Now, after a painstaking study of the entire treatise line by line, we consider ourselves entitled to formulate quite freely all the positive and all the negative features of the treatise. Our attitude to this treatise, contrary to the opinion of most researchers, is dictated not only by the positive, but also by the sublime nature of the impressions we received from its analysis. Let us first speak of the negative aspects of the treatise, and we will immediately see that the denial of its authorship of Iamblichus is not so unfounded. The point is only that the question of authorship itself is of little interest to us, since it does not matter whether this treatise belongs to Iamblichus himself or to someone from his school.

1. Negative traits

There are a lot of negative features in the treatise.

Firstly, all the materials in the treatise are presented in a very disparate, confused, often even simply contradictory way. Therefore, when the opponents of the treatise considered this work too compilative, they were right. This is a compilation, an anthology, a reader, and just a set of very interesting, but poorly coordinated materials.

Secondly, this external compilation corresponds to the frequent absence of an internal system. On the one hand, it seems that we are talking here about numbers. Nevertheless, conclusions are sometimes drawn really from numbers; and for the most part these conclusions have nothing to do with arithmetic, but are purely philosophical. But the matter is not limited to philosophy. Right there, and very abundantly; mythological materials are also used, often far from what we know from the actual history of ancient mythology. Last but not least, etymological considerations, which can now only be regarded as fantastic. Finally, the author does not hesitate to give purely accidental examples of the significance of this number, such as the fact that the septenary determines the possibility of the birth of a child after a seven-month stay in the womb, or that there are seven planets, etc. All such observations are often so naïve and accidental that we have always avoided expounding them in full in the preceding one.

Thirdly, and finally, although the author of the treatise is always based on Pythagorean Platonism and even makes some references to the corresponding authors, nevertheless the historical-philosophical side is presented, it must be said, rather sparingly and poorly, which, of course, cannot but disappoint in the study of Neoplatonism, which in all important and unimportant questions always makes references to classical philosophical literature.

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.