What are space and time according to Kant. Space and time in German classical philosophy of the 18th–19th centuries

The most important part of the Critique of Pure Reason is the doctrine of space and time. In this section I propose to undertake a critical examination of this teaching.

It is not easy to give a clear explanation of Kant's theory of space and time because the theory itself is unclear. It is expounded both in the Critique of Pure Reason and in the Prolegomena. The presentation in the Prolegomena is more popular, but less complete than in the Critique. First, I will try to explain the theory as clearly as I can. Only after I have presented it will I try to criticize it.

Kant believes that the immediate objects of perception are caused partly by external things and partly by our own perceptual apparatus. Locke accustomed the world to the idea that secondary qualities - colors, sounds, smell, etc. - are subjective and do not belong to the object as it exists in itself. Kant, like Berkeley and Hume, although not quite in the same way, goes further and makes primary qualities also subjective. For the most part, Kant has no doubt that our sensations have causes, which he calls “things-in-themselves” or noumena. What appears to us in perception, which he calls a phenomenon, consists of two parts: what is caused by the object - this part he calls sensation, and what is caused by our subjective apparatus, which, as he says, organizes diversity in certain relationships. He calls this last part the form of the phenomenon. This part is not the sensation itself and, therefore, does not depend on the randomness of the environment, it is always the same, since it is always present in us, and it is a priori in the sense that it does not depend on experience. The pure form of sensibility is called “pure intuition” (Anschauung); There are two such forms, namely space and time: one for external sensations, the other for internal ones.

To prove that space and time are a priori forms, Kant puts forward two classes of arguments: one class of arguments is metaphysical, and the other is epistemological, or, as he calls them, transcendental. Arguments of the first class are derived directly from the nature of space and time, arguments of the second - indirectly, from the possibility of pure mathematics. Arguments regarding space are presented more fully than arguments regarding time because the latter are considered to be essentially the same as the former.

Regarding space, four metaphysical arguments are put forward:

1) Space is not an empirical concept abstracted from external experience, since space is presupposed when sensations are attributed to something external, and external experience is possible only through the representation of space.

2) Space is a necessary representation a priori, which underlies all external perceptions, since we cannot imagine that space should not exist, whereas we can imagine that nothing exists in space.

3) Space is not a discursive, or general, concept of the relations of things in general, since there is only one space and what we call “spaces” are parts of it, not examples.

4) Space is represented as an infinitely given quantity that contains within itself all parts of space. This relation is different from that which the concept has to its examples, and, therefore, space is not a concept, but Anschauung.

The transcendental argument regarding space is derived from geometry. Kant claims that Euclidean geometry is known a priori, although it is synthetic, that is, not derived from logic itself. Geometric proofs, he argues, depend on figures. We can see, for example, that if two straight lines intersect at right angles to each other are given, then only one straight line can be drawn through their point of intersection at right angles to both straight lines. This knowledge, as Kant believes, is not derived from experience. But my intuition can anticipate what will be found in the object only if it contains only the form of my sensibility, which predetermines in my subjectivity all actual impressions. Objects of sense must be subject to geometry, because geometry concerns our modes of perception, and therefore we cannot perceive in any other way. This explains why geometry, although synthetic, is a priori and apodictic.

The arguments regarding time are essentially the same, except that arithmetic replaces geometry, since counting requires time.

Let us now examine these arguments one by one. The first of the metaphysical arguments regarding space reads: “Space is not an empirical concept abstracted from external experience. In fact, the representation of space must already lie at the basis in order for certain sensations to be related to something outside of me (that is, to something - in a different place in space than where I am), and also so that I can imagine them as being outside (and next to each other, therefore, not only as different, but also as being in different places." As a result, external experience is the only one possible through the representation of space.

The phrase "outside of me (that is, in a different place than I myself am)" is difficult to understand. As a thing in itself, I am not located anywhere, and there is nothing spatially outside of me. My body can only be understood as a phenomenon. Thus, all that is really meant is expressed in the second part of the sentence, namely, that I perceive different objects as objects in different places. The image that may arise in one's mind is that of a cloakroom attendant hanging different coats on different hooks; the hooks must already exist, but the subjectivity of the wardrobe attendant arranges the coat.

There is here, as elsewhere in Kant's theory of the subjectivity of space and time, a difficulty which he seems never to have felt. What makes me arrange the objects of perception the way I do and not otherwise? Why, for example, do I always see people's eyes above their mouths and not below them? According to Kant, the eyes and mouth exist as things in themselves and cause my separate perceptions, but nothing in them corresponds to the spatial arrangement that exists in my perception. This is contradicted by the physical theory of colors. We do not believe that there are colors in matter in the sense that our perceptions have color, but we do believe that different colors correspond to different wavelengths. Since waves, however, involve space and time, they cannot be the causes of our perceptions for Kant. If, on the other hand, the space and time of our perceptions have copies in the world of matter, as physics suggests, then geometry applies to these copies and Kant's argument is false. Kant believed that the understanding organizes the raw material of sensations, but he never thought that it is necessary to say why the understanding organizes this material in this particular way and not otherwise.

With regard to time, this difficulty is even greater, since when considering time one has to take into account causality. I perceive lightning before I perceive thunder. A thing in itself A causes my perception of lightning, and another thing in itself B causes my perception of thunder, but A not before B, since time exists only in relations of perceptions. Why then do two timeless things A and B produce an effect at different times? This must be entirely arbitrary if Kant is right, and then there must be no relation between A and B corresponding to the fact that the perception caused by A is earlier than the perception caused by B.

The second metaphysical argument states that one can imagine that there is nothing in space, but one cannot imagine that there is no space. It seems to me that a serious argument cannot be based on what can and cannot be imagined. But I emphasize that I deny the possibility of representing empty space. You can imagine yourself looking at a dark cloudy sky, but then you are in space and you are imagining clouds that you cannot see. As Weininger pointed out, Kantian space is absolute, like Newtonian space, and not just a system of relations. But I don’t see how you can imagine absolutely empty space.

The third metaphysical argument reads: “Space is not a discursive, or, as they say, general, concept of the relations of things in general, but a purely visual representation. In fact, one can imagine only one single space, and if one speaks of many spaces, then by them we mean only parts of one and the same unified space, moreover, these parts cannot precede a single all-encompassing space as its constituent elements (from which its composition could be possible), but can only be thought of as being essentially unified in it. “The diversity in it, and, consequently, also the general concept of spaces in general, is based exclusively on restrictions.” From this Kant concludes that space is an a priori intuition.

The essence of this argument is the denial of multiplicity in space itself. What we call "spaces" are neither examples of the general concept of "space" nor parts of a whole. I do not know exactly what their logical status is, according to Kant, but, in any case, they logically follow space. For those who accept, as practically everyone does nowadays, a relativistic view of space, this argument falls away, since neither “space” nor “spaces” can be considered as substances.

The fourth metaphysical argument concerns mainly the proof that space is an intuition and not a concept. His premise is "space is imagined (or represented - vorgestellt) as an infinitely given quantity." This is the view of a person living in a flat area, like the area where Koenigsberg is located. I do not see how a dweller in the Alpine valleys could accept it. It is difficult to understand how something infinite can be “given.” I must consider it obvious that the part of space which is given is that which is filled with objects of perception, and that for other parts we have only the sense of the possibility of movement. And if it is permissible to use such a vulgar argument, then modern astronomers claim that space is not in fact infinite, but is rounded, like the surface of a ball.

The transcendental (or epistemological) argument, which is best established in the Prolegomena, is clearer than the metaphysical arguments, and also more clearly refutable. "Geometry", as we now know, is a name that combines two different scientific disciplines. On the one hand, there is pure geometry, which derives consequences from axioms without asking whether these axioms are true. It does not contain anything that does not follow from logic and is not “synthetic”, and does not need figures such as those used in geometry textbooks. On the other hand, there is geometry as a branch of physics, as it appears, for example, in the general theory of relativity - this is an empirical science in which axioms are derived from measurements and differ from the axioms of Euclidean geometry. Thus, there are two types of geometry: one is a priori, but not synthetic, the other is synthetic, but not a priori. This gets rid of the transcendental argument.

Let us now try to consider the questions that Kant poses when he considers space more generally. If we start from the view, which is accepted in physics as self-evident, that our perceptions have external causes which are (in a certain sense) material, then we are led to the conclusion that all real qualities in perceptions are different from qualities in their imperceptible causes, but that there is a certain structural similarity between the system of perceptions and the system of their causes. There is, for example, a correspondence between colors (as perceived) and waves of certain lengths (as inferred by physicists). Likewise, there must be a correspondence between space as an ingredient of perceptions and space as an ingredient in the system of imperceptible causes of perceptions. All this is based on the principle of “same cause, same effect,” with its opposite principle: “different effects, different causes.” Thus, for example, when visual representation A appears to the left of visual representation B, we will assume that there is some corresponding relation between cause A and cause B.

We have, according to this view, two spaces - one subjective and the other objective, one is known in experience, and the other is only inferred. But there is no difference in this respect between space and other aspects of perception, such as colors and sounds. All of them in their subjective forms are known empirically. All of them in their objective forms are derived through the principle of causality. There is no reason to consider our knowledge of space in any way different from our knowledge of color, and sound, and smell.

As regards time, the matter is different, for if we maintain faith in the imperceptible causes of perceptions, objective time must be identical with subjective time. If not, we are faced with the difficulties already discussed in connection with lightning and thunder. Or take this case: you hear a person speaking, you answer him, and he hears you. His speech and his perceptions of your answer, both as far as you touch them, are in the unperceived world. And in this world, the first comes before the last. Moreover, his speech precedes your perception of sound in the objective world of physics. Your perception of sound precedes your response in the subjective world of perception. And your answer precedes his perception of sound in the objective world of physics. It is clear that the relation "precedes" must be the same in all these statements. While there is therefore an important sense in which perceptual space is subjective, there is no sense in which perceptual time is subjective.

The above arguments assume, as Kant thought, that perceptions are caused by things in themselves, or, as we should say, by events in the world of physics. This assumption, however, is in no way logically necessary. If it is rejected, perceptions cease to be in any essential sense “subjective,” since there is nothing to oppose them.

The "thing in itself" was a very awkward element in Kant's philosophy, and it was rejected by his immediate successors, who accordingly fell into something very like solipsism. The contradictions in Kant's philosophy inevitably led to the fact that philosophers who were under his influence had to quickly develop either in an empiricist or in an absolutist direction. In fact, German philosophy developed in the latter direction until the period after Hegel's death.

Kant's immediate successor, Fichte (1762-1814), rejected "things in themselves" and carried subjectivism to a degree that seemed to border on madness. He believed that the Self is the only ultimate reality and that it exists because it affirms itself. But the Self, which has a subordinate reality, also exists only because the Self accepts it. Fichte is important not as a pure philosopher, but as the theoretical founder of German nationalism in his “Speeches to the German Nation” (1807-1808), in which he sought to inspire the Germans to resist Napoleon after the Battle of Jena. The self as a metaphysical concept was easily confused with Fichte's empirical; since I was a German, it followed that the Germans were superior to all other nations. “To have character and to be German,” says Fichte, “undoubtedly mean the same thing.” On this basis, he developed a whole philosophy of nationalist totalitarianism, which had a very great influence in Germany.

His immediate successor, Schelling (1775-1854), was more attractive, but no less subjectivist. He was closely associated with German romance. Philosophically he is insignificant, although he was famous in his time. An important result of the development of Kant's philosophy was the philosophy of Hegel.

Kant's theory of space and time

Parameter name	Meaning
Article topic:	Kant's theory of space and time
Rubric (thematic category)	Philosophy

The most important part of the Critique of Pure Reason is the doctrine of space and time. In this section I propose to undertake a critical examination of this teaching.

It is not easy to give a clear explanation of Kant's theory of space and time because the theory itself is unclear. It is presented both in the Critique of Pure Reason and in the Prolegomena. The presentation in the Prolegomena is more popular, but less complete than in the Critique. First, I will try to explain the theory as clearly as I can. Only after I have presented it will I try to criticize it.

Kant believes that the immediate objects of perception are caused partly by external things and partly by our own perceptual apparatus. Locke accustomed the world to the idea that secondary qualities - colors, sounds, smell, etc. - are subjective and do not belong to the object as it exists in itself. Kant, like Berkeley and Hume, although not quite in the same way, goes further and makes primary qualities also subjective. For the most part, Kant has no doubt that our sensations have causes, which he calls “things-in-themselves” or noumena. What appears to us in perception, which he calls a phenomenon, consists of two parts: that which is caused by the object - this part he calls sensation, and that which is caused by our subjective apparatus, which, as he says, organizes diversity into certain relationship. He calls this last part the form of the phenomenon. This part is not the sensation itself and, therefore, does not depend on the randomness of the environment, it is always the same, since it is always present in us, and it is a priori in the sense that it does not depend on experience. The pure form of sensibility is called “pure intuition” (Anschauung); There are two such forms, namely space and time, one for external sensations, the other for internal ones.

To prove that space and time are a priori forms, Kant puts forward two classes of arguments: one class of arguments is metaphysical, and the other is epistemological, or, as he calls them, transcendental. Arguments of the first class are derived directly from the nature of space and time, arguments of the second - indirectly, from the possibility of pure mathematics. Arguments regarding space are more fully stated than arguments regarding time because the latter are considered to be essentially the same as the former.

Regarding space, four metaphysical arguments are put forward:

1) Space is not an empirical concept abstracted from external experience, since space is presupposed when relating sensations to something external and external experience is possible only through the representation of space.

2) Space is a necessary representation a priori, which lies at the basis of all external perceptions, since we cannot imagine that space should not exist, whereas we can imagine that nothing exists in space.

3) Space is not a discursive, or general, concept of the relations of things in general, since there is only one space, and what we call "spaces" are parts of it, not examples.

Kant's theory of space and time - concept and types. Classification and features of the category "Kant's Theory of Space and Time" 2015, 2017-2018.

The most important part of the Critique of Pure Reason is the doctrine of space and time.

Kant believes that the immediate objects of perception are caused partly by external things and partly by our own perceptual apparatus. Locke accustomed the world to the idea that secondary qualities - colors, sounds, smell, etc. - are subjective and do not belong to the object, since it exists in itself. Kant, like Berkeley and Hume, although not quite in the same way, goes further and makes primary qualities also subjective. For the most part, Kant has no doubt that our sensations have causes, which he calls “things-in-themselves” or noumena. What appears to us in perception, which he calls a phenomenon, consists of two parts: what is caused by the object - this part he calls sensation, and what is caused by our subjective apparatus, which, as he says, organizes diversity into certain relationship. He calls this last part the form of the phenomenon. This part is not the sensation itself and, therefore, does not depend on the randomness of the environment, it is always the same, since it is always present in us, and it is a priori in the sense that it does not depend on experience. The pure form of sensibility is called “pure intuition” (Anschauung); there are two such forms, namely space and time: one for external sensations, the other for internal ones.

Regarding space, four metaphysical arguments are put forward:

2) Space is a necessary representation a priori, which underlies all external perceptions, since we cannot imagine that space should not exist, whereas we can imagine that nothing exists in space.

3) Space is not a discursive, or general, concept of the relations of things in general, since there is only one space and what we call “spaces” are parts of it, not examples.

4) Space is represented as an infinitely given quantity, which contains within itself all parts of space. This relation is different from that which the concept has to its examples, and, therefore, space is not a concept, but Anschauung.

The transcendental argument regarding space derives from geometry. Kant claims that Euclidean geometry is known a priori, although it is synthetic, that is, not derived from logic itself. Geometric proofs, he argues, depend on figures. We can see, for example, that if two straight lines intersecting at right angles to each other are given, then only a straight line can be drawn through their point of intersection at right angles to both straight lines. This knowledge, as Kant believes, is not derived from experience. But my intuition can anticipate what will be found in the object only if it contains only the form of my sensibility, which predetermines in my subjectivity all actual impressions. Objects of sense must be subject to geometry because geometry concerns our modes of perception, and therefore we cannot perceive in any other way. This explains why geometry, although synthetic, is a priori and apodictic.

The arguments regarding time are essentially the same, with the conclusion that arithmetic replaces geometry, since counting requires time.

Let us now examine these arguments one by one.

The first of the metaphysical arguments regarding space states: “Space is not an empirical concept abstracted from external experience. In fact, the representation of space must already lie at the basis in order for certain sensations to be related to something outside of me (that is, to something in a different place in space than where I am), and also in order for so that I can imagine them as being outside [and next to] each other, therefore, not only as different, but also as being in different places.” As a result, external experience is the only one possible through the representation of space.

The phrase “outside of me (that is, in a place other than where I am)” is difficult to understand. As a thing in itself, I am not located anywhere, and there is nothing spatially outside of me. My body can only be understood as a phenomenon. Thus, all that is really meant is expressed in the second part of the sentence, namely, that I perceive different objects as objects in different places. The image that may arise in someone's mind is that of a cloakroom attendant hanging different coats on different hooks; the hooks must already exist, but the subjectivity of the wardrobe attendant puts the coat in order.

There is here, as elsewhere in Kant's theory of the subjectivity of space and time, a difficulty that he seems never to have felt. What makes me arrange the objects of perception the way I do and not otherwise? Why, for example, do I always see people's eyes above their mouths and not below them? According to Kant, the eyes and mouth exist as things in themselves and cause my separate perceptions, but nothing in them corresponds to the spatial arrangement that exists in my perception. This is contradicted by the physical theory of colors. We do not believe that there are colors in matter in the sense that our perceptions have color, but we do believe that different colors correspond to different wavelengths. Since waves involve space and time, they cannot be the causes of our perceptions for Kant. If, on the other hand, the space and time of our perceptions have copies in the world of matter, as physics suggests, then geometry applies to these copies and Kant's argument is false. Kant believed that the understanding organizes the raw material of sensations, but he never thought that it is necessary to say why the understanding organizes this material in this particular way and not otherwise.

With regard to time, this difficulty is even greater, since when considering time one has to take into account causality. I perceive lightning before I perceive thunder. A thing in itself A causes my perception of lightning, and another thing in itself B causes my perception of thunder, but A not before B, since time exists only in relations of perception. Why then do two timeless things A and B produce an effect at different times? This must be entirely arbitrary if Kant is right, and then there must be no relation between A and B corresponding to the fact that the perception caused by A is earlier than the perception caused by B.

The third metaphysical argument states: “Space is not a discursive, or, as they say, general, concept of the relationships of things in general, but a purely visual representation. In fact, one can imagine only one single space, and if they talk about many spaces, then by them they mean only parts of the same single space, moreover, these parts cannot precede a single all-encompassing space as its constituent elements (from of which its addition would be possible), but can only be thought of as being in it. Space is essentially unified; the diversity in it, and, consequently, also the general concept of spaces in general, is based exclusively on limitations.” From this Kant concludes that space is an a priori intuition.

The fourth metaphysical argument concerns mainly the proof that space is an intuition and not a concept. His premise is “space is imagined (or represented - vorgestellt) as an infinitely given quantity.” This is the view of a person living in a flat area, like the area where Koenigsberg is located. I do not see how a dweller in the Alpine valleys could accept it. It is difficult to understand how something infinite can be “given.” I must consider it obvious that the part of space which is given is that which is filled with objects of perception, and that for other parts we have only the sense of the possibility of movement. And if it is permissible to use such a vulgar argument, then modern astronomers claim that space is not in fact infinite, but is rounded, like the surface of a ball.

The transcendental (or epistemological) argument, which is best established in the Prolegomena, is clearer than the metaphysical arguments and also more clearly refutable. "Geometry", as we now know, is a name that combines two different scientific disciplines. On the one hand, there is pure geometry, which derives consequences from axioms without asking whether these axioms are true. It contains nothing that does not follow from logic and is not “synthetic”, and does not need figures such as those used in geometry textbooks. On the other hand, there is geometry as a branch of physics, as it, for example, appears in the general theory of relativity - this is an empirical science in which axioms are derived from measurements and differ from the axioms of Euclidean geometry. Thus, there are two types of geometry: one is a priori, but not synthetic, the other is synthetic, but not a priori. This gets rid of the transcendental argument.

We have, according to this view, two spaces - one subjective and the other objective, one known in experience, and the other only inferred. But there is no difference in this respect between space and other aspects of perception, such as colors and sounds. All of them in their subjective forms are known empirically. All of them in their objective forms are derived through the principle of causality. There is no reason to consider our knowledge of space in any way different from our knowledge of color, and sound, and smell.

As regards time, the matter is different, for if we maintain faith in the imperceptible causes of perception, objective time must be identical with subjective time. If not, we are faced with the difficulties already discussed in connection with lightning and thunder. Or take this case: you hear a person speaking, you answer him, and he hears you. His speech and his perceptions of your answer, to the extent that you touch them, are in the unperceived world. And in this world, the first comes before the last. Moreover, his speech precedes your perception of sound in the objective world of physics. Your perception of sound precedes your response in the subjective world of perception. And your answer precedes his perception of sound in the objective world of physics. Clearly the relation "precedes" must be the same in all these statements. While there is therefore an important sense in which perceptual space is subjective, there is no sense in which perceptual time is subjective.

The above arguments assume, as Kant thought, that perceptions are caused by things in themselves, or, as we should say, by events in the world of physics. This assumption, however, is in no way logically necessary. If it is rejected, perceptions cease to be “subjective” in any significant sense, since there is nothing to oppose them.

The "thing in itself" was a very awkward element in Kant's philosophy, and it was rejected by his immediate successors, who accordingly fell into something very like solipsism. The contradictions in Kant's philosophy inevitably led to the fact that the philosophers who were under his influence had to quickly develop either in an empiricist or in an absolutist direction, in fact, in the latter direction, and German philosophy developed until the period after Hegel's death.

properties, he argues, depend on figures. We can see, for example, that if two straight lines intersect at right angles to each other are given, then only one straight line can be drawn through their point of intersection at right angles to both straight lines. This knowledge, as Kant believes, is not derived from experience. But my intuition can anticipate what will be found in the object only if it contains only the form of my sensibility, which predetermines in my subjectivity all actual impressions. Objects of sense must be subject to geometry, because geometry concerns our modes of perception, and therefore we cannot perceive in any other way. This explains why geometry, although synthetic, is a priori and apodictic.

The arguments regarding time are essentially the same, except that arithmetic replaces geometry, since counting requires time.

The transcendental (or epistemological) argument, which is best established in the Prolegomena, is clearer than the metaphysical arguments, and also more clearly refutable. "Geometry", as we now know, is a name that combines two different scientific disciplines. On the one hand, there is pure geometry, which derives consequences from axioms without asking whether these axioms are true. It does not contain anything that does not follow from logic and is not “synthetic”, and does not need figures such as those used in geometry textbooks. On the other hand, there is geometry as a branch of physics, as it, for example, appears in the general theory of relativity - this is an empirical science in which axioms are derived from measurements and differ from the axioms of Euclidean geometry. Thus, there are two types of geometry: one is a priori, but not synthetic, the other is synthetic, but not a priori. This gets rid of the transcendental argument.

As regards time, the matter is different, for if we retain faith in the imperceptible causes of perceptions, objective time must be identical with subjective time. If not, we are faced with the difficulties already discussed in connection with lightning and r

Syktyvkar State University

Department of Philosophy and Cultural Studies

Space and time in the theories of Kant and Newton

Executor:

Mazurova Anna

Department of Applied Computer Science in Economics

group 127

Syktyvkar 2012

Introduction

Biography of I. Kant

Kant's theory of space and time

Biography of I. Newton

Newton's theory of space and time

Conclusion

Literature

Introduction

More than 2,500 years have passed since the beginning of the understanding of time and space, however, interest in the problem and disputes between philosophers, physicists and representatives of other sciences around the definition of the nature of space and time have not decreased at all. Significant interest in the problem of space and time is natural and natural; the influence of these factors on all aspects of human activity cannot be overestimated. The concept of space-time is the most important and most mysterious property of Nature, or at least human nature. The idea of space-time suppresses our imagination. It is not without reason that the attempts of philosophers of antiquity, scholastics of the Middle Ages and modern scientists with knowledge of the sciences and experience of their history to understand the essence of time and space did not give unambiguous answers to the questions posed.

Dialectical materialism proceeds from the fact that “there is nothing in the world except moving matter, and moving matter cannot move except in space and time.” Space and time here act as the fundamental forms of existence of matter. Classical physics considered the space-time continuum as a universal arena for the dynamics of physical objects. In the last century, representatives of non-classical physics (particle physics, quantum physics, etc.) put forward new ideas about space and time, inextricably linking these categories with each other. A variety of concepts have emerged: according to some, there is nothing at all in the world except empty curved space, and physical objects are only manifestations of this space. Other concepts argue that space and time are inherent only to macroscopic objects. Along with the interpretation of time - space by the philosophy of physics, there are numerous theories of philosophers who adhere to idealistic views, for example, Henri Bergson argued that time can only be known by irrational intuition, and scientific concepts that represent time as having any direction incorrectly interpret reality.

Biography of I. Kant

KANT (Kant) Immanuel (April 22, 1724, Koenigsberg, now Kaliningrad - February 12, 1804, ibid.), German philosopher, founder of “criticism” and “German classical philosophy.”

He was born into the large family of Johann Georg Kant in Konigsberg, where he lived almost his entire life, without traveling more than one hundred and twenty kilometers outside the city. Kant was brought up in an environment where the ideas of Pietism, a radical renewalist movement in Lutheranism, had a special influence. After studying at the Pietist school, where he discovered excellent abilities for the Latin language, in which all four of his dissertations were subsequently written (Kant knew ancient Greek and French worse, and spoke almost no English), in 1740 Kant entered the Albertina University of Königsberg. Among Kant's university teachers, the Wolffian M. Knutzen especially stood out, introducing him to the achievements of modern science. Since 1747, due to financial circumstances, Kant has been working as a home teacher outside of Königsberg in the families of a pastor, a landowner and a count. In 1755, Kant returned to Konigsberg and, completing his studies at the university, defended his master's thesis “On Fire.” Then, within a year, he defended two more dissertations, which gave him the right to lecture as an associate professor and professor. However, Kant did not become a professor at this time and worked as an extraordinary (that is, receiving money only from listeners, and not from the staff) associate professor until 1770, when he was appointed to the post of ordinary professor of the department of logic and metaphysics at the University of Königsberg. During his teaching career, Kant lectured on a wide range of subjects, from mathematics to anthropology. In 1796 he stopped lecturing, and in 1801 he left the university. Kant's health gradually weakened, but he continued to work until 1803.

Kant's famous lifestyle and many of his habits, especially evident after he bought his own house in 1784. Every day, at five o'clock in the morning, Kant was woken up by his servant, retired soldier Martin Lampe, Kant got up, drank a couple of cups of tea and smoked a pipe, then began preparing for his lectures. Soon after the lectures it was time for lunch, which was usually attended by several guests. The dinner lasted several hours and was accompanied by conversations on a variety of topics, but not philosophical ones. After lunch, Kant took his now legendary daily walk around the city. In the evenings, Kant loved to look at the cathedral building, which was very clearly visible from the window of his room.

Kant always carefully monitored his health and developed an original system of hygiene regulations. He was not married, although he did not have any special prejudices against the female half of humanity.

In his philosophical views, Kant was influenced by H. Wolf, A.G. Baumgarten, J. Rousseau, D. Hume and other thinkers. Using Baumgarten's Wolffian textbook, Kant lectured on metaphysics. He said about Rousseau that the latter’s writings weaned him from arrogance. Hume "awakened" Kant "from his dogmatic sleep."

Kant's theory of space and time

The most important part of the Critique of Pure Reason is the doctrine of space and time. In this section I propose to undertake a critical examination of this teaching.

Kant believes that the immediate objects of perception are caused partly by external things and partly by our own perceptual apparatus. Locke accustomed the world to the idea that secondary qualities - colors, sounds, smell, etc. - are subjective and do not belong to the object as it exists in itself. Kant, like Berkeley and Hume, although not quite in the same way, goes further and makes primary qualities also subjective. For the most part, Kant has no doubt that our sensations have causes, which he calls “things-in-themselves” or noumena. What appears to us in perception, which he calls a phenomenon, consists of two parts: what is caused by the object - this part he calls sensation, and what is caused by our subjective apparatus, which, as he says, organizes diversity into certain relationship. He calls this last part the form of the phenomenon. This part is not the sensation itself and, therefore, does not depend on the randomness of the environment, it is always the same, since it is always present in us, and it is a priori in the sense that it does not depend on experience. The pure form of sensibility is called “pure intuition” (Anschauung); there are two such forms, namely space and time: one for external sensations, the other for internal ones.

Regarding space, four metaphysical arguments are put forward:

) Space is not an empirical concept abstracted from external experience, since space is presupposed when sensations are attributed to something external and external experience is possible only through the representation of space.

) Space is a necessary representation a priori, which underlies all external perceptions, since we cannot imagine that space should not exist, whereas we can imagine that nothing exists in space.

) Space is not a discursive, or general, concept of the relations of things in general, since there is only one space and what we call “spaces” are parts of it, not examples.

) Space is represented as an infinitely given quantity that contains within itself all parts of space. This relation is different from that which the concept has to its examples, and, therefore, space is not a concept, but Anschauung.

The arguments regarding time are essentially the same, except that arithmetic replaces geometry, since counting requires time.

The transcendental (or epistemological) argument, which is best established in the Prolegomena, is clearer than the metaphysical arguments, and also more clearly refutable. "Geometry", as we now know, is a name that combines two different scientific disciplines. On the one hand, there is pure geometry, which derives consequences from axioms without asking whether these axioms are true. It does not contain anything that does not follow from logic and is not “synthetic”, and does not need figures such as those used in geometry textbooks. On the other hand, there is geometry as a branch of physics, as it, for example, appears in the general theory of relativity - this is an empirical science in which axioms are derived from measurements and differ from the axioms of Euclidean geometry. Thus, there are two types of geometry: one is a priori, but not synthetic, the other is synthetic, but not a priori. This gets rid of the transcendental argument.

Biography of Isaac Newton

Newton Isaac (1643-1727), English mathematician, mechanic and physicist, astronomer and astrologer, creator of classical mechanics, member (1672) and president (from 1703) of the Royal Society of London. One of the founders of modern physics, formulated the basic laws of mechanics and was the actual creator of a unified physical program for describing all physical phenomena on the basis of mechanics; discovered the law of universal gravitation, explained the movement of the planets around the Sun and the Moon around the Earth, as well as tides in the oceans, laid the foundations of continuum mechanics, acoustics and physical optics. Fundamental works "Mathematical principles of natural philosophy" (1687) and "Optics" (1704).

Developed (independently from G. Leibniz) differential and integral calculus. He discovered the dispersion of light, chromatic aberration, studied interference and diffraction, developed the corpuscular theory of light, and put forward a hypothesis that combined corpuscular and wave concepts. Built a reflecting telescope. Formulated the basic laws of classical mechanics. He discovered the law of universal gravitation, gave a theory of the movement of celestial bodies, creating the foundations of celestial mechanics. Space and time were considered absolute. Newton's work was far ahead of the general scientific level of his time and was poorly understood by his contemporaries. He was the director of the Mint and established the coin business in England. A famous alchemist, Newton studied the chronology of ancient kingdoms. He devoted his theological works to the interpretation of biblical prophecies (mostly not published).

Newton was born on January 4, 1643 in the village of Woolsthorpe, (Lincolnshire, England) in the family of a small farmer who died three months before the birth of his son. The baby was premature; There is a legend that he was so small that he was placed in a sheepskin mitten lying on a bench, from which he once fell and hit his head hard on the floor. When the child was three years old, his mother remarried and left, leaving him in the care of his grandmother. Newton grew up sickly and unsociable, prone to daydreaming. He was attracted by poetry and painting; far from his peers, he made paper kites, invented a windmill, a water clock, and a pedal carriage.

The beginning of school life was difficult for Newton. He studied poorly, was a weak boy, and one day his classmates beat him until he lost consciousness. It was unbearable for the proud Newton to endure this, and there was only one thing left: to stand out for his academic success. Through hard work, he achieved first place in his class.

Interest in technology made Newton think about natural phenomena; He also studied mathematics in depth. Jean Baptiste Bieux later wrote about this: “One of his uncles, finding him one day under a hedge with a book in his hands, immersed in deep thought, took the book from him and found that he was busy solving a mathematical problem. Amazed by such a serious and active direction such a young man, he persuaded his mother not to further resist her son’s wishes and send him to continue his studies.”

After serious preparation, Newton entered Cambridge in 1660 as a Subsizzfr"a (the so-called poor students who were obliged to serve members of the college, which could not but burden Newton). He began to study astrology in his last year at college.

Newton took astrology seriously and zealously defended it from attacks from his colleagues. His studies in astrology and the desire to prove its significance pushed him to research in the field of the movement of celestial bodies and their influence on our planet.

In six years, Newton completed all the college degrees and prepared all his further great discoveries. In 1665 Newton became a Master of Arts. In the same year, when the plague epidemic was raging in England, he decided to temporarily settle in Woolsthorpe. It was there that he began to actively engage in optics. The leitmotif of all research was the desire to understand the physical nature of light. Newton believed that light is a stream of special particles (corpuscles) emitted from a source and moving in a straight line until they encounter obstacles. The corpuscular model explained not only the straightness of light propagation, but also the law of reflection (elastic reflection) and the law of refraction.

At this time, the work had already largely been completed, which was destined to become the main great result of Newton’s work - the creation of a unified physical picture of the World based on the laws of mechanics formulated by him.

Having posed the problem of studying various forces, Newton himself gave the first brilliant example of its solution, formulating the law of universal gravitation. The law of universal gravitation allowed Newton to give a quantitative explanation of the movement of planets around the Sun and the nature of sea tides. This could not fail to make a huge impression on the minds of researchers. The program for a unified mechanical description of all natural phenomena - both “earthly” and “heavenly” - was established in physics for many years. space time kant newton

In 1668, Newton returned to Cambridge and soon received the Lucasian Chair of Mathematics. This chair was previously occupied by his teacher I. Barrow, who ceded the chair to his favorite student in order to provide him financially. By that time, Newton was already the author of the binomial and the creator (simultaneously with Leibniz, but independently of him) of the method of differential and integral calculus.

Not limiting himself to theoretical research alone, in the same years he designed a reflecting telescope (reflective). The second of the telescopes made (improved) served as the reason for introducing Newton as a member of the Royal Society of London. When Newton refused membership due to the impossibility of paying dues, it was considered possible, given his scientific merits, to make an exception for him, exempting him from paying them.

His theory of light and colors, presented in 1675, caused such attacks that Newton decided not to publish anything on optics while Hooke, his most bitter opponent, was alive. From 1688 to 1694 Newton was a member of Parliament.

A constant oppressive feeling of material insecurity, enormous nervous and mental stress was undoubtedly one of the causes of Newton's illness. The immediate impetus for the disease was a fire in which all the manuscripts he prepared were lost. Therefore, the position of Warden of the Mint, while retaining his professorship at Cambridge, was of great importance to him. Zealously setting to work and quickly achieving noticeable success, Newton was appointed director in 1699. It was impossible to combine this with teaching, and Newton moved to London.

At the end of 1703 he was elected president of the Royal Society. By that time, Newton had reached the pinnacle of fame. In 1705 he was elevated to knighthood, but, having a large apartment, six servants and a wealthy family, he remains alone.

The time of active creativity is over, and Newton limits himself to preparing the publication of “Optics”, the re-edition of the work “Mathematical Principles of Natural Philosophy” and the interpretation of the Holy Scriptures (he is the author of the interpretation of the Apocalypse, an essay on the Prophet Daniel).

Newton died on March 31, 1727 in London and was buried in Westminster Abbey. The inscription on his grave ends with the words: “Let mortals rejoice that such an adornment of the human race lived in their midst.”

Newton's theory of space and time

Modern physics has abandoned the concept of absolute space and time of classical Newtonian physics. Relativistic theory demonstrated that space and time are relative. There are, apparently, no phrases repeated more often in works on the history of physics and philosophy. However, everything is not so simple, and such statements require certain clarifications (albeit of a rather linguistic nature). However, going back to the origins sometimes turns out to be very useful for understanding the current state of science.

Time, as we know, can be measured using a uniform periodic process. However, without time, how do we know that the processes are uniform? Logical difficulties in defining such primary concepts are obvious. The uniformity of the clock must be postulated and called the uniform passage of time. For example, by defining time using uniform and rectilinear motion, we thereby transform Newton's first law into a definition of the uniform passage of time. A clock runs uniformly if a body, which is not acted upon by forces, moves rectilinearly and uniformly (according to this clock). In this case, the movement is thought of relative to an inertial frame of reference, which for its definition also needs Newton’s first law and a uniformly running clock.

Another difficulty is related to the fact that two processes that are equally uniform at a given level of accuracy may turn out to be relatively uneven when measured more accurately. And we constantly find ourselves faced with the need to choose an increasingly reliable standard for the uniformity of the passage of time.

As already noted, the process is considered uniform and measuring time with its help is acceptable as long as all other phenomena are described as simply as possible. Obviously, a certain degree of abstraction is required when defining time in this way. The constant search for the right watch is associated with our belief in some objective property of time to have a uniform pace.

Newton was well aware of the existence of such difficulties. Moreover, in his “Principles” he introduced the concepts of absolute and relative time in order to emphasize the need for abstraction, determination on the basis of relative (ordinary, measured) time of his certain mathematical model - absolute time. And in this his understanding of the essence of time does not differ from the modern one, although due to the difference in terminology a certain confusion arose.

Let us turn to the “Mathematical Principles of Natural Philosophy” (1687). Abbreviated formulations of Newton's definition of absolute and relative time are as follows:

"Absolute (mathematical) time, without any relation to anything external, flows evenly. Relative (ordinary) time is a measure of duration, comprehended by the senses through any movement."

The relationship between these two concepts and the need for them is clearly visible from the following explanation:

“Absolute time is distinguished in astronomy from ordinary solar time by the equation of time. For the natural solar days, taken as equal in the ordinary measurement of time, are in fact unequal to each other. This inequality is corrected by astronomers in order to use a more correct time when measuring the movements of celestial bodies. It is possible that there is no such uniform movement (in nature) by which time could be measured with perfect accuracy. All movements can accelerate or slow down, but the flow of absolute time cannot change."

Newton's relative time is measured time, while absolute time is its mathematical model with properties derived from relative time through abstraction. In general, speaking about time, space and motion, Newton constantly emphasizes that they are comprehended by our senses and are thus ordinary (relative):

“Relative quantities are not the very quantities whose names are usually given to them, but are only the results of measurements of the said quantities (true or false), comprehended by the senses and usually taken for the quantities themselves.”

The need to build a model of these concepts requires the introduction of mathematical (absolute) objects, some ideal entities that do not depend on the inaccuracy of instruments. Newton's statement that "absolute time flows uniformly without any relation to anything external" is usually interpreted in the sense of the independence of time from motion. However, as can be seen from the above quotes, Newton speaks of the need to abstract from possible inaccuracies in the uniform running of any clock. For him, absolute and mathematical time are synonymous!

Newton nowhere discusses the issue that the speed of time may differ in different relative spaces (reference systems). Of course, classical mechanics implies the same uniformity of the passage of time for all reference systems. However, this property of time seems so obvious that Newton, very precise in his formulations, does not discuss it or formulate it as one of the definitions or laws of his mechanics. It is this property of time that was discarded by the theory of relativity. Absolute time, as understood by Newton, is still present in the paradigm of modern physics.

Let us now move on to Newton's physical space. If we understand by absolute space the existence of some selected, privileged frame of reference, then it is unnecessary to remind that it does not exist in classical mechanics. Galileo's brilliant description of the impossibility of determining the absolute motion of a ship is a prime example of this. Thus, the relativistic theory could not abandon what was missing in classical mechanics.

However, Newton’s question about the relationship between absolute and relative space is not clear enough. On the one hand, for both time and space, the term “relative” is used in the sense of “a measurable quantity” (comprehensible by our senses), and “absolute” - in the sense of “its mathematical model”:

"Absolute space, by its very essence, regardless of anything external, always remains the same and motionless. Relative is its measure or some limited moving part, which is determined by our feelings by its position relative to certain bodies, and which in everyday life life is taken for motionless space."

On the other hand, the text contains discussions about a sailor on a ship, which can also be interpreted as a description of the selected frame of reference:

“If the Earth itself moves, then the true absolute motion of the body can be found from the true motion of the Earth in motionless space and from the relative motions of the ship in relation to the Earth and the body in the ship.”

Thus, the concept of absolute motion is introduced, which contradicts Galileo's principle of relativity. However, absolute space and motion are introduced in order to immediately cast doubt on their existence:

“However, it is completely impossible either to see or in any other way to distinguish with the help of our senses the individual parts of this space from one another, and instead we have to turn to dimensions accessible to the senses. By the positions and distances of objects from any body taken as motionless , we define places in general. It is also impossible to determine their (bodies’) true rest by their relative position to each other.”

Perhaps the need to consider absolute space and absolute motion in it is associated with an analysis of the relationship between inertial and non-inertial reference systems. Discussing an experiment with a rotating bucket filled with water, Newton shows that the rotational motion is absolute in the sense that it can be determined, within the framework of the bucket-water system, by the shape of the concave surface of the water. In this respect, his point of view also coincides with the modern one. The misunderstanding expressed in the phrases given at the beginning of this section arose due to noticeable differences in the semantics of the use of the terms “absolute” and “relative” by Newton and modern physicists. Now, when we talk about absolute essence, we mean that it is described in the same way to different observers. Relative things may look different to different observers. Instead of “absolute space and time,” today we say “mathematical model of space and time.”

“Therefore, those who interpret these words in it truly violate the meaning of Holy Scripture.”

The mathematical structure of both classical mechanics and relativistic theory is well known. The properties that these theories impart to space and time follow unambiguously from this structure. Vague (philosophical) discussions about outdated “absoluteness” and revolutionary “relativity” are unlikely to bring us closer to solving the Main Mystery.

The theory of relativity rightly bears this name, since it has, indeed, demonstrated that many things that seem absolute at low speeds are not so at high speeds.

Conclusion

The problem of time and space has always interested man not only on a rational, but also on an emotional level. People not only regret the past, but also fear the future, not least because the inevitable flow of time leads to their death. Throughout its conscious history, humanity, represented by its outstanding figures, has thought about the problems of space and time; few of them managed to create their own theories describing these fundamental attributes of existence. One of the concepts of these concepts comes from the ancient atomists - Democritus, Epicurus and others. They introduced the concept of empty space into scientific circulation and considered it as homogeneous and infinite.

Space and time underlie our picture of the world.

The last century, the century of rapid development of science, was the most fruitful in terms of knowledge of time and space. The appearance at the beginning of the century, first of the special and then of the general theory of relativity, laid the foundation for the modern scientific understanding of the world; many of the provisions of the theory were confirmed by experimental data. Nevertheless, as this work also shows, the question of knowledge of space and time, their nature, interrelation and even presence remains largely open.

Space was considered infinite, flat, “rectilinear,” Euclidean. Its metric properties were described by Euclid's geometry. It was considered as absolute, empty, homogeneous and isotropic (there are no distinguished points and directions) and acted as a “container” of material bodies, as an integral system independent of them.

Time was understood as absolute, homogeneous, uniformly flowing. It occurs immediately and everywhere in the entire Universe “uniformly synchronously” and acts as a process of duration independent of materialistic objects.

Kant put forward the principle of the intrinsic value of each individual, which should not be sacrificed even for the good of the whole society. In aesthetics, contrary to formalism in the understanding of beauty, he declared poetry to be the highest form of art, since it rises to the image of an ideal.

According to Newton, the world consists of matter, space and time. These three categories are independent of each other. Matter is located in infinite space. The movement of matter occurs in space and time.

Literature

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5. Reichenbach G. Philosophy of space and time. - M., 1985