived reality of abstractions present in language, be it natural, formal (logic) or mathematical. But I feel it has a much harder time defining what is real once those abstractions have been stripped down. The case against Microsoft, for example, I found rather weak, and in some sense a rehashing of John Searle’s Chinese room argument (if you can deconstruct a process in it’s components then it is not real, objects are, but a process just happens). The interesting question to me is at what point do we accept that an abstract entity/process becomes real? Is my consciousness real? and in what sense is it different from Microsoft? obviously complexity, but not locality, or materiality, are relevant: if we are living in a simulation, any distinction between Microsoft and me in terms of fisicality breaks down. A definition of the reality of some thing has to be made in terms of how that thing has internal cohesion or state that is independent and resilient to variability of it’s surroundings, Azziuni states that the boundary of objects are arbitrary, and in many ways they are, yet if I accept the reality of my consciousness (not everybody does) I have to accept that some boundaries are pretty real, is it gradual? or is there a phase transition where we can state that a system becomes real?
Mathematics is the study of structure, the real world has structure, and it is only the structure in the world what our brain perceives. For the structure to be real it has to be relative to some stuff, but once the structure is in the stuff, I have no problem in calling this instantiation of the structure as real, not real alone by itself though. But I would go beyond Dennett’s statement that these abstractions are convenient and go out on a limb and say that they are just as real as the stuff they are made of (but not independent of the stuff they are made of), and not simply convenient to express or explain certain situations (maybe I’m miss-interpreting Dennett, have to read more…).
Medieval scholastics spent a lot of time thinking on existence, and had the concept of the transcendentals, properties that everything that existed needed to have: one of them was being, another is unity. Unity to me implies fisicality, attachment to some stuff that makes it real.
Just based on what was presented in this discussion, I’m not convinced that banks are less real than people by the rules of this view, and I’m curious about how time plays into this view. A bank is a collection of physical things that interact, but it supposedly loses its claim to reality because it can ‘live’ online. A person is a collection of physical things that interact, and it supposedly fits neatly into reality because it’s rooted in a physical form. But what about death and legacy, when it comes to people? In a sense, here in January 2022, Socrates is an online bank. Even if I say, “I listened to a podcast where real people talked about xyz,” you both still exist physically, but I’ve taken part of the bank online. Should I sacrifice intuition and comfort and face the cold hard truth that Socrates isn’t real because I can’t find him anywhere? Was he ever real? Is it even sensible to say that a thing “was” real or “will be” real? I remember discussions in other episodes about the question of whether the past is a thing that exists somewhere, or whether the present is the only reality. I’d be really interested to hear Jody Azzouni’s thoughts on that question.
Fascinating discussion. It’s easy to try and poke holes in the theory or look for inconsistencies, but it’s so admirable, and so much harder, to even try to put concrete language around a reality that’s nearly indescribable.
I find it hard to even summarize to myself what Azzouni’s position is, because I am so accustomed to thinking of a structure of emergent levels of reality. Microsoft, banks, Sherlock Holmes and China are all real, it seems to me, but not each in the same way, and of course not in the same way that chairs are real. And neither are chairs real in the same way that atoms are real. And atoms are not real in the same way that quarks are real. It seems to me that Azzouni is insisting on very specific use of the term ‘real,’ although (I could be wrong) it seems to me that he never defines specifically what that is. Would he say that consciousness is not real? (I would say that it is emergent.) Once one begins thinking about emergence, it’s hard to even understand a position like Azzouni’s. I am intrigued by the fact that Carroll, who certainly understands emergence, nevertheless says that he is sympathetic to nominalism.
A problem I have with this discussion is that they did not get into the root question of the observer – what does it mean to think and know? And I don’t mean in the ancient Greek sense of using arguments to “prove” truths, but from a scientific perspective. What is this language we are using? What does understanding mean in the human mind? Language itself is an entity that only exists as we humans humans use it. Just the fact that the word “exists” was a point of debate points to the fact that the idea of philosophy is rooted in our languages. Which are rooted in our species, which point back to sociology/biology as the more “true” path to reality.