PLATO.
LIFE AND LEGACY
 427 (?) – 348 BCE
 Lived about 200 years

after

Pythagoras
 His real name was Aristocles, but
...
PLATO
THE ACADEMY
In

387 BC, Plato established a
school for philosophy, built in a
grove dedicated to the famous
hero, A...
PLATO
THE DIALOGUES
Plato’

s works span
approximately 30 “dialogues”dramatic conversations with
statesmen, citizens, and...
PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
Most

of Plato’s writings are
not about nature, but his
concepts of reality ...
PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
The divided line

Everything

is being
represented as
placed on a single
lin...
PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
The divided line

There

are two
main sections of
the line,
representing tho...
PLATO
MAIN THOUGHTS ON THE NATURE OF REALITY
The divided line

The

upper section
(the intelligible
world) is divided
aga...
PLATO
PRE-EMINENCE OF MATHEMATICS
the

mathematical
objects which are an
essential
preliminary stage
on the mind’s way
to...
PLATO
PRE-EMINENCE OF MATHEMATICS
Plato

had become
convinced that the road to
knowledge lay in exact
reasoning, as in
ma...
PYTHAGORAS
582-520 BC

All is number
PYTHAGORAS
EARLY LIFE
Born

in Samos, Greece,
circa 582 BC
Was taught about early
Ionian, presocratic
philophers Thales,...
pythagoreanism
Pythagoras,

after
leaving his homeland
settled in Crotone, a
Dorian Greek colony
in southern Italy.
Ther...
The numbers
Pythagoras

(and all the
pythagoreans) adored
numbers.
Thought that numbers
express the real (and
usually se...
Pythagoras mathematical
discoveries
Discovered

the
existence of
irrational numbers
His famous
pythagorean
theorem
( a2+...
Pythagoras
the harmony of the spheres
Famous

is his view
that the movement of
the heavenly bodies
produces an unheard
mu...
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Plato and mathematics

  1. 1. PLATO. LIFE AND LEGACY  427 (?) – 348 BCE  Lived about 200 years after Pythagoras  His real name was Aristocles, but his wrestling coach dubbed him “Platon”, on account of his robust figure.  Son of a wealthy Athens family  Served in the Athens army during the Peloponnesian War.  Student of Socrates, by whom he was much influenced.  Along with his mentor Socrates and his student Aristotle, Plato helped to lay the foundations of Western Philosophy and Science.
  2. 2. PLATO THE ACADEMY In 387 BC, Plato established a school for philosophy, built in a grove dedicated to the famous hero, Academos. The Academy continued until it was closed in 529 CE, by Justinian I of Byzantium, over 900 years later. Many intellectuals were schooled in the Academy, the most prominent one being Aristotle.
  3. 3. PLATO THE DIALOGUES Plato’ s works span approximately 30 “dialogues”dramatic conversations with statesmen, citizens, and other recognizable names from Plato’s time and earlier. Socrates is the main interlocutor. It is hard to say what are just Socrates’ own views and what is just Plato’s voice.
  4. 4. PLATO MAIN THOUGHTS ON THE NATURE OF REALITY Most of Plato’s writings are not about nature, but his concepts of reality and knowledge have had a profound impact. In his well-known dialogue, The Republic, there is nicely portrayed his overall view on reality.
  5. 5. PLATO MAIN THOUGHTS ON THE NATURE OF REALITY The divided line Everything is being represented as placed on a single line, extending from the lowest to the highest sense of reality.
  6. 6. PLATO MAIN THOUGHTS ON THE NATURE OF REALITY The divided line There are two main sections of the line, representing those things apprehended by the senses (the lower section) and those things only apprehended by the mind (the upper section).
  7. 7. PLATO MAIN THOUGHTS ON THE NATURE OF REALITY The divided line The upper section (the intelligible world) is divided again in the purest form of reality (the forms and the Good – which is the highest form) and
  8. 8. PLATO PRE-EMINENCE OF MATHEMATICS the mathematical objects which are an essential preliminary stage on the mind’s way to reach the grasping of the ultimate reality For Plato the study of mathematics was a crucial step in the path leading the mind to the truth.
  9. 9. PLATO PRE-EMINENCE OF MATHEMATICS Plato had become convinced that the road to knowledge lay in exact reasoning, as in mathematics. The famous inscription over the entrance of the Academy read: let no one who does not know geometry enter here.
  10. 10. PYTHAGORAS 582-520 BC All is number
  11. 11. PYTHAGORAS EARLY LIFE Born in Samos, Greece, circa 582 BC Was taught about early Ionian, presocratic philophers Thales, Anaximander and Anaximenes. Was drawn away from his land because of his disgust for tyranny of Polycrates.
  12. 12. pythagoreanism Pythagoras, after leaving his homeland settled in Crotone, a Dorian Greek colony in southern Italy. There he founded his own cult, the pythagoreans. It was based on philosophical, political and religious beliefs.
  13. 13. The numbers Pythagoras (and all the pythagoreans) adored numbers. Thought that numbers express the real (and usually secret) essence of all things. Accordingly, they studied mathematics intensively and extensively.
  14. 14. Pythagoras mathematical discoveries Discovered the existence of irrational numbers His famous pythagorean theorem ( a2+b2=c2) The ratios of musical intervals
  15. 15. Pythagoras the harmony of the spheres Famous is his view that the movement of the heavenly bodies produces an unheard musical harmony based on the mathematical relationship of their orbit, known as the harmony of the spheres.

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