Conceptual modeling: How Many? How Much?
The question of what a class of objects is, whether it exists in nature, has been discussed by me for two articles: Class of objects or objects of a class? , Features of conceptual domain modeling . I ask myself: is it possible, when describing a subject domain, to link an object and a class of objects by a semantic link?
The question is actually not idle. I often meet models that do not exactly convey the meaning of what has been said. For example, the owner of the car can say that his car contains a group of wheels. He could say that the car has wheels, and that would be a completely different statement. I am confused by the fact that in the models that I have seen, the difference between these two statements is not made. However, in practice there is a huge difference between them. Try to practice searching for this difference yourself.
Modeling with the help of UML adds fuel to the fire, because, firstly, it does not allow modeling of classes of objects ( Modeling functional and physical events in a logical paradigm ), and secondly, it does not allow us to link the class of objects and the object by semantics. Thus, in the domain modeling domain there is still unexplored empty space. I allow myself to frolic a bit on this field to show how fun it really is. Today I will talk about how my question is related to the concept of numeracy and incalculability of a noun.
Let me remind you that the nouns that are countable are those that denote individual objects that can be counted. An example of a countable noun is the term "spoon". This term refers to a subject that is, firstly, indivisible, and secondly, we can create a multitude of such objects.
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Uncountable nouns denote materials and other objects that are considered in language as a mass or set, and not as separate objects. An example would be such nouns: water, sugar, furniture. Note that in this definition there is a mention of the set. This is what we use now. I will try to prove that uncountable nouns describe sets, not objects. Thus, I will show that our consciousness with equal success operates with both objects and sets of objects.
Suppose we store sugar in the form of pieces of 1 kg. We cut a small piece from this piece and put it in tea. This method of use seems obvious to us, but it is not so obvious.
Suppose that in some countries, sugar is consumed in the form of a piece weighing 1 kg whole. In this world there is no knowledge that sugar is divided into parts. Therefore, a piece of sugar, split in half, is sent to the factory for rework, and do not use it. In such a world, the meter counts sugar only in chunks of 1 kg. The pieces are used as follows: they put it in a vat of water and water everyone with sweet water. Once a sugar worker stumbled and only half of the sugar fell into the vat. The worker was very afraid that he would be punished and pretended that he was not at work. However, what a surprise it was when in the morning it turned out that people were still drinking sweet water and were pleased with it! He told the master about this, and the two of them turned to a local scientist to help him figure out the task. The scientist was looking for an answer for a long time, until he realized that the matter was in the register. Sugar - a substance that can be considered in another way - by weight! Since then, the technology of production of sweet water greatly simplified.
Now it could be done at home literally in a cup. This means that a piece of 1 kg can now be viewed as a collection of pieces. Pieces can be obtained in an arbitrary way, as long as their mass is given. The accounting of sugar has turned from the accounting of pieces in pieces to the accounting of mass of pieces. After some time, people guessed that you can grind sugar for sale, and sell it in the form of piles, like sand. Thus, the accounting of sugar turned into accounting for many small pieces, which no one considered, but they took into account the total mass. That is, now many things were taken into account, not objects. At the end of grinding we get icing sugar. Sugar powder is also a lot of small parts. And we consider it as a set by weight. Further more interesting: the fluid is also a lot. And we consider it like sugar. It turns out that water is a lot.
Now a little linguistics. We say: give me nails, and we can also say: give me water. Nails - in the plural, and water - in the singular. Water in this context is set. Therefore, it is in the singular. We can come up with a name for a lot of nails: a bunch. And then we can say: give me a bunch. A pile is also a designation of a set.
Therefore, I conclude: if we are talking about uncountable nouns, then we are talking about sets. And if about countable, then about objects. But both methods of accounting are available to us equally.
You will say that a substance is a substance and a substance that can be divided. You're wrong. You can share everything, would be technology. For example, you can divide the spoon. But not the way you used to. And in a different way. Imagine that invented the technology of splitting the spoon into pieces. Let these parts occupy volume, can be used as spoons, but these spoons have the property of being less durable, because they are more loose. However, for some purposes it is permissible - to divide the spoon into two equal more loose parts, and for some - not. If we can divide the spoon into parts in an arbitrary proportion, we get an analogue of dividing the substance into parts. But now we were able to divide not a substance, but a functional object into a set of functional objects. So it all depends on the technology available to us and the method of accounting.
In how many ways can water be divided into parts, assuming that the smallest part of the water does not exist? In answering this question, we must commit violence to common sense: we must move on to the concept of a point and the concept of a continuum. There will be a huge amount of methods for dividing water into parts. The power of such a set of divisions is M3, or the continuum of the continuum. It seems to me that the complexity of this design led the Greeks to the version of the molecular structure of matter.
So, if we hear the question: How many ?, then we are talking about objects. If: How Much ?, then we are talking about classes of objects! Discuss?
The question is actually not idle. I often meet models that do not exactly convey the meaning of what has been said. For example, the owner of the car can say that his car contains a group of wheels. He could say that the car has wheels, and that would be a completely different statement. I am confused by the fact that in the models that I have seen, the difference between these two statements is not made. However, in practice there is a huge difference between them. Try to practice searching for this difference yourself.
Modeling with the help of UML adds fuel to the fire, because, firstly, it does not allow modeling of classes of objects ( Modeling functional and physical events in a logical paradigm ), and secondly, it does not allow us to link the class of objects and the object by semantics. Thus, in the domain modeling domain there is still unexplored empty space. I allow myself to frolic a bit on this field to show how fun it really is. Today I will talk about how my question is related to the concept of numeracy and incalculability of a noun.
Let me remind you that the nouns that are countable are those that denote individual objects that can be counted. An example of a countable noun is the term "spoon". This term refers to a subject that is, firstly, indivisible, and secondly, we can create a multitude of such objects.
')
Uncountable nouns denote materials and other objects that are considered in language as a mass or set, and not as separate objects. An example would be such nouns: water, sugar, furniture. Note that in this definition there is a mention of the set. This is what we use now. I will try to prove that uncountable nouns describe sets, not objects. Thus, I will show that our consciousness with equal success operates with both objects and sets of objects.
Suppose we store sugar in the form of pieces of 1 kg. We cut a small piece from this piece and put it in tea. This method of use seems obvious to us, but it is not so obvious.
Suppose that in some countries, sugar is consumed in the form of a piece weighing 1 kg whole. In this world there is no knowledge that sugar is divided into parts. Therefore, a piece of sugar, split in half, is sent to the factory for rework, and do not use it. In such a world, the meter counts sugar only in chunks of 1 kg. The pieces are used as follows: they put it in a vat of water and water everyone with sweet water. Once a sugar worker stumbled and only half of the sugar fell into the vat. The worker was very afraid that he would be punished and pretended that he was not at work. However, what a surprise it was when in the morning it turned out that people were still drinking sweet water and were pleased with it! He told the master about this, and the two of them turned to a local scientist to help him figure out the task. The scientist was looking for an answer for a long time, until he realized that the matter was in the register. Sugar - a substance that can be considered in another way - by weight! Since then, the technology of production of sweet water greatly simplified.
Now it could be done at home literally in a cup. This means that a piece of 1 kg can now be viewed as a collection of pieces. Pieces can be obtained in an arbitrary way, as long as their mass is given. The accounting of sugar has turned from the accounting of pieces in pieces to the accounting of mass of pieces. After some time, people guessed that you can grind sugar for sale, and sell it in the form of piles, like sand. Thus, the accounting of sugar turned into accounting for many small pieces, which no one considered, but they took into account the total mass. That is, now many things were taken into account, not objects. At the end of grinding we get icing sugar. Sugar powder is also a lot of small parts. And we consider it as a set by weight. Further more interesting: the fluid is also a lot. And we consider it like sugar. It turns out that water is a lot.
Now a little linguistics. We say: give me nails, and we can also say: give me water. Nails - in the plural, and water - in the singular. Water in this context is set. Therefore, it is in the singular. We can come up with a name for a lot of nails: a bunch. And then we can say: give me a bunch. A pile is also a designation of a set.
Therefore, I conclude: if we are talking about uncountable nouns, then we are talking about sets. And if about countable, then about objects. But both methods of accounting are available to us equally.
You will say that a substance is a substance and a substance that can be divided. You're wrong. You can share everything, would be technology. For example, you can divide the spoon. But not the way you used to. And in a different way. Imagine that invented the technology of splitting the spoon into pieces. Let these parts occupy volume, can be used as spoons, but these spoons have the property of being less durable, because they are more loose. However, for some purposes it is permissible - to divide the spoon into two equal more loose parts, and for some - not. If we can divide the spoon into parts in an arbitrary proportion, we get an analogue of dividing the substance into parts. But now we were able to divide not a substance, but a functional object into a set of functional objects. So it all depends on the technology available to us and the method of accounting.
In how many ways can water be divided into parts, assuming that the smallest part of the water does not exist? In answering this question, we must commit violence to common sense: we must move on to the concept of a point and the concept of a continuum. There will be a huge amount of methods for dividing water into parts. The power of such a set of divisions is M3, or the continuum of the continuum. It seems to me that the complexity of this design led the Greeks to the version of the molecular structure of matter.
So, if we hear the question: How many ?, then we are talking about objects. If: How Much ?, then we are talking about classes of objects! Discuss?
Source: https://habr.com/ru/post/257217/
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