Mathesis Megiste

Chapter One[1]

Mathesis Megiste is a Pythagorean expression that, translated into English, means supreme instruction. Pythagoras taught his disciples[2] about a knowledge of which man has a potential ownership, partially actualized only by a few sages, and transmissible to learners once duly prepared to assimilate it.

The fundamental first steps were Mathematics, Logic – the art of Reasoning – and Music. With those three preliminary disciplines, the disciple’s mind was equipped to penetrate the mathesis, synthesis and apex of all possible knowledge and means of leading mankind to the transparent comprehension of all fundaments of every science, although lost or veiled pathway.

Mathesis Megiste is the supreme instruction. The term mathesis origins from two roots: ma or man, which means thought, and thesis, meaning position. Properly, Mathesis means positive thought and megiste, superlative of mega, means maximum. The maximum positive thought.

There are four forms of human language: the pragmatic, common in daily conversations; the religious, which – used in religious texts – is a symbolic, metaphorical and allegoric language; the scientific, in which man confers clear concepts to the things he classifies, in order to transform those concepts in instruments of man’s work; and, finally, the divine or philosophical language, which is the Mathesis Megiste, apex of all languages, where the concepts reach its maximum purity and validity in all fields of human knowledge.

Mathesis Megiste constructs a universe of valid discourse for all spheres of human knowledge whilst each different discipline has its universe of discourse restricted to its field. Mathesis Megiste seeks a universal language.

One sector of Mathesis well known to mankind is Mathematics, which language is universal. Since Mathematics is a part of Mathesis, one can say that Mathesis – a generic – is a type of Meta-mathematics, its meta-language, to which one could similarly reduce the other languages related to the different disciplines.

One can easily observe that, throughout the work of all great philosophers, all of them have grasped – at least partially – the matter of the Mathesis. All through Philosophy there is the “discovery” – let’s for the interim use this term – or the revelation of a series of axioms, which are considered as truth per se notas, i.e., as self-evident truths. They do not require demonstration and provide the means to the discipline. Accentuated in the work of the truly great philosophers, these axioms – found either inductively or through eidetic reductions – will constitute a type of “cosmos” with such rigid cohesion that, far downward, they are all united by a single principle, their eidetic source and origin, from which they could have been deducted once there is a method able to extract the virtually enclosed judgments within these fundamental principles. Based in twenty-five centuries of philosophical thought, the purpose of this book is to demonstrate that mankind can achieve it at the present time.

The Pythagoreans affirmed that this science was known by Pythagoras, who could not transmit it to his disciples for not having found them able to receive it, for it is said that of such he complained to his wife Theano and his daughter Myia – his best disciples – as the reason he kept it as a secret, which was not because he wanted to, but for the absence of whoever had ears to hear or eyes to see. Pythagoras was only a practical esoteric, not a theoretical one. He had not intent to keep the knowledge to an elite, as stated by his enemies; he actually wanted that knowledge widespread. Nonetheless, the superior knowledge could not be accessible without previous training and initiation. Otherwise such knowledge would not be properly assimilated, and could be a factor of new confusions. Therefore, it was essential to form groups able to spread it, but not without preparing in advance those who should receive it. Pythagoras wanted to be the good sower: to sow not on dry land, but on properly prepared ground, able to receive the seed.

This is one of the most important and greatly ethical points of all esoteric movement, namely Platonic, Aristotelian and Pythagorean. The secrete thought was hidden not for the mere intention of to be given only to a select group or to remain hidden, but for the reason that it could not be just given to those with no prior preparation. The intention of Pythagoras with building his famous Institute was to create masters, able to disseminate the knowledge and previously prepare those who would receive it. Thus being good seeders, as in the parable of Jesus.

Mathesis Megiste, therefore, aims to be the apex of knowledge, the point of convergence of all disciplines when speculatively treated. Therefore, it has as its object – or its search – the principle (arkhé). The philosophical speculation ought to spin around the principle – or the arkhé, as called by the Greeks – as expressed in the Gospel of St. John, when he says: “In the beginning (arkhé) was the Word (Logos), and the Word (Logos) was with God”. Logos, here, is the ultimate sense of wisdom (sophia), as we shall see in due time.

For obvious reasons, the principle must naturally be confused with what in all religious ideas is called God, since He is always considered, in all of them, as the principle of all things. Mathesis does not dedicate to study God as God, but the principle as principle. It is a different speculation, without excluding the possibility of offering a mathetic foundation to the theological thought.

As our world is dominated by banausia, i.e., the spirit of the specialist, forcedly brought by the technical, scientific and economic development, inevitably these specialists find it difficult to have a common language so they can communicate amongst each other. However, over the past twenty-five centuries, all of the great philosophers intended to transform Philosophy into Mathesis Universalis, able to serve as a point of communication. They all intended to build a philosophical language capable of unifying mankind so that everyone could be understood regardless the variety of disciplines. That is a fair intention, and also, as we shall see, reasoned and justified, and man must necessarily seek it. Subsequently, the purpose of Mathesis is not only the knowledge of the truth, but also the search for an instrument, a suitable language to allow mankind to communicate, not descending to the inferior matters (such as sports, a common subject amongst men of culture) but ascending to a language higher than their own disciplines, upwards and converging to a common point.

It is convenient to distinguish between speculative philosophy and practical philosophy. The first seeks to establish the true and the false, whilst the practical philosophy, a philosophy built by man in his factual activities, naturally does not concern about the truth, but about what is right or wrong.

When analyzing the human ideogenesis and the volitional operations of the human beings, inasmuch as mankind develops a philosophical language, reaching the expressing intelligible species, it works with more pure concepts. Understanding usually tends to the speculative. The Speculative Philosophy is the result of higher human understanding operations. Now, one can observe that the will – orexis, a rational appetite for the goodness – tends to choose between things because those things that are considered desirable benefit the one who desires. The will rationally tends towards goodness, to the convenient things. This orexis naturally drives the human being to all practical achievements and it is an exclusive aspect of the human beings apart from other beings, deprived of will. One can thus consider Practical Philosophy as the higher product of will put into action, i.e., the intellectual achievement of man on his own practice, on his drama, on his action of dominating things and organizing it, on having a vision of his world, which is, still, a product of the will. Therefore, the understanding, taken to its ultimate consequences, reaches Speculative Philosophy, and the will, in its maximum achievement, reaches Practice Philosophy. It is important to properly distinguish these two worlds.

One of the major problems that arises in Psychology – and the subject here is not the trivialities of today but the speculative approach, the Philosophy of Psychology – is to know the nature of the understanding and the nature of the will. Are they both functions of a single principle or derived from two different principles? Later on, those discussions should be easily answered.

Nevertheless, the result – as Mathesis shall demonstrate – can only be one: they have the same origin. Human wills must have the same source. It cannot be explained by physical chemistry, as some modern psychologists do, because the choice of the good, the choice of values, cannot be solved by physical chemistry. Nor can it be explained mechanically. Therefore, another source to explain the will ought to be found. The will manifests in man, but not in animals, in which as estimative aspects is found, other than the human cognitive one. An animal can, by instinct, estimate one thing or another, but never execute a reduction to the universal, with which the will woks, such as humans do.

This theme of Psychology requires lengthy preparation and, since it is not fundamental at this point, shall be discussed later. As for now, it is only important to distinguish between speculative and practical philosophy and provisionally accept that the first would have to be predominantly a work of the understanding, and the practical is primarily a work of the will. Although, they cannot be separated or to be considered as having an abyss between them. Nor should we think, as many do, that man can just stick to the practical philosophy, moving away from the speculative. Discussions around this matter can become sterile. Inasmuch as the validity of the foundations of speculative philosophy are demonstrated, so practical philosophy stands confirmed and modern arguments that these speculatively established postulates does not apply to practical philosophy are results of poor analysis of unprepared people or merely bad faith trying to hide reality. One can find that there is no abyss between speculative and practical philosophy: they not only can work with each other but Dialectics, from this point of view, is the art of working with both simultaneously. True Dialectics must be able to apply the fundamentals of speculative philosophy into practical philosophy as well as, in turn, rise from the practical to the speculative. Action of back and forth or regressive operations, such as the one studied in Psychology, are characterized precisely in the understanding of these two directions: one parts from the universal ideas to the individuals in its general aspects, and the other one parts from the individual to achieve universals of first, second and third levels.

First levels abstractions are those in which one abstracts from own experience, such as the concepts of table, chair, tree. Second levels are those that leave out materiality. The first only elides the accidents, but considers materiality, and the second level elides materiality and only consider the quantitative aspect, such as the abstractions of mathematics in its vulgar sense, and finally the third levels abstractions, that elide materiality and accidents to only consider the formal aspects, independently from the presence of concrete things. The mind takes them only under maximum abstractions, as the metaphysical ones, such as cause, effect, anteriority, object, genus, species, subject and predicate. Those concepts belong to third-level abstractions, however man uses them alongside with the ones from first level, since man always “do” metaphysics whether he likes it or not.

Mathematics has become a language of reality since one can easily put aside the material and accidental aspects and consider all things only from a quantitative aspect. Man has the ability to “mathematize the world”. And it was that mathematization of the world that allowed the development of science, which, no doubt, began to develop when mathematics started to be used by the orientation of the Pythagoreans. Without Mathematics, no higher intellectual development would have been possible.

Science only truly develops insofar as mathematics is inserted into it. Only then, science increases its body of knowledge and achieves consistency in its operations. The same is true in Philosophy as to Logic, since it is a type of Mathematics, which is, in return, a type of Logic, as we shall see.

Logic plays the same role in its relation to Philosophy, since Philosophy becomes increasingly secure insofar as the philosopher becomes more logical, i.e., the more logically proficient the philosopher becomes, the better he philosophizes and draw more accurate conclusions.

The fundamental pillars of the development of human knowledge are in Logic and Mathematics, reason why they are the two key materials of all classical curricula of philosophy. Security in logical and mathematical thinking allows security throughout the rest of human knowledge. Mathematics and Logic have become a common language of our world and serves as meta-language of all disciplines, since mankind can reduce all of them, in their higher aspects, to Mathematics[3] and Logic.

Mathematics, in the Aristotelian sense, should be based on things that were abstracted from their materiality and considered in their accidentality. So, as one is able to build a mathematics of quantity, one could also build a mathematics of qualities and so on, since all other accidents studied by Aristotle are, in some way, linked to these two fundamentals of quality and quantity. And, subsequently, to relation. Meaning that, from these three one could build a mathematics of quantity, a mathematics of quality and a mathematics of relation. Now, as for the mathematics of relation and of quality one could ask whether there should be a withdrawal from the quantitative aspect. And the answer is “no”, since there is a quantitative aspect also in quality, as there is a qualitative aspect in quantity, as well as a quantitative and qualitative aspect in relation. Modern mathematics has pierced the field of relation, such as in the idea of functions, as relation of relations. Nevertheless, it has never developed in the field of quality. Hence it is inapplicable in the field of practical sciences, related to mankind’s ethical life. Thus, Mathematics has failed to provide great contributions to Sociology, Economics, Law, Religion, Art, etc., since it remained only founded in quantitative schemes. Therefore, it is imperative that Mathematics ought to be based on the qualitative aspect so can cover these fields of human knowledge.

To justify a Qualitative Mathematics, that must be built sooner or later, as on all unitive aspects according to their schemes of participation, there should be built its corresponding mathematical segments, since mathematics is an instrument of knowledge, as it is Logic. As Logic mathematizes concepts, Mathematics should logicize the schemes of participation.

The argument of Zeno of EIea offers an example, for in quantity and space – that can be potentially divisible since considering only the extension as such – one could get stuck in the concept of infinity. The mistake of Zeno was to disregard the qualitative aspect of the steps of the tortoise, when in fact, they were also there.

From the moment one works simultaneously with the concepts of quality and quantity, Zeno’s argument becomes puerile. Zeno’s mistake was to think that Achilles steps progressed by points when they were processed by totalities that qualitatively represent substantive determinations. Meaning that they are qualitative determinations, which, consequently, would give a finite number, and then Achilles would overcome the tortoise anyway. In addition, Achilles steps are greater than the tortoise steps, as well as performed in less time. The entire argument of Zeno was founded only quantitatively, therefore, not concretely founded. It was founded only abstractly, and even within that abstraction it was refutable.

A mere quantitative Mathematics cannot be applied to social issues. But the return to Set Theory, unfurled by the Pythagoreans (who studied the theory of Plethoi), can pave the way for qualitative mathematics since the sets, sooner or later, will have to undertake typical qualitative aspects, thus allowing the construction not properly of calculations in the quantitative sense of mathematics, but of other operations typical of the qualitative, such as the operation of analogy, and then, consequently, participation, and others, which may be tomorrow mathematized.

—————-

[1] Fragment of the book The Wisdom of the Principles, unpublished.

[2] When referring to the Pythagoreans, we denote those who actually followed the genuine teachings of the master of Samos, even if this is a debatable matter, as we shall see. To the Pythagoreans, Mathesis Megiste was a language used as meta-language to all mankind’s reachable science.

[3] Mathematics should not be considered only from the aspect given by Western culture, which is the sense of second level abstractions with mere quantitative aspect.

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