The Archimedean Point: Theses 1-10

Book: Concrete Philosophy, vol 1
First Chapter

There is an Archimedean point, of which certainty is beyond our knowledge and is independent from us, but it is ontically and ontologically true: There is something.

We shall start from an analysis of such undeniable truth. If there was no mankind nor an intelligent being able to apprehend concepts, there would still have a real, absolutely assured, accurate, and true thought: There is something.

Mankind and the world – since contingents – could not exist. But there is something, since on the contrary there would be the absolute emptiness, the absolute and total absence of anything, the absolute nothingness. There is either something or the absolute nothingness.

Absolute nothingness would be the total absence of anything, ab-solutum, dis-connected from anything, total and absolute emptiness. At this very moment, we could be a dream or an illusion of a being, we could doubt of our experience and the exterior world. However, we could not affirm that there is nothing, since doubt itself and illusion itself affirm that there is something and not the absolute nothingness.

When one says there is something, one is affirming the presence of what is called being, even though not yet knowing what being is, what its essence is and what one can say about it. Therefore, there is something is a peremptory contradiction to absolute nothingness. To affirm absolute nothingness is to affirm that there is absolutely no thing. However, it is important to note the term absolute, since admitting that there is something is not contradictory to admitting that there is not something, since one thing could exist whilst something else could not. We shall refer to the first nothingness as absolute nothingness and the second nothingness as relative nothingness. If absolute nothingness contradicts there is something, relative nothingness only opposes it, but not excludes it, and, therefore, they can both happen, can both “pose” – both positive, but of inverse positivity.

Between there is something and absolute nothingness, there must be no doubt about the certainty of the first, which acceptance emerges from an intellectual act of complete adhesion and firmness, with no possibility of error. Where could the error be? If one affirms there is something, the only error could be that, in fact, there is not anything, which is denied even by the very act of such thought, by even the most skeptical act of thinking, since if there was nothing, there was not even the emergence of doubt.

Consequently, the affirmation there is something is apodictically demonstrated, so as, in the same extent, the impossibility of the absolute nothingness, since being true that there is something, there is absolutely no absolute nothingness; absolute nothingness is impossible, since there is something.

The first postulate of Concrete Philosophy is, therefore, apodictically demonstrated:

Thesis 1: There is something whilst there is not the absolute nothingness.
Thesis 2: Absolute nothingness, being impossible, cannot do anything.

Absolute nothingness would be the total and absolute absence of being, of power, since how what is not, what does not exist, what is nothing, could do something? In order to “do” something, it is necessary to previously “be” something. Therefore, absolute nothingness, besides from not being, is impossible and cannot do anything. Because if it could do anything, it would “be” something and not the absolute nothingness. However, we have verified that there is something and that the absolute nothingness cannot exist; therefore, we cannot expect anything from it, since it is nothing.

The corresponding verb to the Latin noun res (thing), reor, means to think or to believe. Thing, thus, would be that in what one can think or believe. Such term refers to the time-spatial concrete being, of which man has sensible intuition or of all that cannot predicate the absolute nothingness. The word something, which Latin origin aliquid is formed by aliud (other) and quid (what) – what is distinguished from other, what is distinct, a “thing” – and elucidates, after all, that something is understood as all that poses, happens and of what cannot be said as being a mere nothing. Now, absolute nothingness cannot happen, cannot “pose”, has no positivity; it is pure denial, total absence of any thing, of what can be said as being nothing.

Also the term entitas, entity, in its logos (in its intrinsic reason), means something to which the absolute nothingness cannot be predicated. And all that is not the absolute nothingness is something (aliquid), an entity (entitas). Therefore, everything that is not the absolute nothingness is something that happens, that “poses”, that occurs.

If there weren’t anything, we would have the total absence of any thing that poses, that happens. But, at the same time, one could not say that the absolute nothingness was, then, happening, since it was not posing, nor occurring: it would be the total absence. And it would suffice that anything happened, the presence of anything befell, to the absolute nothingness to become dismissed.

Mankind could not be what we believe it is, but still the absolute nothingness, the total and complete absence of anything, is not a possibility. Something is, happens, occurs. And what this something actually is should be our next subject.

In there is something, the subject completely “reflects” the verb, because outside “something” nothing can be, since nothingness is not and being is the being of something. Therefore, there is real and formal identity between “to be” and “something”, because “to be” is only so when refers to “something”, since nothingness is not. We shall deepen such statements through another ways opportunely.

Thesis 3: One can proves something by presenting it and not only by demonstrating it.

The concept of demonstration (de-monstrare) implies the concept of presenting something so to make another proposition evident, when compared to the first. The first certainty has, naturally, to be presented, since demonstration implies something previously given as absolutely certain. Therefore, the presentation (as in the act of presenting, showing something) suffices to prove the validity of something. The axiom there is something is evident per se and, as such, presents its validity, independent from human schematic – of which schematic contents can vary. There is something is evident and extra mentis (outer human mind).

Thesis 4: Demonstration demands a medium term; “presentation”, however, does not.

Demonstration demands a medium term because it is an operation consisting of comparing what one intends to prove to something else already proved. “Presentation” follows an intuitive mode. The evidence of what is presented is imposed by itself, since its denial would be incongruous. One can directly demonstrate by a mere comparison, as stated above; or indirectly, as a reduction ad absurdum, as in the second case. For instance, if there wasn’t anything, there would be the absolute nothing, which is absurd; therefore, something IS. Such is an indirect demonstration that there is something.

Thesis 5: There are non-deducted propositions, which are per se intelligible and per se evident (axioms)

It would suffice to merely present one example to validate such thesis. There is something and There isn’t the absolute nothingness have such requirements, what presents, therefore, the existence of non-deducted propositions (since they don’t require evidences other than themselves), per se evident , once including within itself a sufficient degree of certainty, indispensable to the axiom and dispensable of demonstration, since disregard comparison with other things in order to demonstrate their validity.

Thesis 6: Philosophy can be constructed with universally valid judgments.

It is common the statement that philosophy cannot be build on top of universally valid judgments. However, such statement is easily refuted, sufficing the establishment of a universally valid judgment whereupon, concretely, one can erect an entire philosophical system, as we shall do.

The theses, which were established as starting points to the foundation of our Concrete Philosophy, are universally valid. Only an appeal to foolishness, rebutted by the appeal itself, would consider the existence of absolute nothingness and not of something. Even such vain and fool statement would state the existence of something. We can doubt of own existence and regard ourselves as an illusion, but it would still be something. If we need ourselves to express an idea or to expose a philosophy, we don’t need ourselves so something exists, because even if we were illusion, we would be the illusion of something that exists. Therefore, such postulate doesn’t depend on us to present itself as evident. It is a universally valid judgment and shall be the foundation of Concrete Philosophy.

Thesis 7: Absolute nothingness is contradictory to there is something.

There is a contradiction when affirming the presence and, simultaneously, the absence of the same aspect in the same object. To say “there is something” is to contradict “there is the absolute nothingness”, since if there is something, the absolute nothingness is excluded. To say “there is the absolute nothingness” is to say “there is not something”, i.e., it is to contradict “there is something”.

Thesis 8: What is, is; is being. What is not is non-being.

Of what is, one can say that has being and is being. The concept of the word being is not definable, since to explain what being is we need the concept of being. But all that exists, is. Being, according to Suarez, is the “aptitude for existence”. To be is to be something, and not a mere nothingness (a total and absolute absence). Only the being can, since only the being has the aptitude to exist and the absolute nothingness, impossible and impotent, has no aptitude for anything, once it is not.

Non-being is what is not. Absolute nothingness is absolute non-being. If anything, one or another, is not, it does not affirm an absolute nothingness, but only that such or such thing is not, i.e., a relative nothingness. Absolute nothingness is an absolute non-being. Relative nothingness is a relative non-being. Postulating the first denies, total and absolutely, that something is. Postulating the second does not deny, total and absolutely, that something is, but only that such and such thing is not.

Accepting that something is does not deny, total and categorically, that something is not. Something is and something is not are two particular and sub-contrary judgments and the truth of one does not necessarily imply the falsity of another. Both can be true, as in fact they are.

Absolute nothingness is impossible, do not, since, in order to do, it is necessary to be. Something has to previously be something in order to do something. What is, occurs, we cannot call it nothing, but something, being. Therefore, what is not does not exist; and only what is, exists. We don’t know yet what this being is, but we know it is.

The term exist means that something effectively is, in the complete exercise of being, since what can become already is, in a certain way, or, in the contrary, would be the absolute nothingness, which is impossible. If something can come to happen, such thing is possible. If it is possible, it cannot come from absolute nothingness, which was already repelled, but from something that is, since nothingness – impossible and impotent – cannot create anything.

Therefore, we can reach the certainty of a final conclusion: There is something, which is, and exists.

There is no doubt that there is something, that something is. It shall be indubitable that something exists, that something is in the full exercise of its being, that is not merely a possibility, once we examine the following arguments:

If there was no thing in the full exercise of its being, we would have only a possible being, i.e., what is still a relative nothingness and shall become – or not – something in the full exercise of being. What is still a possibility is a being in other, because what can be, is, and, to can, has to be in the full exercise of its being, since how it could do something if it has no power?

Therefore, something exists, since, if it didn’t, it would be the possibility of some existing thing, or, in the contrary, it would be the absolute nothingness, which is impossible. Such thesis shall be demonstrated via a different approach later on.

There is something is an ontological truth


In logical truth, there is a correspondence between the mind and the thing, whilst, in ontological truth, there is a correspondence between the thing to which the idea in the mind correspond. Ontological truth is the revelation of the logos of the thing. The judgment there is something has such aptitude and capacity. The ontological truth results from the intrinsic analysis of the thing, which is fit and able to, by itself, reveal and allow an intelligent being of knowing such truth. There is something has, thus, characteristics not only of a logical, but of an ontological truth.

When ontologically considered, there is something is an immediate analytical proposition (per se notas), since something implies, at least, the existence of something, inasmuch as the habitudo (correlation) between subject and predicate are apprehended by analysis. When ontically considered, it would be, thus, a mediate analytical proposition (non per se notas), which knowledge results from human experience. Later on we shall consider under yet other aspects.

In both manners, the proposition there is something is necessary, by an ontological necessity and an ontical consequence. Such aspects fortify even more the apodicticy of the Concrete Philosophy fundamental thesis, which is necessarily evident by any way of intellectual investigation.

The term necessary comes from Latin necesse, and, etymologically, is formed by the negative ne and the verb cedere, with a sense of to go, to forego, to leave, to move away, and also, to give up, to renounce, to abandon. Therefore, the term necesse (necessity) indicates the content of what is not renounceable, of what is unpostponable, of what cannot be otherwise.

The search, within ontological-dialectic, for the nexus of necessity, is the search for the eidetic content of the have-to-be, the only one that can-and-must-be. Man has the ability to construct a variety of noetic-eidetic schemes. Those are the eide, abstractly constructed by our intellect (nous), through an operation (noesis), and its contents (noema) recreate – or not – what-is-bound-to-be and must-imperatively-be. To reach such necessary eidetic content is to reach the ontological content of a thing.

The first measure of ontological-dialectic is, therefore, to search such contents, renouncing all that can not-be, until reaching the non-cede-able. Moreover, the ontological content must arise from an analysis that presents a nexus of necessity. Such operation totally deviates from the mere opinion, since opinion is an affirmative of our mind about contingent things (or noetic-eidetic contents), that could or could not be. The ontological content is only true when all and any contingence is excluded, once discovered the ontological absurdity. To reach the ontological content of what is under scrutiny is, therefore, the primary measure for such dialectic, which, without it, the intended aim cannot be reached, i.e, the construction of universally valid judgments that, being ontologically true, totally diverge from all doxa (opinion).

Thesis 9: The proposition “there is something” is sufficiently evident by itself


The truth within “there is something” does not demand, to be noted, a special mind. It is noted per se – and sufficiently – since its denial would affirm the absolute nothingness, which is absurd. There is something does not demand –and could even dismiss – demonstration. If we gather them, it is only to fortify its objective evidence; and we say “objective evidence” because it is not a truth subjectively apprehended by adequacy, but per se sufficiently true.

Thesis 10: “There is something” is not only an entity of reason, but a real-real entity

It is considered entity of reason (ens rationis, cf. the scholastics) that of which the sole existence is in the human mind. For instance, relations, orderings and general notions. It is considered real entity that of what has an existence outside human mind (extra mentis). A real entity can also have an existential correspondence within human mind. Could there is something deserve an affirmation as being only an entity of reason? If there is something is a entity of reason, we can determine that it is not only so, but also a real entity, because if there is an entity of reason, something has to be the supporter of it. And if there is something can be intellected, there is [really] something, since there has to be something in order to something be intellected, proving, consequently, that there is something is a real-real entity. Such demonstration fortify even more the possibility of an apodictically founded, universally valid truth.

Concrete Philosophy – Introduction

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[1].

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.

[1] 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.