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The generative holistic noetic theory
With its application to the concepts of genus and species
from Porphyry’s Introduction
By
Jaime Vladimir
Torres-Heredia Julca
June 2007
Translated from the
French version “L’hypothèse de la
noétique générative holiste – avec son application aux notions de genre et
d’espèce de l’Isagoge de Porphyre “ presented at Geneva University
(Switzerland) on June 29th 2006 by Jaime Vladimir Torres-Heredia Julca
Notes on this English version :
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Besides it, all concepts, ideas, terms, diagrams and texts of this English
version are the exact translation of all the concepts, ideas, terms, diagrams
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¤v gŒr toÝw m¡resi tò ÷lon
Porphyry, Introduction, (Species)
Contents
I. - Introductory words
II. - Principles of the generative holistic noetic theory
III. - The generative holistic noetic
theory and Porphyry’s genus and species
IV. - The generative holistic noetic
theory and its application to formal sciences in general
V. - Conclusions
VI. - Bibliography
I. - Introductory words:
The problem of genus and species goes at least back to Plato who treated
it using his Theory of Ideas. Then Aristotle dealt with this problem by
proposing his Theory of Universal.
Porphyry dealt with this problem in his Introduction by
specifying that he would do it especially from a logical point of view.
This means he doesn’t deal with the problem of the ultimate nature of the genus
or the species: he will be especially interested, among other things, in the
links there are between the genus, the species, the three other predicables and the individuals[1].
But the links there are between these five predicables
are surely dependent on the deep nature of the species and the genus. That’s
why a study of the nature of genus and species on a noetic
level would also be interesting in order to see whether we can explain in a way
the links and other properties exposed by Porphyry and also by Plato and
Aristotle.
Precisely, the goal of this work is to study what could correspond in
our mind[2]
to the Ideas, the universals, the genus or the species
using a theory the author of this work calls the generative holistic noetic theory (= GHN). This theory relates to the noetic theory insofar as it proposes a model
of the activity of the mind by following the tradition of noetic
researches of Graeco-Roman antiquity, Arab philosophy
and the Western Middle Ages.
The aim of the GHN is to propose
some solutions to problems put by noetic theory like
the problem of abstraction. The GHN also tries to lie within the framework of
contemporary research on holism carried out in fields like semantics,
mathematics, physics or psychology. Finally, the GHN also tries to propose an
explanation to the generative principle that one observes in many formal
sciences, in particular in the generative grammars of Noam
Chomsky[3],
mathematics, etc.
As we will see it further, the
GHN bases itself obviously on works of Plato, Aristotle, Plotinus,
Porphyry, Averroes, Albert the Great, Chomsky, Charles Dunan and of the
philosopher and Spanish physician
Juan de Huarte de San Juan whose work entitled “Examen de ingenios”[4] will be briefly presented. The goal of the
GHN is to resume their works concerning the mind activity but in laying down
three noetic principles that will be further
explained:
- The noema as principle of the thought
- The
generative principle
- The
holistic principle of the noemas’ generation
The goal of this work is not to
treat the part of the noetic theory that relates to
the origins of the thought, but rather to describe the process of
thought on the basis of the principle that there is an intellect that contains a
priori concepts or innate principles and that generates noetic
objects as we will see it further.
Moreover, with regard to the
links between the intellect and the brain, the GHN assumes the principle that
the human brain constitutes information drawn from the sensory data and that
will allow the intellect to form thoughts. These thoughts can have links with
the brain as it is currently studied by cognitive sciences, but the GHN is
interested in the mind as an intellective principle already made up by leaving,
at least initially, the crucial questions about the links between the intellect
and the brain.
II. - Principles of the generative
holistic noetic theory:
The holistic principle within the framework of
semantics:
By studying the language we often notice that the significance of the
words is part of a kind of network that connects the various significances[5].
From this type of
observations, for example, was
developed the thesis of semantic holism that Pascal Engel formulates this way :
" La signification des mots (dans un langage en général, pas seulement
dans un discours philosophique) n’existe pas indépendamment de celles d’autres
mots, de leurs occurrences dans des phrases, et en dernière instance, des
significations des phrases de l’ensemble d’un langage. "[6].
However, it is completely justified to wonder, if we accept the thesis
of semantic holism, what happens on the level of our intellect, more
precisely on the level of our thoughts: does our thought have a holistic
structure?
A formalization
of the holism:
A
holistic system can be characterized by the two following principles[7]
:
(P1)
The whole is more than the sum of its parts
(P2)
The parts take its possibility from its inscription in a whole
These
primitive proposals can be formalized in the following way:
As we will see subsequently, the generative holistic noetic
theory corresponds to these principles.
The intellect:
In GHN intellect is a substance that has the power to create or generate
noetic objects and that contemplates or observes
these noetic objects. The created noetic
objects develop in a holistic environment, which means, among other things,
that the mentioned noetic objects inherit, in a way,
properties of the intellect itself. These noetic
objects, although differentiating from the total intellect, are in the
intellect. And what is called "thought" would correspond to the
contemplation or observation of these new noetic
objects generated by the intellect: this way the latter observes itself, as it
was set out by Aristotle for the First Motor or Plotinus
speaking about the Intellect [8].
This is also closely akin to what Aristotle had written by saying that intellect
becomes all things [9].
This can be interpreted in a holistic way. Indeed, the intelligible form
inherits properties of the total intellect and evolves in the intellect itself.
In addition, Alexander
Aphrodisiensis wrote that
" l’intellect
en acte n’est rien d’autre que la forme pensée, si bien que chacune de ces
choses qui ne sont pas purement et simplement intelligibles devient intellect
lorsqu’elle est pensée (…). "[10].
It is important also to notice
that when we say that the intellect becomes all things, the intellect will also
have, as writes Dunan in describing the thought,
" the characters of all that becomes, mobility, variability, the
succession in the duration, (...), the opposed characters, immutabilities, the
perfect identity ; (...)."[11].
And further on he writes: " If the thought is the mind itself, one can
conceive, if need be, that the thought one and multiple appear in the form of
time or in that of space "[12].
The intellect therefore has a priori elements thanks to which thoughts
will be generated.
The idea of creation of noetic objects and its
comparison with the thought of God are in the work of Juan de Huarte de
It is by this observation of the
intellect by itself through its generated noetic
objects that it is said that the intellect is one and multiple. It is one
because all occurs inside the intellect, but it is multiple because it
generates in itself noetic objects and the whole in a
holistic way as it will be specified further. This problem of the one and the
multiple was amply set out by Plotinus in its Enneades when he describes the One and the Intellect.
Moreover, it should be noticed
that in order to describe intelligence, Aristotle had recourse to the concept
of potential. Indeed, he writes that
intelligence "ne peut même avoir la moindre nature, en dehors de celle qui
consiste à être un possible! "[14]. This
"potential" character will be obviously transmitted to the generated noetic objects as it is explained further.
As we have seen, the intellect produces a noetic
object that we will call from now on the noema.
The noema:
The term noema comes from the Greek nóēma that can have this translation: the thought
as the result of the act of thinking [15].
In the GHN the noema is what the intellect generates
by a creative act that one calls “to think”. To think is, for our intellect, to
create noemas that are in fact products of the
intellect and that have, to some extent, practically all the potential of the
intellect[16].
The noema is a kind of cognitive element that
would be in the heart of thought. Basically a noema
has in a way the potential of the entire intellect. However, the intellect is
the being that thinks and the principal noema in the
thought of man is man himself.
The human mind is a noema that generates other
noemas. And once it has generated them it
contemplates or observes them[17].
And this means the intellect (or the mind or man) observes itself by observing
its creation.
As written previously, since the noemas can
inherit fundamental features from the total intellect, then the intellect can
generate space-noemas, geometrical-noemas, numerical-noemas, etc.
The noema is essentially one and multiple
since it inherits fundamental features from the intellect itself, that is one
and multiple. This will also be specified further when we deal with the problem
of genus and species.
A noema generated by the intellect (what is
called a thought) can generate other noemas
and has two principal aspects:
a)
The actual aspect: precise
characteristics by which a precise noema is
distinguished from the total intellect (while being inside the intellect by
holism). In the actual aspect of the noema, the
heritage, the characters of the parent noemas also
play a part.
b)
The potential aspect:
potentials inherited from the intellect. The noema,
although having an actual aspect, has also the potential to modify some of its
features while remaining the same noema. The
potential aspect also depends on the potentials of the parent noemas.
The process of
generation of the noemas:
Like the total intellect itself, a noema can
generate other noemas that in their turn will
generate other noemas. This idea has also been set
out by Juan de Huarte: he wrote indeed that the
intellect generated sons and grandsons. Obviously, all that
reminds us of the remarks of Plotinus concerning the
generation, or more precisely the procession from the One.
The generated noema will have an actual aspect
that distinguishes it from other noemas and a potential
aspect inherited from its parents. Moreover, the generated noemas
are part of a holistic system. Each generated noema
keeps an attachment to its parents and to the other noemas.
Below we can observe a representation of the generation of the noemas starting from the intellect. As Juan de Huarte has written, Noema
1 can have a son that is Noema
1.1 or another son that would be Noema
1.2 with other actual characteristics that differentiate it from Noema 1.1 :
In order to emphasize well the fact that this generation of noemas occurs in the holistic space of the intellect, we
can make the following diagram that put the accent on the fact that, for
example, Noema 1 inherits potentials
from the intellect while being a little bit different from it by actual
aspects. It is the same concerning Noema
1.2 that inherits potentials from Noema
1 and also from the Intellect by transitivity :
But in order to emphasize well the fact that the generated noemas of the first and of the second generation inherit
potentials from the intellect and from the parent noemas,
we can make the following diagram that concerns Noema
2.1 :
This diagram shows that Noema 2.1
has the potentials and some actual features of the parent noemas inside of him, which precisely corresponds to a
holistic diagram.
As
Porphyry said speaking of the species, the whole is in the part.
However, the question of knowing by which principle the intellect
generates noemas remains open. Indeed, one could
think, as Aristotle does, that we need an actual intellect to see to it that a noema generates other noemas.
Current
characteristics and characteristics in potential
of noemas:
The generated noemas have characteristics that
distinguish them from other noemas. These
characteristics can be actual in a sense, as in the case of the man- noema whose feature is rationality, and they can be in
potential, such as, for example, the
capacity to become a sailor.
When a noema generates another noema, the latter can actualize
certain potentials of the parent noema. Thus the
animal-noema has a geometrical form in potential, in
other words unspecified, but the horse-noema can
already have a more precise geometrical form though there can be indeterminations or potentials until reaching by noemas such particular racehorse, for example.
Process of
abstraction:
By the senses our brain manages to compose sound information, visual
information, etc. From these data our intellect will generate noemas that will apply to this information.
For example, while seeing animals our mind will call upon an
"animal" noema that had already been
generated previously by a process of training that finally corresponds to the
creation of noemas. This "animal" noema corresponds to a living being that moves and that has
the characteristics of what we understand by animal. In the noema
there will be the features of the animal according to the knowledge of whom
generates this noema[18].
Then, if we observe a horse, then we call upon (or we create if we see a
horse for the first time) a "horse" noema
which was generated starting from the "animal" noema.
The horse noema contains in itself the potentials of
the "animal" noema. They are interlinked.
Then if we observe a particular horse we generate a particular noema for this horse and the latter noema
will contain in itself the potentials of the "horse" and
"animal" noemas.
It is the same when one sees Socrates: initially one calls upon the
"animal" noema
that contains itself the "man" noema and
that contains the noema "Socrates". When
one sees Socrates, mentally we generate a noema that
corresponds to him and that, in addition to the characteristics of Socrates,
contains in itself the potentials of "animal" and of "man".
It is crucial to take the creative aspect of the noemas into account or else we could believe that the noemas "animal" and "man" that apply to
Socrates are absolutes. In fact this is not inevitably the case and we can
organize the knowledge differently by creating other noemas
in associating them other linguistic names. Depending on the noema systems generated there will be other systems or
other classifications of beings.
For example, when Linné presented his system
of classification of plants, he generated in him noemas
with the system of holistic heritage but this wasn’t inevitably an absolute
system, hence the discussions that followed. We can build various ontological
systems just as we currently do in the computing systems of artificial
intelligence[19].
The composition or synthesis by generation - the creation of groups or types:
One could believe that the composition of concepts isn’t really a
generation in the strongest sense of the term: if we have noemas
that correspond to pieces of wood and to certain precise metal parts then we
will be able to compose a chair, but we could think that the chair-noema won’t result from parent noemas.
Actually, if we analyze the noemas corresponding to the pieces of wood and to the metal
parts, we will see that they result from the same object-noema
or body-noema. However, it is by starting from
this body-noema that we will be able to
generate metal objects and wooden ones, so that we will have a new holistic noema corresponding to the chair.
This principle of composition can be applied to any other composition of
noemas. The principle in order to compose two or
several noemas is thus to go back to a common
ancestor to all of these noemas and to create, starting
from this common ancestor, a new noema that contains
in itself, in a holistic way, the other noemas (or
parts).
Here is a diagram that shows for example the composition of the chair-noema:
As it can be seen the chair-noema results from
the body-noema that generated "in itself",
in a holistic way, other body-noemas that have other
features (plant, metal) and that form a chair-noema.
In
a general way we can create all kind of groups of noemas.
The groups, that are multiple by nature, will be one by the noema that generates them and that contains them in a
holistic way. In each part-noema of the group of noemas there will be the noema
that has generated them so that the unity is carried out and so that we can say
that each part-noema is indeed a part of the group.
This will be useful further for the holistic generative theory of the numbers.
With this principle we can also create groups of noemas
that have certain common features: for example a group-noema
that binds 6 green cubes.
The movement-noema:
The movement (and also any action, creation, etc.) is also a holistic noema in our mind. Indeed, for example the idea of “eating”
includes movements of the oral muscles, arms, hands, etc. All that is put
together by a holistic noema we can call to eat-noema as we have seen above.
When the movement has a goal or when the action has an object, then the
agent-noema and the object-noema
will become part of a holistic noema, as in the case
of the composition that has been seen above. For example, when by our intellect
we think that a train approaches a city, on the level of the noemas we generate a holistic system-noema
of two generated sub-noemas (the train and the city)
that evolves in the course of time so that the two objects are getting
increasingly closer (in the space-noema).
Unconscious process of creation of noemas and conscience of this process:
The
process of creation of noemas is to a certain extent
unconscious but by a work of introspection one can manage to find links between
the noemas. One can ask itself questions about what
one understands by "bee" for example and gradually our mind finds the
parent noemas of the noema
corresponding to “bee” [20]
again. This is what, according to Plato, Socrates did by asking what were the
things or the concepts like justice.
The hypothesis of the holistic total intellect as interpretation of the noetic theory of Averroes:
Just as the intellect of man can generate noemas
in a holistic space, it can be that the intellects of humans are plunged into a
holistic intellectual space shared by everybody. That would correspond to what
the Andalusian philosopher Averroes
tried to say in writing that there is one potential intellect for all. This
expression can be interpreted within the framework of the generative holistic noetic theory applied
to a more global holistic system that relates to all the intellects of
humans.
Averroes’ proposal can also be understood if one supports
that it is the potential of a total intellect that lies in each man and not an actual
intellect. Each man will do what he wants with the fragment of intellectual
potential that is due to him in a holistic way.
Potential and possibles:
Our
intellect is aware of the generative possibilities of the noemas.
A noema is like a kind of seed which contains in
potential other noemas. The intellect can be
conscious of these potentials because, as we have mentioned it above, the noema is a generation of the human mind that is itself a
total noema. This principle of the potentials of the noemas is at the root of the concepts of possibility,
future, etc.
Training and creation:
Knowledge is made thanks to the noemas but it
doesn’t mean that all knowledge is in the human mind. Men create various kinds
of noemas starting from a priori noemas that are in the intellect and they communicate them
to each other and knowledge (generated noemas) is
shared and the total knowledge of humanity is becoming richer.
The noema without precise features, in short
the intellect as a potential, corresponds to some extent to Aristotle’s tabula rasa. It
doesn’t have a form and yet it is something in a way, but nothing in the way
that it hasn’t generated a noema indeed.
Origin of the principle of causality:
One of the principles of causality that one applies to many phenomena
and theories would come from this generative capacity of the intellect. Indeed,
the mind generates noemas and naturally the idea of
causality is inside us and we apply it to what we observe.
Furthermore, it must be noticed that in nature the things often seem to
occur like in our mind by generation. We especially see it in the living
beings.
Holism of intellect and holism of the universe:
But also in nature there are holistic systems that are currently studied
in fields like physics. One can quote the study of the interlinked photons[21].
It is about photons that, for still unspecified reasons, have links whereas
they are often separated from several kilometres. If one acts on one of the
particles this will instantaneously affect the other whereas apparently nothing
connects them.
One has spoken about the "transmission" of the information of
the particles but it can be that, in a way, we have there a holistic system
where the particles share something in common that can be find simultaneously
in both.
If such a holistic system is possible between two particles, one can
think that this is possible on the level of our brain and our intellect that
would act as holistic systems.
The generative
holistic noetic theory and Plato’s Ideas and
Aristotle’s Universals
Plato’s Ideas can be interpreted as noemas.
As we have seen above, the intellect can generate noemas
that correspond to the concept of animal or man. Moreover Plato
himself proposed in Parmenides to see the as Ideas
thoughts, but as he exposed it, this posed problems because of the links
between these thoughts and the objects of nature. Obviously, this problem
concerns also the GHN because, when an object of nature is observed, we
classify it in various ways according to our noemas
and we can study the nature of the links there will be between our noemas and the objects of nature.
But for Plato the Ideas are eternal and immutable. However, in the GHN
concepts as that of bee are rather creations of our intellect but a question
remains: how the intellect, even if it acts according to the generative holist noetic theory, can generate this idea of animal? The same
question can be put concerning mathematical objects. These thoughts on the
origins of the noemas themselves and the origin of
their potentials concerns the metaphysics and the study of the a priori forms
as Kant proposed it.
As a matter of fact Plato puts questions we can always think about. His
solution is that the ultimate principles, the Ideas, are eternal. It can be
that there are concepts a priori eternal whereas the others are created
by our noetic activity using these a priori concepts.
The question remains open, but that doesn’t prevent us from describing the
intellective process like a holistic generation.
Concerning Aristotle’s universals, we can propose an interpretation that
corresponds to the GHN. Aristotle writes that the universal remains in the
intellect and this can occur in a holistic manner.
III. - The generative holistic noetic theory and Porphyry’s genus and species
The five predicables of the Introduction:
As we have foreseen it above and as we will specify it, the theory of
the GHN agrees with the description of Porphyry’s genus and species (and also
of the other five predicables).
Porphyry presents us the five predicables
(genus, species, difference, property and accident) so that they are linked up
in a hierarchical way as we can see it below:
The Genus:
Concerning
the genus, Porphyry writes:
"4. ‘Genre’
se dit encore d’une autre façon : c’est ce sous quoi l’espèce est rangée,
peut-être ainsi nommée à l’imitation des [significations] précédentes : de
fait, le genre dont nous parlons est une sorte de principe pour ce qui est sous
lui, et il semble embrasser toute la multiplicité qui est sous lui.
5. ‘Genre’ se dit donc de
trois façons, et c’est de la troisième qu’il est question chez les philosophes.
Pour décrire [ce
genre], il le définissent ainsi : [le genre] « c’est ce qui est
prédicable de plusieurs différant par l’espèce, relativement à la
question : ‘qu’est-ce que c’est ?’ », par exemple
[animal]. "[22]
As we can see, Porphyry describes us at first the genus as being that
under what the species is placed. There is an idea of "capacity" or
inclusion. And afterwards he specifies that
the genus is a kind of principe pour ce
qui est sous lui, et il semble embrasser toute la multiplicité qui est sous lui.
It is clear that these remarks correspond to the holistic description
that we have showed above.
It should be noticed that even if Porphyry has written at the beginning
of his work that he would only deal with the problem of the genus and the
species in a logical way, he cannot prevent ontological or even noetic descriptions. When he says that the genus seems
to embrace all the multiplicity that is underneath him, Porphyry enters
already a rather ontological or onto-noetic field,
because it is obvious that the genus as a term cannot embrace anything.
Then he writes: " pour décrire [ce genre], il le
définissent ainsi : [le genre] « c’est ce qui est prédicable de
plusieurs différant par l’espèce, relativement à la question : ‘qu’est-ce
que c’est ?’ », par exemple
[animal] ".
In connection with that, it is clear that to be able to say that several
differ by the species, it is already necessary that by our intellect we can
know that several things differ by the species; moreover it should be known
that a predicable applies to these things that differ by the species. In
order to know that, the GHN proposes, as we have seen above, that the human
intellect produce noemas corresponding to the
species, species-noemas and the intellect
observes its parents and if the intellect notes that the species-noemas have the same parent-noema
then the term to announce this parent-noema will be
applied to the species-noemas[23]
(one will speak then with Porphyry about predication).
Then Porphyry continues :
" En
effet, parmi les prédicables, les uns ne se disent que d’un seul, comme les
individus (par exemple Socrate, cet homme-ci ou cette chose-ci), tandis que les
autres se disent de plusieurs ( comme les genres, les espèces, les différences,
les propres et les accidents qui sont communs et non pas particuliers à un seul
individu { un genre, c’est par exemple, ‘animal’ ; une espèce, par
exemple, l’homme ; une différence, par exemple le capable de raison ;
un propre, par exemple le capable de rire ; un accident, par exemple, le
blanc, le noir, le fait d’être assis} ). " [24].
Concerning the predicables that say itselves from one, it should be noticed that before
applying such a predicable to Socrates for example, our intellect must find a
means of carrying out the unit under the multiplicity of the aspects of
Socrates. Socrates, indeed, has a body extended with arms, legs, etc. He also
has moral, intellectual qualities, etc. All that must be arranged under a unit
in our intellect. This multiple unit will be realized by a noema
applied to what one sees of Socrates and obviously this noema
will inherit properties and potentials from the animal-noema
and from the man-noema. Charles Dunan presents a similar idea[25]:
"The first sensitive object that comes carries out for us in a perfect
manner the multiple unit that remains unity, and the multiplicity one that
remains multiplicity. A house is a heap of stones, without ceasing to be a
house; a heap of stones can form a house, without ceasing to be a heap of
stones. But it is that the consideration of this unique object in itself
consists really of two points of view that are opposed to one another. The
house, it is this object especially as it is one, which doesn’t prevent the house
from being a heap of stones: the heap of stones, it is still this object,
especially as it is multiple, which doesn’t prevent the heap of stones from
being a house. Between these two points of view of the object there is no
medium : it is me to choose, and, according to the choice that I will make, the
object, although essentially one and multiple at the same time, will appear to
me like especially one, or especially multiple ".
The Species:
Concerning
the species Porphyry writes :
« 3. [Les philosophes] définissent donc l’espèce de
la façon suivante : « L’espèce est ce qui est rangé sous le genre,
est dont le genre se prédique relativement à la question : ‘qu’est-ce que
c’est ?’. »
4. Ou encore de la façon suivante : « L’espèce est ce qui est
prédicable de plusieurs différant par le nombre relativement à la
question : ‘qu’est-ce que c’est ?’. ». Néanmoins, cette dernière
définition ne vaut que pour l’espèce la plus spéciale, pour ce qui n’est
qu’espèce, tandis que les autres s’appliquent aussi aux espèces qui ne sont pas
les plus spéciales. "[26].
What we have mentioned above concerning the genus within the framework
of the GHN also applies to the species. In fact the species, in the GHN, is a noema resulting from a genus-noema.
The order of the generation of genus and species can be represented in the
following way:
And as we have specified above, this generation happens in a holistic
way. In order to show this with a diagram that shows the inclusion of the
potentials and actual aspects inherited from the parent-noemas,
one can use the following diagram that relates to the species-noema man, the genus-noema
animal and the intellect:
And as we have seen above, starting from the man-noema
one can generate particular man-noemas like Socrates,
for example, the whole in a holistic way. And starting from the noema corresponding to Socrates, one can create other noemas corresponding to Socrates’ movements or thoughts,
etc. and so on...
This diagram can seem surprising. One could believe that one would be
brought to affirm that an animal is a man because apparently, according to the
diagram, animal is included in man. But in fact
this diagram only tries to indicate that in the noema
(or thought) man the characteristics of the animal are included, or,
more precisely, the animal-noema is contained in a
way in the man-noema. It is because the animal-noema is in a way in the man-noema
that we can affirm, for example, that man can move, etc. Moreover, as it will
be seen below, Porphyry writes, concerning the species : " the whole,
indeed, is in its parts ".
Furthermore we shouldn’t confuse
the horse-noema with the noema-group-of-all-the
horses. Indeed, we could want to define the species horse by extension, in
other words to define it as being the set of individual horses existing but
what we would obtain in our intellect would be the noema-group-of-all-the-animals
and not the horse-noema.
Then Porphyry gives us an
exposition that corresponds to what is called the Porphyry tree:
"5.
Éclaircissons ce que je viens de dire de la façon suivante. Dans chaque catégorie, il y a des [termes] plus
généraux et, inversement, d'autres [termes] absolument spéciaux, et, entre les
plus généraux et les plus spéciaux, d'autres [termes]. Le plus général, c'est
celui au-delà duquel il ne saurait y avoir de genre plus élevé, tandis que le
plus spécial, c'est celui après lequel il ne saurait y avoir d'espèce
subordonnée; et entre le plus général et le plus spécial, il y a d'autres
[termes], qui sont à la fois des genres et des espèces, mais à chaque fois par
rapport à quelque chose d'autre.
6. Éclaircissons ce que nous voulons dire en prenant l'exemple d'une
seule catégorie. L'essence est elle-même un genre; sous elle vient le corps;
sous le corps, le corps animé; sous celui-ci, l'animal; sous l'animal, l'animal
capable de raison; sous celui-ci l'homme; sous l'homme, Socrate, Platon et les
hommes particuliers. Eh bien, parmi ces [termes], l'essence est le plus
général, [c'est-à-dire] ce qui n'est que genre; l'homme est [l'espèce] la plus
spéciale, [c'est-à-dire] ce qui n'est qu'espèce; le corps est bien une espèce
de l'essence, mais genre du corps animé. Et le corps animé, à son tour, est
bien une espèce du corps, mais genre de l'animal; à son tour, l'animal est bien
une espèce du corps animé, et genre de l'animal capable de raison; et l'animal
capable de raison, une espèce de l'animal, mais genre de l'homme; et l'homme,
une espèce de l'animal doté de raison, mais non pas genre des hommes
particuliers, il est seulement espèce; de même tout ce qui, rangé
antérieurement aux individus, en est immédiatement prédiqué, ne peut être
qu'espèce, et non pas également genre. "[27].
From the point of view of the GHN one can make a diagram of the
generated noemas in a holistic way. This diagram
corresponds in any case to the form of the Porphyry tree:
Further Porphyry writes:
" C'est
pourquoi Platon recommandait, en descendant depuis les genres les plus
généraux, de s'arrêter aux espèces les plus spéciales, et d'accomplir cette
descente à travers les termes intermédiaires en procédant à des divisions au
moyen des différences spécifiques; quant aux [individus] en nombre infini, il
faut, disait-il, les laisser de côté, car il ne saurait y en avoir de science.
Quand donc on descend vers les espèces les plus spéciales, il faut faire des divisions
en cheminant à travers la multiplicité, tandis que lorsque l'on remonte vers
les genres les plus généraux il faut rassembler la multiplicité dans l'un;
l'espèce, en effet, et plus encore le genre, est rassembleuse du multiple dans
une nature unique, tandis qu'à l'inverse les particuliers et les individus
fractionnent sans arrêt l'un dans la multiplicité; en effet, c'est par la
participation à l'espèce que les hommes multiples constituent l'homme un,
tandis que par les individus cet homme unique et commun devient plusieurs ; car
le particulier est toujours diviseur, tandis que le commun est rassembleur et
unifiant. "[28].
This passage can also be interpreted with the principle of the holistic
generation. When Porphyry refers to the division, in the GHN one refers to the
generation of noemas and when Porphyry refers to the
rise and to the gathering, in the GHN one speaks either about search for
parents, or about the creation of a group-noema, as
it has been seen above, which also corresponds to a generation.
Finally Porphyry writes :
"16. Donc l'individu est embrassé par l'espèce, et l'espèce par le
genre, car le genre est une sorte de totalité, tandis que l'individu est
partie, l'espèce à la fois tout et partie, mais partie d'autre chose, et totalité
non pas d'autre chose, mais en d'autres choses: le tout, en effet, est dans ses
parties. "
These words by Porphyry are very comprehensible in the point of view of
the GHN. Indeed, he writes that the genus is a kind of totality but so that
this means something it is necessary, for example, that the concept of animal
is in the concept of man as we have seen it previously. And apparently this can
only be carried out in a holistic way as the GHN proposes it.
The difference and the property:
Thereafter the concepts of difference and property can be explained in
the GHN by the characteristics of the noemas as we
have seen it above. When these characteristics relate to the noemas called "species" Porphyry speaks then
about difference.
The accident:
In
Porphyry the accidents correspond to the
potentials of the noemas. Thus the man-noema has the potential to sleep or to have red hair.
The species as potential:
The polygon-noema, for example, is neither a
simple word nor a simple image (it’s obvious!) but an intellectual potential
that enables me to recognize any polygon. It is the same thing for the
recognition of faces. But this recognition would be done by generation of noemas applied to the sensory data organized by the brain.
When we are confronted with some object or other and that we want to say
what it is, it is starting from the image formed by our brain that the
intellect will "test" some noemas to see
whether they can generate noemas corresponding to the
image formed by the brain. Thus, if one is confronted with a hexagon, our
intellect will call upon the polygon-noema to see
whether starting from this noema one can generate an
hexagon-noema for example. If this is the case one
will say that one sees a polygon and more precisely a hexagon.
IV. - The generative holistic noetic theory and its application to formal sciences in general
The generative
holistic noetic theory and its application to
linguistics
The application of the GHN to linguistics is very simple if we have Chomsky’s system of generative grammars in mind. This
system allows to make syntactic analysis.
The syntactic analysis is a branch of computer science linguistics,
computer science logic and artificial intelligence. Its goal is to study the
structures of the natural or artificial languages so that, among other things,
computer systems can determine if a sentence is well built or not.
A small grammar of French can be formally described as following (the
explanation is below):
S —>
NP VP
VP
—> V
VP
—> V NP
NP —> Det N
NP
--> N
Here is the explanation:
- Det =
determinant ("one", "this", "this", etc.)
- N = Name
- V = Verb - NP = nominal Group
- VP = verbal Group
- The symbol "S"
corresponds to a well formed sentence.
The small formal grammar indicates that a well built sentence starts
with a nominal group and ends with a verbal group. Then we indicate that a
verbal group is made up either of a verb, or of a verb followed by a nominal
group. And at the end we indicate that a nominal group is made up either of a
determinant and a name, or of a simple name.
It should be noticed that the order is important. Thus, if one writes
initially the verbal group and then the nominal group, the sentence will be
wrongly built.
Here is an example of an analysis with this grammar:
The
sentences of the type " Sees tree a Pierre " or " a Pierre tree
sees " will not be recognized by the software and the famous message
" SYNTAX ERROR " will be displayed.
The
goal of the software called "syntactic analysor"
is precisely to see whether a sentence respects a given grammar.
Obviously,
the computer system imitates our way of mentally analyzing
the sentences. That’s why we speak about artificial intelligence.
Now, from the point of view of the GHN, the process happens thus on the
level of the syntax :
a) In the case of a heard sentence:
a. For each heard word our intellect calls upon a word-noema.
It is clear that the word-noema, by holism, will have
a significance (a noema) that will precisely give the
grammatical category that corresponds to it. The significance is made by the
creation of holistic groups as we have seen above.
b. For groups of words it constitutes group-noemas
(as we have seen above) of words that correspond to the grammatical categories.
c. At the end if the intellect manages to constitute a group-noema of categories that can be generated starting from the
sentence-noema then the intellect affirms that the
sentence was well constituted. In other words the intellect recognizes the
sentence thanks to the holistic generation of noemas
starting from the sentence-noema.
b) For the case where the sentence is written, the difference is that
initially the intellect will first create letter-noemas
starting from the sight of the ink spread on the sheet, then word-noemas starting from the letter-noemas
and afterwards things will happen like we have seen above concerning the
syntax.
To summarize, what the intellect gradually does is to recognize the
elements of the sentence by the generation of noemas
structured according to the fixed grammatical rules. But these grammatical
rules are possible thanks to the successive generation of group-noemas in the intellect. The sentence-noema
is a noema of the type "group" as we have
seen above and the noemas generated starting from the
sentence-noema are also group of noemas.
It is the same for the VP-noemas, the NP-noemas, etc. that are group-noemas.
The noemas that correspond to the grammatical
categories are similar, for example, to the noema
that corresponds to "musical trio". This noema
contains in a holistic way three human-noemas and
this noema can help us to recognize whether or not a
group of three people is a musical trio. If we see three people, for each one
there will be the human-noema and if the three of
them play music and work together we will be able to generate starting from the
trio-musical-noema a particular noema
(or instance) that corresponds to it in a holistic way and we will say that we
have a musical group indeed. It is the same for the recognition of the
sentences.
But for the comprehension of the sentence, on the level of the thought,
there will be other created noemas. Indeed, for the
sentence "
The origin of the generative tree structures in general:
Chomsky ‘s trees of
grammars, the syntactic trees of the formulas of logic and mathematics, the
taxonomic tables, Porphyry’s tree, etc., all that would draw its origin from
the holistico-generative property of our mind.
Even if each noema has its characteristic, it
keeps links with the rest of the mind.
Definition of the mathematical number within the framework of the GHN:
Within
the framework of the GHN a number is a holist noema-group-being
that has generated and that contains several being-noemas.
Let us study for example the number 3:
There will thus be a group-noema that has
generated three noemas in a holistic way. The three
ellipses at the interior of the large ellipse represent the generated being-noemas. At the interior of each of these three ellipses
there is a small ellipse that represents the unit included in each part. In
other words each of these three generated noemas has
links with the whole-three. This holistic set is one and multiple at the same
time. It is one and three.
In fact the noemas that correspond to the
numbers are like lists of highly general noemas. By
generation the noema-group-three-being can generate
the noema-group-three-horse that corresponds to what
one usually understands by "three horses". Each noema
generated in a number-noema corresponds to a being
and doesn’t really have an accident nor another feature.
For the more complex numbers noemas develop
following for example base 10. The generation occurs by group-noemas containing ten generated noemas.
Now that we know what number 3 is in the GHN, we can wonder what a
number is in general. In fact a number in general, or the number is a being-noema
that has the potential to generate other being-noemas
in a holistic way. This general number-noema can be
used to generate other numbers.
Noemas corresponding to the interpretation:
If we have a noema corresponding to the
drawing X and that we say that X can be a number then we create a holist system
that links a number-noema to the noema
corresponding to the geometrical figure of the X as we have seen previously.
The fact that this occurs in a holistic way would explain why we think
sometimes that there is no thought without language. This would come from the
fact that in our intellect the word-noemas are
holistically interlinked with the significance-noemas
that are the thought that we want to signify. Because of the fact that they are
holistically interlinked one can believe that there is no thought without
language.
V. - Conclusions:
As it has been announced above, the Generative holistic noetic theory is inspired by works of philosophers like
Plato, Aristotle, Alexander of Aphrodisiensis, Plotinus, Averroes, Juan de Huarte de
As we
have said, one of the bases of the GHN is that the thought is one and multiple.
That has links with many physical principles. For example the particles act
like corpuscles or waves. We speak about wave-particle duality. As a
wave the particle will be extended, multiple, and as a corpuscle it will
be one, definite.
The
GHN enabled us to explain as far as possible the links there are between the
genus and the species in Porphyry and this on a noetic
level. The GHN also enabled us to explain the generative processes that we
observe in the majority of formal
sciences.
The
mind evolves with the noemas that become richer
thanks to new observations of nature or thanks to the study of "a
priori" noemas as some geometrical noemas.
The
GHN only proposes one description of the process of thought but it is clear
that the majority of the traditional questions of the noetic
theory remain open. For example one can wonder about the origin of the
potential of the noemas.
Finally,
within the framework of the GHN itself there remain much subjects to develop in
order to see whether it is necessary to reinforce or weaken certain principles
of the theory.
___________________________
VI. - Bibliography
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