Contexts & unrestricted quantification

0:00 Yeah, so the handout is identical to what's going to be on the screen except for where the page breaks go. I was just realizing as I thought about how I proved this out that it might be cruel on people's eyes but every now and again I'm going to be making reference back to some numbered examples so I wanted something on paper for you to look at so I guess I should say before really getting going this really is primarily a philosophy of language talk sorry to say I know it's a horrible thing to hear There's a tiny, tiny, tiny bit of logic at the end, but don't be fooled. There are no theorems coming, and in fact, I was slightly embarrassed by the amount of notation that was involved at the end for the utter lack of any theorems. What's going to happen at the end is just pointing out that there's a fairly familiar object that logicians know and love, which might be a useful thing to think about for the result we get at the end of the paper. And I would have to peek at the end. No, no, no. Too late, too late. However, even though it's a philosophy of language talk, I do get to start with something very familiar to all of you. That's Russell's paradox. What I have up on the screen is a slight tweak on Russell's paradox due to Tim Williamson. It is Russell's paradox. put with slightly less set of theoretic baggage. And so the maneuver is, you think about building an interpretation for a language. And the trick is, you build an interpretation subject to the rules that a distinguished predicate P will hold of all and only the objects.

2:30 And you can go do a Russell trick with this. You can let the R's be all and only the objects O, such that O is not an interpretation under which P applies to O. This should have a very familiar ring. Look at O. Oh, sorry. Build that interpretation. Let O be that interpretation itself. Then according to that interpretation, the object O, which is that interpretation, falls under P, just in case it does not. Standard contradiction. I like this version of the paradox because it makes vivid an issue that I'm going to come back to quite often. What Tim did was he did this without terribly much specific set theoretic apparatus. I haven't said anywhere that I was dealing with sets. I haven't said anywhere that I was dealing with proper classes on your favorite theory of proper classes. You can run pretty much all of this discussion in terms of plural readings of second order quantifiers, if you like. It's very minimal in baggage. What does seem to be going on is that you find an object which cannot be in the domain of the quantifiers that this particular interpretation gives you. If that object O is in the domain of the quantifiers in the interpretation, you have a contradiction. If O is not in the domain of the quantifiers, you don't. And the thing about O, which is going to be important later on, is that O basically is an semantic object. So one way to think about, the way I tend to think about what's going on in Russell's paradox, is that the process of interpreting a language gives you the resources to find an object which cannot be in the domain of the quantifiers as you interpreted the language. The process of interpreting allows you, in effect, to talk your way out of whatever quantifier domain you gave yourself. If you add just a tiny bit more set theory, and this gets much more familiar, the problematic object needn't be one of those little funny Russell things. You can just take it to be the domain of the quantifiers themselves. You take the widest domain of quantification your interpretation gives you, you make that an object that, under fairly minimal and familiar set theoretic assumptions, can't be in the domain. So for pretty much the entire talk, I will just work with that version. I'll talk about the domain of quantification itself being an object, which is one that cannot be in the domain of quantification. All very

5:00 familiar. I mean, this is just repeating Russell's paradox. One thing I guess is worth mentioning more or less as an aside, putting it this way brings it closer to some issues in semantics, closer to some issues about interpretation it tends to make the issues surrounding russell's paradox look a lot closer to issues around the liar paradox um i'm partial to that identification but i'm going to try as best as i can not to talk about it today i'm going to try and stick to the russell issues to the extent that i can now if you think about russell's paradox the way i just presented it. There's a fairly natural way to respond. Certainly not the only way, but one that I think is natural and one that I even think is probably right. So what got was the idea that, look, if you interpret a language, we'll give you the resources to find an object which isn't in the domain of the quantifiers as interpreted. So assume this under the general phenomenon context dependence. What we want to say that each interpretation assigns what I'll call a background domain. It's the domain over which the widest ranging quantifiers in that interpretation range. It's the domain for the unrestricted quantifiers relative to that interpretation. One way of taking the moral of Russell's paradox, as I was putting it, is even background domains are apt to expand. You're able to find an object that was out of any background domain. Try and subsume this under the general category of context dependence. In one context, you fixed a background domain, you find another context relative to which there's a wider background domain. So we try and subsume what looks like this very puzzling behavior of unrestricted quantifiers under something that's supposed to be a fairly familiar phenomenon for natural language. Natural language is rife with context-dependent expressions. in natural language, which doesn't contain one. Maybe impossible, I don't know. And, of course, many, many, many of our favorite examples of context dependence in natural language come from contextual restrictions on quantifier domains. So, in one, I'll try

7:30 to give you a few familiar examples. Most people came to the party. Almost never means most people in the entire universe came to the party. It means most of your friends, most of your colleagues. I took everything with me. Of course, well, did anybody say that this morning when packing? You might have, and you certainly didn't mean the entire universe. And the last one is actual corpus data. You hear that on advertisements all the time. And it's actually a little hard to say exactly what it means. But it isn't the case that the claim is that everything in the universe, tout court, amongst that nothing outlast, the energizer, funny. Oh, the energizer. What is the energizer? Oh, it's a little thing that, it's an advertisement for a battery. The energizer is a little thing that keeps moving and moving. So generally, we see lots and lots and lots of heavy context dependence of quantifier domains and natural language. So the idea is we take what looked like a real problem floating around Russell's paradox and perhaps floating around the liar paradox and say, no, no, no, this is familiar. Lots and lots of quantifier domain context dependence. The only catch is this, and when we see the paradox case, it happens to be context dependence of the background domain. That's the idea. Well, Well, the goals for today, to try and see what we can do with that analogy. And I should tell you in advance that the results are going to be somewhat mixed. I do think that the appeal to familiar examples of natural language context dependence helps. But if you bought what was on the last slide, it's going to be slightly bad news because it's not anywhere near as easy as my fairly blithe and hopefully appealing way of putting things might have at least attempted to make it seem. So what I really want to try and do today is just try and explore this idea of to what extent we could make sense of background domain of quantification being context-dependent, and how, if that's true, it might work. How we can see context as actually affecting shifts in background domains, and what the background domains

10:00 that context might succeed in setting would look like. Now, I mean, I should say before really jumping into this, it's fairly obviously highly Russalian or Tarskian or some sort of hierarchy-like structure in spirit. It tries to make the bitter pill of some sort of hierarchy seem easier to swallow by sugar-coating bits of natural language. And so what I really want to see is how much sugar we can get. I'm really going to today proceed just trying to work out the nuts and bolts of how I think the view goes. I presented Tim's version of Russell's paradox. It's a good thing that I did that because Tim disagrees with absolutely everything I'm going to say. And so I shouldn't want to suggest by just trying to jump into the nuts and bolts of what I think should be going on, that there isn't lots and lots of controversy. I'm sure that at least one person in the room has already had it crossed their mind that it might be impossible for me to accurately say what I'm trying to say. There are lots and lots and lots of vexing problems surrounding this view. I'm going to try for today to not deal with the really vexing ones and see where we can I don't know if it's less vexing. I'm going to try to deal with a different set of vexing problems today if I can. So that's the plan. I wanted to start by looking at what I'm calling ordinary quantifier domain restriction. That's the sort of things we just saw in that list of examples before. Everything is path, nothing outlasts the energizer, and so on, and so on, and so on. It's convenient to start with a tiny, tiny bit of generalized quantifier theory. That seems to be the natural home for this. Aldo already did more generalized quantifier theory than you need, so I will run through this at lightning pace. Occasionally I will use the notation semantic value of an expression of these double brackets. superscript C is for context. For the most part, everything we do today can take this to be an appropriate set. A predicate will have an extension that's a set of individuals, so on and so on. We'll fix the background domain for the moment, which is basically fixing the universe of discourse in the model. So nominals like student are treated as predicates,

12:30 they get assigned sets. Verb phrases like came to class are also basically treated as predicates, they get assigned sets. A sentence like most students came to class breaks down into determiner, an expression like most, every, some, few, etc. And this, as Aldo was talking about yesterday, is basically treated as a type 1-1 generalized quantifier. It takes two set inputs expresses a relation between them. So, Aldo actually already gave you the definition of every as a generalized quantifier. It says, every student came to class just in case the set of students is contained in the set of, came to class. Conveniently, we saw plenty of other examples of this. And, of course, you can do it for the rather large range of expressions that can occupy determiner positions, yesterday. What's next? One thing Aldo didn't talk about which we'll need. If you fix domain n and do what we just did on the last slide, work out relations between subsets of n, you have what's normally referred to as a local generalized quantifier specific to a particular domain. It will become relevant in a moment, pretty much probably for obvious reasons. since I'm going to start worrying about changing background domains. You can simply talk about a global generalized quantifier that's a function from domains to the appropriate local generalized quantifiers you just allow them to vary. I suppose the initial reason people looked at this is, you know, this was done by logicians who wanted to think about logical consequence. They were used to the idea of wanting to vary models. I, of course, am going to do something decidedly more perverse. What's next? Well, the first bit of bad news, which is the bad news that's going to kind of haunt the talk, you might have thought when you've looked at global generalized quantifiers and said, oh, we have this variable parameter n, that a very natural way to account for the examples of quantifier context dependence we talked about a minute ago was simply to allow n to vary. And back in the mid-80s, Don Westerstahl made it overwhelmingly clear that that just won't

15:00 I'm going to come back to these principles, so I stated them a little bit more. Well, actually, Westerstahl states them in similar ways, but I made a little bit of a big deal of these. Two principles. Background domains are large, and textually restricted domains can be small. Intuitively, that sounds right, but it's also necessary for accounting for certain bits of data. At the department meeting today, everyone complained about the governor. I work for Arnold Schwarzenegger, so this has become a professional activity. I was thinking I had to do this sentence in Arnold's accent, but there are real Austrians in the room, I think. I'm not going to be so rude. I mean, everyone does not include the governor. That's a rather small domain. The background domain cannot be shrunk down to the size of everyone or else we wouldn't have a semantic value for Arnold. And there's one thing you're not going to do when you work at the University of California is fail to give Arnold a semantic value. Just not on. Second principle. Background domains are, I insert relatively, I guess that should have been square brackets, stable across stretches of discourse. Whereas contextually, ordinary contextually restricted quantifier domains are not so stable. Reuters-Drault, by the way, makes a somewhat stronger claim. He says they never change. I'm obviously challenging, but he's got a point here anyway. And so you look at this example, a few harbor seals in California live long. Most males, that's most male harbor seals, die in the first year. Most females die before the end of their second year. We have two quantifiers in those subsequent sentences that are changing their domains. It's not changing the meanings of every other expression in the sentence. We need rapid change of the quantifier domains. We've got to have stable interpretations of everything else. That's the sense in which these things need to be stable across stretches of discourse. So, you've got most male harbor seals. Yeah, so we've got Yeah, I suppose actually it's maybe an awkward choice of example. We've got most male harbor seals. It picks up harbor seals contextually and restricts it down to males. We've got most female harbor seals. It picks up harbor seal contextually and restricts it down to female. It might have been a poor choice of example because the contextual restriction is still constant.

17:30 So it's a poor choice of example. Would you take it on faith if I said we could do it better to make up an example on the spot. Yes, that's a poor choice. It is, of course, my fault. I stole Garand's example, but I can't blame it on him. You could have the harbor scenes earlier, right, and then males, and then large versus small males. Yeah. So, yeah. We never formulate a sentence right when standing here. I want to briefly comment that if you don't think quantifier domain restriction of the ordinary kind comes from changing the background domain, changing M. You've got to get it to come in somewhere. For argument's sake, I'm just going to assume that there's a parameter you can find that basically restricts the nominal. So when you say every student came to class, what it looks like, every student, student is now restricted down to student in the contextual development domain. There are some terribly picky details about this, none of which matter. You need to throw a contextual parameter in somewhere. m. So even if I'm right that m varies with context, we'll need some other parameter somewhere. For argument's sake, because my friends do it this way, I'll put it inside the nominal. I don't think anything I'm going to say depends on that. So in a way, I can state what I want to have happen in fairly straightforward terms now. I think there are two context-dependent parameters that show up in quantified noun phrases. which accounts for ordinary quantifier context dependence, and M itself also has to be a context-dependent parameter. The question then becomes, to what extent? You know, it's fine to say, okay, you know, M was sitting there in notation not really doing much. I've now announced, ah, okay, I don't want it just to be sitting there in the notation not really doing much. I want it to do a lot. To what extent can I say that

20:00 the way M behaves, if it's true that it is context-dependent, has anything to do with the way D behaves, if it is, well, that we know is context-dependent. So here's the goal. I want to talk about the way that D is actually set. I want to talk about the pragmatic mechanisms that that are responsible for setting quantifier domains. And I'm gonna try and suggest that, at least to a significant degree, though not completely, we can see M as being answerable to the same kinds of processes that B was. So I'm gonna say that it isn't completely special pleading that allow it to vary. Yeah? Can I just ask the Client Patriarch question about number six on the biggest slide. When you say every student comes to the class, that's a sentence, right? When you say, it looks like, is that a sentence, or is that the metatheoretic truth condition for the sentence? Ah, okay. When you say, it looks like this, is that a sentence which is somehow in our language of thought, which has a parameter, or is it outside in the metatlanguage, the truth condition, which has a parameter? Yeah, I would like to say something stronger than just that it's in the metatlanguage. I would the appropriate logical form of the sentence, which I would like to take to be psychologically real, define the parameter. The parameter in the logical form of the sentence. Now, I don't think anything I'm going to say today hinges on that. One of the things I'm actually worried about in this case, you can give fairly familiar syntactic arguments for the presence of the parameter. Had I such syntactic arguments for the presence of M, I would think it would be a different paper. But that would be what I'd like. So, oh, back to the warning I'm going to try and make as plain as I can a few general principles for how pragmatics works to set domains It's the area in pragmatics where things get ugly fast one of my friends used to complain that the problems I was interested in were as he called it, AI complete that had I a good really good theory of any of these things I would be famous because I'd have solved pretty much every hard problem in AI and so we will bump up to limits very fast

22:30 I'm going to try and sketch some principles which I hope are plausible the first one really is pretty plausible Quantifier domains like to work anaphorically. They like to hunt for previous physical pictures they can use to set the domain. And in particular, and this is what's going to be important, they like to hunt for prior predicative material. So there is a parameter I'm claiming, D, floating around. It's like a pronoun, hunting around for an appropriate antecedent. In example 7 we've got, there are some passengers in the airplane. Most passengers, we've got this parameter. what's it going to be set to? Appropriate predicate is passenger on the airplane. Most passengers intersected with passengers on the airplane, that gives you the right domain, were killed in the crash. The point I wanted to drive home here is it really prefers predicative material when it can do it. So if you look at John came to the party and Sarah came to the party, if I say they have fun, it certainly picks out John and Sarah or the appropriate aggregate of them. If I say everyone had fun, it doesn't want to do that. It really wants to mean people at the party. Even though there's a perfectly good aggregate, there's no predicated material that describes it. The predicated material is there's at the party or to the party or to the party, however we map to predicates. So we tend to look for predicative material. It can combine different bits of predicates and different pieces of the discourse, and it can add singular terms to try and build complex defining conditions. So this is an example I stole from Kamp and Ryla. Susan found most books which Bill needs, but few are important. which Bill needs, not books. So it can grab bits from one part of the sentence and another and glue them together. So far, so good. That was the easy case. The hard case is when you don't have overt linguistic material to map back to. This is where it gets, shall we gently say, messy. The label for what's going on here is accommodation. The idea is you as a speaker,

25:00 if you're faced with a need to set a parameter like a quantifier domain and you can't find endocines in discourse, try and look to the context, find some sort of information somewhere which will tell you what it should be, and in effect you make the discourse as if it had had that material present. I should mention, by the way, that the accommodation gets introduced in the late 70s, and changes rather a lot over the years. So the pictures of accommodation we tend to talk about these days tend to be much more mechanistic, but tend to have in mind the idea that you'd really sort of think of structures as if they were present earlier in the discourse. I don't think that anything I'm going to say crucially hinges on that, but beware, this is a moving target name. There are a few really, really rough and general rules that one could state. They're as loose as, when you're accommodating, try and make sure that you patch up the discourse to make it coherent and informative. Okay, I'm sure that doesn't really sound terribly useful. It does appear to be two separate rules. Whatever amounts for discourse coherence isn't the same thing as making it informative. You can be informative just by jumping to wildly incoherent, disconnected thoughts. We don't tend to see that. The point I wanted to drive home here, and this will be relevant, is that when we're looking for things like informativeness and coherence, we're not restricted to something like the immediate environment around us described in terms of what objects are present or how they're organized or something. We're not restricted to a completely bloodless description of our physical surroundings. It's more complicated than that. So here's an example that I think drives this home. You're saying everything is packed. You're setting off on a trip. Your suitcase is there. You've got your maps in your hand and your keys and some other things in your pockets and you drop something on the ground as you're walking towards the car, and you say, quite truly, everything is packed. It doesn't include the keys, it doesn't include the map, it doesn't include your code, even though those things are in your immediate surroundings, and they're perfectly salient. There's some way, and here

27:30 we get vague, messy, and obscure, but there's some way that we say that, look, there's an appropriate kind of idea of what it is that you're doing when you go on a trip, and understanding going on a trip amounts to makes especially appropriate certain sorts of subdomains, like the things you would appropriately pack in your suitcase. If, you know, your socks were sitting on the ground next to your keys, it would be false to say that everything is packed. But is this really... I'm not completely clear that this is an example of accommodation, right, because here you could claim that it's the non-linguistic context that provides... Yeah, I am... The constraints. Yes, I am going... The way I wanted to use the term, I'm going to account incorporating information from non-linguistic context in this accommodation. So I want to use it somewhat more widely than... You used the word... ...van-der-samp or something. Okay, good. I'm not going to be wedded to representationalist theories of accommodation. I mean, it's a fair question, because the way I was describing the anaphora process did seem related to that. I am, at this point, really undecided when I think about this question. So, the point I just wanted to drive home was that whatever's going on in the Everything is Packed case is highly situation-specific. It isn't just where you are and what's around you, it's what kind of thing you're up to. this seems to be the kind of thing that now we're at the AI complete step this is something along the lines of what people used to talk about in terms of the frame problem, now we tend to talk about plans, I will use the word plan from time to time but I will try and always put it in scare quotes because I don't really know anything about it but we're up at that sort of level one more point that's going to be important about where you get quantifier domains. Quantifier domains tend to include topical material. I'd like to have a stronger claim than 10, but I'll tell you a minute why I'm being a little cagey. So the thing you need to know is, of course, discourses have topics. Discourses are not unconnected bits of random sentences. They tend to be utterances that

30:00 are directed towards topic of conversation. It's pretty common to represent a topic as a question. You think of an utterance as being appropriate, felicitous in the discourse if it effectively answers the question being asked, the question is the topic. I'll usually talk about topical items, talk about topical individuals. If the question is something as weak as, what did John do? You can just say that John is the topic rather than the question what did John do as the topic. Generally, if you've got a topical item, it wants to be in any contextually restrictive quantifier domain. If it's topical, you're talking about it in a way that's very hard to exclude. So here's an example. That's a nice watch you're wearing. Tell me about it. If you then, in the same setting, say everything is packed. This just is no good. Now, I should say, I don't know what the right thing to say about the sentence is. It might just be completely infelicitous. To the extent that it's felicitous, that everything cannot exclude the watch. So there's a real pressure to get topical items in the quantifier domains. On the other hand, things that are clearly non-topical really don't have any great pressure to show up in quantifier domains. So the example I is making up. We've got this guy, John. He's moving to England. He's shipping all his belongings. For some strange reason, we're standing on the dock watching them load all his belongings into a giant shipping container. And he says, everything is small. Really not going to put the shipping container in. It's simply not topical. It's much harder if we bring the the shipping container in as a topic to get it out of the domain, so we had a little discourse to try and force it to be topical. John decided to ship all his belongs to England, so we went out and started investigating shipping containers. He found some that were about the right size. Everything is small. Again, you can tell me what your judgment is there. It's certainly a slightly odd sentence, but again, I just don't think it can have as its domain. It can exclude the shipping container now from its domain. Topical items are strongly pressure to get in. Non-topical items really don't need to. Caveats. I don't think I've found a generalization of this which I'm entirely happy with. In some random notes I've scribbled, I have about 30 potential counterexamples, but I won't tell them to you. I wouldn't have time.

32:30 So let me just, I want to just summarize. Here are the things I think we know about how normal quantifier domains are set. They're built out of predicative material. The predicative material can be complex. You can hunt around for lots of predicates in the discourse. You can use singular terms if you like. When you can't find it there, you've got to accommodate one way or another. When you're constructing a quantifier domain either way, you're constrained to put in topical material. And of course, when you're accommodating, you get to make reference to highly situation-specific information. I'm going to try and use all of those to go at the M problem. But first I need to talk a little bit about how I think the context shifts. The thing I wanted to highlight about the Williamson version of the paradox, but also the sort of standard version of Russell's paradox, if you think that what happens is you discover that the entire domain of quantification can't be in the domain, is that you're drawing attention to what I've given the sort of sloppy label artifacts of discourse, quantifier domains, interpretations. If you like, you can do this with context. Things involved in interpreting language as such. Now, these are not usually part of a quantifier domain. They're, of course, floating around in the background. You're speaking a language, and the things that are interpreting it are certainly in some way nearby. they tend not to show up in the domain. This is one of my favorite examples. My all-too-energetic algebra teacher once walked into the room. We were talking about groups. Everything today is finite. She said anything before she got to the blackboard. Well, it didn't include any semantic values. I don't think that's the way it would be understood. And not because she didn't understand them. I don't know if she knew any semantics. Of course she could have. That just wasn't what she was talking about. Usually, the sorts of things I'm labeling artifacts of the discourse, semantic values, quantifier domains, whatever, are not topical. They don't jump in quantifier domains, and in a strong sense. It's normally quite odd or incoherent to try and incorporate them. If you responded to her saying everything today is finite by saying something like, oh, what about the interpretation of your word every? Well, you might get away with that in a semantics class, but otherwise people we're going to think you're nuts. They usually think I am when I try this.

35:00 To give it a name, I'm going to say that these things are just normally implicit in discourse. They don't tend to be topicalized. What's bad about the... I don't want to say the liar. I do think it's true about the liar, but I'm going to talk about Russell. What's bad about the Russell case as I was describing it before is that I do think that we topicalize one of these artifacts of discourse. The crucial movement when you're doing the Russell thing not just to set up the Russell class, but to make it an object that you're talking about. You have to ask whether O or the domain of modification falls under some predicate. If you don't do that, you don't get the paradox out. So you topicalize an artifact of discourse. To give some notation, the notation will be kind of useful. We'll start with some initial context, C0. Think about the reflective context, as I'm calling it, that's the one where you think about the way the interpretation of the language is working, topicalize some appropriate artifact of the discourse, and you instantly find yourself in a position to run the paradox argument if you want. Now, this C0R, reflective context, we already have reason to think that's a new context. Changing what's topical amounts to changing the context. That, I think, is well-motivated independently. But we also know from the paradox that it absolutely has to be, by my lights, on pain of contradiction. So it's a weird case where you have some pretty good reason to think it was a change, but this time it has to be. It's a very unusual context shift. It violates basic rules for how discourses are supposed to flow, it violates rules for coherence, and it does so by introducing things which are normally just implicit. it. It introduces things as topics, which are normally just background of the working of the language as we're speaking it. So here's the problem, as I see it. We do something like this sort of reasoning. We topicalize the appropriate artifact of the discourse. I'm pretty much always going to assume what we do is we topicalize the background domain of interpretation from C0. Now, we're in a situation where we have to have a strictly wider background domain. We've got a topical item. The topical item has to be in quantifier domains, but Russell's Paradox tells us it absolutely could not be in the old quantifier domain, so we've got to build a bigger one. It's clear that this is not setting a restricted domain.

37:30 This is not changing that d parameter from a few slides ago. This is changing n. But what I want to suggest is that the same general principles we looked at for setting quantifier domains can help to see what you should do if you encounter one of these situations have this new object, a background domain of your previous context, needing to be incorporated. So you need to build yourself a bigger background domain. How do you do it? Well, I'm going to give you a sketch. First thing is, where am I here? Right. I need to set a quantifier domain. It's M rather than D, but forget that for a minute. I need to set a quantifier domain. What were the rules for that? Well, the first thing I do is I start hunting around in previous discourse to try and find some appropriate predicate of material that's going to help me set it. There is none. I've introduced something which was entirely implicit in the previous discourse. I don't have any salient predicates to describe it. I need to trigger an accommodation process. I need to trigger an accommodation process gets triggered, I'm going to suggest that it winds up being one of these ones that's highly specific. It's going to turn out that it's the process that's appropriate for building a background domain rather than just any old bit of accommodation. What should it look like? Well, the first thing you need to do, here's my little plan. Plan, of course, is in scare quotes. This isn't much of a plan. Neither fiendish nor cunning, I suppose. First step, as I said a second ago, we're trying to do something that amounts to setting up a quantifier domain. We want to make it look as if we had predicative material available. Describe the domain. If you didn't have appropriate vocabulary, add it. If you did have appropriate vocabulary, make sure it's working right. That is, make sure if you had semantic vocabulary sitting around in your language that it's now targeted towards the semantics of the language as it was being used in the previous context. That's what we're trying to describe. Now, the next point is just that I have this vocabulary. I need to make sure that what I describe with it is a background domain. What is it that background domains do? They provide subdomains for other quantifiers. Amongst things, they do lots of other things too, but they certainly have to do that.

40:00 What does that mean? They have to be such that when I find predicate of material floating around that I can use to describe subdomains, they actually have to be subdomains. I've thrown in a new object, expanded my vocabulary a little bit. I have to make sure that any subdomain I could describe with these new resources really is one. And effectively, to do that, all I do is I start closing up a little bit over the subsets that I can define in the vocabulary. if you allow yourself the right sorts of semantic expressions you're certainly going to want to find subsets of the initial domain combined sorry, let me state this properly what you're going to want to do is add as object subsets of the initial background domain together with singleton m0 itself that is together with the singleton of the original background domain Why? Because think about a predicate like x of the semantic value of a verb phrase from C0, that's a set of subsets of M0, or it's just the original background domain. You need to build the extension of that appropriate subsets of M0 union singleton M0 to be objects in your background domain. So we start closing up. you probably need to go a little further than closing up once under definable subsets of M0 union single to M0 why? well because most ways of thinking about the semantics of natural language is a few higher type objects floating around quantifiers were already sets of sets if I want to close up under appropriate semantic objects I've probably got to do this I don't know it's hard to find in a semantics book anything other than 5. But, on the other hand, I think we're going to need to do a lot more than that. And the reason is going back to Westerstahl's principles. If we did step 2, which is closing up on other definable subsets of M0, Unitsingles, and M0, or even if we did a few finite iterations, we'd still have pretty small domains. Small in the sense that there'd be lots more stuff that we could add uniformly doing the same thing. that these things are supposed to be big, to respect this, we better do a lot more closing. It's also the case that if we don't do a lot more closing, we're going to have a lot more instability. It's going to be a lot easier to talk ourselves out of the new background

42:30 domain that we build. The less we close up, the easier it is going to be to talk ourselves out of it. So if I succeed at some point further down in the discourse of topicalizing say, the domain of semantic values from C0. If I only closed up exactly as many times as I needed to catch all the semantic values that were in the language that was spoken at C0, I wouldn't have this. If I want to get that in there as well, if I want to not allow this to be a new reflective context, if I want to not allow this that, if I want to not let this be jump. I just close up even more. Now, I don't have an entirely knocked down argument that we absolutely must not count that as new, run through a paradox-like situation that we can't see it as, as I'm using the vocabulary, a new reflective context. But it sure doesn't look like one. It's meta-semantic in a fairly restricted sense. I'm certainly talking about semantic values. But I'm still talking about what's going on semantically in C0. What really should be the mark of a new reflective context is when I start talking about what's going on semantically in what my notation calls C0 super R. That is the reflective thing. So I don't think we want to see something like we have under the... I don't think we want to see this. The main semantic value to C0 counting as a new reflective context. Topicalizing that is counting as stepping to a new reflective context. further than you know five iterations and of course you know the bigger we make this the better both Westerstahl's principles turn out to be right the bigger the domain is the harder it's going to be to get yourself out of it the more it's going to look like Westerstahl thought it should look like and you're probably right so we got to keep iterating the question basically is how far far enough to do the appropriate job and we want to know how far that is Before spending a very brief couple of minutes talking about what might be good ideas about how far, it's worth noting that this question about how far you want to iterate really just tracks the differences between Tarskian and Kripkean approaches. If I iterated not very much, if I just did step two or step two prime, I'm basically Tarskian. Every little change going from semantic to metasemantic counts as a new level, context,

45:00 whatever you want to put it. I iterate a lot, you have to do a lot more work to get to a new level, new context, new, whatever the appropriate thing is. Basically, Kripkean idea. I'm inclined to think the Kripkean move is right. We should try and avoid these changes as much as we can. The more you iterate, the more you look Kripkean, the harder it is to get these changes. But I want to press that even if we do, there is still going to be a genuine hierarchy here. this is open up. However far you put it off, you will still be able to do the appropriate kind of reflection on what I'm labeling C0 sub r, that reflective context for C0. You will be able to really think about the semantics of that. Really thinking about the semantics of that is no better than really thinking about the semantics of C0 and C0. You will bump yourself out eventually. The trick is just to put it off as long as possible. It's so conclusion so far background domain shift if it exists is not the same thing exactly as ordinary quantifier domain restriction separate parameter can't be the same thing on the other hand I do think it's pragmatically on par basically the same kinds of guidelines tell us how to set end tell us how to set domain restrictions. Where it pragmatically differs is where I have to start talking specifically about the features of what makes a background domain a good background domain. It has to satisfy vegetables principles, it has to be big, it has to allow for defining subdomains, those are the things that make background domains good. But the reason I dwelled so long on this idea that when you think about accommodation, you have to use this situation specific information, is that's not unusual. This is the way pragmatics always goes. Now I wish I had a better story about exactly how that process worked. I don't, but I am prepared to say that look, where it gets messy, it gets messy in exactly the same way that ordinary domain restrictions get messy. You have to look for situation-specific things in either case. We shouldn't ignore about this situation-specific thing, but it still seems on par. Different parameter, only place where the basic rules for setting the parameters seem to differ is where they're supposed to. So even though it's somewhat different,

47:30 I do want to say it's basically the same thing. Now, I said there would be a tiny bit of logic. This is so much notation. It's pretty obvious that I was just, you know, setting the thing up so we'd get levels of constructible sets, as what it seemed like we were doing. Because we didn't want to start building constructible sets right away, you'd want to start with the universe of that initial context C0 as ur-elements. Build constructible sets on top of that, stop somewhere appropriate, seems to be a pretty good model of what's going on. The question is, how far to go? So I'm going to skip most of the details here because it's notation which doesn't actually tell you anything. Build the constructible sets with or elements as far as you think appropriate. How far is appropriate? Well, again, I don't have any knock-down arguments. You might stop, if you just did what I call step two prime, you might stop at, say, five or seven. That ran a foul of Esther-Stahl's principles. That was small. You might satisfy Esther-Stahl's principles by going up to any limit ordinal you want. it still doesn't seem to me that that will do enough to satisfy particularly Rechner's second principle the one that says these have to be stable it's too easy to find convoluted statements which are essentially a little bit of set theory restated in terms of semantic values rather than sets if you like that are just going to higher than a small in the orc moment. Now, we might go huge. Take your pick for what you think huge is here. All of L, that would certainly be large and stable. If you wanted all of V, that would be even bigger and stable. I don't think that's a good idea. V, certainly not, because the way we were telling the story, it really looked like the process was looking for predicative material, so V doesn't seem like a good idea. All of L, well, it's certainly built on predicative material. Thinking about this as asking a speaker in a context to, at least in principle, be able to carry out some kind of construction of the domain, we better stop this somewhere which we could make sense of them being able to get their mind around them. Well, I don't want to make any real claims about what they can get their minds around, but asking for all of that looks like more than we want and more than we need.

50:00 My favorite place to stop is just to go up to Hype. mostly because it's a really nice object to work with. I do think it's got a little more going for it than that. If you think that the ordinal you stop at when you're building basically the hyperarithmetic sets is the limit of inductive processes. The limit of the length of inductive processes. If you think that starting an inductive process is something that a speaker in the context could do, if you think about how far they can go, you might want to start they could do by triggering inductions and so think about that limit this seems like a fairly natural place to stop i'm not going to try for a stronger claim than that seems pretty good it's extremely nice uh object to work with um one of the things that's particularly nice about it is that it iterates well and so the you need a hierarchy here right i was just saying i want to put it off as far as possible um but that eventually we'll need to talk ourselves out of of context, if we're able to see 0 so far and talk ourselves up to another one, well, if we stop at hype, we can do it again. Is hype church-cleaning omega 1? Yes, it's a little more general. If the ground structure is the natural number, it's iterating out to omega 1 ck. And it's basically the same thing for any nice structure. If you're The kind of person who thinks that nice means looking like natural numbers, it's basically the same for any nice structure. If you think that a recursively saturated structure is nice, we've got a very different ballgame, but much further than stopping at first limit ordinal, goes quite a bit further up than that. Nice, strong closure conditions, seems to track inductive, does track inductive definitions over the right kinds of structures, seems like a nice target, and iterates. be pushing. Features of the model, given the time, which one do I have? I'm trying to think about what I want. Yeah, I'm going to skip. Features aren't really, oh yeah, there is one feature that's worth mentioning that I do think is going to become important for we do next. Every time you iterate, the next step up knows all about the previous step

52:30 down. So hype is actually a set sitting there in hype hype. That's going to turn out to be important because if you're thinking about what a reflective context should be like, it should really be someplace where you can really understand what's going on in the semantics of the previous context. If what's going on in the semantics of the previous context is somehow captured by having iterated this process to the right point, you better find that that's there in a nice, stable way, and it is. I want to talk about this Williamson objection, because originally the way I got to writing this paper was to try and answer this. Here's what's bothering Williamson. He tries this gambit. Well, look, if you don't have a once and for all fixed absolute background domain, if you have this kind of contextual relativity that I'm in favor of, it isn't just that some obscure, weird, highly general quantification gets flaky. It's that every bit of quantification gets flaky, including nice, practical, restricted things like every donkey braves. Why? Williamson says, look, because to really make it certain that that was not itself unduly and artificially restricted, which of course we know that, actually restricted down to every donkey in Bristol. You'd have to use quantifier I say you can't use, which is the one that says, no, really, absolutely. I mean, when I say donkey, I mean absolutely every donkey. Of course, I mean, I can utter those words. They just don't do much for me. And Tim wants to say this means that what I'm arguing for infects everything. The counter is just that as I set it up, that's not true. But there are some pretty specific features of how I set it up that make this work. Partly it's just the way natural language quantifiers work. Natural language quantifiers as a just brood empirical fact as an empirical fact are restricted in a very there is 16. Truth conditions for a natural language quantifier depend only on the set that gives you the nominal. This is x here. If you don't see that, you don't see what the point is. You can pretend that the background domain is down to x and you can intersect the

55:00 y-parameter with x. You really never need to look off x. And of course, if x wasn't going to change, nothing else about the quantifier is going to change as we go up from context to context. It's built in to the way I was thinking about things that an ordinary predicate like is a donkey, which has nothing to do with semantics, wasn't going to change. If building hype over structure this was just in the structure it's certainly not going to change so nothing happens to x if nothing happens to x nothing happens to the truth conditions and it doesn't matter if you add extra restricted parameters if nothing happens to x nothing interesting happens um what do i want to say about this there is a lingering worry i want to play with this a little bit more because even though So, you know, I rig the system so that Tim's worry doesn't show up. I do think there's something going on here that is a worry. Right, so fine, if I manage to make my predicate donkey really mean donkey, the semantics is set up so that all donkeys' prey would not be affected by moving things from the context. How can I really guarantee that my quantifier doesn't pick up the contextual restriction that I wasn't looking for? How can I really guarantee to you that when I said all donkeys, Bray, I didn't mean all donkeys in Bristol or the way Tim's example went, it was all donkeys on Rakhal. I don't know if there are any donkeys on Rakhal, but the first point I was making was, look, this really doesn't have anything to do with background domains. domains is working, they don't affect it. Everything is stable enough and natural language quantifiers are restricted enough that they don't care what happened outside of the fixed, stable extension of a predicate-like donkey. But that doesn't tell you how I can guarantee that I didn't get a contextual restriction. There's still what I'm labeled here a lingering worry. But the point I want to make is just that I don't think this has anything to do with my weird view on background domains. It's just a question about the metaphysics if you want to call it that. What sets the context? Look, if you believe that contexts are substantially built by speakers' intentions,

57:30 this is trivial. It ranges over all donkeys because I wanted it to. I intended it to be all donkeys. That's all I need. That's not the only view about where context comes from, of course. If you think it's just speakers' intentions, there's no problem. And, of course, if I had this intention and my intention trumped, guaranteed that if I intended it to be all donkeys, it's all donkeys, I could try and signal this to you by, you know, special pleading, by saying, no, I mean absolutely all donkeys. You know, by my lights, that word absolutely doesn't have any direct semantic effect. It still just means engaging over the background. I mean, but that can be a perfectly good way to signal that I, if the metaphysics is such that I get, you know, first call about what the context looks like, I need to try and tell you what it is. I could say absolutely to help with that. If you have other views of context where speakers' intentions don't trump, take your pick for what it would be other than individual speakers' intentions. intentions that have to be shared across all speakers, objective facts about the environment. Take your pick of something that I don't get to set all by myself. If that's the case, then it might be rather hard for me to guarantee the context didn't step in and do something to the semantic bias of my words. That might be. But I guess I want to say at this point that what saying absolutely isn't going to help if the context were such that it was perhaps unbeknownst to me or out of my control, stepping in and making my words talk about less than I wanted to, absolutely won't change it. Go back to the case of being packed for the trip. Absolutely everything is packed. Doesn't do any better or worse than everything is packed. So I don't think this is an issue about background domain, nor do I think it's an issue about the availability of absolute quantification. It just seems to be a problem about what context is like, one I'm not going to try and solve. So, quick conclusions. In a paper that came out not very long ago, I announced that the kind of context dependence I've been talking about today was extraordinary. And I announced it because I couldn't come up with terribly good parallels between natural language and this. And what I was thinking about when I was writing up the paper was, well, how extraordinary is it? And I now regret the name because it isn't that extraordinary. It is different. As I'm putting it here, it's dependent on a separate parameter. It's n-dependence rather than d-dependence. So it is different from the usual thing, but it's not extraordinary. It's another parameter working much the same way as we expect

1:00:00 a contextual parameter to work. There are some remaining issues. I have put a ton I labeled artifacts of discourse. In effect, my response to Tim says, artifacts of discourse aren't donkeys. The way context, the way background domains change is to add funny artifacts of discourse and close up. Adding funny artifacts of discourse and closing up doesn't affect things that were predicates of non-artifacts of discourse, like donkeys. If you have that distinction, and this should sound very Russellian, right? If you have a nice distinction between kinds of the appropriate sort, then Tim's objection won't fly. On the other hand, it would be really nice to have something better to say about exactly what an artifact of discourse is. I mean, I think the list I gave you is pretty typical. I don't think the list is bad. It would be nice to have more to say about it, particularly given that I am putting weight on it. And the final point, there are some things on the philosophy of language side that it would be nice to have that I don't. in so far as I said that M is acting as a parameter it's back to the question at the beginning what evidence do we have that there really is a parameter there the argument I gave you was that we needed it to avoid the paradoxes and that if we saw it there we could see it working pretty normally we would like to have direct evidence that there is a parameter there in some cases we can get it and I don't have it One of the reasons this might still turn out to be a little extraordinary is I don't really know how to find it. But it would be nice. The other thing is, just saying that how this complex dependent parameter gets set doesn't really tell you what it is about the meanings of the relevant expressions that got there to be dependence on this parameter to begin with. It would be nice to have a better story about that, too. Again, I wind up in several crucial places falling back on the idea that paradox makes it required. It would be nice to have a fully, I don't know what the word, not natural, a fully internal philosophy of language story. Direct evidence is a parameter. What's that parameter doing? It interacts with the meanings of every and all in certain ways. Show you that it has to do certain things. Let me look at context. It's exactly how it's said. It would be nice to have that whole story. I don't have it. but I guess I hope that I've tried to make the case that it isn't quite as weird as it might have seemed. I think I'll stop with that. It's probably a good stopping point.

1:02:30 Do you have questions? Yeah, I have a couple kinds of questions. I'm not a fostered language, but I just destroyed what I figured out. So, just a couple questions. So, I mean, I guess there's two kind of things going on. There's natural language use of quantifiers, and then there's empirical questions about what I take it that part of the process is empirically having the best, most explanatory, predictive story about how people use quantifiers. That would be nice. Then there's the paradigms. Why would you think that all this stuff about natural languages has anything to do with this weird philosophical problem that really makes no context about ordinary people who use language? I just don't see the connection. I'm wondering what methodologically was really motivating appeals to natural language use in this highly contrived, bizarre philosophical context. Yeah, okay, so I think the answer is twofold. One, I don't think it's quite as contrived seen. It's a little more vivid with the liar, actually, than the Russell paradox. I tend to see these things in parallel, but the liar's a little more complicated case. People keep clickbooks of naturally occurring liars. Newspaper typos generate them. And the reasoning that gets you to strengthen liars, really bad forms of paradox, once you have these naturally occurring sentences, is not terribly strange. You've just got to think about it for a minute. Now, I did make the point that there's a certain way in which what I call reflecting on semantics as it's going on, and that I do think is kind of crucial to the... I think it's crucial to both cases. The nice thing about the Lyre case is you've got a truth-break again, so you kind of get naturally occurring what works to express some of these semantic things. I did make the point that this is sort of discourse odd. It's against the normal rules of conversation. You know, if you're telling me about how your day went, if we talk to people like this, they're a nuisance. But that doesn't mean it's beyond the scope of what we do in ordinary reasoning that can be carried out in ordinary language. I think it's a little more vivid in the liar, but I don't want to say that this is merely an isolated bit of philosophical logic that couldn't go on. And back to the sort of initials here,

1:05:00 to the extent that I can make it clear how it would go on in ordinary language environments, and to the extent that I can make that seem appealing, the more I can do that, the more I can get you to swallow a hierarchical view. It has all the ugly features of a hierarchy eventually, but the more I can convince you that what's really going on and make this happen, what really drives us into stuff about ordinary speech, the more I get to block the standard objection hierarchies, these are ad hoc tricks, to avoid paradoxes. So the claim could be, not ad hoc trick, something that's really going on anyway, you know, tease scratched by perverse bits of reasoning. I don't think these context shifts are entirely natural. That doesn't mean they're kind of sui-generous. Right, but you've got to say more than that, right, because the role of these paradoxes in your methodology is extremely strong. It sort of drives everything. It's not just one bit of data. It's sort of driving everything, including your response to Williamson. It's sort of central. That I don't see. Because it just looks like pathology. There's a saying in law, right? Hard cases make for bad law. Why isn't that applied here? Yeah, no, fair question. I think the answer is, though it's a pathology, it's a pathology that we can create. I don't have to, particularly with the law, I don't have to teach you very much to get you to run the liar. I don't have to take you to it. I mean, I've got to tell you a little bit about convention. It's not hard. So I do think that it is a problem that occurs in close enough to ordinary language to be relevant. Now, back to the hard cases thing. Hard cases make bad law, and I'm worried about this, except if the hard cases map out possibilities, you've got to deal with them. So part of the project here, you know, had the project in its more hopeful form been finished, I'd have a nice answer to you. No, no, no, I didn't mean the hard case. I started with the hard case, because that's what philosophical editions like, but the hard case only came up as a consequence. I'd like that to happen. Even if it doesn't, I do think the fact that it sets limits on coherence, limits on what can be going on, you've got to deal with it. So the rhetorical stance is, no, no, no, if you don't deal with this, you've got your head in the sand, you're not paying attention to the logic. I don't want to push it that hard, but you can't just do it. short question at the beginning you said given some mild set theoretic assumptions the real

1:07:30 problem amounts to we cannot put the domain of quantification within the domain of quantification and i would like to know what you refer to by by saying set theoretic assumptions because given axiom of foundation of course the domain of quantification is not a member of the domain quantification but we know we can replace that axiom by say axel's anti-foundation and then it's again trivial give me some domain d that we can always extend d to a domain d star such that d star has the same members as d except for d star itself that's no problem at all that doesn't give you too much but at least it gives you the domain of quantification within the domain of quantification Yeah. Well, I mean, part of the reason I didn't say more was what I had in mind was certainly foundation and restricting comprehension would do the trick. I haven't thought seriously about what would happen if we added AFA. Here's what I suspect. We'll get M member of M, but we'll get some other kind of appropriate fact of the discourse somewhere. If you think about the situation theoretic implementation in Barweiss and Echimendi, they get something very close to what I want. They get changes in, I forget the term, resource situations, they get changes in situations that look like context that essentially amount to expanding domains and situations that look like possible worlds. So certainly that form gets something very close. I haven't thought enough about the details about exactly how. So, I was, for argument's sake, going to be happy just to make it, you know, take foundation and run with it, but I don't think I need it. Oh, I was going to come back and go to some of this kind of big questions, as I was aware about the first question, about how the two issues relate, one is the abstract problem, the last paradox, the sematic principle, the T-scheme, what are we doing with the total, single truth predicate? But how does that relate to the more empirical questions in a possible language, questions about pragmatics, interpretation? And there are, in a way, we're thinking about these two different approaches, one is a kind of,

1:10:00 I suppose generally you call it a totalitarian approach, which is a single, unrelativized truth predicate. a quantifier that ranges over everything. And then there are the kind of relativists and the textualists like you and me. But I think what you do want to say is that in any case, in the philosophy of language, the relativization to contexts, to interpretations, is what we need anyway in the philosophy of language. Already in the philosophy of language, we need these relativizations. You know, when you have in the Convention C task is true and out, that actually is crucial for true and out. I agree. I won't disagree. which is imminent in the Koinian sense, then there is no relativization for true L. Because any sentence of my language happens to step up. But for the general convention, T, the true in L bit, which is a relativization of some kind to the language, which is the interpretation of the language. So these relativizations, they play an extra role in the philosophy of language generally. So I think you can naturally gain. Well, if somebody does say it's ad hoc, or for Trotsky to say, you know, truth is, or semantics is all relative to a context or to an interpretation or something like this, then you can garner further support from these phenomena if you're talking about it. Right, exactly. That's exactly the plan. And the reason I wanted to delve into these details is that I want to be prepared to answer the challenge that says, Yeah, you're mislabeling. Yeah, yeah, there's that other stuff that's complex dependence. That's not what's going on here. What I really wanted to be prepared to do is answer that in detail. No, let me show you what's going on here. It's close enough. I mean, so as far as the truth predicate, you know, the preferred view I have is to put all the work on quantifier domain restriction. One truth predicate, if you, you know, you need to quantify over truth bearers in a perfect way. If you like propositions, Truth is, sentence S expresses a true proposition, that is, there exists a P, such that S expresses P and P is true, somehow or another they get a quantifier in there, and that quantifier is over an appropriate background, I mean, it's propositions, we've got to change the apparatus here a little bit. Do you want a hierarchy of propositions? In the long run I do, actually. I mean, what you're really, it's a hierarchy of whatever builds propositions, worlds, situations. The reason I wanted to put it this way was, there's a standard objection of that, which

1:12:30 of course is to try and do it in a super liar-out. Quantify over the relevant things, contexts, whatever I use to block it, you quantify over and you try to... What are your ends, ranging in? And so, to the extent that I can substantiate just the claim that whatever your widest domain is it's restricted, I can say, you know, generically, you know, of course, you know, you tried to do a super liar, but I can quantify restricted too, because it's a quantifier. There's something very puzzling, though, about the dialectic of this debate, because some people say, look, everything ranges over everything, you know, obviously, and you want to, and I want to say, no, it actually doesn't ever range over everything, but I'm using the word everything in order to deny that I'm talking about everything. I don't have to direct, so I think the Tarskian case, right, 2 and L, that's not, I don't think that there's such a strong analogy to the content dependence, because Tarski really creates for every case new truth predicates, right, so the context dependent case, you want to say, there's one truth predicates. But there's still a hierarchical structure implicit. Yeah, but the context, so there is the unity of truth, right? I think the problem for Tarski is that there isn't no one truth. I think that's really different, really this analogy. I think you can think of truth as a relation between a formula and an interpretation. I think there is binary relation. Yeah, well, sure, but of course, in Tarski's way, so he says, well, for every language we have a separate problem how to conserve the truth. It's a really different kind of setting for a question than when you say, well, we want one truth predicate and the language can be a parameter for that or something like that. Well, for a tentacle remark, I would be in favor of making it much more local, right? Languages are really kind of weird. I think from the standpoint of philosophy of language, languages do not really exist. Even if they do, they really can't do it in the way Tarski did. Yes. They're far different objects than Tarski saw them. If they exist, they're quite different from what Tarski saw they were, and B, they do not exist.

1:15:00 Interesting condition. I think Jeff touched upon it already, but maybe you can explain it. If I knew that background domain change in context, but is there ever absolutely a restricted contribution? No. Are you about to get upset about the whole thing? No. There's no... For this to work, I mean... It's really hierarchical in a couple of senses. There's no way to get out of the hierarchy. That's part and parcel of any good hierarchical view. If you get out of the hierarchy, you can reinstate the paradox. If I could have... You can't say the hierarchy. You have to say something like a hierarchy. You can talk about the hierarchy, so it looks like you're putting a limit. And then you can diagonalize out again, and you've got to... There are two books that I like to... You can't say that. So there are two books that I always, if I'm not traveling far, but when I talk about this, I like to bring it with me. One is my favorite cookbook, which is entitled How to Cook Everything. But the other is Barclay's Dialogues, and I get to talk about speaking with the Volga a lot here. No, I mean, so if there was a single absolute domain, you'd run Russell, you'd run my, well, my, Tim's, this take on Russell's paradox there. is raging over that, and you'd be in every bit as bad trouble as before. On the face of it, although they might be awkward, we do say things like everything is. Yes. And so the claim is, if you think about the way the background demands are set, they'll always be big. Basically, they'll always be big enough to modulo these funny bits of semantics. And so if you try and really push generalization to the point where you're We're going to seriously try and take in what I call artifacts of the discourse. You could get into trouble. I'm going to have to bite that bullet. I'm not sure how bad that is. We've got paradoxes there. Why does there have to be a unified theory? Why couldn't there be a theory of use in which when you're explaining use, you do postulate the existence of a universal domain? And then for the theoretical philosophers' talk stuff, the esoteric theory, you don't because there's a lot of paradoxes. I don't understand why there have to be a unified theory that gets both right. In a way, I wouldn't want to put it that way, but in a way that is a kind of consequence, right?

1:17:30 There are lots of stable domains for me. They're restricted, but they're stable. And it's big domains that are not as unstable as they might have been, but they're unstable. That does mean a couple of different kind of things we can look at. I mean, insofar as, you know, the kind of line that I was pushing, and I think Jeff was coming to my defense on, insofar as we think that appeals to natural language helps out on this, it's very awkward to say that, you know, there's this weird special subject that doesn't get spoken about in natural language. That would be bad. So I don't want to push the way we're putting it too far, lest I fall into there being special language for doing philosophy. But short of that, if you wanted to, the point that, you know, domains like donkeys are stable, I'm happy just to stick with you know I just had a somewhat absurd contribution to make about context-dependent a real example of a context-dependent paradox I suppose is all I'm not sure what is several years ago the university sent out put up notices trying to get students to sign up for their examinations and And there were penalties involved if you didn't sign up for the examination on time. The notices came in two sheets. So the details, there was a sort of attention-catching bit, and then below were the details. And the attention-catching bit simply said, failure to read this notice could cost you money. The first time I ran across it, the bottom half of it had fallen off. It's not quite a paradox. Well, it's annoying, but it isn't quite a paradox. It could very well be true. Well, that's what I'm wondering, because you'll never know if you've read it. As soon as you see it, you think, oh my God, and then you realize, I've read the notice, I'm okay. It has a bit of a self-fulfilling character. Somehow, as soon as you read the notice, the context, if you say, whoever fails to read this notice could lose money, right? As soon as you read it, the context shifts, because you were in the reference of the pronoun there before you read it.

1:20:00 Yeah, I mean, I'm a believer in very rapid context shifts, so I'm happy that context shifts there. I'm not seeing the paradoxical bite, but it is an odd case. You should laugh at it, that's what I'm with. Well, here's one. I mean, there are lots of bad uses of context dependence that aren't paradoxes in the sense of Valiar or Russell's paradox, but are a bit odd. So how many people's answering machines say, hello, I'm not here right now? Well, you had a logical false code. It's context logics. But yeah, I mean, so there are things you can do with context, no doubt, many of them. Yeah, I was wondering about why, about the number of iterations we have, so we ended up having elementary sets, and we were already talking about quantifying out, so it seems that also the number of steps you need will be dependent on, well, not the context, I don't know, whatever, so according to the kind of problem you want to solve, he will have to iterate it more or less often. I think that's, yeah, I mean, so one of the reasons for wanting to just take on board all this nice theory that the logicians can be developed is that's built in, right, that was the closure ordinal for building height dependence on the ground structure. The ground structure is representing something like the semantics in the initial context. We move to what I'm calling and you construct something like the hyper-elementary sets above it. But how far do you go to do that, of course, depends on what the initial context was, what the initial structure was like. So yeah, it's going to... I'm not sure if I got the worry. Does that address it? Yeah, I guess so. So if you could start with anything, even, say, for model of set theory... And I was finally going to worry about your final frame viewing. I have to agree. One thing I want to be careful about is not to make the claim that you always get some restricted background domain

1:22:30 turn into the claim that there's some category of objects you can't quantify over, because that would go against what I was just saying about artifacts of discourse. So insofar as you've got a good grasp on the domain of sets, good set theory, I've got to agree that you can quantify a role in a very start in the ground. That means that the rough suggestion I was making about how to build background domains was going to give out long before we get that big ground structures. I mean, I guess, you know, do you have any tricks up your sleeve for doing this? Well, the only question was related. I don't, I have no more tricks up my sleeve. I'm hoping that somebody else does. But the other, let me say one more sort of methodological thing. If I get a kind of rough picture about what sort of thing a background domain looks like and it turns out that, you know, my talk about L was pretty weak. It seemed like there was definability going on. It seemed like gal as an union structure, if we're looking at that, if it turns out that's a kind of toy model, that's less than I want, but I'll take it nonetheless as at least a little step. And if it's a toy model that just stops working when you get to full size, or even close to full size, maybe you could simply backtrack, right? First you have the whole universe, but as soon as you have to do your construction, you say, well, evidently it couldn't be the with some large initial piece, and that's good. First, the small structure. It's accommodation. Don't worry about that until you could do it for small structures and work out what's the pleasure of them. Yeah, let me say one other thing. If you think about this the way that people in either psycholinguistics or cognitive psychology do, any better be finite. And if you think about building a finite domain, well, it's not even clear to me that I'm like instructable sets. And if we're really down to the finite, it would be the right toolkit. There might be very different things. You know, people who do... I don't... I was... In trying to write up this paper, I was running around reading things about applications of model generation techniques to natural language semantics, hoping that it would give me some elegant little thing that I could say worked here. And I didn't find such a thing, but there are other techniques that might be... Particularly if you're worried about...

1:25:00 and you know the kind of the philosophical dialectic always goes into you know we need gigantic domains and so you're worried about zsc seems like the right one if you hand this to question to a psychologist they're going to look at a really different if the domain's more than i don't know kind of a ten it's already big for them so it might be that they're different I'm just trying to make a stab at what might be a closure of these WP 1 or 2, but it seems to me that, as you've said, closing it in any, stopping any odd limit all because it's if you're not good enough, you don't have enough closure. High verbal structure seems a reasonable thing to go for. You have a certain amount of reflection. But you are talking at the same time about having, semantics for second or third or higher order. This is only going to give you, won't even give you full first order reflection. You try to reflection or something like this. You've expanded your domain, made things. You have closed up under inductive definitions You've got all that information in there, but then you're still going to want to talk about this whole business here, you're going to want to talk about first order, or you're going to commit you to going to the next type of collection, and where's a suitable stopping place. And my guess as to where this is going to stop is not just where you get first order collection, If you want to be able to do more than that, you want to say, if I were to go to the next type as well, I'm not going to have any more new, for example, sigma-1. So, no, I'm guessing stronger than that. I'm saying you want to go to the full first pi-1-1 reflected in that. There you have the next admissible set. So there, that ordinal gives you a number of the L hierarchy over your starting structure of sigma-1 facts, and the next admissible set will be true. The next admissible set, anything that you have in that, actually inside that set, is already true down below. No, no. So I'm guessing on a pi-1-1. But this is a suggestion. One question. It's going to depend a little bit, when we think about the higher type objects we need to add.

1:27:30 If I have to add, say, full second order or something like that, it's going to get big. if I start constraining my high-type objects by definability conditions, as you might if you're thinking of them as semantic values or things along the lines, is that going to change the situation much? Or is it all just this big? Relational quantification over this height level. This should lie you alone. Something to look at. Yeah, no, thanks. That's an interesting idea. I propose to thank the speaker. There's a coffee now, and I propose to read the coffee in a row, standing to Washington. Can I have this coffee already? I don't tend to have a coffee in a row. Well, at the last 12 or 15, I can pay you back in euros, if you take cash to the airport, and you can pull it up. I can buy money from you in euros, actually. Also, one thing that I couldn't think of in my town, So, because there are many analogies to the paradoxes in the business of Syria communication, right? Oh, yeah. So, if we communicate, then there's implicit that I intend that we'll start to believe what I say. Oh, so you can tolerate it. Yes, yes. Ground business, et cetera. I mean, they're infinite. They don't seem to be vicious in some ways. No, no, but I think that would be, because the question here is, of course, are these extensions? Oh, I see. Oh, right. Good point. Yes, I see. You could generate other examples. Good. Right. That's useful. That's great. But I'm not... But that's right. I mean, it's not the same, but it gets you in the same ballpark. Yeah, right. And that would be a kind of strength in your case against the kind of two completely different

1:30:00 projects argument. Right. Good. No, thanks. I couldn't think of an example. Oh, I have 22 pounds, and, uh, when I took the camp last time, it was 70 pounds, and, uh, it was 70 pounds. Okay, um, now it's only 25 in the afternoon today. But then we should ask, um, for more than a camp. Yeah.