Current location - Training Enrollment Network - Mathematics courses - What is the philosophical content of the law of quantitative change and qualitative change?
What is the philosophical content of the law of quantitative change and qualitative change?
The concepts of quality, quantity and degree have two levels. To understand the laws of quantitative change and qualitative change, we need to accurately grasp the meanings of these three concepts. We know that quality and existence are the same concept, so its basic stipulation is existence. The objective existence in reality, no matter how different from each other, the first qualitative stipulation is existence. This is the same feature that everything has. As a kind of existence, it has the characteristics of directness. Because things themselves are constantly developing and changing, there is a unity of opposites between what is and what is not. From being to nothing is the basic form of qualitative change, and it is the expression of the complete process of concrete things' movement. Therefore, when we discuss the characteristics of the law of quantitative change and qualitative change, the whole process of change begins with existence and ends with non-existence. From existence to non-existence, the whole process of change will be regarded as the boundary contained in the laws of quantitative change and qualitative change. In philosophy, existence is a direct stipulation, and its characteristic is "one" or oneness. However, in addition to embodying the basic characteristics of existence, there are also various provisions for specific things. For example, a yellow banana apple has various attributes, such as color, shape, taste, weight, moisture and so on. These different regulations are also a qualitative reflection. These concrete qualities are completely different from existence. Existence is "one", stipulation is "many", and it is the unity of diversity. These laws need to be grasped through analysis. Therefore, the concrete quality, that is, the epistemological characteristics of various provisions, is indirect, while the abstract quality, that is, existence, is direct, so we can intuitively grasp the existence of things. The characteristics of things need to be analyzed to grasp. In this way, there are two levels of qualitative characteristics, which are manifested in two different forms: existence and stipulation. Existence is abstract, and stipulation is concrete. As an abstract quality, it is characterized by directness, while as a concrete quality, it is characterized by indirection. We draw the characteristics of quality through logical pictures, as follows: ┌ External form is existence, characteristics are direct, single nature ┤ Internal form is prescriptive, characteristics are indirect, diversity is philosophical, and quantity is the manifestation and existence state of quality. Quantity in philosophy and quantity in mathematics are the unity of opposites. The identity of the two is that quantity is the existence form of quality. The opposite quantity in mathematics is a purely abstract quantity, a prescriptive quantity without considering quality, or a purely abstract quantity. The quantity and quality of philosophy are inseparable, and quality is integrated, which constitutes the basis of philosophical materialism. Everything itself is the unity of quality. Without quality, there is no quantity, and there is no infinite quality. Quality and quantity always coexist. Mathematics is characterized by the study of pure quantitative relations and spatial forms. Therefore, the quality and quantity are completely separated, and the pure quantity relationship is grasped after the quality is abstracted. Therefore, mathematical quantity is a pure quantity without quality, and philosophical quantity is a quantity containing quality stipulation. This is the first level of difference. The second level difference lies in the interior of quality. Because the arrangement and structure of elements are different, they will form different qualities. Therefore, qualitatively speaking, the differences in arrangement and structure are also the contents of philosophical measurement tools. Mathematical quantities have no such meaning. Grasping the arrangement form and structure from the inside of quality is a remarkable feature of philosophical measurement tools. Philosophy is a science that studies the relationship between different qualities, while mathematics is a science that studies the relationship between different quantities. The relationship between philosophy and mathematics is unity of opposites, and their identity is manifested in the fact that they are both general sciences, and the degree of abstraction has reached the extreme height. Their opposition lies in that mathematics analyzes problems from the perspective of pure quantity, while philosophy grasps the relationship between quality in the unity of opposites between quantity and quality. Therefore, in the stipulation of quantity, philosophy determines the connotation of quantity from the perspective of quality, and defines the concept of quantity according to the characteristics of quality. In mathematics, there is only the concept of quantity completely separated from quality. In philosophy, this separated quantitative change, which has nothing to do with qualitative change, is also the object of concern, but it is not the focus of philosophical theory. Because philosophy pays attention to quantity from a qualitative point of view, this homogeneous and unrelated philosophical theory of quantitative relationship is usually ignored when it does not involve qualitative change, and only when its change causes qualitative change will it pay attention to such quantitative problems. Because this quantitative relationship, which is divorced from quality, stays outside things and belongs to the object of intuitive intelligence level in epistemology, rationality advances to indirectness. Grasp the unity of opposites between quality and quantity from the inside of things themselves. For a specific thing, because there is only one quantity, there is no external quantity that is out of quality at this time. Therefore, its quantity is only a stipulation closely related to quality, that is, the existing form of quality, including the shape of things themselves, such as the size and shape of yellow bananas and apples. These provisions are the connotation of the concept of quantity in philosophy. It can be seen that philosophical quantity is a concept defined from the thing itself, not a pure quantitative concept. A thing completely eliminates the external scalar that has nothing to do with quality. Starting from the thing itself, grasping the unity of opposites between quality and quantity is the basic feature of philosophy. At this point, the pure quantity separated from quality no longer exists, and the rest is the regulation of quantity closely related to quality. Philosophical quantity can only grasp the existence form of quality. Because things are constantly changing, the existing form of quality is also constantly changing. This change in the form of existence is also a concrete manifestation of the stipulation of quantity. In a word, the existing form of quality is not fixed, but constantly changing. There is constancy in change, and this constancy is the form of existence. No matter how the form changes, it is still a qualitative form of existence. The existing form of mass is the size and shape of an object. There are not many quantitative concepts here, because there is only one. Therefore, how much belongs to mathematical quantity, and the size belongs to philosophical quantity. When a thing becomes bigger and smaller, it is a change of form, so this change belongs to the stipulation of quantity. Size belongs to the existing form of quality. Just like a baby growing up, this change in size is a feature of quantitative change. From the external expression of quality, we define the connotation of quantity by size and shape. From the internal analysis of mass, we find that different elements, different arrangement forms and molecular structures will also produce different masses. Therefore, this structural form also belongs to the stipulation of quantity. In this way, the concept of quantity in philosophy has two levels of stipulation: internal and external. The internal expression is the structural form, and the external expression is the size of the form. They are represented by logical diagrams as follows: ┌ Exterior is the size of form, which is characterized by directness; ┤ └ Interior is the quantity of phenomenon form, which is characterized by indirectness and is the unity of quantity and quality of essential form, which is the basis of materialism. From the very beginning, Hegel's logic deviated from the unified materialistic foundation of quality, and thus put forward the movement of "from quality to quantity, from quantity to quality", which is the concrete expression of Hegel's idealism on the link of existence. In the theory of scientific dialectics, this movement form of "from quality to quantity, from quantity to quality" does not exist, because this movement form is based on the idealism of quality separation, and everything is integrated with quality. Therefore, there is neither movement from quality to quantity nor movement from quantity to quality. Starting from existence, as long as we adhere to the materialistic principle of qualitative unity, people will find that the change of things always starts from quantitative change and ends with qualitative change. Therefore, the law of change embodies the characteristics of quantitative change and qualitative change, which is also the fundamental reason why we call the law of change quantitative change and qualitative change. From the beginning of quantitative change to the end of qualitative change, quantitative change causes qualitative change, which is the whole connotation of the law of quantitative change and qualitative change. Quality is existence, stipulation, and quantity is the form of existence. As a form of existence, its relationship with quality is unity of opposites, not indifference. With the change of existing form, when it reaches a certain limit, it will produce qualitative change. The joint point of qualitative change is called degree in philosophy As for the concept of degree, the concepts of homogeneity and quantity also have two levels, namely, orderly change and disorderly change. It is a fixed joint point for orderly change. For disorderly change, it is the limit point of change. Represented by a logical diagram, it is like this: ┌ orderly change, manifested as joint points, characterized by certainty or fixity; Direct ┤ └ disorderly change, manifested as the limit point, characterized by variability and inadaptability; Indirectly, people usually pay more attention to the orderly change of joint points because it is intuitive and easy to master. The limit point of disorderly change is often ignored. We have grasped this point accurately through the philosophical proof of "1+ 1". The change of prime number belongs to disorderly change, and there is no law to follow. However, an even number is the sum of two prime numbers. Although the decomposition form is constantly changing, it remains unchanged in the change, which is manifested in that any big even number can be decomposed into the sum of two prime numbers. For any big even number, under what circumstances can we grasp the form of the sum of two prime numbers it has? We know from the dialectical formula that this disorderly change is characterized by the extreme point of motion. For any big even number, the extreme points that can be decomposed into the sum of two prime numbers are all in half of the even number, that is, half. As long as it is within this limit, any big even number can be decomposed into the sum of two prime numbers. Only in this way can we grasp the boundary of disorderly change, which is different from orderly change. This limit is expressed in the form of limit point. For different even numbers, it will always deviate from this limit point more or less. But as long as it is within this limit point, you can find a form in which a big even number is decomposed into the sum of two prime numbers. From this point of view, the limit point stipulates the limit and final limit of a large even number decomposed into the sum of two prime numbers, rather than the qualitative change as long as it reaches this joint point like the orderly change of joint points. The limit point defines the end point of change, not the joint point of qualitative change. In other words, it is the stipulation of the end point of dialectical movement. As a dialectical movement process, there is always a beginning and an end for a specific even number. Although the specific even number is constantly changing, its dialectical movement process has an end limit, that is, the degree of disorderly change, and it shows its own boundary in the form of limit points.