Santos, Mario Ferreira dos. Filosofia Concreta. 3rd ed. Vol. 1. São Paulo: Logos, 1961.
For a more discerning Western philosophical thought, Philosophy is not a mere ludus but a scrutiny to obtain an epistemic, speculative and theoretical knowledge able to lead man into the comprehension of the first and last causes of everything.
May had been the case that philosophy – on unable hands – served only to unbridled research of various subjects at the will of affectivities and non-reason. Nevertheless, a more solid investigation in Western thought is the construction of apodictic judgment, i.e., necessary and sufficiently demonstrated to justify and verify the proposed postulates, thus allowing a safer ground to the act of philosophizing. Nevertheless, one can feel that philosophy – in certain regions and certain times – was founded in assertive judgments, mere statements of accepted postulates, which received a firm adherence from those who had found in it something adequate to their emotional and intellectual experience. Reason why philosophy, in the Eastern world, almost cannot be separated from religion and can even be confused with it. Religion is based on assertive judgment, for which faith is sufficient and demonstration is expendable.
Amongst the ancient Greek – mainly Skeptics and Pessimists – the acceptance of an idea imposed a demonstration. As when St. Paul tried to Christianize the Greek people, they were not satisfied with affirmations but demanded demonstrations.
Philosophy in Greece was not only speculative – which was also, esoterically, in other regions – but was characterized mainly for the search of apodicticy. Philosophy sought to demonstrate its principles and with this eagerness went throughout the centuries until our time.
In Natural Science demonstration is made predominantly via experiments. However, in Mathematics demonstration is processed by a more strict ontological precision. That is undeniably the nexus between experimental science and Philosophy. To philosophize with absolute certainty is to demonstrate with mathematical precision and never forget that the philosophically constructed schemes are analogous to the ones science examines and studies.
Assertive judgments suffice faith, but the true philosopher demands apodictic conclusions.
The aim to formulate a Concrete Philosophy, i.e., a philosophy able to yield a unitive vision – not only of ideas but also of facts, not only of the philosophical field but also of science – it must be able to enter transcendental subjects. It must demonstrate its theses and postulates with a mathematic rigor and also justify its principles with the analogy of experimental facts.
Only then Philosophy can be concrete, no longer halting over one single sector of reality or sphere of knowledge but encompassing in its process the entire field of human epistemic activities. Its axioms or principles must be effectual to all spheres and regions of the human knowledge. A regional principle – effectual to a single sphere and not subordinate to transcendental laws – is a provisory principle. An established law or principle must have validity in all fields of human knowledge since only in that case a nexus to arrange the epistemic knowledge in a coordinated manner can be developed, achieving the Pythagorean harmony principle, which is the adequacy of analogized opposites of which subsidiary functions are subordinated to the principal function and the constant is given by totality.
A quick look at the history of Greek Philosophy confirms the development of a tendency to demonstrate the philosophical postulates right after the appearance of Pythagoras in Magna Greece. One can easily deduce that the yearning of apodicticy observed in this philosophizing – made exoteric – was due mainly to the influence of mathematical studies and, amongst them, to geometry, which constantly demands demonstrations based in previously proved proposition. The same modus operandi was transferred to the theoretical knowledge, only recognized as such when apodictically founded.
Philosophy, leaning towards this pathway, although starting from empirical knowledge and from doxa, became a legitimate episteme, a refined knowledge. Therefore, this leaning is an ethical norm for the true philosophizing.
The firsts noetical schemes of the Greek philosophize had to come from common conceptualization and therefore carry the adherences of its origin. But there was an expressive tendency to veer from prejudices of the psychologistic kind and lean towards a mathematical sense, as seen in the Pythagorean thought of higher degree.
Pythagoras was a great disseminator of mathematical knowledge acquired throughout his travels and studies. Even though some scholars have doubts about Pythagoras historical existence – and that is not the discussion here – Pythagorism is definitely a historical fact and it is known that it encouraged the study of mathematics in addition to the fact that many notable mathematicians emerged from within the Pythagoric School.
Demonstration is separated from mathematics and moreover that is not merely an auxiliary science, a mere method, as some intends to consider. It has a deeper ontological meaning but this is not the moment to justify this statement.
Mathematization of philosophy is the only way to avert it from the dangers of esthetics and mere assertions. That is not to say that the presence of the Esthetics is an evil in itself but the danger is when the Esthetics tends to suffice by itself and reduces Philosophy to the domain of conceptualization, of mere psychological contents without the depuration that an ontological analysis can offer.
And that is the reason the pythagoreans demanded for the beginners the preliminary knowledge of mathematics, as well as Plato – this great Pythagorean – considered indispensable the knowledge of geometry before entering the Academia.
It is important to carefully examine the term “concrete”, which etymological origin comes from the augmentative cum and from crescior,be grown. Cum, besides the augmentative, can also be considered as the preposition with, thus indicating, “growing with”, since concretion implies in its ontological structure the presence not only of what is affirmed as a specifically determined entity, but also of its indispensable coordinates. It is appropriate to repel the common and vulgar meaning of concrete as only what is captured by the senses.
To reach the concretion of something one needs not only the sensible knowledge of the thing – if it is an object of the senses – but also its law of intrinsic proportionality and its haecceity, which includes the concrete scheme, i.e., the law (logos) of intrinsic proportionality of its singularity, and also the ruling laws of its formation, existence, subsistence, and ending.
A concrete knowledge is a circular one – as in the same meaning given by Ramon Llull – in a manner that connects everything related to the object under study, analogizes to its defining laws and connects to the supreme ruling law of reality. Therefore, it is a harmonic knowledge that apprehends the analogal opposites, which are subordinated to the normal given by its pertaining totality. That is what we call Decadialectics, which does not only encircle the ten fields of hierarchical reasoning – as studied in our book “Logics and Dialectics” – but also includes a connection with Symbolical Dialectic and Concrete Thought that assembles the entirety of human knowledge – through the analogal logoi – by analogizing a fact of object of study to the schematic totality of universal – and therefore, ontological – laws.
A triangle is – ontologically speaking – “this” triangle. One can know it for its figure can be drawn. But a concrete knowledge of the triangle implies the knowledge of the triangularity law – which is the intrinsic proportionality law of the triangles – and its subordination to the laws of geometry, i.e., the group of other figures’ intrinsic proportionality laws, subordinated to the established norms of geometry. That is a more “concrete” knowledge. And it could be even more so if one concretionizes the laws of geometry to the ontological laws.
So as to justify our philosophical work, Concrete Philosophy can be understood as the search and justification of postulates of an ontological knowledge, efficacious throughout all segments and spheres of reality – for there are different and many aspects of reality, such as the physical, the metaphysical and ontological, the psychological, the historical, etc., each one with its respective criteria of truth and certainty.
Therefore, to subordinate a specific knowledge to the Normal given by the fundamental laws of Ontology – which are manifestations of the supreme laws of Being – is to “connect” knowledge so as to make it concrete.
 Proclus ascribed to Pythagoras the creation of geometry as a science inasmuch as – because of him – geometry is not limited to exemplify only by empirical proofs. The Egyptians, for instance, applied geometry only to immediate practical means, but Pythagoras was able to transform it into science. The theorems are apodictically demonstrated inasmuch as profoundly investigated due to the use of pure thought without resorting to matter. Thus its truthfulness are self-sustainable with no need of support from real facts or individual subjects.
This Pythagorean desire can be observed in the work of Philolaus, fragment 4: “Indeed, it is the nature of Number which teaches us comprehension, which serves us as guide, and teaches us all things which would otherwise remain impenetrable and unknown to every man. For there is nobody who could get a clear notion about things in themselves, nor in their relations, if there was no Number or Number-essence. By means of sensation. Number instills a certain proportion. and thereby establishes among all things harmonic relations, analogous to the nature of the geometric figure called the gnomon; it incorporates intelligible reasons of things, separates them, individualizes them, both in limited and unlimited things.”
To sum up, according to the Pythagoreans, number is the guarantee of the immutable authenticity of Being, for it reveals the truth and makes no mistakes nor leads to illusions or errors. Or, in the words of Philolaus, “the nature of Number and Harmony are numberless, for what is false has no part in their essence and the principle of error and envy is thoughtless, irrational, indefinite nature. Never could error slip into Number, for its nature is hostile thereto. Truth is the proper, innate character of Number”.
Only Number can provide a solid foundation for a true scientific study. And who could deny that scientific progress finds its foundations in the Pythagorean thought?
Moreover, the number (arithmos) – for the Pythagoreans of a higher degree – was not only quantitative but qualitative and even transcendental.