=Paper=
{{Paper
|id=Vol-2116/paper4
|storemode=property
|title=An Ontology Diagram for Coordination of the Hylomorphically Treated Entities
|pdfUrl=https://ceur-ws.org/Vol-2116/paper4.pdf
|volume=Vol-2116
|authors=Algirdas Budrevicius
|dblpUrl=https://dblp.org/rec/conf/diagrams/Budrevicius18
}}
==An Ontology Diagram for Coordination of the Hylomorphically Treated Entities==
https://ceur-ws.org/Vol-2116/paper4.pdf
An Ontology Diagram for Coordination of the
Hylomorphically Treated Entities
Algirdas Budrevicius[0000-0001-6712-3521]
Vilnius University, Vilnius, Universiteto g. 3, LT-01513, Lithuania
algirdas.budrevicius@kf.vu.lt
Abstract. An Ontology diagram based on the two-dimensional Cartesian coor-
dinate system is described. The diagram is meant both for philosophy and Arti-
ficial Intelligence (e.g., knowledge representation) applications. Generally, the
diagram provides the fundamental articulation of reality. It visualizes relations
among the form and matter and their compounds—entities, such as a thing,
something and nothing. Aristotle’s hylomorphism, the Square of Opposition,
and the Cartesian coordinate system motivates idea of the diagram. The Carte-
sian coordinate system is treated in terms of structure. Matter and form are
viewed as its axes; their intersection then is considered an Ontology coordinate
system. Positive values of the coordinates imply presence, and negative imply
privation of form or matter, correspondingly. Intersection of the axes creates
four quadrants; presence of form and matter (i.e., their compound) makes sub-
stance, or thing. The meaning of quadrants is analyzed in terms of ontology,
logic, and semiotics. The Ontology diagram might reveal new possibilities to
use the Cartesian idea of coordination for humanities and social science applica-
tions. Optimistically, it might become as useful, as the Cartesian coordinate sys-
tem proved to be for mathematics, physics and other domains of science.
Keywords: Ontology Diagram, Hylomorphism, Cartesian Coordinate System,
Semiotics.
1 Introduction
Philosophical ideas and theories traditionally are described in terms of texts. In com-
parison to exact sciences, visual means and diagrams, in particular, are rarely used in
philosophy. Unfortunately, only a few successful and commonly admitted diagrams
are used. The Square of Opposition probably is one of the best known [1]. In this
paper, a diagram for better understanding of basic relations of ontology is considered.
The term ontology is used in two related senses. In the first sense, it is considered a
branch of philosophy—the theory of Being [2]. Ontology—as a philosophical theo-
ry—in this paper is treated in terms of Aristotle’s hylomorphism. In Metaphysics,
Aristotle accounts for Being in terms of two metaphysical principles, the matter and
form [3]. Aristotle chooses hulê (it means wood in Greek) to denote the first principle;
it also may be treated as content; he uses a word shape (morphê in Greek) to denote
the second principle. His theory of Being, accordingly, is denoted by a compound
Y.Sato and Z.Shams (Eds.), SetVR 2018, pp. 60-67, 2018.
An Ontology Diagram for Coordination of... Budrevicius
term hylomorphism—matter-formism. It should be noted that meaning of the form is
not limited to its geometrical treatment as shape. It may have many different interpre-
tations; in particular, Aristotle also treats it as function, when noting that vision is a
form of the eye. Similar idea to treat things as conjunction of form and content is
common in modern times.
In the second sense, the word ontology (and ontologies) is treated as a term used in
Artificial Intelligence research (e.g., in relation to knowledge representation—as set
of concept definitions [4]). Ontologies are often represented by means of diagrams. A
term Ontology chart and Ontology diagram is used in this context.
The purpose of this paper is to describe an Ontology diagram for visual presenta-
tion of the top-level entities and relations among them, accounted for in terms of hy-
lomorphism. The Ontology diagram also may be treated as a case of an Ontology
chart used for knowledge representation in Artificial Intelligence applications—since
the diagram represents the top-level ideas of ontology.
An inspiring idea for building the Ontology diagram is a two-dimensional Carte-
sian system of coordinates. The system is treated in terms of its structure. Form and
matter—the two initial ideas of hylomorphism—are taken as its axes. The four quad-
rants then make the four corresponding top-level entities. The Cartesian coordinate
system also imposes corresponding logical relations among the entities.
2 A Hylomorphism Based Ontological Coordinate System
2.1 Structural Treatment of the Cartesian Coordinate System
An inspiring idea for building the Ontology diagram is the two-dimensional Cartesian
coordinate system. The system was proposed by Descartes [5] as a tool for coordina-
tion of points in space. For building an Ontology diagram, the Cartesian system is
treated in terms of its structure, as Fig. 1 shows. The system subdivides the space into
four quadrants. The coordinates of the structurally treated system do not imply quanti-
ty, what means, for example, that such relations as more or less are not applicable.
The arrows on the axes then indicate only presence (+) or absence (-) of a coordinate.
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An Ontology Diagram for Coordination of... Budrevicius
y
-+ ++
x
-- +-
Fig. 1. The structurally treated Cartesian coordinate system
2.2 Diagram Based on the Ontological Coordinate System
The structurally treated Cartesian coordinate system can be applied for articulation of
Being considered in terms of hylomorphism. Matter and form in such a case is viewed
as two axes of the system. Their intersection then makes an Ontological coordinate
system as Fig. 2 shows. It also may be called a Hylomorphic coordinate system.
Form
Privation III II
of matter Matter
IV I
Privation
of form
Fig. 2. The Ontological coordinate system
There are two options for numbering the quadrants of the Ontological coordinate
system. From the point of view of Aristotle’s ontology, matter is viewed as initial
mode of Being. The numbering, therefore, should naturally begin from the quadrant
determined by presence of matter and privation of form. Such an order is used in the
Fig. 2. Alternatively, a traditional order—used in the Cartesian coordinate system
might be used. The numbering then would start from the quadrant determined by
presence of both, matter and form. Ontologically, such an order would imply that a
compound of form and matter (i.e., substance) is treated as an initial mode of Being.
The term privation of matter in the Fig. 2 needs additional comments. Privation is
not the same as absence. Aristotle gave the following example of privation. A blind
man has a privation of ability to see; however it cannot be said that a stone has priva-
tion of vision, because it has no eyes. It is easy to imagine a privation of form (e.g., as
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An Ontology Diagram for Coordination of... Budrevicius
in case of a formless thing), but absence of matter, especially in terms of Aristotle, is
not thinkable. Aristotle used the term privation only in relation to form, but not mat-
ter. It should be also noted that the terms privation and absence further will be used as
synonyms, implying the meaning privation.
3 A Hylomorphism Based Ontology Diagram
The quadrants of the Ontological coordinate system (Fig. 2) can be further considered
from several perspectives: hylomorphic, logical, and semiotic.
3.1 A Hylomorphic Perspective
Each quadrant of the Ontological coordinate system is determined as a compound of
its hylomorphic components; therefore, the first and natural interpretation should be
done in terms of form and matter. This perspective is the most fundamental one. The
Ontological coordinate system in terms of its hylomorphic components is presented in
the Fig. 3.
Form
Form and Form and
no matter matter
Privation of Matter
matter
No form and Matter and
no matter no form
Privation of
form
Fig. 3. The Ontology diagram presented in terms of the hylomorphic components
3.2 A Logical Perspective
An inspiring idea to consider the logic of the Ontological coordinate system is the
Square of Opposition, also known as the Boethius’ Square; its idea originates from
Aristotle’s On Interpretation [6]. The Square visually represents relations among the
four basic types of propositions [1]. They are listed in the Table 1.
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An Ontology Diagram for Coordination of... Budrevicius
Table 1. The four basic types of propositions
Name Proposition Symbol
Universal affirmative Every S is P A
Universal negative No S is P E
Particular affirmative Some S is P I
Particular negative Some S is not P O
It is proposed in this paper to compare the Square of Opposition with the Ontology
diagram presented in terms of hylomorphic components (Fig.3). Then it is easy to
notice that each quadrant can be interpreted as proposition of the Square of Opposi-
tion, as Table 2 shows.
Table 2. Interpretation of propositions for the Ontology diagram
Quadrant Proposition Interpretation
(See Fig. 2) (See Fig. 3)
Every coordinate is positive (both,
II Universal affirmative
form and matter are present)
No coordinate is positive (both,
IV Universal negative
form and matter are absent)
Some coordinate is positive (one
III Particular affirmative
coordinate, e.g., form is present)
Some coordinate is negative (one
I Particular negative
coordinate, e.g., form is absent)
Also, it should be noted that propositions for the second and fourth quadrants
(Some coordinate is …) have two options: Form is …, or Matter is …; consequently,
there should be two corresponding options of the Ontology diagram. Only one is con-
sidered in this paper.
3.3 A Semiotic Perspective
The Ontology diagram can be also treated in terms of the ontological meaning of its
quadrants. Each quadrant of the diagram in such a case is interpreted as a mode of
Being determined by means of a pair of its coordinates. A pair of form and matter in
the second quadrant then makes substance, or thing (see Fig. 4), putting it in a simpler
way. The thing is a fully determined mode of Being, since both its components, form
and matter are present.
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An Ontology Diagram for Coordination of... Budrevicius
Form
(Immaterial)
Thing
Some-thing
Privation of Matter
matter
(Material)
No-thing
Some-thing
Privation of
form
Fig. 4. The meaning of quadrants of the Ontology diagram
The other three modes of Being in the Ontology diagram are not fully determined,
because they lack either form or matter, or both. In our common language, we may
denote the partly determined mode by a word something; its relation with the thing
can be more clearly seen by means of presenting it as some-thing. The latter is either
immaterial some-thing, when it corresponds to the mode determined by presence of
form and privation of matter, or material some-thing, when determined by privation
of form and presence of matter. The fourth quadrant presents a fully undetermined
mode of Being because it is described in terms of privation of both, form and matter.
It may be termed as no-thing.
An example to illustrate semiotic treatment of the Ontology diagram is provided in
the Fig. 5.
Form
Project House
Privation of Matter
matter
Plot of Building
land materials
Privation of
form
Fig. 5. A thing House presented in terms of the Ontology diagram
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An Ontology Diagram for Coordination of... Budrevicius
The above described interpretation of the quadrants presents a most natural ontolo-
gy of the thing. Other interpretations of the same—top-level—modes of Being are
possible. The word anything can be considered instead of something. Taking into
account relation between something and anything, the Ontology diagram for the thing
can be presented in an alternative way (see Fig. 6).
Form
(Material) Thing
any-thing
Privation Matter
of matter
(Formal)
No-thing any-thing
Privation of
form
Fig. 6. An alternative interpretation of the Ontology diagram (presented in terms of anything
instead of something)
4 Discussion
The Ontological coordinate system provides a hylomorphic treatment of the thing—in
terms of the form and matter. An alternative is mechanistic, common for physics
treatment of the thing when it is defined in terms of a set of its properties. The latter
prevails in modern times. The Ontology diagram treats the thing in terms of its logical
relation to similar entities; the treatment, therefore, may be qualified as logical. Also,
it might be denoted as Cartesian, in the sense that it is based on the idea of the Carte-
sian coordinate system. Most fundamentally, in terms of a metaphysical perspective,
the thing can even be treated as a transcendental.
The thing in the Ontology diagram is treated as a simple ontological entity—in
terms of one form and one matter. Other types of entities also sometimes are treated
as things: e.g., mind, animal, artefact. The latter types of thing have more than one
form and matter; in such a sense they are complex things. An advanced—complex
Ontology diagram should be considered to represent such types of entities.
The form and matter in the Ontology diagram are viewed in terms of logical propo-
sitions; their deeper meaning—as metaphysical principles—is not considered in this
paper. Certain symmetry between the form and matter is present in the diagram, since
privation of form and privation of matter, both are possible; Aristotle, however,
speaks only about privation of form. The symmetry implements a binary principle.
The universality of the binary approach in the treatment of reality was also claimed by
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An Ontology Diagram for Coordination of... Budrevicius
Leibniz. Later, in the twentieth century, the binary principle was implemented in the
fundamentals of information technologies.
In this paper, only basic idea of the Ontology diagram is described. Ideas presented
in this paper are based on author’s previous research, mainly related to semiotics. In
particular, it is described in the book Sign and Form [7]. The following directions of
further research should be considered. A relation between the Ontology diagram and
the Square of Opposition, in particular to the Semiotic Square, should be explored in
more details. Possibilities of the Ontology diagram for the account of cognitive phe-
nomena should be explored—taking into account that hylomorphism can be extended
for the account of cognition. An entire system of the hylomorphism based Ontology
diagrams might be developed.
5 Conclusions
The Ontology diagram is constructed by means of merging the fundamental ideas of
Aristotle, Boethius and Descartes. It implements very simple—but fundamental—idea
of logical coordination of entities. Cartesian coordinate system during the last few
centuries proved to be a powerful tool for mathematics, physics and other domains of
science. The hylomorphism based Ontology diagram developed on its basis might
reveal new possibilities to use the Cartesian idea of coordination for the humanities
and social science applications. In particular, for philosophy, it was applied in treating
the problem of objecthood; for semiotics, it was applied to build the models of the
signified object and the sign as homomorphism [7].
References
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2. Hofweber, T.: Logic and ontology. The Stanford encyclopedia of philosophy.
https://plato.stanford.edu/archives/win2017/entries/logic-ontology, accessed 2017/11/02
3. Aristotle: Metaphysics, book Z and H. Bostock, D. (Translation and commentary), Claren-
don Aristotle series. Clarendon Press, Oxford (1994)
4. Gruber, T.: A translation approach to portable ontology specifications. Knowledge Acqui-
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Aristotle. Random House, New York (1941)
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