Plato (Greek: Πλάτων, Plátōn, "broad") (428/427 BC – 348/347 BC), was a Classical Greek philosopher, who, together with his mentor, Socrates, and his student, Aristotle, helped to lay the foundations of Western philosophy. Plato was also a mathematician, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the western world. Plato was originally a student of Socrates, and was as much influenced by his thinking as by what he saw as his teacher's unjust death.
Plato's sophistication as a writer can be witnessed by reading his Socratic dialogues. Some of the dialogues, letters, and other works that are ascribed to him are considered spurious. Although there is little question that Plato lectured at the Academy that he founded, the pedagogical function of his dialogues, if any, is not known with certainty. The dialogues since Plato's time have been used to teach a range of subjects, mostly including philosophy, logic, rhetoric, mathematics, and other subjects about which he wrote.
Ariston tried to force his attentions on Perictione, but failed of his purpose; then the ancient Greek god Apollo appeared to him in a vision, and, as a result of it, Ariston left Perictione unmolested. Another legend related that, while he was sleeping as an infant, bees had settled on the lips of Plato; an augury of the sweetness of style in which he would discourse philosophy.
Ariston appears to have died in Plato's childhood, although the precise dating of his death is difficult. Perictione then married Pyrilampes, her mother's brother, who had served many times as an ambassador to the Persian court and was a friend of Pericles, the leader of the democratic faction in Athens. Pyrilampes had a son from a previous marriage, Demus, who was famous for his beauty. Perictione gave birth to Pyrilampes' second son, Antiphon, the half-brother of Plato, who appears in Parmenides.
In contrast to his reticence about himself, Plato used to introduce his distinguished relatives into his dialogues, or to mention them with some precision: Charmides has one named after him; Critias speaks in both Charmides and Protagoras; Adeimantus and Glaucon take prominent parts in the Republic. From these and other references one can reconstruct his family tree, and this suggests a considerable amount of family pride. According to Burnet, "the opening scene of the Charmides is a glorification of the whole [family] connection ... Plato's dialogues are not only a memorial to Socrates, but also the happier days of his own family".
Plato makes it clear, especially in his Apology of Socrates, that he was one of Socrates' devoted young followers. In that dialogue, Socrates is presented as mentioning Plato by name as one of those youths close enough to him to have been corrupted, if he were in fact guilty of corrupting the youth, and questioning why their fathers and brothers did not step forward to testify against him if he was indeed guilty of such a crime (33d-34a). Later, Plato is mentioned along with Crito, Critobolus, and Apollodorus as offering to pay a fine of 30 minas on Socrates' behalf, in lieu of the death penalty proposed by Meletus (38b). In the Phaedo, the title character lists those who were in attendance at the prison on Socrates' last day, explaining Plato's absence by saying, "Plato was ill" (Phaedo 59b).
The relationship between Plato and Socrates is not unproblematic, however. Aristotle, for example, attributes a different doctrine with respect to the ideas to Plato and Socrates (Metaphysics 987b1–11), but Plato never speaks in his own voice in his dialogues. In the Second Letter, it says, "no writing of Plato exists or ever will exist, but those now said to be his are those of a Socrates become beautiful and new" (341c); if the Letter is Plato's, the final qualification seems to call into question the dialogues' historical fidelity. In any case, Xenophon and Aristophanes seem to present a somewhat different portrait of Socrates than Plato paints. Some have called attention to the problem of taking Plato's Socrates to be his mouthpiece, given Socrates' reputation for irony.
The precise relationship between Plato and Socrates remains an area of contention among scholars.
On Plato's mind is the father-son relationship, the "question" of whether a father's interest in his sons has much to do with how well his sons turn out. A boy in ancient Athens was socially located by his family identity, and Plato often refers to his characters in terms of their paternal and fraternal relationships. Socrates was not a family man, and saw himself as the son of his mother, who was apparently a midwife. A divine fatalist, Socrates mocks men who spent exorbitant fees on tutors and trainers for their sons, and repeatedly ventures the idea that good character is a gift from the gods. Crito reminds Socrates that orphans are at the mercy of chance, but Socrates is unconcerned. In the Theaetetus, he is found recruiting as a disciple a young man whose inheritance has been squandered. Socrates twice compares the relationship of the older man and his boy lover to the father-son relationship (Lysis 213a, Republic 3.403b), and in the Phaedo, Socrates' disciples, towards whom he displays more concern than his biological sons, say they will feel "fatherless" when he is gone. Many dialogues, like these, suggest that man-boy love (which is "spiritual") is a wise man's substitute for father-son biology (which is "bodily").
In several dialogues, Socrates floats the idea that Knowledge is a matter of recollection, and not of learning, observation, or study. He maintains this view somewhat at his own expense, because in many dialogues, Socrates complains of his forgetfulness. Socrates is often found arguing that knowledge is not empirical, and that it comes from divine insight. He is quite consistent in believing in the immortality of the soul, and several dialogues end with long speeches imagining the afterlife. More than one dialogue contrasts knowledge and opinion, perception and reality, nature and custom, and body and soul. The only contrast to this is his Parmenides.
Several dialogues tackle questions about art: Socrates says that poetry is inspired by the muses, and is not rational. He speaks approvingly of this, and other forms of divine madness (drunkenness, eroticism, and dreaming) in the Phaedrus (265a–c), and yet in the Republic wants to outlaw Homer's great poetry, and laughter as well. In Ion, Socrates gives no hint of the disapproval of Homer that he expresses in the Republic. The dialogue Ion suggests that Homer's Iliad functioned in the ancient Greek world as the bible does today in the modern Christian world: as divinely inspired literature that can provide moral guidance, if only it can be properly interpreted.
On politics and art, religion and science, justice and medicine, virtue and vice, crime and punishment, pleasure and pain, rhetoric and rhapsody, human nature and sexuality, love and wisdom, Socrates and his company of disputants had something to say.
"Platonism" is a term coined by scholars to refer to the intellectual consequences of denying, as Socrates often does, the reality of the material world. In several dialogues, most notably the Republic, Socrates inverts the common man's intuition about what is knowable and what is real. While most people take the objects of their senses to be real if anything is, Socrates is contemptuous of people who think that something has to be graspable in the hands to be real. In the Theaetetus, he says such people are "eu a-mousoi", an expression that means literally, "happily without the muses" (Theaetetus 156a). In other words, such people live without the divine inspiration that gives him, and people like him, access to higher insights about reality.
Socrates's idea that reality is unavailable to those who use their senses is what puts him at odds with the common man, and with common sense. Socrates says that he who sees with his eyes is blind, and this idea is most famously captured in his allegory of the cave, and more explicitly in his description of the divided line. The allegory of the cave (begins Republic 7.514a) is a paradoxical analogy wherein Socrates argues that the invisible world is the most intelligible ("noeton") and that the visible world ("(h)oraton") is the least knowable, and the most obscure. (This is exactly the opposite of what Socrates says to Euthyphro in the soothsayer's namesake dialogue. There, Socrates tells Euthyphro that people can agree on matters of logic and science, and are divided on moral matters, which are not so easily verifiable.)
Socrates says in the Republic that people who take the sun-lit world of the senses to be good and real are living pitifully in a den of evil and ignorance. Socrates admits that few climb out of the den, or cave of ignorance, and those who do, not only have a terrible struggle to attain the heights, but when they go back down for a visit or to help other people up, they find themselves objects of scorn and ridicule.
According to Socrates, physical objects and physical events are "shadows" of their ideal or perfect forms, and exist only to the extent that they instantiate the perfect versions of themselves. Just as shadows are temporary, inconsequential epiphenomena produced by physical objects, physical objects are themselves fleeting phenomena caused by more substantial causes, the ideals of which they are mere instances. For example, Socrates thinks that perfect justice exists (although it is not clear where) and his own trial would be a cheap copy of it.
The allegory of the cave (often said by scholars to represent Plato's own epistemology and metaphysics) is intimately connected to his political ideology (often said to also be Plato's own), that only people who have climbed out of the cave and cast their eyes on a vision of goodness are fit to rule. Socrates claims that the enlightened men of society must be forced from their divine contemplations and compelled to run the city according to their lofty insights. Thus is born the idea of the "philosopher-king", the wise person who accepts the power thrust upon him by the people who are wise enough to choose a good master. This is the main thesis of Socrates in the Republic, that the most wisdom the masses can muster is the wise choice of a ruler.
The word metaphysics derives from the fact that Aristotle's musings about divine reality came after ("meta") his lecture notes on his treatise on nature ("physics"). The term is in fact applied to Aristotle's own teacher, and Plato's "metaphysics" is understood as Socrates' division of reality into the warring and irreconcilable domains of the material and the spiritual. The theory has been of incalculable influence in the history of Western philosophy and religion.
The Theory of Forms typically refers to Plato's belief that the material world as it seems to us is not the real world, but only a shadow of the real world. Plato spoke of forms in formulating his solution to the problem of universals. The forms, according to Plato, are roughly speaking archetypes or abstract representations of the many types and properties (that is, of universals) of things we see all around us.
Many have interpreted Plato as stating that knowledge is justified true belief, an influential view which informed future developments in modern analytic epistemology. This interpretation is based on a reading of the Theaetetus wherein Plato argues that belief is to be distinguished from knowledge on account of justification. Many years later, Edmund Gettier famously demonstrated the problems of the justified true belief account of knowledge. This interpretation, however, imports modern analytic and empiricist categories onto Plato himself and is better read on its own terms than as Plato's view.
Really, in the Sophist, Statesman, Republic, and the Parmenides Plato himself associates knowledge with the apprehension of unchanging Forms and their relationships to one another (which he calls "expertise" in Dialectic). More explicitly, Plato himself argues in the Timaeus that knowledge is always proportionate to the realm from which it is gained. In other words, if one derives their account of something experientially, because the world of sense is in flux, the views therein attained will be mere opinions. And opinions are characterized by a lack of necessity and stability. On the other hand, if one derives their account of something by way of the non-sensible forms, because these forms are unchanging, so too is the account derived from them. It is only in this sense that Plato uses the term "knowledge."
In the Meno, Socrates uses a geometrical example to expound Plato's view that knowledge in this latter sense is acquired by recollection. Socrates elicits a fact concerning a geometrical construction from a slave boy, who could not have otherwise known the fact (due to the slave boy's lack of education). The knowledge must be present, Socrates concludes, in an eternal, non-experiential form.
Plato's philosophical views had many societal implications, especially on the idea of an ideal state or government. There is some discrepancy between his early and later views. Some of the most famous doctrines are contained in the Republic during his middle period, as well as in the Laws and the Statesman. However, because Plato wrote dialogues, it is assumed that Socrates is often speaking for Plato. This assumption may not be true in all cases.
Plato, through the words of Socrates, asserts that societies have a tripartite class structure corresponding to the appetite/spirit/reason structure of the individual soul. The appetite/spirit/reason stand for different parts of the body. The body parts symbolize the castes of society.
According to this model, the principles of Athenian democracy (as it existed in his day) are rejected as only a few are fit to rule. Instead of rhetoric and persuasion, Plato says reason and wisdom should govern. As Plato puts it:
Plato describes these "philosopher kings" as "those who love the sight of truth" (Republic 475c) and supports the idea with the analogy of a captain and his ship or a doctor and his medicine. Sailing and health are not things that everyone is qualified to practice by nature. A large part of the Republic then addresses how the educational system should be set up to produce these philosopher kings.
However, it must be taken into account that the ideal city outlined in the Republic is qualified by Socrates as the ideal luxurious city, examined to determine how it is that injustice and justice grow in a city (Republic 372e). According to Socrates, the "true" and "healthy" city is instead the one first outlined in book II of the Republic, 369c–372d, containing farmers, craftsmen, merchants, and wage-earners, but lacking the guardian class of philosopher-kings as well as delicacies such as "perfumed oils, incense, prostitutes, and pastries", in addition to paintings, gold, ivory, couches, a multitude of occupations such as poets and hunters, and war.
In addition, the ideal city is used as an image to illuminate the state of one's soul, or the will, reason, and desires combined in the human body. Socrates is attempting to make an image of a rightly ordered human, and then later goes on to describe the different kinds of humans that can be observed, from tyrants to lovers of money in various kinds of cities. The ideal city is not promoted, but only used to magnify the different kinds of individual humans and the state of their soul. However, the philosopher king image was used by many after Plato to justify their personal political beliefs. The philosophic soul according to Socrates has reason, will, and desires united in virtuous harmony. A philosopher has the moderate love for wisdom and the courage to act according to wisdom. Wisdom is knowledge about the Good or the right relations between all that exists.
Wherein it concerns states and rulers, Plato has made interesting arguments. For instance he asks which is better - a bad democracy or a country reigned by a tyrant. He argues that it is better to be ruled by a bad tyrant (since then there is only one person committing bad deeds) than be a bad democracy (since here all the people are now responsible for such actions.)
According to Plato, a state which is made up of different kinds of souls, will overall 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 one person, rule by a tyrant).
For a long time Plato's unwritten doctrine has been considered unworthy of attention. Most of the books on Plato seem to diminish its importance. Nevertheless the first important witness who mentions its existence is Aristotle, who in his Physics (209 b) writes: "It is true, indeed, that the account he gives there [i.e. in Timaeus] of the participant is different from what he says in his so-called unwritten teaching (ἄγραφα δόγματα)." The term ἄγραφα δόγματα literally means unwritten doctrine and it stands for the most fundamental metaphysical teaching of Plato which he disclosed only to his most trusted fellows and kept secret from the public.
The reason for not revealing it to everyone is partially discussed in Phaedrus (276 c) where Plato criticizes the written transmission of knowledge as faulty, favoring instead the spoken logos: "he who has knowledge of the just and the good and beautiful ... will not, when in earnest, write them in ink, sowing them through a pen with words which cannot defend themselves by argument and cannot teach the truth effectually." The same argument is repeated in Plato's Seventh Letter (344 c): "every serious man in dealing with really serious subjects carefully avoids writing." In the same letter he writes (341 c): "I can certainly declare concerning all these writers who claim to know the subjects which I seriously study ... there does not exist, nor will there ever exist, any treatise of mine dealing therewith." Such secrecy is necessary in order not "to expose them to unseemly and degrading treatment" (344 d).
It is however said that Plato once disclosed this knowledge to the public in his lecture On the Good (Περὶ τἀγαθοῦ), in which the Good (τὸ ἀγαθόν) is identified with the One (the Unity, τὸ ἕν), the fundamental ontological principle. The content of this lecture has been transmitted by several witnesses, among others Aristoxenus who describes the event in the following words: "Each came expecting to learn something about the things which are generally considered good for men, such as wealth, good health, physical strength, and altogether a kind of wonderful happiness. But when the mathematical demonstrations came, including numbers, geometrical figures and astronomy, and finally the statement Good is One seemed to them, I imagine, utterly unexpected and strange; hence some belittled the matter, while others rejected it." Simplicius quotes Alexander of Aphrodisias who states that "according to Plato, the first principles of everything, including the Forms themselves are One and Indefinite Duality (ἡ ἀόριστος δυάς) which he called Large and Small (τὸ μέγα καὶ τὸ μικρόν) ... one might also learn this from Speusippus and Xenocrates and the others who were present at Plato's lecture on the Good"
Their account is in full agreement with Aristotle's description of Plato's metaphysical doctrine. In Metaphysics he writes: "Now since the Forms are the causes of everything else, he [i.e. Plato] supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small [i.e. the Dyad], and the essence is the One (τὸ ἕν), since the numbers are derived from the Great and Small by participation in the One" (987 b). "From this account it is clear that he only employed two causes: that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms. He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms - that it is this the duality (the Dyad, ἡ δυάς), the Great and Small (τὸ μέγα καὶ τὸ μικρόν). Further, he assigned to these two elements respectively the causation of good and of evil" (988 a).
The most important aspect of this interpretation of Plato's metaphysics is the continuity between his teaching and the neoplatonic interpretation of Plotinus or Ficino which has been considered errorneous by many but may in fact have been directly influenced by oral transmission of Plato's doctrine. The first scholar who recognized the importance of the unwritten doctrine of Plato was Heinrich Gomperz who described it in his speech during the 7th International Congress of Philosophy in 1930. All the sources related to the ἄγραφα δόγματα have been collected by Konrad Gaiser and published as Testimonia Platonica. These sources have subsequently been interpreted by scholars from the german Tübingen School such as Hans Joachim Krämer or Thomas A. Szlezák.
Thirty-five dialogues and thirteen letters have traditionally been ascribed to Plato, though modern scholarship doubts the authenticity of at least some of these. Plato's writings have been published in several fashions; this has led to several conventions regarding the naming and referencing of Plato's texts.
The usual system for making unique references to sections of the text by Plato derives from a 16th century edition of Plato's works by Henricus Stephanus. An overview of Plato's writings according to this system can be found in the Stephanus pagination article.
One tradition regarding the arrangement of Plato's texts is according to tetralogies. This scheme is ascribed by Diogenes Laertius to an ancient scholar and court astrologer to Tiberius named Thrasyllus.
In the list below, works by Plato are marked (1) if there is no consensus among scholars as to whether Plato is the author, and (2) if scholars generally agree that Plato is not the author of the work. Unmarked works are assumed to have been written by Plato.
The remaining works were transmitted under Plato's name, most of them already considered spurious in antiquity, and so were not included by Thrasyllus in his tetralogical arrangement. These works are labelled as Notheuomenoi ("spurious") or Apocrypha.
Lewis Campbell was the first to make exhaustive use of stylometry to prove objectively that the Critias, Timaeus, Laws, Philebus, Sophist, and Statesman were all clustered together as a group, while the Parmenides, Phaedrus, Republic, and Theaetetus belong to a separate group, which must be earlier (given Aristotle's statement in his Politics that the Laws was written after the Republic; cf. Diogenes Laertius Lives 3.37). What is remarkable about Campbell's conclusions is that, in spite of all the stylometric studies that have been conducted since his time, perhaps the only chronological fact about Plato's works that can now be said to be proven by stylometry is the fact that Critias, Timaeus, Laws, Philebus, Sophist, and Statesman are the latest of Plato's dialogues, the others earlier.
Increasingly in the most recent Plato scholarship, writers are skeptical of the notion that the order of Plato's writings can be established with any precision, though Plato's works are still often characterized as falling at least roughly into three groups. The following represents one such devision which is relatively common. It should, however, be kept in mind that many of the positions in the ordering are still highly disputed, and also that the very notion that Plato's dialogues can or should be "ordered" is by no means universally accepted.
The following are often considered "transitional" or "pre-middle" dialogues:
Late in the early dialogues Plato's Socrates actually begins supplying answers to some of the questions he asks, or putting forth positive doctrines. This is generally seen as the first appearance of Plato's own views. The first of these, that goodness is wisdom and that no one does evil willingly, was perhaps Socrates' own view. What becomes most prominent in the middle dialogues is the idea that knowledge comes of grasping unchanging forms or essences, paired with the attempts to investigate such essences. The immortality of the soul, and specific doctrines about justice, truth, and beauty, begin appearing here. The Symposium and the Republic are considered the centrepieces of Plato's middle period. The Parmenides and Theaetetus are often considered to come late in this period and transitional to the next, as they seem to treat the Theory of Forms critically (Parmenides) or not at all (Theaetetus).
The Parmenides presents a series of criticisms of the theory of Forms which are widely taken to indicate Plato's abandonment of the doctrine. Some recent publications (e.g., Meinwald (1991)) have challenged this characterisation. In most of the remaining dialogues the theory is either absent or at least appears under a different guise in discussions about kinds or classes of things (the Timaeus may be an important, and hence controversially placed, exception). Socrates is either absent or a minor figure in the discussion. An apparently new method for doing dialectic known as "collection and division" is also featured, most notably in the Sophist and Statesman, explicitly for the first time in the Phaedrus, and possibly in the Philebus. A basic description of collection and division would go as follows: interlocutors attempt to discern the similarities and differences among things in order to get clear idea about what they in fact are. One understanding, suggested in some passages of the Sophist, is that this is what philosophy is always in the business of doing, and is doing even in the early dialogues.
The late dialogues are also an important place to look for Plato's mature thought on most of the issues dealt with in the earlier dialogues. There is much work still to be done by scholars on the working out of what these views are. The later works are agreed to be difficult and challenging pieces of philosophy. On the whole they are more sober and logical than earlier works, but may hold out the promise of steps towards a solution to problems which were systematically laid out in prior works.
Plato never presents himself as a participant in any of the dialogues, and with the exception of the Apology, there is no suggestion that he heard any of the dialogues firsthand. Some dialogues have no narrator but have a pure "dramatic" form (examples: Meno, Gorgias, Phaedrus, Crito, Euthyphro), some dialogues are narrated by Socrates, wherein he speaks in first person (examples: Lysis, Charmides, Republic). One dialogue, Protagoras, begins in dramatic form but quickly proceeds to Socrates' narration of a conversation he had previously with the sophist for whom the dialogue is named; this narration continues uninterrupted till the dialogue's end.
The three dialogues, Phaedo, Symposium, and Theaetetus, also begin in dramatic form but then proceed to virtually uninterrupted narration by followers of Socrates, and all, apparently, based on their distant memory or secondhand reports. Phaedo, an account of Socrates' final conversation and hemlock drinking, is narrated by Phaedo to Echecrates in a foreign city many years after the execution took place. The Symposium is narrated by Apollodorus, a Socratic disciple, apparently to Glaucon. Apollodorus assures his listener that he is recounting the story, which took place when he himself was an infant, not from his own memory, but as remembered by Aristodemus, who told him the story years ago. In the beginning of the Theaetetus (142c-143b), Euclides says that he compiled the conversation from notes he took based on what Socrates told him of his conversation with the title character. The rest of the Theaetetus is presented as a "book" written in dramatic form and read by one of Euclides' slaves (143c). Some scholars take this as an indication that Plato had by this date wearied of the narrated form. With the exception of the Theaetetus, Plato gives no explicit indication as to how these orally transmitted conversations came to be written down. Other dialogues, such as the Phaedo, Symposium, and Parmenides, do suggest that such conversations were faithfully recalled and transmitted by Socrates' followers.
Two other important dialogues, the Symposium and the Phaedrus, are linked to the main storyline by characters. In the Apology (19b, c), Socrates says Aristophanes slandered him in a comic play, and blames him for causing his bad reputation, and ultimately, his death. In the Symposium, the two of them are drinking together with other friends. The character Phaedrus is linked to the main story line by character (Phaedrus is also a participant in the Symposium and the Protagoras) and by theme (the philosopher as divine emissary, etc.) The Protagoras is also strongly linked to the Symposium by characters: all of the formal speakers at the Symposium (with the exception of Aristophanes) are present at the home of Callias in that dialogue. Charmides and his guardian Critias are present for the discussion in the Protagoras. Examples of characters crossing between dialogues can be further multiplied. The Protagoras contains the largest gathering of Socratic associates.
In the dialogues for which Plato is most celebrated and admired, Socrates is concerned with human and political virtue, has a distinctive personality, and friends and enemies who "travel" with him from dialogue to dialogue. This is not to say that Socrates is consistent: a man who is his friend in one dialogue may be an adversary or subject of his mockery in another. For example, Socrates praises the wisdom of Euthyphro many times in the Cratylus, but makes him look like a fool in the Euthyphro. He disparages sophists generally, and Prodicus specifically in the Apology, yet tells Theaetetus in his namesake dialogue that he admires Prodicus and has directed many pupils to him. In Cratylus (384b-c), Socrates says that he studied with Cratylus, and took his one-drachma course because he could not afford the full fifty-drachma course. Socrates' ideas are also not consistent within or between or among dialogues.
Plato's thought is often compared with that of his most famous student, Aristotle, whose reputation during the Western Middle Ages so completely eclipsed that of Plato that the Scholastic philosophers referred to Aristotle as "the Philosopher". However, in the Byzantine Empire, the study of Plato continued.
The Medieval scholastic philosophers did not have access to the works of Plato, nor the knowledge of Greek needed to read them. Plato's original writings were essentially lost to Western civilization until they were brought from Constantinople in the century before its fall, by George Gemistos Plethon. Medieval scholars knew of Plato only through translations into Latin from the translations into Arabic by Persian and Arab scholars. These scholars not only translated the texts of the ancients, but expanded them by writing extensive commentaries and interpretations on Plato's and Aristotle's works (see Al-Farabi, Avicenna, Averroes).
Only in the Renaissance, with the general resurgence of interest in classical civilization, did knowledge of Plato's philosophy become widespread again in the West. Many of the greatest early modern scientists and artists who broke with Scholasticism and fostered the flowering of the Renaissance, with the support of the Plato-inspired Lorenzo de Medici, 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.
Notable Western philosophers have continued to draw upon Plato's work since that time. Plato's influence has been especially strong in mathematics and the sciences. He helped to distinguish between pure and applied mathematics by widening the gap between "arithmetic", now called Number Theory and "logistic", now called arithmetic. He regarded logistic as appropriate for business men and men of war who "must learn the art of numbers or he will not know how to array his troops," while arithmetic was appropriate for philosophers "because he has to arise out of the sea of change and lay hold of true being. Plato's resurgence further inspired some of the greatest advances in logic since Aristotle, primarily through Gottlob Frege and his followers Kurt Gödel, Alonzo Church, and Alfred Tarski; the last of these summarised his approach by reversing Aristotle's famous declaration of sedition from the Nicomachean Ethics (1096a15: Amicus Plato sed magis amica veritas - "Plato is a friend, but truth is a greater friend") to Inimicus Plato sed magis inimica falsitas ("Plato is an enemy, but falsehood is a greater enemy"). Albert Einstein drew on Plato's understanding of an immutable reality that underlies the flux of appearances for his objections to the probabilistic picture of the physical universe propounded by Niels Bohr in his interpretation of quantum mechanics. Conversely, thinkers that diverged from ontological models and moral ideals in their own philosophy, have tended to disparage Platonism from more or less informed perspectives. Thus Friedrich Nietzsche attacked Plato's moral and political theories, Martin Heidegger argued against Plato's alleged obfuscation of Being, and Karl Popper argued in The Open Society and Its Enemies (1945) that Plato's alleged proposal for a government system in the Republic was prototypically totalitarian. Leo Strauss is considered by some as the prime thinker involved in the recovery of Platonic thought in its more political, and less metaphysical, form. Deeply influenced by Nietzsche and Heidegger, Strauss nonetheless rejects their condemnation of Plato and looks to the dialogues for a solution to what all three thinkers acknowledge as 'the crisis of the West.'
b. Diogenes Laertius mentions that Plato "was born, according to some writers, in Aegina in the house of Phidiades the son of Thales". Diogenes mentions as one of his sources the Universal History of Favorinus. According to Favorinus, Ariston, Plato's family, and his family were sent by Athens to settle as cleruchs (colonists retaining their Athenian citizenship), on the island of Aegina, from which they were expelled by the Spartans after Plato's birth there. Nails points out, however, that there is no record of any Spartan expulsion of Athenians from Aegina between 431-411 BC. On the other hand, at the Peace of Nicias, Aegina was silently left under Athens' control, and it was not until the summer of 411 that the Spartans overran the island. Therefore, Nails concludes that "perhaps Ariston was a cleruch, perhaps he went to Aegina in 431, and perhaps Plato was born on Aegina, but none of this enables a precise dating of Ariston's death (or Plato's birth). Aegina is regarded as Plato's place of birth by Suda as well.
c. Plato was a common name, of which 31 instances are known at Athens alone.