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168-470: Scriptures written by Pythagoras suggest that he developed a similar theory earlier than Plato, though Pythagoras's theory was narrower, proposing that the non-physical and timeless essences that compose the physical world are, in fact, numbers. The early Greek concept of form precedes attested philosophical usage, and is represented by a number of words which mainly relate to vision , sight, and appearance . Plato uses these aspects of sight and appearance from

336-563: A Sonchis of Sais ). According to the Christian theologian Clement of Alexandria ( c.  150  – c.  215  AD), "Pythagoras was a disciple of Sonchis, an Egyptian archprophet, as well as a Plato of Sechnuphis ." Some ancient writers claimed that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians. Other ancient writers, however, claimed that Pythagoras had learned these teachings from

504-569: A pseudepigraphal poem. Empedocles , who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals. The identity of the morning star and evening star was known to the Babylonians over a thousand years earlier. Sizeable Pythagorean communities existed in Magna Graecia, Phlius , and Thebes during

672-639: A Form." Ross also objects to Aristotle's criticism that Form Otherness accounts for the differences between Forms and purportedly leads to contradictory forms: the Not-tall, the Not-beautiful, etc. That particulars participate in a Form is for Aristotle much too vague to permit analysis. By one way in which he unpacks the concept, the Forms would cease to be of one essence due to any multiple participation. As Ross indicates, Plato didn't make that leap from "A

840-515: A Scythian priest of Apollo by the name of Abaris the Hyperborean : Abaris stayed with Pythagoras, and was compendiously taught physiology and theology; and instead of divining by the entrails of beasts, he revealed to him the art of prognosticating by numbers, conceiving this to be a method purer, more divine, and more kindred to the celestial numbers of the Gods. This shouldn't be confused with

1008-456: A blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form "triangle" that allows us to know the drawing on the chalkboard is a triangle, and the Form "triangle" is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, time only affects the observer and not

1176-547: A close friend of Plato and he is quoted in Plato's Republic . Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn , Plato's middle dialogues, including Meno , Phaedo , and The Republic , have

1344-478: A continuation of this goodness? Death is a place where better and wiser gods rule and where the most noble souls serve in their presence: "And therefore, so far as that is concerned, I not only do not grieve, but I have great hopes that there is something in store for the dead ... something better for the good than for the wicked." The soul attains virtue when it is purified from the body: "He who has got rid, as far as he can, of eyes and ears and, so to speak, of

1512-422: A deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word. Riedweg suggests that Pythagoras may have personally encouraged these legends, but Gregory states that there

1680-425: A distinct singular thing but caused plural representations of itself in particular objects. For example, in the dialogue Parmenides , Socrates states: "Nor, again, if a person were to show that all is one by partaking of one, and at the same time many by partaking of many, would that be very astonishing. But if he were to show me that the absolute one was many, or the absolute many one, I should be truly amazed." Matter

1848-462: A divine figure, sent by the gods to benefit humankind. Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time. For Pythagoreans, the highest reward a human could attain was for their soul to join in the life of the gods and thus escape the cycle of reincarnation. Two groups existed within early Pythagoreanism:

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2016-433: A five-year initiation period, during which they were required to remain silent. Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations. Iamblichus provides a list of 235 famous Pythagoreans, seventeen of whom are women. In later times, many prominent female philosophers contributed to

2184-479: A fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo". Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was supposedly once seen at both Metapontum and Croton at

2352-489: A golden wreath atop his head and to have worn trousers after the fashion of the Thracians . Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control ; he was always cheerful, but "abstained wholly from laughter, and from all such indulgences as jests and idle stories". Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when

2520-562: A group of objects, how is one to decide if it contains only instances of a single Form, or several mutually exclusive Forms? The theory is presented in the following dialogues: Pythagoras Pythagoras of Samos ( Ancient Greek : Πυθαγόρας ; c.  570  – c.  495  BC) was an ancient Ionian Greek philosopher , polymath , and the eponymous founder of Pythagoreanism . His political and religious teachings were well known in Magna Graecia and influenced

2688-459: A lady of Crete and the daughter of Pythenax and had several children with her. Porphyry writes that Pythagoras had two sons named Telauges and Arignote , and a daughter named Myia, who "took precedence among the maidens in Croton and, when a wife, among married women." Iamblichus mentions none of these children and instead only mentions a son named Mnesarchus after his grandfather. This son

2856-436: A lawgiver. The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything. According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad ) represented

3024-592: A little beauty in another – all the beauty in the world put together is the Form of Beauty. Plato himself was aware of the ambiguities and inconsistencies in his Theory of Forms, as is evident from the incisive criticism he makes of his own theory in the Parmenides . In Cratylus , Plato writes: But if the very nature of knowledge changes, at the time when the change occurs there will be no knowledge, and, according to this view, there will be no one to know and nothing to be known: but if that which knows and that which

3192-601: A major revival in the first century BC among Middle Platonists , coinciding with the rise of Neopythagoreanism . Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus , Johannes Kepler , and Isaac Newton . Pythagorean symbolism was also used throughout early modern European esotericism , and his teachings as portrayed in Ovid 's Metamorphoses would later influence

3360-462: A mischaracterization of Plato. Plato did not claim to know where the line between Form and non-Form is to be drawn. As Cornford points out, those things about which the young Socrates (and Plato) asserted "I have often been puzzled about these things" (in reference to Man, Fire and Water), appear as Forms in later works. However, others do not, such as Hair, Mud, Dirt. Of these, Socrates is made to assert, "it would be too absurd to suppose that they have

3528-537: A new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus. Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur. Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations. Diogenes Laërtius reports an account from Heraclides Ponticus that Pythagoras told people that he had lived four previous lives that he could remember in detail. The first of these lives

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3696-489: A person should always put the right sandal on before the left. The exact meanings of these sayings, however, are frequently obscure. Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings, but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them: New initiates were allegedly not permitted to meet Pythagoras until after they had completed

3864-405: A popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb , to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough . The Pythagorean theorem was known and used by

4032-640: A proclivity towards tyranny. Other accounts claim that Pythagoras left Samos because he was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens. He arrived in the Greek colony of Croton (today's Crotone , in Calabria ) in what was then Magna Graecia . All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment. He served as an advisor to

4200-413: A remembrance of the soul's past lives and Aristotle's arguments against this treatment of epistemology are compelling. For Plato, particulars somehow do not exist, and, on the face of it, "that which is non-existent cannot be known". See Metaphysics III 3–4. Nominalism (from Latin nomen , "name") says that ideal universals are mere names, human creations; the blueness shared by sky and blue jeans

4368-510: A result of Pherecydes's influence. Another story, which may be traced to the Neopythagorean philosopher Nicomachus , tells that, when Pherecydes was old and dying on the island of Delos , Pythagoras returned to care for him and pay his respects. Duris , the historian and tyrant of Samos, is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras's wisdom exceeded his own. On

4536-428: A secure basis for philosophy, science, and morality. Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and both were probably influenced by Orphism . The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans. Bertrand Russell , in his A History of Western Philosophy , contends that

4704-434: A significant readership throughout antiquity, and was commented on by a number of ancient philosophers, such as Harpocration of Argos , Porphyry , Iamblichus , Paterius, Plutarch of Athens , Syrianus and Proclus . The two most important commentaries on the dialogue that have come down to us from the ancient world are those by Olympiodorus of Alexandria and Damascius of Athens. The Phaedo has come to be considered

4872-562: A simplified version known today as " Pythagorean numerology ", involving a variant of an isopsephic technique known – among other names – as pythmenes ' roots ' or ' base numbers ' , by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word; these 'roots' or 'base numbers' could then be interpreted with other techniques, such as traditional Pythagorean attributions. This latter form of numerology flourished during

5040-447: A soul is: ... polluted, is impure at the time of her departure, and is the companion and servant of the body always and is in love with and bewitched by the body and by the desires and pleasures of the body, until she is led to believe that the truth only exists in a bodily form, which a man may touch and see, and drink and eat, and use for the purposes of his lusts, the soul, I mean, accustomed to hate and fear and avoid that which to

5208-479: A specific building that was still in use during his own time, appears to be motivated by Samian patriotic interest. Around 530 BC, when Pythagoras was about forty years old, he left Samos. His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos, Riedweg notes that this explanation closely aligns with Nicomachus's emphasis on Pythagoras's purported love of freedom, but that Pythagoras's enemies portrayed him as having

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5376-423: A strong "Pythagorean coloring", and his last few dialogues (particularly Philebus and Timaeus ) are extremely Pythagorean in character. According to R. M. Hare , Plato's Republic may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton. Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are

5544-534: A synthesis of everything Pythagoras had learned from Orpheus, from the Egyptian priests, from the Eleusinian Mysteries , and from other religious and philosophical traditions. Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent. Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros

5712-472: A vow of silence that they would not reveal these symbols to non-members. Those who did not obey the laws of the community were expelled and the remaining members would erect tombstones for them as though they had died. A number of "oral sayings" ( akoúsmata ) attributed to Pythagoras have survived, dealing with how members of the Pythagorean community should perform sacrifices, how they should honor

5880-413: A wise man" Simmias expresses confusion as to why they ought hasten to follow Socrates to death. Socrates then states "... he, who has the spirit of philosophy, will be willing to die; but he will not take his own life." Cebes raises his doubts as to why suicide is prohibited. He asks, "Why do you say ... that a man ought not to take his own life, but that the philosopher will be ready to follow one who

6048-539: Is a large one and continues to expand. Rather than quote Plato, Aristotle often summarized. Classical commentaries thus recommended Aristotle as an introduction to Plato, even when in disagreement; the Platonist Syrianus used Aristotelian critiques to further refine the Platonic position on forms in use in his school, a position handed down to his student Proclus . As a historian of prior thought, Aristotle

6216-560: Is a shared concept, communicated by our word "blueness". Blueness is held not to have any existence beyond that which it has in instances of blue things. This concept arose in the Middle Ages, as part of Scholasticism . Scholasticism was a highly multinational, polyglottal school of philosophy, and the nominalist argument may be more obvious if an example is given in more than one language. For instance, colour terms are strongly variable by language; some languages consider blue and green

6384-420: Is able to provide correct answers to his interrogator, it must be the case that his answers arose from recollections of knowledge gained during a previous life. Socrates presents his third argument for the immortality of the soul, the so-called Affinity Argument , where he shows that the soul most resembles that which is invisible and divine, and the body resembles that which is visible and mortal. From this, it

6552-525: Is another proof of the soul's immortality. Socrates' second argument, the Theory of Recollection , shows that it is possible to draw information out of a person who seems not to have any knowledge of a subject prior to his being questioned about it ( a priori knowledge). This person must have gained this knowledge in a prior life, and is now merely recalling it from memory. Since the person in Socrates' story

6720-461: Is concluded that while the body may be seen to exist after death in the form of a corpse, as the body is mortal and the soul is divine, the soul must outlast the body. As to be truly virtuous during life is the quality of a great man who will perpetually dwell as a soul in the underworld. However, regarding those who were not virtuous during life, and so favored the body and pleasures pertaining exclusively to it, Socrates also speaks. He says that such

6888-407: Is considered particular in itself. For Plato, forms, such as beauty, are more real than any objects that imitate them. Though the forms are timeless and unchanging, physical things are in a constant change of existence. Where forms are unqualified perfection, physical things are qualified and conditioned. These Forms are the essences of various objects: they are that without which a thing would not be

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7056-407: Is dying?" Socrates replies that while death is the ideal home of the soul, man, specifically the philosopher, should not commit suicide except when it becomes necessary. Man ought not to kill himself because he possesses no actual ownership of himself, as he is actually the property of the gods . He says, "I too believe that the gods are our guardians, and that we men are a chattel of theirs". While

7224-410: Is known exist ever, and the beautiful and the good and every other thing also exist, then I do not think that they can resemble a process of flux, as we were just now supposing. Plato believed that long before our bodies ever existed, our souls existed and inhabited heaven, where they became directly acquainted with the forms themselves. Real knowledge, to him, was knowledge of the forms. But knowledge of

7392-413: Is mentioned most often. Similar miracle stories were told about both Pythagoras and Pherecydes, including one in which the hero predicts a shipwreck, one in which he predicts the conquest of Messina , and one in which he drinks from a well and predicts an earthquake. Apollonius Paradoxographus , a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as

7560-478: Is no direct evidence of this. Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he

7728-497: Is not B" to "A is Not-B." Otherness would only apply to its own particulars and not to those of other Forms. For example, there is no Form Not-Greek, only particulars of Form Otherness that somehow suppress Form Greek. Regardless of whether Socrates meant the particulars of Otherness yield Not-Greek, Not-tall, Not-beautiful, etc., the particulars would operate specifically rather than generally, each somehow yielding only one exclusion. Plato had postulated that we know Forms through

7896-494: Is not at all clear how these two roles of the soul are related to each other. But we observe this casual oscillation nevertheless throughout the dialogue and indeed throughout the whole corpus. For instance, consider this passage from Republic I: Is there any function of the soul that you could not accomplish with anything else, such as taking care of something ( epimeleisthai ), ruling, and deliberating, and other such things? Could we correctly assign these things to anything besides

8064-468: Is not developed. Similarly, in the Republic , Plato relies on the concept of Forms as the basis of many of his arguments but feels no need to argue for the validity of the theory itself or to explain precisely what Forms are. Commentators have been left with the task of explaining what Forms are and how visible objects participate in them, and there has been no shortage of disagreement. Some scholars advance

8232-406: Is not the nearest approach to the knowledge of their several natures made by him who so orders his intellectual vision as to have the most exact conception of the essence of each thing he considers? The philosopher, if he loves true wisdom and not the passions and appetites of the body, accepts that he can come closest to true knowledge and wisdom in death, as he is no longer confused by the body and

8400-400: Is not upset facing death and assures them that they ought to express their concerns regarding the arguments. Simmias then presents his case that the soul resembles the harmony of the lyre . It may be, then, that as the soul resembles the harmony in its being invisible and divine, once the lyre has been destroyed, the harmony too vanishes, therefore when the body dies, the soul too vanishes. Once

8568-524: Is one of the best-known dialogues of Plato 's middle period, along with the Republic and the Symposium . The philosophical subject of the dialogue is the immortality of the soul. It is set in the last hours prior to the death of Socrates , and is Plato's fourth and last dialogue to detail the philosopher's final days, following Euthyphro , Apology , and Crito . One of the main themes in

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8736-452: Is one thing," (52a, emphasis added). Plato's conception of Forms actually differs from dialogue to dialogue, and in certain respects it is never fully explained, so many aspects of the theory are open to interpretation. Forms are first introduced in the Phaedo , but in that dialogue the concept is simply referred to as something the participants are already familiar with, and the theory itself

8904-399: Is that?" Plato was going a step further and asking what Form itself is. He supposed that the object was essentially or "really" the Form and that the phenomena were mere shadows mimicking the Form; that is, momentary portrayals of the Form under different circumstances. The problem of universals – how can one thing in general be many things in particular – was solved by presuming that Form was

9072-1059: Is the "transmigration of souls" or metempsychosis , which holds that every soul is immortal and, upon death, enters into a new body . He may have also devised the doctrine of musica universalis , which holds that the planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton . Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy , and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there. Pythagoras influenced Plato, whose dialogues , especially his Timaeus , exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art . His teachings underwent

9240-592: Is the ability to grasp the world of Forms with one's mind. A Form is aspatial (transcendent to space) and atemporal (transcendent to time). In the world of Plato, atemporal means that it does not exist within any time period, rather it provides the formal basis for time. It therefore formally grounds beginning, persisting and ending. It is neither eternal in the sense of existing forever, nor mortal, of limited duration. It exists transcendent to time altogether. Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like

9408-510: Is the one from Diogenes Laërtius 's Lives and Opinions of Eminent Philosophers . The two later biographies were written by the Neoplatonist philosophers Porphyry and Iamblichus and were partially intended as polemics against the rise of Christianity . The later sources are much lengthier than the earlier ones, and even more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus used material from

9576-777: The Protrepticus . Aristotle's disciples Dicaearchus , Aristoxenus , and Heraclides Ponticus (who all lived in the 3rd century BC) also wrote on the same subject. Most of the major sources on Pythagoras's life are from the Roman period , by which point, according to the German classicist Walter Burkert , "the history of Pythagoreanism was already   ... the laborious reconstruction of something lost and gone." Three ancient biographies of Pythagoras have survived from late antiquity, all of which are filled primarily with myths and legends. The earliest and most respectable of these

9744-467: The Babylonians and Indians centuries before Pythagoras, but he may have been the first to introduce it to the Greeks. Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof . Burkert rejects this suggestion as implausible, noting that Pythagoras was never credited with having proved any theorem in antiquity. Furthermore, the manner in which

9912-639: The Byzantine era , and was first attested among the Gnostics of the second century AD. By that time, isopsephy had developed into several different techniques that were used for a variety of purposes; including divination, doctrinal allegory, and medical prognosis and treatment. In the visits to various places in Greece— Delos , Sparta , Phlius , Crete , etc.—which are ascribed to him, he usually appears either in his religious or priestly guise, or else as

10080-492: The Celts and Iberians . Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers. Some identify Hermodamas of Samos as a possible tutor. Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer . Others credit Bias of Priene , Thales, or Anaximander (a pupil of Thales). Other traditions claim

10248-689: The Magi in Persia or even from Zoroaster himself. Diogenes Laërtius asserts that Pythagoras later visited Crete , where he went to the Cave of Ida with Epimenides . The Phoenicians are reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy. By the third century BC, Pythagoras was already reported to have studied under the Jews as well. Contradicting all these reports,

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10416-427: The Phaedo is the idea that the soul is immortal . In the dialogue, Socrates discusses the nature of the afterlife on his last day before being executed by drinking hemlock . Socrates has been imprisoned and sentenced to death by an Athenian jury for not believing in the gods of the state (though some scholars think it was more for his support of " philosopher kings " as opposed to democracy) and for corrupting

10584-626: The Phaedrus the Forms are in a " place beyond heaven " ( hyperouranios topos ) ( Phdr. 247c ff); and in the Republic the sensible world is contrasted with the intelligible realm ( noēton topon ) in the famous Allegory of the Cave . It would be a mistake to take Plato's imagery as positing the intelligible world as a literal physical space apart from this one. Plato emphasizes that the Forms are not beings that extend in space (or time), but subsist apart from any physical space whatsoever. Thus we read in

10752-601: The Symposium of the Form of Beauty: "It is not anywhere in another thing, as in an animal, or in earth, or in heaven, or in anything else, but itself by itself with itself," (211b). And in the Timaeus Plato writes: "Since these things are so, we must agree that that which keeps its own form unchangingly, which has not been brought into being and is not destroyed, which neither receives into itself anything else from anywhere else, nor itself enters into anything anywhere ,

10920-466: The mathematikoi ("learners") and the akousmatikoi ("listeners"). The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings; whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific. Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed

11088-617: The Babylonians employed Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources. Pythagoras's biographers state that he also was the first to identify the five regular solids and that he was the first to discover the Theory of Proportions . According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard

11256-444: The Egyptian priests at Diospolis (Thebes), and that he was the only foreigner ever to be granted the privilege of taking part in their worship. The Middle Platonist biographer Plutarch ( c.  46  – c.  120  AD) writes in his treatise On Isis and Osiris that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile Solon received lectures from

11424-527: The Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place. Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC. The building was apparently set on fire, and many of the assembled members perished; only the younger and more active members managed to escape. Sources disagree regarding whether Pythagoras

11592-466: The affinity argument should be called 'the kinship argument' instead because the argument is based on learning about the soul's nature from discussing its kin (i.e., the divine). The scene is set in Phlius where Echecrates who, meeting Phaedo, asks for news about the last days of Socrates. Phaedo explains why a delay occurred between his trial and his death, and describes the scene in a prison at Athens on

11760-527: The age of 40, which would give a date of birth around 570 BC. Pythagoras's name led him to be associated with Pythian Apollo ( Pūthíā ); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke [ ἀγορεύω , agoreúō ] the truth no less than did the Pythian [ πυθικός puthikós ]". During Pythagoras's formative years, Samos was a thriving cultural hub known for its feats of advanced architectural engineering, including

11928-467: The bodily eye is dark and invisible, but is the object of mind and can be attained by philosophy; do you suppose that such a soul will depart pure and unalloyed? Persons of such a constitution will be dragged back into corporeal life, according to Socrates. These persons will even be punished while in Hades. Their punishment will be of their own doing, as they will be unable to enjoy the singular existence of

12096-485: The body ... dispersing and vanishing away into nothingness in her flight." In order to alleviate Cebes's worry that the soul might perish at death, Socrates introduces his first argument for the immortality of the soul. This argument is often called the Cyclical Argument . It supposes that the soul must be immortal since the living come from the dead. Socrates says: "Now if it be true that the living come from

12264-407: The body is an impediment to the attainment of truth. Of the senses' failings, Socrates says to Simmias in the Phaedo : Did you ever reach them (truths) with any bodily sense? – and I speak not of these alone, but of absolute greatness, and health, and strength, and, in short, of the reality or true nature of everything. Is the truth of them ever perceived through the bodily organs? Or rather,

12432-431: The boys' "raging willfulness" was quelled. The Pythagoreans also placed particular emphasis on the importance of physical exercise ; therapeutic dancing , daily morning walks along scenic routes , and athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised. Pythagorean teachings were known as "symbols" ( symbola ) and members took

12600-566: The building of the Tunnel of Eupalinos , and for its riotous festival culture. It was a major center of trade in the Aegean where traders brought goods from the Near East . According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions. Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy . He

12768-415: The centuries until the beginning of Western philosophy , when they became equivocal, acquiring additional specialized philosophic meanings. Plato used the terms eidos and idea ( ἰδέα ) interchangeably. The pre-Socratic philosophers , starting with Thales , noted that appearances change, and began to ask what the thing that changes "really" is. The answer was substance , which stands under

12936-409: The changes and is the actually existing thing being seen. The status of appearances now came into question. What is the form really and how is that related to substance? The Forms are expounded upon in Plato's dialogues and general speech, in that every object or quality in reality—dogs, human beings, mountains, colors, courage, love, and goodness—has a form. Form answers the question, "What

13104-463: The city of Metapontum , where they took shelter in the temple of the Muses and died there of starvation after forty days without food. Another tale recorded by Porphyry claims that, as Pythagoras's enemies were burning the house, his devoted students laid down on the ground to make a path for him to escape by walking over their bodies across the flames like a bridge. Pythagoras managed to escape, but

13272-452: The company of," as Socrates says, "... men departed, better than those whom I leave behind." For he will dwell amongst those who were true philosophers, like himself. The Phaedo presents a real challenge to commentators through the way that Plato oscillates between different conceptions of the soul. In the cyclical and Form-of-life arguments, for instance, the soul is presented as something connected with life, where, in particular in

13440-418: The dead are generated from the living, through life, and that the living are generated from the dead, through death. The souls of the dead must exist in some place for them to be able to return to life. Socrates further emphasizes the cyclical argument by pointing out that if opposites did not regenerate one another, all living organisms on Earth would eventually die off, never to return to life. Cebes realizes

13608-435: The dead, then our souls must exist in the other world, for if not, how could they have been born again?". He goes on to show, using examples of relationships, such as asleep-awake and hot-cold, that things that have opposites come to be from their opposite. One falls asleep after having been awake. And after being asleep, he awakens. Things that are hot came from being cold and vice versa. Socrates then gets Cebes to conclude that

13776-479: The death of the body, and the afterlife will be full of goodness. Simmias confesses that he does not wish to disturb Socrates during his final hours by unsettling his belief in the immortality of the soul, and those present are reluctant to voice their skepticism . Socrates grows aware of their doubt and assures his interlocutors that he does indeed believe in the soul's immortality, regardless of whether or not he has succeeded in showing it as yet. For this reason, he

13944-413: The development of Neopythagoreanism . Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans and the meat of non-sacrificial animals such as fish and poultry. Both of these assumptions, however, have been contradicted. Pythagorean dietary restrictions may have been motivated by belief in

14112-452: The dialogue from that day to Echecrates , a Pythagorean philosopher . Socrates offers four arguments for the soul's immortality: Some scholars have debated the accuracy of these names: for instance, David Ebrey has argued that the recollection argument should be titled 'the recollecting argument' because 'recollection' names the end-result of a process, whereas Plato is discussing the process of recollecting itself; he also has argued that

14280-449: The doctrine of metempsychosis . Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet. Eudoxus of Cnidus , a student of Archytas, writes, "Pythagoras was distinguished by such purity and so avoided killing and killers that he not only abstained from animal foods, but even kept his distance from cooks and hunters." Other authorities contradict this statement. According to Aristoxenus , Pythagoras allowed

14448-420: The earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras. The Athenian rhetorician Isocrates ( c.  436  – c.  338  BC) was the first to describe Pythagoras as having visited Egypt. Aristotle ( c.  384  – c.  322  BC) wrote a treatise On the Pythagoreans , which no longer exists. Some of it may be preserved in

14616-697: The early Greek concept in his dialogues to explain his Forms, including the Form of the Good . The theory itself is contested by characters within Plato's dialogues, and it remains a general point of controversy in philosophy. Nonetheless, it is considered to be a classical solution to the problem of universals . The original meaning of the term εἶδος ( eîdos ), "visible form", and related terms μορφή ( morphḗ ), "shape", and φαινόμενα ( phainómena ), "appearances", from φαίνω ( phaínō ), "shine", Indo-European *bʰeh₂- or *bhā- remained stable over

14784-399: The early fourth century BC. Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia. According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year. Archytas was also a renowned mathematician and musician. He was

14952-531: The elites in Croton and gave them frequent advice. Later biographers tell fantastical stories of the effects of his eloquent speeches in leading the people of Croton to abandon their luxurious and corrupt way of life and devote themselves to the purer system which he came to introduce. Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love" and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself". According to Porphyry, Pythagoras married Theano ,

15120-533: The entire series great, is missing. Moreover, any Form is not unitary but is composed of infinite parts, none of which is the proper Form. The young Socrates did not give up the Theory of Forms over the Third Man but took another tack, that the particulars do not exist as such. Whatever they are, they "mime" the Forms, appearing to be particulars. This is a clear dip into representationalism , that we cannot observe

15288-418: The exact details of Pythagoras's teachings are uncertain, it is possible to reconstruct a general outline of his main ideas. Aristotle writes at length about the teachings of the Pythagoreans, but without mentioning Pythagoras directly. One of Pythagoras's main doctrines appears to have been metempsychosis , the belief that all souls are immortal and that, after death, a soul is transferred into

15456-476: The exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans . One Pythagorean maxim was " koinà tà phílōn " ("All things in common among friends"). Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as

15624-640: The famous third man argument of Parmenides, which proves that forms cannot independently exist and be participated. If universal and particulars – say man or greatness – all exist and are the same then the Form is not one but is multiple. If they are only like each other then they contain a form that is the same and others that are different. Thus if we presume that the Form and a particular are alike then there must be another, or third Form, man or greatness by possession of which they are alike. An infinite regression would then result; that is, an endless series of third men. The ultimate participant, greatness, rendering

15792-478: The fields of music , astronomy , and medicine . Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides" —that is, a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . According to

15960-496: The final argument, this connection is spelled out concretely by means of the soul's conceptual connection with life. This connection is further developed in the Phaedrus and Laws where the definition of soul is given as self-motion. Rocks, for instance, do not move unless something else moves them; inanimate, unliving objects are always said to behave this way. In contrast, living things are capable of moving themselves. Plato uses this observation to illustrate his famous doctrine that

16128-501: The final day, naming those present. He tells how he had visited Socrates early in the morning with the others. Socrates's wife Xanthippe was there, but was very distressed and Socrates asked that she be taken away. Socrates relates how, bidden by a recurring dream to "make and cultivate music", he wrote a hymn and then began writing poetry based on Aesop's Fables . Socrates tells Cebes to "bid him (Socrates's friend Evenus) farewell from me; say that I would have him come after me if he be

16296-465: The first to teach that the Earth was spherical , the first to divide the globe into five climatic zones , and the first to identify the morning star and the evening star as the same celestial object (now known as Venus ). Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from

16464-424: The forms cannot be gained through sensory experience because the forms are not in the physical world. Therefore, our real knowledge of the forms must be the memory of our initial acquaintance with the forms in heaven. Therefore, what we seem to learn is in fact just remembering. No one has ever seen a perfect circle, nor a perfectly straight line, yet everyone knows what a circle and a straight line are. Plato uses

16632-522: The globe into five climatic zones . Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy . The teaching most securely identified with Pythagoras

16800-461: The gods, how they should "move from here", and how they should be buried. Many of these sayings emphasize the importance of ritual purity and avoiding defilement. For instance, a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments. Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs and teach that

16968-490: The grounds of all these references connecting Pythagoras with Pherecydes, Riedweg concludes that there may well be some historical foundation to the tradition that Pherecydes was Pythagoras's teacher. Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis. Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras might have met Thales of Miletus , who would have been around fifty-four years older than him. Thales

17136-400: The harmony is dissipated, we may infer that so too will the soul dissipate once the body has been broken, through death. Socrates pauses, and asks Cebes to voice his objection as well. He says, "I am ready to admit that the existence of the soul before entering into the bodily form has been ... proven; but the existence of the soul after death is in my judgment unproven." While admitting that

17304-420: The historian Herodotus of Halicarnassus ( c.  484  – c.  420  BC), who describes him as one of the greatest Greek teachers and states that Pythagoras taught his followers how to attain immortality . The accuracy of the works of Herodotus is controversial. The writings attributed to the Pythagorean philosopher Philolaus of Croton ( c.  470  – c.  385  BC) are

17472-423: The immortality of the soul, Phaedo pauses his narration. Phaedo remarks to Echecrates that, because of this objection, those present had their "faith shaken," and that there was introduced "a confusion and uncertainty". Socrates too pauses following this objection and then warns against misology , the hatred of argument. Socrates then proceeds to give his final proof of the immortality of the soul by showing that

17640-411: The influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought." A revival of Pythagorean teachings occurred in the first century BC when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed

17808-425: The kind of thing it is. For example, there are countless tables in the world but the Form of tableness is at the core; it is the essence of all of them. Plato's Socrates held that the world of Forms is transcendent to our own world (the world of substances) and also is the essential basis of reality. Super-ordinate to matter, Forms are the most pure of all things. Furthermore, he believed that true knowledge/intelligence

17976-451: The latter term is used of substance. The figures that the artificer places in the gold are not substance, but gold is. Aristotle stated that, for Plato, all things studied by the sciences have Form and asserted that Plato considered only substance to have Form. Uncharitably, this leads him to something like a contradiction: Forms existing as the objects of science, but not-existing as substance. Scottish philosopher W.D. Ross objects to this as

18144-439: The lost writings of Aristotle's disciples (Dicaearchus, Aristoxenus, and Heraclides) and material taken from these sources is generally considered to be the most reliable. There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account. Herodotus , Isocrates , and other early writers agree that Pythagoras

18312-480: The modern vegetarian movement. No authentic writings of Pythagoras have survived, and almost nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical . The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon ( c.  570  – c.  478  BC), who had been one of his contemporaries. In

18480-711: The mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries . The Neoplatonists wrote of a "sacred discourse" Pythagoras had written on the gods in the Doric Greek dialect, which they believed had been dictated to Pythagoras by the Orphic priest Aglaophamus upon his initiation to the orphic Mysteries at Leibethra . Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship. Iamblichus describes Pythagoreanism as

18648-401: The neighboring colony of Sybaris in 510 BC. After the victory, some prominent citizens of Croton proposed a democratic constitution , which the Pythagoreans rejected. The supporters of democracy, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. Followers of Cylon and Ninon attacked

18816-451: The novelist Antonius Diogenes , writing in the second century BC, reports that Pythagoras discovered all his doctrines himself by interpreting dreams . The third-century AD Sophist Philostratus claims that, in addition to the Egyptians, Pythagoras also studied under sages or gymnosophists in India . Iamblichus expands this list even further by claiming that Pythagoras also studied with

18984-499: The number philosophy attributed to him was really an innovation by Philolaus. According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics. Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic , but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics. Both Plato and Isocrates state that, above all else, Pythagoras

19152-529: The objects as they are in themselves but only their representations. That view has the weakness that if only the mimes can be observed then the real Forms cannot be known at all and the observer can have no idea of what the representations are supposed to represent or that they are representations. Socrates' later answer would be that men already know the Forms because they were in the world of Forms before birth. The mimes only recall these Forms to memory. The topic of Aristotle's criticism of Plato's Theory of Forms

19320-415: The origin of all things and the number two (the dyad ) represented matter. The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo . The number four signified the four seasons and the four elements . The number seven was also sacred because it

19488-456: The perfect circle is discovered, not invented. Plato often invokes, particularly in his dialogues Phaedo , Republic and Phaedrus , poetic language to illustrate the mode in which the Forms are said to exist. Near the end of the Phaedo , for example, Plato describes the world of Forms as a pristine region of the physical universe located above the surface of the Earth ( Phd. 109a–111c). In

19656-433: The perfect ones were not real, how could they direct the manufacturer? One difficulty lies in the conceptualization of the "participation" of an object in a form (or Form). The young Socrates conceives of his solution to the problem of the universals in another metaphor: Nay, but the idea may be like the day which is one and the same in many places at once, and yet continuous with itself; in this way each idea may be one and

19824-481: The permanent reality behind superficial appearances. Early Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies. The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type ( εἶδος ), which was mathematically calculated. When dimensions changed, architects sought to relay permanence through mathematics. Maurice Bowra believes that these ideas influenced

19992-404: The philosopher seeks always to rid himself of the body, and to focus solely on things concerning the soul, to commit suicide is prohibited as man is not sole possessor of his body. For, as stated in the Phaedo : "the philosopher more than other men frees the soul from association with the body as much as possible". Body and soul are separate, then. The philosopher frees himself from the body because

20160-471: The philosophies of Plato , Aristotle , and, through them, the West in general. Knowledge of his life is clouded by legend; modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. In antiquity, Pythagoras

20328-507: The poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend. Alcmaeon of Croton ( fl.   c.  450  BC), a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The poet Heraclitus of Ephesus (fl.   c.  500  BC), who

20496-401: The point) have a location. They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word). A Form is an objective "blueprint" of perfection. The Forms are perfect and unchanging representations of objects and qualities. For example, the Form of beauty or the Form of a triangle. For the form of a triangle say there is a triangle drawn on

20664-549: The priestess Aristoclea ( Aristokleia ). Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries , or the Delphic oracle . Porphyry repeats an account from Antiphon , who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle". Here, Samians debated matters of public concern. Supposedly,

20832-692: The proportion, not of the elements (materials), but of the interrelation of parts with one another and with the whole. In the Greek architectural orders, every element was calculated and constructed by mathematical relations. Rhys Carpenter states that the ratio 2:1 was "the generative ratio of the Doric order , and in Hellenistic times an ordinary Doric colonnade, beats out a rhythm of notes." Phaedo Phædo or Phaedo ( / ˈ f iː d oʊ / ; Greek : Φαίδων , Phaidōn [pʰaídɔːn] ), also known to ancient readers as On The Soul ,

21000-440: The relationship between the Cyclical Argument and Socrates' Theory of Recollection . He interrupts Socrates to point this out, saying: ... your favorite doctrine, Socrates, that our learning is simply recollection, if true, also necessarily implies a previous time in which we have learned that which we now recollect. But this would be impossible unless our soul had been somewhere before existing in this form of man; here then

21168-666: The result of confusion with a different man named Pythagoras, who was an athletics trainer. Diogenes Laërtius records Milo's wife's name as Myia. Iamblichus mentions Theano as the wife of Brontinus of Croton. Diogenes Laërtius states that the same Theano was Pythagoras's pupil and that Pythagoras's wife Theano was her daughter. Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime and quotes several opinions attributed to her. These writings are now known to be pseudepigraphical . Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over

21336-731: The rise of a "new" Pythagoreanism in Alexandria . At around the same time, Neopythagoreanism became prominent. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy and probably understood the soul as a "kind of mathematical harmony". The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory. Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines. Greek sculpture sought to represent

21504-780: The same colour, others have monolexemic terms for several shades of blue, which are considered different; other languages, like the Mandarin qing denote both blue and black. The German word "Stift" means a pen or a pencil, and also anything of the same shape. The English "pencil" originally meant "small paintbrush"; the term later included the silver rod used for silverpoint . The German " Blei stift" and " Silber stift" can both be called "Stift", but this term also includes felt-tip pens, which are clearly not pencils. The shifting and overlapping nature of these concepts makes it easy to imagine them as mere names, with meanings not rigidly defined, but specific enough to be useful for communication. Given

21672-568: The same in all at the same time. But exactly how is a Form like the day in being everywhere at once? The solution calls for a distinct form, in which the particular instances, which are not identical to the form, participate; i.e., the form is shared out somehow like the day to many places. The concept of "participate", represented in Greek by more than one word, is as obscure in Greek as it is in English. Plato hypothesized that distinctness meant existence as an independent being, thus opening himself to

21840-425: The same time . When Pythagoras crossed the river Kosas (the modern-day Basento ), "several witnesses" reported that they heard it greet him by name. In Roman times, a legend claimed that Pythagoras was the son of Apollo. According to Muslim tradition , Pythagoras was said to have been initiated by Hermes (Egyptian Thoth ). Pythagoras was said to have dressed all in white. He is also said to have borne

22008-451: The school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach. Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends. Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos, but cautions that Antiphon's account, which makes reference to

22176-451: The senses. In life, the rational and intelligent functions of the soul are restricted by bodily senses of pleasure, pain, sight, and sound. Death, however, is a rite of purification from the "infection" of the body. As the philosopher prepares for death his entire life, he should greet it amicably and not be discouraged upon its arrival, for since the universe the gods created for us in life is essentially "good", why would death be anything but

22344-490: The soul in death because of their constant craving for the body. These souls are finally "imprisoned in another body". Socrates concludes that the soul of the virtuous man is immortal, and the course of its passing into the underworld is determined by the way he lived his life. The philosopher, and indeed any man similarly virtuous, in neither fearing death, nor cherishing corporeal life as something idyllic, but by loving truth and wisdom, his soul will be eternally unperturbed after

22512-444: The soul is a self-mover: life is self-motion, and the soul brings life to a body by moving it. Meanwhile, in the recollection and affinity arguments, the connection with life is not explicated or used at all. These two arguments present the soul as a knower (i.e., a mind). This is most clear in the affinity argument, where the soul is said to be immortal in virtue of its affinity with the Forms that we observe in acts of cognition. It

22680-565: The soul is immortal as it is the cause of life. He begins by showing that "if there is anything beautiful other than absolute beauty it is beautiful only insofar as it partakes of absolute beauty". Consequently, as absolute beauty is a Form, and so is Life, then anything which has the property of being animated with Life, participates in the Form of Life. As an example he says, "will not the number three endure annihilation or anything sooner than be converted into an even number, while remaining three?". Forms, then, will never become their opposite. As

22848-439: The soul is that which renders the body living, and that the opposite of life is death, it so follows that, "... the soul will never admit the opposite of what she always brings." That which does not admit death is said to be immortal. Socrates thus concludes, "Then, Cebes, beyond question, the soul is immortal and imperishable, and our souls will truly exist in another world. "Once dead, man's soul will go to Hades and be in

23016-574: The soul is the better part of a man, and the body the weaker, Cebes is not ready to infer that because the body may be perceived as existing after death, the soul must therefore continue to exist as well. Cebes gives the example of a weaver. When the weaver's cloak wears out, he makes a new one. However, when he dies, his more freshly woven cloaks continue to exist. Cebes continues that though the soul may outlast certain bodies, and so continue to exist after certain deaths, it may eventually grow so weak as to dissolve entirely at some point. He then concludes that

23184-487: The soul's immortality has yet to be shown and that we may still doubt the soul's existence after death. For, it may be that the next death is the one under which the soul ultimately collapses and exists no more. Cebes would then, "... rather not rely on the argument from superior strength to prove the continued existence of the soul after death." Seeing that the Affinity Argument has possibly failed to show

23352-466: The soul, and say that they are characteristic ( idia ) of it? No, to nothing else. What about living? Will we deny that this is a function of the soul? That absolutely is. Throughout the 20th century, scholars universally recognized this as a flaw in Plato's theory of the soul, with this trend continuing and then ultimately being rejected in the 21st century. Here are some examples of what scholars have said about this puzzle: Plato's Phaedo had

23520-493: The sound of their hammers clanging against the anvils. Thinking that the sounds of the hammers were beautiful and harmonious, except for one, he rushed into the blacksmith shop and began testing the hammers. He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical. In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been

23688-405: The story that following the discussion, he and the others were there to witness the death of Socrates. The Phaedo was first translated into Latin from Greek by Apuleius but no copy survived, so Henry Aristippus produced a new translation in 1160. The dialogue is told from the perspective of one of Socrates's students, Phaedo of Elis , who was present at Socrates's death bed. Phaedo relates

23856-439: The theory of Pythagoras and his students, who believed that "all things are numbers". During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture. Greek sculptors and architects attempted to find the mathematical relation ( canon ) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor Polykleitos wrote in his Canon that beauty consists in

24024-421: The tool-maker's blueprint as evidence that Forms are real: ... when a man has discovered the instrument which is naturally adapted to each work, he must express this natural form, and not others which he fancies, in the material .... Perceived circles or lines are not exactly circular or straight, and true circles and lines could never be detected since by definition they are sets of infinitely small points. But if

24192-477: The tradition linking Pythagoras to the tetractys is probably genuine. Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton . In his landmark study Lore and Science in Ancient Pythagoreanism , Walter Burkert argues that Pythagoras was a charismatic political and religious teacher, but that

24360-446: The triangle. It follows that the same attributes would exist for the Form of beauty and for all Forms. Plato explains how we are always many steps away from the idea or Form. The idea of a perfect circle can have us defining, speaking, writing, and drawing about particular circles that are always steps away from the actual being. The perfect circle, partly represented by a curved line, and a precise definition, cannot be drawn. The idea of

24528-421: The two approaches were compatible. The study of mathematics and music may have been connected to the worship of Apollo. The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body. One anecdote of Pythagoras reports that when he encountered some drunken youths trying to break into the home of a virtuous woman, he sang a solemn tune with long spondees and

24696-426: The use of all kinds of animal food except the flesh of oxen used for ploughing , and rams . According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat. Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In

24864-411: The view that Forms are paradigms, perfect examples on which the imperfect world is modeled. Others interpret Forms as universals, so that the Form of Beauty, for example, is that quality that all beautiful things share. Yet others interpret Forms as "stuffs," the conglomeration of all instances of a quality in the visible world. Under this interpretation, we could say there is a little beauty in one person,

25032-455: The whole body, these being in his opinion distracting elements when they associate with the soul hinder her from acquiring truth and knowledge – who, if not he, is likely to attain to the knowledge of true being?" Cebes voices his fear of death to Socrates: "... they fear that when she [the soul] has left the body her place may be nowhere, and that on the very day of death she may perish and come to an end immediately on her release from

25200-476: The youth of the city. By engaging in dialectic with a group of Socrates's friends, including the two Thebans , Cebes , and Simmias , Socrates explores various arguments for the soul's immortality in order to show that there is an afterlife in which the soul will dwell following death and, for couples and good people, be more at one with "every loving thing" and be more powerful than the Greek gods . Phaedo tells

25368-562: Was a contemporary of the philosophers Anaximander , Anaximenes , and the historian Hecataeus , all of whom lived in Miletus , across the sea from Samos. Pythagoras is traditionally thought to have received most of his education in the Near East. Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures. Like many other important Greek thinkers, Pythagoras

25536-466: Was a native of Samos , descending from a geomoroi family. Apollonius of Tyana , gives her name as Pythaïs. Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful, wise, and beneficial to humankind. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates , at

25704-544: Was a philosopher, scientist, mathematician, and engineer, also known for a special case of the inscribed angle theorem . Pythagoras's birthplace, the island of Samos , is situated in the Northeast Aegean Sea not far from Miletus . Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea . Porphyry agrees with this assertion but calls

25872-557: Was as Aethalides the son of Hermes , who granted him the ability to remember all his past incarnations. Next, he was incarnated as Euphorbus , a minor hero from the Trojan War briefly mentioned in the Iliad . He then became the philosopher Hermotimus , who recognized the shield of Euphorbus in the temple of Apollo. His final incarnation was as Pyrrhus, a fisherman from Delos . One of his past lives, as reported by Dicaearchus ,

26040-505: Was as a beautiful courtesan. Another belief attributed to Pythagoras was that of the " harmony of the spheres ", which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony. According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together. In his philosophical dialogue Protrepticus , Aristotle has his literary double say: When Pythagoras

26208-492: Was asked [why humans exist], he said, "to observe the heavens", and he used to claim that he himself was an observer of nature, and it was for the sake of this that he had passed over into life. Pythagoras was said to have practiced divination and prophecy . The earliest mentions of divination by isopsephy in Greek literature associate it with Pythagoras; he was viewed as the founder of this practice. According to his biographer, Iamblichus, he taught his method of divination to

26376-667: Was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, mocked Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery." The Greek poets Ion of Chios ( c.  480  – c.  421  BC) and Empedocles of Acragas ( c.  493  – c.  432  BC) both express admiration for Pythagoras in their poems. The first concise description of Pythagoras comes from

26544-427: Was credited with devising the tetractys , the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his Life of Pythagoras , states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it. Andrew Gregory concludes that

26712-470: Was credited with many mathematical and scientific discoveries, including the Pythagorean theorem , Pythagorean tuning , the five regular solids , the Theory of Proportions , the sphericity of the Earth , and the identity of the morning and evening stars as the planet Venus . It was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide

26880-457: Was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives. Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem , as well as discoveries in

27048-420: Was invaluable, however this was secondary to his own dialectic and in some cases he treats purported implications as if Plato had actually mentioned them, or even defended them. In examining Aristotle's criticism of The Forms, it is helpful to understand Aristotle's own hylomorphic forms , by which he intends to salvage much of Plato's theory. Plato distinguished between real and non-real "existing things", where

27216-463: Was known as the founder of a new way of life. The organization Pythagoras founded at Croton was called a "school", but, in many ways, resembled a monastery . The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other to

27384-470: Was present when the attack occurred and, if he was, whether or not he managed to escape. In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes. According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape, leading a small group of followers to the nearby city of Locris , where they pleaded for sanctuary, but were denied. They reached

27552-445: Was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it. Suda writes that Pythagoras had 4 children (Telauges, Mnesarchus, Myia and Arignote). The wrestler Milo of Croton was said to have been a close associate of Pythagoras and was credited with having saved the philosopher's life when a roof was about to collapse. This association may have been

27720-654: Was said to have studied in Egypt . By the time of Isocrates in the fourth century BC, Pythagoras's reputed studies in Egypt were already taken as fact. The writer Antiphon , who may have lived during the Hellenistic Era, claimed in his lost work On Men of Outstanding Merit , used as a source by Porphyry, that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself, that he studied with

27888-496: Was so despondent at the deaths of his beloved students that he committed suicide. A different legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape, but that he came to a fava bean field and refused to run through it, since doing so would violate his teachings, so he stopped instead and was killed. This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself. Although

28056-455: Was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine , that even numbers were feminine , and that the number five represented marriage, because it was the sum of two and three. Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras

28224-405: Was the son of Mnesarchus, and that he was born on the Greek island of Samos in the eastern Aegean . According to these biographers, Pythagoras's father was not born on the island, although he got naturalized there, but according to Iamblichus he was a native of the island. He is said to have been a gem-engraver or a wealthy merchant but his ancestry is disputed and unclear. His mother

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