1987 / 2007

Prof. Dr Socrates Kaplanis Patra 29.08.2007
T.E.I. of Patra, Greece
Institutional Coordinator

Giannena
Various Maps of ancient Greek lands, where Greek
Civilization and Philosophy flourished.


The forerunner of the European civilization both in its diversity and unity is to be found in the Hellenic world.

to quote:
1.Theodor Gomperz in “ Griechische Denker” Liepsig, 1922:
“..Almost all our intellectual culture has a Greek descent.
The deep understanding of its philosophical streams is a prerequisite to get free from its impact. In this case, to ignore the past, is not only unwanted, is merely impossible….the whole of our thinking/reflections, the notional order in which they move about, are to an

outstanding degree outcomes of the great thinkers of this past….”, and

2. Paul Valery:
“
We owe to Greece the very feature which perhaps distinguishes us the most profoundly from the rest of humanity.
We owe it spiritual discipline the extraordinary example of perfection in all areas.
We owe it a way of thinking which refers things to man the whole man…”

Ancient Greece is a period in the Greek history, like a continuous evolution, that for around 1000 years was considered to be the seminal culture, which provided the foundation of Western Civilisation.
The Greek culture had a direct influence to the Roman
Empire which carried a version of it to the other parts of
Europe, if not the known part of the world.

The civilisation of the ancient Greeks has been immensely influential on the Language, Politics, Educational
Systems, Philosophy, Science and Arts giving rise to
Renaissance , while again resurgent during various neo-classical periods, in the
18 th
and 19 th
century, in Europe and America, contributed to the modern societies…



The identity of the Western World was gradually established and forged, using primarily the Greek philosophical analysis, during 3 important periods .

st

Renaissance, [15 th -16 th cent.], influenced by scholars who left, (fled), Byzantium/ Constantinopole/ Instanbul, passed to Italy and trans-planted, cultivated and taught the Greek
Letters, Art, Sciences and Philosophy.
Here, is an example of an edition by Ianos Laskaris, a Greek scholar , who went to Florence to live after Constantinopole was conquered, (1453 A.D.)
The script uses the clergy calligraphic fonts of that period.

nd

The Age of Reason and the Age of Enlightenment ,
[1600-1800 A.D.]: disclosing, re-approaching the scripts and teaching of the ancient Greek Philosophers, re-elaborating the Hellenic approach to Life, to Gen(n)esis , to Existence, to the Being…
…to mention few of those personalities:

Francis Bacon,[ 1561-1621], the first to introduce the experimental Philosophy , was taught Aristotelic analysis .


Descartes, [1596 La Haye- 1650 Stockholm]
He was much interested in the traditional Aristotelian
Philosophy.

Voltaire a pseudonyme, [pseudos=lie and onoma=name] of Francois Marie Arouet, [1694-1778], Paris

Emmanuel Kant, [1724-1804], K ö eningsberg

rd
th
th
.
…to start with,
Erwin Schroedinger , [1887-1961], a Nobel Laureate, on
“
Nature`s dualism”
in his book “ Nature and the Greeks
” highlights, enlightens, discloses, pinpoints the Greek Philosophers ideas, axioms ,
[axioma= postulate], the Questioning to Gen(n)esis , the
Reason…..
He outlines their Cosmology and Cosmo-theory , as a model.
His command on the Greek language was marvelous.

,
Philosophers, mysts, scholars, archeologists and other scientists of various philosophical schools ,[ Diels, Burnet,
Gomperz, Mendel, Russel, Heidegger, Hume, Hegel,
Berkeley, Nietzche and so many others…] explore the Reason, Cause- Causality, Certainty and
Uncertainty, Absolute and Relative, Deterministic and
Stochastic ,
[always the two opposites; teaching principles by Empedocles ], towards the Truth , with tools the Greek Philosophical Questioning, the Dispute: the Socratic dialogues and the Aristotelic analysis, which investigates things and beings examining if they are by virtue, or under action, or by chance.

The latter to occur is not scientific as repeatability is not guaranteed.

A deep insight into the Man…a tool to think, to search…
…to develop.


Cosmogony & Cosmology, Cosmo-theory,
Theogony, Theology, ( mainly oriented to Metaphysics and secondly to morals )

The stories are not a collection of myths, ….they do not constitute mythology.
They provide a logic interpretation through a systematic effort to answer rationally convincing:
“where I am”, “What it is” “What it is for”, “What was for”
“τι ην είναι ?” Aristotle`s question

Herodotus, [5 th
century B.C.], from the Greek city of
Halicarnassus, (now modern Bodrum) in S.W. Turkey, and
Thucydides, [460-395 B.C.], Athens, a general and historian give quite a lot of information of the events historical and others that happened in this known part of the world.

.

Both come from the innumerable depths in History.
The Cosmic egg in the Cosmogonies stands for Genesis.
It erupts and… the Light… Fanis …..
Eros
…Dionysos appears.
In fact, this is the Bing- Bang theory of our scientific models.



The duality of the Man: a.
Titanic property…the mortal b.
The devine property …which comes from Dionysos
God, see Orphic myth.

In Isiodos Theogony , first was Chaos , then the Earth and Tartar and Eros ( Fanis )
From Chaos were born Night ( Nychta ) and Erevos.
From Nychta were born Ether and Day.

In Ieronymos rhapsodies :
Chronos, (=Time), was the first.
Then , Ether was born along with Chaos and Erevos .

:

Thales, [624-546 B.C.] from Militos, the Greek city in
Minor Asia, in the Ionian coast, under Turkey today, is the first of the 7 sages of Greece.
He is considered as the father of Science and he is credited with
5 theorems in Geometry . Teacher of Anaximandros , [611-545
B.C.] from Militos, too.

Thales predicted the solar eclipse in 28 May 585 B.C.
He measured the height of pyramids from their shadow, exactly when the time the shadow of a man is equal to his height.
That is he used the similarity of Tri angles. electron…and electrify
was due to his observations conveyed to next generations.

Pythagoras,[ 582-497 B.C.] from Samos island.
His Tetractis and his theorems , like a
2
+ b
2
= c
2 the geometric mean, and the Golden Ratio, number, φ,
[1.610….]
The Geometric mean: x
2
= p*q

if p=2q , and q=1 , then x= square root of
√
2 !!!! geometrically determined. are the basic tools for mathematical logic and proof.
Greeks focused their interests to Geometry: [Geo or Gaia=
Gi=Earth and meter= mέtro and metrό= measure].

Some of the greatest mathematical minds of all ages, from
Pythagoras and Euclid in ancient Greece , through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer
Johannes Kepler , to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio,
φ
, and its properties.
He, also, taught a type of an heliocentric system

The original Tetraktys was a figure like this: and represented the number ten as the triangle of four. It showed at a glance that 1+2+3+4=10.
Speusippos tells us of several properties which the Pythagoreans discovered in the dekad .
It is, for instance, the first number that has in it an equal number of prime and composite numbers.

How much of this goes back to Pythagoras himself, we cannot tell; but we are probably justified in referring to him the conclusion that it is
"according to nature" that all Hellenes and barbarians count up to ten and then begin over again.

It is obvious that the tetraktys may be indefinitely extended so as to exhibit the sums of the series of successive integers in a graphic form, and these sums are accordingly called " tri angular numbers."

This symbolic geometry also exists in the Greek tradition. The
Tetraktys of Pythagoras reminds us of that. Pythagoras’s disciples swore by this figure, saying:

I swear by the one who revealed to our soul the Tetratkys, which has in itself the source and the root of eternal nature.

2000 years later than Pythagora and Diofantus, the great
French Mathematician Fermat , [ 1601-1665], expanding this mathematica l inquiry gave his generalized relationship, (known as the Last Theorem ), unsolved for centuries: a n + b n =c n
This is an example of the influence of Sciences by the Greek
Philosophical schools in the Ages of Reason and of
Enlightenment.

Herakleitos , [545- 497 B.C.] from Efessos, Minor Asia coast, now in Turkey, with his axiom
“Ta
Pan ta Rheei
”
= “all flow”…so, nothing remains the same.
All lectures on the 2 nd
Law of Thermodynamics , start with his axiom ( axioma= αξίωμα)= postulate

Democritus , [ 460-370 B.C.] from Thrace, the city of
Avdira, with the atomic theory
. “ Matter is made by atoms and free space”....
… atoms cannot be divided.
The Dualistic Competition:
Mind: The colours are phenomenological ,( not true), the same is the sweet and the sour; in reality there are only atoms and vacuum that is : Being and not-Being.
Senses:
Poor mind, you obtain your proofs from us and you plan to beat s with them.
Your victory is your defeat.


Lucretius, [ 99-55 B.C., Rome] Roman poet and philosopher influenced by Democritus said: “ I will reveal these atoms from which nature creates all things”

Later, Aristotle argued on the perfect division of the
INFINITY down to an infinite set of points… (the Theory of
Continuity: Aristotle and Zinon). It is the opposite, compared with the Democritus philosophy of the limit to division.
This mathematical formulation is still a riddle for mathematicians till our days, (Cantor, 19 th
cent., T. Fanney,
20 th cent., Robinson 21 st cent.)

Empedocles, [ 490-430] from Acragas, a Greek city in
Sicily .
In his poetic work “ on the Narure” combined Herakleitos and Parmenides principles,( the Being is motionless), and taught that “no absolute genesis and wear may exist; only, continuous change of the 4 sustances- tetrackys - and
Friendship and Hatred which work upon them
Note: this Greek philosophy provides the basic principle of the energy production, by thermodynamic cycles which a working fluid undergoes.

Parmenides, [around 505 B.C] from Elea, Magna Graecia, in Italy now.
“ it is the same-identical or equivalent(?) that someone ponders on something and this to be.. the esse”

The Dualism : Spirit and Senses….

their unification, ( according to Plotinos, from the Greek city
Lykopolis in Egypt, 205 – 270 in Rome, A.D.) or their interaction, discretisation or inter-exchangeability or transformation ?
These meanings may provide delicate differences in Scientific and Philosophical domains.

These are new conceptual configuration modes based on the mastery of the linguistic expression and/or the power of mind expression.
.

This led, also, Ilya Prigogine , [ 25.01.1917 Moscow- May
28 2005], a Nobel Prize Laureate, ( 1977), to develop his theory on
“ the auto- ( self )- organization of Cosmosmatter
”.


, in Athens,( 470-399) B.C. and his method:
Definition, Analysis and Synthesis .

, Athens, (428-348), philosophizes on the Soul, the existence through senses and the true pragmatic environment,
( the pragmatic is what we sense? Is it the same with natural and vanced technical sensors? ), the level of Ideas
…
(the 4 th Dimension ???) do lead to the
Dualism in all aspects of the inquiry.
He is influenced by Phythagora,too, in some of his beliefs.
His great work,
“on the
Democracy” [ Demos and K rato], highlights- discusses the politician and the political ethos and justice, associated to the polis (= city) management
It illuminates and broadens our mind horizons even today.


The impact of his Academy, the first University, (with referees in the papers to be published by the Academy) in the world, is invaluable
In addition, the stream of neo-Platonic philosophers contributed in Renaissance and later to the development of the societies.


The 4 Socratic Dialogues in which the aretaic, ( areti a
Greek word used for the Virtue) issues are investigated:
1. Harmidis…. about the Judicious
2. Lachis………………about Bravery
3. Phaedon ………. about the Prudency
4. on the Democracy
…about the
Politician and Justice

Those Dialogues address the properties of virtue (or in
Greek areti ), or in other words the aretaic characteristics , like the aretaic turn
( the philosophical version in the last century emphasizing the role of characters to ethics
…a turn towards virtues )

In Plato`s work Kratylos, Socrates exemplifies the structure –meaning of the words and their synthesis.
This is a challenge for everybody to underpin the perception, conception of an idea and transfer of thoughts-meanings down to senses….to speech...to comprehension by the thirds.
This is the Golden Age where the values received prime importance and Democratic cities achieved the Ariston.


The citizens all over the Greek land practised , in many cases, sponsored by Demos in:

Arts: Theatre, (Epidavros with its best acoustic in the world), Poetry, Poems and Poets Music , ( Pythagora: the music tones) and Moussae
Sculpture, Painting and Architecture.

Logic- Reasoning, ( this language is an Epos of Logic) and
Ethos- ethics /morals, to cultivate the Talent and the Character of all citizens.
(mind, soul, spirit), and

a health body to host a health mind.
It is justified, therefore, concern for:
Athletics, athletism, gymnastics and Gymnasium…the
Olympic
Games….Peace
.

Health :
Therapy , Medicine, Doctors, Hygiene,

Asklepios, a hero and a great doctor as Homer and
Isiodos refer to; the same Sophocles and Socrates do.

Hippocrates( ic) Oath, 460 BC , in Kos island,

Claudius Galenos, [131-201 in Rome

The City, ( Demos ) participates in:
Intellectual and linguistic methodic analysis , critics and dispute to forge the personality of all citizens to think critically and decide for the benefit of Demos .

After such a policy free mind leaders with Rhetoric talent, writers and lawyers; city speakers flourish.
The Greek cities are managed with a Democratic ethos that is centered around the citizens and their prosperity.

Concern for:


Harmony, Symmetry , order, deontology, Ontology,( the inquiry into the meaning of existence itself), epistemology ,
Teleo-logy …… telos, (= end ) and teleios , (= perfect )
The teleologic approach, the Meta-physica, builds the
Theology frame , while Plato develops the frame of the organisation and management of the city, too.

Philosophy (philos = friend, and Sophia =wisdom , this is the answer that Pythagora gave when people said he was wise) :
It is a discipline concerned with questions on how one should live, ( Ethics ), what sort of things exist(ed), what is their essence, their kind…( metaphysica) , what is the genuine knowledge? ( epistemology ), what are the principles of reasoning ( Logic ).

To bring a person to a high level of understanding and sharing of all these,( methexis), an exact dynamic tool had to be developed.
That was the Greek language; a superb tool not just for effective communication, but also to philosophise:
“
Laconizein ( to speak like the Spartians) esti (is the same as to) Philosopheen ( Philosophise).
It is a superb logic structure, (a Domus of Logic) causa and….the reasoning…

The roots of many words are still found in many languages;also, the composite parts of the words, (affix, suffix). Others, have a Greek structure which grants the exact meaning in short wording.
-ism, -ist. –istic, -ic
Dis- Eu- A- In- Meta- Pro- Pre- macro- , micro-, telemetry, tele-vision, tele-scope, tele-scopy….

Philo- , cosmo-, homo- , hetero- Hyper- , Pan- , Cyclo-, Poly-
Para- , Eco-, Auto-, Photo-, Phon(o)-
There are so many other examples one may across reading essays, studies, news and generally language scripts.

All these concepts, ideas, beliefs and principles highlighted before, were passed as a heritage to the new societies, as tools to disclose those truths and progress further.
This is what really happened after the Age of Renaissance
The philosophical achievements and development of the centuries of the Golden Age are reflected in the works of a great Mathematicians , Phycisists and engineers of that time.
One remarkable feature is Archimides from the Greek city of Syracuse, in Sicily, Italy now.
His works in the Theory of numbers, in Geometry ;
in Physics, ( levers; he said : give me a stand point and I may move Gaia =the Earth), in Hydrostatics , in Optics (concentrating solar collectors), in engineering ( the wormscrew, still in use in many hydro plants, or even water pumping etc).
The famous irrational number π = 3.14... , or can be estimated to any accuracy using the expression which is supremely regular:
π = 4( 1/1 -1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 -1/15 +....)
, Stageira city in Macedonia, (384-322 B.C.)
“
τι ην είναι
?”

is the basic question in Metaphysica, [ meta= μετά= after and Physics=
Φυσική
,
Φύση
= Nature from Φύω= fyo= grow, the plant grows, and
Φως=fos
=Light],
Aristotle called this work of his Theology, the “ First
Science
”
In Meta-Physica :
Time ( Chronos ) and Space are the same, are identical, are of the same thing .

Meta ta Physica Biblio Λ 1071

Note, also, that Albert Einstein said:” Space and Time are nodes in which we think, not conditions in which we live”
Aristotle`s works were for centuries the source of knowledge and the point of departure for intellectual inquiry in the fields of letters and sciences.
The editio princeps of Aristotle`s complete works in the original was issued by Aldo press, in Italy, in 5 volumes (1495-1498
AD), during Renaissance

In general ,
Greek philosophers argued upon two opposite theories with concern to Nature and Existence.
This created a dualistic approach . This dualism ( see
Schroedinger) became the source for the big break- throughs, along the centuries.

A great example of the dilemma :
“ who is right Herakleitos or Parmanides
?”

The latter attracted the philosophical efforts of Ilya
Prigogine.
Ilya Prigogine, [ 25.01.1917 Moscow- May 28 2005 ]

Parmenidis : nothing is new . All exist and will exist for ever.
“…to Think about…it is esse.

Herakleitos : the opposite attitude.
“ ta panta rheei, and nothing remains the same
”
This opposition re-appears for 2500 years in the Western world cultural history.

Newton`s Dynamic theory conforms with the Parmenides one.

Both do accept Causality and that Time= Chronos is absolute and reversible. ( Determinismus)
Philosopher s split.
Many like Hegel, Bergson, Heidegger believe that Time is unidirectional, the arrow of Time has a unique flow…goes up.

To repudiate Time-Chronos is the same as to believe that
Life is a utopia, chimera , of a ghost type or better to be false pretences.

Both intellectual approaches are true under certain conditions.
1.
the Cosmo-theory of Dynamics and
2.
the Cosmo-theory of Thermodynamics.

In the first, events do not happen in reality, as they are pre-determined.


On the other hand, according to Thermodynamics
“all flow towards the thermal Death”.
Therefore, the appearance of structures away from the equilibrium, ( Ilya Prigogine), is very important, as Time appears to be Creative.
That is, away the equilibrium new events start happening.

Oloi
neos

.

Then , the Byzantine : the Religious era, epoch , the Re-naissance ( reGen(n)esis
)…
…after 5 th
century AD till the 15 th
century….

Especially , the Medieval Philosophy, ( from St. Augustine
354-430 A.D till 1500 A.D.), which is defined partly by the process of re-discovering the ancient culture developed by the Greeks and Romans and partly by the need to address theological problems and to integrate sacred doctrine ( in Christianity and Judaism) and secular learning…

15 hundred years later, St Tomas Aquinas (1225-1274
A.D.)…”a pupil” of Aristotle(!), is an example of the importance and role the Greek scholars and philosophy played for the Western World development.

The Greek scholars transfer the ancient spirit , the
Philosophical scripts to the West:
Roma, Pisa, Venice, Florence, Bologna, Pandova, Ferrara etc.
Italy hosts the majority of the Greek scholars who left
Constantinopole.

They convey the philosophical spirit of the Period of
Classical Hellenism ; also, before and after it.


All these should be re-co llected,
( Co= syn , and lego= speak about being able to deploy things using mind and senses!) , for building the pillars of the Western world.

, eg Gomperz, Burnet, Heidegger, Kant etc who were perfect users of the Hellenic intellectual and
Linguistic heritage dug deep into the Greek philosophy; to analyse , ( ana - lyo ) systematically values, principles associated to the human life.
The systematic cultivation passed into the Universities,
( a New Institution to accommodate, cultivate the societal needs and progress through freedom in search and communication),
which appeared everywhere since then..

Critical thought was stimulated by Cartesian philosophy and by progress of the exact human sciences.
This phenomenon was pan-European.

A passion for Mathematics, Physics, Chemistry , Medicine
, Astronomy , and natural history developed in all countries.

At the same time, new historical, economical, political and social thought made headway.

New philosophers pushing back the shadows of the past forged a path to Enlightenment and joined forces in various structures and groups building networks which covered the whole W. World.

The ideas of Enlightenment aged along with their advocates. The new generations looked to new horizons.

The message of Em. Kant demolished the Cartesian and showed , argued about the Limits of Reason.


The last centuries, 19th-21th, new trends and versions of the Philosophical streams appeared and argued on the basis of ethics, morals, consequencies, rationalism, mind and soul.

There appeared movements like:

Rationalism and Empiricism

Skepticism

Idealism

Pragmatism

Phenomenogy

Consequentialism, deontology and the aretaic turn

Let us reflect and discuss:

Would European thought have been able to reach such heights without the initial push and re-push from Socrates,
Plato, Aristotle , Epicurus etc?

Sciences were, also, inherited by the Greeks.
In all the European languages the various scientific disciplines have Greek words/names.

Hellenic civilization gave Europe the complete range in
Arts along with a taste in Harmony and Beauty
( eumorphia; eu= good and morphi=shape, form)

Centuries ago, Greeks provided rational interpretation for the creation of Nature and the Man.

Ancient Greece created the forms of social and political life which later became characteristics of the European civilization, namely the polis


That was the breeding ground for the types of governments which appeared throughout Europe`s history .

The democratic socialisation ethos which brings people together is Language and Culture. Peoples Osmosis.

The Initiative of yours to go for learning Greek might drive you to paths of Science and Philosophy that you have never thought of; at least you will make friends to build the continuity of our society.

You must go on trying for the Best, the Platonic Virtue,
ARETI, the ARISTON.

The Greek philosophers and their language might be a very useful tool in your adventures in Life.
Appendix : on the Dualism in the Hellenic Philosophy.
The ancient philosopher, Heraclitus , maintained that everything is in a state of flux. Nothing escapes change of some sort (it is impossible to step into the same river).
On the other hand, Parmenides argued that everything is what it is, so that it cannot become what is not (change is impossible because a substance would have to transition through nothing to become something else, which is a logical contradiction).
Thus, change is incompatible with being so that only the permanent aspects of the Universe could be considered real.
An ingenious escape was proposed in the fifth century B.C. by
Democritus .
He hypothesized t hat all matter (plus space and time) is composed of tiny indestructible units, called atoms .
This idea seems motivated by the question of how finely one can go on cutting up matter. While Democritus performed no experiments and had only the flimsiest evidence for postulating the existence of atoms , his

t heory was kept alive by the Roman poet Lucretius which survived the
Dark Ages to be discovered in 1417.
The atoms in Democritus theory themselves remain unchanged, but move about in space to combine in various ways to form all macroscopic objects. Early atomic theory stated that the characteristics of an object are determined by the shape of its atoms.
So, for example, sweet things are made of smooth atoms , bitter things are made of sharp atoms .
In this manner permanence and flux are reconciled and the field of atomic physics was born .
Although Democritus' ideas were to solve a philosophical dilemma , the fact that there is some underlying, elemental substance to the Universe is a primary driver in modern physics , the search for the ultimate subatomic particle.
 Heraclitus = everything changes, Parmenides = change is logically impossible
 how can matter change yet maintain its existence?
 answer = it is composed of indestructible units called atoms
 Dalton = determines that each element corresponds to a unique atom
 develops system of chemical symbols based on atomic mass
 compounds =
 atoms linked as molecules opens way for new laws of
It was John Dalton, in the early 1800's , who determined that each chemical element is composed of a unique type of atom, and that the atoms differed by their masses. He devised a system of chemical symbols and, having ascertained the relative weights of atoms, arranged them into a table. In addition, he formulated the theory that a chemical combination of different elements occurs in simple numerical ratios by weight, which led to the development of the laws of definite and multiple proportions.
He then determined that compounds are made of molecules, and that molecules are composed of atoms in definite proportions. Thus, atoms determine the composition of matter, and compounds can be broken down into their individual elements.

physics
References.
1.Nature and the Greeks; comments on Erwin Schroedinger seminars.
M. Bitbol, Cambridge University Press, 1954
2. H. Diels, “ Die Fragmente der Vorsocratiker” 1 st edition, Berlin,
1903
3. “About Time” by Paul Davies, Penguin Books,1993
The Publishing activity of the Greeks during the Italian Renaissance,
1469-1523 A.D
Published by Benaki Museum in Athens, 1987
4.Phythagorae AC Phocylidiis Carmina Graecolatina
Lipsiae, Michael Lantzenberger, Anno MDC IIII
5. Fermat`s Last Theorem, S. Singh, Harper Perrenial, 1997
6.Orpheus and Greek Religion, W.K.C. Guthrie
Methuen &Co ltd 1952
7. Is Future predetermined?
Lecture by Ilya Prigogine in the National Technical University of
Athens, 2003
8. Meta Physica of Aristotle, Cactos Publishing Co. in Greek, Athens,
1993
9. Theodor Gomperz, “Griechische Denker” vol. 1, p. 432, 4 th edition,
Leipsig 1922.
10. Galileo`s Finger, by Peter Atkins, Oxford University Press2003
11. Lecture on “the Greek Philosophers about Genesis, Time and the
Beginning” by Socrates Kaplanis, Patra, 2006
12. “Other Worlds” by Paul Davies, Penguin Books, 1990.
13. Aristotle, Fragments, by Jonathan Barnes and gavin Lawrence in
“The Complete works of Aristotle” Princeton Univ. Press, pp. 2384-
2462, 1984
14. A History of Greek Philosophy, Guthrie W.K.C. Vol. 1, 1962,
Cambridge Univ. Press.
15. “Greek Arithmetic, Geometry and Harmonics: Thales to Plato” in Routledge History of Philosophy Vol. I:From the Beginning to
Plat, C.C.W Taylor(ed), London: Routledge, pp 271-322
.