PLATO. PLATO. LIFE AND LEGACYLIFE AND LEGACY

427 (?) – 348 BCELived about 200 years after

PythagorasHis real name was Aristocles, but

his wrestling coach dubbed him “Platon”, on account of his robust figure.

Son of a wealthy Athens familyServed 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.

PLATOPLATOTHE ACADEMYTHE 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.

PLATOPLATOTHE DIALOGUES 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.

PLATOPLATOMAIN THOUGHTS ON THE NATURE OF REALITYMAIN 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.

PLATOPLATOMAIN THOUGHTS ON THE NATURE OF REALITYMAIN THOUGHTS ON THE NATURE OF REALITY

The divided lineThe divided line

Everything is being represented as placed on a single line, extending from the lowest to the highest sense of reality.

PLATOPLATOMAIN THOUGHTS ON THE NATURE OF REALITYMAIN THOUGHTS ON THE NATURE OF REALITY

The divided lineThe 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).

PLATOPLATOMAIN THOUGHTS ON THE NATURE OF REALITYMAIN THOUGHTS ON THE NATURE OF REALITY

The divided lineThe 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

PLATO PLATO PRE-EMINENCE OF MATHEMATICSPRE-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.

PLATO PLATO PRE-EMINENCE OF MATHEMATICSPRE-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.

PYTHAGORASPYTHAGORAS

582-520 BC

All is number

PYTHAGORASPYTHAGORASEARLY LIFEEARLY 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.

pythagoreanismpythagoreanism

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.

The numbersThe 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.

Pythagoras mathematical Pythagoras mathematical discoveriesdiscoveries

Discovered the existence of irrational numbers

His famous pythagorean theorem ( a2+b2=c2)

The ratios of musical intervals

PythagorasPythagorasthe harmony of the spheresthe 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.