Concrete Philosophy – v. 1
Mario Ferreira dos Santos
Introduction
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.
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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.
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