Aristotle was a philosopher during the Classical period in Ancient Greece, the founder of the Lyceum and the Peripatetic school of philosophy and Aristotelian tradition. Along with his teacher Plato, he is considered the "Father of Western Philosophy", his writings cover many subjects – including physics, zoology, logic, aesthetics, theatre, rhetoric, linguistics, economics and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him, it was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry; as a result, his philosophy has exerted a unique influence on every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in the city of Stagira in Northern Greece, his father, died when Aristotle was a child, he was brought up by a guardian. At seventeen or eighteen years of age, he joined Plato's Academy in Athens and remained there until the age of thirty-seven.
Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, tutored Alexander the Great beginning in 343 BC. He established a library in the Lyceum which helped him to produce many of his hundreds of books on papyrus scrolls. Though Aristotle wrote many elegant treatises and dialogues for publication, only around a third of his original output has survived, none of it intended for publication; the fact that Aristotle was a pupil of Plato contributed to his former views of Platonism, following Plato's death, Aristotle developed an increased interest in natural sciences and adopted the position of immanent realism. Aristotle's views on physical science profoundly shaped medieval scholarship, their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, were not replaced systematically until the Enlightenment and theories such as classical mechanics. Some of Aristotle's zoological observations found in his biology, such as on the hectocotyl arm of the octopus, were disbelieved until the 19th century.
His works contain the earliest known formal study of logic, studied by medieval scholars such as Peter Abelard and John Buridan. Aristotle's influence on logic continued well into the 19th century He influenced Islamic thought during the Middle Ages, as well as Christian theology the Neoplatonism of the Early Church and the scholastic tradition of the Catholic Church. Aristotle was revered among medieval Muslim scholars as "The First Teacher" and among medieval Christians like Thomas Aquinas as "The Philosopher", his ethics, though always influential, gained renewed interest with the modern advent of virtue ethics, such as in the thinking of Alasdair MacIntyre and Philippa Foot. In general, the details of Aristotle's life are not well-established; the biographies written in ancient times are speculative and historians only agree on a few salient points. Aristotle, whose name means "the best purpose" in Ancient Greek, was born in 384 BC in Stagira, about 55 km east of modern-day Thessaloniki.
His father Nicomachus was the personal physician to King Amyntas of Macedon. Both of Aristotle's parents died when he was about thirteen, Proxenus of Atarneus became his guardian. Although little information about Aristotle's childhood has survived, he spent some time within the Macedonian palace, making his first connections with the Macedonian monarchy. At the age of seventeen or eighteen, Aristotle moved to Athens to continue his education at Plato's Academy, he remained there for nearly twenty years before leaving Athens in 348/47 BC. The traditional story about his departure records that he was disappointed with the Academy's direction after control passed to Plato's nephew Speusippus, although it is possible that he feared the anti-Macedonian sentiments in Athens at that time and left before Plato died. Aristotle accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor. After the death of Hermias, Aristotle travelled with his pupil Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island and its sheltered lagoon.
While in Lesbos, Aristotle married Hermias's adoptive daughter or niece. She bore him a daughter, whom they named Pythias. In 343 BC, Aristotle was invited by Philip II of Macedon to become the tutor to his son Alexander. Aristotle was appointed as the head of the royal academy of Macedon. During Aristotle's time in the Macedonian court, he gave lessons not only to Alexander, but to two other future kings: Ptolemy and Cassander. Aristotle encouraged Alexander toward eastern conquest and Aristotle's own attitude towards Persia was unabashedly ethnocentric. In one famous example, he counsels Alexander to be "a leader to the Greeks and a despot to the barbarians, to look after the former as after friends and relatives, to deal with the latter as with beasts or plants". By 335 BC, Aristotle had returned to Athens. Aristotle conducted courses at the school for the next twelve years. While in Athens, his wife Pythias died and Aristotle became involved with Herpyllis of Stagira, who bore him a son whom he named after his father, Nicomachus.
According to the Suda, he had an erômenos, Palaephatus of Abydus. This period in Athens, between 335 and 323 BC, is when Aristotle is believed to have composed many of his works, he wrote many dialogues. Those works that have survived are in treatise form and were not
Eudoxus of Cnidus
Eudoxus of Cnidus was an ancient Greek astronomer, mathematician and student of Archytas and Plato. All of his works are lost, though some fragments are preserved in Hipparchus' commentary on Aratus's poem on astronomy. Sphaerics by Theodosius of Bithynia may be based on a work by Eudoxus, his name Eudoxus means "honored" or "of good repute". It is analogous to the Latin name Benedictus. Eudoxus's father Aeschines of Cnidus loved to watch stars at night. Eudoxus first travelled to Tarentum to study from whom he learned mathematics. While in Italy, Eudoxus visited Sicily. Around 387 BC, at the age of 23, he traveled with the physician Theomedon—who some believed was his lover—to Athens to study with the followers of Socrates, he attended lectures of Plato and other philosophers for several months, but due to a disagreement they had a falling-out. Eudoxus could only afford an apartment at the Piraeus. To attend Plato's lectures, he walked the 7 miles in each direction each day. Due to his poverty, his friends raised funds sufficient to send him to Heliopolis, Egypt, to pursue his study of astronomy and mathematics.
He lived there for 16 months. From Egypt, he traveled north to Cyzicus, located on the south shore of the Sea of Marmara, the Propontis, he traveled south to the court of Mausolus. During his travels he gathered many students of his own. Around 368 BC, Eudoxus returned to Athens with his students. According to some sources, around 367 he assumed headship of the Academy during Plato's period in Syracuse, taught Aristotle, he returned to his native Cnidus, where he served in the city assembly. While in Cnidus, he built an observatory and continued writing and lecturing on theology and meteorology, he had one son and three daughters, Actis and Delphis. In mathematical astronomy, his fame is due to the introduction of the astronomical globe, his early contributions to understanding the movement of the planets, his work on proportions shows insight into real numbers. When it was revived by Tartaglia and others in the 16th century, it became the basis for quantitative work in science for a century, until it was replaced by Richard Dedekind.
Craters on Mars and the Moon are named in his honor. An algebraic curve is named after him. Eudoxus is considered by some to be the greatest of classical Greek mathematicians, in all antiquity second only to Archimedes, he rigorously developed Antiphon's method of exhaustion, a precursor to the integral calculus, used in a masterly way by Archimedes in the following century. In applying the method, Eudoxus proved such mathematical statements as: areas of circles are to one another as the squares of their radii, volumes of spheres are to one another as the cubes of their radii, the volume of a pyramid is one-third the volume of a prism with the same base and altitude, the volume of a cone is one-third that of the corresponding cylinder. Eudoxus introduced the idea of non-quantified mathematical magnitude to describe and work with continuous geometrical entities such as lines, angles and volumes, thereby avoiding the use of irrational numbers. In doing so, he reversed a Pythagorean emphasis on number and arithmetic, focusing instead on geometrical concepts as the basis of rigorous mathematics.
Some Pythagoreans, such as Eudoxus' teacher Archytas, had believed that only arithmetic could provide a basis for proofs. Induced by the need to understand and operate with incommensurable quantities, Eudoxus established what may have been the first deductive organization of mathematics on the basis of explicit axioms; the change in focus by Eudoxus stimulated a divide in mathematics. In combination with a Greek intellectual attitude unconcerned with practical problems, there followed a significant retreat from the development of techniques in arithmetic and algebra; the Pythagoreans had discovered that the diagonal of a square does not have a common unit of measurement with the sides of the square. This discovery had heralded the existence of incommensurable quantities beyond the integers and rational fractions, but at the same time it threw into question the idea of measurement and calculations in geometry as a whole. For example, Euclid provides an elaborate proof of the Pythagorean theorem, by using addition of areas and only much a simpler proof from similar triangles, which relies on ratios of line segments.
Ancient Greek mathematicians calculated not with quantities and equations as we do today, but instead they used proportionalities to express the relationship between quantities. Thus the ratio of two similar quantities was not just a numerical value. Eudoxus was able to restore confidence in the use of proportionalities by providing an astounding definition for the meaning of the equality between two ratios; this definition of proportion forms the subject of Euclid's Book V. In Definition 5 of Euclid's Book V we read: Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth when, if any equimultiples whatever be taken of the first and third, any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike
The Isagoge or "Introduction" to Aristotle's "Categories", written by Porphyry in Greek and translated into Latin by Boethius, was the standard textbook on logic for at least a millennium after his death. It was composed by Porphyry in Sicily during the years 268–270, sent to Chrysaorium, according to all the ancient commentators Ammonius and David; the work includes the influential hierarchical classification of genera and species from substance in general down to individuals, known as the Tree of Porphyry, an introduction which mentions the problem of universals. Boethius' translation of the work, in Latin, became a standard medieval textbook in European schools and universities, setting the stage for medieval philosophical-theological developments of logic and the problem of universals. Many writers, such as Boethius himself, Abelard, wrote commentaries on the book. Other writers such as William of Ockham incorporated them into their textbooks on logic; the earliest Latin translation, now no longer extant, was made by Marius Victorinus in the fourth century.
Boethius relied upon it in his own translation. The earliest known Syriac translation was made in the seventh century by Athanasius of Balad. An early Armenian translation of the work exists; the Introduction was translated into Arabic by Ibn al-Muqaffa‘ from a Syriac version. With the Arabicized name Isāghūjī it long remained the standard introductory logic text in the Muslim world and influenced the study of theology, philosophy and jurisprudence. Besides the adaptations and epitomes of this work, many independent works on logic by Muslim philosophers have been entitled Isāghūjī. Porphyry's discussion of accident sparked a long-running debate on the application of accident and essence; the predicables is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its subject. The list given by the schoolmen and adopted by modern logicians is based on the original fivefold classification given by Aristotle: definition, differentia, accident.
The scholastic classification, obtained from Boëthius's version of the Isagoge, modified Aristotle's by substituting species for definition. In medieval textbooks, the all-important Arbor porphyriana illustrates his logical classification of substance. To this day, taxonomy benefits from concepts in Porphyry's Tree, in classifying living organisms: see cladistics; the work is celebrated for prompting the medieval debate over the status of universals. Porphyry writes For the moment, I shall decline to say, concerning genera and species, whether they subsist, whether they are bare, pure isolated conceptions, whether, if subsistent, they are corporeal or incorporeal, or whether they are separated from or in sensible objects, other related matters; this sort of problem is of the deepest, requires more extensive investigation.αὐτίκα περὶ τῶν γενῶν τε καὶ εἰδῶν τὸ μὲν εἴτε ὑφέστηκεν εἴτε καὶ ἐν μόναις ψιλαῖς ἐπινοίαις κεῖται εἴτε καὶ ὑφεστηκότα σώματά ἐστιν ἢ ἀσώματα καὶ πότερον χωριστὰ ἢ ἐν τοῖς αἰσθητοῖς καὶ περὶ ταῦτα ὑφεστῶτα, παραιτήσομαι λέγειν βαθυτάτης οὔσης τῆς τοιαύτης πραγματείας καὶ ἄλλης μείζονος δεομένης ἐξετάσεως.
Though he did not mention the problem further, his formulation constitutes the most influential part of his work, since it was these questions that formed the basis of medieval debates about the status of universals. Do universals exist in the mind, or in reality? If in reality, are they physical things, or not? If physical, do they have a separate existence from physical bodies, or are they part of them? Barnes, Jonathan. Introduction to Introduction by Porphyry. Clarendon Press King, Daniel; the Earliest Syriac Translation of Aristotle's Categories: Text and Commentary. Brill "Porphyrii Isagoge translatio". Corpus scriptorum latinorum. Retrieved 2008-05-03. Pearse, R. "Porphyry, Introduction to the logical Categories of Aristotle. Preface to the online edition". Manuscripts. Retrieved 2008-05-03. Porphyry, translation by Octavius Freire Owen MS 484/15 Commentum super libro Porphyrii Isagoge.
Plato was an Athenian philosopher during the Classical period in Ancient Greece, founder of the Platonist school of thought, the Academy, the first institution of higher learning in the Western world. He is considered the pivotal figure in the history of Ancient Greek and Western philosophy, along with his teacher and his most famous student, Aristotle. Plato has often been cited as one of the founders of Western religion and spirituality; the so-called Neoplatonism of philosophers like Plotinus and Porphyry influenced Saint Augustine and thus Christianity. Alfred North Whitehead once noted: "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."Plato was the innovator of the written dialogue and dialectic forms in philosophy. Plato appears to have been the founder of Western political philosophy, his most famous contribution bears his name, the doctrine of the Forms known by pure reason to provide a realist solution to the problem of universals.
He is the namesake of Platonic love and the Platonic solids. His own most decisive philosophical influences are thought to have been along with Socrates, the pre-Socratics Pythagoras and Parmenides, although few of his predecessors' works remain extant and much of what we know about these figures today derives from Plato himself. Unlike the work of nearly all of his contemporaries, Plato's entire oeuvre is believed to have survived intact for over 2,400 years. Although their popularity has fluctuated over the years, the works of Plato have never been without readers since the time they were written. Due to a lack of surviving accounts, little is known about education. Plato belonged to an influential family. According to a disputed tradition, reported by doxographer Diogenes Laërtius, Plato's father Ariston traced his descent from the king of Athens and the king of Messenia, Melanthus. Plato's mother was Perictione, whose family boasted of a relationship with the famous Athenian lawmaker and lyric poet Solon, one of the seven sages, who repealed the laws of Draco.
Perictione was sister of Charmides and niece of Critias, both prominent figures of the Thirty Tyrants, known as the Thirty, the brief oligarchic regime, which followed on the collapse of Athens at the end of the Peloponnesian War. According to some accounts, Ariston tried to force his attentions on Perictione, but failed in his purpose; the exact time and place of Plato's birth are unknown. Based on ancient sources, most modern scholars believe that he was born in Athens or Aegina between 429 and 423 BC, not long after the start of the Peloponnesian War; the traditional date of Plato's birth during the 87th or 88th Olympiad, 428 or 427 BC, is based on a dubious interpretation of Diogenes Laërtius, who says, "When was gone, joined Cratylus the Heracleitean and Hermogenes, who philosophized in the manner of Parmenides. At twenty-eight, Hermodorus says, went to Euclides in Megara." However, as Debra Nails argues, the text does not state that Plato left for Megara after joining Cratylus and Hermogenes.
In his Seventh Letter, Plato notes that his coming of age coincided with the taking of power by the Thirty, remarking, "But a youth under the age of twenty made himself a laughingstock if he attempted to enter the political arena." Thus, Nails dates Plato's birth to 424/423. According to Neanthes, Plato was six years younger than Isocrates, therefore was born the same year the prominent Athenian statesman Pericles died. Jonathan Barnes regards 428 BC as the year of Plato's birth; the grammarian Apollodorus of Athens in his Chronicles argues that Plato was born in the 88th Olympiad. Both the Suda and Sir Thomas Browne claimed he was born during the 88th Olympiad. Another legend related that, when Plato was an infant, bees settled on his lips while he was sleeping: an augury of the sweetness of style in which he would discourse about philosophy. Besides Plato himself and Perictione had three other children; the brothers Adeimantus and Glaucon are mentioned in the Republic as sons of Ariston, brothers of Plato, though some have argued they were uncles.
In a scenario in the Memorabilia, Xenophon confused the issue by presenting a Glaucon much younger than Plato. Ariston appears to have died in Plato's childhood, although the precise dating of his death is difficult. Perictione 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, famous for his beauty. Perictione gave birth to Pyrilampes' second son, the half-brother of Plato, who appears in Parmenides. In contrast to his reticence about himself, Plato introduced his distinguished relatives into his dialogues, or referred to them with some precision. In addition to Adeimantus and Glaucon in the Republic, Charmides has a dialogue named after him; these and other references suggest a considerable amount of family pride and enable us to reconstruct Plato's family tree. According to Burnet, "the opening scene of the Ch
Speusippus was an ancient Greek philosopher. Speusippus was Plato's nephew by his sister Potone. After Plato's death, c.348 BC, Speusippus inherited the Academy, near age 60, remained its head for the next eight years. However, following a stroke, he passed the chair to Xenocrates. Although the successor to Plato in the Academy, Speusippus diverged from Plato's teachings, he rejected Plato's Theory of Forms, whereas Plato had identified the Good with the ultimate principle, Speusippus maintained that the Good was secondary. He argued that it is impossible to have satisfactory knowledge of any thing without knowing all the differences by which it is separated from everything else; the standard edition of the surviving fragments and testimonies is Leonardo Tarán's Speusippus of Athens: A Critical Study with a Collection of the Related Texts and Commentary. Speusippus was a native of Athens, the son of Eurymedon and Potone, a sister of Plato; the pseudonymous Thirteenth Letter of Plato claims. We hear nothing of his life until the time when he accompanied his uncle Plato on his third journey to Syracuse, where he displayed considerable ability and prudence in his amicable relations with Dion.
His moral worth is recognised by Timon, though only that he may heap the more unsparing ridicule on his intellect. The report about his sudden fits of anger, his greed, his debauchery, are derived from a impure source: Athenaeus and Diogenes Laërtius can adduce as authority for them scarcely anything more than the abuse in some spurious letters of Dionysius the Younger, banished by Dion, with the cooperation of Speusippus. Having been selected by Plato as his successor as the leader of the Academy, he was at the head of the school for only eight years, he died, it appears, of a lingering paralytic illness a stroke. He was succeeded as the head of the school by Xenocrates. Diogenes Laërtius gives us a list of some of the titles of the many dialogues and commentaries of Speusippus, of little help in determining their contents, the fragments provided by other writers provide us with only a little extra. Speusippus was interested in bringing together those things which were similar in their philosophical treatment, to the derivation, laying down, of the ideas of genera and species: for he was interested in what the various sciences had in common, how they might be connected.
Thus he furthered the threefold division of philosophy into Dialectics and Physics, for which Plato had laid the foundation, without losing sight of the mutual connection of these three branches of philosophy. For he maintained that no one could arrive at a complete definition who did not know all the differences by which a thing, to be defined was separated from the rest. With Plato, moreover, he distinguished between that, the object of thought, that, the object of sensuous perception, between the cognition of the reason and sensuous perception, he tried, however, to show how perception can be taken up and transformed into knowledge, by the assumption of a perception, which, by participation in rational truth, raises itself to the rank of knowledge. By this he seems to have understood an immediate, mode of conception. Speusippus rejected Plato's Theory of Forms, he tried to determine the idea of substance more distinctly by separating its types, the difference between which he considered would result from the difference between the principles on which they are based.
Thus he distinguished substances of number, of size, of soul, while Plato had referred them, as separate entities, to the ideal numbers. Speusippus made still more kinds of substance, beginning with the One, assuming principles for each kind of substance, one for numbers, another for spatial magnitudes, another for the soul. Speusippus must have recognised something common in those different kinds of substances, inasmuch as, firstly, he set out from the absolute One, regarded it as a formal principle which they had in common, secondly, he appears to have assumed that multitude and multiformity was a common primary element in their composition, but it is only the difficulties which led him to make this and similar deviations from the Platonist doctrine, of which we can get any clear idea, not the way in which he thought he had avoided those difficulties by distinguishing different kinds of principles. The criticism of Aristotle, directed against Speusippus, shows how little satisfied he was with the modification of the original Platonist doctrine.
With this deviation from Plato's doctrine is connected another which takes a wider range. As the ultimate principle, Speusippus would not, with Plato, recognise the Good, with others, going back to the older Theologi, maintained that the principles of the universe were to be set down as causes of the good and perfect, but were not the good and perfect itself, which must rather be regarded as the result of generated existence, or development, just as the seeds of plants and animals are not the formed plants or animals t
The Byzantine Empire referred to as the Eastern Roman Empire or Byzantium, was the continuation of the Roman Empire in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople. It survived the fragmentation and fall of the Western Roman Empire in the 5th century AD and continued to exist for an additional thousand years until it fell to the Ottoman Turks in 1453. During most of its existence, the empire was the most powerful economic and military force in Europe. Both the terms "Byzantine Empire" and "Eastern Roman Empire" are historiographical terms created after the end of the realm. Several signal events from the 4th to 6th centuries mark the period of transition during which the Roman Empire's Greek East and Latin West diverged. Constantine I reorganised the empire, made Constantinople the new capital, legalised Christianity. Under Theodosius I, Christianity became the Empire's official state religion and other religious practices were proscribed.
Under the reign of Heraclius, the Empire's military and administration were restructured and adopted Greek for official use in place of Latin. Thus, although the Roman state continued and its traditions were maintained, modern historians distinguish Byzantium from ancient Rome insofar as it was centred on Constantinople, oriented towards Greek rather than Latin culture, characterised by Eastern Orthodox Christianity; the borders of the empire evolved over its existence, as it went through several cycles of decline and recovery. During the reign of Justinian I, the empire reached its greatest extent after reconquering much of the Roman western Mediterranean coast, including North Africa and Rome itself, which it held for two more centuries; the Byzantine–Sasanian War of 602–628 exhausted the empire's resources and contributed to major territorial losses during the Early Muslim conquests of the 7th century, when it lost its richest provinces and Syria, to the Arab caliphate. During the Macedonian dynasty, the empire expanded again and experienced the two-century long Macedonian Renaissance, which came to an end with the loss of much of Asia Minor to the Seljuk Turks after the Battle of Manzikert in 1071.
This battle opened the way for the Turks to settle in Anatolia. The empire recovered during the Komnenian restoration, by the 12th century Constantinople was the largest and wealthiest European city. However, it was delivered a mortal blow during the Fourth Crusade, when Constantinople was sacked in 1204 and the territories that the empire governed were divided into competing Byzantine Greek and Latin realms. Despite the eventual recovery of Constantinople in 1261, the Byzantine Empire remained only one of several small rival states in the area for the final two centuries of its existence, its remaining territories were progressively annexed by the Ottomans over the 15th century. The Fall of Constantinople to the Ottoman Empire in 1453 ended the Byzantine Empire; the last of the imperial Byzantine successor states, the Empire of Trebizond, would be conquered by the Ottomans eight years in the 1461 Siege of Trebizond. The first use of the term "Byzantine" to label the years of the Roman Empire was in 1557, when the German historian Hieronymus Wolf published his work Corpus Historiæ Byzantinæ, a collection of historical sources.
The term comes from "Byzantium", the name of the city of Constantinople before it became Constantine's capital. This older name of the city would be used from this point onward except in historical or poetic contexts; the publication in 1648 of the Byzantine du Louvre, in 1680 of Du Cange's Historia Byzantina further popularised the use of "Byzantine" among French authors, such as Montesquieu. However, it was not until the mid-19th century that the term came into general use in the Western world; the Byzantine Empire was known to its inhabitants as the "Roman Empire", the "Empire of the Romans", "Romania", the "Roman Republic", as "Rhōmais". The inhabitants called themselves Romaioi and as late as the 19th century Greeks referred to Modern Greek as Romaiika "Romaic." After 1204 when the Byzantine Empire was confined to its purely Greek provinces the term'Hellenes' was used instead. While the Byzantine Empire had a multi-ethnic character during most of its history and preserved Romano-Hellenistic traditions, it became identified by its western and northern contemporaries with its predominant Greek element.
The occasional use of the term "Empire of the Greeks" in the West to refer to the Eastern Roman Empire and of the Byzantine Emperor as Imperator Graecorum were used to separate it from the prestige of the Roman Empire within the new kingdoms of the West. No such distinction existed in the Islamic and Slavic worlds, where the Empire was more straightforwardly seen as the continuation of the Roman Empire. In the Islamic world, the Roman Empire was known as Rûm; the name millet-i Rûm, or "Roman nation," was used by the Ottomans through the 20th century to refer to the former subjects of the Byzantine Empire