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- Duration: 47:15
- Published: 22 Sep 2008
- Uploaded: 05 Jul 2011
- Author: YaleCourses
Region | Western Philosophy |
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Era | Ancient philosophy |
Color | #B0C4DE |
Caption | Plato: copy of portrait bust by Silanion |
Name | Plato (Πλάτων) |
Birth date | c. 428–427 BC |
Birth place | Athens |
Death date | c. 348–347 BC (age approx 80) |
Death place | Athens |
School tradition | Platonism |
Main interests | Rhetoric, Art, Literature, Epistemology, Justice, Virtue, Politics, Education, Family, Militarism |
Influences | Socrates, Homer, Hesiod, Aristophanes, Aesop, Protagoras, Parmenides, Pythagoras, Heraclitus, Orphism |
Influenced | Most of subsequent western philosophy, including Aristotle, Augustine, Neoplatonism, Cicero, Plutarch, Stoicism, Anselm, Machiavelli, Descartes, Hobbes, Leibniz, Mill, Schopenhauer, Nietzsche, Heidegger, Arendt, Gadamer, Imam Khomeini, Russell and countless other philosophers and theologians |
Notable ideas | Platonic realism |
The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings. I allude to the wealth of general ideas scattered through them.
Plato's sophistication as a writer is evident in his Socratic dialogues; thirty-six dialogues and thirteen letters have been ascribed to him. Plato's writings have been published in several fashions; this has led to several conventions regarding the naming and referencing of Plato's texts.
Plato's dialogues have been used to teach a range of subjects, including philosophy, logic, ethics, rhetoric, and mathematics.
The traditional date of Plato's birth (428/7) is based on a dubious interpretation of Diogenes Laertius, who says "When [Socrates] was gone, [Plato] joined Cratylus the Heracleitean and Hermogenes, who philosophized in the manner of Parmenides. Then, at twenty-eight, Hermodorus says, [Plato] went to Euclides in Megara". As Nails says, "The text tself gives no reason to infer that Plato left immediately for Megara and implies the very opposite" In the Seventh Letter (Plato) Plato says that his coming of age coincided with the taking of power by the Thirty, "But a youth under the age of twenty made himself a laughingstock if he attempted to enter the political arena ... it thus appears that Plato is turning twenty ... Hence I date Plato's birth to 424/3"
Ariston tried to force his attentions on Perictione, but failed in 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".
Throughout his later life, Plato became entangled with the politics of the city of Syracuse. According to Diogenes Laertius, Plato initially visited Syracuse while it was under the rule of Dionysus. During this first trip Dionysus's brother-in-law, Dion of Syracuse, became one of Plato's disciples, but the tyrant himself turned against Plato. Plato was sold into slavery and almost faced death in Cyrene, a city at war with Athens, before an admirer bought Plato's freedom and sent him home. After Dionysius's death, according to Plato's Seventh Letter, Dion requested Plato return to Syracuse to tutor Dionysus II and guide him to become a philosopher king. Dionysius II seemed to accept Plato's teachings, but he became suspicious of Dion, his uncle. Dionysus expelled Dion and kept Plato against his will. Eventually Plato left Syracuse. Dion would return to overthrow Dionysus and ruled Syracuse for a short time before being usurped by Calippus, a fellow disciple of Plato.
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 and the dramatic nature of the dialogue form
Aristotle attributes a different doctrine with respect to the ideas to Plato and Socrates (Metaphysics 987b1–11). Putting it in a nutshell, Aristotle merely suggests that his idea of forms can be discovered through investigation of the natural world, unlike Plato's Forms that exist beyond and outside the ordinary range of human understanding.
Plato often discusses the father-son relationship and 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.
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. In many middle period dialogues, such as the Phaedo, Republic and Phaedrus Plato advocates a belief 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.
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.
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 be 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 the belief expressed by Socrates in some of Plato's dialogues, that the material world as it seems to us is not the real world, but only an image or copy of the real world. Socrates spoke of forms in formulating a solution to the problem of universals. The forms, according to Socrates, are roughly speaking archetypes or abstract representations of the many types of things, and properties we feel and see around us, that can only be perceived by reason (); (that is, they are universals). In other words, Socrates sometimes seems to recognise two worlds: the apparent world, which constantly changes, and an unchanging and unseen world of forms, which may be a cause of what is apparent.
Many have interpreted Plato as stating that knowledge is justified true belief, an influential view that 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 one's 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 one's 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, 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:
: "Until philosophers rule as kings or those who are now called kings and leading men genuinely and adequately philosophise, that is, until political power and philosophy entirely coincide, while the many natures who at present pursue either one exclusively are forcibly prevented from doing so, cities will have no rest from evils,... nor, I think, will the human race." (Republic 473c-d)
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. According to him, 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, than be a bad democracy (since here all the people are now responsible for such actions, rather than one individual committing many bad deeds.) This is emphasised within the Republic as Plato describes the event of mutiny onboard a ship. Plato suggests the ships crew to be in line with the democratic rule of many and the captain, although inhibited through ailments, the tyrant. Plato's description of this event is parallel to that of democracy within the state and the inherent problems that arise.
According to Plato, a state 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).
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 that 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 that 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 erroneous by many but may in fact have been directly influenced by oral transmission of Plato's doctrine. A modern 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.
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 most scholars 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 relatively common such division. 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.
Among those who classify the dialogues into periods of composition, Socrates figures in all of the "early dialogues" and they are considered the most faithful representations of the historical Socrates. They include The Apology of Socrates, Charmides, Crito, Euthyphro, Ion, Laches, Less Hippias, Lysis, Menexenus, and Protagoras (often considered one of the last of the "early dialogues"). Three dialogues are often considered "transitional" or "pre-middle": Euthydemus, Gorgias, and Meno.
Whereas those classified as "early dialogues" often conclude in aporia, the so-called "middle dialogues" provide more clearly stated positive teachings that are often ascribed to Plato such as the theory of forms. These dialogues include Cratylus, Phaedo, Phaedrus, Republic, Symposium, Parmenides, and Theaetetus. Proponents of dividing the dialogues into periods often consider the Parmenides and Theaetetus to come late in this period and be transitional to the next, as they seem to treat the theory of forms critically (Parmenides) or not at all (Theaetetus).
The remaining dialogues are classified as "late" and are generally agreed to be difficult and challenging pieces of philosophy. This grouping is the only one proven by stylometic analysis. The so-called "late dialogues" include Critias, Laws, Philebus, Sophist, Statesman, and Timaeus.
(Anselm Feuerbach, 1873)]] Two dialogues Phaedo and Symposium also begin in dramatic form but then proceed to virtually uninterrupted narration by followers of Socrates. Phaedo, an account of Socrates' final conversation and hemlock drinking, is narrated by Phaedo to Echecrates in a foreign city not long 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.
The Theaetetus is a peculiar case: a dialogue in dramatic form imbedded within another dialogue in dramatic form. 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.
If Plato's important dialogues do not refer to Socrates' execution explicitly, they allude to it, or use characters or themes that play a part in it. Five dialogues foreshadow the trial: In the Theaetetus (210d) and the Euthyphro (2a–b) Socrates tells people that he is about to face corruption charges. In the Meno (94e–95a), one of the men who brings legal charges against Socrates, Anytus, warns him about the trouble he may get into if he does not stop criticizing important people. In the Gorgias, Socrates says that his trial will be like a doctor prosecuted by a cook who asks a jury of children to choose between the doctor's bitter medicine and the cook's tasty treats (521e–522a). In the Republic (7.517e), Socrates explains why an enlightened man (presumably himself) will stumble in a courtroom situation. The Apology is Socrates' defense speech, and the Crito and Phaedo take place in prison after the conviction. In the Protagoras, Socrates is a guest at the home of Callias, son of Hipponicus, a man whom Socrates disparages in the Apology as having wasted a great amount of money on sophists' fees.
In the dialogues Plato is most celebrated and admired for, 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, whom he also slyly jabs in the Cratylus for charging the hefty fee of fifty drachmas for a course on language and grammar. However, Socrates tells Theaetetus in his namesake dialogue that he admires Prodicus and has directed many pupils to him. 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 of its fall, by George Gemistos Plethon. It is believed that Plethon passed a copy of the Dialogues to Cosimo de' Medici when in 1438 the Council of Ferrara, called to unify the Greek and Latin Churches, was adjourned to Florence, where Plethon then lectured on the relation and differences of Plato and Aristotle, and fired Cosimo with his enthusiasm. 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 the customary paraphrase of Aristotle's famous declaration of sedition from the Academy (Nicomachean Ethics 1096a15), from 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.'
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