1.
Zeno of Citium
–
Zeno of Citium was a Hellenistic thinker from Citium, Cyprus, and probably of Phoenician descent. Zeno was the founder of the Stoic school of philosophy, which he taught in Athens from about 300 BC, based on the moral ideas of the Cynics, Stoicism laid great emphasis on goodness and peace of mind gained from living a life of Virtue in accordance with Nature. It proved very successful, and flourished as the dominant philosophy from the Hellenistic period through to the Roman era, Zeno was born c.334 BC, in Citium in Cyprus. Most of the details known about his life come from the anecdotes preserved by Diogenes Laërtius in his Lives, Diogenes relates a legend that Zeno was a merchant, after surviving a shipwreck, Zeno wandered into a bookshop in Athens and was attracted to some writings about Socrates. He asked the librarian how to find such a man, in response, the librarian pointed to Crates of Thebes, the most famous Cynic living at that time in Greece. Zeno is described as a haggard, tanned person, living a spare and this coincides with the influences of Cynic teaching, and was, at least in part, continued in his Stoic philosophy. From the day Zeno became Crates’s pupil, he showed a bent for philosophy. As Zeno began to run off in embarrassment with the lentil-soup flowing down his legs, Crates chided Why run away, apart from Crates, Zeno studied under the philosophers of the Megarian school, including Stilpo, and the dialecticians Diodorus Cronus, and Philo. He is also said to have studied Platonist philosophy under the direction of Xenocrates, Zeno began teaching in the colonnade in the Agora of Athens known as the Stoa Poikile in 301 BC. His disciples were initially called Zenonians, but eventually came to be known as Stoics. Among the admirers of Zeno was king Antigonus II Gonatas of Macedonia, Zeno is said to have declined an invitation to visit Antigonus in Macedonia, although their supposed correspondence preserved by Laërtius is undoubtedly the invention of a later rhetorician. Zeno instead sent his friend and disciple Persaeus, who had lived with Zeno in his house, among Zenos other pupils there were Aristo of Chios, Sphaerus, and Cleanthes who succeeded Zeno as the head of the Stoic school in Athens. Zeno is said to have declined Athenian citizenship when it was offered to him, fearing that he would appear unfaithful to his native land, Diogenes Laërtius has preserved many clever and witty remarks by Zeno, the veracity of which cannot be ascertained. Laërtius reports about his death, As he was leaving the school he tripped and fell, striking the ground with his fist, he quoted the line from the Niobe, I come, I come, why dost thou call for me. And died on the spot through holding his breath, during his lifetime, Zeno received appreciation for his philosophical and pedagogical teachings. Among other things, Zeno was honored with the crown. The crater Zeno on the Moon is named in his honor, because Zenos ideas were later expanded upon by Chrysippus and other Stoics it can be difficult to determine precisely what he thought. But his general views can be outlined as follows, In his treatment of Logic, Zeno was influenced by Stilpo, Zeno urged the need to lay down a basis for Logic because the wise person must know how to avoid deception
Zeno of Citium
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Zeno of Citium
Zeno of Citium
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Modern bust of Zeno in Athens
Zeno of Citium
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Zeno, portrayed as a medieval scholar in the
Nuremberg Chronicle
2.
El Escorial
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It is one of the Spanish royal sites and functions as a monastery, basilica, royal palace, pantheon, library, museum, university and hospital. It is situated 2.06 km up the valley from the town of El Escorial, El Escorial was, at once, a monastery and a Spanish royal palace. Originally a property of the Hieronymite monks, it is now a monastery of the Order of Saint Augustine and it is also a boarding school. Philip engaged the Spanish architect, Juan Bautista de Toledo, to be his collaborator in the design of El Escorial, Philip appointed him architect-royal in 1559, and together they designed El Escorial as a monument to Spains role as a center of the Christian world. On 2 November 1984, UNESCO declared The Royal Seat of San Lorenzo of El Escorial a World Heritage Site and it is a popular tourist attraction, often visited by day-trippers from Madrid – more than 500,000 visitors come to El Escorial every year. El Escorial is situated at the foot of Mt. Abantos in the Sierra de Guadarrama, Quentin in Picardy against Henry II, king of France. He also intended the complex to serve as a necropolis for the interment of the remains of his parents, Charles I and Isabella of Portugal, himself, in addition, Philip envisioned El Escorial as a center for studies in aid of the Counter-Reformation cause. The buildings cornerstone was laid on 23 April 1563, the design and construction were overseen by Juan Bautista de Toledo, who did not live to see the completion of the project. With Toledos death in 1567, direction passed to his apprentice, Juan de Herrera, under whom the building was completed in 1584, to this day, la obra de El Escorial is a proverbial expression for a thing that takes a long time to finish. Since then, El Escorial has been the site for most of the Spanish kings of the last five centuries. Two Bourbon kings, Philip V and Ferdinand VI, as well as King Amadeus, are not buried in the monastery, the floor plan of the building is in the form of a gridiron. The traditional belief is that design was chosen in honor of St. Lawrence. St. Lawrence’s feast day is 10 August, the date as the 1557 Battle of St. Quentin. In fact, however, the origin of the layout is quite controversial. The grill-like shape, which did not fully emerge until Herrera eliminated from the conception the six interior towers of the facade, was, by no means. In fact, palaces of this design were commonplace in the Byzantine. Statues of David and Solomon on either side of the entrance to the basilica of El Escorial lend further weight to the theory that this is the origin of the design. A more personal connection can be drawn between the David-warrior figure, representing Charles V, and his son, the stolid and solomonically prudent Philip II
El Escorial
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A distant view of the Royal Seat of San Lorenzo de El Escorial
El Escorial
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West facade of the monastery.
El Escorial
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El Escorial: floor plan, based on the floorplan of
Solomon's Temple.
El Escorial
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Courtyard of the Kings and the Basilica.
3.
Velia
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Velia was the Roman name of an ancient city of Magna Graecia on the coast of the Tyrrhenian Sea. It was founded by Greeks from Phocaea as Hyele around 538–535 BC, the name later changed to Ele and then Elea before it became known by its current Latin and Italian name during the Roman era. Its ruins are located in the Cilento region near the modern village Velia, the village is a frazione of the comune Ascea in the Province of Salerno, Campania, Italy. The city was known for being the home of the philosophers Parmenides and Zeno of Elea, the site of the acropolis of ancient Elea was once a promontory called Castello a Mare, meaning castle on the sea in Italian. It now lies inland and was renamed to Castellammare della Bruca in the Middle Ages, the town is situated close to the Tyrrhenian coast in a hill zone nearby Marina di Casalvelino and Marina di Ascea, on a road linking Agropoli to the southern Cilentan Coast. Its population is located in the plain by the sea and in the hill zones of Enotria, Bosco. Velia also had a station on the Naples-Salerno-Reggio Calabria line. According to Herodotus, in 545 BC Ionian Greeks fled Phocaea, in modern Turkey, the location is nearly at the same latitude as Phocaea. Elea was not conquered by the Lucanians, but eventually joined Rome in 273 BC and was included in ancient Lucania, according to Book 6 of Virgils Aeneid, Velia is the place where the body of Palinurus washed ashore. Bricks were also employed in later times, their form is peculiar to this place, square, with a thickness of nearly 4 in. There are some remains of cisterns on the site, and, the Eleatics were a school of pre-Socratic philosophers. The group was founded in the early 5th century BC by Parmenides, other members of the school included Zeno of Elea and Melissus of Samos. Xenophanes is sometimes included in the list, though there is dispute over this. Statius, father of the Roman poet Publius Papinius Statius was born in Hyele, list of ancient Greek cities This article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. article name needed. Official website Cilento National Park website
Velia
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View of the excavations and the tower at Velia
Velia
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Ruins of the Greek theater
Velia
Velia
4.
Syracuse, Sicily
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Syracuse is a historic city in Sicily, the capital of the province of Syracuse. The city is notable for its rich Greek history, culture, amphitheatres, architecture and this 2, 700-year-old city played a key role in ancient times, when it was one of the major powers of the Mediterranean world. Syracuse is located in the southeast corner of the island of Sicily, the city was founded by Ancient Greek Corinthians and Teneans and became a very powerful city-state. Syracuse was allied with Sparta and Corinth and exerted influence over the entirety of Magna Graecia, described by Cicero as the greatest Greek city and the most beautiful of them all, it equaled Athens in size during the fifth century BC. It later became part of the Roman Republic and Byzantine Empire, after this Palermo overtook it in importance, as the capital of the Kingdom of Sicily. Eventually the kingdom would be united with the Kingdom of Naples to form the Two Sicilies until the Italian unification of 1860, in the modern day, the city is listed by UNESCO as a World Heritage Site along with the Necropolis of Pantalica. In the central area, the city itself has a population of around 125,000 people, the inhabitants are known as Siracusans. Syracuse is mentioned in the Bible in the Acts of the Apostles book at 28,12 as Paul stayed there, the patron saint of the city is Saint Lucy, she was born in Syracuse and her feast day, Saint Lucys Day, is celebrated on 13 December. Syracuse was founded in 734 or 733 BC by Greek settlers from Corinth and Tenea, there are many attested variants of the name of the city including Συράκουσαι Syrakousai, Συράκοσαι Syrakosai and Συρακώ Syrako. The nucleus of the ancient city was the island of Ortygia. The settlers found the fertile and the native tribes to be reasonably well-disposed to their presence. The city grew and prospered, and for some time stood as the most powerful Greek city anywhere in the Mediterranean, colonies were founded at Akrai, Kasmenai, Akrillai, Helorus and Kamarina. The descendants of the first colonists, called Gamoroi, held power until they were expelled by the Killichiroi, the former, however, returned to power in 485 BC, thanks to the help of Gelo, ruler of Gela. Gelo himself became the despot of the city, and moved many inhabitants of Gela, Kamarina and Megera to Syracuse, building the new quarters of Tyche, the enlarged power of Syracuse made unavoidable the clash against the Carthaginians, who ruled western Sicily. In the Battle of Himera, Gelo, who had allied with Theron of Agrigento, a temple dedicated to Athena, was erected in the city to commemorate the event. Syracuse grew considerably during this time and its walls encircled 120 hectares in the fifth century, but as early as the 470s BC the inhabitants started building outside the walls. The complete population of its territory approximately numbered 250,000 in 415 BC, Gelo was succeeded by his brother Hiero, who fought against the Etruscans at Cumae in 474 BC. His rule was eulogized by poets like Simonides of Ceos, Bacchylides and Pindar, a democratic regime was introduced by Thrasybulos
Syracuse, Sicily
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Ortygia island, where Syracuse was founded in
ancient Greek times.
Mount Etna is visible in the distance.
Syracuse, Sicily
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A Syracusan
tetradrachm (c. 415–405 BC), sporting
Arethusa and a
quadriga.
Syracuse, Sicily
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Decadrachme from Sicile struck at Syracuse and sign d'Évainète
Syracuse, Sicily
–
The siege of Syracuse in a 17th-century engraving.
5.
Pre-Socratic philosophy
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Pre-Socratic philosophy is ancient Greek philosophy before Socrates and schools contemporary to Socrates that were not influenced by him. In Classical antiquity, the Presocratic philosophers were called physiologoi, Aristotle called them physikoi because they sought natural explanations for phenomena, as opposed to the earlier theologoi, whose philosophical basis was supernatural. Diogenes Laërtius divides the physiologoi into two groups, Ionian, led by Anaximander, and the Italiote, led by Pythagoras, hermann Diels popularized the term pre-socratic in Die Fragmente der Vorsokratiker in 1903. However, the term pre-Sokratic was in use as early as George Grotes Plato, edouard Zeller was also important in dividing thought before and after Socrates. Major analyses of pre-Socratic thought have been made by Gregory Vlastos, Jonathan Barnes and it may sometimes be difficult to determine the actual line of argument some Presocratics used in supporting their particular views. While most of them produced significant texts, none of the texts has survived in complete form, all that is available are quotations by later philosophers and historians, and the occasional textual fragment. The Presocratic philosophers rejected traditional mythological explanations of the phenomena they saw them in favor of more rational explanations. These philosophers asked questions about the essence of things, From where does everything come, how do we explain the plurality of things found in nature. How might we describe nature mathematically, others concentrated on defining problems and paradoxes that became the basis for later mathematical, scientific and philosophic study. Later philosophers rejected many of the answers the early Greek philosophers provided, furthermore, the cosmologies proposed by them have been updated by later developments in science. Western philosophy began in ancient Greece in the 6th century BCE, the Presocratics were mostly from the eastern or western fringes of the Greek world. Their efforts were directed to the investigation of the ultimate basis and they sought the material principle of things, and the method of their origin and disappearance. As the first philosophers, they emphasized the unity of things. Only fragments of the writings of the presocratics survive. The knowledge we have of them derives from accounts - known as doxography - of later philosophical writers, the first Presocratic philosophers were from Miletus on the western coast of Anatolia. Thales is reputedly the father of Greek philosophy, he declared water to be the basis of all things, next came Anaximander, the first writer on philosophy. He assumed as the first principle an undefined, unlimited substance without qualities, out of which the primary opposites, hot and cold, moist and dry, became differentiated. His younger contemporary, Anaximenes, took for his air, conceiving it as modified, by thickening and thinning, into fire, wind, clouds, water
Pre-Socratic philosophy
–
History of
Western philosophy
6.
Metaphysics
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Metaphysics is a branch of philosophy exploring the fundamental nature of reality. In this vein, metaphysics seeks to answer two questions, Ultimately, what is there. Topics of metaphysical investigation include existence, objects and their properties, space and time, cause and effect, a central branch of metaphysics is ontology, the investigation into the basic categories of being and how they relate to one another. Another branch is metaphysical cosmology, which seeks to understand the origin, there are two broad conceptions about what world is studied by metaphysics. The strong, classical view assumes that the objects studied by metaphysics exist independently of any observer, the weaker, more modern view assumes that the objects studied by metaphysics exist inside the mind of an observer, so the subject becomes a form of introspection and conceptual analysis. Some philosophers, notably Kant, discuss both of these worlds and what can be inferred about each one, some philosophers and scientists, such as the logical positivists, reject the entire subject of metaphysics as meaningless, while others disagree and think that it is legitimate. Ontology deals with the determination whether categories of being are fundamental and it is the inquiry into being in so much as it is being, or into beings insofar as they exist—and not insofar as particular facts may be obtained about them or particular properties belong to them. Most ontologies assume or assert the existence of categories including objects, properties, space, immediate questions arising from this include the nature of objects. Only properties can be observed directly, so what does it mean for an object to exist, how can we be sure that such objects exist at all. The word is has two uses in English, separated out in ontology. It can denote existence as in there is an elephant in the room, some philosophers also include sub-classing as a third form of is-ness or being, as in the elephant is a mammal. Some philosophers, notably of the Platonic school, contend that all refer to existent entities. Other philosophers contend that nouns do not always name entities, between these poles of realism and nominalism, stand a variety of other positions. An ontology may give an account of which refer to entities, which do not, why. Other controversial categories of objects and properties which may be argued to exist or not include aesthetic and moral properties, stances about the status of such things may form the foundation for other branches of philosophy such as aesthetics, ethics and political philosophy. Identity is a fundamental metaphysical issue, metaphysicians investigating identity are tasked with the question of what, exactly, it means for something to be identical to itself. Other issues of identity arise in the context of time, what does it mean for something to be itself across two moments in time, how do we account for this. Another question of identity arises when we ask what our criteria ought to be for determining identity, and how does the reality of identity interface with linguistic expressions
Metaphysics
–
Plato –
Kant –
Nietzsche
7.
Ontology
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Ontology is the philosophical study of the nature of being, becoming, existence or reality as well as the basic categories of being and their relations. Although ontology as an enterprise is highly hypothetical, it also has practical application in information science and technology. Some philosophers, notably of the Platonic school, contend that all refer to existent entities. Other philosophers contend that nouns do not always name entities, between these poles of realism and nominalism, stand a variety of other positions. An ontology may give an account of which refer to entities, which do not, why. Principal questions of ontology include, What can be said to exist, into what categories, if any, can we sort existing things. What are the meanings of being, what are the various modes of being of entities. Various philosophers have provided different answers to these questions, one common approach involves dividing the extant subjects and predicates into groups called categories. Such an understanding of ontological categories, however, is merely taxonomic, what does it mean for a being to be. Is existence a genus or general class that is divided up by specific differences. Which entities, if any, are fundamental, how do the properties of an object relate to the object itself. What features are the essential, as opposed to merely accidental attributes of a given object, how many levels of existence or ontological levels are there. Can one give an account of what it means to say that an object exists. Can one give an account of what it means to say that an entity exists. What constitutes the identity of an object, when does an object go out of existence, as opposed to merely changing. Do beings exist other than in the modes of objectivity and subjectivity, i. e. is the subject/object split of modern philosophy inevitable. e. Being, that which is, which is the present participle of the verb εἰμί, eimí, i. e. to be, I am, and -λογία, -logia, i. e. logical discourse. The first occurrence in English of ontology as recorded by the OED came in a work by Gideon Harvey, Archelogia philosophica nova, or, New principles of Philosophy
Ontology
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Parmenides was among the first to propose an ontological characterization of the fundamental nature of reality.
8.
Parmenides
–
Parmenides of Elea was a pre-Socratic Greek philosopher from Elea in Magna Graecia. He was the founder of the Eleatic school of philosophy, the single known work of Parmenides is a poem, On Nature, which has survived only in fragmentary form. In this poem, Parmenides describes two views of reality, in the way of truth, he explains how reality is one, change is impossible, and existence is timeless, uniform, necessary, and unchanging. In the way of opinion, he explains the world of appearances, in which ones sensory faculties lead to conceptions which are false, Parmenides was born in the Greek colony of Elea, which, according to Herodotus, had been founded shortly before 535 BC. He was descended from a wealthy and illustrious family,450 BC, which, if true, suggests a year of birth of c.515 BC. He was said to have been a pupil of Xenophanes, and regardless of whether they knew each other. Diogenes Laërtius also describes Parmenides as a disciple of Ameinias, son of Diochaites, the Pythagorean, the first hero cult of a philosopher we know of was Parmenides dedication of a heroon to his teacher Ameinias in Elea. Parmenides was the founder of the School of Elea, which also included Zeno of Elea, of his life in Elea, it was said that he had written the laws of the city. His most important pupil was Zeno, who according to Plato was 25 years his junior, Parmenides had a large influence on Plato, who not only named a dialogue, Parmenides, after him, but always spoke of him with veneration. William Smith also wrote in Dictionary of Greek and Roman Biography and Mythology, Reason is our guide, on the latter the eye that does not catch the object and re-echoing hearing. Thought and that which is thought of coinciding, the passages of Plato, Aristotle, Theophrastus, and others. Parmenides is one of the most significant of the pre-Socratic philosophers and his single known work, a poem conventionally titled On Nature, has survived only in fragments. Approximately 160 verses remain today from a total that was probably near 800. The poem was divided into three parts, A proem, which introduced the entire work, A section known as The Way of Truth. The proem is a sequence in which the narrator travels beyond the beaten paths of mortal men to receive a revelation from an unnamed goddess on the nature of reality. Aletheia, an estimated 90% of which has survived, and doxa, in the proem, Parmenides describes the journey of the poet, escorted by maidens, from the ordinary daytime world to a strange destination, outside our human paths. Carried in a chariot, and attended by the daughters of Helios the Sun. The goddess resides in a well-known mythological space, where Night and its essential character is that here all opposites are undivided, or one
Parmenides
–
Parmenides
Parmenides
–
Parmenides. Detail from
The School of Athens by
Raphael.
9.
Plato
–
Plato was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world. He is widely considered the most pivotal figure in the development of philosophy, unlike nearly all of his philosophical contemporaries, Platos entire work is believed to have survived intact for over 2,400 years. Along with his teacher, Socrates, and his most famous student, Aristotle, Plato laid the foundations of Western philosophy. 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. In addition to being a figure for Western science, philosophy. Friedrich Nietzsche, amongst other scholars, called Christianity, Platonism for the people, Plato was the innovator of the written dialogue and dialectic forms in philosophy, which originate with him. He was not the first thinker or writer to whom the word “philosopher” should be applied, few other authors in the history of Western philosophy approximate him in depth and range, perhaps only Aristotle, Aquinas and Kant would be generally agreed to be of the same rank. Due to a lack of surviving accounts, little is known about Platos early life, the philosopher came from one of the wealthiest and most politically active families in Athens. Ancient sources describe him as a bright though modest boy who excelled in his studies, the exact time and place of Platos birth are unknown, but it is certain that he belonged to an aristocratic and influential family. Based on ancient sources, most modern scholars believe that he was born in Athens or Aegina between 429 and 423 BCE. According to a tradition, reported by Diogenes Laertius, Ariston traced his descent from the king of Athens, Codrus. Platos mother was Perictione, whose family boasted of a relationship with the famous Athenian lawmaker, besides Plato himself, Ariston and Perictione had three other children, these were two sons, Adeimantus and Glaucon, and a daughter Potone, the mother of Speusippus. The brothers Adeimantus and Glaucon are mentioned in the Republic as sons of Ariston, and presumably brothers of Plato, but in a scenario in the Memorabilia, Xenophon confused the issue by presenting a Glaucon much younger than Plato. Then, at twenty-eight, Hermodorus says, went to Euclides in Megara, as Debra Nails argues, The text itself gives no reason to infer that Plato left immediately for Megara and implies the very opposite. Thus, Nails dates Platos birth to 424/423, 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. Ariston appears to have died in Platos childhood, although the dating of his death is difficult. Perictione then married Pyrilampes, her mothers brother, who had served many times as an ambassador to the Persian court and was a friend of Pericles, Pyrilampes had a son from a previous marriage, Demus, who was famous for his beauty. Perictione gave birth to Pyrilampes second son, Antiphon, the half-brother of Plato and these and other references suggest a considerable amount of family pride and enable us to reconstruct Platos family tree
Plato
–
Plato: copy of portrait bust by
Silanion
Plato
–
Plato from
The School of Athens by
Raphael, 1509
Plato
–
Plato and
Socrates in a medieval depiction
Plato
–
Plato (left) and Aristotle (right), a detail of
The School of Athens, a fresco by
Raphael. Aristotle gestures to the earth, representing his belief in knowledge through empirical observation and experience, while holding a copy of his
Nicomachean Ethics in his hand. Plato holds his
Timaeus and gestures to the heavens, representing his belief in
The Forms
10.
Aristotle
–
Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, at seventeen or eighteen years of age, he joined Platos 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, teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books and he believed all peoples concepts and all of their knowledge was ultimately based on perception. Aristotles views on natural sciences represent the groundwork underlying many of his works, Aristotles views on physical science profoundly shaped medieval scholarship. Their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, some of Aristotles zoological observations, such as on the hectocotyl arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known study of logic, which was incorporated in the late 19th century into modern formal logic. Aristotle was well known among medieval Muslim intellectuals and revered as The First Teacher and his ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotles philosophy continue to be the object of academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his style as a river of gold – it is thought that only around a third of his original output has survived. Aristotle, whose means the best purpose, was born in 384 BC in Stagira, Chalcidice. His father Nicomachus was the physician to King Amyntas of Macedon. Aristotle was orphaned at a young age, although there is little information on Aristotles childhood, he probably 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 Platos Academy and he remained there for nearly twenty years before leaving Athens in 348/47 BC. Aristotle then accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor, there, he traveled with Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island. Aristotle married Pythias, either Hermiass adoptive daughter or niece and she bore him a daughter, whom they also named Pythias. Soon after Hermias death, Aristotle was invited by Philip II of Macedon to become the tutor to his son Alexander in 343 BC, Aristotle was appointed as the head of the royal academy of Macedon. During that time he gave not only to Alexander
Aristotle
–
Roman copy in marble of a Greek bronze bust of Aristotle by
Lysippus,
c. 330 BC. The
alabaster mantle is modern.
Aristotle
–
Aristotelianism
Aristotle
–
School of Aristotle in
Mieza,
Macedonia, Greece
Aristotle
–
"Aristotle" by
Francesco Hayez (1791–1882)
11.
Protagoras
–
Protagoras was a pre-Socratic Greek philosopher and is numbered as one of the sophists by Plato. In his dialogue, Protagoras, Plato credits him with having invented the role of the professional sophist, Protagoras was born in Abdera, Thrace, opposite the island of Thasos. According to Aulus Gellius, he made his living as a porter. Democritus realized that Protagoras had tied the load together with such perfect geometric accuracy that he must be a mathematical prodigy, Democritus promptly took him into his own household and taught him philosophy. Protagoras became well known in Athens and even became a friend of Pericles, the dates of his lifetime are not recorded, but extrapolated from writings that have survived the ages. In Protagoras Plato wrote that, before a gathering of Socrates, Prodicus and this suggests a birth date of not later than 490 BC. In the Meno he is said to have died at approximately the age of 70, after 40 years as a practicing Sophist. His death, then, may be presumed to have occurred circa 420 BC, was his death to be attributed to the javelin, to the man who threw it, or to the authorities responsible for the conduct of the games. Even though he was mentored by Democritus, Protagoras did not share his enthusiasm for the pursuit of mathematics, Protagoras was skeptical about the application of theoretical mathematics to the natural world, he did not believe they were really worth studying at all. According to Philodemus, Protagoras said that The subject matter is unknowable, nonetheless, mathematics was considered to be by some a very viable form of art, and Protagoras says on the arts, art without practice and practice without art are nothing. Protagoras also was known as a teacher who addressed subjects connected to virtue and he especially was involved in the question of whether virtue could be taught, a commonplace issue of fifth century BC Greece, that has been related to modern readers through Platos dialogue. He also seems to have had an interest in orthoepeia—the correct use of words—although this topic is strongly associated with his fellow sophist Prodicus. In his eponymous Platonic dialogue, Protagoras interprets a poem by Simonides, focusing on the use of words, their meaning. This type of education would have been useful for the interpretation of laws, Diogenes Laërtius reports that Protagoras devised a taxonomy of speech acts such as assertion, question, answer, command, etc. Aristotle also says that Protagoras worked on the classification and proper use of grammatical gender, the titles of his books such as, Technique of Eristics prove that Protagoras also was a teacher of rhetoric and argumentation. Diogenes Laërtius states that he was one of the first to part in rhetorical contests in the Olympic games. Protagoras also said that on any matter, there are two opposed to one another, and according to Aristotle, Protagoras was criticized for having claimed to make the weaker argument stronger. Protagoras is credited with the philosophy of relativism, which he discusses in his work, by this, Protagoras meant that each individual is the measure of how things are perceived by that individual
Protagoras
–
Democritus (center) and Protagoras (right) 17th century painting by
Salvator Rosa in
Hermitage Museum
12.
Greek language
–
Greek is an independent branch of the Indo-European family of languages, native to Greece and other parts of the Eastern Mediterranean. It has the longest documented history of any living language, spanning 34 centuries of written records and its writing system has been the Greek alphabet for the major part of its history, other systems, such as Linear B and the Cypriot syllabary, were used previously. The alphabet arose from the Phoenician script and was in turn the basis of the Latin, Cyrillic, Armenian, Coptic, Gothic and many other writing systems. Together with the Latin texts and traditions of the Roman world, during antiquity, Greek was a widely spoken lingua franca in the Mediterranean world and many places beyond. It would eventually become the official parlance of the Byzantine Empire, the language is spoken by at least 13.2 million people today in Greece, Cyprus, Italy, Albania, Turkey, and the Greek diaspora. Greek roots are used to coin new words for other languages, Greek. Greek has been spoken in the Balkan peninsula since around the 3rd millennium BC, the earliest written evidence is a Linear B clay tablet found in Messenia that dates to between 1450 and 1350 BC, making Greek the worlds oldest recorded living language. Among the Indo-European languages, its date of earliest written attestation is matched only by the now extinct Anatolian languages, the Greek language is conventionally divided into the following periods, Proto-Greek, the unrecorded but assumed last ancestor of all known varieties of Greek. The unity of Proto-Greek would have ended as Hellenic migrants entered the Greek peninsula sometime in the Neolithic era or the Bronze Age, Mycenaean Greek, the language of the Mycenaean civilisation. It is recorded in the Linear B script on tablets dating from the 15th century BC onwards, Ancient Greek, in its various dialects, the language of the Archaic and Classical periods of the ancient Greek civilisation. It was widely known throughout the Roman Empire, after the Roman conquest of Greece, an unofficial bilingualism of Greek and Latin was established in the city of Rome and Koine Greek became a first or second language in the Roman Empire. The origin of Christianity can also be traced through Koine Greek, Medieval Greek, also known as Byzantine Greek, the continuation of Koine Greek in Byzantine Greece, up to the demise of the Byzantine Empire in the 15th century. Much of the written Greek that was used as the language of the Byzantine Empire was an eclectic middle-ground variety based on the tradition of written Koine. Modern Greek, Stemming from Medieval Greek, Modern Greek usages can be traced in the Byzantine period and it is the language used by the modern Greeks, and, apart from Standard Modern Greek, there are several dialects of it. In the modern era, the Greek language entered a state of diglossia, the historical unity and continuing identity between the various stages of the Greek language is often emphasised. Greek speakers today still tend to regard literary works of ancient Greek as part of their own rather than a foreign language and it is also often stated that the historical changes have been relatively slight compared with some other languages. According to one estimation, Homeric Greek is probably closer to demotic than 12-century Middle English is to modern spoken English, Greek is spoken by about 13 million people, mainly in Greece, Albania and Cyprus, but also worldwide by the large Greek diaspora. Greek is the language of Greece, where it is spoken by almost the entire population
Greek language
–
Idealized portrayal of
Homer
Greek language
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regions where Greek is the official language
Greek language
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Greek language road sign, A27 Motorway, Greece
13.
Pre-Socratic
–
Pre-Socratic philosophy is ancient Greek philosophy before Socrates and schools contemporary to Socrates that were not influenced by him. In Classical antiquity, the Presocratic philosophers were called physiologoi, Aristotle called them physikoi because they sought natural explanations for phenomena, as opposed to the earlier theologoi, whose philosophical basis was supernatural. Diogenes Laërtius divides the physiologoi into two groups, Ionian, led by Anaximander, and the Italiote, led by Pythagoras, hermann Diels popularized the term pre-socratic in Die Fragmente der Vorsokratiker in 1903. However, the term pre-Sokratic was in use as early as George Grotes Plato, edouard Zeller was also important in dividing thought before and after Socrates. Major analyses of pre-Socratic thought have been made by Gregory Vlastos, Jonathan Barnes and it may sometimes be difficult to determine the actual line of argument some Presocratics used in supporting their particular views. While most of them produced significant texts, none of the texts has survived in complete form, all that is available are quotations by later philosophers and historians, and the occasional textual fragment. The Presocratic philosophers rejected traditional mythological explanations of the phenomena they saw them in favor of more rational explanations. These philosophers asked questions about the essence of things, From where does everything come, how do we explain the plurality of things found in nature. How might we describe nature mathematically, others concentrated on defining problems and paradoxes that became the basis for later mathematical, scientific and philosophic study. Later philosophers rejected many of the answers the early Greek philosophers provided, furthermore, the cosmologies proposed by them have been updated by later developments in science. Western philosophy began in ancient Greece in the 6th century BCE, the Presocratics were mostly from the eastern or western fringes of the Greek world. Their efforts were directed to the investigation of the ultimate basis and they sought the material principle of things, and the method of their origin and disappearance. As the first philosophers, they emphasized the unity of things. Only fragments of the writings of the presocratics survive. The knowledge we have of them derives from accounts - known as doxography - of later philosophical writers, the first Presocratic philosophers were from Miletus on the western coast of Anatolia. Thales is reputedly the father of Greek philosophy, he declared water to be the basis of all things, next came Anaximander, the first writer on philosophy. He assumed as the first principle an undefined, unlimited substance without qualities, out of which the primary opposites, hot and cold, moist and dry, became differentiated. His younger contemporary, Anaximenes, took for his air, conceiving it as modified, by thickening and thinning, into fire, wind, clouds, water
Pre-Socratic
–
History of
Western philosophy
14.
Philosopher
–
A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside of either theology or science. The term philosopher comes from the Ancient Greek φιλόσοφος meaning lover of wisdom, the coining of the term has been attributed to the Greek thinker Pythagoras. Typically, these brands of philosophy are Hellenistic ones and those who most arduously commit themselves to this lifestyle may be considered philosophers. The separation of philosophy and science from theology began in Greece during the 6th century BC, thales, an astronomer and mathematician, was considered by Aristotle to be the first philosopher of the Greek tradition. While Pythagoras coined the word, the first known elaboration on the topic was conducted by Plato, in his Symposium, he concludes that Love is that which lacks the object it seeks. Therefore, the philosopher is one who seeks wisdom, if he attains wisdom, therefore, the philosopher in antiquity was one who lives in the constant pursuit of wisdom, and living in accordance to that wisdom. Disagreements arose as to what living philosophically entailed and these disagreements gave rise to different Hellenistic schools of philosophy. In consequence, the ancient philosopher thought in a tradition, as the ancient world became schism by philosophical debate, the competition lay in living in manner that would transform his whole way of living in the world. Philosophy is a discipline which can easily carry away the individual in analyzing the universe. The second is the change through the Medieval era. With the rise of Christianity, the way of life was adopted by its theology. Thus, philosophy was divided between a way of life and the conceptual, logical, physical and metaphysical materials to justify that way of life, philosophy was then the servant to theology. The third is the sociological need with the development of the university, the modern university requires professionals to teach. Maintaining itself requires teaching future professionals to replace the current faculty, therefore, the discipline degrades into a technical language reserved for specialists, completely eschewing its original conception as a way of life. In the fourth century, the word began to designate a man or woman who led a monastic life. Gregory of Nyssa, for example, describes how his sister Macrina persuaded their mother to forsake the distractions of life for a life of philosophy. Later during the Middle Ages, persons who engaged with alchemy was called a philosopher - thus, many philosophers still emerged from the Classical tradition, as saw their philosophy as a way of life. Among the most notable are René Descartes, Baruch Spinoza, Nicolas Malebranche, with the rise of the university, the modern conception of philosophy became more prominent
Philosopher
–
The School of Athens, by
Raphael, depicting the central figures of
Plato and
Aristotle, and other ancient philosophers exchanging their knowledge.
15.
Magna Graecia
–
The settlers who began arriving in the 8th century BC brought with them their Hellenic civilization, which was to leave a lasting imprint in Italy, such as in the culture of ancient Rome. Most notably the Roman poet Ovid referred to the south of Italy as Magna Graecia in his poem Fasti, according to Strabo, Magna Graecias colonization started already at the time of the Trojan War and lasted for several centuries. Also during that period, Greek colonies were established in places as widely separated as the eastern coast of the Black Sea, Eastern Libya and they included settlements in Sicily and the southern part of the Italian Peninsula. The Romans called the area of Sicily and the foot of Italy Magna Graecia since it was so densely inhabited by the Greeks, the ancient geographers differed on whether the term included Sicily or merely Apulia and Calabria, Strabo being the most prominent advocate of the wider definitions. With colonization, Greek culture was exported to Italy, in its dialects of the Ancient Greek language, its religious rites, an original Hellenic civilization soon developed, later interacting with the native Italic civilisations. Many of the new Hellenic cities became very rich and powerful, like Neapolis, Syracuse, Acragas Paestum, other cities in Magna Graecia included Tarentum, Epizephyrian Locri, Rhegium, Croton, Thurii, Elea, Nola, Ancona, Syessa, Bari and others. Following the Pyrrhic War in the 3rd century BC, Magna Graecia was absorbed into the Roman Republic, a remarkable example of the influence is the Griko-speaking minority that still exists today in the Italian regions of Calabria and Apulia. Griko is the name of a language combining ancient Doric, Byzantine Greek, there is a rich oral tradition and Griko folklore, limited now but once numerous, to around 30,000 people, most of them having become absorbed into the surrounding Italian element. Some scholars, such as Gerhard Rohlfs, argue that the origins of Griko may ultimately be traced to the colonies of Magna Graecia, one example is the Griko people, some of whom still maintain their Greek language and customs. For example, Greeks re-entered the region in the 16th and 17th century in reaction to the conquest of the Peloponnese by the Ottoman Empire, especially after the end of the Siege of Coron, large numbers of Greeks took refuge in the areas of Calabria, Salento and Sicily. Greeks from Coroni, the so-called Coronians, were nobles, who brought with them substantial movable property and they were granted special privileges and tax exemptions. Other Greeks who moved to Italy came from the Mani Peninsula of the Peloponnese, the Maniots were known for their proud military traditions and for their bloody vendettas, many of which still continue today. Another group of Maniot Greeks moved to Corsica, Ancient Greek dialects Greeks in Italy Italiotes Graia Graïke Graecus Griko people Griko language Hellenic civilization Names of the Greeks Cerchiai L. Jannelli L. Longo F. The Greek Cities of Magna Graecia and Sicily, in Dictionary of Greek and Roman Geography. 21 June,2005,17,19 GMT18,19 UK, salentinian Peninsula, Greece and Greater Greece. Traditional Griko song performed by Ghetonia, traditional Griko song performed by amateur local group. Second Interdisciplinary Symposium on the Hellenic Heritage of Southern Italy, the Greeks in the West, genetic signatures of the Hellenic colonisation in southern Italy and Sicily
Magna Graecia
–
Cities of Magna Graecia and other Greek settlements in Italy (in red)
Magna Graecia
–
Northwestern
Magna Graecia
–
Greek temples of
Paestum,
Campania
Magna Graecia
–
Mosaic from
Caulonia,
Calabria
16.
Dialectic
–
The term dialectic is not synonymous with the term debate. While in theory debaters are not necessarily emotionally invested in their point of view, debates are won through a combination of persuading the opponent, proving ones argument correct, or proving the opponents argument incorrect. Debates do not necessarily require promptly identifying a clear winner or loser, however clear winners are determined by either a judge. The term dialectics is also not synonymous with the term rhetoric, concepts, like logos or rational appeal, pathos or emotional appeal, and ethos or ethical appeal, are intentionally used by rhetoricians to persuade an audience. Socrates favoured truth as the highest value, proposing that it could be discovered through reason and logic in discussion, ergo, Socrates valued rationality as the proper means for persuasion, the discovery of truth, and the determinant for ones actions. To Socrates, truth, not aretē, was the greater good, therefore, Socrates opposed the Sophists and their teaching of rhetoric as art and as emotional oratory requiring neither logic nor proof. Different forms of reasoning have emerged throughout history from the Indosphere. These forms include the Socratic method, Hindu, Buddhist, Medieval, Hegelian dialectics, Marxist, Talmudic, the purpose of the dialectic method of reasoning is resolution of disagreement through rational discussion, and, ultimately, the search for truth. One way to proceed—the Socratic method—is to show that a given hypothesis leads to a contradiction, thus, another dialectical resolution of disagreement is by denying a presupposition of the contending thesis and antithesis, thereby, proceeding to sublation to synthesis, a third thesis. Fichtean/Hegelian dialectics is based upon four concepts, Everything is transient and finite, gradual changes lead to crises, turning points when one force overcomes its opponent force. The concept of dialectic existed in the philosophy of Heraclitus of Ephesus, hence, the history of the dialectical method is the history of philosophy. In classical philosophy, dialectic is a form of reasoning based upon dialogue of arguments and counter-arguments, advocating propositions and counter-propositions. The outcome of such a dialectic might be the refutation of a relevant proposition, or of a synthesis, or a combination of the opposing assertions, or a qualitative improvement of the dialogue. Moreover, the term dialectic owes much of its prestige to its role in the philosophies of Socrates and Plato, Aristotle said that it was the pre-Socratic philosopher Zeno of Elea who invented dialectic, of which the dialogues of Plato are the examples of the Socratic dialectical method. According to Kant, however, the ancient Greeks used the word dialectic to signify the logic of false appearance or semblance, to the Ancients, it was nothing but the logic of illusion. In Platos dialogues and other Socratic dialogues, Socrates attempts to examine someones beliefs, at times even first principles or premises by which we all reason, Socrates typically argues by cross-examining his interlocutors claims and premises in order to draw out a contradiction or inconsistency among them. According to Plato, the detection of error amounts to finding the proof of the antithesis. However, important as this objective is, the aim of Socratic activity seems to be to improve the soul of his interlocutors
Dialectic
–
Hegel and
Hegelianism
17.
Bertrand Russell
–
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, writer, social critic, political activist and Nobel laureate. At various points in his life he considered himself a liberal, a socialist, and a pacifist and he was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom. In the early 20th century, Russell led the British revolt against idealism and he is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege, colleague G. E. Moore, and protégé Ludwig Wittgenstein. He is widely held to be one of the 20th centurys premier logicians, with A. N. Whitehead he wrote Principia Mathematica, an attempt to create a logical basis for mathematics. His philosophical essay On Denoting has been considered a paradigm of philosophy, Russell mostly was a prominent anti-war activist, he championed anti-imperialism. Occasionally, he advocated preventive nuclear war, before the opportunity provided by the monopoly is gone. He went to prison for his pacifism during World War I, in 1950 Russell was awarded the Nobel Prize in Literature in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought. Bertrand Russell was born on 18 May 1872 at Ravenscroft, Trellech, Monmouthshire and his parents, Viscount and Viscountess Amberley, were radical for their times. Lord Amberley consented to his wifes affair with their childrens tutor, both were early advocates of birth control at a time when this was considered scandalous. Lord Amberley was an atheist and his atheism was evident when he asked the philosopher John Stuart Mill to act as Russells secular godfather, Mill died the year after Russells birth, but his writings had a great effect on Russells life. His paternal grandfather, the Earl Russell, had asked twice by Queen Victoria to form a government. The Russells had been prominent in England for several centuries before this, coming to power, Lady Amberley was the daughter of Lord and Lady Stanley of Alderley. Russell often feared the ridicule of his grandmother, one of the campaigners for education of women. Russell had two siblings, brother Frank, and sister Rachel, in June 1874 Russells mother died of diphtheria, followed shortly by Rachels death. In January 1876, his father died of bronchitis following a period of depression. Frank and Bertrand were placed in the care of their staunchly Victorian paternal grandparents and his grandfather, former Prime Minister Earl Russell, died in 1878, and was remembered by Russell as a kindly old man in a wheelchair. His grandmother, the Countess Russell, was the dominant family figure for the rest of Russells childhood, the countess was from a Scottish Presbyterian family, and successfully petitioned the Court of Chancery to set aside a provision in Amberleys will requiring the children to be raised as agnostics. Her favourite Bible verse, Thou shalt not follow a multitude to do evil, the atmosphere at Pembroke Lodge was one of frequent prayer, emotional repression, and formality, Frank reacted to this with open rebellion, but the young Bertrand learned to hide his feelings
Bertrand Russell
–
Russell as a four year-old
Bertrand Russell
–
Bertrand Russell
Bertrand Russell
–
Childhood home,
Pembroke Lodge
Bertrand Russell
–
Russell in 1907
18.
Parmenides (dialogue)
–
Parmenides is one of the dialogues of Plato. It is widely considered to be one of the more, if not the most, challenging, the Parmenides purports to be an account of a meeting between the two great philosophers of the Eleatic school, Parmenides and Zeno of Elea, and a young Socrates. The heart of the opens with a challenge by Socrates to the elder and revered Parmenides. But this difficulty vanishes, says Socrates, if we are prepared to make the distinction between sensibles on one hand and Forms, in which sensibles participate, on the other, at this point, Parmenides takes over as Socrates interlocutor and dominates the remainder of the dialogue. After establishing that Socrates himself has made the distinction between Forms and sensibles, Parmenides asks him what sorts of Form he is prepared to recognize. Parmenides suggests that when he is older and more committed to philosophy, he will consider all the consequences of his theory, even regarding seemingly insignificant objects like hair and mud. For the remainder of the first part of the dialogue, Parmenides draws Socrates out on certain aspects of the Theory of Forms, if particular things come to partake of the Form of Beauty or Likeness or Largeness they thereby become beautiful or like or large. Parmenides presses Socrates on how precisely many particulars can participate in a single Form, on one hand, if the Form as a whole is present in each of its many instances, then it would as a whole be in numerically different places, and thus separate from itself. Socrates suggests that the Form might be like a day, Parmenides counters that this would be little different from a single sail covering a number of people, wherein different parts touch different individuals, consequently, the Form is many. But if this second Form of Largeness is also large, then there should be a third Form of Largeness over the large things, hence, instead of there being one Form in every case, we are confronted with an indefinite number. This Largeness regress is commonly known under the given to it by Aristotle. To the suggestion that each Form is a thought existing in a soul, thus maintaining the unity of the Form, thus we still have to explain the participation relation. Further, if things share in Forms which are no more than thoughts, then either things consist of thoughts and think, or else they are thoughts, Socrates now suggests that the Forms are patterns in nature of which the many instances are copies or likenesses. Parmenides argues that if the many instances are like the Forms, yet if things are like, then they come to be like by participating in Likeness, therefore Likeness is like the likeness in concrete things, and another regress is generated. Called the great difficulty by Parmenides, the theory of Forms arises as a consequence of the assertion of the existence of the Forms. Forms do not exist in our world but have their being with reference to one another in their own world, similarly, things of our world are related among themselves, but not to Forms. Just as Mastership has its being relative to Slavery, so mastership in our world has its being relative to slavery in our world, no terrestrial master is master of Slave itself, and no terrestrial master-slave relation has any relationship to the ideal Master-Slave relation. And so it is with knowledge, all our knowledge is such with respect to our world, not to the world of the Forms, while ideal Knowledge is knowledge of the things not of our world but of the world of the Forms
Parmenides (dialogue)
–
Plato from
The School of Athens by
Raphael, 1509
19.
Physics (Aristotle)
–
The Physics of Aristotle is one of the foundational books of Western science and philosophy. As Martin Heidegger once wrote, The Physics is a lecture in which he seeks to determine beings that arise on their own, τὰ φύσει ὄντα, with regard to their being. This book determines the warp and woof of the whole of Western thinking, even at that place where it, as modern thinking, but opposition is invariably comprised of a decisive, and often even perilous, dependence. Without Aristotles Physics there would have been no Galileo, bertrand Russell, however, says of Physics and On the Heavens that they were. extremely influential, and dominated science until the time of Galileo. The historian of philosophy, accordingly, must study them, in spite of the fact that hardly a sentence in either can be accepted in the light of modern science. The chief purpose of the work is to discover the principles and causes of change, or movement, or motion, the Physics is composed of eight books, which are further divided into chapters. In this article, books are referenced with Roman numerals, chapters with Arabic numerals, additionally, the Bekker numbers give the page and line numbers used in the Prussian Academy of Sciences edition of Aristotles works. Book I discusses the scientists approach to nature and the world of changing things, Topics include, remarks on method, a discussion of how some ancestors viewed nature, and the basic elements of change. Change elements include, a lack, which is overcome by its opposite, the 1966 monograph by Connell is a particularly good expansion and defense of the contents of this book. Aristotles approach to the world as summarized in chapter 1 is to start with the most general albeit vague aspects of the world before proceeding to specifics. This approach contrasts sharply with that of science, which starts with particulars before advancing to generalities. Chapter 2 begins his consideration of the first principles of motion by initiating a review of the opinions of previous thinkers, chapters 3 and 4 are among the most difficult in all of Aristotles works and involve subtle refutations of the thought of Parmenides, Melissus and Anaxagoras. In chapter 5, he continues his review of his predecessors, chapter 6 narrows down the number of principles to two or three. He presents his own account of the subject in chapter 7, Aristotles concept of matter is rather different from what we moderns might expect from the use of the word in modern mathematical science. Descartes axiomatically redefined the concept of matter in the Enlightenment to exclude any characteristics that would make it unsuitable for abstract, mathematical treatment, the matter is not specifically described, but consists of whatever remains in the change of substance from grass to horse. Matter in this understanding does not exist independently, but exists interdependently with form, Matter and form are analogical terms. It is helpful to conceive of the relationship of matter and form as very similar to that between parts and whole, parts existing separately do not remain parts, but become new wholes. Book II introduces the term nature as a source or cause of being moved, thus, those entities are natural which are capable of starting to move, e. g. growing, acquiring qualities, displacing themselves, and finally being born and dying
Physics (Aristotle)
–
Aristotelianism
20.
Classical Athens
–
Athenian democracy was established in 508 BC under Cleisthenes following the tyranny of Isagoras. This system remained remarkably stable, and with a few brief interruptions remained in place for 180 years, the peak of Athenian hegemony was achieved in the 440s to 430s BC, known as the Age of Pericles. The radical politician of aristocratic background, Cleisthenes, then took charge, the reforms of Cleisthenes replaced the traditional four Ionic tribes with ten new ones, named after legendary heroes of Greece and having no class basis, which acted as electorates. Each tribe was in divided into three trittyes, while each trittys had one or more demes —depending on their population—which became the basis of local government. The tribes each selected fifty members by lot for the Boule, the public opinion of voters could be influenced by the political satires written by the comic poets and performed in the city theaters. Most offices were filled by lot, although the ten strategoi were elected, prior to the rise of Athens, Sparta, a city-state with a militaristic culture, considered itself the leader of the Greeks, and enforced a hegemony. In 499 BC Athens sent troops to aid the Ionian Greeks of Asia Minor and this provoked two Persian invasions of Greece, both of which were repelled under the leadership of the soldier-statesmen Miltiades and Themistocles. In 490 the Athenians, led by Miltiades, prevented the first invasion of the Persians, guided by king Darius I, in 480 the Persians returned under a new ruler, Xerxes I. Simultaneously the Athenians led a naval battle off Artemisium. However, this action was not enough to discourage the Persian advance which soon marched through Boeotia, setting up Thebes as their base of operations. This forced the Athenians to evacuate Athens, which was taken by the Persians, subsequently the Athenians and their allies, led by Themistocles, defeated the Persian navy at sea in the Battle of Salamis. It is interesting to note that Xerxes had built himself a throne on the coast in order to see the Greeks defeated, spartas hegemony was passing to Athens, and it was Athens that took the war to Asia Minor. These victories enabled it to bring most of the Aegean and many parts of Greece together in the Delian League. He fostered arts and literature and gave to Athens a splendor which would never return throughout its history and he executed a large number of public works projects and improved the life of the citizens. Hence, he gave his name to the Athenian Golden Age, silver mined in Laurium in southeastern Attica contributed greatly to the prosperity of this Golden Age of Athens. During the time of the ascendancy of Ephialtes as leader of the democratic faction, the conflict marked the end of Athenian command of the sea. The war between Athens and the city-state Sparta ended with an Athenian defeat after Sparta started its own navy, Athenian democracy was briefly overthrown by the coup of 411, brought about because of its poor handling of the war, but it was quickly restored. The war ended with the defeat of Athens in 404
Classical Athens
–
Early
Athenian coin, 5th century BC.
British Museum.
Classical Athens
–
Delian League ("Athenian Empire") shown in yellow, Athenian territory shown in red, situation in 431 BC, before the
Peloponnesian War.
Classical Athens
–
The modern
National Academy in Athens, with Apollo and Athena on their columns, and Socrates and Plato seated in front.
Classical Athens
–
Map of the environs of Athens showing
Piraeus,
Phalerum, and the
Long Walls
21.
Socrates
–
Socrates was a classical Greek philosopher credited as one of the founders of Western philosophy. He is a figure known chiefly through the accounts of classical writers, especially the writings of his students Plato and Xenophon. Platos dialogues are among the most comprehensive accounts of Socrates to survive from antiquity, though it is unclear the degree to which Socrates himself is hidden behind his best disciple, nothing written by Socrates remains extant. As a result, information about him and his philosophies depends upon secondary sources, furthermore, close comparison between the contents of these sources reveals contradictions, thus creating concerns about the possibility of knowing in-depth the real Socrates. This issue is known as the Socratic problem, or the Socratic question, to understand Socrates and his thought, one must turn primarily to the works of Plato, whose dialogues are thought the most informative source about Socrates life and philosophy, and also Xenophon. These writings are the Sokratikoi logoi, or Socratic dialogues, which consist of reports of conversations apparently involving Socrates, as for discovering the real-life Socrates, the difficulty is that ancient sources are mostly philosophical or dramatic texts, apart from Xenophon. There are no straightforward histories, contemporary with Socrates, that dealt with his own time, a corollary of this is that sources that do mention Socrates do not necessarily claim to be historically accurate, and are often partisan. For instance, those who prosecuted and convicted Socrates have left no testament, historians therefore face the challenge of reconciling the various evidence from the extant texts in order to attempt an accurate and consistent account of Socrates life and work. The result of such an effort is not necessarily realistic, even if consistent, amid all the disagreement resulting from differences within sources, two factors emerge from all sources pertaining to Socrates. It would seem, therefore, that he was ugly, also, Xenophon, being an historian, is a more reliable witness to the historical Socrates. It is a matter of debate over which Socrates it is whom Plato is describing at any given point—the historical figure. As British philosopher Martin Cohen has put it, Plato, the idealist, offers an idol, a Saint, a prophet of the Sun-God, a teacher condemned for his teachings as a heretic. It is also clear from other writings and historical artefacts, that Socrates was not simply a character, nor an invention, the testimony of Xenophon and Aristotle, alongside some of Aristophanes work, is useful in fleshing out a perception of Socrates beyond Platos work. The problem with discerning Socrates philosophical views stems from the perception of contradictions in statements made by the Socrates in the different dialogues of Plato and these contradictions produce doubt as to the actual philosophical doctrines of Socrates, within his milieu and as recorded by other individuals. Aristotle, in his Magna Moralia, refers to Socrates in words which make it patent that the virtue is knowledge was held by Socrates. Within the Metaphysics, he states Socrates was occupied with the search for moral virtues, however, in The Clouds, Aristophanes portrays Socrates as accepting payment for teaching and running a sophist school with Chaerephon. Also, in Platos Apology and Symposium, as well as in Xenophons accounts, more specifically, in the Apology, Socrates cites his poverty as proof that he is not a teacher. Two fragments are extant of the writings by Timon of Phlius pertaining to Socrates, although Timon is known to have written to ridicule, details about the life of Socrates can be derived from three contemporary sources, the dialogues of Plato and Xenophon, and the plays of Aristophanes
Socrates
–
A bust of Socrates in the Louvre
Socrates
–
Socrates Tears Alcibiades from the Embrace of Sensual Pleasure by
Jean-Baptiste Regnault (1791)
Socrates
–
Socrates and
Alcibiades, by
Christoffer Wilhelm Eckersberg
22.
Lives and Opinions of Eminent Philosophers
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Lives and Opinions of Eminent Philosophers is a biography of the Greek philosophers by Diogenes Laërtius, written in Greek, perhaps in the first half of the third century AD. The Lives and Opinions of Eminent Philosophers was written in Greek and professes to give an account of the lives, the work doesnt have an exact title in the manuscripts and appears in various lengthy forms. Laërtius treats his subject in two divisions which he describes as the Ionian and the Italian schools, the biographies of the former begin with Anaximander, and end with Clitomachus, Theophrastus and Chrysippus, the latter begins with Pythagoras, and ends with Epicurus. The Socratic school, with its various branches, is classed with the Ionic and he also includes his own poetic verse, albeit pedestrian, about the philosophers he discusses. The work contains incidental remarks on many other philosophers, and there are useful accounts concerning Hegesias, Anniceris, and Theodorus, Persaeus, Book VII is incomplete and breaks off during the life of Chrysippus. The whole of Book X is devoted to Epicurus, and contains three letters written by Epicurus, which explain Epicurean doctrines. The three most useful manuscripts are known as B, P, and F, manuscript B dates from the 12th century, and is in the National Library of Naples. Manuscript P is dated to the 11th/12th century, and is in the Bibliothèque nationale de France, manuscript F is dated to the 13th century, and is in the Laurentian Library. There seem to have some early Latin translations, which have no longer survived. A 10th-century work entitled Tractatus de dictis philosophorum shows some knowledge of Diogenes, the first printed editions were Latin translations. The first, Laertii Diogenis Vitae et sententiae eorum qui in philosophia probati fuerunt, the Greek text of the lives of Aristotle and Theophrastus appeared in the third volume of the Aldine Aristotle in 1497. The first edition of the whole Greek text was published by Hieronymus Froben in 1533. The Greek/Latin edition of 1692 by Marcus Meibomius divided each of the ten books into paragraphs of equal length, the first critical edition of the entire text, by H. S. Long in the Oxford Classical Texts, was not produced until 1964, a new edition, by Tiziano Dorandi, was published by Cambridge University Press in 2013. There have been three English translations of the complete Lives, the first was a late 17th-century translation by ten different persons. A better translation was made by Charles Duke Yonge, but although this was more literal, the translation by Robert Drew Hicks for the Loeb Classical Library, remains the best translation, although it is slightly bowdlerized. Lives of the Sophists Mochus Dorandi, Tiziano, ed. Introduction, Diogenes Laertius, Lives of Eminent Philosophers. The lives, opinions, and remarkable sayings of the most famous ancient philosophers, the first volume written in Greek, by Diogenes Laertius, made English by several hands
Lives and Opinions of Eminent Philosophers
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Dionysiou monastery, codex 90, a 13th-century manuscript containing selections from
Herodotus,
Plutarch and (shown here) Diogenes Laertius
Lives and Opinions of Eminent Philosophers
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Title page of an edition in Greek and Latin, 1594
23.
Valerius Maximus
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Valerius Maximus was a Latin writer and author of a collection of historical anecdotes. He worked during the reign of Tiberius, nothing is known of his life except that his family was poor and undistinguished, and that he owed everything to Sextus Pompeius, proconsul of Asia, whom he accompanied to the East in 27. Pompeius was the center of a circle to which Ovid belonged, he was also an intimate friend of the most literary prince of the imperial family. His attitude towards the imperial household has often been misunderstood, but, if the references to the imperial administration are carefully scanned, they will be seen to be extravagant neither in kind nor in number. Few will now grudge Tiberius, when his whole action as a ruler is taken into account, such a title as salutaris princeps, the few allusions to Caesars murderers and to Augustus hardly pass beyond the conventional style of the writers day. The only passage which can fairly be called fulsome is the violently rhetorical tirade against Sejanus, the style of Valeriuss writings seems to indicate that he was a professional rhetorician. According to the manuscripts, its title is Factorum ac dictorum memorabilium libri IX, Nine Books of Memorable Deeds, most of the tales are from Roman history, but each section has an appendix consisting of extracts from the annals of other peoples, principally the Greeks. The authors chief sources are Cicero, Livy, Sallust and Pompeius Trogus, and even on the historical side we owe something to Valerius. He often used sources now lost, and where he touches on his own time he affords us some glimpses of the much debated and he is also a typical example of Silver Latin, a literary period often criticised for poor writers. In Valerius are all the tendencies of the age. Direct and simple statement is avoided and novelty pursued at any price, in the manuscripts of Valerius a tenth book is given, which consists of the so-called Liber de Praenominibus, the work of some grammarian of a much later date. The collection of Valerius was much used for school purposes, like other schoolbooks it was epitomated. One complete epitome, probably of the 4th or 5th century, bearing the name of Julius Paris, has come down to us, kempf, contain the epitomes of Paris and Nepotianus. New editions have been produced by R. Combès with a French translation, J. Briscoe, shackleton Baily with an English translation. Recent discussions of Valerius work include W, a translation into Dutch was published in 1614, and was read by Rembrandt and other artists, stimulating interest in some new subjects such as Artemisia drinking her husbands ashes. Attribution This article incorporates text from a now in the public domain, Chisholm, Hugh. VALERI MAXIMI FACTORVM ET DICTORVM MEMORABILIVM LIBRI NOVEM at The Latin Library, his most famous work, Valerius Maximus and the Rhetoric of the New Nobility. University of North Carolina Press, Chapel Hill,1992, practical Ethics for Roman Gentlemen, the Work of Valerius Maximus
Valerius Maximus
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Page from an
incunable of Valerius Maximus, Facta et dicta memorabilia, printed in red and black by
Peter Schöffer (
Mainz, 1471)
Valerius Maximus
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Simon de Hesdin presents his translation of Valerius Maximus' 'Facta et dicta memorabilia' to Charles V, king of France
24.
Phalaris
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Phalaris was the tyrant of Akragas in Sicily, from approximately 570 to 554 BC. Phalaris was entrusted with the building of the temple of Zeus Atabyrius in the citadel, under his rule, Agrigentum seemed to have attained considerable prosperity. He supplied the city water, adorned it with fine buildings. On the northern coast of the island, the people of Himera elected him general with absolute power, according to the Suda he succeeded in making himself master of the whole of the island. He was at last overthrown in an uprising headed by Telemachus, the ancestor of Theron of Acragas. Phalaris was renowned for his excessive cruelty, among his alleged atrocities is cannibalism, he was said to have eaten suckling babies. Some scholars of the early 20th century proposed a connection between Phalaris bull and the bull-images of Phoenician cults, and hypothesized a continuation of Eastern human sacrifice practices and this idea has subsequently fallen out of favor. The story of the bull cannot be dismissed as pure invention, pindar, who lived less than a century afterwards, expressly associates this instrument of torture with the name of the tyrant. There was certainly a brazen bull at Agrigentum that was carried off by the Carthaginians to Carthage and this is said to have been later taken by Scipio the Elder and restored to Agrigentum circa 200 BC. Some four centuries after his death, Phalaris was the object of a literary reinvention whereby he came to be seen as a leader who was a patron of philosophy. This new reputation was due to 1) a paradoxical defence of his character attributed to Lucian, in 1699, Richard Bentley published a famous Dissertation on the Epistles of Phalaris in which he proved the spuriousness of the epistles. This article incorporates text from a now in the public domain, Chisholm, Hugh
Phalaris
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Phalaris condemning the sculptor Perillos to the
Bronze Bull
25.
Plutarch
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Plutarch was a Greek biographer and essayist, known primarily for his Parallel Lives and Moralia. He is classified as a Middle Platonist, Plutarchs surviving works were written in Greek, but intended for both Greek and Roman readers. Plutarch was born to a prominent family in the town of Chaeronea, about 80 km east of Delphi. The name of Plutarchs father has not been preserved, but based on the common Greek custom of repeating a name in alternate generations, the name of Plutarchs grandfather was Lamprias, as he attested in Moralia and in his Life of Antony. His brothers, Timon and Lamprias, are mentioned in his essays and dialogues. Rualdus, in his 1624 work Life of Plutarchus, recovered the name of Plutarchs wife, Timoxena, from internal evidence afforded by his writings. A letter is still extant, addressed by Plutarch to his wife, bidding her not to grieve too much at the death of their two-year-old daughter, interestingly, he hinted at a belief in reincarnation in that letter of consolation. The exact number of his sons is not certain, although two of them, Autobulus and the second Plutarch, are often mentioned. Plutarchs treatise De animae procreatione in Timaeo is dedicated to them, another person, Soklarus, is spoken of in terms which seem to imply that he was Plutarchs son, but this is nowhere definitely stated. Plutarch studied mathematics and philosophy at the Academy of Athens under Ammonius from 66 to 67, at some point, Plutarch took Roman citizenship. He lived most of his life at Chaeronea, and was initiated into the mysteries of the Greek god Apollo. For many years Plutarch served as one of the two priests at the temple of Apollo at Delphi, the site of the famous Delphic Oracle, twenty miles from his home. By his writings and lectures Plutarch became a celebrity in the Roman Empire, yet he continued to reside where he was born, at his country estate, guests from all over the empire congregated for serious conversation, presided over by Plutarch in his marble chair. Many of these dialogues were recorded and published, and the 78 essays, Plutarch held the office of archon in his native municipality, probably only an annual one which he likely served more than once. He busied himself with all the matters of the town. The Suda, a medieval Greek encyclopedia, states that Emperor Trajan made Plutarch procurator of Illyria, however, most historians consider this unlikely, since Illyria was not a procuratorial province, and Plutarch probably did not speak Illyrian. Plutarch spent the last thirty years of his serving as a priest in Delphi. He thus connected part of his work with the sanctuary of Apollo, the processes of oracle-giving
Plutarch
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Ruins of the Temple of
Apollo at
Delphi, where Plutarch served as one of the priests responsible for interpreting the predictions of the
oracle.
Plutarch
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Parallel Lives,
Amyot translation, 1565
Plutarch
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Plutarch's bust at
Chaeronea, his home town.
Plutarch
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A page from the 1470 Ulrich Han printing of Plutarch's
Parallel Lives.
26.
Simplicius of Cilicia
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Simplicius of Cilicia was a disciple of Ammonius Hermiae and Damascius, and was one of the last of the Neoplatonists. He was among the pagan philosophers persecuted by Justinian in the early 6th century and he wrote extensively on the works of Aristotle. His works have preserved much information about earlier philosophers which would have otherwise been lost, Simplicius was a disciple of Ammonius Hermiae, and Damascius, and was consequently one of the last members of the Neoplatonist school. The school had its headquarters in Athens and it became the centre of the last efforts to maintain Hellenistic religion against the encroachments of Christianity. Imperial edicts enacted in the 5th century against paganism gave legal protection to pagans against personal maltreatment, in the year 528 the emperor Justinian ordered that pagans should be removed from government posts. Some were robbed of their property, some put to death, the order specified that if they did not within three months convert to Christianity, they were to be banished from the Empire. In addition, it was any longer to teach philosophy. But they were disappointed in their hopes, chosroes, in a peace treaty concluded with Justinian c.533 stipulated that the philosophers should be allowed to return without risk and to practise their rites, after which they returned. Of the subsequent fortunes of the seven philosophers we learn nothing and we know little about where Simplicius lived and taught. That he not only wrote, but taught, is proved by the address to his hearers in the commentary on the Physica Auscultatio of Aristotle, as to his personal history, especially his migration to Persia, no definite allusions are to be found in the writings of Simplicius. The works which have survived are his commentaries upon Aristotles de Caelo, Physica Auscultatio, there is also a commentary on Aristotles de Anima under his name, but it is stylistically inferior and lacks the breadth of historical information usually used by Simplicius. It has been suggested that it was written by Priscian of Lydia, Simplicius wrote his commentary on the Physica Auscultatio after the death of Damascius, and therefore after his return from Persia. When it was that he wrote his explanations of the Categories, whether before or after those on the above-mentioned Aristotelian treatises, it is impossible to ascertain. Besides these commentaries of Simplicius which have preserved, the de Anima commentary mentions explanations on the metaphysical books. Simplicius, as a Neoplatonist, endeavoured to show that Aristotle agrees with Plato even on those points which he controverts, so that he may lead the way to their deeper, hidden meaning. In his view not only Plotinus, but also Syrianus, Proclus, and Ammonius, are great philosophers, many of the more ancient Greek philosophers he also brings into a connection with Platonism. His commentaries can, therefore, be regarded as the richest in their contents of any that have come down to us concerning Aristotle and it is true he himself complains that in his time both the school and the writings of the followers of Zeno had perished. But where he cannot draw immediately from the sources, he looks round for guides whom he can depend upon
Simplicius of Cilicia
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Commentary on Aristotle's De Caelo by Simplicius. This 14th-century manuscript is signed by a former owner,
Basilios Bessarion.
27.
Syllogism
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A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. In its earliest form, defined by Aristotle, from the combination of a statement and a specific statement. For example, knowing that all men are mortal and that Socrates is a man, Syllogistic arguments are usually represented in a three-line form, All men are mortal. In antiquity, two theories of the syllogism existed, Aristotelian syllogistic and Stoic syllogistic. Aristotle defines the syllogism as. a discourse in which certain things having been supposed, despite this very general definition, in Aristotles work Prior Analytics, he limits himself to categorical syllogisms that consist of three categorical propositions. From the Middle Ages onwards, categorical syllogism and syllogism were usually used interchangeably and this article is concerned only with this traditional use. The use of syllogisms as a tool for understanding can be dated back to the logical reasoning discussions of Aristotle, the onset of a New Logic, or logica nova, arose alongside the reappearance of Prior Analytics, the work in which Aristotle develops his theory of the syllogism. Prior Analytics, upon re-discovery, was regarded by logicians as a closed and complete body of doctrine, leaving very little for thinkers of the day to debate. Aristotles theories on the syllogism for assertoric sentences was considered especially remarkable, Aristotles Prior Analytics did not, however, incorporate such a comprehensive theory on the modal syllogism—a syllogism that has at least one modalized premise. Aristotles terminology in this aspect of his theory was deemed vague and in many cases unclear and his original assertions on this specific component of the theory were left up to a considerable amount of conversation, resulting in a wide array of solutions put forth by commentators of the day. The system for modal syllogisms laid forth by Aristotle would ultimately be deemed unfit for practical use, boethius contributed an effort to make the ancient Aristotelian logic more accessible. While his Latin translation of Prior Analytics went primarily unused before the twelfth century and his perspective on syllogisms can be found in other works as well, such as Logica Ingredientibus. With the help of Abelards distinction between de dicto modal sentences and de re modal sentences, medieval logicians began to shape a coherent concept of Aristotles modal syllogism model. For two hundred years after Buridans discussions, little was said about syllogistic logic, the Aristotelian syllogism dominated Western philosophical thought for many centuries. In the 17th century, Sir Francis Bacon rejected the idea of syllogism as being the best way to draw conclusions in nature. Instead, Bacon proposed a more inductive approach to the observation of nature, in the 19th century, modifications to syllogism were incorporated to deal with disjunctive and conditional statements. Kant famously claimed, in Logic, that logic was the one completed science, though there were alternative systems of logic such as Avicennian logic or Indian logic elsewhere, Kants opinion stood unchallenged in the West until 1879 when Frege published his Begriffsschrift. This introduced a calculus, a method of representing categorical statements by the use of quantifiers, in the last 20 years, Bolzanos work has resurfaced and become subject of both translation and contemporary study
Syllogism
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Relationships between the four types of propositions in the
square of opposition (Black areas are empty, red areas are nonempty.)
28.
Seneca the Younger
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Seneca the Younger, fully Lucius Annaeus Seneca and also known simply as Seneca, was a Roman Stoic philosopher, statesman, dramatist, and—in one work—humorist of the Silver Age of Latin literature. As a tragedian, he is best-known for his Medea and Thyestes and he was a tutor and later advisor to emperor Nero. He was forced to take his own life for alleged complicity in the Pisonian conspiracy to assassinate Nero, however, some sources state that he may have been innocent. His father was Seneca the Elder, his brother was Lucius Junius Gallio Annaeanus. Seneca was born in Cordoba in Hispania, and raised in Rome, griffin also infers from the ancient sources that Seneca was born in either 8,4, or 1 BC. She thinks he was born between 4 and 1 BC and was a resident in Rome by AD5, Seneca says that he was carried to Rome in the arms of his mothers stepsister. Griffin says that, allowing for rhetorical exaggeration, means it is fair to conclude that Seneca was in Rome as a small boy. Be that as it may, it is clear that he was in Rome at an early stage in his life. Caligula and Fabius were critics of his works, and Columella, Pliny, Tacitus, from AD54 to 62, Seneca acted as Neros advisor, together with the praetorian prefect Sextus Afranius Burrus. One byproduct of his influence was that Seneca was appointed consul in 56. Senecas influence was said to have especially strong in the first year. Tacitus and Dio suggest that Neros early rule, during which time he listened to Seneca, however, the ancient sources suggest, over time, Seneca and Burrus lost their influence over the emperor. In 59 they had agreed to Agrippinas murder, and afterward. This may have contributed as well to his own downfall, following Burrus death in 62, Seneca became the subject of criticism by what Tacitus describes as Neros more disreputable advisers. Charges included allegations of excessive wealth, the grandeur of his property, Seneca requested an audience with Nero in which he sought permission to retire from public duties, pleading age and infirmity. The two then parted on apparently warm terms, Seneca subsequently adopted a quiet lifestyle on his country estates, concentrating on his studies and seldom visiting Rome. In AD65, Seneca was caught up in the aftermath of the Pisonian conspiracy, although it is unlikely that Seneca conspired, Nero ordered him to kill himself. Seneca followed tradition by severing several veins in order to bleed to death, a generation after the Julio-Claudian emperors, Tacitus wrote an account of the suicide, which in view of his Republican sympathies is perhaps somewhat romanticized
Seneca the Younger
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Ancient bust of Seneca, part of the
Double Herm of Socrates and Seneca (
Antikensammlung Berlin)
Seneca the Younger
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This Baroque marble imaginary portrait bust of Seneca, by an anonymous sculptor of the 17th century (
Museo del Prado).
Seneca the Younger
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Manuel Domínguez Sánchez, The suicide of Seneca (1871),
Museo del Prado
Seneca the Younger
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Plato, Seneca, and
Aristotle in a medieval manuscript illustration (c. 1325–35)
29.
Infinity
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Infinity is an abstract concept describing something without any bound or larger than any number. In mathematics, infinity is treated as a number but it is not the same sort of number as natural or real numbers. Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th, in the theory he developed, there are infinite sets of different sizes. For example, the set of integers is countably infinite, while the set of real numbers is uncountable. Ancient cultures had various ideas about the nature of infinity, the ancient Indians and Greeks did not define infinity in precise formalism as does modern mathematics, and instead approached infinity as a philosophical concept. The earliest recorded idea of infinity comes from Anaximander, a pre-Socratic Greek philosopher who lived in Miletus and he used the word apeiron which means infinite or limitless. However, the earliest attestable accounts of mathematical infinity come from Zeno of Elea, aristotle called him the inventor of the dialectic. He is best known for his paradoxes, described by Bertrand Russell as immeasurably subtle, however, recent readings of the Archimedes Palimpsest have found that Archimedes had an understanding about actual infinite quantities. The Jain mathematical text Surya Prajnapti classifies all numbers into three sets, enumerable, innumerable, and infinite, on both physical and ontological grounds, a distinction was made between asaṃkhyāta and ananta, between rigidly bounded and loosely bounded infinities. European mathematicians started using numbers in a systematic fashion in the 17th century. John Wallis first used the notation ∞ for such a number, euler used the notation i for an infinite number, and exploited it by applying the binomial formula to the i th power, and infinite products of i factors. In 1699 Isaac Newton wrote about equations with an number of terms in his work De analysi per aequationes numero terminorum infinitas. The infinity symbol ∞ is a symbol representing the concept of infinity. The symbol is encoded in Unicode at U+221E ∞ infinity and in LaTeX as \infty and it was introduced in 1655 by John Wallis, and, since its introduction, has also been used outside mathematics in modern mysticism and literary symbology. Leibniz, one of the co-inventors of infinitesimal calculus, speculated widely about infinite numbers, in real analysis, the symbol ∞, called infinity, is used to denote an unbounded limit. X → ∞ means that x grows without bound, and x → − ∞ means the value of x is decreasing without bound. ∑ i =0 ∞ f = ∞ means that the sum of the series diverges in the specific sense that the partial sums grow without bound. Infinity can be used not only to define a limit but as a value in the real number system
Infinity
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Infinity represented in
screenshot form
30.
William Smith (lexicographer)
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Sir William Smith was an English lexicographer. Smith was born in Enfield in 1813 of Nonconformist parents and he attended the Madras House school of John Allen in Hackney. Originally destined for a career, he instead was articled to a solicitor. In his spare time he taught classics, and when he entered University College London he carried off both the Greek and Latin prizes. He was entered at Grays Inn in 1830, but gave up his studies for a post at University College School. Smith next turned his attention to lexicography and his first attempt was A Dictionary of Greek and Roman Antiquities, which appeared in 1842, the greater part being written by him. Then followed the Dictionary of Greek and Roman Biography and Mythology in 1849, a parallel Dictionary of Greek and Roman Geography appeared in 1857, with some leading scholars of the day associated with the task. In 1867, he became editor of the Quarterly Review, a post he held until his death. Meanwhile, he published the first of several school dictionaries in 1850, and in 1853 he began the Principia series, then came the Students Manuals of History and Literature, of which the English literature volume went into 13 editions. He himself wrote the Greek history volume and he was joined in the venture by the publisher John Murray when the original publishing partner met difficulties. Murray was the publisher of the 1214-page Latin–English Dictionary based upon the works of Forcellini and this was periodically reissued over the next thirty-five years. It goes beyond classical Latin to include many entries not found in dictionaries of the period, including Lewis. Perhaps the most important of the books Smith edited were those that dealt with ecclesiastical subjects, the Atlas, on which Sir George Grove collaborated, appeared in 1875. From 1853 to 1869 Smith was classical examiner to the University of London and he sat on the Committee to inquire into questions of copyright, and was for several years registrar of the Royal Literary Fund. He edited Gibbon, with Guizots and Milmans notes, in 1854–1855, Dictionary of Greek and Roman biography and mythology Smith was created a DCL by Oxford and Dublin, and the honour of a knighthood was conferred on him in 1892. He died on 7 October 1893 in London and this article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. article name needed. Works by William Smith at Project Gutenberg Works by or about William Smith at Internet Archive Smith, a Short Biographical Dictionary of English Literature
William Smith (lexicographer)
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Sir William Smith.
Smith, William, ed. (1870). "Parmenides". Dictionary of Greek and Roman Biography and Mythology. p. 125.
Laërtius, Diogenes (1925). "Others: Zeno of Elea". Lives of the Eminent Philosophers. 2:9. Translated by Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.
