Another circumstance that in recent decades has constantly led the terms "symbol" or "symbolism" to complete discrediting is the activity of many of those writers who, beginning in the last quarter of the nineteenth century, specifically called themselves "symbolists" and their trend "symbolism." This trend failed to explain and formulate what was contained in the theory of symbolism. If we take, for example, Russian or French symbolism, then for half a century there was not a single author who would have given a detailed theory of the symbol, except for individual remarks or small arguments. And since symbolism was too refined and unpopular in wide circles, the term "symbolism" itself also turned out to be unpopular, almost unstudied and, from the point of view of most readers, simply unnecessary and negative. However, even here the history of aesthetic doctrines protests against such a narrow and so little analyzed concept of symbol, which we find in the symbolism of recent decades. The understanding of the symbol, as the history of science shows, is extremely broad and diverse, and in a certain sense even necessary for both science and art, and moreover, not in the case of any backward state, but at the stages of their advanced and flourishing development. Here we must abandon not only Plekhanov's hieroglyphs, but all theoretical narrowness in general, and consider this subject simply in its essence, consider it historically and consider it freely theoretically.

It is necessary to assimilate most clearly the theory of symbolism, which is strong in physics, mathematics and other sciences, and which, under the influence of Mach and Avenarius, turned out to be a fairly popular theory among natural scientists. These latter wanted at all costs to renounce the obligatory recognition of the objective world, or rather, simply not to take it into account.

They reasoned as follows. Whether the world exists or does not exist is your own business; And think as you want here. As for us, natural scientists, we only care about what is in our sense perceptions, and that at the present moment; All these laws of nature, and nature itself, are nothing more than a complex of human sensations, which yesterday were one, today another, and tomorrow there will be a third, and so on ad infinitum. There is no truth, but only subjective images, hypotheses, equations, fictions, symbols.

This kind of philosophy is a complete distortion of ordinary, natural, and purely human experience. The latter has always said, is saying, and will continue to say, that although we do not possess absolute truth, we are always striving for it, and that scientific constructions are not at all only our illusions, only our fictions, supposedly created only "for the convenience" of thought itself, and are not at all only subjective symbols.

The famous mathematician A. Poincaré said that the laws of nature are created by us only for the "convenience" of our own thought.

Symbols in science or in art must not transform nature and the entire objective world into mere subjectivist symbols. Otherwise, all our study of world symbolism, from primitive thinking to the present day, will remain an empty and useless exercise.

If we agree to understand by symbol first of all the reflection of objective reality, and only then everything else, then there will be quite a lot of this rest.

If anyone is interested in the question of how the concept of the symbol has been gradually extended, he should first of all look at the definitions of the symbol which are given below, in § 1 of our bibliography, which gives first of all such general publications as encyclopedias and dictionaries.

If we take Russian encyclopedias and dictionaries of the 18th and 19th centuries, then basically the symbol here is understood simply as a sign, without further explanation. But already in the Brockhaus-Efron encyclopedia there is a great expansion of the horizons in which the symbol can and should be used. Let's skip symbolism as a specific trend in literature and art of the late 19th and early 20th centuries. However, even here the term "symbol" reached such a semantic expansion that in 1910 A. Bely counted twenty-three different definitions of this term (below, pp. 274-284).

Let us make one more remark before passing on to the positive theory of the symbol. That the subjectivist-symbolist theory does not suit us, we have said enough about this. But there is another enemy to the objective theory of the symbol, which rests on the obvious fact that no symbol can only be dissected, only analyzed, and that it necessarily also contains that which is no longer analytical, of which the symbol is an expression. Again, this is obvious. However, in the pursuit of the objective objectivity of the symbol, the structure of the symbol itself cannot be ignored. It is necessary to be able to combine analytism with that synthetism, without which it is impossible to understand the symbol as a function of reality at all. In this regard, S. S. Averintsev writes in his article "The Symbol": "The existentialist philosophy of M. Heidegger generally removes the problem of the analytical interpretation of the symbolism of poetry in the name of the "pure presence" of the poem: "We know the mystery in no way through the fact that we expose and dissect it, but solely through the fact that we keep the secret as a mystery" ("Erlüuterungen zu Hülderlins Gedicht", Fr./am M., 1951, S. 8, 23). This anti-analytism has its basis in the objective nature of the symbol and can be "removed" only in a positive theory of the symbol that is able to fully take into account its rational and non-rational aspects, without mystifying the latter. It is precisely this kind of positive theory of the symbol that we must now strive for.

When we embark on the path of free theoretical-historical investigation, we are at once convinced that the concept of symbol comes very close to other neighboring concepts, and often so closely that it becomes a very delicate task to distinguish it from these neighboring categories. But, as a matter of fact, this is how it should be in history. That which we have theoretically singled out and opposed to the other, in fact, in the real-historical works of "science, literature and art", turns out to be closely intertwined with its opposites and often passes into them. Plato's famous ideas or Aristotle's prime mover, on closer examination, turn out to be nothing more than symbols. Leibniz's monadology or Teichmüller's personalism are undoubtedly fundamentally symbolic. On the other hand, such a positivist as I. Taine, who understood beauty as an idea seen through temperament, undoubtedly used the concept of a symbol. Bergson's "creative evolution" and all of Freudianism are symbolic through and through, although the corresponding authors avoid using the term "symbol." The doctrine of G. Cohen and P. Natorp about hypothesis, method, and law is also essentially symbolism, and Husserl was prevented from being a symbolist only by his overly contemplative theory of eidos.

All this does not mean that opposites historically merged into one or another unity should not be logically opposed by us. On the contrary, only a clear logical opposition of what is opposite, only this can become the basis for understanding the actual interweaving of opposites in history. Therefore, the clear logic and theoretical dialectics of the symbol should not frighten us in any way, but, on the contrary, should help us to understand historical reality.

Tentatively, it can be said that the essence of a symbol includes that which is never a direct datum of a thing or reality, but its givenness, not the thing itself, or actuality, as a product but its generative principle, not its proposition, but its assumption, its positing. Mathematically speaking, a symbol is not merely a function (or reflection) of a thing, but this function is here decomposable into an infinite series, so that if we possess a symbol of a thing, we have, in fact, an infinite number of different reflections or expressions of the thing, which can express this thing with any precision and with any approximation to the given function of the thing.

Another very important mathematical model for constructing the concept of "symbol" is the extraction of the root, which cannot be expressed with the help of a finite number of arithmetic signs. Thus, for example, extracting the square root from the number 2 or from the number 3 can never arrive at a final result, since the square root of these numbers is said to be "not extracted." Here we get as the root one whole unit and an infinite number of decimal places. No matter how many decimal places we calculate, we will never get the exact square root of 2 or 3. The more we calculate (9) of these decimal places, the more precise our root will be, but in the final sense only an infinite number of decimal places could give us an accurate idea of this root. Nevertheless, one circumstance plays a decisive role here: these decimal places do not arise haphazardly, not randomly, not chaotically, but by virtue of a certain law and in the form of a certain system. Our schoolchildren know this law and this system very well when they begin to calculate the square root of 2 or 3. After all, there is a certain rule for obtaining any number of decimal places in this case. This means that the emergence of the latter is subject to a certain law, a certain system. We cannot get an infinite number of decimal places. But still, school mathematics is enough to understand what this square root of 2 or 3 is. And any schoolchild who has studied the basics of mathematics in high school is excellent at operating with these irrational quantities, no worse than with rational ones, since irrational quantities have their own special rules. So the symbol is a kind of task that cannot be calculated accurately and carried out with the help of a finite number of quantities. And yet it is something absolutely precise, absolutely lawful, and in the most ideal sense of the word systemic.