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Neopythagorean
Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic and Roman philosophy which revived Pythagorean doctrines. Neopythagoreanism was influenced by middle Platonism and in turn influenced Neoplatonism. It originated in the 1st century BC and flourished during the 1st and 2nd centuries AD. The ''Encyclopædia Britannica'' Eleventh Edition describes Neopythagoreanism as "a link in the chain between the old and the new" within Hellenistic philosophy. Central to Neopythagorean thought was the concept of a soul and its inherent desire for a ''unio mystica'' with the divine. The word ''Neopythagoreanism'' is a modern (19th century) term, coined as a parallel of "Neoplatonism". History In the 1st century BC Cicero's friend Nigidius Figulus made an attempt to revive Pythagorean doctrines, but the most important members of the school were Apollonius of Tyana and Moderatus of Gades in the 1st century AD. Other important Neopythagoreans include the mathematician Nicomachu ...
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Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek colony of Crotone, Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia. Already during Pythagoras' life it is likely that the distinction between the ''akousmatikoi'' ("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the ''mathematikoi'' ("those who learn") existed. The ancient biographers of Pythagoras, Iamblichus () and his master Porphyry (philosopher), Porphyry ( ) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the Greco-Roman mysteries, mystery schools of antiquity, the adherents, ''akou ...
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Pythagoras
Pythagoras of Samos (;  BC) was an ancient Ionian Greek philosopher, polymath, and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy. Modern scholars disagree regarding Pythagoras's education and influences, but most agree that he travelled to Croton in southern Italy around 530 BC, where he founded a school in which initiates were allegedly sworn to secrecy and lived a communal, ascetic lifestyle. In antiquity, Pythagoras was credited with mathematical and scientific discoveries, such as the Pythagorean theorem, Pythagorean tuning, the five regular solids, the theory of proportions, the sphericity of the Earth, the identity of the morning and evening stars as the planet Venus, and the division of the globe into five climatic zones. He was reputedly the first man to call himself a philosopher ("lover of wi ...
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Nicomachus Of Gerasa
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'', which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education. Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the book, which suggests that he was a respected scholar ...
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Apollonius Of Tyana
Apollonius of Tyana (; ; ) was a Greek philosopher and religious leader from the town of Tyana, Cappadocia in Roman Anatolia, who spent his life travelling and teaching in the Middle East, North Africa and India. He is a central figure in Neopythagoreanism and was one of the most famous " miracle workers" of his day. His exceptional personality and his mystical way of life, which was regarded as exemplary, impressed his contemporaries and had a lasting cultural influence. Numerous legends surrounding him and accounts of his life are contained in the extensive ''Life of Apollonius''. Many of the ancient legends of Apollonius consist of numerous reports about miracles that he was said to have performed as a wandering sage with his lifelong companion Damis. He was tried for allegedly having used magic as a means of conspiring against the emperor; after his conviction and subsequent death-penalty, his followers believed he underwent heavenly ascension. Most modern scho ...
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Ancient Roman Philosophy
Ancient Roman philosophy is philosophy as it was practiced in the Roman Republic and its successor state, the Roman Empire. Roman philosophy includes not only philosophy written in Latin, but also philosophy written in Greek in the late Republic and Roman Empire. Important early Latin-language writers include Lucretius, Cicero, and Seneca the Younger. Greek was a popular language for writing about philosophy, so much so that the Roman Emperor Marcus Aurelius chose to write his ''Meditations'' in Greek. History Interest in philosophy was first shown at Rome in 155 BC, by an Athenian embassy consisting of the Academic skeptic Carneades, the Stoic Diogenes of Babylon, and the Peripatetic Critolaus. Roman philosophy was heavily influenced by Hellenistic philosophy; however, unique developments in philosophical schools of thought occurred during the Roman period as well, with many philosophers adapting teachings from more than one school. Both leading schools of law of the Roman p ...
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Neoplatonism
Neoplatonism is a version of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a series of thinkers. Among the common ideas it maintains is monism, the doctrine that all of reality can be derived from a single principle, "the One". Neoplatonism began with Ammonius Saccas and his student Plotinus (c.  204/5 – 271 AD) and stretched to the sixth century. After Plotinus there were three distinct periods in the history of neoplatonism: the work of his student Porphyry (third to early fourth century); that of Iamblichus (third to fourth century); and the period in the fifth and sixth centuries, when the academies in Alexandria and Athens flourished. Neoplatonism had an enduring influence on the subsequent history of Western philosophy and religion. In the Middle Ages, Neoplatonic ideas were studied and discussed by Christian, Jewish, and Muslim thinkers. ...
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Hellenistic Philosophy
Hellenistic philosophy is Ancient Greek philosophy corresponding to the Hellenistic period in Ancient Greece, from the death of Alexander the Great in 323 BC to the Battle of Actium in 31 BC. The dominant schools of this period were the Stoics, the Epicureans and the Academic Skepticism, Skeptics. Background The Preceding classical period in Ancient Greek philosophy had centered around Socrates (c. 470–399 BC), whose students Antisthenes, Aristippus, and Plato went on to found Cynicism (philosophy), Cynicism, Cyrenaicism, and Platonism, respectively. Plato taught Aristotle who created the Peripateticism, Peripatetic school and in turn, had tutored Alexander the Great. Socrates' thought was therefore influential for many of these schools of the period, leading them to focus on ethics and how to reach ''eudaimonia.'' Early Platonism, known as the "Old Academy" begins with Plato, followed by Speusippus (Plato's nephew), who succeeded him as the head of school (until 339  ...
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Numenius Of Apamea
Numenius of Apamea (, ''Noumēnios ho ex Apameias''; ) was a Greek philosopher, who lived in Rome, and flourished during the latter half of the 2nd century AD. He was a Neopythagorean and forerunner of the Neoplatonists. Philosophy Statements and fragments of his apparently very numerous works have been preserved by Origen, Theodoret, and especially by Eusebius, and from them we may learn the nature of his Platonist-Pythagorean philosophy, and its approximation to the doctrines of Plato. Numenius was a Neopythagorean, but his object was to trace the doctrines of Plato up to Pythagoras, and at the same time to show that they were not at variance with the dogmas and mysteries of the Brahmins, Jews, Magi and Egyptians. His intention was to restore the philosophy of Plato, the genuine Pythagorean and mediator between Socrates and Pythagoras in its original purity, cleared from the Aristotelian and Stoic doctrines, and purified from the unsatisfactory and perverse explanations, ...
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Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ...
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Moderatus Of Gades
Moderatus of Gades () was a Greek philosopher of the Neopythagorean school, who lived in the 1st century AD. He was a contemporary of Apollonius of Tyana. He wrote a great work on the doctrines of the Pythagoreans, and tried to show that the successors of Pythagoras had made no additions to the views of their founder, but had merely borrowed and altered the phraseology. Life Moderatus was from Gades, in Andalusia. He was probably a relative of the writer Columella (Lucius Junius Moderatus Columella), who shared the same cognomen and was also from Gades. Almost nothing is known about the life of Moderatus. The only concrete clue is provided by Plutarch, who reports that when he, Plutarch, returned to Rome after a long absence, Lucius, a disciple of Moderatus, who came from Etruria, was attending a banquet hosted by Sextius Sulla, a friend of Plutarch's. Since the banquet took place around 90 AD, it can be assumed that the teaching activity of Moderatus fell in the second half of t ...
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Nigidius Figulus
Publius Nigidius Figulus ( – 45 BC) was a scholar of the Late Roman Republic and one of the praetors for 58 BC. He was a friend of Cicero, to whom he gave his support at the time of the Catilinarian conspiracy. Nigidius sided with the Optimates in the civil war between Julius Caesar and Pompeius Magnus. Among his contemporaries, Nigidius's reputation for learning was second only to that of Varro. Even in his own time, his works were regarded as often abstruse, perhaps because of their esoteric Pythagoreanism, into which Nigidius incorporated Stoic elements. Jerome calls him ''Pythagoricus et magus'', a "Pythagorean and mage," and in the medieval and Renaissance tradition he is portrayed as a magician, diviner, or occultist. His vast works survive only in fragments preserved by other authors. Political career By 63 BC, Nigidius had been admitted to the Senate. He may have been aedile in 60 BC, when Cicero mentions that Nigidius was in a position to cite (''compellare'') a ...
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Monad (philosophy)
The term ''monad'' () is used in some cosmic philosophy and cosmogony to refer to a most basic or original substance. As originally conceived by the Pythagoreans, the Monad is therefore Supreme Being, divinity, or the totality of all things. According to some philosophers of the early modern period, most notably Gottfried Wilhelm Leibniz, there are infinite monads, which are the basic and immense forces, elementary particles, or simplest units, that make up the universe. Historical background According to Hippolytus, the worldview was inspired by the Pythagoreans, who called the first thing that came into existence the "monad", which begat (bore) the dyad (from the Greek word for two), which begat the numbers, which begat the point, begetting lines or finiteness, etc. It meant divinity, the first being, or the totality of all beings, referring in cosmogony (creation theories) variously to source acting alone and/or an indivisible origin and equivalent comparators. Py ...
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