Transcription
I'm sorry for not being here earlier, but I'll give my talks in two days. These will be talks about semantics. It's a cognitive approach to semantics, not really a linguistic one. But on the other hand, I will try to make it linguistic applications of this theory of semantics. So, I will base most of my, most of my talks on this book, "Geometry of Meaning," that appeared a couple of years ago. But I will also talk about some new stuff that I've been working on after, after the book.
Before I start, I need to know a little bit about your background in order to adapt my, my examples for it. So, who of you have a background in computer science? You may raise your hand more than once. Who have a background in linguistics? That's good. And who have a science, psychology, philosophy? Who thinks of them, who thinks of themself as a cognitive scientist? Okay, very good. Okay, newer science, I forgot to ask about neuroscience. Okay, I will not talk very much about neuroscience, I'm afraid. I'm a cognitive science, I feel really, really like a cognitive science scientist, but I will give things a little bit from, well, it will be, it will be talks in cognitive science. There will be very little pure psychology. There would be some philosophy, some linguistics, and a little bit of computational science. I will talk about, on the order from, from Lucas, I will talk about representation. I will talk about learning. When it comes to applications, I have to, I don't know how much time I will have to talk about the applications, but I have two basic lines I can get. One is the direction of linguistics, the other one is direction of computing, computer science, I mean, computational implementations of semantics. Who would like to have the linguistic applications? You can decide later, okay? Who would like to have the computational applications? Okay, it's a mixed bag. Okay, so we will simply see what I do about it, but that would be at the end. So, that's the preliminaries.
My motivation for these talks is a kind of an enigma. Here, come on. So, there is an enigma of language learning, and that is that we learn to understand words very quickly. When you finish high school, you understand about 50, 60 thousand words of your mother tongue. You don't use them, but you understand that. And that means, if you calculate that, come on, yeah, you learn from the age of two about, to understand eight to ten words per day. And, come on, very often we only need to hear a word once in order to grasp good meanings. So, yeah, so the question is, how does this wonderful learning work? And we don't know very much about it. We don't have good models of that kind of quick learning of understanding words. And understanding words means, basically, understanding the underlying concept. Understanding a word means knowing its meaning. That is the semantics. I mean, I will talk about semantics of language. I would not say very much about grammar or syntax, but, but this would be focused on, on understanding new words and how we can do it. And my take on this process is that words have structures that speed up learning. That's one component of it. And, and in particular, I will, in the middle of my talk, I will, I will talk about why we have word clauses. What is the cognitive reason for why we have word classes? That's the one of the main points of all, or my talk here. There is, if you are linguist, world classes are defined syntactically. I think that's a mistake. I think that word losses should be defined semantically. And that's what I want to give you here, a semantic theory of world classes. But before that, I will talk about concert representation in, in, in general. And by all means, please interrupt me at any stage. I mean, questions, comments, protests, applauses, whatever. I mean, in any form of interaction, it's good. That makes the thing much more light. So, please, please interrupt me.
So, before I get into my program, I want to talk about a little bit, very general terms, about representations. The meaning of representation in cognitive sciences. And you can say that traditionally, there are, you can disorder into three groups. And the first one is the, is the, I need to stand here. I'm sorry, I don't like that. It's the, here's the what's called symbolism. That was the beginning of, of AI, of cognitive science. Everything was formulated in some formal language, ideally in logical formalism. Then in computer programming languages, you try to describe everything in terms of some kind of symbolic representation. The second one is connectionism, neural networks, that somehow lives as a complement to the symbolic approach. But I want to advocate a third approach that I call conceptual spaces. That approach builds on spatial structures, having concepts represented in spaces, in some kind of geometric structures. And that's why I call my book "The Geometry of Meaning," because I, I want this form of representation. So, I want to spend most of my time talking about what I mean by, by these spatial representations. But let me say a few words about each of these three representations.
So, the first paradigm, this was the beginning of cognitive science in AI in 1956. The computer was a new thing at the time. It was taken as a metaphor for, for cognition. The brain was thought of as being a Turing machine. So, you had a, there was some kind of hidden program, and you gave it input, and then there was processing going on, and then there was some kind of output. That was the, the general metaphor. And the brain was seen as an information system, in parallel to what was going on in the computers. And the idea was that there was a central processor, was never found, by the way, but there was an assumption. And then there were memory systems, who had long-term memory, short-term memory, and so on. A lot of memory research was already nated by this method, from this metaphor. But the underlying assumption is that there is a code that runs the system. And this code was then thought to be some kind of symbolic code, maybe not logic, but something closely related to, to, to logical representation. Yeah, and of course, the Turing machine is a symbol manipulator. So, cognition was thought of manipulating symbols. That was, that was the key idea of, of this aspect of representation.
Now, if you sit down and try to feed information into a Turing machine, you need to have predicates or variables, if you know programmer. And one big question is, and then, yeah, this was these were the building blocks for, for describing information. And that was, was what was running the program, so to speak, the formulas. And then concepts was thought of, you, you built on this Aristotelian idea that a concept is given by necessary and sufficient conditions. And these conditions were then formulated in some kind of logical formulas. For those of you who know the computer language Prolog, it's basically built on this idea that you run concepts on all necessary and sufficient conditions. But you still have to have the basic predicate. So, here is a typical example. Here, define grandmother. Somebody is a grandmother if you see my female, and there is a Y such that Y is, let's see now, Y is the child of X, and there is a Y, and there is a Z, so that Y is a child of X, and Z is a child of Y. That's what's the meaning of grandmother is. I mean, this is a typical definition of giving necessary sufficient condition, and the given in logical formulas. Map.
But a major problem for this approach is, where do we get the predicates? Where do they come from? And to bring predicates are those symbols that are supposed to represent the concepts. Where do we get them from? Well, if you're doing things in this era, you, as a programmer, or you as a samantha sister, you as an audition, or you as a linguist, had to feed in these things by yourself. And some, a approaches later, I mean, using connectionism and so on, try to circumvent this question. But that, that's, that's the basic problem. And the second problem is, how can you learn the meaning of it over predicate? I mean, here is a location, you have to feed in these formulas or whatever. But, yeah, you know the meaning before you do it. But we don't know meanings of concepts when we, when we are born. We learn new concepts all the time. How do we do it? Well, I don't think we do it by necessary sufficient conditions. There is a lot of empirical evidence that this method does not work. This is not how we learn new concepts. So, there was some progress using this, some applications, but in general, it's not, in my opinion, it's not a good model of human cognition. It's not a good model of human concept learning.
Yes, very good. Give me an example of what you mean by how the basic predicates get into our minds. No, of course, I'm a bit polemic here, and I agree to that. But for your first thing, that it's not the brain that is giving the computation, it's the mind. That's a very deeper and a philosophical question that I want to, I don't want to talk about this. Your second one, you mentioned folder, and I think that further is the best example of this approach. I mean, and I mean saying that this is what gifts and give semantics, but he has to assume that the mean, he assumes at least that the basic predicates are innate. And I, I think that approach has, has a lot of problems. I mean, first of all, we don't know what are the basic protocol predicates. I mean, he never gives a good theory of what, where the exactly what all the basic predicates. And then I, I think it's a very strong assumption to say that all these predicates are innate. These would be my quick and immediate responses to, to further's a position. But, yeah, okay, go, go on.
Once much more. Now you're getting into HD textures are normally done in, in a non-symbolic systems. So then you get into another paradigm, and we can talk about that later. Of course, this has been complemented by other methods that generates can be used to generate basic predicates. That's okay. That's okay. That's, that's what has been used in, in, in, in many systems. Okay, okay. Yeah, that's one answer, but it's not pure symbolism. Okay. Yeah, yeah. Thank, thank you. Yeah. So, no, it's useful. You're perfectly right. This is used for processing, but I still have this. That's why I started with this enigma. How do we learn the meaning is over like world language? And this approach has, in my opinion, has problems explaining how we can learn a language now quickly. That's that. Okay. No, that's fine. That's, that's fine. So, but I, I want to explain it. So, I mean, our, at least have some direction in some answers in direction of it. So, okay, I'm unfair. That's okay. Let's go, let's go on because I don't, this is not what I really want to talk about. No.
The other one, connectionism. And here you take the Eternity metaphor around, and you start with the brain. I mean, these are, and these are neurons, and then you build an artificial system that is supposed to do the same thing. Okay, with connections in different places. Or I have to put it here. So, yeah, input and outer of the neurons in the brain. You take the neuro activities, the processing function of a neuron as a unit, and then you build complicated networks. So, here are just still very well-known example. This is a back propagation and network. I don't want to get into this print disk, a description of how it works. This is Subic recurrent Network. There are lots of different architectures. None of them really map onto what we know under of the brain. They can be used to solve different, different problems. I mean, back propagation is, it's very often used to solve and pattern recognition problems. This is the basis of what is now called deep learning. And deep learning, you have several layers of, of all networks, and you have to train it and train it and train it. And recurrent networks of quite often used to analyze linguistic input. Elma networks and so on. Yeah.
You don't know what is given 30. You have some kind of perception system. They are the receptors. That's the input layer. Sorry, to the system. You don't know what is represented in the system. There's a disability representation. In the Turing machine, each, each memory unit keeps track of a particular memory. Here, the memories is spread all over the system. One problem is that we don't really know what is represented, what, what is learns. I mean, you learn by here, you learn by training. You make feed lots of inputs into the system, and then you slowly adjust these weights. And if you're lucky, the system can learn to classify your input. But we, it's very opaque what is really learnt in most cases. And in general, learning is very slow because these, the adjustments of the, of the connections must be done in a slow fashion, otherwise the system, the learning breaks down. So, you need to practice it on thousands and thousand of examples to learn know something. And this is in contrast to human concept learning, which goes very quickly. So, that's one reason I don't think this is a very good model of, of human learning. We can talk about the applications later, but anyway, so this is connectionist.
Man, my favorite Pope paranoid, and that is concepts are modeled in topological geometrical structures. It's a space is basically. This is what I want to talk about tonight. I have introduced this notion of conceptual spaces. Information is organized in spatial structures. Here is my, or the paradigm example, the color space. So, this is a representation of humor and color perception. Three dimensions. You have the color circle, red, blue, green, yellow. And then you have the intensity from gray to more and more intensive colors. And then you have the brightness from whites to black. These dimensions are not totally independent. When you get close to white, you can make fewer discriminations and so on. This is human color vision. Other animals have other color spaces. There are animals with two dimensions. There are animals with four-dimensional color spaces. This is a more an empirical fact, and this is established by having lots of people looking at similarities of colors and using methods like multi-dimensional scaling or something like that to extract the underlying spatial structure. There are variations of this model, but basically human color perception can be described in a three-dimensional space. So, this is, this is one example. And then, of course, this is a perceptual model, model of our perception. Then we can discuss how this perceptual model shows itself in how language and concepts are constructed. But I'll get back to that in a few minutes. And, and the point here is that when I say that you judge similarities of colors, that means that if two points are close to one another at this point and that point are close to one another, that means that they are similar. So, distances are inverse similarities in spaces. Here, the closer they are, the more similar to two color perceptions are.
Now, one problem I would not talk about today and tomorrow's, where do these facial structures come from? I mean, this is a basic problem for the theory concept of spaces. I will talk about that on Saturday in the, in, in the workshop. I have some new ideas, but in the book, I didn't writes very much about this. But this is my, my, the topic of my, my workshop talk. Okay, so that's the, that's the third approach. So, I've just given you this, the, as a kind of background for what's been going on in the cognitive sciences when we are, when we are talking about concepts. The symbolic, the connectionist, and outer space. I will focus almost 100% on the spatial representation of concerts. But I want you to keep this contrast in mind. And please protest if you think that this, this doesn't solve the, the, the problems that I want them to solve. That's, that's okay. Yeah. Here comes the protest. I'm sorry, information. Yeah, yeah, categorization. Yeah, this is a model for how we learn concepts quickly. This is where they're basically, what I want to use. I mean, there are other uses, and I'll probably mention some of them. And I also want to show that this model can explain some linguistic structures, in particular, why we have word classes. But that's, yeah. Mmm-hmm. I'm sorry. Yeah. Thank you very much. It is also based for categorization. Yes. And it's made for, I'll give you an example how we can learn much quicker of using spatial structures than we can learn in connection assistance. So, that we can help the problem of quick learning. But for me, that's the part of the concert learning. Yeah, yeah, concept of acquisition problem. But you're right, it can do categorization. Okay.
Now, this is, this is the background. Now I get into the main, main part of my, my presentation here. So, I will give you talk about six different topics. The first one is, what is the matter? I mean, what do we want for my semantic theory? The second one is, then to present my ideas of concept to spaces, and in particularly the idea of semantic domains. Third topic is, how can we be sure that with mean the same things? I mean, I, I have may have my meaning of a word, and you may have your meaning of a word. How do we know it that we talk about the same thing? This is the meeting of minds problem. Then, this is the core of my, my talks, and it called me through grounding of word losses. That, that would be what it's all leading up to, basically. As part of that, I will give you a high cognitive theory of actions and events. That's in order to explain, for instance, how verbs work. People in these areas have not paid very much attention to how we learn verbs, and that's one thing I've been working on. And then finally, a little bit about how we can get compositionality of meanings from, from this approach. This is menu. So, let's start.
What is semantics? Soon, and I have put down a number of questions for assume that that is the semantic theory should be able to answer. Of course, I've picked these questions myself. So, I, I have some ideas about how to answer them. But instead, let's go on. First question is, what, what kinds of things are meanings? And, yeah, that's the first question. Second question, what is the relation between things we say and their meanings? I mean, how can we get through this mapping between words and meanings? That's the basic idea of semantics. There are some connection between, between what we say and their meanings. Now, this is the learnability question. I have already mentioned it. You have to be able to learn the meanings of words. And then this is the, how do we know that we talk about the same things question? The social question that we, we share a language, you share an understanding of a language. How does that work? Very few people have ever actually worked on this problem. Yeah. And then language is, it's not a separate unit. I don't, I don't believe in the Chomskyan idea of language acquisition device. That language is separate from other cognitive processes. For me, language is something that goes together with other cognitive processes. So, I have this, what is the relation between perceptual processes and meaning? How can we talk about what we see, for instance? And then I have a particular focus on, on action. How can we talk about what we do? That's another. But there are actually lots of questions relating our other cognitive process, perceptual, memory processes to, and their linguistic problems. So, these are my questions, and I hope I will give some answers to all of them during, during these four hours. Okay.
So, what are meanings? Well, basically, there are two traditions. If you look at the philosophy of semantics, there is what I call a realistic answer, and there is a conceptualistic answer. The realistic also says that meanings are out in the world. The meaning of the word horse is the set of all horses. In that's an extensional definition. So, meanings are out in the world. In the philosophical tradition, that's mainly associated with people like Vega and Tusky, and so on. But its forms the basis of a lot of analytic philosophy. The conceptualistic theory says that meanings are in the head. That meanings are kind of cognitive structures. And I go for the conceptualistic theory. As you will, I would not be a realist here. Meanings are something that exists in our, in our minds. So, this is the basic division, and I'll get back to that in a second.
Now, what is the relation between communicative acts in their meanings? Then we see lots of answers in analytic philosophy. The focus has been on what's called truth functional semantics. I mean, I already talked about this realism versus conceptualism. But within philosophy, most of the truth functional semantics built on and realists. There are exceptions. There are people who try to try to be more pragmatic, for people like Storm Acker and others who want to have a non-realistic interpretation of truth function or semantics. But they are not very many. Basically, most of the analytic philosophy has this truth function because truth relates to what's out there in the world. And this is, you can distinguish two flavors of truth function or semantics. One is what is called extension of semantics. I mean, there is a language having words like horse or cat, and then there is the world. And so, you define the meaning of horse in terms of what's out there in the world. You define the meaning of a sentence depending on how the world looks like and so on. You'll give, you give, I'm sorry, yeah, you give truth function, you truth function conditions for, for these are the meanings. Then the second flavor is what's called intentional semantics. And it turns out that for many words, it's not enough to talk about one world. Have to talk about several possible words. And then you get into possible world semantics. I don't want to talk about the details of this. But this is what's called intentional semantics. But still, semantics is thought of as a mapping between the language and a number of words. Now, instead, and meanings are then given as truth conditions. This has been driving force in lot of analytic philosophy to give the truth conditions for all kinds of concepts. So, I gave you the example, so grandmother, that's a typical example of, of defining truth conditions for, what is the meaning of somebody being a grandmother? So, truth functional semantics builds on realism. Cognitive semantics, which is a branch of all cognitive linguistics, being some conceptual listener. And then you have people like Larnaca, Lake, have told me, House, Kovacs, lots of people working in, in, in, in this area. And here is my take on that, that semantics is really a, this is, this is the mind, and, and language is part of the mind. And semantics is a mapping between something and linguistic structure, and something a conceptual structure that you have, that you have in mind. And then, of course, you have to somehow relate to the world. But that's not that relation is not part of semantics. This is, this is my, my idea here. Yeah.
Yes, yeah. This relation is a relation of when you succeed or not succeed. It's a question of of pragmatics, of being able to communicate in order to jointly perform actions that give you success. It's a, it's a, it's a kind of game theoretic approach to you or to do that to, mmm, and I'll talk more about that tomorrow. No, yeah, yeah. Yes, in a sense, reference. We would be coordination of meanings. So, I mean, yeah, well, I'll get back. I'll get back to it. I don't, if I have time, if I get two applications, I'll try to do it. But I, I will give you when I get to this, how we can communicate, what, how we can share meanings, I will give you the answer to how I see to look at reference. It's very good that you say that. That can be combined. Yes, they can be combined to some extent. I mean, we can take some ideas from, from traditional semantics and put them in here. But in general, I want to put focus on, on this, on this. So, yeah, okay. I didn't, well, I should mention, I probably will do that soon. I should mention that with, in cognitive semantics, people have thought that these conceptual structures are represent, can be represented as image schemas. Some of you may, I mean, if you're in cognitive linguistics, you know what image scheme are. So, and that's a way of making more or less precise what, what is meant by the conceptual structures here. Yeah, just wait. I will, I will, I will get back to that. Not, not meaning me. They also did the answer is no. Yeah, but, but they also is not what is not at all in line with the traditional semantics. That there is a mapping from meanings to the world. There is, I'll give you the answer in maybe not today, but, yeah, today later in the afternoon, I'll, I'll get to it. Yeah, meaning is not independent of the world. But you see why.
And then, how can meanings be learned? And I will talk, I will not say much about that because I will, I will spend talk about that later today, or maybe, I mean, no day, but maybe not in the morning. Let's see how far I get. Then we have the dissociate one, and, what is the relation between individual speakers and the communal language? And one or the no forceful criticism against this conceptualist approach. It comes from the philosopher Putnam. And he has this famous quote saying that meanings ain't in the head. They can't be in the head. And he says that he can't distinguish a beach from an element. These are two different kinds of the trees. But he knows that there are people who can make this distinction. He doesn't, for him, the image scheme of a beach and an Elmo, whatever his concept of bitchin and elm are identical. I mean, they're just trees. He doesn't know very much about trees, but he knows that these two words have different meanings. So, the meaning country at least not in Putnam's head. There must be somewhere, somewhere else. And Putnam uses this argument to say that meanings can't be in the heads. And in the head of an individual, there must be some kind of realistic complement to it. So, you get that, that's his argument. I don't like his argument. I have an alternative answer to this, to this enigma. So, I'll, I'll get back to that. But I want to say that, okay, this is, this is the problem. Yeah, okay.
So, how can we share mental representations if everybody has their own meaning space? I mean, Putnam has his, I have mine, and you yours. How can we know that we talked about the, the something being the meaning of a world? We know we talked about meanings as there are unique, the, the meaning of the word horse, and the meaning of the word L, and so on. Now, this is a new idea. No, it's not a new idea, but something that is not normally dealt with in cognitive semantics. That semantics is not just me in my head. It's also a product of me interacting with other people. And if I use the word in, in, in a particular way, and you don't understand me, I have to adjust. We have to coordinate our meanings. And this coordination is what gives the meaning of all the word. I'll give you a model of this in, in the afternoon today. So, meaning is a result, not only what goes on in my hat head, but also what goes on in your head, and our interactions. That was created meaning. So, it's an emergence from a, not phenomenon in, in, in community of, of interacting people. And this is a thing that is a little bit, the difficult to model. But I'll give you one model. So, I talk about a meeting of minds as the basis for semantics. Now, this fact that we have to share meanings, that will actually put constraints on how meanings are constructed. So, that, that will, that will give constraints on how are we trait meanings. And I will give you an example of that later. So, my way of modeling this is to use conceptual spaces. We all have our conceptual space. But then I'll use some ideas from game theory, that is coordination, coordination games. So, this is my, my theory. Was a [Music] [Music]
Yes, I will, but you have to wait until the afternoon because then I will give you the modern. So, it's a very good question. I mean, it's a very serious problem for action. It's a serious problem for cognitive semantics to answer this question. I'm not saying I'm giving you a full answer, but I'll give you some, some order of it. And, and that one will be based on this concept of spaces plus game theory. So, very simplistic picture, you have to be two individuals here, one individual with conceptual structure, another one, and you have to somehow, somehow get a up story. This is what I call the meeting of minds. These, these meanings must be coordinated. And then exactly how this coordination is done. Now, I will talk about in the, India afternoon. It's not sure that my perception of red is the same as your perception of red. This is the famous phenomenon of qualia in, in philosophy. But somehow we are able to coordinate our, our perception somehow with a, within language. Okay, yeah.
So, my answer to, to, to Putnam's question is to say that meanings are in the heads. You need a community of speaker in order to determine the meaning of a language, or meaning of different words. Now, final questions. The cognitive ones. Relations between perceptual processes and meaning. Basic question is, how can we talk about what we see? And the brain doesn't only use linguistic reps, or representations of meanings. We have representations of vision, of sound, and language, in music. We have different, I don't want to, you really wouldn't use the code word code, but somehow we have different modalities of, of representation in, in our brain. And the question is, how can we, how can we coordinate these, these codes? And this is a very basic problem. Any child who can speak can see a picture and stop talking about what's on the picture. You can take any visual input, you can describe your visual input. This is a fantastic process. We don't know how to, how we do it. And conversely, anybody who, any child who hears a story, bedtime story, whatever, can sit down and draw some kind of picture. What goes on on the story? You can take what you hear and turn it into visual, visual phenomenon. We can do this translation between vision and language. And we know very little about how it's done. But it's really a fascinating problem. Yeah. This is what I said. Oh, now I get to the image schemas. This is the relation between perception and meaning. So, people like, as I said, Lana Karen, and here, Mark Johnson, and philosophy like of, and others have been working on this. Here's one example from, from LAN Acker. So, this is how he represents the verb to climb. So, there is this basic time dimension. You have a process. Climbing is the process. And you have three different frames for what's going on here. There is a vertical landmark, this is the LM, and there is a trajector, that's the thing doing the climbing. And then you have a process that means that this trajector is in contact with the landmark, and it's moving, move, sorry, moving upwards along the long destroy texture. That's the basic image schema for what's going on in climbing. Then you can turn it into an image schema for the word climber. And climber means that now you're focusing on the, you're focusing on the, the trajector head, the person doing the climbing. Now, now here, the, these thick lines means that you have your focus is there. And here in the verb, the focus is on the, on the temporal dimension. Here, the focus is on the, on the thing. Its, it's now turned its turn from a process into an object. But basically, it's the same structure. It's, it's a matter of shifting your attention from the process to the, to the object doing it. And that's the difference between the climb and the climber. This is a typical example from how, how people in cognitive linguistics treat meanings of our words. And Lake of, another people to doing tell me as if it's lots of people now are doing similar things with other, other who works here. Yeah. It relates to get shot psychology. I don't really want to get into the details here, but they have a lot of influence on that.
The second question, relation between action and process. Lots of people know, I should say, very few people have been working on this problem. So, it verbs normally express either actions or results of actions. And I will get back to that tomorrow when I talk about two verbs. And now my take on this is that this is a picture from Mars book on, on, now it's not from Mars look, it's a later article with Vina, how to represent actions. So, they look at, they have small differential equations here. They look at the patterns of movement here. They do it in terms of patterns of movement. I think, and I will try to give you arguments for that, it's better to look at the patterns of forces. So, when you're doing things, you're, you're performing certain force patterns. So, my idea aware that I will explain later is that actions are described, can be described as force patterns. But I'll get back to that. So, this brings in the force domains. Here, some people in cognitive linguistics, in particular, told me has been working with force dynamics as part of the, part of the image schemas. If you know Tommy's work, you know what I mean here. So, that's the end of the first topic, what is semantics? I would spend, I'm not sure I will be finished with the second topic this hour, but let me, let me start. Okay. Yeah, go ahead.
Yes, and I know you're perfectly right, and I'm not saying that the child learns the full meaning of a word in, in one shot. Yeah, yeah. No, no, I didn't say it. So, you didn't misunderstand me. So, yeah, that's, that's perfect. Yeah, yeah. Can I just stop you here? This means that there is not, I mean, talking about the third meaning of a word may not be a very well-defined concept. Meanings develop as we learn more. So, about the concept. But still, you, you are able, a child is able to grouse for the basic components of the meaning. And I'll tell you in a while what I mean by the basic amounts of the meaning of the word very quickly. Then the meanings developed. Yeah.
I want actually very little. I mean, okay, let me make a confession. It's, it's not explicit, but it's implicit. I want to develop a syntax tree semantics, and I'm not sure I can succeed. I will, I will get back to syntax if I have time for the applications at the end. But this is actually one of my girl goes to have to have a syntax free semantics. And now I'm aware of the things you're mentioning here. And of course, we, I'm already contradicting myself a little bit because I'm saying that I want to have a, I want to have a semantic characterization of word clauses. Now, you recognize a word class by their syntactic components. In you, for many language, you can see whether the word is a verb or a noun or an adjective by the syntactic marking. And that gives you a clue to what is the meaning of the word, because you know what kind of category it's referring to. So, in that sense, my, my, my theory is not perfectly syntax free. But I only use it syntax as a kind of marker for to understand what kind of word we are dealing with when we're, we're learning it works. Yes, yes, yes, yes. Yeah, yeah. Let's say this. I like these examples, but so let's save them until I get to the verbs. Yep. Yeah.
[Music] [Music] [Music] Yeah, no, you're perfectly right. And, and, and in particular, we can talk about, we can have very interesting conversations about fictional things. I mean, you can have serious debates about Star Wars, or about about unicorns, or about witches. PGH has this famous paper on intentional identity. We talk about hoping, nope, talk about the witch. And I think that means the same thing. But of course, the which doesn't exist. So, how do we know they're talking about the same thing? We don't know it. But we can still have wonderful conversations about witches and unicorns and other fictional things because to some extent, we have some form of alignment of the concepts in our heads. The alignment is not perfect because there is no reality hitting back in, in, in, in these cases. So, I hope I can give you a partial answer to how we can do it in my account. Yeah. Yes, yes. Yeah, yeah. And it's, yeah, I mean, unicorn is created because we know what the horse is, and we know with the horn is, and where we could just put the horn on a horse, and then we get the unicorn. We have the components, and that allows us to talk about [Music] [Music] We can reach like a mutual understanding through like socialistic. Okay. Mmm-hmm. Yeah.
First question, connection is mr. model of all the second language darling? No, I don't think it works. But I'm not, I'm not sure I can give you a detailed argument. The second question, come on, oil Chomsky, Chomsky, sorry. Yeah, no, of course, we have words and we have syntax. I will not talk about syntax. Chomsky thinks that, I mean, Chomsky doesn't really have a theory of words. I mean, he takes them as units, and they are given some right. He talks about phonology, but that has nothing to do with me, the semantics. He talks about how you put words together. I will say a little bit about how you put words together at the end of my talk here. But in general, I'm not very much interested in this syntactic structure. So, when he talks about code, he mainly talks about the syntactic structure. Man, that's the title of his book. And, and, but I'm, I'm talking about the mapping between words and, and meanings. There's this, this is thicker. So, words for me is a form of code. Yes, but I haven't developed any any theory of syntax that that would match what sure Chomsky. So, there is a bit of mismatch between our programs. You meeting of minds, accommodation is a word I have problems with because I want a model of accommodation, and I, I don't really see any good models of all of that. There are people Pickering, Garrett, and so on, who who do some could they call it alignment instead of a, which is which is similar, still not, not a very good model of alignment. So, and I don't have a really good model either. But I, next in the afternoon, I'll say a bit more about how I mean, what I mean by this meeting of minds. Okay.
Can I spend two minutes on conceptual spaces? But by the way, thank you for the questions. That means I, I would not spend any, save any, any special time for questions at the end, unless you want any more questions now. Yeah, okay, go ahead. I have nine minutes. Okay, have we started late? You mean, okay, good. Yeah, no, that's fine. I like your example here because we have developed the language is very good at talking about what we see. Language is not very good about talking about what we hear. I mean, in particular, if we come to music, I mean, it's very difficult to give a description of a musical piece in language. It's very bad at that. We're not very good at talking about what we say. I can recognize the face after seeing it once, but I have no, it's very difficult to give a verbal description of all the face. I mean, people try, but it's, it's, it's very difficult. So, for spacial relations, we have a very good language. For faces, we have a bad language. So, that means that language is good at certain, certain perceptual phenomena, but not at others. And that's a very interesting point. What, what perceptual phenomena do we have linguistic tools for? And I mean, I know some, but I don't know, and I don't have an answer to the general, general question. Yeah.
Special language works very good for relation, spatial relations, not, not for more precise. I mean, if, like, like describing the structure of a face. The general answer, I, I think to the question of what, what can we talk about, what, what could we use language for, is would be an evolutionary one. What do we need language for? What kind of things do we need to communicate about? We don't need to, we don't need to have a description of how voice sounds, or how musical piece sounds. We can share it, but we don't need to describe it. We need language. I mean, I have a theory of the evolution of language, which I will not talk about. But we need to talk, coordinate things. We coordinate actions. That's, that's basically. And describing spatial relations is very important to it, for coordinating actions. So, that's why we can talk about it. This would be a very brief outline of my, or my answer to that question. But I haven't developed it. Yep.
Yeah, yes, right. Yeah, yeah, very good. Now, the word you, you used here, musicians can hear music by having it described. Described means that you, you see the score of a piece, and a skilled musician can hear the music just looking at the score, just as we can read the text and so on. But that score is then, I wouldn't say it's, it's, it's language. It's a different representation. It's a representation of the pitch, in the duration of terms, and, and, and so on, and, and how they go together in harbin. Is it, it is, it is a different representation, but it's not really, I wouldn't call it the linguistic representation. No, no. You can talk about a single elements of the music, but you can't, you can't describe the Ninth Symphony of Beethoven, or whoever, in, in words. Wittgenstein, you can said you can whistle it, but that's a, that's the difference, the difference code. Now, I, I know, I think actually language is very bad for describing, describing languages, such is describing music here. Okay, thank you.
Now I have five minutes. So, then I'll take this benefit. Now, now I don't want to have any more questions at the relevance. So, conceptual spaces. This is my previous book. I will, I already said something about the topological geometric construction, but I will use the notion of a dimension. And dimensions here are color, size, shape, weight, position. I haven't open list of dimension there. I'll give you examples later. So, here is two very pretty simple examples of dimensions. Time dimension. We think of in Western cultures as a real line. There is a designated point that is now. Then there is the future, which in, in most metaphorically, most Western cultures mean going to the, to the right, and it's in front of us. And there is the past, which is behind us. Some cultures changed the ordering of this, but that's another story. Now, compare this with the weight. I mentioned the weight dimension is only half a rail line. It's only positive numbers. We don't talk about negative weights. So, the dimensions here, or have a different topological structure. One is has an end points, the other one doesn't have an end point. So, there is very trivial examples of, of different, different structures here. And I already mentioned the color space. Yeah, dimensions were sorted into domains. So, the color explains has three dimensions. Sizes, one. White has one. Position has three. Shape, we don't know about, what, what it is. We'll, yeah, we don't know very much how we recognize shapes, but we are very good at it. And I've already says this, that less dense, the less distance in a space means greater similarity of meaning.
Now, here comes my idea of concepts of representative convex radians. This is for me a kind of theory and that can be empirically tested. And Jose has protested against my, my idea here, but let's not take that, that debate here. Not, but convex means, let, let me do an example here. Here's the counter space again. So, we have these perceptual dimensions, and convexity means that they, the concepts that we form, the color concepts that we form, like the concept of red, means that the definition of convexity is that if this point is called red, and that point is called red, then anything in between is also called red. So, the notion of betweenness here, if something is for lands our concept, another thing falls under the concept, that anything in between also falls under the concept. That's the definition of convexity. And that means that there will be no bays in the four shapes here. I'll, yeah, I don't want to get into the mathematics here, but that's, that's the basic meaning of convexity. So, in my talk, I will use these concepts, the notion of a domain, and the notion of convexity, quite, quite frequently. So, why do I want to have convexity? Why is this a good notion? And by the way, note that this notion of betweenness, that's a very fundamental geometric notion. I mean, that forms, yeah, as it's not the only, a geometric concept, but that's, that, in, in symbolic codes, in, in logic, and so on, and it's very difficult to describe betweenness. But if you have a spatial structure, between this comes for free. And then you can define, define a convexity, you can define betweenness in connectionist system as well, but it's less clear there. It connects the prototype theory. I mean, this is one example where I connect two psychological theories of concepts. So, let's take an example. Assume that you have a two-dimensional space. The argument works for any dimension. So, it doesn't matter, but I can draw through it. I mentions here. This is a two-dimensional space, and you have prototypes here. You have prototypical colors. So, you have prototypical birds. So, you have prototypical, I fruits, or whatever. Every way started in prototype. And, and, let me have one more minute to finish this argument. So, these are the locations of the prototypes. Now, given the prototypes, you can very simple rule of generalization. Say that if you see a new thing, this is a new observation you make. It has these two properties, these two values of the two dimensions. Then you classify it with the closest proper taste, the most similar product prototype. So, any new thing is sorted within closest property prototype. Now, I use the word closest, and that means I'm assuming there is a metric, which is a bit stronger than just assume in betweenness. So, I have a metric space. Then you can talk about the closest prototype. And this simple rule gives rise to what is called a Voronoi tessellation. It's a Russian mathematician, and the Voronoi tessellation means that this line is the line that divides the midline between P1 and P2. This line is the midline between P2 and P3, and so on. You see, you can see the middle lines here. And if you draw all these middle lines, you end up with areas like this, regions. And it's the two line mathematical proof to show that these regions are always convex. So, if you have prototypes, if you have a metric space, and if you do this classification, always sorting objects by the closest prototype, then you end up with a convex categorization of other space. But when it builds on these assumptions of all, of metric space. Now, I stop the aluminum in the middle of the presentation of conceptual spaces, but we will continue in the afternoon. A quick question. Yes. Yeah, I mean, if you go by Eleanor theory, you have the basic level, you have subordinate or super. I'm assuming that all the prototypes are on the same dais. You're perfectly right. So, thanks for today, or for the morning, and we'll see you again in the afternoon. [Applause]