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Platonism
Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism has had a profound effect on Western thought. At the most fundamental level, Platonism 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 nomina ...
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Plato
Plato ( ; Greek language, Greek: , ; born  BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms. He influenced all the major areas of theoretical philosophy and practical philosophy, and was the founder of the Platonic Academy, a philosophical school in History of Athens, Athens where Plato taught the doctrines that would later become known as Platonism. Plato's most famous contribution is the theory of forms, theory of forms (or ideas), which aims to solve what is now known as the problem of universals. He was influenced by the pre-Socratic thinkers Pythagoras, Heraclitus, and Parmenides, although much of what is known about them is derived from Plato himself. Along with his teacher Socrates, and his student Aristotle, Plato is a central figure in the history of Western philosophy. Plato's complete ...
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Symposium (Plato)
The ''Symposium'' (, ''Symposion'') is a Socratic dialogue by Plato, dated . It depicts a friendly contest of extemporaneous speeches given by a group of notable Athenian men attending a Symposium, banquet. The men include the philosopher Socrates, the general and statesman Alcibiades, and the comic playwright Aristophanes. The Panegyric, panegyrics are to be given in praise of Eros, the god of love and sex. In the ''Symposium'', Eros is recognized both as erotic lover 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. The 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 effor ...
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Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ...
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Western Thought
Western philosophy refers to the philosophical thought, traditions and works of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" , "to love" and σοφία '' sophía'', "wisdom". History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology (the nature and origin of the universe), while rejecting unargued fables in place for argued theory, i.e., dogma superseded reason, albeit in a rudimentary form. They were specifically ...
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Platonic Realism
The Theory of Forms or Theory of Ideas, also known as Platonic idealism or Platonic realism, is a philosophical theory credited to the Classical Greek philosopher Plato. A major concept in metaphysics, the theory suggests that the physical world is not as real or true as Forms. According to this theory, Forms—conventionally capitalized and also commonly translated as Ideas—are the timeless, absolute, non-physical, and unchangeable essences of all things, which objects and matter in the physical world merely participate in, imitate, or resemble. In other words, Forms are various abstract ideals that exist even outside of human minds and that constitute the basis of reality. Thus, Plato's Theory of Forms is a type of philosophical realism, asserting that certain ideas are literally real, and a type of idealism, asserting that reality is fundamentally composed of ideas, or abstract objects. Plato describes these entities only through the characters (primarily Socrates) in h ...
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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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Theory Of Forms
The Theory of Forms or Theory of Ideas, also known as Platonic idealism or Platonic realism, is a philosophical theory credited to the Classical Greek philosopher Plato. A major concept in metaphysics, the theory suggests that the physical world is not as real or true as Forms. According to this theory, Forms—conventionally capitalized and also commonly translated as Ideas—are the timeless, absolute, non-physical, and unchangeable essences of all things, which objects and matter in the physical world merely participate in, imitate, or resemble. In other words, Forms are various abstract ideals that exist even outside of human minds and that constitute the basis of reality. Thus, Plato's Theory of Forms is a type of philosophical realism, asserting that certain ideas are literally real, and a type of idealism, asserting that reality is fundamentally composed of ideas, or abstract objects. Plato describes these entities only through the characters (primarily Socrates) in ...
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Abstract Object Theory
Abstract object theory (AOT) is a branch of metaphysics regarding abstract objects. Originally devised by metaphysician Edward Zalta in 1981, the theory was an expansion of mathematical Platonism. Overview ''Abstract Objects: An Introduction to Axiomatic Metaphysics'' (1983) is the title of a publication by Edward Zalta that outlines abstract object theory. AOT is a dual predication approach (also known as "dual copula strategy") to abstract objectsDale Jacquette, ''Meinongian Logic: The Semantics of Existence and Nonexistence'', Walter de Gruyter, 1996, p. 17. influenced by the contributions of Alexius Meinong and his student Ernst Mally. On Zalta's account, there are two modes of Predicate (mathematical logic), predication: some objects (the ordinary Abstract and concrete, concrete ones around us, like tables and chairs) ''exemplify'' properties, while others (abstract objects like numbers, and what others would call "nonexistent objects", like the Round square copula, round ...
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Form Of The Good
The Form of the Good, or more literally translated "the Idea of the Good" (), is a concept in the philosophy of Plato. In Plato's Theory of Forms, in which Forms are defined as perfect, eternal, and changeless concepts existing outside space and time, the Form of the Good is the mysterious highest Form and the source of all the other Forms. 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 conv ...
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Third Man Argument
''Parmenides'' () is one of the dialogues of Plato. It is widely considered to be one of the most challenging and enigmatic of Plato's dialogues. 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 occasion of the meeting was the reading by Zeno of his treatise defending Parmenidean monism against those partisans of plurality who asserted that Parmenides' supposition that there is a ''one'' gives rise to intolerable absurdities and contradictions. The dialogue is set during a supposed meeting between Parmenides and Zeno of Elea in Socrates' hometown of Athens. This dialogue is chronologically the earliest of all as Socrates is only nineteen years old here. It is also notable that he takes the position of the student here while Parmenides serves as the lecturer. Most scholars agree that the dialogue does not record historic conversations, and is most likely an in ...
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Sophist (dialogue)
The ''Sophist'' (; Henri Estienne (ed.), ''Platonis opera quae extant omnia'', Vol. 1, 1578p. 217) is a Platonic dialogue from the philosopher's late period, most likely written in 360 BC. In it the interlocutors, led by Eleatic Stranger employ the method of division in order to classify and define the sophist and describe his essential attributes and differentia vis a vis the philosopher and statesman. Like its sequel, the '' Statesman'', the dialogue is unusual in that Socrates is present but plays only a minor role. Instead, the Eleatic Stranger takes the lead in the discussion. Because Socrates is silent, it is difficult to attribute the views put forward by the Eleatic Stranger to Plato, beyond the difficulty inherent in taking any character to be an author's "mouthpiece". Background The main objective of the dialogue is to identify what a sophist is and how a sophist differs from a philosopher and statesman. Because each seems distinguished by a particular form of knowl ...
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Abstract Objects
In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classified as abstract objects, whereas plants, dogs, and planets are considered concrete objects. Philosophers have proposed several criteria to define this distinction: # ''Spatiotemporal existence'' – Abstract objects exist outside space-time, while concrete objects exist within space-time. # ''Causal influence'' – Concrete objects can cause and be affected by other entities (e.g., a rock breaking a window), whereas abstract objects (e.g., the number 2) lack causal powers and do not cause anything to happen in the physical world. # ''Metaphysical relation'' – In metaphysics, concrete objects are specific, individual things ( particulars), while abstract objects represent general concepts or categories ( universals). # ''Ontological domain ...
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