Detecting Some Limits of Formal Ontologies

Detecting Some Limits of Formal Ontologies

Ivan Ryant

CTU, Faculty of Information Technologies, Thákurova 7, Praha 6, Czech Republic

and Gymnázium Ústavní 400, Praha 8, Czech Republic

[email protected], [email protected]

ABSTRACT

This case study tries to detect and exemplify some

of the presumptions and limits that formal ontolo-

gies cannot cross. A comprehensible example is

demonstrated. Usefulness of formal ontologies is

not questioned, but the examples show limits of

their paradigm. No particularly surprising findings

are made, just commonly accepted knowledge is

highlighted in examples, which complements the

formal ontologies. Neglecting that knowledge hin-

ders foundational ontologies from efficient support

of domain conceptual models formalization to be

valid.

KEYWORDS

Paradigm, preoccupation, ontology, conceptualizat-

ion, formal ontology

1 INTRODUCTION

What particular domain has been chosen for the

case study presented in this paper and why?

Formalization of domain ontology requires so-

me apriori knowledge of the domain, especially

because foundational ontologies don’t help us

with identification of particular concepts. Thus,

how the expert knowledge of the domain can be

acquired?

Particularly, behaviour analysis is a method

of original, immediate cognition. It requires fur-

ther processing of the collected samples of be-

haviour by empirical induction. That processing

is not only excessively laborious, but it unfortu-

nately can scarcely guarantee completeness of

the resulting domain model, since the very set of

collected samples can scarcely be complete.

And these are probably among the good reasons

why analysts usually resort to the methods of

reusing domain knowledge of other people, al-

though with the risk that errors are adopted, too.

Probably the best case happens, if the do-

main analyst is both educated and experienced

expert in the domain. Otherwise, the analyst

usually strives to obtain the knowledge from

experts and experienced users of some existing

system in the domain. Most usual are interviews

with users and consultations with experts. Those

sources of knowledge are complemented with

reading of manuals, textbooks, standards, and

legislation, which requires the art of interpreting

informal text.

Considering the pros and cons in context and

purpose of this case study, analysis of text has

been chosen as a primary method. It especially

allows to show simple and clear examples. Add-

itionally, various interpretations and ideas ex-

tracted from the text have been consulted then

with experts in order to minimize errors.

What domain has been chosen? Scarcely any

burning ontological issue can be demonstrated

on habitual simplistic libraries or e-shops. And

the domains of tax management or telephone

exchanges (that the author is familiar with) may

be strange to the reader of this paper. What do-

main is the best to demonstrate the very ontol-

ogy? It would be nice to deal with the very qu-

estions of being and not being. Various cultures

have their myths about the roots of being – ab-

out the origin of the world. And just one of tho-

se myths has been chosen as a domain to be

analyzed, learned and formally modelled in this

case study. The story of Genesis is probably the

best known of the myths and its various inter-

pretations seem comprehensible for everyone. It

is an old story, and its interpretation evolved in

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the course of history and changes of cultural en-

vironments. It is perfectly preserved both in its

nearly original Masoretic version, as well as in

several translations with their semantic shifts. It

can be compared with several other myths, as

well as with modern scientific theories. It is a

perfect material for making clear examples.

2 AN ATTEMPT TO FORMALIZE

GENESIS IN ONTOUML

The biblical Book of Genesis tells the well-

known story of the God, who created the world,

plants, animals, a man, and a woman. The de-

scendants of the first pair of people are enumer-

ated then, and details of their lives are told.

Let’s concentrate in this paper just on the first

day of creation, because it is ontologically

crucial.

The most readers understand the text as a

story of somebody similar to a magician, who

pulls the rabbits out of his hat – the story which

takes place in an actual space, where the actual

matter is formed and transformed, and which

evolves in time. Nevertheless, this view seems

not to be correct, simply because there were no

space, no matter, and no time at the very begin-

ning. Let us leave the difficult questions about

material world to theologists and physicists and

focus on the ontological aspect of the text.

The story of creation can be interpreted not

as a story, but as a stepwise description, or ex-

planation, of domain ontology of the world.

Every step of the explanation can be depicted in

an OntoUML diagram.

2.1 The First Sentence

In the beginning God created the heavens and

the earth.1

The Bible is written by people for people in a

human language and thus, it allows various (or

alternative) interpretations. That means, my dia-

grams depict just one alternative from the var-

iety of possible valid and invalid models.

Neither formality of OntoUml, nor exactness of

its definition can guarantee correctness of do-

main understanding, correct choice of an alter-

native, or validity of the model (see [1], pp. 27,

80, 157; compare Ullmann’s to Frege’s triang-

le). No model can be valid on itself only,

regardless of its purpose.

Another source of uncertainty and ambiguity

is the fuzzy distinction between the language of

description and the domain being described.

Terms like heavens and earth probably belong

to the domain. But how about beginning and

God? Beginning may be assumed to be a word

from the description language, since it is intuit-

ively understandable and it doesn’t take part in

the act of creation. The God, on the other hand,

is He who creates the world, and that’s why

God is included into the model. Notice that God

isn’t provided with any stereotype: He is neither

a material thing or a living body (like «kinds»

and «subkinds»), nor just an abstract concept

(because He is a very special spiritual being).

Nevertheless, even our idea of God evolves, as

we learn it in the course of reading Genesis.

What we have learned of Him in the first

sentence? – He can create things. And, may be,

1 see American Standard Version in “Bible Gateway,”

http://www.biblegateway.com/

Figure 1: Ontological model of Gen 1:1

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in the course of creation, He has created even

Himself…

Why are the concepts of earth and heavens

stereotyped just as «kinds»? – Simply because

there is mentioned no other concept that could

be considered a superkind of them. Nonetheless,

we may wish to improve robustness of the mo-

del, and introduce a general “subject of creat-

ion” concept to be referenced by the creator ro-

le. “Subject of creation” becomes then a com-

mon ancestor for both heavens and earth. But

the foundational ontolgy of [1] doesn’t help us

to determine, what stereotype should we put on

that common term. It may be either «category»,

in which case the “subject of creation” doesn’t

have identity, or it may even be «kind», in

which case heavens and earth must become its

«subkinds». Choice between concepts that

have and that haven’t identity is left on the

interpretation of the domain knowledge. Anci-

ent metaphysicists discussed the issues about

identity in more detail in contrast to contemp-

orary foundational ontologies. You may oppose

that identity is something evident. Yes, it is true:

evidence is something elementary mystical, but

neither rational nor empirical.

2.2 The Second Sentence

And the earth was waste and void; and dark-

ness was upon the face of the deep: and the

Spirit of God moved upon the face of the

waters.

Words like “waste”, “void”, “dark”, “deep”

and “water” (or “empty”, “formless”, “невиди-ма и неустроена”2 in other translations) don’t

mean any of created things, but they characteri-ze the primordial state of creation. They don’t

refer to things but to properties that can char-

acterize things. That is the difference between characterizing universals and sortals, as expla-

ined in [1]. Those characterizing universals are apparently attributed to nothingness. Nothing-

ness is empty, dark, and deep. Nothingness can-not contain anything, neither it can be composed

of anything – it is empty. The concept of being empty doesn’t need any opposite term: it makes

sense on itself. Similarly, darkness doesn’t need

light to be conceptualized. This seems unaccept-able for us: the sole concept without any oppos-

ite cannot carry information. But this indica-tes rather our wrong preconception than an er-

ror in the conceptual modelling in Genesis. Mo-re of the Aristotelian metaphysics [2] helps to

understand this bias, and then the original Heb-rew text becomes more understandable. Notice

that darkness characterizes the concept of no-

thing positively – it is an attribute of nothing-ness, it isn’t described negatively – by what it

isn’t. Nothingness is also deep: it has no bottom,

2 approx. “invisible and messy” in church-slavonic tra-

nslation by Cyril and Methodius (see e.g. “Библия,”

http://www.wco.ru/biblio/books/bible_cs/bible_cs_pd

f/gen.pdf), verbatim from Septuagint (see e.g. “Kata

Biblon Greek Septuagint and Wiki English Translat-

ion,” [s.l.]: Thomas Moore, 2013, http://en.katabiblon

.com/us/index.php?text=LXX&book=Gn&ch=1)


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no shore, and no level – there is no space in no-thingness (notice negative description, again).

People imagine water as a liquid matter that has its gravity, extends in space and changes as the time passes. We cannot grasp water – it flows through our fingers. Liquid water keeps no specific shape. But this description cannot be true at the very beginning, when no matter, no space, and no time was created. The concept of water can be defined here with its only attribute that pertains to the initial context of Genesis – it is formless. Nota bene: total absence of form means absence of any information, maximum disorder, or chaos.

The Hebrew phrase “תהו ובהו” [tóhú va-vóhú] is translated as “waste and void”, or “without form and void”, or “inane and empty”. It is a ke-y phrase in the second sentence. It is nowadays used to express chaos. The Germans say “tohu-wa-bohu” as an expression for disorder and con-fusion. Particularly, Martin Buber and Franz Rosenzweig translate it as “Irrsal und Wirrsal”3 – confusion and noise. That translation may resemble an idea of Big Bang (which belongs to physics) but it cannot satisfy an ontologist, since noise must necessarily have a source, something noisy, but definitely not nothing. On the other hand, “waste and void” can easily be interpreted as “nothingness”. This modern and post-modern interpretation refers to entropy, thermodynam-ics, and this way also to the information theory.

While the phrase “waste and void” is a com-

fortable theme for amusing speculations ad libi-

tum, there still remains another important quest-

ion – and that question is really difficult to an-

swer. There was nothing in the very beginning

but “the Spirit of God moved upon the face of

the waters” (or “hovered” in other translations).

What is that “Spirit of God”? Common sense

suggests, it cannot be something because there

was not anything. On the other hand, it must be

something because it differs from “waters”, over

which it was hovering. I am able to provide an

explanation although it may not conform to

theological exegesis.

3 see Martin Buber, F. Rosenzweig, “Die Schrift,”

[s.l.]: GVH Wissenschaft & Gemeindepraxis, 2007

Acceptable explanation for purposes of this

paper may be e.g. that the “Spirit of God” is the

most proper potency of nothingness to change

into something, or perhaps the very change as it

is contained in the nothingness, the change be-

ing started, and ripping inexorably to its frui-

tion. It is a feature virtually inseparable from the

very essence of nothingness, without which the

nothingness is not itself. The conscious nothing-

ness becomes a concept of nothingness, and the

very concept of nothingness is something. That

is probably information in its germ, raw, pure

form, which formed formless primordial χαος

into matter, which formed κοσμος from no-

thingness – a world that obeys order and makes

sense. The nothingness can scarcely be devoid

of capability to change from nothing to some-

thing – of the capability to change its own un-

certainty into the certainty, i.e. of the inform-

ation.

Notice that creation out of nothing contra-

dicts the formal rules of foundational ontolo-

gy. According to [1] p. 221, every universal

must have instances, but the concept of nothing

has no instances, since it is a speculative com-

plement to the notion of something. We will see

that the root of this contradiction lies more

deeply – in incompatibility between the ration-

al paradigm of formal foundational ontolog-

ies and the dialectical paradigm of Aristotelian

manner of scientific thinking.

2.3 The Third Sentence

And God said, Let there be light: and there was

light.

Notice, what power a word has: it can create

things. It looks like a magic, but the word of

God is not a magic formula. Some important

ontological principle got lost here in translations

and ages. Reading the original text is necessary

in order to get better understanding.

The diagram in fig. 3 shows light as it would

be just another thing, which God created. The

more detailed analysis shows that this interpret-

ation is simplistic. Why?

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God created light unless there were any

physical source of light. There was neither the

Sun nor the Moon, neither flashbulbs nor cand-

les. No particles cruised the space, no electro-

magnetic field spread there. There was no matt-

er: no gravity tied things together, no space ex-

panded, no time passed. The physicists explain

that at the very beginning of Big Bang no

physical rules held. Then the space started to ex-

pand, and the matter and energy were still extre-

mely condensed – they had a form of ubiquitous

light without any apparent source. That is phys-

ical interpretation, sticking in the paradigm of

physics.

Ontology, on the contrary, must conceptual-

ize matter with gravity, space and time, prior to

formulating principles of physics. God chose ti-

me to be created first – of course, time without

matter is physical nonsense, but conceptually,

time can be separated, time is a good first ele-

mentary step to formulate principles of physics.

And time is based on the common principle of

change, and change assumes some opposite

concepts – in this case the contrast between

darkness and light. Why? The mere darkness is

a property of nothingness. Darkness doesn’t

need light. It is light in potentiam.

Notice that God didn’t created everything out

of nothing in a single big step (although actual

“nothing” can be thought of as potential “every-

thing”). On the contrary, He built just “some-

thing” in the first step and gradually the whole

universe in many elementary conceptual steps,

bit by bit.

2.4 The Fourth Sentence

And God saw the light, that it was good: and

God divided the light from the darkness.

Light is good. Notice again: the sole concept

is introduced without any opposite.

The good is not created. It is again a charac-

terizing universal. Of course, the «mode» with

a relation to another «mode», but without direct

link to anything being characterized, seems

strange. This incompleteness of the model re-

quires probably further analysis of the following

text, which exceeds the scope of this simple

case study.

Notice also that the concept of good is intro-

duced prior to gravity, space, and time. It looks

like the good should not be matter of place,

moment, custom, or opinion, but it is an ab-

solute ethical value. The good doesn’t define

things, but it is a universal property that tra-

nscends any particular thing. The idea of tra-

nscendence is Aristotelian [2], and thus may be

alien to the original Hebrew thinking. Interpret-

ations like this appear especially in the Middle

Ages with Thomas Aquinas and are routinely

(and unconsciously) accepted today as evident.

2.5 The Fifth Sentence

And God called the light Day, and the

darkness he called Night. And there was

evening and there was morning, one day.

Time starts passing. The concept of time is

introduced as alternating dark and light. For the

flow of time, the concept of alternation is sub-

stantial. Alternation is kind of change, and it is

introduced here. However, it is apparent that

time here is still not a physical quantity, because

there is no physical source of light. From the

Divine ontological viewpoint, time can be in-

terpreted rather as the mere principle of flow

of changes. That principle will be utilized later

in order to define physical time.


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Neither we humans perceive time only as a

physical quantity but mainly as one of the

qualities of our sojourn in the world. We act

always in the present. The future is for us a

selection of several more or less likely

possibilities, one of which will become actual.

The past was present before it passed. Although

we believe that only one past actually happened,

we are often looking after it, as it were one of

the many variants of “possible” pasts. If we

didn’t live in time, we could neither remember,

nor hope, nor expect, nor feel surprised. Time is

a prerequisite for conscious human existence.

Day, evening, night and morning alternate

during one day – they are «phases» of a day as

a whole. The word “day” is overloaded here: it

means (1) a light «phase» of a whole day, (2) a

day as a whole, and according to some trans-

lations, even (3) measure of time. The American

Standard Version reads “one day”, probably be-

cause in that moment the one whole day got cre-

ated and there was no other consecutive day at

that moment. But the 21-st Century King James

Version reads on contrary “the first day”, prob-

ably because the second, third etc. days follow.

The original Hebrew text can explain this

ambiguity.

3 HUMANISTIC AND RATIONAL

BACKGROUND BEHIND FORMAL

ONTOLOGIES

In contrast to medieval dogmatism, humanism emphasizes individuals and freedom of think-ing. Humanists translated Bible from its origin-al languages to modern national languages, e.g. KJV4 and the Czech Bible of Kralice5. The Czech translators introduced a strange idea into Gen 1:2: the earth was ugly (“nesličná”) at the beginning. It looks like the Czech humanists (unlike Aristotle) added æsthetic values to the set of transcendental predicates of metaphysics.

Confidence in the power of human reason also grows up from humanism. Founders of rat-ionalism (Descartes, Pascal, Leibniz…) laid the foundations of mathematical logic with its sim-plicity, formal exactness, and ease of use (in contrast to Aristotelian syllogism). They created a new, modern scientific paradigm with its pre-occupations and uncrossable limits. Mathemati-cal logic also introduces several drawbacks in formal ontologies, particularly:

4 see e.g. “The Official King James Bible Online,”

http://www.kingjamesbibleonline.org/1611-Bible/ 5 see e.g. “Bible Kralická,“ http://cs.wikisource.org/

wiki/Bible_(Kralick%C3%A1)/Genesis


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mathematical logic omits pragmatic aspect

of concepts, it deprives things of purpose

and sense, and this way, it prevents entities

to be identified correctly

Leibniz principle of identity doesn’t allow

things to change in their accidents (like roles

and phases) without losing identity

While the first deficiency remains unsolved

in foundational ontologies (as shown in this

paper in analysis of Gen 1:1), the second one is

avoided e.g. by temporal (Guarino [3]) or modal

(Guizzardi [1]) extension to mathematical logic.

Logic is a tool and formal set theory is a do-

main ontology of mathematics. It means that the

contemporary foundational ontologies are

built upon domain ontology of mathematics –

on sets, mappings etc. Is this really a correct

way, how to construct foundational ontologies?

Rationalism seems to exclude Aristotelian

dialectical thinking from the ontological tool-

box, as well as transcendentalia from the onto-

logy itself. Nevertheless, Norbert Wiener in his

famous book [4] broadly discusses how cyber-

netics and especially the information theory are

based on those old ideas of χαος and κοσμος, on

belief that being is good by definition, on belief

in creation, and on eschatological expectations.

He associates nothingness with primordial

chaos, and form (or regularity) with cosmos.

Then he develops a compelling ethical theory

that suits well to the existential situation of the

human society in the postindustrial world. This

way, among others, Wiener creates his specific

interpretation of the book of Genesis.

4 GREEK REINTERPRETATION OF

GENESIS

Comparison of Greek myths with other Ind-Eu-

ropean ones exhibits possible influence of old

Mediterranean culture on Greek Ind-European

mythology.

Let us particularly compare Gen 1:2 with the

myth of Θεογονια (Creation of Gods) by Ησίο-

δος6: “ητοι μεν πρωτιστα Χαος γενετ, αυταρ

6 see e.g. Ησίοδος, “Θεογονια,” http://www.perseus.

tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.

01.0129%3Acard%3D104


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επειτα Γαι ευρυστερνος” (at first Chaos got

born, then the Earth broad-breasted). We can

see an evident parallel between Gen 1:2 and

Θεογονια, which has led later to synthesis of

both, as demonstrated in this paper.

Light without physical source (Gen 1:3) –

more likely brightness, or “Αιθήρ” – is a con-

cept, which we also encounter in Θεογονια: the

“Αιθήρ” and the Day got born from the Night,

and the Night got born from Chaos (“εκ Χάεος

δ Ερεβός τε μέλαινά τε Νυξ εγένοντο: Νυκτος

δ αυτ Αιθήρ τε και Ημέρη εξεγένοντο“).

In the early third century B.C. in Egypt, the

team of 72 Hebrew scholars translated the He-

brew Bible to Greek – the Septuagint. The

translation suffered some semantic shifts (e.g.

κύριος παντοκράτωρ”) and even“ – ”יהוה צבאות“

mistakes (e.g. “רקע” – “στερέωμα”), mostly by

the influence of the Hellenistic cultural environ-

ment. Hellenism dominated in the ancient world

in the time, when Septuagint got translated.

Greeks adopted and adapted foreign ideas from

the entire ancient world, including India and

(indirectly) probably also China (e.g. influence

of Lao’c on Plato is a subject of speculations).

And on the contrary, the Hellenistic thinking

influenced other nations and their way of life

and thinking, including interpretation of the

Hebrew Genesis. Particularly, Aristotelian

metaphysics contributed to the new semantic

layer of interpretation of Genesis. For example,

the idea that creation means giving shape to

χαος is of Greek, and, may be, even Aristotelian

origin. Nonetheless, meaning of the Hebrew

word “א in Gen 1:1 has (created – [bara]) ”בר

nothing to do with shape or form. Similarly,

“άόρατος καί άκατασκεύαστος” definitely is not

a true translation of “תהו ובהו” in Gen 1:2.

“άόρατος καί άκατασκεύαστος” means ap-

proximately: “invisible and unconstructed”.

Notice (1) that negated attribute “invisible” is

used for nothingness and (2) that “uncon-

structed” refers to the absence of structure, only

one specific aspect of nothingness. And it is just

the absence of structure, what is assumed to be

the main attribute of the modern concept of

chaos, especially in the thermodynamics and in

the theory of information. But it is not the

original meaning of “תהו ובהו”.

The word “תהו” appears then as formlessness

in the English translation KJB: “And the earth

was without form, and voyd, and darkenesse

was vpon the face of the deep: and the Spirit of

God mooued vpon the face of the waters.” –

probably under the influence of Septuagint. We

have seen that this tradition is also maintained

in translations to church-slavonic “невидима и

неустроена”.

Aristotle was familiar with several things

that are strange to Gen 1:1 – Gen 1:5, but not

to later translations and interpretations. He knew

how to use negation (στέρησις), as well as spe-

culation based on negation. In addition, he al-

most always worked with pairs of opposing

concepts (substance – accident, potentiality –

actuality, stuff – form) – he worked with

elementary 1-bit information. This way, he

speculatively distinguished in every actual thing

the stuff (υλη) and form (μορφη). And to each

actual thing, he speculated of its potential de-

terminations (δυναμεις): ability to take or not to

take form (δυναμεις του παθειν η απαθειν) and

the ability to give form (είδος) to an amorphous

stuff (δυναμεις του ποιειν). Each thing in

metaphysics can change its accidents and this

way it can evolve. Surprisingly, although it is

basically descriptive, the Aristotelian meta-

physics is fairly well dialectical. Here we can

see clearly the idea of creation as forming an

amorphous stuff, which aligns well with

contemporary thinking in ontology as well as in

cybernetics, informatics, and information

theory.

Nowadays, we can continue extending the

Aristotelian metaphysics. Some accidents may

be taken for lower-order things, each with its

own substance and accidents. An accident,

which is modelled as a state in a statechart, may

be decomposed into more detailed statechart – it

is one of the principles of decomposition in

Harel’s statecharts.

Thomas Aquinas reinterpreted Christian

philosophy in the Middle Ages. He synthesized

Christianity with Aristotelian metaphysics. This

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introduced Aristotelian logic, dialectical think-

ing and abstract speculations into the interpret-

ation of Bible, including the story of Genesis.

5 UNDERSTANDING THE MASORETIC

TEXT OF GENESIS

In order to validate our contemporary ontology

of Genesis, we need to distinguish additional

semantical shifts from the original meaning, as

it is preserved in the rabbinic interpretation.

The Hebrew text is in the left column. It

reads from right to left. Only consonants have

their characters. Groups of (usually three) con-

sonants carry the meaning. Vowels are indicated

by punctuation – a kind of “diacritics”. In the

middle column, every sentence is transcribed

phonetically letter by letter divided with hyph-

ens and with the stress emphasized in boldface.

Translation is provided in the right column.

5.1 The First Sentence

Various alternative interpretations of the first

sentence are tractable. Let us take an example.

Rabbi of Prague, Mr. David Peter told me that

the word “מים is used in common (heavens) ”ש

Hebrew even as an appeal to God. This would

mean (continued Mr. Peter) that God created

primarily Himself in the beginning, and then

the earth.

That anecdote is not so naïve, as it may seem at

the first glance (no surprise, it is the rabbinic

anecdote). Allow me a speculation in Aristotel-

ian fashion: If there was nothing at the very

beginning, then God was necessarily not actual

but just potential. And with the first act of

creation, the God became actual: while acting,

He actualized (and realized) Himself. Notice

that an act is definitely actual but “reality” is

only a conceptualization of phenomena and

notice that phenomena may be true as well as

delusive. Thus we have a concept of actual God

and He is called “אלהים” (the God) through the

whole first chapter of the Book of Genesis – but

not “יהוה” ([Adonai], the LORD). We may con-

sider “יהוה” to be His given name and thus He

becomes a living being as late as in the moment

when the name “יהוה” is given to Him – this is

just my intuition (definitely no professional

exegesis). However, my reasoning of actual and

possible scarcely can appropriately explain the

meaning of the original Hebrew text.

The point is that none of the possible inter-

pretations can be regarded as the only correct

interpretation. Critical reflection and discussion

is the human way to understanding, while only

the omniscient God knows the absolute truth

(He is the Truth).

Table 1. The first sentence word by word (see American Standard Version)

Hebrew word Pronounciation Meaning

be- in ב

”r-e-sh-í-t head, or here rather “beginning ראשית

א ba-r-a created – is used only in connection with God בר

,is an expression of reverence ”ים“ E-lo-h-í-m God – the suffix of plural אלהים

like capital “G” in “God”

e-t preposition indicating that the object follows את

ha- the ה

מים sha-má-yí-m heavens ש

ve- and ו

e-t preposition of object את

ha- the ה

á-re-c earth ארץ

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5.2 The Second Sentence

The original Hebrew way of thinking was natu-

ral and direct (like natural deduction, or direct

proof). New terms are described positively.

Negation is not a proper tool in the old Hebrew

thinking. Terms are not defined by negation of

other terms. Reductio ad absurdum doesn’t take

place in the logical toolbox of the oldest layer

of Genesis. Further, concepts in old Hebrew

thinking don’t require their opposite counter-

parts: black and white, good and evil, etc. The

modern man is used to think dialectically, in

pairs of opposites. Thinking in single concepts

doesn’t allow differentiation, it seems, it cannot

carry any single bit of information. But nothi-

ngness means no information, of course. Let us

realize that all this discussion doesn’t say much

of the old Hebrew way of thinking, but on the

contrary, it sheds more light on our modern

preconceptions and unconscious stereotypes.

A key expression of the whole sentence is

a famous saying “תהו ובהו”, which translates

probably as “waste and void” but often also

otherwise. According to Mr. Peter, the word

– may etymologically refer to amazement ”תהו“

to the amazement of nothingness. We have seen

in previous paragraphs, how the interpretation

of the phrase “תהו ובהו” shifted through

centuries.

5.3 The Third Sentence

Where does word take its power to create

things? In Hebrew way of thinking, it is no sur-

prise: Hebrew word דבר (da-va-r) means both

“word” as well as “thing”. Even for Gottlob

Frege both the word and the thing are just vari-

ous aspects of a concept – so far so good. But

where came the very concept of the “word”

from? For only the “רוח אלהים”, the Spirit of

God hovered over the waters. Psalms 33:6

Table 2. The second sentence word by word


ve- and – here it indicates narration ו

ha- the ה

á-re-c earth ארץ

ה ית há-y-tá was ה

tó-h-ú empty, waste תהו

va- and ו

vó-h-ú void – this word doesn’t occur in any other known text but only בהו

here; its meaning can be just estimated from context, as a

complement to the word “תהו”

ve- and ו

khó-she-kh darkness חשך

a-l- on, over על

p-né-y face פני

te-h-ó-m the deep תהום

ve- and ו

r-ú-akh Spirit רוח

E-lo-h-í-m of God אלהים

me-ra-khe-fe-t was hovering מרחפת

a-l- on, over על

p-né-y face פני

ha- the ה

ים má-yí-m waters מ

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explain this: “By the word (בדבר) of the LORD

the heavens were made, their starry host by the

breath ( רוח) of his mouth.” Everything gets

clear, as we realize that the Hebrew word “ רוח”

means both “breath” (or even breeze) as well as

“spirit”. Similarly, the Latin word “spirit” is

derived from “spirare” (to breath), or the Greek

word πνεύμα means both “soul” and “breath”.

We can see that creating things by word is

exactly what we search for: conceptual

modelling. This example shows, how crucially

is ontology dependent of language (compare [1],

p. 79).

5.4 The Fourth Sentence

In this sentence, the concept of being good

appears for the first time. Notice that the

distinction between good and evil belongs to

the man and civilization. It appears first time in

Gen 2:9 – “ע -tree of the know) ”עץ, הדעת טוב ור

ledge of good and evil). Nature, on the contra-

ry, is good simply by being: the fox is not bad,

when it kills a rabbit, it’s just its nature, and

that is good. Also, the light is good just by its

Divine creation, without having to define evil.

So far the rabbinical interpretation.

Ontologists may continue reading. It repeats

in the following text of Gen:1 like a refrain:

Table 4. The fourth sentence word by word


vay-yá-r-‘ and saw – the silent phoneme at the end is not pronounced וירא

E-lo-h-í-m God אלהים

e-t- indication of object את

ha- the ה

ó-r light (brightness)-‘ אור

kh-í that is why, that (it was) כי

t-o-v good טוב

בדלוי vay-ya-v-dé-l and separated – narrative form of the verb


b-é-n between (either) בין

ha- the ה

ó-r light-‘ אור

u-v-é-n and between (or) ובין

ha- the ה

khó-še-kh darkness חשך

Table 3. The third sentence word by word


vay- and – indicates narration ו

yó-me-r said יאמר


ye-h-í let there be יהי

ó-r light (brightness) – the first consonant aleph is mute, a stroke is-‘ אור

pronounced instead in order to separate the preceding word

from the next one

va- and – indicates narration ו

y-h-í there was יהי

ó-r light (brightness)-‘ אור

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every time God creates anything, He sees, it is

good. It probably doesn’t mean that God attri-

butes every new thing with the property of be-

ing good, but on contrary, it may rather mean

that the concept of “good” is defined step by

step with every elementary act of creation. As

late as the man is created, the opposite term of

“evil” can be introduced. Only then the dual

concept of good and evil is completed in the

fashion that satisfies us ontologically.

5.5 The Fifth Sentence

There is an ambiguity between e.g. American

Standard Version and 21-st Century King Ja-

mes Version. The former reads “one day”,

while the latter reads “the first day”. The reason

is in the Hebrew original text: the word “ד ”אח

[ekhad] may mean “one” (e.g. Gen 42:13), “the

first one” (Gen 2:11), or even “the only one”

(Dt 6:4).

6 CONCLUSIONS

This case study exemplifies some limits of

formal foundational ontologies (the same limits

hold for [1], as well as [3] or Heller’s and Her-

re’s GFO etc.), especially:

formal ontologies don’t help to identify en-

tities in a domain

dialectical thinking cannot be substituted by

the logic of formal ontologies

formal ontologies omit transcendental

predicates of metaphysics and provide no

substitution

formal ontologies don’t guarantee validity

of the resulting domain ontology

Nevertheless, there is no doubt that formal

ontologies cannot be substituted by philosoph-

ical ontologies, either, because of several com-

monly known reasons, e.g.:

formal ontologies help to detect formal er-

rors in models

formal ontologies allow to automate further

development of software based on domain

ontologies

formal ontologies allow formal verification

of domain models as well as other useful

tasks based on formal deduction

This case study also exemplifies that the an-

cient Aristotelian metaphysics can be updated

for the needs of contemporary ontological

Table 5. The fifth sentence word by word


א vay-yi-q-rá and called – narrative form of the verb ויקר


la- to – preposition of direction or belonging ל

ó-r light-‘ אור

y-ó-m day יום

ve- and ו

la- to – preposition of direction or belonging ל

שךח khó-she-kh darkness

א ר א“ as ”קרא“ qa-r-a he called – notice the same root ק ”ויקר

ילה la-y-lá-h night ל

va-y-hí and was ויהי

e-re-v evening ערב

va-y-hí and was ויהי

vó-qe-r morning בקר

y-ó-m day יום

ד e-kha-d one אח

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efforts in order to compensate the deficiencies

of contemporary formal ontologies.

7 ACKNOWLDGMENTS

My special thanks for many hours of selfless

consultations and for kind comments belong to

the Chief Rabbi of Prague, Mr. David Peter; to

the preacher of the Czech Brethren Evangelical

Church and Commander of the Order of St.

Lazarus of Jerusalem, doc. MUDr. Zdeněk

Susa, CSc.; to the teacher at the Catholic

Theological Faculty of the Charles University,

doc. Josef Hřebík Th.D. S.S.L.; to the pastor

of the Czech Brethren Evangelical Church and

the consenior of the Liberec seniorate, Mgr.

Filip Susa, Th.D; to the mathematician, doc.

RNDr. Alena Šolcová, Ph.D.; to the English

teacher at the Gymnázium Ústavní, Mgr. Jaro-

slava P. Siváková; to the readers and workers

of the RVP Methodological Portal of the

Ministry of Education of the Czech Republic,

especially to PhDr. Ondřej Neumajer, Ph.D.;

to doc. Ing. Vojtěch Merunka, Ph.D.; to the

head of the Software Engineering Department

of the Faculty of Information Technologies of

the Czech Technical University, Ing. Michal

Valenta, Ph.D.; to my colleagues from the

Centre for Conceptual Modelling at CTU FIT:

Ing. Zdeněk Rybola, Ing. David Buchtela,

Ph.D., Ing. Martin Podloucký, and last but not

least to the head of the CCM Ing. Robert

Pergl, Ph.D.

8 REFERENCES

[1] Giancarlo Guizzardi, “Ontological Foundations for

Structural Conceptual Models,” CTIT Telematica Instituut, Enschede, 2005.

[2] Aristotle, “Metaphysics,” http://classics.mit.edu/Aristotle/metaphysics.html

[3] Nicola Guarino, C. Welty, “Towards a methodology for ontology based model engineering,” in Proceedings of IWME-2000: International Workshop on Model Engineering, 2000, http://www.ladseb.pd.cnr.it/ infor/Ontology/Papers/ecoop-00-ws.pdf

[4] Norbert Wiener, “Cybernetics and Society. The Human Use of Human Beings,” Boston: Mougton Mifflin, 1949.

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Detecting Some Limits of Formal Ontologies

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