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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 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 nominalists need not acce ...
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Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution of higher learning on the European continent. Along with his teacher, Socrates, and his student, Aristotle, Plato is a central figure in the history of Ancient Greek philosophy and the Western and Middle Eastern philosophies descended from it. He has also shaped religion and spirituality. The so-called neoplatonism of his interpreter Plotinus greatly influenced both Christianity (through Church Fathers such as Augustine) and Islamic philosophy (through e.g. Al-Farabi). In modern times, Friedrich Nietzsche diagnosed Western culture as growing in the shadow of Plato (famously calling Christianity "Platonism for the masses"), while Alfred North Whitehead famously said: "the safest general characterization of the European philosophical tra ...
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Platonic Realism
Platonic realism is the philosophical position that universals or abstract objects exist objectively and outside of human minds. It is named after the Greek philosopher Plato who applied realism to such universals, which he considered ideal forms. This stance is ambiguously also called Platonic idealism but should not be confused with idealism as presented by philosophers such as George Berkeley: as Platonic abstractions are not spatial, temporal, or mental, they are not compatible with the later idealism's emphasis on mental existence. Plato's Forms include numbers and geometrical figures, making them a theory of mathematical realism; they also include the Form of the Good, making them in addition a theory of ethical realism. Plato expounded his own articulation of realism regarding the existence of universals in his dialogue '' The Republic'' and elsewhere, notably in the ''Phaedo'', the '' Phaedrus'', the ''Meno'' and the '' Parmenides''. Universals In Platonic rea ...
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Western Thought
Western philosophy encompasses the philosophical thought and work 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" grc, φιλεῖν , "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 mythical answers to such questions. They were specifically interested in the (the cause or first principle) of the ...
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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 mathematical analysis, 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 mathematical object, abstract objects and the use of pure reason to proof (mathematics), prove them. These objects consist of either abstraction (mathematics), abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of inference rule, deductive rules to already established results. These results include previously proved theorems, axioms ...
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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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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 ...
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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 MeinongZalta (1983:xi). and his student Ernst Mally. On Zalta's account, there are two modes of predication: some objects (the ordinary concrete ones around us, like tables and chairs) ''exemplify'' properties, while others (abstract objects like numbers, and what others would call "non-existent objects", like the round square, and the mountain made entirely of gold) merely ...
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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. Arist ...
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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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Sophist (dialogue)
The ''Sophist'' ( el, Σοφιστής; la, Sophista 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 dist ...
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Abstract Objects
In metaphysics, the distinction between abstract and concrete refers to a divide between two types of entities. Many philosophers hold that this difference has fundamental metaphysical significance. Examples of concrete objects include plants, human beings and planets while things like numbers, sets and propositions are abstract objects. There is no general consensus as to what the characteristic marks of concreteness and abstractness are. Popular suggestions include defining the distinction in terms of the difference between (1) existence inside or outside space-time, (2) having causes and effects or not, (3) having contingent or necessary existence, (4) being particular or universal and (5) belonging to either the physical or the mental realm or to neither. Despite this diversity of views, there is broad agreement concerning most objects as to whether they are abstract or concrete. So under most interpretations, all these views would agree that, for example, plants are concrete ...
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Propositions
In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the non-linguistic bearer of truth or falsity which makes any sentence that expresses it either true or false. While the term "proposition" may sometimes be used in everyday language to refer to a linguistic statement which can be either true or false, the technical philosophical term, which differs from the mathematical usage, refers exclusively to the non-linguistic meaning behind the statement. The term is often used very broadly and can also refer to various related concepts, both in the history of philosophy and in contemporary analytic philosophy. It can generally be used to refer to some or all of the following: The primary bearers of truth values (such as "true" and "false"); the objects of belief and other propositional attitudes ...
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