When was plato alive

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 ] 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 AD when it was closed down by the Christian Emperor Justinian who claimed it was a pagan establishment. Having survived for years it is the longest surviving university known.

References show. Biography in Encyclopaedia Britannica. F Lasserre, The birth of mathematics in the age of Plato London, J Moravcsik, Plato and Platonism : Plato's conception of appearance and reality in ontology, epistemology, and ethics, and its modern echoes Oxford, K Reidemeister, Das exakte Denken der Griechen.

C J Rowe, Plato A Wedberg, Plato's Philosophy of Mathematics E Filloy, Geometry and the axiomatic method. Ense nanza 7 - 8 , 39 - Pures Appl.

T Koetsier, Negation in the development of mathematics : Plato, Lakatos, Mannoury and the history of the intermediate-value theorem in analysis, in Perspectives on negation Tilburg, , - K Maurin, Plato's cave parable and the development of modern mathematics, Rend.

Torino 40 1 , 1 - Russian , Trudy Sem. MGU Istor. Classical Sci. Exact Sci. W Pohle, The mathematical foundations of Plato's atomic physics, Isis 62 , 36 - Formal Logic 4 , - Athenon 33 , - Regarding the sensibles, he borrows from Heraclitus; regarding the intelligibles, from Pythagoras; and regarding politics, from Socrates. A little later, Diogenes makes a series of comparisons intended to show how much Plato owed to the comic poet, Epicharmus 3.

Diogenes Laertius 3. In the Seventh Letter, we learn that Plato was a friend of Archytas of Tarentum, a well-known Pythagorean statesman and thinker see d-e , and in the Phaedo, Plato has Echecrates, another Pythagorean, in the group around Socrates on his final day in prison. Nonetheless, it is plain that no influence on Plato was greater than that of Socrates. According to Diogenes Laertius, the respect was mutual 3. Supposedly possessed of outstanding intellectual and artistic ability even from his youth, according to Diogenes, Plato began his career as a writer of tragedies, but hearing Socrates talk, he wholly abandoned that path, and even burned a tragedy he had hoped to enter in a dramatic competition D.

He may, indeed, have written some epigrams; of the surviving epigrams attributed to him in antiquity, some may be genuine.

Plato was not the only writer of dialogues in which Socrates appears as a principal character and speaker. A recent study of these, by Charles H. Kahn , , concludes that the very existence of the genre—and all of the conflicting images of Socrates we find given by the various authors—shows that we cannot trust as historically reliable any of the accounts of Socrates given in antiquity, including those given by Plato.

But it is one thing to claim that Plato was not the only one to write Socratic dialogues, and quite another to hold that Plato was only following the rules of some genre of writings in his own work. Such a claim, at any rate, is hardly established simply by the existence of these other writers and their writings.

The question has led to a number of seemingly irresolvable scholarly disputes. One way to approach this issue has been to find some way to arrange the dialogues into at least relative dates. It has frequently been assumed that if we can establish a relative chronology for when Plato wrote each of the dialogues, we can provide some objective test for the claim that Plato represented Socrates more accurately in the earlier dialogues, and less accurately in the later dialogues.

The uncontroversial internal and external historical evidence for a chronological ordering is relatively slight. Aristotle Politics 2. Internal references in the Sophist a and the Statesman also known as the Politicus; a, b show the Statesman to come after the Sophist. The Timaeus 17bb may refer to Republic as coming before it, and more clearly mentions the Critias as following it 27a. Similarly, internal references in the Sophist a, c and the Theaetetus e may be thought to show the intended order of three dialogues: Parmenides, Theaetetus, and Sophist.

Even so, it does not follow that these dialogues were actually written in that order. At Theaetetus c, Plato announces through his characters that he will abandon the somewhat cumbersome dialogue form that is employed in his other writings. Since the form does not appear in a number of other writings, it is reasonable to infer that those in which it does not appear were written after the Theaetetus.

Scholars have sought to augment this fairly scant evidence by employing different methods of ordering the remaining dialogues. Originally done by laborious study by individuals, stylometry can now be done more efficiently with assistance by computers.

Neither of these general approaches has commanded unanimous assent among scholars, and it is unlikely that debates about this topic can ever be put entirely to rest. We have more to say on this subject in the next section. Our own view of the probable dates and groups of dialogues, which to some extent combine the results of stylometry and content analysis, is as follows all lists but the last in alphabetical order :.

Early-Transitional Either at the end of the early group or at the beginning of the middle group, c. Late-Transitional Either at the end of the middle group, or the beginning of the late group, c. Late c. In Henri Estienne whose Latinized name was Stephanus published an edition of the dialogues in which each page of the text is separated into five sections labeled a, b, c, d, and e.

The standard style of citation for Platonic texts includes the name of the text, followed by Stephanus page and section numbers e. Republic d. Scholars sometimes also add numbers after the Stephanus section letters, which refer to line numbers within the Stephanus sections in the standard Greek edition of the dialogues, the Oxford Classical texts.

Several other works, including thirteen letters and eighteen epigrams, have been attributed to Plato. These other works are generally called the spuria and the dubia. The spuria were collected among the works of Plato but suspected as frauds even in antiquity. The dubia are those presumed authentic in later antiquity, but which have more recently been doubted. Ten of the spuria are mentioned by Diogenes Laertius at 3. Works whose authenticity was also doubted in antiquity include the Second Alcibiades or Alcibiades II , Epinomis, Hipparchus, and Rival Lovers also known as either Rivals or Lovers , and these are sometimes defended as authentic today.

If any are of these are authentic, the Epinomis would be in the late group, and the others would go with the early or early transitional groups. Seventeen or eighteen epigrams poems appropriate to funerary monuments or other dedications are also attributed to Plato by various ancient authors.

Most of these are almost certainly not by Plato, but some few may be authentic. None appear to provide anything of great philosophical interest. The dubia include the First Alcibiades or Alcibiades I , Minos, and Theages, all of which, if authentic, would probably go with the early or early transitional groups, the Cleitophon, which might be early, early transitional, or middle, and the letters, of which the Seventh seems the best candidate for authenticity. Some scholars have also suggested the possibility that the Third may also be genuine.

If any are authentic, the letters would appear to be works of the late period, with the possible exception of the Thirteenth Letter, which could be from the middle period.

Nearly all of the dialogues now accepted as genuine have been challenged as inauthentic by some scholar or another. In the 19th Century in particular, scholars often considered arguments for and against the authenticity of dialogues whose authenticity is now only rarely doubted. Of those we listed as authentic, above in the early group , only the Hippias Major continues occasionally to be listed as inauthentic.

The strongest evidence against the authenticity of the Hippias Major is the fact that it is never mentioned in any of the ancient sources. However, relative to how much was actually written in antiquity, so little now remains that our lack of ancient references to this dialogue does not seem to be an adequate reason to doubt its authenticity.

In style and content, it seems to most contemporary scholars to fit well with the other Platonic dialogues. Although no one thinks that Plato simply recorded the actual words or speeches of Socrates verbatim, the argument has been made that there is nothing in the speeches Socrates makes in the Apology that he could have not uttered at the historical trial.

But as we have said, most scholars treat these as representing more or less accurately the philosophy and behavior of the historical Socrates—even if they do not provide literal historical records of actual Socratic conversations.

Some of the early dialogues include anachronisms that prove their historical inaccuracy. Contemporary scholars generally endorse one of the following four views about the dialogues and their representation of Socrates:. There is just too little and too little that is at all interesting to be found that could reliably be attributed to Socrates from any other ancient authors.

As a result of his attempt to discern the true meaning of this oracle, Socrates gained a divinely ordained mission in Athens to expose the false conceit of wisdom. Platonic dialogues continue to be included among the required readings in introductory and advanced philosophy classes, not only for their ready accessibility, but also because they raise many of the most basic problems of philosophy.

Unlike most other philosophical works, moreover, Plato frames the discussions he represents in dramatic settings that make the content of these discussions especially compelling.

In these dialogues, we also find Socrates represented as holding certain religious beliefs, such as:. Scholarly attempts to provide relative chronological orderings of the early transitional and middle dialogues are problematical because all agree that the main dialogue of the middle period, the Republic, has several features that make dating it precisely especially difficult.

As we have already said, many scholars count the first book of the Republic as among the early group of dialogues. But those who read the entire Republic will also see that the first book also provides a natural and effective introduction to the remaining books of the work.

If this central work of the period is difficult to place into a specific context, there can be no great assurance in positioning any other works relative to this one. Nonetheless, it does not take especially careful study of the transitional and middle period dialogues to notice clear differences in style and philosophical content from the early dialogues. In the early dialogues, moreover, Socrates discusses mainly ethical subjects with his interlocutors—with some related religious, methodological, and epistemological views scattered within the primarily ethical discussions.

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This Day In History. History Vault. Platonic Academy Around , the year-old Plato returned to Athens and founded his philosophical school in the grove of the Greek hero Academus, just outside the city walls.

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