Medova A.A. The concept of time and its significance for the model of human essence. Comparative analysis of the concepts of I. Kant and Maurice Merleau-Ponty. Kant's interpretation of space and time as pure forms of contemplation II Kant believes that space and time

Abstract topic:

Space and time in Kant's philosophy.

Plan.

Introduction

1. Immanuel Kant and his philosophy.

2. Space and time.

Conclusion.

Literature.

Introduction.

Immanuel Kant (1724-1804) is considered the founder of German classical philosophy - a grandiose stage in the history of world philosophical thought, covering more than a century of spiritual and intellectual development - intense, very bright in its results and extremely important in its impact on human spiritual history. He is associated with truly great names: along with Kant, these are Johann Gottlieb Fichte (1762-1814), Friedrich Wilhelm Schelling (1775-1854), Georg Wilhelm Friedrich Hegel (1770-1831) - all highly original thinkers. Each one is so unique that it's hard not to wonder if it's even possible to speak of German classical philosophy as a relatively unified, holistic entity? And yet it is possible: with all the rich variety of ideas and concepts, the German classics are distinguished by adherence to a number of essential principles that are successive for this entire stage in the development of philosophy. It is they who allow us to consider German classical philosophy as a single spiritual education.

The first feature of the teachings of thinkers ranked among the German classics is a similar understanding of the role of philosophy in the history of mankind, in the development of world culture. Philosophy. they entrusted the highest spiritual mission - to be the critical conscience of culture. Philosophy, absorbing the living juices of culture, civilization, broadly understood humanism, is called upon to carry out a broad and deep critical reflection in relation to human life. It was a very bold claim. But the German philosophers of the XVIII-XIX centuries. achieved undeniable success in its implementation. Hegel said: "Philosophy is ... its contemporary era, comprehended in thinking." And the representatives of the German philosophical classics really managed to capture the rhythm, dynamics, demands of their anxious and turbulent time - a period of profound socio-historical transformations. They turned their eyes both to human history as such and to human essence. Of course, for this it was necessary to develop a philosophy of a very wide range of problems - to cover in thought the essential features of the development of the natural world and human existence. At the same time, a single idea of ​​the highest cultural-civilizing, humanistic mission of philosophy was drawn through all the problematic sections. Kant, Fichte, Schelling, Hegel also exalt philosophy so highly because they think of it as a rigorous and systematic science, however, a specific science in comparison with both natural science and disciplines that more or less concretely study a person. And yet, philosophy feeds on the life-giving sources of scientificity, focuses on scientific models and strives (and must) build itself as a science. However, philosophy not only relies on science, obeying the criteria of scientificity, but itself gives science and scientificity broad humanistic and methodological orientations.

At the same time, it would be wrong to present the matter as if other areas of human life and culture acquire self-reflection only from philosophy. Critical self-awareness is the business of the whole culture.

The second feature of German classical thought is that it had the mission to give philosophy the appearance of a widely developed and much more differentiated than before, a special system of disciplines, ideas and concepts, a complex and multifaceted system, the individual links of which are linked into a single intellectual chain of philosophical abstractions. It is no coincidence that the German philosophical classics are extremely difficult to master. But here is the paradox: it was this highly professional, extremely abstract, difficult to understand philosophy that could have a huge impact not only on culture, but also on social practice, in particular on the sphere of politics.

So, German classical philosophy also represents unity in the sense that its representatives Kant, Fichte, Schelling, Hegel build their very complex and branched teachings, systems that include philosophical problems of a very high generalization. First of all, they philosophically talk about the world, about the world as a whole, about the laws of its development. This is the so-called ontological aspect of philosophy - the doctrine of being. In close unity with it, the doctrine of cognition is built, i.e. theory of knowledge, epistemology. Philosophy is also being developed as a doctrine of man, i.e. philosophical anthropology. At the same time, the classics of German thought tend to talk about a person, exploring various forms of human activity, including the social life of a person. They reflect on society, social man within the framework of the philosophy of law, morality, world history, art, religion - such were the various areas and disciplines of philosophy in the era of Kant. So, the philosophy of each of the representatives of the German classics is a branched system of ideas, principles, concepts related to the previous philosophy and innovatively transforming the philosophical heritage. All of them are also united by the fact that they solve the problems of philosophy on the basis of very broad and fundamental worldview reflections, a comprehensive philosophical view of the world, man, and all being.

1. Immanuel Kant and his philosophy.

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

Born into a large family of Johann Georg Kant in Koenigsberg, where he lived almost all his life, without leaving the city for more than one hundred and twenty kilometers. Kant was brought up in an environment where the ideas of pietism, a radical renewal movement in Lutheranism, had a special influence. After studying at a pietist school, where he showed excellent abilities for the Latin language, in which all four of his dissertations were subsequently written (Kant knew less Greek and French, and almost did not speak English), in 1740 Kant entered the Albertina University of Koenigsberg. Among Kant's university professors, Wolffian M. Knutzen stood out, who introduced him to the achievements of modern science. From 1747, due to financial circumstances, Kant worked as a home teacher outside of Konigsberg in the families of a pastor, landowner, and count. In 1755, Kant returned to Konigsberg and, completing his studies at the university, defended his master's thesis "On Fire". Then during the year he defends two more dissertations, which gave him the right to lecture as an assistant professor and professor. However, Kant did not become a professor at that time and worked as an extraordinary (i.e., receiving money only from students, and not from the state) assistant professor until 1770, when he was appointed to the post of ordinary professor at 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 lifestyle and many of his habits are famous, especially after he bought his own house in 1784. Every day, at five o'clock in the morning, Kant was awakened by his servant, retired soldier Martin Lampe, Kant got up, drank a couple of cups of tea and smoked a pipe, then proceeding to prepare for lectures. Shortly after the lectures, it was dinner time, which was usually attended by several guests. The dinner lasted several hours and was accompanied by conversations on various, but not philosophical, topics. After dinner, Kant took what became a legendary daily walk through the city. In the evenings, Kant liked to look at the building of the cathedral, which was very clearly visible from the window of his room.

Kant always carefully monitored his health and developed an original system of hygienic prescriptions. He was not married, although he did not have any special prejudices regarding the female half of humanity.
In his philosophical views, Kant was influenced by H. Wolf, A. G. Baumgarten, J. J. Rousseau, D. Hume, and other thinkers. According to the Wolffian textbook by Baumgarten, Kant lectured on metaphysics. Of Rousseau he said that the writings of the latter weaned him from arrogance. Hume "awakened" Kant "from his dogmatic slumber".

"subcritical" philosophy.
There are two periods in Kant's work: "pre-critical" (until about 1771) and "critical". The pre-critical period is the time of Kant's slow release from the ideas of Wolf's metaphysics. Critical - the time when Kant raised the question of the possibility of metaphysics as a science and the creation of new guidelines in philosophy, and above all the theory of the activity of consciousness.
The pre-critical period is characterized by Kant's intensive methodological searches and his development of natural science questions. Of particular interest are Kant's cosmogonic research, which he outlined in his 1755 work "The General Natural History and Theory of the Sky". The basis of his cosmogonic theory is the concept of an entropic Universe, spontaneously developing from chaos to order. Kant argued that in order to explain the possibility of the formation of planetary systems, it is enough to admit matter endowed with forces of attraction and repulsion, while relying on Newtonian physics. Despite the naturalistic nature of this theory, Kant was sure that it did not pose a danger to theology (it is curious that Kant still had problems with censorship on theological issues, but in the 1790s on a completely different issue). In the pre-critical period, Kant also paid much attention to the study of the nature of space. In his dissertation "Physical Monadology" (1756), he wrote that space as a continuous dynamic environment is created by the interaction of discrete simple substances (the condition of which Kant considered the existence of a common cause for all these substances - God) and has a relative character. In this regard, already in his student work "On the true assessment of living forces" (1749), Kant suggested the possibility of multidimensional spaces.
The central work of the pre-critical period - "The only possible basis for the proof of the existence of God" (1763) - is a kind of encyclopedia of Kant's pre-critical philosophy with an emphasis on theological problems. Criticizing here the traditional proofs of the existence of God, Kant at the same time puts forward his own, "ontological" argument, based on the recognition of the necessity of some kind of existence (if nothing exists, then there is no material for things, and they are impossible; but the impossible is impossible, which means what existence is necessary) and the identification of this primordial existence with God.

Transition to criticism.

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 Informatics 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 2500 years have passed since the beginning of the understanding of time and space, however, the interest in the problem and the disputes of philosophers, physicists and representatives of other sciences around the definition of the nature of space and time do not decrease at all. Significant interest in the problem of space and time is natural and logical, 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, of human nature. The notion of space-time stifles our imagination. No wonder the attempts of the philosophers of antiquity, the scholastics of the Middle Ages and modern scientists, who have knowledge of the sciences and experience in their history, to understand the essence of time - space did not give unambiguous answers to the questions posed.

Dialectical materialism proceeds from the fact that "there is nothing in the world but moving matter, and moving matter cannot move otherwise than in space and time." Space and time, here act as fundamental forms of the existence of matter. Classical physics considered the space-time continuum as a universal arena of 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 arisen: according to some, there is nothing in the world at all, except for empty curved space, and physical objects are only manifestations of this space. Other concepts claim 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, Anri Bergson argued that time can only be known by non-rational intuition, and scientific concepts that represent time as having any direction misinterpret 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".

Born into a large family of Johann Georg Kant in Koenigsberg, where he lived almost all his life, without leaving the city for more than one hundred and twenty kilometers. Kant was brought up in an environment where the ideas of pietism, a radical renewal movement in Lutheranism, had a special influence. After studying at a pietist school, where he showed excellent abilities for the Latin language, in which all four of his dissertations were subsequently written (Kant knew less Greek and French, and almost did not speak English), in 1740 Kant entered the Albertina University of Koenigsberg. Among Kant's university professors, Wolffian M. Knutzen stood out, who introduced him to the achievements of modern science. From 1747, due to financial circumstances, Kant worked as a home teacher outside of Konigsberg in the families of a pastor, landowner, and count. In 1755, Kant returned to Konigsberg and, completing his studies at the university, defended his master's thesis "On Fire". Then during the year he defends two more dissertations, which gave him the right to lecture as an assistant professor and professor. However, Kant did not become a professor at that time and worked as an extraordinary (i.e., receiving money only from students, and not from the state) assistant professor until 1770, when he was appointed to the post of ordinary professor at 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.

The famous way of life of Kant and many of his habits, especially manifested after he bought his own house in 1784. Every day, at five o'clock in the morning, Kant was awakened by his servant, retired soldier Martin Lampe, Kant got up, drank a couple of cups of tea and smoked a pipe, then proceeding to prepare for lectures. Shortly after the lectures, it was dinner time, which was usually attended by several guests. The dinner lasted several hours and was accompanied by conversations on various, but not philosophical, topics. After dinner, Kant took what became a legendary daily walk through the city. In the evenings, Kant liked to look at the building of the cathedral, which was very clearly visible from the window of his room.

Kant always carefully monitored his health and developed an original system of hygienic prescriptions. He was not married, although he did not have any special prejudices regarding 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. According to the Wolffian textbook by Baumgarten, Kant lectured on metaphysics. Of Rousseau he said that the writings of the latter weaned him from arrogance. Hume "awakened" Kant "from his dogmatic slumber".

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.

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 the presentation will I try to criticize it.

Kant believes that immediate objects of perception are conditioned 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 in exactly 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 conditioned by the object - this part he calls sensation, and that which is conditioned by our subjective apparatus, which, as he says, orders the variety into certain relations. This last part he calls the form of appearance. This part is not the sensation itself and therefore does not depend on the contingency 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.

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

With regard to space, four metaphysical arguments are put forward:

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

) Space is the necessary a priori representation 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, which contains within itself all parts of space. This relation is different from that which the concept has to its instances, and consequently space is not a concept, but an Anschauung.

The transcendental argument about space is derived from geometry. Kant claims that Euclidean geometry is known a priori, although it is synthetic, that is, not deducible from logic itself. Geometric proofs, he argues, depend on figures. We can see, for example, that if two lines intersecting at right angles to one another are given, then only one straight line can be drawn through their point of intersection at right angles to both lines. This knowledge, according to Kant, 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 determines in my subjectivity all real impressions. The objects of sense must obey geometry, because geometry concerns our ways of perceiving, and therefore we cannot perceive in any other way. This explains why geometry, although synthetic, is a priori and apodictic.

The arguments for time are essentially the same, except that geometry is replaced by arithmetic, since counting takes time.

Let us now examine these arguments one by one. The first of the metaphysical arguments about space is: “Space is not an empirical concept abstracted from external experience. Indeed, the representation of space must already be 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 represent 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 nowhere, and there is nothing spatially outside of me. My body can only be understood as a phenomenon. Thus, everything 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 then arise in one's mind is that of a cloakroom attendant who hangs different coats on different hooks; the hooks must already exist, but the subjectivity of the cloakroom attendant tidies up the coat.

Here, as elsewhere in Kant's theory of the subjectivity of space and time, there is a difficulty that he never seems to have felt. What makes me arrange the objects of perception the way I do it, 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 evoke my separate perceptions, but nothing in them corresponds to the spatial arrangement that exists in my perception. This is contrary to 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 believe that different colors correspond to different wavelengths. Since waves, however, include 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 intellect arranges the raw material of sensations, but he never thought about what needs to be said, why the intellect arranges this material in this way and not otherwise.

With regard to time, the difficulty is even greater, since when considering time, causality must be taken into account. I perceive lightning before I perceive thunder. The thing-in-itself A causes my perception of lightning, and the other thing-in-itself B causes my perception of thunder, but A not before B, since time exists only in relation of perceptions. Why then two timeless things A and B act at different times? This must be wholly arbitrary if Kant is right, and then there must be no relation between A and B corresponding to the fact that the perception evoked by A precedes the perception evoked 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 yourself are in space and you imagine clouds that you cannot see. As Weininger pointed out, Kant's space is absolute, like Newton's space, and not just a system of relations. But I don't see how one can imagine an absolutely empty space.

The third metaphysical argument says: "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 they mean only parts of one and the same single space, moreover, these parts cannot precede the single all-encompassing space as its constituent elements (of which its addition would be possible), but can only be conceived as being in it. ; the manifold in it, and therefore also the general concept of spaces in general, is based solely on limitations. 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, according to Kant, their logical status is, 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 an inhabitant of the Alpine valleys could accept it. It is difficult to understand how something infinite can be "given". I must take it for granted that the part of space that is given is that which is filled with objects of perception, and that for other parts we have only a sense of the possibility of movement. And if it is permissible to apply such a vulgar argument, then modern astronomers maintain that space is not really 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 is also more clear to be refuted. "Geometry", as we now know, is a name that combines two different scientific disciplines. On the one hand, there is pure geometry, which deduces consequences from axioms without questioning 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 - it 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 raises when he considers space in a more general way. If we proceed 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 come to the conclusion that all real qualities in perceptions differ from qualities in their unperceived 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 a certain length (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 unperceived causes of perceptions. All this is based on the principle "same cause, same effect", with the 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 relationship between cause A and cause B.

We have, according to this view, two spaces - one subjective and the other objective, one known in experience, and the other only deduced. 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 by means of 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 situation is different, for if we keep faith in the imperceptible causes of perceptions, objective time must be identical with subjective time. If not, we run into the difficulties already considered 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 insofar as you touch them, are in an unperceivable world. And in this world, the first precedes the last. In addition, 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 presuppose, 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 by no means logically necessary. If it is rejected, perceptions cease to be in any essential sense 'subjective', since there is nothing that can be opposed to them.

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

Kant's immediate successor, Fichte (1762-1814), rejected "things in themselves" and carried subjectivism to a degree that apparently bordered on madness. He believed that the Self is the only finite reality and that it exists because it asserts 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 "Speech to the German Nation" (1807-1808), in which he sought to inspire the Germans to resist Napoleon after the battle of Jena. The ego, 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 a 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.

Biography of Isaac Newton

Newton Isaac (1643-1727), English mathematician, mechanic and physicist, astronomer and astrologer, creator of classical mechanics, member (1672) and president (since 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 based on mechanics; discovered the law of universal gravitation, explained the motion of the planets around the Sun and the Moon around the Earth, as well as the 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 of 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 expressed a hypothesis that combined corpuscular and wave representations. Built a mirror telescope. Formulated the basic laws of classical mechanics. He discovered the law of universal gravitation, gave a theory of the motion of celestial bodies, creating the foundations of celestial mechanics. Space and time were considered absolute. Newton's works were far ahead of the general scientific level of his time, and were obscure to his contemporaries. He was the director of the Mint, established the monetary business in England. A famous alchemist, Newton dealt with the chronology of the ancient kingdoms. He devoted theological works to the interpretation of biblical prophecy (mostly unpublished).

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 out 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, he, far from his peers, made kites, invented a windmill, a water clock, a pedal cart.

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

Interest in technology made Newton think about the phenomena of nature; he was also deeply involved in mathematics. Jean Baptiste Bie later wrote about this: “One of his uncles, finding him one day under a hedge with a book in his hands, immersed in deep reflection, took the book from him and found that he was busy solving a mathematical problem. Struck by such a serious and active direction so young a man, he persuaded his mother not to resist further the desire of her son 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 the members of the college, which could not but burden Newton). He began to study astrology in his last year of college.

Newton took astrology seriously and defended it zealously against attacks from his colleagues. Studies in astrology and the desire to prove its significance prompted 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 degrees of the college and prepared all his further great discoveries. In 1665 Newton became a master of arts. In the same year, when the plague 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, which was destined to become the main great result of Newton's works, was already completed, in the main - the creation of a single, based on the laws of mechanics of the physical picture of the World formulated by him.

Having set the task of studying various forces, Newton himself gave the first brilliant example of its solution by formulating the law of universal gravitation. The law of universal gravitation allowed Newton to give a quantitative explanation of the motion of the planets around the Sun, the nature of sea tides. This could not but make a huge impression on the minds of researchers. The program of a unified mechanical description of all natural phenomena - both "terrestrial" and "celestial" for many years was established in physics. space time kant newton

In 1668 Newton returned to Cambridge and he soon received the Lucas Chair in Mathematics. Before him, this department was occupied by his teacher I. Barrow, who ceded the department to his beloved student in order to financially provide for him. 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 limited to theoretical studies alone, in the same years he designed a reflecting telescope (reflective). The second of the manufactured telescopes (improved) was the reason for the presentation of Newton as a member of the Royal Society of London. When Newton resigned his membership due to the impossibility of paying membership dues, it was considered possible, in view of his scientific merits, to make an exception for him, exempting him from paying them.

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

The 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 prepared by him perished. Therefore, it was of great importance for him to be the caretaker of the Mint with the preservation of a professorship at Cambridge. Zealously setting to work and quickly achieving notable 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 the dignity of knighthood, but, having a large apartment, six servants and a rich departure, he remains still alone.

The time for active creativity is over, and Newton is limited to preparing the publication of "Optics", reprinting the work "Mathematical Principles of Natural Philosophy" and interpreting the Holy Scriptures (he owns the interpretation of the Apocalypse, an essay on the prophet Daniel).

Newton died on March 31, 1727 in London and is 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 Newton's classical physics. Relativistic theory has demonstrated that space and time are relative. Apparently, there are 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 (however, a linguistic sense is enough). However, going back to the origins is sometimes very helpful in understanding the current state of science.

Time, as is known, can be measured using a uniform periodic process. However, without time, how do we know that the processes are uniform? There are obvious logical difficulties in defining such primary concepts. The uniformity of the clock should be postulated and called the uniform passage of time. For example, by defining time with the help of uniform and rectilinear motion, we thereby turn Newton's first law into a definition of the uniform course of time. The clock runs uniformly if the body, on which no forces act, moves in a straight line and uniformly (according to this clock). In this case, the motion is conceived in relation to the 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 can turn out to be relatively non-uniform with a more accurate measurement. And we are constantly 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 the measurement of time with its help is acceptable as long as all other phenomena are described as simply as possible. It is obvious that a certain degree of abstraction is required in such a definition of time. The constant search for the right clock is connected 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, definition on the basis of relative (ordinary, measured) time of his some mathematical model - absolute time. And in this, his understanding of the essence of time does not differ from the modern one, although a certain confusion arose due to differences in terminology.

Let us turn to the "Mathematical Principles of Natural Philosophy" (1687). The 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 seen from the following explanation:

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

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

"Relative quantities are not the same 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 the possible inaccuracies of the uniform movement of any clock. For him, absolute and mathematical time are synonymous!

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

Now let's move on to Newton's physical space. If absolute space is understood as the existence of a certain preferred frame of reference, then it is superfluous 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 vivid example of this. Thus, the relativistic theory could not refuse what was missing in classical mechanics.

Nevertheless, 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" (comprehended by our senses), and "absolute" in the sense of "its mathematical model":

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

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

"If the Earth itself is moving, then the true absolute motion of the body can be found from the true motion of the Earth in stationary space and from the relative motions of the ship in relation to the Earth and the body in relation to 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 absolutely impossible to see or otherwise distinguish with the help of our senses the individual parts of this space from one another, and instead of them we have to turn to measurements accessible to the senses. By the positions and distances of objects from any body taken for a motionless , we define places in general. It is also impossible to determine their true (bodies) rest by their relative position to each other.

Perhaps the need to consider absolute space and absolute motion in it is related to the analysis of the relationship between inertial and non-inertial frames of reference. Discussing the experiment with a rotating bucket that is filled with water, Newton shows that the rotational motion is absolute in the sense that it can be determined, without going beyond 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 the section arose because of the noticeable differences in the semantics of the use of the terms "absolute" and "relative" by Newton and modern physicists. Now, speaking of absolute essence, we mean that it is described in the same way for 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 the Holy Scripture."

The mathematical structure of both classical mechanics and relativistic theory is well known. The properties endowed by these theories of space and time follow unambiguously from this structure. Vague (philosophical) arguments about outdated "absoluteness" and revolutionary "relativity" hardly bring us closer to unraveling the Main Secret.

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

Conclusion

The problem of time and space has always interested a person 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. Mankind, represented by its prominent figures throughout its conscious history, has thought about the problems of space and time, few of them managed to create their own theories that describe these fundamental attributes of being. 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 are at the heart of our picture of the world.

The last century - the century of the rapid development of science was the most fruitful in terms of the 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 conception of the world, many of the provisions of the theory were confirmed by experimental data. Nevertheless, as shown, including this work, the question of knowledge of space and time, their nature, interrelation and even existence remains open in many respects.

The 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 selected points and directions) and acted as a "receptacle" of material bodies, as an integral system independent of them.

Time was understood as absolute, homogeneous, evenly flowing. It goes at once 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 self-worth 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

1. Bakhtomin N.K. The theory of scientific knowledge of Immanuel Kant: Experience of modern. reading the Critique of Pure Reason. Moscow: Nauka, 1986

2. Blinnikov L.V. Great Philosophers. - M., 1998

3. Isaac Newton Mathematical Principles of Natural Philosophy

4. Kartsev V. "Newton", 1987, series "Life of Remarkable People"

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


. Next, Kant produced two
no less subjectivist "interpretations" of views
to space and time. The essence of the first, "metaphysical
of their interpretation lies in the provisions that
“space is a necessary a priori representation
the intuition underlying all external contemplation,
and “time is a necessary representation lying
at the basis of all contemplation." The essence of the second, "trans-
centendental" interpretation of them consists, firstly,
in the clarification that space is "only the form of all
phenomena of external senses”, and time is “immediate
essential condition of internal phenomena (our soul)
and thus indirectly also the condition of external phenomena
2* 35
ny". Secondly - and this is the main thing - that the space
and time are not objective determinations of things and
have realities outside the “subjective conditions of contemplation”
chanting." Kant proclaims theses about "transcendental
“real ideality” of space and time, affirmed
expecting "that space is nothing, as soon as
we discard the conditions for the possibility of any experience
and take it for something underlying things
in itself”, and that time, “if we ignore the subjective
conditions of sensory contemplation, perceive absolutely nothing
begins and cannot be counted among the subjects of
mime by itself...” (39, 5, 130, 135, 138, 133, 137, 134, 140).
As V. I. Lenin pointed out, “recognizing the a priori
space, time, causality, etc., Kant
corrects his philosophy in the direction of idealism" (2,
18, 206). It follows from the above theses that all
contemplated in space and time does not represent
itself of "things-in-themselves", being as such infallible
a clear indicator of their non-representation in consciousness.
And it is precisely from these theses that the agnostic conclusion follows.
waters, that since people contemplate everything in space
and time, and since sensible intuitions are
are the necessary basis for intellectual posture
knowledge, the human mind is fundamentally devoid of
the ability to know things-in-themselves.
The proclamation of the "transcendental ideal-
sti" of space and time was directly directed
against understanding them as forms of the existence of
rii, which was approached by the new European material
lim. This "ideality" meant the denial of
that extension and motion are attributes of matter
rii, its inalienable essential properties. Open-
making reference to the "validity of the changes" as
waters in favor of the objective reality of time, Kant
stated that outside of sensory representation "there was no
would also be an idea of ​​change.” Essentially de-
la, all the certainties of the sensible
material bodies were interpreted by Kant as having
its source in human consciousness, i.e. subject-
positively idealistic.
Note that the "dematerialization" produced by Kant
zation" of the world of phenomena spread implicitly
also on things-in-themselves. The point is that, according to Kant,
no certainty of feelings can be inherent
36
perceived bodies (extension, inextensibility
permeability, mobility, etc.); "performance
about the body in contemplation does not contain anything that could
to be inherent in objects in themselves ... "
(39. 3. 140-141, 145). So, already within the framework of the “transcen-
dental aesthetics" Kant's "thing-in-itself"
was ambiguous and even having opposite
false meanings: materialistic and antimatter
leafy.
Theses about the "empirical reality" of space
stva and time, also arising from the "metaphysical
th "interpretation of the latter, did not have a materialistic
sense and were, one might say, only a turnover
side of the theses about their "transcendental
ideality." According to Kant, space and time are "empi-
are rhytically real" in the only sense that they
have significance "for all things that
can ever be given to our senses..."
(39.3.139), that is, for phenomena. In other words, everything
things as phenomena (and only as phenomena!)
methods of sensual contemplation with the necessity of
exist in space and time. This universality
and the need for the existence of phenomena in space
Kant called “objective significance”
bridge" of the latter, thereby subjectively-ideal-
statically interpreting objectivity itself.
Kant believed that the conclusions about space and time
me as necessary a priori representations, le-
living in the basis of contemplation, give a philosophical designation
foundation of the ability of mathematics to put forward propositions
niya, having a universal and necessary significance.
The fact is that, according to Kant, one of the two
the main branches of mathematics - geometry - has
spatial representations as their basis,
and another branch - arithmetic - temporary representations
leniya.
For materialistically thinking scientists and philo-
Sofov's Kantian justification of the "possibility of mathematics
tiki as a science" did not give anything positive, and if
take him seriously, it was even capable of compro-
label this science. However, in the minds of those who have experienced
the impact of destructive criticism of the mathematical
knowledge from the Berkeley subjective idea
lisma (and Kant himself may have belonged to them)
and gravitated towards a different, free from this kind of criticism
37
varieties of subjective idealism, this
foundation restored the scientific status of mathematics
tiki, and therefore for them it was of great significance.
chenie.
Transcendental Logic" The "transcendental
dental logic" Kant distinguished from the pre-existing "ob-
general logic" as "substantial" logic from the logic of "formal
Noah". According to Kant, this general logic, dealing with a priori
principles of thinking, "distracted ... from any content in-)
knowledge, i.e., from any relation to the object, and considers
only a logical form in relation to knowledge to each other, i.e.
form of thought in general. Considering this logic insufficient, Kant
declared that there must still be a "logic that is not distracted
from any content of knowledge”, but “determining the origin
knowledge, volume and objective significance” of a priori knowledge, and its
should be called "transcendental logic" because it
deals only with the laws of reason and reason ... only so much
ku, since it a priori refers to objects ... "(39. 3. 157,
158 - 159). This is the first expression in German classical philosophy
the critical attitude to formal logic that arose on
basis of the approach to the idea of ​​dialectical logic, there was no antagonism
static to the previous logic and focused not on its
negation, but rather an addition to a deeper, from the point of view
Kant, a logical concept that solves new and more complex
cognitive tasks.
Giving content to logic is ensured, according to Kant,
close and constant connection of cognitive thinking with sensual
mi ideas explored in the transcendental
tik, i.e. with "contemplations". Kant considered this binding a function
reason, defining the latter precisely as “the ability ...
pour the object of sensual contemplation ... "and stating that" he must
wives to be first of all investigated in logic". After in-
chale "Criticism ..." Kant characterized sensuality and thought-
as completely different cognitive abilities,
which should be carefully separated and distinguished one from the other
goy", he then persistently and consistently pursues the thought
that “only from the combination” of sensibility and reason “can
knowledge can arise.” This is explained by the fact that "without sensual
sti not a single object would be given to us, and without reason, not a single
It would be nice to think." Expressing the belief that "thoughts without
contents are empty”, and “contemplations without concepts are blind” (39.3.155),
Kant argued, on the one hand, the basic meaning of sensual
stages of knowledge (which was a manifestation of the materialistic shadow
densii in "transcendental logic"), and on the other hand, sub-
outlined the need not to dwell on it in the process of
knowledge, but subject it to rational processing. In accordance with
In the general reasoning of Kant, an approach is noticeable to the understanding that
the transition from the sensory level of cognition to the rational one is ha-
character of a qualitative leap, i.e., dialectical. Related to this,
in particular, Kant's emphasis on activity ("spontaneity")
reason versus passivity ("receptivity")
sensuality.
38
The doctrine of reason and the problem of natural science
as a science ("transcendental analytics")
Calling the doctrine of rational knowledge "transcendental
dental analytics", Kant explains that this part
his logic is produced not by ordinary analysis, but by “dissected
the reduction of all our a priori knowledge to the beginning of
pure intellectual knowledge” (39.3.164). Such beginnings
Lamy Kant considered, firstly, concepts, and secondly,
fundamentals, which are the rules of co-
unification of concepts into judgments. Therefore Kant divided
transcendental analytics to the analytics of concepts
and fundamentals analytics.

What can we learn, Kant asked, from these confusing antinomies? His answer is: our concepts of space and time do not apply to the world as a whole. The concepts of space and time apply, of course, to ordinary physical things and events. But space and time themselves are neither things nor events. They cannot be observed; by nature they are of a completely different character. Most likely they limit things and events in a certain way, they can be compared with a system of objects or with a system catalog for ordering observations. Space and time do not refer to the actual empirical world of things and events, but to our own spiritual arsenal, the spiritual tool with which we comprehend the world. Space and time function like instruments of observation. When we observe a certain process or event, we localize it, as a rule, directly and intuitively into a space-time structure. Therefore, we can characterize space and time as a structural (ordered) system based not on experience, but used in any experience and applicable to any experience. But such an approach to space and time involves a certain difficulty if we try to apply it to a region that is beyond the scope of all possible experience; our two proofs of the beginning of the world serve as an example of this.

The unfortunate and doubly erroneous name of "transcendental idealism" was given by Kant to the theory which I have presented here. He soon regretted his choice, as it led some of his readers to regard Kant as an idealist and to believe that he rejected the alleged reality of physical things, passing them off as pure representations or ideas. In vain did Kant try to explain that he had rejected only the empirical character and reality of space and time - the empirical character and reality of the kind that we attribute to physical things and processes. But all his efforts to clarify his position were in vain. The difficulty of the Kantian style decided his fate; thus he was doomed to go down in history as the founder of "German idealism." Now is the time to reconsider this assessment. Kant always stressed that physical things are real in space and time - real, not ideal. As for the absurd metaphysical speculations of the school of "German idealism", the title chosen by Kant "Critique of Pure Reason" heralded his critical offensive against such speculations. Pure reason is criticized, in particular a priori "pure" conclusions of the mind about the world, which do not follow from sensory experience and are not verified by observations. Kant criticizes "pure reason", thus showing that a purely speculative, not carried out on the basis of observations, reasoning about the world must always lead us to antinomies. Kant wrote his "Critique ...", which was formed under the influence of Hume, with the aim of showing that the boundaries of a possible sensible world coincide with the boundaries of reasonable theorizing about the world.

Confirmation of the correctness of this theory, he considered found when he discovered that it contains the key to the second important problem - the problem of the significance of Newtonian physics. Like all physicists of that time, Kant was completely convinced of the truth and indisputability of Newton's theory. He believed that this theory could not be only the result of accumulated observations. What could still serve as the basis for its truth? To solve this problem, Kant first of all investigated the grounds for the truth of geometry. Euclidean geometry, he said, is based not on observation, but on our spatial intuition, on our intuitive understanding of spatial relationships. A similar situation occurs in Newtonian physics. The latter, although confirmed by observations, is nevertheless the result not of observations, but of our own methods of thinking, which we use to order, connect, and understand our sensations. Not facts, not sensations, but our own mind - the whole system of our spiritual experience - is responsible for our natural scientific theories. The nature we know, with its order and laws, is the result of the ordering activity of our spirit. Kant formulated this idea as follows: "Reason does not draw its laws a priori from nature, but prescribes them to her"

properties, he argues, depend on the figures. We can see, for example, that if two lines intersecting at right angles to one another are given, then only one straight line can be drawn through their point of intersection at right angles to both lines. This knowledge, according to Kant, 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 determines in my subjectivity all real impressions. The objects of sense must obey geometry, because geometry concerns our ways of perceiving, and therefore we cannot perceive in any other way. This explains why geometry, although synthetic, is a priori and apodictic.

The arguments for time are essentially the same, except that geometry is replaced by arithmetic, since counting takes time.

Let us now examine these arguments one by one. The first of the metaphysical arguments about space is: “Space is not an empirical concept abstracted from external experience. Indeed, the representation of space must already be 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 represent 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 nowhere, and there is nothing spatially outside of me. My body can only be understood as a phenomenon. Thus, everything 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 then arise in one's mind is that of a cloakroom attendant who hangs different coats on different hooks; the hooks must already exist, but the subjectivity of the cloakroom attendant tidies up the coat.

Here, as elsewhere in Kant's theory of the subjectivity of space and time, there is a difficulty that he never seems to have felt. What makes me arrange the objects of perception the way I do it, 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 evoke my separate perceptions, but nothing in them corresponds to the spatial arrangement that exists in my perception. This is contrary to 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 believe that different colors correspond to different wavelengths. Since waves, however, include 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 intellect arranges the raw material of sensations, but he never thought about what needs to be said, why the intellect arranges this material in this way and not otherwise.

With regard to time, the difficulty is even greater, since when considering time, causality must be taken into account. I perceive lightning before I perceive thunder. The thing-in-itself A causes my perception of lightning, and the other thing-in-itself B causes my perception of thunder, but A not before B, since time exists only in relation of perceptions. Why then two timeless things A and B act at different times? This must be wholly arbitrary if Kant is right, and then there must be no relation between A and B corresponding to the fact that the perception evoked by A precedes the perception evoked 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 yourself are in space and you imagine clouds that you cannot see. As Weininger pointed out, Kant's space is absolute, like Newton's space, and not just a system of relations. But I don't see how one can imagine an absolutely empty space.

The third metaphysical argument says: "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 they mean only parts of one and the same single space, moreover, these parts cannot precede the single all-encompassing space as its constituent elements (of which its addition would be possible), but can only be conceived as being in it. ; the manifold in it, and therefore also the general concept of spaces in general, is based solely on limitations. 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, according to Kant, their logical status is, 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 an inhabitant of the Alpine valleys could accept it. It is difficult to understand how something infinite can be "given". I must take it for granted that the part of space that is given is that which is filled with objects of perception, and that for other parts we have only a sense of the possibility of movement. And if it is permissible to apply such a vulgar argument, then modern astronomers maintain that space is not really 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 is also more clear to be refuted. "Geometry", as we now know, is a name that combines two different scientific disciplines. On the one hand, there is pure geometry, which deduces consequences from axioms without questioning 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 - it 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 raises when he considers space in a more general way. If we proceed 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 come to the conclusion that all real qualities in perceptions differ from qualities in their unperceived 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 a certain length (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 unperceived causes of perceptions. All this is based on the principle "same cause, same effect", with the 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 relationship between cause A and cause B.

We have, according to this view, two spaces - one subjective and the other objective, one known in experience, and the other only deduced. 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 by means of 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 situation is different, for if we keep faith in the imperceptible causes of perceptions, objective time must be identical with subjective time. If not, we run into the difficulties already considered in connection with lightning and g

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