The Divided Line
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The Divided Line
The analogy of the divided line ( grc-gre, γραμμὴ δίχα τετμημένη, grammē dicha tetmēmenē) is presented by the Greek philosopher Plato in the ''Republic'' (509d–511e). It is written as a dialogue between Glaucon and Socrates, in which the latter further elaborates upon the immediately preceding analogy of the sun at the former's request. Socrates asks Glaucon to not only envision this unequally bisected line but to imagine further bisecting each of the two segments. Socrates explains that the four resulting segments represent four separate 'affections' (παθήματα) of the psyche. The lower two sections are said to represent the visible while the higher two are said to represent the intelligible. These affections are described in succession as corresponding to increasing levels of reality and truth from conjecture ( εἰκασία) to belief ( πίστις) to thought ( διάνοια) and finally to understanding ( νόησις). Furthermore, this a ...
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Ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of culturally and linguistically related city-states and other territories. Most of these regions were officially unified only once, for 13 years, under Alexander the Great's empire from 336 to 323 BC (though this excludes a number of Greek city-states free from Alexander's jurisdiction in the western Mediterranean, around the Black Sea, Cyprus, and Cyrenaica). In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Roughly three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Classical G ...
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Belief
A belief is an attitude that something is the case, or that some proposition is true. In epistemology, philosophers use the term "belief" to refer to attitudes about the world which can be either true or false. To believe something is to take it to be true; for instance, to believe that snow is white is comparable to accepting the truth of the proposition "snow is white". However, holding a belief does not require active introspection. For example, few carefully consider whether or not the sun will rise tomorrow, simply assuming that it will. Moreover, beliefs need not be ''occurrent'' (e.g. a person actively thinking "snow is white"), but can instead be ''dispositional'' (e.g. a person who if asked about the color of snow would assert "snow is white"). There are various different ways that contemporary philosophers have tried to describe beliefs, including as representations of ways that the world could be (Jerry Fodor), as dispositions to act as if certain things are true (Rod ...
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Protagoras
Protagoras (; el, Πρωταγόρας; )Guthrie, p. 262–263. was a pre-Socratic Greek philosopher and rhetorical theorist. He is numbered as one of the sophists by Plato. In his dialogue '' Protagoras'', Plato credits him with inventing the role of the professional sophist. Protagoras also is believed to have created a major controversy during ancient times through his statement that, "Man is the measure of all things," interpreted (possibly wrongly, since he disagreed) by Plato to mean that there is no objective truth; Protagoras seems to have meant that each person's own personal history, experiences and expectations, developed over their lifetime, determine their judgments, opinions, and statements regarding "truth" (which is the title of the book in which Protagoras made this statement). When a person makes a judgment about a certain thing—good or bad or beautiful or unjust—that person will differ from other people's judgments because their experience has been differen ...
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Heraclitus
Heraclitus of Ephesus (; grc-gre, Ἡράκλειτος , "Glory of Hera"; ) was an ancient Greek pre-Socratic philosopher from the city of Ephesus, which was then part of the Persian Empire. Little is known of Heraclitus's life. He wrote a single work, only fragments of which have survived. Most of the ancient stories about him are later said to be fabrications based on interpretations of the preserved fragments. His paradoxical philosophy and appreciation for wordplay and cryptic utterances has earned him the epithet "the obscure" since antiquity. He was considered a misanthrope who was subject to melancholia. Consequently, he became known as "the weeping philosopher" in contrast to the ancient philosopher Democritus, who was known as "the laughing philosopher". The central idea of Heraclitus' philosophy is the unity of opposites. One of his most notable applications of this idea was to the concept of impermanence; he saw the world as constantly in flux, changing as it ...
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Dialectic
Dialectic ( grc-gre, διαλεκτική, ''dialektikḗ''; related to dialogue; german: Dialektik), also known as the dialectical method, is a discourse between two or more people holding different points of view about a subject but wishing to establish the truth through reasoned argumentation. Dialectic resembles debate, but the concept excludes subjective elements such as emotional appeal and the modern pejorative sense of rhetoric. Dialectic may thus be contrasted with both the eristic, which refers to argument that aims to successfully dispute another's argument (rather than searching for truth), and the didactic method, wherein one side of the conversation teaches the other. Dialectic is alternatively known as ''minor logic'', as opposed to ''major logic'' or critique. Within Hegelianism, the word ''dialectic'' has the specialised meaning of a contradiction between ideas that serves as the determining factor in their relationship. Dialectical materialism, a theory ...
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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 is ...
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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, and ap ...
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Noetics
In philosophy, noetics is a purposed branch of metaphysics concerned with the study of mind as well as intellect. There is also a reference to the science of noetics, which covers the field of thinking and knowing, thought and knowledge, as well as mental operations, processes, states, and products through the data of the written word. Philosophy The term itself means “the proper exercise of nous” whereas ''nous'' (“mind, understanding, intellect”) is described as “the highest faculty in man, through which - provided it is purified - he knows God or the inner essences or principles of created things through direct apprehension or spiritual perception”. In ancient Greek and medieval philosophy, noetic topics included the doctrine of the active intellect (Aristotle, Averroes) and the doctrine of the Divine Intellect (Plotinus). The entire philosophy of noetics, which include the notions by Immanuel Kant, John Locke, René Descartes, Georg Wilhelm Friedrich Hegel, and Je ...
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Line (geometry)
In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment in everyday life, which has two points to denote its ends. Lines can be referred by two points that lay on it (e.g., \overleftrightarrow) or by a single letter (e.g., \ell). Euclid described a line as "breadthless length" which "lies evenly with respect to the points on itself"; he introduced several postulates as basic unprovable properties from which he constructed all of geometry, which is now called Euclidean geometry to avoid confusion with other geometries which have been introduced since the end of the 19th century (such as non-Euclidean, projective and affine geometry). In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic ...
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