Finite and infinite
Is the world infinite? It may seem that this question, at least the question of time infinity, is one way or another exhausted by cosmological models of modern physics. The fact that the cognition of the dialectic of the finite and infinite (as well as of everything in general) is not reduced to dry natural science models, especially to models of the physics field alone, "convinces the very kind of clear night sky," this majestic magnificence of the universe sparkling with a myriad of stars. As the poet said: "The abyss of stars opened was full; // There is no number of stars, the abyss of the bottom". The sight of the starry sky and even the thought of it awakens poetry and love of truth in man, i.e. philosophy. The infinity of the starry sky is the first image of infinity that opens to us. The universe opens up to our minds such an abyss, to the depth of which it is impossible to penetrate either by the power of clear and systematic thinking, or by amplifying our vision with instruments.
In our daily life, in everything that surrounds us, we come across finite objects, phenomena. By what means finite ! The geometric body is finite if its dimensions are limited. Finiteness over time is limited by some events. As Blaise Pascal said, "the finite will in no way find a firm support between the two infinities that embrace it, but they do not allow one step closer to themselves" ( Thoughts ). Finiteness can mean a finite enumeration, , so to say, a finite descriptiveness in space and time (and also outside these categories). Consequently, finite is bounded in space, finite-enumerable, temporary, transient.
And what does infinite mean? Aristotle says: there is an infinite where, when taking a certain amount, one can always take something after him. So, the sun is something finite: it can not be conceivable without something else, because to the reality of it is not only it itself, but the entire solar system as a heavenly whole. The solar system is also something finite, because every celestial body in this system has to do with each other) to the heavenly body. Moreover, the entire solar system has other systems outside of itself, and they are finite in themselves: the galaxy and metagalaxy are finite, and so on. Thus, everything that exists as something defined, has primarily a certain boundary, or limit, and is finite. If all the finite has a limit, then the infinite has no limit: it does not limit anything.
In our understanding of the infinite there are several aspects. First, by infinity we mean all sufficiently large or small enough, which depends on the conditions of the problem under consideration. For example, in comparison with human velocities, the speed of light (300,000 km/s) is practically infinite, so in everyday life we can dispense with the mechanics of Newton, not Einstein; Infinity here is something that goes beyond the limits of experience. Concerning the infinite, and the wisest are in the darkness of ignorance. In ancient Greece the philosopher Architas thought of himself as infinity: take a spear and throw it away; go to the place where it fell, and again throw in a straight line even further; and no matter how many times we repeat this procedure, we never and will never come across a border beyond which it would be impossible to throw a spear more and more. Hence, the space is infinite, because it's so simple and clear! So understood infinity G. Hegel called "bad": "No matter how far I move the star, I can still go further. The world is nowhere boarded up. "
So, secondly, in our minds is the image of "bad" infinity as unlimited possibilities for the repetition of the same thing. But this is only quantitative, and therefore limited understanding of infinity, an example of which is a natural number of numbers, which includes the possibility of unlimited addition of new and new units. Hegel considered this understanding of infinity to be wrong. In contrast to the "bad", true infinity, according to Hegel, is the process of constant going beyond the finite, but not only quantitative, but also qualitative, and even output > essential: one measure of the certainty of the system goes to a qualitatively different - both in the great and the small. Any arbitrarily large system is finite in space and in time. But as you move from one link of the hierarchy world into another one system of properties and relations passes into another, having its own measure, i.e. qualitative and quantitative certainty. And in this sense, infinity appears as a qualitative variety of hierarchically organized systems of the universe. True infinity is conceived as a process and in the sense that the Universe does not exist once and for all, there is a continuously creating reality. Nature is "whole, and yet always unfinished" (Goethe). The finite is the constantly emerging and vanishing moment of the endless process of changing things. Generally speaking, the infinite exists in a way that always takes a different and different, and the taken is always finite, but always different and different (Aristotle). The change is generally associated with the output of the system for its spatial, temporal, quantitative and qualitative boundaries. The never-ending web the connections of things, the phenomena of the world, their energy-informational interactions is a continuous way beyond the individual finite. Being, as infinitely defined, is in change, motion, in the again and again realizing of the positing of a new and new certainty and in the death of this certainty and the generation of a new one, this is why we are compelled to see a truly infinite being, and not in the negative infinity of space and time itself .
True infinity - is the process of a constant qualitative neoformation, which includes the infinity of space and time, the dialectically unfolding process of finding boundaries and their loss, achieving equilibrium and, at the same time, striving to violate it; a constantly, strenuously pulsating process of unity of opposites. Infinite, turning into a finite, gives all the variety of actual existence of concrete things and processes. In this sense, potential being, as infinite, generates an infinite variety of possibilities and an infinite number of finite bodies and phenomena that are actual. Here is the third kind of philosophical infinity.
Fourth, the infinity of time is expressed by the notion of eternity, which can be inherent only in the world as a whole, every concrete system of which is transient. But eternity is not identical with time infinity, but only contains the latter, as explained above. Especially eternity is not identical with the mathematical infinity of the time interval. In quantitative terms, eternity is expressed in the actual infinity of the successive intervals of existence of systems and events (centuries, millennia, etc.). In qualitative terms, eternity is associated with an infinite sequence of changes in the forms of existence.
Fifthly, epistemological infinity is conceived as, in principle, never a complete process of expansion and deepening of cognition by the subject of objective reality. Compared with past generations, we know about the world incomparably greater, but there is still an abyss of the unknown, which will be comprehended by the next generation.
Finally, sixthly, there is a mathematical understanding of infinity. At its origins (Guk, Barrow, Newton, Leibniz), mathematical analysis freely treated infinitesimal and infinitely large quantities. The subsequent development of the foundations (Cauchy, Dirichlet, etc.) expelled the actual infinity, replacing them with potential ones. Practically this meant that number (infinitely large or infinitesimal) was replaced by the process ("infinitely large" or "infinitesimal" sequence). Comprehension of infinities as genuinely potential becoming, led to the theory of algorithms, as well as intuitivistic and constructive approaches to the foundations of mathematics. The actual infinitely large and infinitesimal (that is, the numbers incommensurable in size with the "usual" finite) suddenly resurfaced in the so-called non-standard analysis. Philosophy inevitably encounters varieties of mathematical infinity when it wants to express the qualitative content of other types of infinity.
Let's return now to the already mentioned cosmological models. The simplest of them proceed from the assumption of spatial homogeneity and isotropy of the Universe on a large scale. In other words, although the matter is distributed unevenly in space (there are stars, galaxies, galactic clusters, interstellar and intergalactic empty space), it is believed that in "very large scales" all this unevenness should be neglected. Obviously, here lies the notion of the infinity of space in the first sense: size space in general is recognized as immeasurably large even size individual galaxies. In cosmological models there is a parameter that has a sense of time (cosmological time ). In his choice there is a certain arbitrariness, i.e. it is not "absolute time". The radius of curvature of space depends on cosmological time. Visually changing the curvature of the universe can be imagined with the help of a rubber ball: when inflating it with air, the radius increases, and all distances between points on the surface increase proportionally. The radius of the universe is increasing from the starting point with zero radius to some maximum value - the universe expands (like a rubber ball). The expansion is replaced by the compression phase, which ends again with zero radius, i.e. transformation of the universe into a point, etc. In other words, before us is a pulsating world in which an infinite extension of the "starting point" occurs. It should be borne in mind that near the very moments of the beginning of expansion and final compression, the space-time representations of the classical general theory of relativity seem to become inapplicable. A certain yet unknown synthesis with quantum theory must be realized here. At the points of the Big Bang and the Big Compression, the spatio-temporal forms of the existence of matter acquire a qualitatively special character. Physicists believe that this coming synthesis will give us a new understanding of the "act of the birth of the material universe."
So far, the problem of infinity was considered by us in relation to the cosmic scale of the existence of matter; we dealt with the so-called extensive infinity. But the world of equally infinite depths of the smallest particles of matter is the so-called intense infinity. From areas in millions of light years, a human thought penetrated the region of the order of trillionths of a centimeter. It is possible that there the space and time have special properties, which can be indicated by the so-called "ultraviolet divergences" quantum field theory.
Thus, we are surrounded by a double infinity. Around us is the infinite extent of the Universe, in which not only ourselves, but the Solar system is just a kyle in a vast ocean. And on the other hand, deep into the infinite complexity of the world, in which each drop of water in itself forms a kind of universe. We are as if in the middle between infinitely large and infinitely small. At one time, Anaxagoras introduced the concept of infinite divisibility into philosophy: "In the smallest there is not the smallest, but always the lesser." The division of the spatial extent extends to infinity, not reaching zero, of the mathematical point. If the world is infinite in all directions, then the universe can not be the middle.
The middle of the universe is the human domain, the world of times and distances that we feel. If we can talk about an infinite universe (at least conditionally), resorting to the idea of the middle, in order to somehow comprehend our place in the world, then perhaps we can resort to how the great Aristotle defined the middle: "The middle is what the itself follows another, and what the other follows. " Further Aristotle says: limited is generally always middle. The middle is a macrocosm, only relative to which the microcosm of elementary particles and the megamir of Cosmos are defined. The dialectic of existence: the infinite is revealed through the finite and in the finite.
Processes and objects in the world are finite, but the totality of finite processes and things is infinite. There are no boundaries beyond which there could be something that is not covered by the notion of objective reality: it is in everything, it is everything. The concept of the boundary makes sense only in relation to the finite. And our imagination absorbing the distance, and the cosmonauts of the future will not be able to meet such a supernatural obstacle as nonexistence.
Let us emphasize in conclusion: the task of philosophy is not to offer a final solution to the problem of infinity. Relying on the whole array of concrete scientific knowledge, on the history of cognition, culture as a whole, philosophy reveals the deep meaning of the search activity of theoretical thought aimed at solving one of the most mysterious secrets of being. By what experiment can the principle of infinity of the universe be checked? We know the finite systems in the composition of the now visible whole. And since the infinite consists of finite formations, then, comprehending them, we through the finite enter into the mystery of the infinite.
Man's experience of the abyss of the universe and the impermanence of his being
Theoretical thought has long been known - as a philosophical conclusion from the achievements of scientific knowledge - the infinity of the universe, containing immensity of worlds and world systems: "In human life there are moments when we forget that we live only in one point of an immeasurable Universe." However, attempts to comprehend the essence of this phenomenon caused far-reaching ambiguous feelings among thinkers with different emotional spirits. Thus, for B. Pascal, the very idea of infinity, to which man is surrounded in space and time, was the source of the dreary, depressed state of the soul. He said that man is only a thinking bubble, lost in a terrible, uncomfortable and even hostile abyss. The entire visible world, according to Pascal, is nothing but an inconspicuous stroke on the immeasurably vast field of existence. No thought can cover these immense spaces and times. No matter how much we strain the thought, we get all the same only atoms in comparison with reality. This is an infinite sphere, in which the center is everywhere, and the circle is not nowhere ... Returning to himself, continues Pascal, let the person think what he is in comparison with what is in nature; let him imagine how he is lost in this remote corner of nature. Let from this little prison given to him for residence - I mean the world we see - learn to give real value to the earth, to cities, to states, to oneself ... Who will consider himself in this way, that, without doubt, will be horrified, seeing that it seems to be hanging between two abysses - between infinity and nonexistence, it will shudder at the sight of these miracles. He is infinitely removed from the extreme points: the end and the beginning of things for him are unquestionably hidden in the impenetrable darkness; he is equally unable to see that nothing from which he is extracted, and the infinite that must absorb him.
F. Hegel, as it were, echoed Pascal, saying: "Since the intellect comprehends the infinite only as something negative, and thus as the otherworld, he believes that he exerts more honor to the infinite, The more pushes him away from him as something alien. "
Time is the form in which, according to A. Schopenhauer, nothingness of things opens before us as their impermanence, because this is it, time, under our hands turns all our pleasures and joys into nothingness, and then we ask ourselves with surprise: where did they go? The very nothingness is, therefore, the only objective element of time, in other words, only it, this nothingness, is that which corresponds to time, and in the inner essence of things what it is, time, is an expression . That is why time serves a priori as a necessary form of all our perceptions: everything must appear in it, even ourselves. And because of this our life is primarily similar to payment, which is all calculated from copper cents and which must still be paid off. These pennies are days, maturity is death, for in the end time is an estimate that nature makes to all of its creatures: it turns them into nothing. Such are the views of Schopenhauer, developed in the work, the very name of which is filled with gloomy pessimism: "On the insignificance and sorrows of life."
The culture of the philosophical mind whispers to me: This can be disagreed, but it must be known. I vaguely remember: once and for someone I read that long and intense thoughts on this topic (extremely interesting, but oppressive to our soul) for some end up in the wrong in their mental attitude.
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