Transcription
You know how to categorize a new object, so convexity helps you in, in, in offloading memories. So that's it, it's the principle of the author of a cognitive economy. So that's the first, first answer to why convexity.
The second answer is that it makes learning much more efficient. And this is the problem I, I started from: how can we explain how we learn words very quickly? So assume again that we have, that we have a two-dimensional space. Now I haven't drawn the borders, and this is a learning story. Let me give you a simple, simple story. You're a father, you bring your two or three-year-old daughter to the city pond. And then at the city pond, you see a lot of birds. There are some birds that are geese, there are some birds that are swans, there are some birds that are ducks. So your point is, you tell the daughter to say that this bird, I mean, these are the properties of the bird in the bird space, whatever bird space is like. And you say that this is a duck, and that's this one, and that's the goose. And no, this is the goose, and that's this one. That's what I said. And you see a number of examples like that. And this little girl sees the empirical examples. You get these instances, and the ducks are kind of similar. They're located in this region of property space. The geese are a bit also similar, and the swans are or here. Well, maybe there are even more similar. Anyway, you get a few examples of each word, and you get the locations in property space of this. On the basis of that, the girl can form an average. And the cross is all I mean, I take a very simplistic story here, the mean of the positions in the space. And given these means, you can take the means as a prototype. And then the, the, that mean will generate the Voronoi tessellation. And if the girl sees, you see, a new object, you know what it, what it's more similar to. I mean, it's more similar to a duck than this one. So you know that this should be called a duck. So the point here is, once you have the space, you basically only need one example to form some kind of, some kind of prototype. I mean, if the only example you've seen of a duck is this particular duck, then that, that will be your concept of a duck. And then you can use that to generalize.
Yeah, yeah, yeah. No, this is, this is a put number, the mean of positions. So you have positions in the space. This is positions, and, and I'm assuming a metrical space again. I mean, there's two, to simplify things. So it's the mean of the positions. And in this space, yeah, it has a mean, if ever its shape, it has an average, calorie, it has an average. So it's a lot, a lot of features that, that, that determine they. But I mean, I haven't given your bird space, and that's a complicated story. But I mean, this is the general principle of learning from a few examples. Here, you're observed the properties are support, location in space. And then you, if you have different locations in the space, you can, you can, you can calculate the mean of the locations.
So now we continue this story, and suddenly, suddenly there is a new object. There's a new bird, and it's a mandarin duck. It's a bit odd as a duck. It doesn't really look like it. It's a bit strange, but the father insists that this is called the duck. Even if it's these hatched lines or they're already at the older categorization. So the girl now gets a new example. It's a bit odd. The mean changes. The mean moves. And that means you have a new categorization. So the point of this story is to say that the categorization is not fixed. How you categorize things is dependent on your experience. So you'll learn more about concepts by seeing more exemplars. And, and of course, if you have a rich experience, seeing a new exemplar will not move your concept very much. But if you only have seen one or two examples, you, you may change borders between the concepts quite radically. So when I say that you only need one example to learn a concept, that means once you have an example, you think you assume that that's the prototypical one. And then from there, you go on using the word as you, as you have done before.
Go ahead. No. Yeah, yeah. No, no. Penguin is perceptually not very much like other birds. And then you have to go to other features, like it's laying eggs, and then it has body parts like wings and so on. Even if the wings don't look like wings. I mean, you have to go to biological category, category. So this is how you learn later that the penguin is a bird, bigger, or because it has the nice, by the right biological properties, rather than the right perceptual properties. It's a different process because when you're still talking about the biological features of a bird, you're leaving the perceptions. I mean, in my story, I was focusing on the perceptual features of birds. But we know that there are the domains. I'll get back to that part in a little while. Yeah, yeah, yeah. It does. And I can give you examples of that. I mean, people thought that all swans were white, and then suddenly you went to Australia, and you found black swans. There was a big change in the concept of a swan. But there were other characteristics that decided that people still call, continue to call this bird a swan. Maybe Benji on the [Music]. Yep, yeah, yeah. But it's also dependent on what features, what properties, what domains are you considered to be essentially the more important for a concept. So I'll get back to that point. Anyway, this model also explains why children overgeneralize concepts, overgeneralize the use of concepts. Because if the only animals a child has learned is a cat and a dog, it's a city, it's a city child, and it only sees cats and dogs. And then you go out in the countryside, and you suddenly see a cow. What will the child try and say? Call the cow a dog. Yeah, we call it a dog because it's overgeneralized. I'd say the only knows the words cat and dog. It now sees an animal, so it will overgeneralize dogs and apply to, to cow. And of course, what happens then? When you make finer discriminations, you partition the space more, you end up with more and more and more prototypes. And then you get to find a partition, anything, and so on. But I mean, this is a very simplistic model. I mean, I'm not saying that all spaces are metrical, that we do it by this simple mean calculation. But I mean, this simple model shows that given a spatial structure, you can explain how you can start using concepts only after one, a couple of examples, and then use it in, well, sometimes successful, sometimes not so successful way. Okay, that's quick learning. Now, later, I will talk about the empirical support for this from from linguistics. But let me skip that, save that for, for a little bit, until I get into the world classes where we'll see a little bit of support for convexity in, in, in any concept. I want to make, I mean, I was complaining when I talked about the symbolic approach, that everything has to be formulated as a predicate. Now, I wanted to introduce a new distinction. This is my distinction between properties and concepts. So this is a way of dividing predicate into two groups. So I use a product notion of a property for something that is, is in, in one single domain. So red is a property because it relates to the color domain, and big is a property because it relates to the size domain, and so on. Then concepts for me are something that is more complicated, may have more regions. Like when I talk about animals or fruits, or, I mean, ordinary objects. They have an animal has a size and a shape and a sound and a smell and a weight and a temperature. I mean, it has properties and lots of, lots of domains. So I want to define a corner, well, I should say object concept, basically as a set of, of convex regions in a number of domains. And then some information about which domains are the more central ones. I mean, some of them are not so important for, for identifying the concepts, some are more important. I'm not really an essentialist, but it's something like in essence, the idea of the concept. And then also we have information about how the domains, regions, and different domains are, are correlated. So let me give you an example here. Let's take the concept of an apple. So when you're a kid, you learn about the color of apples. They are red, green, and yellow. You'll never see blue or black apples. And you have, I mean, you have taste spaces for dimension of web, sweetness, sourness, bitterness, and saltiness, maybe mommy taste as well, if you, if you like. But basically, apples go by or have values for sweetness and sourness. That's where you find them. You can have more or less sweet apples, and so on. Shape space is a bit complicated, but I'm sorry, not shape space. Let's go back. So it's in the round, radial shape space. The major distinction between apples and pears is the shape. I mean, the colorant and other things. And then when you learn more about apples, you learn, I mean, as an addict, you learn about the nutrition of it. If you become an expert, if you become a pomologist, as they are called, you learn about skin, skin type, and seed type, and I don't know, flesh type of apples, lots of finer, finer than domains that you add to a notion of apple. The point here is that a concept is an open, it's an open thing. You can add more domains, see more knowledge about the concept. But when you want to encounter an apple, you have to perceive your properties of the color and maybe the taste and the shape of the apple. That's the first domains you pick up as a child when you learn about them. But concepts are open-ended. Happy. I'm not, I'm not talking about necessary and sufficient conditions here. So shape space is very interesting because we can very easily identify shapes, but we don't know how we do it in our brains. And there are a number of shape theories. This was the first one that was presented by David Marr in early 1980s, where he'd used cylinders as a kind of, kind of building block store for shapes. They actually used generalife cylinders. And the point here is that a cylinder, you can describe with two coordinates, its length and its thickness. And then you can talk a little bit about how these pieces are put together. I mean, you can define this as a kind of multi-dimensional vector. Each of these things. So that Mars in the representation defines a clearly defines a shape space. I mean, in terms of the thickness and the length and the angles and a connection points and so on. But then this is maybe not the best representation of how we perceive shapes. There are other theories. I don't want to get into that. But we are, we are using shaping information in particular as, as children. I mean, Linda Smith has shown that there is this very strong shaped bias in how children learn, learn object concepts. So shape is very important for early concept learning. Then we give up to shaped importance later. So let me go back to my, oh, sorry. Yes, I should go back to this idea. So this is what I mean by the prominence values. They change over time as you learn more about the concept. And they didn't say anything about information about her the radiance. Of course, there is a correlation between the color an apple or and the sweetness of an apple. Red apples tend to be sweeter than green apples. We know this. We expect to be the red apples to be sweeter than the green water. So we know something about that. I've forgotten who I have an example by, forgotten where it comes from. But the example is the following. You somehow end up in an island in another place. And on this island, you meet one person. The person is a man. Person has a brown skin, and the person is very fat, is obese. And that's the only person information you have. You have one example. Now, I ask you to estimate the probability that the next person is a new mate on the island is a man. What is the probability the next person on the island you meet is a man? Come on, give me a number. Fifty percent. Yes, correct answer. Almost super, around fifty percent. Very narrow, narrowly you would get that kind of instrument. Okay, what is the next? What is the probability that the next person you meet on the island has a brown skin? Come on. One. Okay, now if you do this experiment, you normally get an answer like 0.28, 0.9. I mean, higher up. What is the probability that the next person you meet on the island is obese? Very fat. No, no, no. It's you only have one observation. You have to guess about the next person. What is the probability? And if you do this experimentally, you get a very wide distribution. Anything from 0.1 to 0.99. I mean, it's very unknown. The point of this example is that we know that biologically there are good reasons for why the population on an island should be distributed almost 50/50 in terms of sexes. May not be so. But we still guess it. Color of skin, caliber person is probably fairly constant, but might be exceptions. But I mean, you have the point of this example is that have one individual, and that's enough to give you a fair amount of estimates of what is the probability of that feature of other, other individuals. But the probability depends on, on the feature, of course. Okay, that's what I wanted to say about the correlation about the radiance here. Okay, now that's not the end of my introduction to constructive spaces and semantic domains. Now I want to get into semantics as a meeting of minds. And now we get entertainment or something. At the same time, I would like to say that there are two kinds of, when we communicate, there are two processes. One is slow, no, one is fast, and the other is snow. The first one is when we draw attention to the same thing, when we have joint attention, or when we build up in the dialogue, we build up a common ground. I mean, I'll tell you what common ground is very soon. And the slow process is when we talk about how, how we correlate the meaning of works in linguistics. This is sometimes called the distinction between the pragmatics of communication and this is the semantics of communication. But I don't think there is a very sharp order between semantics and pragmatics. And the idea of common ground, I take from Herbert Clark. And when you start talking, having a discussion with a friend, you're telling a story, giving some gossip, giving advice, or whatever. You, in the dialogue, you introduce the number of references. You're still talking about the person, you start talking about an event, and as the dialogue proceeds, you build up the common ground of reference of actions of events and properties that you have mentioned. And you can build on that. And in particular, in the use of pronouns, you build on that. I mean, I talk about the man I met on the street with his strange hat, and then I say, he was very old, and so on. And this meaning of he refers back to an air reference. The pronoun builds on this kind of common ground. And we have all kinds of the most relatives in other words that really built on this kind of fast process of building up shared information. This is exactly what I just said, that you're accumulates during a dialogue. And it's also been shown that you design your utterances. I mean, I wouldn't use the word the man unless I've already introduced him. Otherwise, I would say a man, I met a man on the street, and so on, using the indefinite marks that this is unknown to you. And the definite marks that we, I've mentioned this before, you should know who I'm referring to. So we have determiners as part of this. I don't want to get into the details here because it's not really semantics. But now I want to talk more about how we can make minds meet. And actually convexity plays a role here. And I'm getting back to this, this problem here, how can we share mental representations? And the famous case is Humpty Dumpty, who says that whenever I use the word, it means just what I choose it to mean, nothing more, nothing less. And then Alice protests and says that if you can, the question is whether you can make words mean that things. And normally, we don't go around as Humpty Dumpty's. I mean, don't assume that when I use the word, you know what it means. I, I'm playing on some kind of common, common usage of words here. So the question is, why are we not all Humpty Dumpty's? That's what I want to learn also. And I've developed a model together with my colleague in in Venice, not Masam of Ugly, and that we call modern or fixed-point semantics. And it's, it's, I mean, sharing meanings, it's a little bit like like reaching agreement on, on, on a contract. We negotiate meanings to rather than what I'm sometimes I decide that what the word means, and you don't have anything to say. But typically, we, if we don't understand it, we negotiate their meanings. And here is a very abstract definition of semantics. And the semantics is a function that maps a, a word or a communicative expression on some kind of mental states. I say something, you form a mental state, and then we have the converse thing. I have a mental state, and I turn it into an expression, a word. So the semantics is this two-way mapping between semantics and mental expressions. But in terms of a dialogue, it works like this, that I have a mental representation of a color green, and then I say, then I say the word green, and you, you listen, and you form a mental representation of what I'm saying. And, and then you say, okay, great. And then I understand that this gets vacant forms of mental representation in my mind. And if, sorry, if this ends up at the same place as my original statement, then it is a fixed point. I mean, I, the communication should be big, what is called a communicative mapping here. So that's, that's the idea of of sharing, sharing meanings. But the problem is, is it's a little bit, yeah, little bit more complicated. So minds meet when this function maps states of mind on, on states of mind. When there is a fixed point, this is what I try to illustrate with the previous picture. Come on. And the way we model is it is as equilibria in communication games. Now, lots of people have talked about language games. It started with David Lewis and so on. But what we do is to add some kind of topology and geometry to these mental states. I mean, this is the concept of spaces. And we show that that helped, that addition will help in, in generating fixed points. Before I get to the general augment, I will illustrate this with an example that is taken from a work by a communication game studied by Diego and Robert Van Roy some years ago. And their, their a game is, you have a space, they call it the counter space, but it has nothing to do with calluses, mainly they have a mayonnaise face of colors. Mathematical terms, it's compact, convex, doesn't matter. And the signaler has a finite number of messages. These messages are already nary, just tokens. You can choose between A and B, or between A and B and C, or between A, B, and C. And do you have a small number of messages? And at the beginning, the receiver knows nothing about what is the meaning of A or B or C. So it's, it's totally unknown what the messages are. And then the game proceeds as follows. That made sure that is a computer selects a point in the space, the sender selects one of the messages, and the receiver listens to the message. And then the receiver points to a point in the space. And the, the game is such that the closer the receiver points to the original point, the more the sender and the receiver are rewarded. So it's, it's, it's a cooperative game. The, the sender is saying A, B, or C, or D, and the receiver has to guess what is the original points in the counter space. Of course, at the beginning, everything is random. But soon, or not soon, but after a number of iterations, they will converge on a. Yeah, this is what I just said. So this is the results of the simulations. At the beginning, everything is random. If the sender has two messages, they are either A or B, then you end up with a solution like this. I mean, a stable state, to fit in equilibrium in game theoretical terms. And whenever this thing, the nurse says A, the pointer, the receiver will point to this point. Whenever the, the receiver says, I'm sorry to say, sender says B, then the receiver will point to this point. And these points have the property that they minimize the average distance within the regions. So that's a mathematical property. They minimize the average because they're rewarded for being as close as possible. So if you point to the middle points here, that minimizes the average point of distances, you have, you get the maximal reward. That's the, that's the reason. So they have done commute, computer simulations showing that this is what you end up with. And this is actually they can share. Here, I'm getting back to this now. They're rewarded for this similarity. And I show that there is a Nash equilibrium, missus became a theoretical term, that is the Voronoi tessellation. You end up with a curve Voronoi tessellation, all the of the color space in this communication, if you have a finite number of, of signals. Now, this is dependent on the notion of similarity. You add your rewarded for how close you come to, to the points. So that's the way in which, in which, and the geometry comes in through the thing here. And the fixed points, then, I mean, these points can be seen as the prototypes. The dew points in that are the central points here, because if nature selects this point, then, then the descender will say A, I mean, corresponding to the red region here. And then the, the pointer will point back to that fixed point. So the prototypes turn out to be fixed points in this, in this communication here. So that's, that's their model. Now, there are a couple of assumptions here. First of all, that they all have the same space. And that's not always the case. I mean, I may have one space, you may have another one. How can we make sure that we can find a shared meaning here? So I see you, this is somehow coordinating the meaning of words. That's one thing to notice is that there is no unique solution here. Any rotation of a solution will also be a solution. So there is no unique outcome of it. You can rotate today, the prototypes. But if you, if you interact, if you communicate a large number of times, you will agree on where are the fixed points, where are the prototypes. And that's, that's the, that's becomes then the meaning of the message is A, B, and C in this artificial example here. What Larson and I did was to generalize this example. So I don't want to spend time on this because it's a bit of mathematics. But now I, we right, we don't assume that we have the same space. They can have different spaces. It doesn't have to be the same. And we only assume that these spaces will come from convex and compact. Don't bother if you know the math, it's okay. If you don't, it doesn't matter very much. The product space will also be compact in convex. You have this representation interpretation function. That means going from one expression to the minds of the other. And then going back again. So it's officially a mapping from C to C. I mean, the product space. We assume that the mapping, this kind of mapping is continuous. And this assumption of continuity means that if two positions in the space are close enough, that means well, they are similar enough. But then they should also be given the code by the same name. So this is a very strong and natural assumption of worse things that are similar in some kind of space are called by the same word, fall under the same concept. That's an assumption that we formulate as continuity. I mean, that's what it boils down to in mathematical terms. So this is a way of of saying that language preserves these similarity relations by sorting. I mean, a word quite being similar things together. That's the meaning of of continuity here. And, and then we use a, well, this fixed point is the definition. Then we use a famous theorem by Brouwer, saying that every continuous map has at least one fixed point. This means that if we have satisfy these conditions that I just gave you, then, then there will be, there exists a meeting of minds. Now, the interpretation of this is that if individual meanings are well-shaped, that means convex and compact, then, and if language is not a plastic enough to preserve the spatial structure of concepts, that means similar things are giving us the same, fall under the same concepts. That will exist a meeting of mind. I mean, this is what there are six points in the theorem say. We can solve this problem of coordinating our, our minds. This result doesn't say anything about how we do it. It just shows that if we have these kind of structures, convex and compact, and so on, then there exists a solution. We can find it. We can find it. We can agree on a solution. Yeah, then of course, there is a long history on how we find a fixed point. And we come into a language, we were born into a society where are already language exists. But language is flexible, meanings change slowly over time, and so on. What language is doing is is preserving neighborhoods. I mean, I have my interpretation. I can choose between a finite number of words. And we have to map it on to you or your space. But it will preserve neighborhoods. So if points are similar here, they will be mapped to similar points over here. That's that's what meant by continuity. So it continuous function mapping a meaning space is compatible with that we only have a finite number at this great number of signals. And that's how language works. We have a, we don't have a continuous set of expressions. We have finite, finite number of words, even if there are quite many. Of course, this process is not perfect. I mean, here's the story of the tourist coming and asking the police for the way to the museum. And this pretty starts saying that walk to the next red light, and then through the traffic circle, turn right, turn left at the next traffic light, blah, blah, cross the railway, you get this. And then you have to translate it back into a spatial representation. And this doesn't work. I mean, this mapping is not perfect. But we still can work by it. We can make a croc summations of it. So to sum up this, I've given you an, oh, I should, yeah, okay, let me do it. So I've given you a model of how we can share meanings based on this kind of communication. And where we are rewarded for solving dues, so to speak, having the same meaning of a word concept. So they, the meanings emerge through the interaction between the members of a linguistic community. Meanings of our language is not giving by God or by anybody else. I mean, it's, it's, it's a kind of emergence phenomenon that results from a lot of communication between people. And language is a game where we can fail or succeed and so on. Of course, we can lie as well, which is another part of game theory. Well, I don't want to get into semantics is the fixed points for the game. That's what I talked about. Now, we had the question earlier whether whether this semantics is independent of reality. The concepts or mental constructs, they are generated by by communication. But reality comes in by where to tell whether you're succeed in your coordination or whether you fake that. So to give you a simplistic example, assume that we are in a bad telephone line. We agree, we need to agree, it's very important meeting. So we agree that we meet in the, in the Student Union in Cambridge next Tuesday. And then the telephone line breaks down. Now, if you go to Cambridge, England, and I go to Cambridge, Massachusetts, and you go there Tuesday, five days from now, and you go to choose state the following week, I mean, there is an next week, maybe two, maybe we totally fail in coordinating our actions. I mean, we use the word Cambridge, the next weekend, into two different ways. So then we have to adjust. We have to negotiate by Cambridge, we mean Cambridge, England, and nothing else, and so on. So this is where reality hits back. Where and when communication fails, we have to re and negotiate and readjust our courses. We have to find a fixed point that we agree on. And then the, that we agree is shown by that we succeed in coordination. I hope that you hear that I'm not using the word truth anywhere here. I mean, you can't hear that I'm not using it. But anyway, I want to emphasize I'm not. Yeah, and this is a pragmatic theory. I get the meaning via the successes and failures in interactions. And the successes and failures is where the world gets into the determination of the order of the meanings. Yeah, so this is a good place for me to stop for questions. Yeah, go ahead. Yeah, yeah. Not very much. I mean, this the colorblind example is exactly Putnam's example of B Jenelle. Because problem is, it's not colorblind, but it's three blind. So he can't distinguish between beaches and ends. But he knows that there are these words. And colorblind people knows that there are words like green and red and so on. That can learn by by using these correlations between domains to use color words fairly accurately. I mean, that can distinguish between them. And the contest English between the green and a red apple. But there might be other aspects of the apple that it correlates with these color words. So colorblind people can actually learn to use color words by exploiting the correlations with other other domains. That would be my answer to your question. Yeah, yeah, yeah. Sure. Yeah, no. Penguin's face is the same as bird face. That there is a number of features that all the bird space thing space has many other domains that bird space don't have. I mean, so it's a question of what domains you include in the space you are talking about. That there will be. So penguin spaces, penguin is a resub region of of birthday. Sir, it's out in the corner somewhere because in in the prototype, you die, fly, and I sing, and I build nests. But about the penguins don't do that. Yep. Yeah, I, I'll give you this example in, in a little while. When you're perfectly right, I focus on on perceptual domains because we know something about the structure of color space. We know, we know how size space and temperature. I mean, we know these perceptual properties. When it comes to more abstract things, we don't know very much. But you mentioned kinship, didn't you? Yeah. And a kinship is a good example. I'll actually give you a, give you a kinship space in something when I don't know when, but it will come partially. But again, I, I think I will answer also answer your question when as I go on. Yep. Yeah, yeah. Picking and Garrett worked with what I call the fast process. I mean, how you hear him. And they are basically doing this, this building up dialogue process. What's how you do the alignment there? I mean, they're, they're giving a model of Herbert Clark's ground and building up a common ground. And they have a bit more precision that he has in the model. Now, that process is different from this slow process of coordinating a fixed point of meaning, which takes a longer time, which builds on on a society with a lot of communication way and so on. But even, even in, in a, the first purpose, you may have succeeded successes and failures. I mean, I may talk about, I used to pronoun he, and you, you forgot them, and you don't understand what I'm referring to. And then they would say that that's a breaker, you, you give me some feedback. I have to make specify who I'm referring to and so on. But I mean, basically, they're doing what I call the false process. I'm not doing semantics, they're doing the pragmatic process of alignment during dialogue. Yeah, so it's a property of the gossip short-stay. So my question is that you can, you can use builder day. It doesn't matter very much where, where you start. So yeah, yeah, you can't define between this in terms of convexity. There are here, you can do that. But basically similarity, well, well, similarity is not between us. But you can, you can say that one color is between another one. And will people make that kind of between calibers between calorie and see, and people make that kind of judgment, sir, size or whatever here. Okay, that's okay. One more. Okay. Yeah, no, I'm being a bit sloppy, being a bit sloppy here. A domain is a specific thing like a color or a shape or size or whatever. And the space is a product of domains. So I can have, when you talk about objects, the, the bird space is a product of several domains. And so on. Each domain has the number of dimensions. Kelo space has three dimensions. Shape space, I don't know how many dimensions it has. Dimensions. Mm, and so on. So for me, I use the term space a little bit sloppily here. I agree to that. But basically, it's a product of domains. That would be my more formal definition. But I, I agree, I use space too often, I guess. Now I get into, I have 15 more minutes, I suppose, to start on the major topics on my, or my talk. I mean, this what I've said up to now is the kind of preparation. I've set the foundation for what I mean by semantic theory. I answered most of the six questions is gave at the beginning. Now we get into this problem of explaining why we have word classes and what are their semantic contents. So why do we have word classes? So these are some examples of what you learn about world classes in school. There are more, lots of them. And there are different ways of defining them. And actually, there is no universal classification of word classes. The word classes we learned about school work best for Indo-European languages. They derived from Sanskrit. Sanskrit scholars and then they've been modified by Latin scholars. And then we've taken over these categories in our. So if you try to apply this in the European world classes to other other languages, it may not fit very well. And there you have this example, click on on categories. I mean, nouns in in Korea, that didn't fit. So your, your intuition. So I mean, there are problems. But I, I don't want to get in time. I'm not a comparative linguist. I will assume that we have, we worked with these these were classes that we get from Indo-European languages. And, and even within the, we cover up things in different ways. That means some languages use more nouns and others more verbs. And verbs in different ways. I'll get in, in that. And as I said at the beginning, when you learn, take linguistic courses, the, the world classes are defined, defined syntactically. So nouns or things that can have plurals and, yeah, verbs define, I don't know how, what is the syntactic definition of an an adjective? Is a noun modifier of a noun phrase? I don't know what. But they are the word clause is not defined by their their syntactic properties. When you learn about world clause in, in school, I mean, in particular, if you go to primary school, you learn that nouns are about things, adjectives are about properties, verbs are about actions, and so on. You get this kind of semantics modeling or description of all of the world classes. Now, I want to get back to that. I think there is a lot of sense in doing doing nothing. So this is my aim in this part of the talk, to give a cognitive and to some extent communicative motivation for why we have these work losses. Now I get back a little bit of repetition here. What I mean by an object category, and I already said that there is a foreign object category like apple or horse or chair. There is a set of relevant domains. And as I explained, this set of the main specs may be expanded as you learn more about the concept. And, ya, set the conversation radians. I already talked about that. And some of them are, you have different weights of the domains depending on the context. To take the English word row and caviar, then though they denote exactly the same things, namely fish eggs. So when do you use the term row? Well, that's in the biological context, when you talk about the, the reproduction of all of the fission and so on. And you use the word caviar if you talk about food. When row turns into food. So it's a different context. But the extension, do the things in the world are exactly the exactly the same. Okay, that's, but that depends on, on there are sailors waits for the domains. We talked a little bit about that. And I already said that. So, okay, this was made, basically repetition of, or what I said earlier here. I didn't talk very much about porthole relations. But that's also included in, in the definition. I have, I don't have a very good description of how to model part-whole relations in, in conceptual spaces. I have made some attempts, but that to some extent still a, an unsolved problem. How to describe that dogs have four legs and stuff like that. Now, the reason I repeat this is that nouns, not all nouns, but the nouns that kids learn first are based on object categories. Kids learn the first notes that they learn or are about objects, object categories. So I, I want to use that as the semantic basis for nouns. I don't say that this is all that is included in now. So I will, I will get back to that in, in a few minutes. So they are information with one simple now. One question is, of course, what domains are important for a category like Dai, like dog? I mean, the shape of a dog is quite, quite central. Maybe the sound of a dog, I don't know, where the smell of a dog is so important. The, the temperature of a dog is not important in categories. I see categorizing dog. And maybe color is a little bit important. So I mean, when we do with, there are certain domains that are more essential than others. I talked a little bit about that already. But we can have, we can look at what's called definition of generics. I mean, the dog has four legs. It's part of the meaning, so to speak. If the cup has the color. But if you look at an idea, now we get into an abstract concept here. To say that an idea has a color doesn't work because idea is a concept, is a noun that that doesn't have that domain, doesn't include the color domain as part of its, of its meaning. So different downs have are associated with different domains. So that's, that's a first lesson to learn here. And they're more or less salient. Or I don't want to use essential here because there is a philosophical tradition of essentialism that a dog essentially has four legs. But I know many dogs without four legs. So it doesn't, that doesn't really work. Then we can also look at individual objects. A single, a single object. And a single object has can be described as a point in space. It has a particular size, length, and width. It has a particular weight. It has a particular temperature. It has to be, a lot of, lots of properties. So if you have a very rich conceptual space, including all the domains you want to talk about, and objects would be a single point in the space. You specify all the properties. And mathematically, a, an object is did generate the region. I mean, it's, it's a radio with only one point. You can think of it an answer by by automaticity. It is convex. The important thing here is that the, the properties are always consistent. You don't have an object that is both red and green. You don't have an object that is both hot and cold. And, and so on. They are there. That's the point. You have some kind of consistent combination of, of properties. If you go to traditional analytic philosophy, then you have to introduce what is called meaning postulates, saying that no green things are not red, and red things are not green. You have to have these kinds of of preposterous to step to make sure that you don't get conflicts between the, between the different properties. And many points represent merely possible objects. We can come from, we can combine properties in many different ways and create objects that don't exist in the real world. And then already mentioned, mentioned unicorns. We can, we can, we can have shape space. And in a certain part of shape space, there are unicorns. In other other parts of shape space, there are sinks. And I don't know what. I mean, all those fantasy, can't arson, and other fantasy animals. They are possible because they are possible shapes according to shape space, or and other other properties. I don't think that the Cantor is a very good biologically because having both four legs and two arms would make you an insect. But that's not, not well, it's a biological problem. Often getting a thing to work. But anyway, and this, I mean, this is a very simple model of friction allottee. We can talk about objects that have properties that don't exist in the world. But if the properties, if the properties of consistent, they are possible objects. Yeah, then physical objects are special. They are supposed to be spatial, temporal, continuous. And that means that this bottle is only at one place in, in thousands of seconds from here on. It's not in New York at the same time. Maybe it can't move that quickly. And so on. There is a kind of spatial temporal continuity. Our minds. Now, we talk a little bit of psychology. Her child psychology file works according to what's called object permanence. That is, if I hide, if I do like this, you still think that the bottle exists because there is a spatial temporal continuity. And you are not surprised if it comes back again because in your mind, you have object permanence. We are not born with this. Children have to develop the object permanence. But this is, this is something I, I could model this because another physical object has a location. And I can follow the trajectory of all the objects in, in space, in the product space of space and time. And, and then the, the object permanence, then means that this predictor is a continuous path. That's what it means. So I can give some kind of modeling in terms of conceptual spaces. Now, I already said that when I talked about nouns, but now the basic semantics of nouns and names is their communicative function is to identify a referent. And Michele talked about these communication games in robots where you have to identify the yellow triangular and, and so on. That's the, the objects. What are these games called? I mean, the naming games, or naming games? Yeah, I mean, we do that. I mean, give me the blue bottle. I mean, this, we do that all the time. We are used mountain. And when adjectives, I get to that, as identifying her reference. And all the name gave me, I don't have a good name. Well, I could say, Lucas, come here. I mean, I use Lucas to identify an individual. They identify a name here. And nouns refer to object categories. Already said that. Names refer to objects to singular and singular. But still, I mean, known the names function dramatically quite similarly. And they are, they have lots of, lots of similarities. So names, I would say, as as the generate radians, one single point in. Now, nouns don't identify unique reference. Even if I say, give me the bottle, you wouldn't know which bottle I'm, I'm a meaning here. I mean, if I want the left one or the right one, the one with the dark blue or the
Light blue cap. You wouldn't know if I just say "the bottle" here. So nouns are not perfect as communication devices. If I had called this "this" and this one "atom" and this one "Bob," I could have said, "Give me atom," and then you would have known if you had given them given them names. I could do that. So why doesn't everything have a name? Then we will solve the referentiality problem. Now, well, the obvious answer is that our minds wouldn't, our memories wouldn't.
So, solve this problem. Nouns are cognitively economical. I can use a general term like "bottle" to identify a small subgroup. I could, and by pointing, I can add information. I mean, pointing is like having an adjective on top of it. Now, so cognitively economical. And I gave you this story of prototypes. I mean, prototypes give you a way of, sir, dividing the world into a small number, fairly small number of categories or radians. And that will help you to identify what I mean when I say the word "bottle" or "gel" or whatever. So that's the point of of having nouns. I mean, we we have nouns because they gave us help. They're all flawed. Our memories, instead of having names for everything, nouns will make it easier for us to remember how to use different words.
Now, I get into this. This will be my last topic here. Into how we can use the idea of domains to give subclasses of of nouns. And and there are actually quite, mminton. I mean, it hasn't been studied very much. And I I can do a little bit of work here. So if you talk about the place, about the Austin area, core, or the main square, or whatever, they only require a space domain. I don't need anything but the location to identify a space place. I can give it more more dimensions. I can say that that it's it's a big place. I can say it's a nice place, or it's whatever, it's dangerous. I can add more more them. But basically, places only rely on the space domain.
Mass nouns. What distinguishes mass nouns from count nouns? Masses don't have shapes. I haven't seen this distinction in in the literature, but it's a very simple way of identifying what is a mass noun. It's something that doesn't have to have a shape.
Concrete nouns. They require object category domains. The noble category names are sizes, shapes, weights, temperatures, or and all these, all these domains that are associated with physical objects. This is what I talked about through the perceptive stuff we talked about earlier. And one thing that characterizes abstract nouns is that they're not have a location. I mean, call objects, concrete nouns, they have locations. Things have locations in space. Abstract areas don't have locations. They don't have any values on on on the space. Like, okay, I can say that this idea is in is in my head, but that's what aliens require the force domain. They gence are supposed to act and axis, or it means that you could exert some kind of force that I will get taxed to that when I get to verbs. An intentional agent has to have goals. You have to stop, have to read some representation of goldeneyes. I haven't talked about to go to me, but I can point to missions talk here when you talked about moving from one space to another. It's a representation of where you want the thing to be located, or what what properties you want to exchange. Everything you can represent your domains.
So if I sum this up now, I have an ugly picture. And this is a picture I'm working on. And I would need some help in doing this a bit better. But basically, what I do, I thought nouns into into different different types. Their place nouns, concrete nouns, nouns that's like the ones I talked about. And then we have different domain senses, space domain, or big categories domains that I talked about, size, shape, and so on, material, whether it's going to water, shape, space, for space of motion, space, go space, and maybe other other mental spaces. And then we can see that different types of nouns require different domains. So a place noun needs plus, plus means it's more or less in essential, and plus means that it often occurs. Question mark means that it's optional, and minus means that it's impossible. So that's the science here. So place needs space, location, can have some other properties. Concrete, yeah, you can talk about where it's located, but it needs these properties. Mass noun forbids, forbids shape here, that's the important distinction here. Abstract nouns don't have these properties. I don't know whether abstract nouns have shapes. I mean, who that these are optional. I think agency needs to force the main, intentional needs to go domain. So what I'm doing here by looking at what domains are the central ones for different types of new things, I get the classification of nouns.
And now down here are a list of adjectives that go with the different domains. So there are space magic themes there, or there are orbits category domains, and so on. And the point here is that given this this sorting of adjectives, I can use the minus signs to make predictions about impossible combinations of adjectives and an announcer. So to give you examples here, groundwater doesn't work because water is a mass noun, and mass nouns don't have shape. You can't talk about groundwater. You can't talk about happy gold because happy is an intentional thing, and gold that doesn't have any values on the emotional domains. You can't talk about the strong garden. A garden, the place, is the place, its context, earth, any force. You can talk about red happiness because happiness don't have these properties. I mean, of course, there are metaphorical uses of this. I mean, but basically, given this categorization of knowledge in terms of what domains that allow, what the domains are required, and what the domains that prohibit, I can make empirical predictions about what adjectives, nouns, combinations you will not find in language itself.
One. But this is, I mean, as I said, this is just a very early attempt to to do a classification of. I mean, this probably needs a lot more work in Northmoor, a lot more specification of what's included in in these classes, but it's a first attempt. And that's that's late working on involved in. I haven't really finished it. Sorry. So I haven't gone the wrong direction.
Some languages like Japanese have these noun classifiers. So certain, certain, you have to have certain endings here. So you have things that mark cylindrical things, flat things. These are shaft-shaped classifiers. You have you have these marks, living things, and so on. There are different suffixes that are used to to tell about the noun class here. And my question, I mean, I don't know enough about these languages to answer it myself, is whether you can do a similar story about these noun classifiers in terms of what are the what are the domains that are involved in these noun classifiers? That's a kind of hypothesis for my points of view that we can use the idea of domains to analyze these these noun classifiers. But I give that as a as a task to the other to the linguists in the in in the room here. So there, that thing. Okay, I'll stop here because now I'm finished with with with nouns. And tomorrow we'll continue with the other other word clauses.