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Platonic Philosophy
Platonism is the philosophy of Plato and school of thought, philosophical systems closely derived from it, though contemporary platonists do not necessarily accept all of the doctrines of Plato. Platonism had a profound effect on Western thought. Platonism at least affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism." Philosophers who affirm the existence of abstract objects are sometimes called platonists; those who deny their existence are sometimes called nominalists. The terms "platonism" and "nominalism" have established senses in the history of philosophy, where they denote positions that have little to do with the modern notion of an abstract object. In this connection, it is essential to bear in mind that modern platonists (with a small 'p') need not accept any of the doctrines of Plato, just as modern nominalis ...
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Head Platon Glyptothek Munich 548
A head is the part of an organism which usually includes the ears, brain, forehead, cheeks, chin, eyes, nose, and mouth, each of which aid in various sensory functions such as sight, hearing, smell, and taste. Some very simple animals may not have a head, but many bilaterally symmetric forms do, regardless of size. Heads develop in animals by an evolutionary trend known as cephalization. In bilaterally symmetrical animals, nervous tissue concentrate at the anterior region, forming structures responsible for information processing. Through biological evolution, sense organs and feeding structures also concentrate into the anterior region; these collectively form the head. Human head The human head is an anatomical unit that consists of the skull, hyoid bone and cervical vertebrae. The term "skull" collectively denotes the mandible (lower jaw bone) and the cranium (upper portion of the skull that houses the brain). Sculptures of human heads are generally based ...
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Theory Of Forms
The theory of Forms or theory of Ideas is a philosophical theory, fuzzy concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggests that these Forms are the only objects of study that can provide knowledge. The theory itself is contested from within Plato's dialogues, and it is a general point of controversy in philosophy. Nonetheless, the theory is considered to be a classical solution to the problem of universals. The early Greek concept of form precedes attested philosophical usage and is represented by a number of words mainly having to do with vision, sight, an ...
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Form Of The Good
"Form of the Good", or more literally "the idea of the good" () is a concept in the philosophy of Plato. The definition of the Good is a perfect, eternal, and changeless Form, existing outside space and time. It is a Platonic ideal. Uses in ''The Republic'' The first references that are seen in ''The Republic'' to the Form of the Good are within the conversation between Glaucon and Socrates (454 c–d). When he is trying to answer such difficult questions pertaining to the definition of justice, Plato identifies that we should not "introduce every form of difference and sameness in nature" instead we must focus on "the one form of sameness and difference that was relevant to the particular ways of life themselves" which is the form of the Good. This form is the basis for understanding all other forms, it is what allows us to understand everything else. Through the conversation between Socrates and Glaucon (508 a–c), Plato analogizes the form of the Good with the sun as it i ...
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Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was ...
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Archetype
The concept of an archetype (; ) appears in areas relating to behavior, historical psychology, and literary analysis. An archetype can be any of the following: # a statement, pattern of behavior, prototype, "first" form, or a main model that other statements, patterns of behavior, and objects copy, emulate, or "merge" into. Informal synonyms frequently used for this definition include "standard example", "basic example", and the longer-form "archetypal example"; mathematical archetypes often appear as " canonical examples". # the Platonic concept of ''pure form'', believed to embody the fundamental characteristics of a thing. # a collectively-inherited unconscious idea, a pattern of thought, image, etc., that is universally present, in individual psyches, as in Jungian psychology # a constantly-recurring symbol or motif in literature, painting, or mythology. This definition refers to the recurrence of characters or ideas sharing similar traits throughout various, seemingly u ...
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Republic (Plato)
The ''Republic'' ( grc-gre, Πολῑτείᾱ, Politeia; ) is a Socratic dialogue, authored by Plato around 375 BCE, concerning justice (), the order and character of the just city-state, and the just man. It is Plato's best-known work, and one of the world's most influential works of philosophy and political theory, both intellectually and historically. In the dialogue, Socrates discusses the meaning of justice and whether the just man is happier than the unjust man with various Athenians and foreigners.In ancient times, the book was alternately titled ''On Justice'' (not to be confused with the spurious dialogue of the same name). They consider the natures of existing regimes and then propose a series of different, hypothetical cities in comparison, culminating in Kallipolis (Καλλίπολις), a utopian city-state ruled by a philosopher-king. They also discuss ageing, love, theory of forms, the immortality of the soul, and the role of the philosopher and of poe ...
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Symposium (Plato)
The ''Symposium'' ( grc, Συμπόσιον, ) is a philosophical text by Plato, dated . It depicts a friendly contest of extemporaneous speeches given by a group of notable men attending a banquet. The men include the philosopher Socrates, the general and political figure Alcibiades, and the comic playwright Aristophanes. The speeches are to be given in praise of Eros, the god of love and desire. In the ''Symposium'', Eros is recognized both as erotic love and as a phenomenon capable of inspiring courage, valor, great deeds and works, and vanquishing man's natural fear of death. It is seen as transcending its earthly origins and attaining spiritual heights. This extraordinary elevation of the concept of love raises a question of whether some of the most extreme extents of meaning might be intended as humor or farce. ''Eros'' is almost always translated as "love", and the English word has its own varieties and ambiguities that provide additional challenges to the effort to unde ...
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Phaedo
''Phædo'' or ''Phaedo'' (; el, Φαίδων, ''Phaidōn'' ), also known to ancient readers as ''On The Soul'', is one of the best-known dialogues of Plato's middle period, along with the '' Republic'' and the '' Symposium.'' The philosophical subject of the dialogue is the immortality of the soul. It is set in the last hours prior to the death of Socrates, and is Plato's fourth and last dialogue to detail the philosopher's final days, following '' Euthyphro'', '' Apology'', and ''Crito''. One of the main themes in the ''Phaedo'' is the idea that the soul is immortal. In the dialogue, Socrates discusses the nature of the afterlife on his last day before being executed by drinking hemlock. Socrates has been imprisoned and sentenced to death by an Athenian jury for not believing in the gods of the state (though some scholars think it was more for his support of " philosopher kings" as opposed to democracy) and for corrupting the youth of the city. By engaging in dialectic ...
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Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher 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, the West in general. Knowledge of his life is clouded by legend, but he appears to have been the son of Mnesarchus, a gem-engraver on the island of Samos. Modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded a school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. This lifestyle entailed a number of dietary prohibitions, traditionally said to have included vegetarianism, although modern scholars doubt that he ever advocated complete vegetarianism. The t ...
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Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geome ...
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Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ...
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