Book: The Wisdom of the Eternal Laws.
After considering the principles, we shall now scrutinize one of the most important fields of Mathesis Megisthe, perhaps the most important of them all: the study of laws, of the logoi qua laws. It is no longer, as before, the logoi arkhai whilst pure possibilities, qua arithmoi arkhai, but of the laws as such, of the laws that (descending from the plane of principles to plane of manifestations], effectively rule over all orders of reality.
We reach those laws through speculation – as studied in our previous works. Such speculation is also done with a certain analogy with the Pythagorean thought. It was based on the sacred Pythagorean Decad that we “reconstruct” those laws, reason why we called them the Pythagorean laws. Such ascription does not necessarily have a historical sense, i.e., does not imply that the formulation we give to those laws were, in fact, that that were effective within the Pythagorean school, but we believe it is perfectly coherent with the Pythagorean secret conception of Mathesis.
Since, in philosophy, we only accept the authority of demonstration, it behooves us to not only present those laws, but demonstrate them; and not only demonstrate their validity, but also demonstrate them as fundamental laws of all beings. Nonetheless, we shall not dwell on those demonstrations unless strictly necessary, since we can rely on thesis, arguments and postulates already stated in our previous books.
By saying that the attribution of those laws to Pythagoras has no historical sense, we indicate that it has a logical and doctrinal one. They are perfectly coherent with the Pythagorean thought and, as we have already stated in Pythagoras and the Theme of Number, represent what he could have reached – if he had not actually reached – if he had coherently prolonged the consequences and applications of his thought according to the principles he postulated. Presumably and verisimilarly, we can state that those laws should have been Pythagorean laws. Naturally, a historical demonstration would be impossible, since the works on the esoteric parts of his doctrine has never come to us, if they had been written at all. Supposing they had been written, they can be currently known only via fragments of scattered works by Pythagorean authors. Based on those universally accepted texts, we gathered elements to substantiate the reconstruction of those laws, at least on their ontological and mathetical aspects. Given the coherence of those laws with the doctrine expressed in the referred texts, we can assume that the demonstrations of their validity, as we present it, must be similar to the ones known by the Pythagoreans of the third degree and they should have come to the same conclusion through the development of their thoughts according to the dialectical laws of consequence.
However, the question of historical validity is not our primary interest. What matter is that, Pythagorean or not, those laws are valid. If, throughout the following analyses, we should extract arguments from Pythagorean texts, we must seek, on the other hand, to strengthen our arguments in accordance to our way of considering things (i.e., Concrete Philosophy).
First and foremost, whenever referring to Pythagoreanism, one should not mistake the arithmoi mathematikoi, which belongs to the inferior triad, with the arithmoi arkhai, of the superior triad. The latter corresponds to the Platonic “forms”, the Augustinian “exemplary ideas”, to the Neopythagorean and Neoplatonic paradeigmata, i.e., to the universal Ideas, eidetically (and not only noetically) considered.
Another important distinction is the existence of two ways – or levels – of considering the logoi, or principles. On one hand, we can consider them as archetypical forms, exemplary ideas, arithmoi arkhai, paradeigmata – or yet as, according to the scholastic terminology, pura possibilia, pure possibilities – and, on the other, as laws or norms that rule and reign over the existing things. In this last case, the logoi are norms not only for their noematic content, but also for the purpose effectively performed. It is of the laws in this effective sense that we shall, herein, discuss.
Those laws – that rule things – constitute what the Pythagoreans identified as the “Sacred Tetrad”, “Tetractys”, also known as Sacred Decad, since the sum of the first four numbers (1+2+3+4) is ten. They called this set of ten laws, the “Mother of all Things”, as referring to the matrix, the source that, ruling, repeats and, by repeating, makes repeat, produces repetition, makes emerge the similar things and the things that, being dissimilar from some, are similar to others. Those ten laws can be identified as Law of One, Law of Two, Law of Three, etc., until the Decad.
- Law of Unity
Law of One would, consequently, be the Law of Unity. Now, the principle of all things has to, necessarily, be something positive: if the existing things are positive, their principle ought to be positive. The positive principle, the affirming principle, which testifies itself and positivates itself, is precisely what is called Being. The principle of all positive things is Being. Nothingness cannot be the principle of anything. Unity, as stated before, is characterized as indivisum in se et divisum ab alio (undivided in itself and divided from everything else).
Therefore, unity is the law of integral. In all and any form of existence, its being is one. All that is being, all that we can admit as presence or adsence, must be a unity. The unity and the being are mutually convertible. Where there is unity, there is being; where there is being, there is unity. The number 1 symbolizes the first law. The one is the first law that rules all things. The law of unity imperiously rules the being, since it is one. Only nothingness is not unitary, since nothingness is nothing.
There is, certainly, a hierarchy of being, a hierarchy of intensist levels of the being; each being participates on the unity according to its own level of intensity, which, by its turn, is “comproportionate” to the nature of each being. But, whatever the level of intensity, all things are unities: on a higher or lower level of intensity, always unities. The law of unity presides over all beings, which participate, thus, in the Supreme Unity of Being.
The utmost unity is the absolute unity of the simple simplicity of the being, of the Supreme Being, which is only being, without deficiency. All that exists depend on the Supreme Being. All unities originates from “It”; all beings participate in this One, participate in the great law of integral, in the Supreme Law of One, that rules all things. All that is finite is unitarily what it is and tends to become an integral part of a unity. No thing happens that is not unitarily (according to higher or lower intensist levels, it doesn’t matter). This law is the supreme logos, the first of all laws: All that is finite is unitarily what it is and tends to become an integral part of a unity.
Now, the arithmetical number 1, the arithmoi mathematikoi 1, symbolizes unity and, therefore, can also symbolize everything that exists, can symbolize all entities in what they have of unitary. The 1 symbolizes all things whilst unitarily considered. Founded on genuinely Pythagorean texts, we can verify that, according to them, the Supreme Being One, which is absolutely simple and which essence and existence are identical, a pure form, a pure logos, is, in the Pythagorean terminology, the “Father”. This “Father”, who is the One considered in itself, generates a “second one”, which is the One considered as operation, as operatio. It is generated by a procession in intra. From this generation in intra emerges the Creator One, which is precisely denominated “Son”.
The Indeterminate Dyad
The same conception can be found in Christianity: the Father and the Son emerge as the symbol of the narrowest of the correlations, since the Son is son of the Father and the Father is father of the Son, so that the affirmation of one is the affirmation of the other.
In philosophical language, the first One, which is the Hen Prote, is existentially and essentially itself, immutable and eternal: the Being whilst Being is absolutely being, immutable and eternal. But this Being is active, it acts, performs, operates. Such “operation” is a second role of the same Being and implies choice, predilection and pretermission (between possibilities), implies, therefore, intellection, intellect. Thus, the Hen Prote, the First One, is pure Will, Wanting, Omnipotence, whilst the Second One, which performs what the potentiality of the First One can, is intellect. The Second One, the Hen Deuteron, the Hen generated from the Supreme Being, has a creative function. This second Hen is what will properly give rise to the so-called Indeterminate Dyad, the Pythagorean Hen Dyas Aoristos. It is a dyadic One, the Son, the Creator, which is the Being whilst it operates, creates. But it is not abysmally separated from the former, since one is the other, but operating on a second function.
Now, why is the Dyad called indeterminate? The dyad is undetermined because determination implies determinability. Our mind is, by nature, abstractive, has the tendency to separate in distinct concepts what, in reality, happens identically (i.e., united, as unity). Now, the indeterminate dyad is characterized by a power to unlimitedly determinate, by an undetermined capacity of determination; and, in turn, determination necessarily implies that something is determined. To have an undetermined determination, is necessary to have a undetermined determinability, i.e., something that can receive unlimited determinations. Which means, each active power must correspond to a passive power; an active potentiality, to a passive potentiality; so, translating it into a Aristotelian language, we can reduce to the following terms: act can always determinate, and potentially is always determined; but an absolute determination is impossible, since it would be an actuality and there would be a contradiction in adjectis, since infinite is the endless power to determinate and, if everything was already determined, the determined would have reach the limit of its determination; moreover, a determining being, as such, if fully actualized in the determined actuality, would reach the quantitative unlimited in actuality, which is absurd. Therefore, the act of determinate implies a limit, the limit of determination, and it limits both the determined and determinable things.
But what is determined is unlimitedly what is determined; what has received a determination is, as such, unlimitedly itself, but limited by what is not it; and is also limited in what it is, since it is until where it is, inasmuch as it is what it is. Thus, the creative action realizes the unlimited, which is, as itself, unlimited itself, but limited by itself inasmuch as only is what it is whither is what it is, and limited by what is not it, which is what it is not yet possible to be. The determined is not limited by nothingness, since nothingness does not limit, has no capacity to limit; it is limited by the own form of the created thing and such limitation consists of possibilities of not-yet-actualized determinations.
As we have demonstrated in Pythagoras and the Theme of Number, the Indeterminate Dyad is potentially infinite and it is all that can be determined; is, simultaneously, the infinite potentiality to determine and the infinite potentiality of being determinate. In this case, the formative act can endlessly determine all that can determine, and the material potentiality, which is passive, can endlessly be determined in all that can be determined. We are dealing with a potential-quantitative infinite and not an actual-qualitative infinite, since the latter, as we know, is absurd. Now, the Indeterminate Dyad has no limits in itself; it is undetermined and unlimited as such, but limiting and determining in its acting. Those two aspects are not independent, since were created by Hen, by “One”, depending on it and not having, hence, the absolute simplicity of the Supreme Being, nor having, this Dyad, Its infinity (of the One), which is eternal. The Dyad has no actual infinity, but only a potential infinity, which is given by the power, by the infinite potentiality, active, to determine without final limit.
We find in this thought the foundation of the Pythagorean “ab aeterno creation”, since the Indeterminate Dyad has no beginning in time, since time would imply determination and determined things. Time starts when the formative act shapes a materiable potentiality. Time refers to limitedly determined things. Thus, the Dyad, which is not eternal since is not tota simul durable, contains the most diverse relations. Hen, therefore, is not temporal, since time can only occur in the succession of the determined things by that generated Dyad; Hen belongs, therefore, to a tota simul duration, whilst the Indeterminate Dyad is not simultaneous in its determinations, but in it occurs a succession, so that the duration of this dyad is sempiternal, happens through a succession, whilst Hen Prote and Hen Deuteron are both eternal.
 “The logos of an entity is its law of intrinsic proportionality, the reason of its essential form, which synthetically expresses the entire range of possibilities of manifestation of that entity (…)”. (Editor’s Note)
 The sentences between brackets were added by the editor of the republished version, Olavo de Carvalho. Such edition has several explanatory footnotes, which we shall translate whenever indispensable.
 The superior triad encompasses: 1) the arithmoi arkhai or archetypical numbers that express the supreme principles (object of the three first volumes of the Mathesis’ series); 2) the structures of the real being (the laws studied within the present book); 3) the forms (arithmoi eidotikoi) of the particular real entities. The inferior triad comprehends, also in descending order: 1) the mathematical numbers; 2) the geometric forms; 3) the sensible things.
 On his book The Wisdom of Unity.
 A term proposed by Suarez, from the latin word adsum, as to substitute presence when referring to the being a se, since presence indicates a relation, a “being in face of other”, such as happens to the being ab alio. God has adsence; we have presence. (Editor’s note)
 Or levels of intensity, cf. Lupasco.