Ep. 240: David Lewis on Possible Worlds and Language Games (Part One)

0:00 Mark: You're listening to the Partially Examined Life, a podcast by some guys who at one point set on doing philosophy for a living, but then thought better of it. Our question for episode 240 is something like, how does context determine how we understand each other? Or maybe do possible worlds exist? And we read three selections by David Lewis, Scorekeeping in a Language Game from 1979, chapter four of his book Counterfactuals from 1973, and Truth in Fiction from 1978. For more information, visit partiallyexaminelife.com this is Mark Linsenmeier broadcasting from many possible worlds simultaneously in Madison, Wisconsin.

0:36 Wes: This is Wes Alwan, existentially quantified in actual Cambridge.

0:40 Dylan: This is Dylan Casey, for whom it's explicitly true that I do not have a third nostril.

0:47 Matt: And this is Matt Teichman, actually located in Chicago, Illinois, but my modal counterparts are located in the respective modal counterparts of Chicago, Illinois, in Other worlds.

0:56 Mark: All right, welcome back, Matt. So you are our go to guy for analytic philosophy. And we knew this was going to be a day when Seth was not going to be available. So this is a figure who he long wanted to cover. I think I found an email from you recommending certain things. What, from 2015 or something? It was a long time ago.

1:18 Matt: Yeah, we've been talks about this for a while. Well, thank you. I love being your token analytic philosopher, and I love it all the more for the fact that I don't even believe in analytic philosophy. So that makes it all the more perfect.

1:29 Wes: What does not believing in analytic philosophy mean?

1:31 Matt: I've been a little bit influenced in my thinking about this by Brian Leiter. So basically, I think the analytic continental distinction is mostly operative these days as sort of a sociological distinction, but that the methods pursued by people in different philosophy departments are so diverse, it doesn't really make sense to think of there as being an analytic method or a continental method anymore. And furthermore, to be more in a collaborative spirit, I just think it's like more productive and helpful for us to think of everybody as being on the same team. I think that leads to more fruitful collaborations and more interesting work.

2:04 Mark: Well, just so you know, I actually thought about you were one of the candidates for our Judith Butler episode recently too, because you had expressed a strong interest and had taught a class in gender.

2:14 Matt: That's right. And I had Butler on that syllabus. She's very difficult. I still wouldn't claim to have a very good understanding of her work necessarily, but I tried to build some bridges there. I think I did A whole lecture trying to draw a metaphor between Butler's thoughts on gender and invisible, unthinkable genders and stuff from model theory. It was pretty weird.

2:33 Mark: So I found a parallel between Gender Trouble and dealing with David Lewis and what we read today, which is that the thing that they're both known for, they're both known for some flashy, very, very controversial thing that is probably just on the face of it, absurd, but they have so much else going for it, it's easy to be distracted by that. So I was picking out the focus on biological sex in particular being a social construction as the sort of red herring it is in the Gender Trouble book. Yes, she does argue for it, but she argues for it in much more detail elsewhere in the book that we didn' and so I was very concerned in that discussion that we not focus on that.

That we focus on the other good things in that book and here the shiny bauble to attract us, the thing. Pretty much the only thing I knew about David Lewis is his literal belief in the existence of possible worlds. And so the chapter from Counterfactuals, which is called Foundations, the book Counterfactuals is a lot of modal logic and I guess it's best known for as a whole dealing with causality in a counterfactual way. That didn't come up in the chapter we read in that at all. But we are reading where he actually gives a short form. I guess he had a later book in 1986 on the plurality of worlds where he argues in great detail.

But we got a taste of it here. But the other two essays we read are straightforwardly Philosophy of Language. I mean, they all deal with modality in some way or another. So they are all related in some way. Do we want to kind of go around the horn and give an initial impression or opening statement, what we want to get out today? The relative importance of the various topics brought up in here.

4:07 Dylan: I'll start as a great revelation of the fact that not only do I not have an advanced degree in philosophy and my undergraduate degree was in political philosophy, I had never heard of David Lewis. No idea who this guy is. I loved reading the Stanford article, the Beginning, where it says David Lewis was one of the most important philosophers of the 20th century. And I thought that was awesome because I felt like I, like, sat down next to Michael Jordan and never having watched basketball or something like that, I felt like that was the kind of error that I had made in philosophy that I never even heard the name, like, before we Read Kripke on here.

I'd never read Kripke before, but I had heard of Kripke before, but I never heard of David Lewis. But it turns out I also was just now delighted by the fact that the thing that I found most weird is the thing that Mark just said is the most weird thing about David Lewis, which is that he believes explicitly in possible worlds. And that was like one of my things. In fact, in my notes, it's right where he says, I believe that there are possible worlds. I have it circled and say, what does this mean exactly? And so that's very delighting. I found them more interesting than I found them very interesting.

Not more interesting than I expected to be. They didn't have any expectations because they never heard of the guy. But I also think that particularly the Truth in Fiction and the Foundations go together really well. But honestly, probably all three of them go well together. Kudos for picking them out. And I myself am just looking forward to learning a lot from some people who have read a lot more Analytical philosophy and quotes to follow.

5:52 Mark: Matthew Wes, did you had to do any of this before?

5:56 Wes: Well, we did some modal logic stuff at ut, right?

5:59 Matt: Yeah.

5:59 Mark: And I feel like we read the truth in fiction essay that at least seemed familiar. Talking about Sherlock Holmes.

6:05 Wes: I hadn't read that. I hadn't read any of these essays. I just know the possible worlds, semantics and all that stuff was in the air. And I found it baffling back then. It was a real shock. It's a real shock coming from St. John's as was all of analytic philosophy. You know, I think Dylan is on the right track. We should try to figure out and explain what he means by that because I'm not sure either.

6:32 Mark: Matt, you said you had strong opinions coming into this, so you chose this Originally you had chosen actually four different articles that all went in different directions. And I said, no, no, no, that's too much. So you up picked it down to these two and then added Truth in Fiction sort of at the last minute, which does kind of bind the two topics together in a certain way.

6:49 Matt: Yeah, he wrote on a huge number of topics and his views about all the topics are interconnected in all kinds of fascinating ways. A little bit like the philosopher Donald Davidson in that respect. You can kind of read around a couple different papers and they sort of reinforce each other. Just as a quick response to Dylan's remark, I've been saying for years, academic philosophy needs better pr. It's like the most famous people are like not even known at all once you leave the confines of academic philosophy. So what is a possible world? Well, one reason I suggested we read this chapter out of the book Counterfactuals, which is an earlier book rather than the later stuff, is that he changed his view a little bit from the late 60s, early 70s to the 80s and 90s.

I'm actually a little bit less up on his later view, but nonetheless, the early view is the one that I find the most plausible because it's the one where he's kind of the most modest about the metaphysics. So, possible world.

7:41 Mark: Can we just give a little the context? So he didn't invent modal logic, right? That was carnap, came up with the idea. We're talking about possibility and necessity. I believe that was carnap in meaning and necessity. Is that right?

7:55 Matt: So the idea that you can explain the idea of possible and necessary. So just to take some examples, necessarily Matt is not taller than himself. That's like a logical necessity. Or necessarily, if I throw the ball up in the air, it'll come back down. That's like physical necessity, given the fact that we're on planet Earth. So we talk about necessarily this, necessarily that, possibly this, possibly that. A more common way to talk about it in natural language is to use words like must and may and might. And the idea that you can explain what necessarily means in terms of possible worlds, I believe goes back to Leibniz.

So the idea from Leibniz is that if something's necessarily the case, like it must be the case, absolutely. The strongest sense of the term must, that means it's true in every possible world. So in every situation you might be able to imagine, if in every situation you might be able to imagine such and such is true, then such and such is necessarily true. And then kind of the dual of this idea from Leibniz is that, well, what does it mean to say something is possibly true? It just means it's true in some possible world. So I don't have a sister, but it's possible that I might have had a sister, or it's possible that I had a sister.

And the way that Leibniz tries to cash that out is by saying there exists a possible world at which Matt has a sister. So that idea goes back a long way.

9:12 Mark: And did Leibniz have a literal belief when he said that, that there are in his ontology, possible worlds as true existent things, or is it just a way of speaking, a shorthand for possibilities or something more modest than it makes

9:27 Wes: a difference whether we're just talking about, you know, to say what's necessary is a matter of what we can imagine is one thing, but to make an ontology out of it is another.

9:38 Dylan: Or also even if you made it stronger than imagining made it stronger. Some kind of strong conditions of consistency and stuff like that. That's a lot different than this notion of, I guess what I conventionally think of existing.

9:54 Matt: Totally. Yeah. So it's been a little while since I've read the relevant Leibniz stuff. My sense from having read it a while back is that Leibniz did take the existence of these non actual possible world seriously.

10:07 Mark: See, the only thing I remember about Leibniz though with that is that we are in the best of all possible world. Yes.

10:12 Matt: So that was part of his moral philosophy that he was mocked for by Voltaire.

10:15 Mark: Yes. That God could see all the possible worlds that he could have created, but because he loves us, because he's all good, he would only create the best possible one. So that would seem to indicate that he didn't also create all the other possibilities. Because it's not just we're special, we're the chosen people. No, it's that his creation would have to be the best that there could be. Because if we say he created all possible worlds literally and we're in one of them, then wouldn't the same logic that we say that we're in all possible worlds apply to all those other worlds? Like he couldn't actually have created all of them. Or if he did, we would have no guarantee that we are in the best possible one. Because everybody's got to be somewhere.

10:56 Wes: Right?

10:56 Matt: And this gets into an interesting early modern topic, which is is God subject to the rules of what's possible and necessary? Is God subject to the ultimate laws of the universe? Or does God just create the ultimate laws of the universe? And different early modern philosophers had different perspectives on that. Yeah. Again, it's been a long time since I've read this stuff, so maybe take my opinion off the top of my head right here. Not looking at anything with a grain

11:17 Mark: of salt, but we've got some historical antecedents and I know that we actually read episode 191 conceptual schemes Donald Davidson and Rudolf Carnap where Carnap said that what you should include in your ontology is just whatever quantifiers have to range over. In other words, if you want to ask the ontological question, are there actually numbers? Well, Carnap thought that was kind of a weird question. It's kind of a Meaningless question. Remember he was one of those kind of borderline logical positivists. In other words, a lot of the questions that philosophers ask are actually non questions are actually bullshit.

But if you need to have an ontology at all, which why not? Then you might as well just say whenever you want to make true sentences and you need to have quantifiers in them, in other words, for all X, F of X or something. So what is the for all X range over and whatever you need to that? Well then just consider it in your ontology. So in other words, if you want to make statements about numbers and you don't want to think those statements are reducible to some other kinds of statements, maybe they are right. Carnap, in his Aufbau book that we talked about with you, I believe did seem to want to like reduce talk of complex entities to whether atomic sentences or perceptual simples or.

He had a couple different ways of approaching it. But in any case, prima facie we're going to talk about numbers. So let's just say numbers are real. Let's not worry about those anti Platonists that say oh that's just crazy, numbers can't be real, they're only atoms in the void, they're only physical objects. Numbers aren't physical objects. Numbers are just abstractions from like let's just put numbers in our ontology because quantifiers range over them. And this is exactly the reasoning that Lewis uses in here, that if we say it's possible that you had a sister.

Well, we're translating that according to the Leibniz formulation is there is a possible world in which you have a sister, then the quantifier, right, there is an X. Let's call that possible worlds. Or if we say something is necessary, it ranges over all possible worlds. Just call that range of things that the quantifier has to go over part of our ontology. In other words, all possible worlds actually do exist because we have to quantify over them. I shouldn't have said actually exist, but sorry.

13:26 Dylan: He says essentially that kind of qualification at the very beginning of the Foundation's paper in the second paragraph that where possible worlds amount to ways things could have been. And it's not that there are, it's absent of constraints, there's all kinds of constraints. But he wants to say that taking that claim at face value that all these possible worlds, that the way things could have been, that they all exist, doesn't get us into trouble and everything like that, what does it add to say that possible worlds exist. Is it just a claim that amounts to saying, well, you don't have to say that they don't exist. So let's not worry about that part.

14:05 Wes: He thinks they need to exist. So let's go to that part of his argument. I don't really understand it either.

14:12 Matt: I could maybe venture an argument for that via a little bit of background here. Why don't I read the part that Dylan was alluding to? So he says, this is just on page. What is it, 84 of counterfactuals. I believe that things could have been different in countless ways. I believe permissible paraphrases. What I believe, taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called ways things could have been. I prefer to call them possible worlds. So a possible world is a way the world might have been the actual world.

Presumably, just as a little bit of background on this, since we were talking about kind of intellectual antecedents and sort of what Lewis is responding to. So definitely agree with Mark that Lewis is responding to Willard Van Orman Quine's idea from, I think a paper we've talked about on this podcast called on what There Is, the big quote from that is to be is to be the value of a bound variable. And Lewis is definitely influenced by Quine here. In fact, Quine was a modal skeptic. Quine thought that all this like non actual possible stuff was a bunch of bunk.

So Lewis is in a way trying to answer Quine's objection with his approach here. But probably I would think of as the more important bit of background for this is Saul Kripke's Relational Semantics for Modal Logic. All right, so that's a bit of a mouthful. But what it was, it was a unified account of what necessarily, in all its different flavors, means. So sometimes when we say necessarily, we mean, let's say when we use the word must or should. Sometimes when we use the words must and should, we're talking about morality. We're talking about you mustn't smoke in here.

You shouldn't smoke in here. You should lend a helping hand to your neighbor. So sometimes we talk about moral necessity, sometimes we talk about what philosophers call epistemic necessity, where the words like should and ought and must and may are talking about what we know. So I don't know who that is. Oh, wait, that ought to be Mike. I know who Mike is. So that would be an example of using ought in the epistemic sense. Where you're talking about the range of what you know. And then we also use like must, should, ought, and the word necessity and possibility to talk about like physical laws.

So like, you know, if you shoot a target at blah, blah, blah, range, the target's going to get hit, or if we're talking about the past, like that kind of gun must have hit such and such type of target at such and such range. It seems like we're talking about physical necessity. So what Saul Kripke did, by the way, at age 16, with his relational semantics for modal logic was he gave a unified mathematical definition of all these different senses of necessary and possible, such that morally necessary and physically necessary and logically necessary were all flavors of the same thing.

And that was sort of like a technical challenge that people really struggled to meet before Kripke came along with this. Relational semantics. So I think part of what Lewis is presuming here is that Kripke's relational semantics, which uses some notion of a possible world, that is to say, the mathematical definition of what necessarily and possibly mean in modal logic, according to Kripke, involve these mathematical models that have something in them we call possible worlds. The success of that semantics for logic in getting over this problem suggests that there might be something really important to this idea of a possible world.

So I think that's also sort of part of the background here, even though Lewis doesn't explicitly mention it.

17:25 Wes: Yeah, let's look at the argument that's in the text.

17:28 Dylan: 85 is where you want to start. Okay.

17:30 Wes: If our modal idioms are not quantifiers over possible worlds, then what else are they? And I want to actually skip to three, because this is the main alternative. Three, I think, to most of us would be the intuitively acceptable alternative. So we might take them as quantifiers over so called possible worlds that are really some sort of respectable linguistic entities. Or I might say just thoughts or something I'm imagining, say maximal consistent sets of sentences of some language. We might call these things possible worlds, but hasten to reassure anyone who is worried that secretly we were talking about something else that he likes better. But again, the theory would be either circular or incorrect according as we explain consistency in modal terms or in deductive or purely model theoretic terms. I don't understand that yet.

18:24 Matt: I think the idea there is that. All right, suppose I'm a skeptic about possible worlds that are not the actual world. I think these things are bs. But you know, what does make sense is like a set of sentences. Let's say a complete description of an alternate possible world. I can imagine a complete description of an alternate possible world. It's just a really long. It's like a long book. I describe it in English or whatever. I describe it with a bunch of sentences.

18:44 Wes: Yeah, it's like fiction.

18:45 Matt: Yeah, fiction perhaps we'll get to that in a bit. Right, but then thing is like, well what kind of set of sentences is a possible world then? Because some sentences are logically incompatible with each other. If you just say that a possible world is a set of sentences, it seems like that's too inclusive because that's going to include all the like logically contradictory set of sentences. And then the idea here is like how are we going to try to rule out the logically contradictory ones except by appeal to the idea of possibility? Aren't we going to sneak in our idea of like, well these two sentences can't both be possible at the same time. But we can't do that because we're trying to use this idea of a set of sentences being a possible world to define what possibility is.

19:21 Dylan: So the example that he gives, the reason I went to 88 is it's a kind of example. I think of this the second full paragraph after having talked about some things about metaphysics. He says among my opinions that philosophy must respect are not only my naive belief in tables and chairs, but also my naive belief that these tables and chairs might have been otherwise arranged. Realism about possible worlds is an attempt, the only successful attempt I know of to systematize these pre existing modal opinions. For instance, I believe that there are worlds where physics is different from the physics of our world, but none where logic and arithmetic are different from the logic and arithmetic of our world.

There is nothing but the systematic expression of naive pre philosophical opinion that physics could be different but not logic or arithmetic. I do not know of any non circular argument that I could give in favor of that opinion. I have no more use for a philosophical doctrine that denies my firm unjustified modal opinions than I have for one that denies my firm unjustified belief in tables and chairs. The reason I went to this is the way Matt was talking about necessity and possibility. Where we usually think of that in terms of moral doctrine and moral philosophy.

And is this kind of thinking that gets applied to metaphysics? Is this way of thinking about possibility seems very analogous to the way we would be thinking about possibilities in morality.

20:53 Mark: Wes had read the third option that he gives. If we don't want to accept the literal Existence of possible worlds. The first one is we might take them as unanalyzed primitives. This is not an alternative theory at all, but an abstinence from theorizing. But I think that actually might be right.

21:08 Matt: Right.

21:09 Mark: Because he's saying that the third one, they're just state descriptions. They're just maximal consistent sentences. The book that Matt was describing, but it has to be a consistent book. In other words, we need the law of non contradiction. And he says you can't rely on the law of non contradiction because the whole point in talking about possibility and necessity is to explain, among other things, the law of non contradiction. Well, what if you just say we can't explain the law of non contradiction. In fact, we. In our truth episode where Strawson or one of these guys was arguing that if you try to define truth, you end up defining it in terms that in turn need to be defined back to truth.

I think it was Davidson was saying, no, that's okay, because concepts sort of enter as a group unless we're foundationalists that we don't need to have something boiled down to, you know, I guess if you're Aristotle describing this, you probably have to say, yeah, the law of non contradiction is just basic. And if you want to build possible worlds, semantics out of that, in other words, describing them as sets of consistent sentences, consistency can just be something like truth. That really isn't going to have any helpful analysis.

22:16 Matt: I seem to remember Aristotle saying that someone who tries to deny the law of contradiction is like a plant. Which is one of my favorite lines in philosophy.

22:24 Wes: Yes, you lose the ability to speak.

22:28 Matt: That's a really good point, I think, about foundationalism, non foundationalism. So I happen to be kind of anti foundationalist. I don't like the idea that anything is self explaining. And I think Lewis is kind of, he's struggling a little bit with that here. I think part of him wants to not be a foundationalist and part of him is just being pressured into being one implicitly. Because most people at the time were. The reason I like this version of the view better than the later one is that this one is more clearly pushing back a bit on foundationalism.

He adverts to this stuff like the part that Dylan read where it's like, well, look, I just have these knee jerk, super intuitive, unjustified, and I want to just systematize them and I'm not going to try to find a justification for them because I don't even know what that would be. But who are you to sit here and tell me that, like, there's no such thing as another way the world might have been. Obviously there's another way the world might have been. It's not like we're locked into actuality. That's nuts. We talk about ways the world might have been.

We talk about other possible worlds maybe a little bit less often than we talk about ways the world might have been. But, yeah, these are just two ways of talking, and they're super intuitive ways of talking. So let's take them seriously. I think one way for him, possibly not to be a foundationalist here, but still hold on to some of the stuff that we read, the 1, 2, and 3, is by thinking about logic. Like, one of the things you do when you study modal logic is you think about what follows from what. And that might be simple if you're dealing with really simple statements, but it gets a little tricky as soon as you have different logical operators interacting.

Just to take a quick example of that, does it follow from the fact that it's necessarily the case that either A or B, that it's either the case that A is necessarily true or that B is necessarily true? And you probably have to think about that a little bit. Good example to bring out why it's not true is imagine that we live in the gender binary. Imagine the gender binary is accurate. Just for the sake of argument, then it would make sense to say it's necessarily the case that everybody is either a boy or a girl, but it certainly wouldn't follow from that.

That it's either the case that someone is necessarily a boy or that they're necessarily a girl. So in thinking a little bit about what follows from what and how these operators kind of interact with each other, this is what sort of, like logicians obsess over all the time. The ability to do that is maybe based on the ability to kind of translate, talk about ways the world could have been into something else that lends itself to more systematization. So you can kind of test hypotheses about what follows from what. So I think, like applying this stuff to logic to think more carefully about the meanings of subtle shades of difference in the meanings of more complicated sentences is potentially why he doesn't want to just take must and should and might and all that as an unanalyzed primitive.

24:52 Mark: Part of the reason I wanted to connect this doctrine to Carnaps was because the context of the Carnap paper, which was called Empiricism, Semantics and Ontology, that we discussed in episode 191 was anything that a quantifier ranges over. Let's call that part of our ontology. But we talked about that in the context of conceptual schemes and taking Carnap, maybe as a defense, contra Davidson's, on the very idea of a conceptual scheme that there is some sense to make of, in other words, different contexts of discourse. So if you say that what ontology has to be is the kind of things that exist in the world, that sounds like, you know, there's only one domain and you could restrict that for the purposes of certain conversations.

But when you're talking about your ontology, that's all. Quantifiers range over everything, really, unless otherwise restricted. But the fact that I tripped up and said David Lewis thinks that possible worlds actually exist.

25:50 Matt: Exist.

25:51 Mark: That's not right. Whereas the word actually, like it sounds like if something exists, it actually exists. Right. That's just the definition of actually. Actually doesn't add anything. But for David Lewis, it actually does,

26:04 Matt: because that's part of the trick.

26:06 Mark: Yeah, they exist, but they possibly exist. In other words, they exist as possible worlds. They don't actually exist if that means existing in the actual world.

26:16 Wes: Actual is an indexical. So this world is actual for me, but a different version of Wes in another possible world. That world is actual for him.

26:28 Matt: Yeah, exactly.

26:28 Wes: Yeah, they're all actual for someone, I guess, if there's someone for them to be actual to.

26:32 Matt: Yeah, just like I is the speaker for some speakers. Yeah, yeah.

26:36 Dylan: I'm sorry, I don't mean to be just deeply incredulous, but I feel like we're doing some good work about going through the beginning where the things that he says, alternatives that could be true that he wants to reject. But I'm still not clear on, like, a concise way to understand what's the added value. Why do you need to have this? And I agree with Wes's statement earlier that he seems to need to have it, but I don't understand where he's hanging his hat in that respect. Unless it's just that he doesn't like the alternatives that he presents for modal idioms, that he's just trying to solve the problem of modal idioms and this is the only way that he could solve it. And he points to it because it solves the problem and is not objectionable, and that's the reason why it works. And is that as strong as we

27:23 Matt: got, it's going to give a unified meaning to morally necessary and physically necessary. The morally necessary truths are going to be ones that are true in all of the worlds where the rules are followed and the statements that are physically necessary are going to be true in all the worlds where the laws of physics are followed. So you have kind of the same definition across both of those things.

27:46 Dylan: But why does exist. Why does it need to actually exist

27:51 Wes: to the average person? If I said, well, my keyboard might have been on the floor right now. It's not, it's on my desk. But if I put it there to the average person, it's just like, yeah, I can imagine that. But there's one actual world. There's lots of different possibilities I might imagine. But what's the use of saying, okay, we have to talk about all those different possibilities as existing? I think maybe we need to explain more to listeners. What's useful about that. We've given some explanation of that, but I think we need to do more if we're really going to get past that. Basic intuition for the average person is that we're just imagining possibilities and that's it. That's in the imagination.

28:30 Dylan: I would say it even stronger than that for a second because you gave that example. When I say it's possible that it could be on the floor, it could be on the table, and we'd also say that it's impossible for it to be on the moon. And there's good thinking and content to what you're thinking about contextually for that,

28:48 Wes: Dylan, you're ignoring the possible world in which I have a rocket that I put the keyboard out and I send it to the moon.

28:55 Dylan: How about the keyboard in the middle of the sun? I mean, my only point is that there are rules and constraints in those possibilities when we talk about them. And we could, following either the scorekeeping paper or the Truth in Fiction paper, have a discussion about how those rules might evolve or change. Right. And so the space of possibility might change, but there's content to us saying it's possible or not possible.

29:24 Wes: Yeah. Let's say a little bit more about the utility for a symbolic logic, for a semantics. Let's say the utility of taking a sentence like it's possible that the keyboard is the table, because we would say it might have been the case that the keyboard was on the table. Something like that. What do we do in symbolic logic and what's useful in developing a semantics, what's useful about talking about translating that into possible worlds talk.

29:51 Matt: So if you say my keyboard might be on the floor, imagine two different things that could mean one thing. It might mean I'm using the word might, so I'll use could.

30:00 Wes: I guess that's fine.

30:01 Matt: So one thing it could mean is, like, I'm looking for my keyboard. I can't find it, and I'm thinking of, like, where are the places? Ah, well, it could be on the floor. Okay, so why don't I go look at the floor? Like, I don't know where it is. I'm looking for it. And that would be like, an epistemic sense of the term. It might be on the floor. Alternatively, let's say you and I are sitting here and we're looking at the keyboard, and it's definitely not actually on the floor. We're looking at it right now. It's just on the desk. We know exactly where it is.

But we're speculating like, well, what if it was on the floor? I mean, it. You know, it might very well be on the floor. And if it was on the floor, it would be dusty. That's kind of a stupid conversation. But, you know, just to stick with the example, we're definitely not wondering where it is. So the role that, like, might is playing there doesn't have anything to do with us trying to figure out where it is. Rather, what we're doing is we're speculating about something like the laws governing the keyboard in some sense or something like that.

30:51 Wes: No, we do this all the time, though. We. For a game or something. What if I had moved the bishop to a different place? Or what if I hadn't gone to the store yesterday and become infected with coronavirus? Or telling a child who almost threw the keyboard on the floor, what if you had done that and broken it? So we do that all the time.

31:09 Matt: So the cool thing from the point of view of mathematical logic is that you're in a position to say so. Dylan's holding up a book whose title is what if to the camera. For those just listening at home. The thing you can do in mathematical logic is you can say that those two mights mean the same thing, except for one thing. There's only one difference between them. And the only difference between them is that in the I'm wondering where the keyboard is case, the set of worlds that I'm looking at to see whether the keyboard being on the floor is true in any of them.

That set of worlds I'm looking at is restricted differently. It's restricted to the set of worlds in which everything that I know to be the case is the case. And in the we're speculating case, the set of worlds that we're looking at is a set of worlds in which the normal laws that apply to the actual world, the laws of physics, the laws of social convention, whatever, stuff like that, the stuff we can take for granted and assume all the worlds in which those laws still hold. We're going to look to see if in any of those worlds the keyboard is on the table, and if so, it's true.

So it's almost the same meaning between those two very different flavors of the word might. The only thing that changes is which set of worlds you start off by looking at. And that turns out to have tons of really interesting mathematical applications. You can look at variations in this initial set of worlds to look at that could be very interesting and draw correspondences between all these different kind of mathematical structures.

32:31 Mark: You get to use set theory.

32:33 Dylan: So, big deal. I can come up with mathematically consistent rule sets that look like physical laws and talk about what those worlds look like and use my logic to come to conclusions about that. I can ask questions like, can I create life out of elements other than carbon? Stuff like that. That all seems perfectly sensible and interesting. Why do they have to exist?

32:59 Matt: So I think the interesting thing here is that the bar he sets for them existing is lower than in some other writings and fans. Yes, it's very low. It's just. Would you say that there was another way the world might have been? If the answer is yes, which it obviously is, then that's all I mean by possible world, that's just all it is. For the possible world to exist is, you would say there's a way the world might be.

33:19 Wes: Yes, but he doesn't want to say that. That's just in your imagination. We would normally translate that sentence into there is another world the way the world might have been. We translate that into, I can imagine the world having been different and a possible world. Semantics has to go further than that.

33:36 Dylan: Yes.

33:37 Matt: So the thing is, you can't just imagine anything. And I think that's part of why there's this idea that there's objectively, some worlds are possible and some worlds are not possible. So I can't imagine a world in which I'm taller than myself. So I can't just imagine any old thing. So whatever the constraints are on imaginability or something like that, that's part of what he's sort of attempting to get at with this idea that they exist and they're real.

33:57 Wes: I see. So constraints on imaginability. It seems like there should be some existent to form the basis of Those constraints.

34:08 Mark: You're not going to like this, Dylan, no matter how much we struggle with it. Don't.

34:11 Matt: I thought he sounded like don't like it. Beginning part.

34:16 Wes: Well, I think we don't know enough about possible world semantics from these readings, right. To fully get the appeal. I think that's part of the problem we're dealing with here.

34:25 Dylan: Maybe I have too high of an expectation here, which is. I feel like this is the nub of solving some problem that exists separate from this, that he's solving some other kind of problem that's important, which I don't even know even to do anything other than say that there's a problem he's solving. I don't even know how to say what that is. So I'm sort of looking for two things. One is the problem that he's trying to solve, which the closest thing I've heard that Matt provided for his context is how to talk about possibility and necessity morally and physically at the same time.

And that those two kinds of things are different ideas historically or in previous philosophical thought. And the problem that Lewis is solving is a way in which to talk about those in a consistent manner in the same way. So that I just said that. I'll take that for granted. I don't really get what those differences are. Maybe that's a separate episode.

35:23 Wes: So here's another way to. And Matt can correct me if I'm wrong, but I'm trying to rephrase something that you were just saying. When we make a non modal statement, the cat is on the mat. We ask ourselves about the truth conditions of that and we have to say, well, there's something in the world, there's some factor in the world that makes that statement true. And if I make a modal statement, the cat could be on the mat. We take it for granted that that's true, that's a true statement, and we want to look for some existent conditions to say why it's true, otherwise why would it be true? So what makes that true? You know, it can't just be in our heads. It has to be something real. And then how do we parse out what is real, what exists that would make that sentence true?

36:08 Matt: I totally agree. I think he's under the influence of the correspondence theory of truth here, where if a statement is true, it's because there's some stuff and there's a way that the stuff is arranged, or the way that the stuff is, or something that affects that your statement corresponds to.

36:22 Dylan: So the idea there is that Anything that's true has something that it corresponds to.

36:29 Matt: Yeah, I think. Yeah. If you like the correspondence theory of truth, then you're going to try to find that everywhere you see a true statement.

36:34 Mark: Yeah. So this is like a Kantian transcendental argument. In other words, what must be the case for our practices to make sense, to distinguish this. This talk that possible worlds are real is very different than anything that's in science fiction. Right. There's fringe. There's been a bunch of science fiction that's kind of taken this and said, well, what if we could travel to these other possibilities? But it's just defined in here that if there was any connection, they wouldn't be possibilities. There would be remote parts of the same world to say that they're not actual, that they're merely possible.

You know, again with actuality being an indexical, so from our perspective, they are merely possible, then it cannot be possible for us to hook up with that other world in any way but this transcendental, inexperienceable way. This is why I'm saying, like, you know, for Kant, the thing in itself is a transcendental thing. We can never by definition have any direct experience of it. It is merely something that we have to posit for our language to make sense.

37:36 Wes: See, it sounds almost Meinongian. Right. He mentions Meinong at the beginning, where there's these entities. It was one of the attempts to get around false statements that involve references to things that don't exist. Something like that. So where you say you have these subsistent entities, and that way I'm not bedeviled by those problems.

37:54 Matt: Yeah, he's definitely influenced by Meinong here. But one important difference is that Meinong thinks that there are impossible worlds and Lewis thinks by definition that doesn't make any sense. So Lewis is more restrictive on what he'll include in the set of worlds than Meinong is. Meinong includes literally everything we ever say, even if it doesn't make any sense.

38:11 Wes: Right.

38:12 Mark: So I want us to consider page 87. He gives two potential objections to what he's talking about. The first one, he says realism about possible worlds might be thought implausible on grounds of parsimony, though this could not be a decisive argument against it. Distinguish two kinds of parsimony, however qualitative and quantitative. A doctrine is qualitatively parsimonious if it keeps down the number of fundamentally different kinds of entity. However, doctrine is quantitatively parsimonious if it keeps down the number of instances of the kinds it Posits. So in other words, if you don't like possible worlds because it creates all these things, then you're engaging in quantitative parsimony. And he thinks that is bull. Like that's not the way science even works.

38:56 Matt: Right.

38:57 Mark: If we say we want one fundamental law of unified field theory, or we want just all matter to be reduced to atoms or quarks, we want as few entities as possible. We don't mean the fewest number of quarks, we just mean the fewest types of entities. We want them all to be quarks. And so he's saying, look, they're all just worlds. Do you know what this world is? Right. Well, it's more like that. It's no more mysterious than saying, you know, it's all atoms and the other atoms are just like the ones that we can experience here.

39:29 Wes: So I think most people are going to think of possible worlds almost like a kind of science fictiony parallel universe or something like that. Does it really mean to say that there's another world right now in which Wes is doing all the same stuff, but the keyboard is on the floor? Are there infinite number of different versions of Wes all doing their thing right now? It's that kind of objectionable idea, I think, that most people would be trying to grapple with in this case. Or does he just mean something almost much, much more abstract and logical, which is just. He's saying, yes, if I can say that it's true that something is possible, then that possibility exists. That's all I'm saying. It's not that there's another Wes out there doing something else right now. It's just that there's another possible Wes, something like that.

40:21 Dylan: The way he's talking about it now, I'm thinking that if I thought of our actual world and I thought about it as just a line, the line of our existence, of our world. He essentially wants to say that I'll pick just two dimensions. There's a sheet of possible worlds and our actual world is the one that runs through it. Mark used a similar kind of analogy, saying that there was when we were talking about Leibniz, we were saying Leibniz said ours is the best of all possible worlds and there's all these other possible worlds that would be recognizable as a world.

Let's just have it be that loose. Right? Is what he's opening up the thinking about to is the actual world is one world. And we don't want to get confused about possible worlds always being actual worlds. Is that there's always one actual world, but there's a universe of possible worlds that inform our understanding and are informed by our understanding of our actual world. And that that space of possibility has to be there in order to account for would, should, could, might kinds of discussions. They have to exist in order to account for that way of talking about possibility.

But when we say they exist, we're going to split hairs and say they're not actual.

41:42 Mark: Do you think I'm being too optimistic, Matt, and still wanting to take him? He doesn't say I'm not being a nominalist here, but he says that he objects to the other. Oh, no, I merely mean a bunch of sentences. I mean an idea in my head. He just thinks that there's problems with those formulations. So maybe he doesn't want to come up with his own formulation. Let's just call it existence. But I still feel like he's being deflationary about what existing amounts to. In other words, like carnap. He's actually being a nominalist and saying again, yeah, existence is just what a quantifier ranges over. That's. That's all.

42:19 Wes: It's not all it's cracked up to be.

42:20 Dylan: He's deflationary about what existence means.

42:24 Matt: That's exactly why I like this version of his view. It's because it's deflationary about what it means to say the worlds exist.

42:30 Wes: So later on you're saying he comes out more.

42:33 Matt: He gets a little closer to this view that's, in my opinion, weirder than this. This version of you, I think, is kind of sticking with common sense. If you hear there are other possible worlds as just literally being completely synonymous with the world might have been different from the way it is, which he seems to be saying. That's how you should hear it here. Then. I think this version of the view is pretty common sense. Once you get into the later version of the view, we sort of flirts a little bit more, at least on my interpretation, could be wrong with the idea that there's a special kind of truth, a metaphysical truth, that's different from a logical truth.

It's different from a physical truth, different from moral truth. And metaphysics is a study of these special kinds of truths. So in other words, he tries to kind of like flesh out the notion of what it would be for these things to exist in ways that, for me at least, it's harder to imagine what it would be to verify a statement about metaphysics that's not somehow reducible to these other things. That's not just doesn't go back to common sense, doesn't go back to logic, doesn't go back to physics. There's a special mode of existence these things have that's different from all the other stuff we've been talking about.

It's harder to imagine people making progress in their disagreements on, I guess is the issue for me.

43:36 Mark: You threw in verification there. Are you saying that Lewis thinks that the existence of these other worlds verifies our statements? Because that would imply that we have some knowledge about them, whereas we don't, according to, you know, we just have sort of what's required by the theory.

43:53 Dylan: Don't we have knowledge about them?

43:55 Matt: Yeah, I think according to the counterfactuals view, we do have knowledge about them. I mean, basically by our knowledge of logic, the world's sort of systematizing logical inference. It's maybe a little bit more nuanced than that, but that's basically the idea,

44:06 Mark: I think I was just thinking about what verification has meant historically. Verification means you can go look with your eyes, not that you can, using your logical apparatus, transcendentally deduce.

44:18 Matt: I sort of meant it in a much more general sense of the term, like any kind of evidence at all. So you could consider, like a math proof, which doesn't involve looking at anything, to be evidence of a math theorem. You consider, I don't know, testimony from somebody. Evidence. Evidence in the most general sense of the term. And to me, the idea that there's a distinctive form of metaphysical evidence that's different from all these other kinds of evidence, I'm just sort of like not sure what exactly that would be.

44:40 Mark: Maybe to wrap this topic up and wrap up our first half here on page 87, there was a second objection that he answers that I think maybe gets at what's lingering still here, bottom of the page. Perhaps some who dislike the use of possible worlds in philosophical analysis are bothered not because they think they have reason to doubt the existence of other worlds, but only because they wish to be told more about these supposed entities before they know what to think. How many are there? In what respects do they vary and what is common to all of them?

He gives some other things. If worlds were creatures of my imagination, I could imagine them to be any way I like, and I could tell you all you wish to hear simply by carrying on my imaginative creation. But as I believe that there really are other worlds, I am entitled to confess there is much about them I do not know and that I do not know how to find out. So he actually says that there are sort of a number of theories of possible worlds that are consistent with the evidence. In other words, the transcendental deduction, that's a way of responding to.

Is there really a world, you know, running in parallel to this one, where Wes is doing the same thing but his keyboard is on the floor? Is that real? Is there really? Well, what is that? Like, why would his keyboard be on the floor? What does that even mean? Like, why would his keyboard be in the moon? You know, if you start asking these questions, especially in that voice,

45:55 Matt: all questions should be asked in that voice. That should be an accent.

45:59 Mark: Yeah. Then you're kind of missing the point that if the only evidence, the only thing we can know about them is what comes out of this transcendental deduction, this inference of reason, then we simply can't say anything about them beyond that. And that's all the theory requires, and that's all that existence.

46:15 Wes: But we can make a lot of hypothetical statements though, right?

46:18 Matt: That's what we're stuck with. Knowledge of them by hypothetical statements. And we can't. We're never going to be able to learn anything more about them because we can't, you know, travel to them, as Mark was saying earlier.

46:25 Wes: Yeah.

46:26 Dylan: I mean, doesn't it sort of make all hypothetical statements that have any content about things that actually exist or actually not actually exist? I have to be very careful now because.

46:36 Matt: Yeah, you do have to be careful.

46:37 Dylan: We split the hair between actuality and existence.

46:42 Wes: You need hypotheticals and counterfactuals to describe lawful behavior within the existing universe. Right?

46:49 Dylan: Yes. And that's how you do that. And everything that you describe in such a way does exist. There's a separate question of which ones are actual or which one is actual.

47:01 Matt: Yeah. One. From my perspective as a speaker, I actually inhabit this world, somebody in another possible world. When they're speaking, they're speaking from the point of view of somebody who actually inhabits that world. But yeah, you can only have it one at a time.

47:15 Dylan: Maybe we'll get to this later when we continue with the scorekeeping or the truth in fiction. It does make it easier for me to make sense of talking about. And maybe this is part of what he means by possible worlds running through scenarios in which we can have a discussion about what those scenarios, how those scenarios play out. Thinking about strategy, for instance, in a game. That's why you might have scorekeepers, language game. Also his way of talking about having a discussion about what was thinking through the things that weren't actually said in a story, or trying to evaluate whether or not it's reasonable that a character acted in this way or that way, that in talking about possible worlds, the way he's talking about it is it gives a constraint in language to context.

48:03 Mark: We'll bring this back up in discussing the other papers, I guess, just for a final word, at least for me on this paper. So the rest of the essay, there's still quite a few pages left, but he's kind of thinking about. So he actually refers to Quine, who apparently you said, Matt dismisses all this as nonsense, but perhaps we could characterize what all the possible worlds are. Well, like the sorts of worlds that Democritus would be okay with. In other words, there's just atoms in the void. Then maybe we can say there's just possible arrangements of matter, you know, in space and time.

So you could look at any given. You could kind of come up with a coordinate system to say, okay, in this piece of matter, at these coordinates, at this space and time, is there matter or is there not? Yes or no. So you can, like come up with a binary, a mathematical thing. And then he wants to say, well, maybe that world isn't Democritean. Maybe there's. It's not just a matter of, you know, matter is either there or it's not. Maybe there are different densities of matter. Maybe there are fields in addition to matter. But he thinks, like, you could potentially come up with all the different parameters.

You know, maybe we don't have Euclidean space, time, maybe we have some other kind of space time and just get a bigger and bigger mathematical function that could represent all of the potential worlds. And thereby part of what he's concerned with is how do you represent similarity between worlds? That's going to be key in the remainder of our discussion here. Well, if you could come up with a mathematical system, then you could, well, look at the values and say, how different are the values of this world? So the values of that world. He thinks this is actually all sort of a red herring that he actually does want to stick with.

No, we can't know anything more about the possible worlds than what I've already said. You know, that they have some logical reference to the actual world. Because if you use the physics that we know, oh, well, we think space might not be Euclidean. So let's throw in that there could also, you know, there could be many more things that we haven't even thought of. Even just keeping track of the number of worlds in mathematical terms could just be something that is Even in principle, insurmountable, because they're always going to be, you know, they're unknown unknowns, right?

They're not just known unknowns, but they're unknown unknowns. And likewise, he thinks that we don't need something mathematical like that to account for similarity between worlds. If I ask, is the world where west put his keyboard on the floor, but otherwise everything is the same, is that more similar to the actual world where the one where somehow he had gotten a rocket and sent his keyboard to the moon? Clearly the former is more similar to the actual world than the latter. And like, we don't need some super weird mathematical thing to be able to chart that similarity more exactly.

50:42 Matt: So I think that was a great explanation of that part of the paper. I just want to mention, like, there's a hilarious footnote here where he says, let's just say for the sake of argument, we're not going to do this, but let's just imagine that we were to try to mathematically formalize what a world is. And let's have the simplest possible mathematical model of a world. It's a set of 3D coordinates, real valued 3D coordinates. And the only thing that can be true is for each coordinate, either the point can be occupied or it could be unoccupied. And a world is just a distribution of points in this space.

That's like the simplest possible mathematical model, maybe of a possible world, even if actual. There I go again. Even if the possible worlds were in fact that simple, you can prove that there are mathematically way, way more of those things than there are sets of sentences. So here's another clever little argument here against the idea that a possible world is a set of sentences. A set of sentences can only be countably infinitely big. But those coordinate systems with the points either occupied or not occupied, there are uncountably infinitely many of those.

So that's another fun little tidbit that whizzes by in this part of the book.