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(Roman copy of a Greek statue, 4th Century B.C.)

Plato (c. 428 - 348 B.C.) was a hugely important Greek philosopher and mathematician from the Socratic (or Classical) period.

He is perhaps the best known, most widely studied and most influential philosopher of all time. Together with his mentor, Socrates, and his student, Aristotle, he provided the main opposition to the Materialist view of the world represented by Democritus and Epicurus, and he helped to lay the foundations of the whole of Western Philosophy.

In his works, especially his many dialogues, he blended Ethics, Political Philosophy, Epistemology, Metaphysics and moral psychology into an interconnected and systematic philosophy. In addition to the ideas they contained (such as his doctrine of Platonic Realism, Essentialism, Idealism, his famous theory of Forms and the ideal of "Platonic love"), many of his writings are also considered superb pieces of literature.

Plato was the founder of the famous Academy in Athens, the first institution of higher learning in the western world. The philosophical school which he developed at the Academy was known as Platonism (and its later off-shoot, Neo-Platonism).


Plato was born in Athens (or possibly in Aegina, according to some sources) some time between 429 and 423 B.C. (most modern scholars use an estimate of 428 or 427 B.C.) He was possibly originally named Aristocles after his grandfather, and only later dubbed "Plato" or "Platon" (meaning "broad") on account of the breadth of his eloquence, or of his wide forehead, or possibly on account of his generally robust figure.

His father was Ariston (who may have traced his descent from Codrus, the last of the legendary kings of Athens); his mother was Perictione (who was descended from the famous Athenian lawmaker and poet Solon, and whose family also boasted prominent figures of the oligarchic regime of Athens known as the Thirty Tyrants). He had two brothers, Adeimantus and Glaucon, and a sister, Potone. Plato later introduced several of his distinguished relatives into his dialogues, indicating considerable family pride.

When Ariston died early in Plato's childhood, his mother married her own uncle, Pyrilampes, who was also a friend of Pericles (the leader of the democratic faction in Athens), and who had served many times as an ambassador to the Persian court. Together, they had another son, Antiphon, who was therefore Plato's half-brother.

Coming as he did from one of the wealthiest and most politically active families in Athens, Plato must have been instructed in grammar, music and gymnastics by the most distinguished teachers of his time, and certainly his quickness of mind and modesty were widely praised. He had also attended courses of philosophy and was acquainted with Cratylus, a disciple of Heraclitus, before meeting Socrates. This life-changing event occurred when Plato was about twenty years old, and the intercourse between master and pupil probably lasted eight or ten years. As a youth he had loved to write poetry and tragedies, but burnt them all after he became a student of Socrates and turned to philosophy in earnest. It is plain that no influence on Plato was greater than that of Socrates.

Plato was in military service from 409 to 404 B.C. and, for a time, he imagined a life in public affairs for himself. He was even invited to join the administration of the regime of the Thirty Tyrants (through the connection with his uncle, Charmides, who was himself a member), but he was soon repelled by their violent acts and backed out. In 403 B.C., democracy was restored to Athens, and Plato had renewed hopes of entering politics again, although the excesses of Athenian political life in general persuaded him to hold back. The execution of Socrates in 399 B.C. had a profound effect on him, and he decided to have nothing further to do with politics in Athens.

After Socrates' death, he joined a group of Socratic disciples who had gathered in the Greek city of Megara under the leadership of Euclid of Megara, before leaving and traveling quite widely in Italy, Sicily, Egypt and Cyrene. During his time in Italy, he also studied with students of Pythagoras and came to appreciate the value of mathematics.

When he returned to Athens in about 385 or 387 B.C., Plato founded the Academy (or Akademia), one of the earliest and most famous organized schools in western civilization and the prototype for later universities, on a plot of land containing a sacred grove just outside the city walls of ancient Athens, which had once belonged to the Athenian hero Akademos. Plato had been bitterly disappointed with the standards displayed by those in public office, and his intention was to train young men in philosophy and the sciences in order to create better statesmen, as well as to continue the work of his former teacher, Socrates. Among Plato's more noteworthy students at the Academy were Aristotle, Xenocrates (396 - 314 B.C.), Speusippus (407 - 339 B.C.) and Theophrastus (c. 371 - 287 B.C.).

Except for two more rather ill-advised and ill-fated trips to Syracuse in Sicily in 367 B.C. and 361 B.C. to tutor the young ruler Dionysius II, Plato presided over his Academy from 387 B.C. until his death in 347 B.C., aged about 80. He was supposedly buried in the school grounds, although his grave has never been discovered.

On Plato's death, his nephew Speusippus succeeded him as head of the school (perhaps because his star pupil Aristotle's ideas had by that time diverged too far from Plato's). The school continued to operate for almost 900 years, until A.D. 529, when it was closed by the Byzantine Emperor Justinian I, who saw it as a threat to the propagation of Christianity.

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Plato is perhaps the first philosopher whose complete works are still available to us. He wrote no systematic treatises giving his views, but rather he wrote a number (about 35, although the authenticity of at least some of these remains in doubt) of superb dialogues, written in the form of conversations, a form which permitted him to develop the Socratic method of question and answer. In his dialogues, Plato discussed every kind of philosophical idea, including Ethics (with discussion of the nature of virtue), Metaphysics (where topics include immortality, man, mind, and Realism), Political Philosophy (where topics such as censorship and the ideal state are discussed), Philosophy of Religion (considering topics such as Atheism, Dualism and Pantheism), Epistemology (where he looked at ideas such as a priori knowledge and Rationalism), the Philosophy of Mathematics and the Theory of Art (especially dance, music, poetry, architecture and drama).

We have no material evidence about exactly when Plato wrote each of his dialogues, nor the extent to which some might have been later revised or rewritten, nor even whether all or part of them were ever "published" or made widely available. In addition to the ideas they contained, though, his writings are also considered superb pieces of literature in their own right, in terms of the mastery of language, the power of indicating character, the sense of situation, and the keen eye for both tragic and comic aspects.

None of the dialogues contain Plato himself as a character, and so he does not actually declare that anything asserted in them are specifically his own views. The characters in the dialogues are generally historical, with Socrates usually as the protagonist (particularly in the early dialogues). It is generally thought that the views expressed by the character of Socrates in Plato's dialogues were views that Socrates himself actually held, and the works had the effect of gradually rehabilitating Socrates's rather tarnished image among Athenians in the wake of his death. As time went on, though, the dialogues began to deal more with subjects that interested Plato himself, rather than merely providing a vehicle for the ideas of Socrates. It seems likely that Plato's main intention in his dialogues was more to teach his students to think for themselves and to find their own answers to the big questions, rather than to blindly follow his own opinions (or those of Socrates).

Among the (likely earlier) Socratic dialogues are: "Apology", "Charmides", "Crito", "Euthyphro", "Ion", "Laches", "Lesser Hippias", "Lysis", "Menexenus" and "Protagoras". The following are often considered "transitional" dialogues: "Gorgias", "Meno" and "Euthydemus". The middle dialogues are generally seen as the first appearances of Plato's own views: "Cratylus", "Phaedo", "Phaedrus", "Symposium", "Republic", "Theaetetus" and "Parmenides". The late dialogues probably indicate Plato's more mature thought, including criticisms of his own theories: "Sophist", "Statesman", "Philebus", "Timaeus", "Critias" and "Laws". The huge "Republic" in particular is considered one of the single most influential works in the whole of Western Philosophy, although his account of Socrates' trial in the "Apology" may be the most read.

Central to Plato's Metaphysics is his theory of Platonic Realism, which inverts the common sense intuition about what is knowable and what is real. Confusingly, this is also known as Platonic Idealism, and indeed Idealism may be a better description. Plato believed that universals (those properties of an object which can exist in more than one place at the same time e.g. the quality of "redness") do in fact exist and are real. However, they exist in a different way than ordinary physical objects exist, in a sort of ghostly mode of existence, unseen and unfelt, outside of space and time, but not at any spatial or temporal distance from people's bodies (a type of Dualism).

Part and parcel of Plato's Platonic Realism is his theory of Forms or Ideas, which refers to his belief that the material world as it seems to us is not the real world, but only a shadow or a poor copy of the real world. This is based on Plato's concept (or Socrates' through Plato) of hylomorphism, the idea that substances are forms inhering in matter. He held that substance is composed of matter and form, although not as any kind of a mixture or amalgam, but composed homogeneously together such that no matter can exist without form (or form without matter). Thus, pure matter and pure form can never be perceived, only comprehended abstractly by the intellect.

Forms, roughly speaking, are the pure and unchanging archetypes or abstract representations of universals and of all the things we see around us, and they are in fact the true basis of reality. These ideal Forms are instantiated by one or many different particulars, which are essentially material copies of the Forms, and make up the world we perceive around us. Plato was therefore one of the first Essentialists in that he believed that all things have essences or attributes that make an object or substance what it fundamentally is. According to Plato, true knowledge or intelligence is the ability to grasp the world of Forms with one's mind, even though his evidence for the existence of Forms is intuitive only.

This idea was most famously captured and illustrated in Plato's Allegory of the Cave, from his best-known work, "The Republic". He represented man's condition as being chained in the darkness of a cave, with only the false light of a fire behind him. He can perceive the outside world solely by watching the shadows on the wall in front of him, not realizing that this view of existence is limited, wrong or in any way lacking (after all, it is all he knows). Plato imagined what would occur if some of the chained men were suddenly released from this bondage and let out into the world, to encounter the divine light of the sun and perceive “true” reality. He described how some people would immediately be frightened and want to return to the familiar dark existence of the cave, while the more enlightened would look at the sun and finally see the world as it truly is. If they were then to return to the cave and try to explain what they had seen, they would be mocked mercilessly and called fanciful, even mad. In the allegory, Plato saw the outside world, which the cave's inhabitants glimpsed only in a second-hand way, as the timeless realm of Forms, where genuine reality resides. The shadows on the wall represent the world we see around us, which we assume to be real, but which in fact is a mere imitation of the real thing.

Plato's theory of Forms was essentially an attempt to solve the dichotomy between Parmenides' view (that there is no real change or multiplicity in the world, and that reality is one) and that of Heraclitus (that motion and multiplicity are real, and that permanence is only apparent) by means of a metaphysical compromise. Plato himself, though, was well aware of the limitations of his theory, and in particular he later concocted the "Third Man Argument" against his own theory: if a Form and a particular are alike, then there must be another (third) thing by possession of which they are alike, leading to an infinite regression. In a later (rather unsatisfactory) version of the theory, he tried to circumvent this objection by positing that particulars do not actually exist as such: rather, they "mime" the Forms, merely appearing to be particulars.

In the "Timaeus", Plato gave his account of the natural sciences (physics, astronomy, chemistry and biology) and the creation of the universe by the Demiurge. Unlike the creation by the God of medieval theologians, Plato's Demiurge did not create out of nothing, but rather ordered the cosmos out of already-existing chaotic elemental matter, imitating the eternal Forms. Plato took the four elements (fire, air, water and earth), which he proclaimed to be composed of various aggregates of triangles, and made various compounds of these into what he called the Body of the Universe.

In recent years, more emphasis has been placed on Plato's unwritten teachings, which were passed on orally to his students and not included in the dialogues (on several occasions, Plato stressed that the written transmission of knowledge was faulty and inferior to the spoken logos). We have at least some idea of this from reports by his students, Aristotle and others, and from the continuity between his teachings and the interpretations of Plotinus and the Neo-Platonists. One recurring theme is that the first principle of everything, including the causation of good and of evil and of the Forms themselves, is the One (the cause of the essence of the Forms). It can be argued, then, that Plato's concept of God affirms Monotheism, although he also talked of an Indefinite Duality (which he also called Large and Small).

In Epistemology, although some have imputed to Plato the remarkably modern analytic view that knowledge is justified true belief, Plato more often associated knowledge with the apprehension of unchanging Forms and their relationships to one another. He argued that knowledge is always proportionate to the realm from which it is gained, so that, if one derives an account of something experientially then (because the world of sense is always in flux) the views attained will be mere opinions. On the other hand, if one derives an account of something by way of the non-sensible Forms, then the views attained will be pure and unchanging (because the Forms are unchanging too). In several dialogues, Plato also floated the idea that knowledge is a matter of recollection ("anamnesis"), and not of learning, observation or study. Thus, knowledge is not empirical, but essentially comes from divine insight.

To a large extent, it is Plato who is responsible for the modern view of the Sophist as a greedy and power-seeking instructor who uses rhetorical sleight-of-hand and ambiguities of language in order to deceive, or to support fallacious reasoning. He was at great pains in his dialogues to exonerate Socrates from accusations of Sophism. Plato, and Aristotle after him, also believed in a kind of Moral Universalism (or Moral Absolutism), opposing the Moral Relativism of the Sophists.

In Ethics, Plato had a teleological or goal-orientated worldview, and the aim of his Ethics was therefore to outline the conditions under which a society might function harmoniously. He considered virtue to be an excellence of the soul, and, insofar as the soul has several components (e.g. reason, passions, spirit), there will be several components of its excellence: the excellence of reason is wisdom; the excellence of the passions are attributes such as courage; and the excellence of the spirit is temperance. Finally, justice is that excellence which consists in a harmonious relation of the other three parts. He believed, then, that virtue was a sort of knowledge (the knowledge of good and evil) that is required to reach the ultimate good (or eudaimonia), which is what all human desires and actions aim to achieve, and as such he was an early proponent of Eudaimonism or Virtue Ethics.

Plato's philosophical views had many societal and political implications, especially on the idea of an ideal state or government (much influenced by the model of the severe society of Sparta), although there is some discrepancy between his early and later views on Political Philosophy. Some of his most famous doctrines are contained in the "Republic" (the earliest example of a Utopia, dating from his middle period), as well as in the later "Statesman" and the "Laws".

In general terms, Plato drew parallels between the tripartite structure of the individual soul and body ("appetite-stomach", "spirit-chest" and "reason-head") and the tripartite class structure of societies. He divided human beings up, based on their innate intelligence, strength and courage, into: the Productive (Workers), laborers, farmers, merchants, etc, which corresponds to the "appetite-stomach"; the Protective (Warriors), the adventurous, strong and brave of the armed forces, which corresponds to the "spirit-chest"; and the Governing (Rulers or Philosopher Kings), the intelligent, rational, self-controlled and wise, who are well suited to make decisions for the community, which corresponds to the "reason-head". The Philosophers and the Warriors together are thus the Guardians of Plato's ideal state.

Plato concluded that reason and wisdom (rather than rhetoric and persuasion) should govern, thus effectively rejecting the principles of Athenian democracy (as it existed in his day) as only a few are fit to rule. A large part of the "Republic" then addresses how the educational system should be set up (his important contribution to the Philosophy of Education) to produce these Philosopher Kings, who should have their reason, will and desires united in virtuous harmony (a moderate love for wisdom, and the courage to act according to that wisdom). The Philosopher King image has been used by many after Plato to justify their personal political beliefs.

He also made some interesting arguments about states and rulers. He argued that it is better to be ruled by a tyrant (since then there is only one person committing bad deeds) than by a bad democracy (since all the people are now responsible for the bad actions). He predicted that a state which is made up of different kinds of souls will tend to decline from an aristocracy (rule by the best) to a timocracy (rule by the honorable), then to an oligarchy (rule by the few), then to a democracy (rule by the people) and finally to tyranny (rule by a single tyrant).

In the "Laws", probably Plato's last work and a work of enormous length and complexity, he concerned himself with designing a genuinely practicable (if admittedly not ideal) form of government, rather than with what a best possible state might be like. He discussed the empirical details of statecraft, fashioning rules to meet the multitude of contingencies that are apt to arise in the "real world" of human affairs, and it marks a rather grim and terrifying culmination of the totalitarian tendencies in his earlier political thought.

Plato's views on Aesthetics were somewhat compromised and he had something of a love-hate relationship with the arts. He believed that aesthetically appealing objects were beautiful in and of themselves, and that they should incorporate proportion, harmony and unity among their parts. As a youth he had been a poet, and he remained a fine literary stylist and a great story-teller. However, he found the arts threatening in that they are powerful shapers of character. Therefore, to train and protect ideal citizens for an ideal society, he believed that the arts must be strictly controlled, and he proposed excluding poets, playwrights and musicians from his ideal Republic, or at least severely censoring what they produced. He also argued that art is merely imitation of the objects and events of ordinary life, effectively a copy of a copy of an ideal Form. Art is therefore even more of an illusion than is ordinary experience, and so should be considered at best entertainment, and at worst a dangerous delusion.

In the "Symposium" and the "Phaedrus", Plato introduces his theory of erôs or love, which has come to be known as "Platonic love". Although he invented the image of two lovers being each other's "other half", he clearly regards actual physical or sexual contact between lovers as degraded and wasteful forms of erotic expression. Thus, unless the power of love is channeled into "higher pursuits" (culminating in the knowledge of the Form of Beauty), it is doomed to frustration, and people sadly squander the real power of love by limiting themselves to the mere pleasures of physical beauty. On an unrelated note, he is also responsible for the famous myth of Atlantis, which first appears in the "Timaeus".

Plato's consideration of epistemology, or the theory of knowledge, comes mainly in the "Theaetetus". In it, he (through the person of Socrates) considers three different theses - that knowledge is perception, that knowledge is true judgment, and that knowledge is true judgment together with an account - refuting each of them in turn, without leaving us with any definitive conclusion or solution. One is left, though, with the impression that Plato's own view is probably that what constitutes knowledge is actually a combination or synthesis of all these separate theses.

Although the study of Plato's thought continued with the Neo-Platonists, his reputation was completely eclipsed during Medieval times by that of his most famous student, Aristotle. This is mainly because Plato's original writings were essentially lost to Western civilization until they were brought from Constantinople in the century before its fall by the Greek Neo-Platonist George Gemistos Plethon (c. 1355 - 1452). The Medieval Scholastic philosophers, therefore, did not have access to the works of Plato, nor the knowledge of Greek needed to read them. Only during the Renaissance, with the general resurgence of interest in classical civilization, did knowledge of Plato's philosophy become widespread again in the West, and many of the greatest early modern scientists and artists who broke with Scholasticism saw Plato's philosophy as the basis for progress in the arts and sciences. By the 19th Century, Plato's reputation was restored, and at least on par with Aristotle's.

Plato's influence has been especially strong in mathematics and the sciences. Although he 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"). He concentrated on the idea of "proof", insisting on accurate definitions and clear hypotheses, all of which laid the foundations for the systematic approach to mathematics of Euclid (who flourished around 300 B.C.)

However, Plato also helped to distinguish between pure and applied mathematics by widening the gap between "arithmetic" (now called Number Theory) and "logistic" (now called Arithmetic). Plato's resurgence in the Modern era further inspired some of the greatest advances in Logic since Aristotle, primarily through Gottlob Frege and his followers Kurt Gödel (1906 - 1978), Alonzo Church (1903 - 1995) and Alfred Tarski (1901 - 1983).

Plato's name is also attached to the "Platonic solids" (convex regular polyhedrons), especially in the "Timaeus", in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air and water, with the fifth Platonic solid, the dodecahedron, being his model for the whole universe. Plato's beliefs as regards the universe were that the stars, planets, Sun and Moon all move around 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.

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