Plato's Academy

[Sun Goddess]

Plato
------------------------------------------------------------------------

Born: 427 BC in Athens, Greece
Died: 347 BC in Athens, Greece------------------------------------------------------------------------

Before giving details of Plato's life we will take a few moments to discuss how definite the details are which we give below. The details are mostly given by Plato himself in letters which seem, on the face of it, to make them certain. However, it is disputed whether Plato did indeed write the letters so there are three possible interpretations. Firstly that Plato wrote the letters and therefore the details are accurate. Secondly that although not written by Plato, the letters were written by someone who knew him or at least had access to accurate information on his life. The third possibility, which unfortunately cannot be ruled out, is that they were written by someone as pure fiction.

Next we should comment on the name 'Plato'. In [13] Rowe writes:-


It was claimed that Plato's real name was Aristocles, and that 'Plato' was a nickname (roughly 'the broad') derived either from the width of his shoulders, the results of training for wrestling, or from the breadth of his style, or from the size of his forehead.

Plato was the youngest son of Ariston and Perictione who both came from famous wealthy families who had lived in Athens for generations. While Plato was a young man his father died and his mother remarried, her second husband being Pyrilampes. It was mostly in Pyrilampes' house that Plato was brought up. Aristotle writes that when Plato was a young man he studied under Cratylus who was a student of Heracleitus, famed for his cosmology which is based on fire being the basic material of the universe. It almost certain that Plato became friends with Socrates when he was young, for Plato's mother's brother Charmides was a close friend of Socrates.

The Peloponnesian War was fought between Athens and Sparta between 431 BC and 404 BC. Plato was in military service from 409 BC to 404 BC but at this time he wanted a political career rather than a military one. At the end of the war he joined the oligarchy of the Thirty Tyrants in Athens set up in 404 BC, one of whose leaders being his mother's brother Charmides, but their violent acts meant that Plato quickly left.

In 403 BC there was a restoration of democracy at Athens and Plato had great hopes that he would be able to enter politics again. However, the excesses of Athenian political life seem to have persuaded him to give up political ambitions. In particular, the execution of Socrates in 399 BC had a profound effect on him and he decided that he would have nothing further to do with politics in Athens.

Plato left Athens after Socrates had been executed and travelled in Egypt, Sicily and Italy. In Egypt he learnt of a water clock and later introduced it into Greece. In Italy he learned of the work of Pythagoras and came to appreciate the value of mathematics. This was an event of great importance since from the ideas Plato gained from the disciples of Pythagoras, he formed his idea [6]:-


... that the reality which scientific thought is seeking must be expressible in mathematical terms, mathematics being the most precise and definite kind of thinking of which we are capable. The significance of this idea for the development of science from the first beginnings to the present day has been immense.

Again there was a period of war and again Plato entered military service. It was claimed by later writers on Plato's life that he was decorated for bravery in battle during this period of his life. It is also thought that he began to write his dialogues at this time.

Plato returned to Athens and founded his Academy in Athens, in about 387 BC. It was on land which had belonged to a man called Academos, and this is where the name "Academy" came from. The Academy was an institution devoted to research and instruction in philosophy and the sciences, and Plato presided over it from 387 BC until his death in 347 BC.

His reasons for setting up the Academy were connected with his earlier ventures into politics. He had been bitterly disappointed with the standards displayed by those in public office and he hoped to train young men who would become statesmen. However, having given them the values that Plato believed in, Plato thought that these men would be able to improve the political leadership of the cities of Greece.

Only two further episodes in Plato's life are recorded. He went to Syracuse in 367 BC following the death of Dionysius I who had ruled the city. Dion, the brother-in-law of Dionysius I, persuaded Plato to come to Syracuse to tutor Dionysius II, the new ruler. Plato did not expect the plan to succeed but because both Dion and Archytas of Tarentum believed in the plan then Plato agreed. Their plan was that if Dionysius II was trained in science and philosophy he would be able to prevent Carthage invading Sicily. However, Dionysius II was jealous of Dion who he forced out of Syracuse and the plan, as Plato had expected, fell apart.

Plato returned to Athens, but visited Syracuse again in 361 BC hoping to be able to bring the rivals together. He remained in Syracuse for part of 360 BC but did not achieve a political solution to the rivalry. Dion attacked Syracuse in a coup in 357, gained control, but was murdered in 354.

Field writes in [6] that Plato's life:-


... makes it clear that the popular conception of Plato as an aloof unworldly scholar, spinning theories in his study remote from practical life, is singularly wide of the mark. On the contrary, he was a man of the world, an experienced soldier, widely travelled, with close contacts with many of the leading men of affairs, both in his own city and elsewhere.

Plato's main contributions are in philosophy, mathematics and science. However, it is not as easy as one might expect to discover Plato's philosophical views. The reason for this is that Plato wrote no systematic treatise giving his views, rather he wrote a number of dialogues (about 30) which are written in the form of conversations. Firstly we should comment on what superb pieces of literature these dialogues are [6]:-


They show the mastery of language, the power of indicating character, the sense of a situation, and the keen eye for both its tragic and its comic aspects, which set Plato among the greatest writers of the world. He uses these gifts to the full in inculcating the lessons he wants to teach.

In letters written by Plato he makes it clear that he understands that it will be difficult to work out his philosophical theory from the dialogues but he claims that the reader will only understand it after long thought, discussion and questioning. The dialogues do not contain Plato as a character so he does not declare that anything asserted in them are his own views. The characters are historic with Socrates usually the protagonist so it is not clear how much these characters express views with which they themselves would have put forward. It is thought that, at least in the early dialogues, the character of Socrates expresses views that Socrates actually held.

Through these dialogues, Plato contributed to the theory of art, in particular dance, music, poetry, architecture, and drama. He discussed a whole range of philosophical topics including ethics, metaphysics where topics such as immortality, man, mind, and Realism are discussed.

He discussed the philosophy of mathematics, political philosophy where topics such as censorship are discussed, and religious philosophy where topics such as atheism, dualism and pantheism are considered. In discussing epistemology he looked at ideas such as a priori knowledge and Rationalism. In his theory of Forms, Plato rejected the changeable, deceptive world that we are aware of through our senses proposing instead his world of ideas which were constant and true.

Let us illustrate Plato's theory of Forms with one of his mathematical examples. Plato considers mathematical objects as perfect forms. For example a line is an object having length but no breadth. No matter how thin we make a line in the world of our senses, it will not be this perfect mathematical form, for it will always have breadth. In the Phaedo Plato talks of objects in the real world trying to be like their perfect forms. By this he is thinking of thinner and thinner lines which are tending in the limit to the mathematical concept of a line but, of course, never reaching it. Another example from the Phaedo is given in [6]:-


The instance taken there is the mathemtical relation of equality, and the contrast is drawn between the absolute equality we think of in mathematics and the rough, approximate equality which is what we have to be content with in dealing with objects with our senses.

Again in the Republic Plato talks of geometrical diagrams as imperfect imitations of the perfect mathematical objects which they represent.

Plato's contributions to the theories of education are shown by the way that he ran the Academy and his idea of what constitutes an educated person. He also contributed to logic and legal philosophy, including rhetoric.

Although Plato made no important mathematical discoveries himself, his belief that mathematics provides the finest training for the mind was extremely important in the development of the subject. Over the door of the Academy was written:-


Let no one unversed in geometry enter here.

Plato concentrated on the idea of 'proof' and insisted on accurate definitions and clear hypotheses. This laid the foundations for Euclid's systematic approach to mathematics. In [2] his contributions to mathematics through his students are summarised:-


All of the most important mathematical work of the 4th century was done by friends or pupils of Plato. The first students of conic sections, and possibly Theaetetus, the creator of solid geometry, were members of the Academy. Eudoxus of Cnidus - author of the doctrine of proportion expounded in Euclid's "Elements", inventor of the method of finding the areas and volumes of curvilinear figures by exhaustion, and propounder of the astronomical scheme of concentric spheres adopted and altered by Aristotle - removed his school from Cyzicus to Athens for the purpose of cooperating with Plato; and during one of Plato's absences he seems to have acted as the head of the Academy. Archytas, the inventor of mechanical science, was a friend and correspondent of Plato.

In mathematics Plato's name is attached to the Platonic solids. In the Timaeus there is a mathematical construction of the elements (earth, fire, air, and water), in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air, and water. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

Plato's beliefs as regards the universe were that the stars, planets, Sun and Moon move round the Earth in crystalline spheres. The sphere of the Moon was closest to the Earth, then the sphere of the Sun, then Mercury, Venus, Mars, Jupiter, Saturn and furthest away was the sphere of the stars. He believed that the Moon shines by reflected sunlight.

Perhaps the best overview of Plato's views can be gained from examining what he thought that a proper course of education should consist. Here is his course of study [2]:-


... the exact sciences - arithmetic, plane and solid geometry, astronomy, and harmonics - would first be studied for ten years to familiarise the mind with relations that can only be apprehended by thought. Five years would then be given to the still severer study of 'dialectic'. Dialectic is the art of conversation, of question and answer; and according to Plato, dialectical skill is the ability to pose and answer questions about the essences of things. The dialectician replaces hypotheses with secure knowledge, and his aim is to ground all science, all knowledge, on some 'unhypothetical first principle'.

Plato's Academy flourished until 529 AD when it was closed down by the Christian Emperor Justinian who claimed it was a pagan establishment. Having survived for 900 years it is the longest surviving university known.

Article by: J J O'Connor and E F Robertson

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Plato.html
--------------------------------------------------------------------------------

[Sun Goddess]

The Academy of Plato

Since the words "academy" and "academic" come from the name of the area where Plato taught, it is worth spending a moment to describe the park which was used for gymnastics from the sixth century BC. Academus or Hecademus, a mythical hero who had a cult following, left a garden and grove, which was about a mile north west of the centre of the city of Athens, to the citizens to use for gymnastics. The area, named after Academus, was developed by Hippias, the son of Peisistratos, who built a wall round it and put up statues and temples. Excavations have deteceted the foundations of Hippias's wall. The statesman Kimon planted olive and plane trees there and diverted the river Cephisus to make the dry land fertile. Festivals were held there, as were athletic events in which runners would races between the altars, and funeral games also took place in the Academy.

It must have been a beautiful park when Plato, who had a house nearby and a garden within the area, began to teach there in around 387 BC. The first point that we must make is that the modern use of the word 'academy' will give us a false impression of what Plato actually set up. Chermiss writes [1]:-


What, then, did Plato really do in his Academy? ... 'Academy' and 'Academic' are terms which men of formal training ... have been pleased to apply to themselves and their organisations. It is not surprising, therefore, that by a more or less unconscious retrojection modern scholars have attached the particular significance which 'Academy' has in their own milieu to the garden of Plato's which was situated in the suburb northwest of Athens called 'Academia' after a mythical hero ...

The fresco The School of Athens by Raphael represents the modern idea of an academy and he has placed Plato and Aristotle into such a setting, but the reality of Plato's Academy must have been totally different. A similar sentiment is expressed by Glucker [3]:-


To us ... the word 'Academy' has come to mean an institution of learning, a learned society, or at least a place of theoretical ('academic') education. In ancient Athens, the Academy was first and foremost a public park dominated by its gymnasium, and the connection between it and Plato's school was only one of the numerous historical reminiscences in an area rich in history.

Glucker goes on to look at the writings of Pausanias who gives what is essentially a tourist guide to Athens written in the second century AD (when the Academy was still supposed to be in existence). He describes the graves, altars, and olive trees of the Academy (i.e. the olive grove). He says that a memorial to Plato is found not far from the Academy but there is no mention of Plato's school nor, for that matter, is there any mention that Plato was connected with the Academy which is simply a park.

What then was Plato's Academy? Chermiss writes [1]:-


All the evidence points unmistakably to the same conclusion: the Academy was not a school in which an orthodox metaphysical doctrine was taught, or an association of members who were expected to subscribe to the theory of ideas ... The metaphysical theories of the director were not in any way 'official' and the formal instruction in the Academy was restricted to mathematics. ...
Plato's influence on these men, then, was that of an intelligent critic of method, not that of a technical mathematician with the skill to make great discoveries of his own; and it was by his criticism of method, by his formulation of the broader problems to which the mathematician should address himself, and ... by arousing in those who took up philosophy an interest in mathematics that he gave a great impulse to the development of the science.

We should look at perhaps the only 'fact' which is usually given about the Academy in Plato's time. This is that above the door Plato inscribed "Let no one who is not a geometer enter". This is not stated in any literature which has come down to us earlier than a document from the middle of the 4th century AD which, therefore, was written about 750 years after Plato founded the Academy. Before we discuss whether it is likely that indeed this was written above the door of the Academy, let us give what is probably a more accurate translation - "Let no one who cannot think geometrically enter".

First we note that above the doors of sacred places there was often placed an inscription "Let no unfair or unjust person enter". What is reported above the door of the Academy is exactly the same Greek words except "unfair or unjust" has been replaced by "non-geometrical". Next we note that the sentiment is exactly what Plato might have written, for it expresses an idea which runs throughout his writings. However, it seems highly unlikely that something of this nature would be handed down by word of mouth for 750 years before being written down, so despite it being an attractive idea, it is almost certainly fictitious.

It appears that the Head of the Academy was elected for life by a majority vote. The first few to lead the Academy were: Plato, Speuisppus, Xenocrates, Polemon, Crates and Crantor. Aristotle was a member of the Academy for many years but never became its Head. We should note, however, that Cicero, writing in the first century BC, traces the Academy back earlier than Plato and gives its leaders up to 265 BC as: Democritus, Anaxagoras, Empedocles, Parmenides, Xenophanes, Socrates, Plato, Speusippus, Xenocrates, Polemo, Crates, and Crantor. A new phase began when Arcesilaus became Head of the Academy in 265 BC. Some authors see this as the beginning of the New Academy as opposed to the that from the time of Plato to that of Crantor which is called the Old Academy. Cicero gives the leaders of the New Academy as: Arcesilaus, Lacydes, Evander, Hegesinus, Carneades, Clitomachus, and Philo.

Philo left Athens in about 85 BC and went to Rome. About a year earlier Lucius Sulla had marched an army on Athens. During the siege of Athens many of the trees in the Academy park were cut down to provide timber for the war effort but there is no evidence that by this time the school led by Philo had any connection with the Academy parkland. It appears that after Philo left Athens the activity in the school ended and there is little evidence that it was restarted before the 2nd century AD. The usual suggestion that Plato's Academy existed from 387 BC until Justinian closed it down in 529 AD is, therefore, not only inaccurate because it appears that there was no Academy from 85 BC until the 2nd Century AD but also because the Academy continued to exist after Justinian's edict to close the pagan schools. Damascius was Head of the Academy in 529 AD and he left Athens at this time with Simplicius and other members of the school. However Simplicius returned to Athens where he certainly wrote, undertook research and was Head of a very restricted Academy until his death in 560 AD.

http://www-groups.dcs.st-and.ac.uk/~history/Societies/Plato.html

[Sun Goddess]

Platon, the son of Ariston
of Kollytos
of the Neleidai
of the Athenaioi


Legend and History:


The ancient Akademeia was not a school; it was a public park with groves and "beautiful old trees" (Plut. Vit. Cim. xiii 7-8; Plin. NH xii 5.9; schol. Ar. Nub. 1005), and it was located in one of Athens's most beautiful suburbs (Thuc. ii 34). This park was a sacred precinct and dedicated to an Attic hero named Akademos or Hekademos -- from whom the area obtained its name (Paus. i 30.2; schol. Soph. OC 56).

Akademos had owned the property in the time of Theseus, and the cult dedicated to him dates back to at least the earliest years of the sixth century. It was Akademos who revealed to the Dioskouroi (Kastor and Polydeukes [The Gemini]) where Theseus had hidden Helen of Troy. Because of Akademos's actions, the Dioskouroi honoured Akademos, and the Spartans would not ravage the groves out of respect when they invaded Attica (Plut. Vit. Thes. xxxii).

The area was also sacred to Athene (Suda s.v. " 'Akadhm…a"), but several other immortals (and heroes) were present as well (Paus. i 30.102; Ath. xiii 609d; Apul. De Plat. i 1; FGrHist 244 F 120, 147).


The term "Akademeia" does not admit to exact definition. Ancients used it not only to identify Platon's school but the area enclosed by the precinct wall as well as the surrounding area. Originally, the land was arid, but the statesman Kimon made it into a well-watered grove, building running tracks and shady walks (Plut. Vit. Cim. xiii 7), and the original name for this entire region was Hekademeia (D.L. iii 7-8, viz. 8.1; Stravropoullos, BCH xcii [1968]; Alexandris, AAA i [1968] 101-7; Travlos, PDAA [1972] 42f.).

In spite of our uncertainty concerning exactly what the Hekademeia was, it was a location, and it was a location rich with religious celebration. Several ancient festivals were held there. In one contest, runners would conduct races from one of three altars torch races where the goals rested (in each case) within the walls of Athens. Funeral games also took place in the areas as well as a Dionysiac procession from Athens to the Hekademeia and then back to the polis (Paus. i 29.2, 30.2; Plut. Vit. Sol. i 7).  Platon's "school," the Akademeia, was thus incorporated into the much larger and more colourful setting of the polis.


Platon:


If we combine the various traditions concerning Platon's Akademeia into a narrative account, a somewhat elaborate but nonetheless clear portrait of this philosophical diatribê (pastime; way of life) emerges: About 388/7 BCE, the son of Ariston chose a remote and unhealthy locale to dedicate a Mouseion (Temple of the Muses). Platon established his temenos (an allotted piece of sacred land) among the groves and gymnaseion (exercise gardens) dedicated to the Attic hero Akademos (Hekademos).

Platon erected his Mouseion following a trip to Sicily, and he began writing and regular instruction to groups of followers in that grove. Soon thereafter, Annikeris (or Platon himself) purchased a little garden (kepidion) near Kolonos, and Platon continued to pursue philosophy in both locations, while living in the garden, for about forty years. He was later buried near the Hekademeia, in the garden facing Kolonos, and the sculptor Silanion erected a statue of the philosopher, dedicating it to the Muses as well (D.L. iii 7-8, 19-20, 25; iv 1, 19; Plut. Vit. Dion v 5-6; Olymp. in Alc. ii 122, 145-6; in Grg. xli 8; Proll. ii 30-33; Paus. i 30.2; Procl. In R. ii 1.9; Aristid. Or. xlvi; Suda s.vv. " 'Akadhm…a," "Pl£twn," and " 'Aristippoj.").

Individuals had come from all over Greece to pursue philosophy in the Akademeia, but Platon accepted only those "intoxicated to learn what was in their souls" (Olymp. Proll. ii 30-33). A student then listened as Platon walked about the gymnaseion reading from his dialogues and lecturing, and they all enjoyed moderate but pleasant banquets (Phlp. in Cat. iii 4-6, 9-11; Olymp. Proll. v 21-22; Ammon. in Porph. xlvi 5-8). The meals were conducted according to an elaborate set of rules, but Platon did not hold these feasts simply to celebrate till dawn. He held his banquets so "that [he and his companions] might manifestly honor the gods and enjoy each others company and chiefly to refresh themselves with learned discussion" (Ath. v 186b; xii 547f; xiii 585b; D.L. v 25).

The tradition that Platon's diatribê was founded in an unhealthy locale is late Christian embroidery. The embellishment persisted in spite of the fact Kimon had renovated the gardens, making them some of the most beautiful in the Attic countryside. They remained beautiful well into Roman times.

http://php.iupui.edu/~cplaneau/Plato%20and%20His%20World/Plato%20Academy%20Introduction.html
--------------------------------------------------------------------------------

[Sun Goddess]

THE ORGANIZATION OF PLATO'S ACADEMY. As the founder of the Academy, Plato had the lifelong dignified position of thiasarch (scholarch). Plato appointed Speussipus as his successor, but thereafter the scholarch was elected for life by the young members. The youthful members held all the minor offices, e.g., gatekeeper for the temple (who was concerned with the offering of sacrifices), secretary (who registered the members), and censor (who prepared symposia and who kept order in them). The symposia (banquets) were regarded in the Academy as solemn festive acts and were preceded by sacrifice or prayer. Plato saw to it that moderation was observed in sensual joys so that the symposium by the proper use of the intellect's power could become primarily a joy for the soul. Plato's followers (e.g., Speussipus) developed rules for the symposia.

Today some scholars question the view that Plato's Academy was a band or for the worship of the muses and Apollo, the lord of the muses, although the strong bonds of such a band would explain the broad autonomy and persistence of the school as an institution that relied on an untouchable estate which was a holy property. The members of Plato's Academy could only make use of this property. Since it was inviolable, it remained undiminished for centuries. The school had no statutes. Its organization depended upon the director. It accepted both young disciples (e.g., Aristotle at seventeen years of age), and mature scholars (e.g., Eudoxus of Cnidus, who came to Plato's Academy with his own disciple). Before someone was accepted into Plato's Academy, he had to pass an examination conducted by Plato himself. The teaching was in the form of lectures, seminars, colloquia and discussions (cited texts were the starting point in opening a discussion). The discussions took place while they strolled about the garden or in the porticos of the city. The master himself, Plato, held lectures. When he was traveling, students would lecture in his place. The school was endowed with laboratoria and a library. The library possessed, among other things, the writings of the master as they appeared in succession. Plato's Academy for the first time in the history of education led to contact between the various sciences. It often looked in part to the traditions of the school of Pythagoras, and became a model itself for other schools: the Aristotelian, Stoic and Epicurean schools, and in a certain way it was the beginning of the universities of the future. Plato's disciples came from many cities in northern Greece, Macedonia, and the shores of the Black Sea.

THE DIDACTIC GOALS OF PLATO'S ACADEMY. Plato regarded the education of "fitting souls" as his most important aim in life, more important than his own philosophical work (Phaedr., 276 E; 277 a). Plato stated that the aim of the Academy was to educate disciples, philosophers who in the future would occupy positions of authority in the state and be guided by true philosophy. In Plato's Academy, education had the purpose of forming future men of state as sages and politicians, a chosen group of just men formed in the good who would propagate justice from the Academy to society "[…]I was forced to say, when praising true philosophy that it is by this that men are enabled to see what justice in public and private life really is. Therefore, I said, there will be no cessation of evils for the sons of men, till either those who are pursuing a right and true philosophy receive sovereign power in the States, or those in power in the States by some dispensation of providence become true philosophers." (Epist., VII 326 B). Plato often expressed the desire that the same people should be philosophers and the rulers of great states. However, Plato states it takes half a century to form a man, since an educated philosopher should still spend fifteen years in the active life of the political community to acquire experience and battle temptations. Only those who have cultivated philosophy with perseverance for a long time are capable of taking up these goals: "[…]it does not admit of exposition like other branches of knowledge; but after much converse about the matter itself and a life lived together, suddenly a light, as it were, is kindled in one soul by a flame that leaps to it from another, and thereafter sustains itself." The teaching of philosophy may awaken such an illuminating knowledge (or remembrance in the soul), and only this can truly form and educate the free man.

http://www.kul.lublin.pl/efk/angielski/hasla/a/academyplato.html

[Sun Goddess]

TEACHING IN PLATO'S ACADEMY. The candidates for philosophy had to undergo a fitting preparation. Plato made mathematics the introduction to philosophy. He held that the study of mathematics was of great benefit in forming intellectual skills. According to legend, inscribed over the entrance of the Academy were the words "Let no one enter here who does not know geometry". In the Republic (VII 528 a), Plato classified the mathematical sciences on the basis of the views of the Pythagoreans. They divided the mathematical sciences according to the questions each answered. The question "how many" belonged to arithmetic and music. "How great" was the question of geometry and mechanics. Plato presented the mathematical sciences in the following order: arithmetic, geometry (he distinguished plane geometry — or planimetry, and spatial geometry — stereometry), astronomy, and music. He thought that these sciences are connected by formal relations that can be seen, for example, in their diminishing degrees of abstraction. The mathematical sciences mentioned above put to the test and exercise the minds of students who are capable of philosophical meditations. The candidates for philosophy can be chosen from among the students of mathematics. According to Plato, it is not enough to stay at the level of teaching and lectures on the principles of numbers, but the minds of students should be directed to ever more abstract levels of thought, e.g., they may start from the first three numbers and pass on to meditations on the abstract concepts of unity and plurality. These meditations can facilitate the transition of the soul from knowledge of the world of changing things to an intuition of the world of beings "without form", namely to an intuition of ideas. In the same way, astronomy is a mathematical science that studies the combination of repetitive cyclical motions, and it leads at the end to the discovery of the plan of the demiurge who established the order of the world.

THE STAGES OF DEVELOPMENT OF PLATO'S ACADEMY. The Old Academy.   Plato was the scholarch of the Academy for forty years and developed his philosophical system there. After the death of the master, the first director of Plato's Academy was his nephew Speusippus (347–339). Speusippus primarily studied the theory of logical classifications and the science of numbers. The next scholarch was Xenocrates of Chalcedon (339-314) who studied demonology (Platonic theology). The third scholarch after Plato was Polemon of Athens (314-269) who chiefly studied ethics. In 268, Crates briefly ruled the Academy and was also interested in ethics. Some of the disciples who contributed to the fame of the Old Academy were Heraclides of Pontus (he founded his own school), Eudoxus of Cnidus, Philippus of Opus (an astronomer), and Crantor of Soloi (the first commentator of Plato's Timaeus). The most famous disciple of Plato was Aristotle (384-322), who created his own great philosophical system and founded his own school, the Lyceum. The Peripatos (Aristotle's Lyceum) and the Stoa (Zeno of Citium was a disciple of the Cynic Crates and of the Academic Polemon, both scholarchs of Plato's Academy) are regarded as independent branches of Plato's Academy.

The Middle Academy.   The school departed significantly from Plato's teachings and moved in the direction of scepticism when Arcesilaus (315–240) became scholarch. Arcesilaus held that we may have only subjective certainty of the truth, but not certainty as referring to the world. Some time after Arcesilaus, Carneades (214–129) was scholarch. Carneades continued in scepticism and proclaimed a theory of probability. According to him, the investigation of mental images leads us to the various degrees of probability.

The New Academy.   After Philo of Larissa held the position of scholarch (c. 110 BC), the Academy tried to return to Plato's original teaching, but it leaned toward Stoicism, while moderating the positions of Scepticism and allowing for the possibility of some knowledge of things. Basically, the Academy was inclined to eclecticism and combined the most acceptable views of the Stoics, Sceptics, Platonists, and later the Peripatetics as well. Antiochus of Ascalon (130-69 BC) introducted electicism into Plato's Academy and held that universal or common conviction is the criterium for truth.

Plato's Academy later would be more and more influenced by neo-Pythagoreanism. The Academy developed in different cities and these offshoots were not always connected with the Athenian home of Plato's Academy. With Ammonius Saccas (d. c. 242 AD), we may begin to speak of a neo-Platonic school, and Ammonius Saccas is regarded as the initiator of neo-Platonism. Plotinus (204–270) was his disciple for eleven years in his Alexandria school. The Syrian school developed the neo-Platonic conceptions (Porphyry of Syria, Iamblichus of Ceole Syria). The main representatives of neo-Platonism in Plato's Academy who developed their views in the Athenian school at the end of the fourth century and the beginning of the fifth century were Plutarch of Athens, the son of Nestorius, Proclus, Marinus of Naples, Isidore, Damascius and Simplicius. Plato's Academy in Athens was closed in 529 AD after almost nine centuries by the command of the Emperor Justinian. Justinian gave a special edict that "henceforth never again shall there anyone lecture on philosophy or explain the laws in Athens" (Codex Iustinianum. After this edict, the Platonists fled to Persia.

Z. Jordan, O matematycznych podstawach systemu Platona [On the mathematical foundations of Plato's system], Pz 1937; F. Eby, C. F. Arrowood, The History and Philosophy of Education Ancient and Medieval, EC 1940, 196312; Ueberweg III (passim); P. Riché, De l'éducation antique à l'éducation chevarelesque, P 1968; M. Clarke, Higher Education in the Ancient World, Lo 1971; J. P. Lynch, Aristotle's School. A Study of a Greek Educational Institution, Be, Los Angeles, Lo 1972; R. Barrow, Plato and Education, Lo 1976; W. K. C. Guthrie, A History of Greek Philosophy V, C 1978; K. Gaiser, Philodemos Academica. Die Berichte über Platon und die alte Akademie, St. Bad Cannstatt 1988; Reale IV.

http://www.kul.lublin.pl/efk/angielski/hasla/a/academyplato.html

[Sun Goddess]

Plato's Academy

On the outskirts of ancient Athens--though long since engulfed by the sprawling suburbs of the modern city--was a grove of trees about a quarter-mile across, dedicated to the memory of the semi-mythical hero Hecadamos (easily mispronounded as Academos).  He had told Castor and Pollux where their sister Helen (of Troy, but really she had come from Sparta) was hidden.  Because of this, whenever the Spartans invaded Athens, they spared this shrine.

The site was occupied from the end of the dark ages (around 900 BC) and by Plato's time it was well-watered and well-planted and adorned with a large rectangular public gymnasium building.  Plato began meeting his students here from around 388 BC, a decade after the death of Socrates.  He and his followers eventually took over the site and  incorporated a school of philosophy there.  Plato spent the rest of his life teaching there.  The young Aristotle came there at the age of 17 to study with him and stayed for 20 years. 

There is no good reason to doubt the tradition that Plato died around 348 and was buried on the grounds of the Academy.  The location of his grave is hopelessly lost.  He was certainly not buried in the huge, elaborate sarcophagus abandoned in the middle of the site; it dates from  at least 500 years after his time.

The Academy has remained, from Plato's day to the present, the most famous school of philosophy in the world.  Generations of his students succeeded one another as head of the Academy, continuing his tradition of teaching.  In Roman times, it was fashionable for the sons of the aristocracy to spend a year in Athens studying at one of the philosophical schools--preferably the most prestigious of them--Plato's.  Cicero, for instance, did his year here in the first c. B.C., as did both the future emperor Julian (the Apostate) and his classmate, Saint Gregory of Nazianzen, in the 350's A.D.

At left is an aerial view of one part of the Academy excavations, showing a gymnasium of Roman times.  In all likelihood this is where Cicero and later the future pagan emperor and future Christian saint strolled and argued with one another. 

The photo at right shows an older part of the site, a rectangular peristyle, or "peripatos".  This is simply a large square courtyard surrounded by covered walkways which allow for pleasant strolling out of the sun (or rain).  It dates from the 4th century BC and is in all likelihood the place where Plato taught and Aristotle studied.

 http://www.cerritos.edu/jmadden/intro/Plato's%20Academy.htm

[Sun Goddess]

Aristotle

(384 B.C. - 322 B.C.)

Aristotle's Early Life
Aristotle was born in 384 B.C.

Aristotle was born into a rich family.

Aristotle's father was a physician.

Aristotle lived from 384 - 322 B.C. and is considered to be one of the great thinkers of the ancient world. He was born in 384 BC in the city of Stagira, Macedonia. His father was the personal physician to the King of Macedonia. In 367 B.C. Aristotle left Stagira to further his education in Athens, Greece. He attended the Academy that was founded by Plato. At one point Plato stated that Aristotle was the "intelligence of the school". Aristotle attended the Academy (almost twenty years) until Plato's death in 347B.C.. The reason he gave for leaving was that he disappoved of the emphasis on mathematics and theory in the Academy, and the decline in natural philosophy. However, it is believed that he was displeased that Plato designated his nephew as his successor, passing over his own merits.


------------------------------------------------------------------------


Aristotle's Middle Life

Aristotle began studies at Plato's Academy at the age of 17.

Aristotle left Athens for Asia Minor.

For four years Aristotle traveled all over the Greek islands and Asia Minor. In Asia Minor, Aristotle met his wife, Pythias. From 345 to 343 Aristotle lived on the island of Lesbos, at Mytilene where he studied biology and his favorite, natural history. Here he met Theophrastus who became his scientific collaborator and later succeeded him as head of the school (the Lyceum, which he founded later on in Athens). In 343, Aristotle received an invitation to tutor Alexander, the son of King Phillip of Macedonia (who would later come Alexander the Great). For at least two years Aristotle lead Alexander through a rigorous program. They soon separated after their differences got in the way of Alexander's learning.
------------------------------------------------------------------------


Aristotle's Later Life

Aristotle lectured for twelve years at the Lyceum.

Aristotle's theories would hold for 2,000 years, until Copernicus corrected them.

Alexander the Great died in 323 B.C., forcing Aristotle to leave Athens.

Aristotle died in 322 B.C., at the age of 63.

In the year 336 B.C. Alexander the Great became supreme ruler of Macedonia. His ambition got the best of him and he began launching multiple conquests at one time. Soon his empire ranged from India in the east to Egypt in the west, Alexander no longer had time for Aristotle to lecture him. Aristotle, unwilling to return to Plato's Academy (now under the direction of Plato's nephew who began a different direction of study) began lecturing at the Lyceum, a Athenian gymnasium. He earned the nickname "Peripatetic" from lecturing while walking down the Lyceum's walkways ("Peripatetic" is Greek for "walking about"). During the next twelve years at the Lyceum, he lectured on all subject matters, and soon began to doubt the theories of Plato. Aristotle's new theories about a geocentric universe (everything revolved around earth) would dismiss those of Plato's, and hold for the next 2000 years, until Copernicus unveiled his heliocentric theories.

Alexander the Great died in the year 323 B.C., either by disease or poison, while on campaign in the far east. Anti-Macedonians began to uprise in Athens challenging Antipon (Alexander's succesor). Because of Aristotle's special relationship with Alexander, he no longer felt comfortable in Athens. The Anti-Macedonians waged war, and liberated the Greek states from Macedonian rule. They saw Aristotle as Anti-Greek, and charged him with "impeity" (disbelief in the established gods), a charge which led to the conviction and death of Socrates (via hemlock) years before.

With himself and Socrates in mind, he swore that he wouldn't let the Athenians sin twice against philosophy. He willingly left for Chalcis, and began his exile from Greece. After he and his companion, Herpyllis, spending less than a year in Chalcis, Aristotle died in 322 B.C., at the age of 63.
------------------------------------------------------------------------


Aristotle's Contribution to Math


Aristotle believed in three theoretical sciences, and mathematics was one of them. Aristotle was not primarily a mathematician, but did use and contribute to math, in order to excel in other sciences. Contrary to popular belief, Aristotle was not primarily a mathematician. Infact, most of his work was done in theories of sciences, and philosophy. He really didn't contribute many math theories. He did, however, contribute greatly to logic, and other sciences, such as biology. His theories discussed planets, position of stars, and human and animal behavior.

Aristotle's writings on the general subject of logic were grouped by the later Peripatetics under the name Organon, or instrument. From their perspective, logic and reasoning was the chief preparatory instrument of scientific investigation. Aristotle himself, however, uses the term "logic" as equivalent to verbal reasoning. The Categories of Aristotle are classifications of individual words (as opposed to propositions), and include the following ten: substance, quantity, quality, relation, place, time, situation, condition, action, passion. They seem to be arranged according to the order of the questions we would ask in gaining knowledge of an object. For example, we ask, first, what a thing is, then how great it is, next of what kind it is. Substance is always regarded as the most important of these. Substances are further divided into first and second: first substances are individual objects; second substances are the species in which first substances or individuals inhere.

Aristotle also had a strong sense of politics, and believed in justice. Another interesting fact, is that Aristotle, despite being a well-known philosopher, was wrong almost all the time! He was correct on only a few of his theories. Most of his theories were incorrect, or so far-fetched that no one would believe him. He thought that the sun went around the earth! That is just one of his mistakes.

Aristotle devised a theory, that says: "A triangle drawn in a semi circle is a right triangle." This theory is one of aristotle's most known, and one of his most helpful mathematics theories. This is the most useful theories of Aristotle.

Aristotle's words and ideas stood for his actions. He was not a man of action....he spoke, and let someone else use his ideas. He always said that his mathematical and logical ideas should be used for good, and only to help people. Aristotle's definition of logic, was actually, verbal reasoning. He believed that all things could be settled with words. That is what made him such a great thinker.

Aristotle was well known for his syllogisms. He invented these to express why things are the way that they are. An example is: All men are mortal, John is a man, therefore, John is a mortal.

In Geometry, he devised the theorem that states that a triangle drawn in a semi-circle is a right triangle.


Aristotle was wrong on his theories, more than he was correct


Aristotle's works on logic were classified, and applied to many real-life situations

Aristotle was very well known for the Syllogism

------------------------------------------------------------------------


Quotes


The following ten quotes are among the most famous, and our favorite.
* "Without friends, no one would choose to live, though they had all other goods."
* "What is a friend? A single soul dwelling in two bodies."
* "Wicked men obey from fear; good men, from love."
* "Misfortune shows those who are not really friends."
* "We can do noble acts without ruling the earth and sea."
* "There was never a genius without a tincture of madness."
* "All paid jobs absorb and degrade the mind."
* "We make war that we may live in peace."
* "We cannot learn without pain."
* "Hope is a waking dream."

------------------------------------------------------------------------


Aristotle's Works on Math Logic


All of Aristotle's works on the general subject of logic were later grouped by Peripatetics under the name Organon (instrument). Aristotle's definition of logic is verbal reasoning. Categories, Aristotle's first writing about logic classified ten different words: substance, quantity, quality, relation, place, time, situation, condition, action, and passion. Substance is always regarded as the most important of these. Substances are further divided into first and second: first substances are individual objects; second substances are the species in which first substances or individuals are grouped. The heart of Aristotle's logic is the syllogism, the classic example of which is as follows: All men are mortal; Socrates is a man; therefore, Socrates is mortal. The syllogistic form of logical argumentation dominated logic for 2,000 years. Five out of six original works are available for download in the table below, through MIT's Classic Literature site.

http://www.andrews.edu/~calkins/math/biograph/199900/bioarist.htm

[Sun Goddess]

Quotations by Plato

--------------------------------------------------------------------------------
Let no one ignorant of Mathematics enter here.
[Said to have been above the doorway of his Academy.]
He who can properly define and divide is to be considered a god.

The ludicrous state of solid geometry made me pass over this branch. Republic, VII, 528.

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

Mathematics is like draughts [checkers] in being suitable for the young, not too difficult, amusing, and without peril to the state.

The knowledge of which geometry aims is the knowledge of the eternal.
Republic, VII, 52.

I have hardly ever known a mathematician who was capable of reasoning.
Quoted in N Rose Mathematical Maxims and Minims (Raleigh N C 1988).

There still remain three studies suitable for free man. Arithmetic is one of them.
Quoted in J R Newman, The World of Mathematics (New York 1956).

[Of the five Platonic solids]
So their combinations with themselves and with each other give rise to endless complexities, which anyone who is to give a likely account of reality must survey.
The Timaeus

[The Earth is] like one of those balls made of twelve pieces of skin.
Theatetus

He who can properly define and divide is to be considered a god.
Quoted in F Bacon, Novum Organum

I can show you that the art of calculation has to do with odd and even numbers in their numerical relations to themselves and to each other.
Charmides

... arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tngible objects into the argument.
The Republic

... those who have a natural talent for calculation are generally quick-witted at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would have been.
The Republic

... arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up.
The Republic

...no intelligent man will ever be so bold as to put into language those things which his reason has contemplated.

A wise man speaks because he has something to say; a fool because he has to say something.
Quoted in Des MacHale, Wisdom (London, 2002).

Let early education be a sort of amusement. You will then be better able to find out the natural bent.
Quoted in Des MacHale, Wisdom (London, 2002).

One of the penalties for refusing to participate in politics is that you end up being governed by your inferiors.
Quoted in Des MacHale, Wisdom (London, 2002).

Our love for our children springs from the soul's greatest yearning for immortality.
Quoted in Des MacHale, Wisdom (London, 2002).

The greatest penalty of evil-doing is to grow into the likeness of a bad man.
Quoted in Des MacHale, Wisdom (London, 2002).