Needless to say, all these shortcomings of the treatise gave researchers grounds to reject the authorship of Iamblichus. But, as we have said, it is not a matter of authorship and authenticity, but of the content of the treatise itself. And now we will say why this content should be presented as very significant in the historical-philosophical and historical-aesthetic planes. We will now try to formulate this significance briefly.

2. Positive traits

In the first place, in order to understand this treatise, it is necessary to be critical of the terms "number" or "arithmetic" themselves. In fact, this is not arithmetic at all, and if we use the Greek term, then for us it is not arithmetic at all, but, we would say, arrhythmology. However, strictly speaking, this is not even arrhythmology. The fact is that by his "number" the author of the treatise understands in general the structure of every thing and its indivisible wholeness. In that case, we would not even call it arrhythmology, but rather structuralology. It's not about numbers. The fact is that the author of the treatise, following the Pythagorean-Platonic tradition, and to a large extent following the entire ancient philosophical aesthetics, can think of the whole of reality only structurally. All things, in so far as they are the object of thought, are extremely clear, extremely distinct, always having a beginning, a middle, and an end. Therefore, when it is said that nine is ether, or five is a living body, or eight is two cubed (and since the two is becoming femininity, then the eight is femininity that has reached its three-dimensional bodily perfection), in all these cases only one thing is clear to us: everything in the world is structural, in matter, in bodies, and in souls. Both in the gods and in the entire cosmos. And if we approach this treatise not in a narrow arithmetical way, making ridiculous demands on it, but if we approach it structurally, then this whole treatise becomes a remarkable monument of ancient thought in general, which could only imagine everything in the world sculpturally.

Secondly, this structure, and ultimately this sculpture, is presented in the treatise not only persistently and persistently, but in its own way, in a surprising way, also consistently. And the most interesting thing is that this is not just a logical sequence (any philosophical sequence is a logical sequence), but also a purely dialectical sequence. And this is also interesting because there is absolutely no dialectical terminology in the treatise and, of course, there is no tabulatically fixed dialectics, which in its final form will be formed only at the stage of Proclus. But this sequence in the treatise is strikingly thought out and clearly formulated, although in view of the compilation-textbook nature of the treatise it requires a considerable effort of thought from the researcher.

Thirdly, in general, the dialectics of one and binary is given very sensibly. For if every thing is something, it means that it is a singularity; And since there are an infinite number of such particularities, it follows that there must also be a singularity in general, which is already higher than individual particulars and is their ultimate generality. Let us ask ourselves: is this not the simplest, and not the most comprehensible, and not the most elementary dialectic? Yes, this is undoubtedly dialectics, and undoubtedly ancient dialectics, nurtured by the ancient philosophical genius over the course of a millennium.

The same must be said of the two. If the absolute unity folds everything in itself, condenses everything in itself, draws everything into one inseparable point, then, of course, it is immediately necessary to formulate the principle of unfolding, the principle of eternal becoming, eternal going out of oneself beyond one's limits, eternal striving and daring, eternal searching. Yes, it is. But it is precisely the dual presented in our treatise that is this becoming, this unfolding, this eternally other-being daring. Let us forget about the arithmetical two and about those external operations that we perform with the help of the two in our everyday calculations and calculations. The best way to lose the essence of the Pythagorean-Platonic binary is to think of it as the arithmetical two of our school textbooks. Why, you ask, was the arithmetic deuce necessary? And this is because a philosopher must think clearly, and the most distinct thought is a mathematical thought. Therefore, the double that is presented in the treatise, while not being our arithmetical two, nevertheless bears the stamp of the last clarity and irreproachable distinction of one conceivable object from another. In other words, this binary becoming must also be understood structurally. The binary itself is not a structure; But it is more than a structure. It is the principle of internal filling and internal formation within any arithmetical structure. After all, structure could be understood too rationally, too discretely, when there are parts in a certain whole, but they are so disparate and so discrete that it is impossible even to pass from one such part of the whole to its other parts and the whole itself. It is precisely the binary that is offered to us that prevents any attempts to conceive of structure as something only separate. Yes, yes, structure is a single whole. But it is the dual that is precisely the guarantor that within this wholeness we can continuously and completely pass from one element to the other. The binary is the principle of the continuum present within any structure, in whatever separate and dissected form it may be represented.

Here the defender of the traditional multiplication table of our textbooks has a lot to learn. Each number is different from another number, such as 1 from 2, 2 from 3, 3 from 4, etc. But it is also true that between every two adjacent numbers there is a whole abyss of transitional fractional numbers; and this abyss is so incalculable that it is never possible to go from 1 to 2, or from 2 to 3, or from 3 to 4. We also need to learn to understand how we can suddenly go from 1 to 2 and not go from 2 at once, go from 2 to 3 at once and at the same time and not go over. This is a remarkable dialectic, and in this treatise it is beautifully represented by the theory of one and two.

Fourthly, the treatise not only establishes these two dialectical principles, but gives a consistent development of everything that is formed by these two principles.

It is clear, first of all, what a trinity is. If neither the one nor the binary spoke of any form or structure, then the trinity is a symbol of this first structure, where there is not only the indivisibility of the unit and the divisibility of the dual, but also their formation into a single figure. And then the quaternary is that which is the carrier of the structure, that is, the body, which in the quintuple is treated as a living body, and in the sixfold as an organism. Already at the stage of the six, thought encounters what is usually called the cosmos, since the cosmos is an organically living body, a mental-bodily structure. But this is still the beginning of the dialectical depiction of the cosmos. In the septenary, the cosmos is enriched by the presence in it of a ubiquitous and equally rhythmic well-being, which at the stage of the eightfold reaches cosmic panharmony, and at the stage of the ninefold - to the actively arranged sphericity of the cosmos.

This, in fact, is the end of the picture of the cosmos, thought out by the methods of dialectical arrhythmology. Only one question remains: what is the cosmos taken as a whole, if nothing else exists besides it? Obviously, it can now only be said that it is precisely the cosmos, and not something else. And this question did not arise before, because at the previous stages we were inside the cosmos and talked about those structures that are inside the cosmos, and only at the ninefold stage did we start talking about the cosmos as a whole as an actively landscaped sphericity. Now, after all these internal and external definitions of the cosmos, the question is raised about what the cosmos itself is in general. And as soon as we said that the cosmos is precisely the cosmos, this meant that from the cosmos itself we passed to the idea of the cosmos, that is, to its paradigm, by virtue of which it received its eternal arrangement. The decimal character characterizes the cosmos as the complete identity of the prototype embedded within it and the material corporeality of the cosmos. And only now can the task of dialectical arrhythmology be considered complete.

It has become a habit to present all these Pythagorean-Platonic numbers as a continuous and incoherent confusion, as incredible fantasy, or even simply as a mixture of childish naïve stupidity and mystical delirium. We allow ourselves to hope that the study we have proposed above for the first time destroys this age-old injustice, which almost all previous investigators showed in relation to ancient Pythagorean Platonism. It seems that in this treatise this is not a mess at all, but a consistently developed line from chaos to the cosmos, a line of primordial antiquity. Characteristically, among the definitions of unity, "chaos" directly appears, both in essence and even terminologically, in comparison with which the ten is a complete cosmos in itself in the fullness of its ideal predetermined and material realization. Whoever does not see the sequential arrangement of the philosophical material in this treatise is not only deprived of the opportunity to analyze this treatise, but also understands nothing of the thousand-year history of Pythagorean Platonism. True, the material of the treatise, as we have often seen above, is given both compilatively and ontologically, and often contradictory. But science exists to sort out any confusion and to bring the factual confusion of historical materials to complete clarity and intelligibility.

Fifthly, just as the term "arithmetic" appearing in the title of a treatise is usually misunderstood and misunderstood, it is also common and useless to imagine what "theology" is, which is also present in the title of the treatise as a grammatical participle from the corresponding verb "to theologize". It would be inappropriate here to cite and analyze the innumerable tastes of what theology is. We are not interested here in the ideas and tastes of the contemporary reader, but in the tastes and ideas that are present in the treatise itself. And in the treatise itself, "god" or "deity" and any myth in general is understood only as the ultimate generalization of various areas of the cosmos and the cosmos itself as a whole.

Let us imagine the sea as a whole, with all its geographical, physical, biological, and socially significant features, and not only now, but always, throughout all eternity. This is Poseidon as the ultimate generalization of the sea and everything marine. The same must be said of Demeter as the ultimate generalization of the entire agricultural region. And about Athena in connection with the generalization of honest and just war or heroism, and in another sense - as a symbol of wisdom. The same is thought of Ares, who is the ultimate generalization of a villainous, treacherous, and unjust war, or a war for war's sake.