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In The Republic (509d–510a), Socrates describes the divided line to Glaucon this way: . Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, [1] and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness ...
Diairesis is Plato's later method of definition based on division, developed in the Platonic dialogues Phaedrus, Sophist, Statesman, and Philebus. Further applications are found in the Laws [2] and Timaeus. It is a means of attempting to reach a definition by which a collection of candidates is repeatedly divided into two parts with one part ...
Various scholars also debate the possibility of a connection between the work in the allegory and the cave and the work done by Plato considering the analogy of the divided line and the analogy of the Sun. The divided line is a theory presented to us in Plato's work the Republic. This is displayed through a dialogue given between Socrates and ...
Platonic division may refer to: The Analogy of the Divided Line, Plato's schematic representation of all possible metaphysics, epistemology, and ethics on four hierarchical levels in the Republic, Book 6; Plato's tripartite theory of soul, Plato's partitioned organization of the Soul as presented in the Phaedo and the Republic
The red line is tangential to the curve at the point marked by a red dot. In a sense, [a] all lines in Euclidean geometry are equal, in that, without coordinates, one can not tell them apart from one another. However, lines may play special roles with respect to other objects in the geometry and be divided into types according to that relationship.
External Link (Psychology, Philosophy, and Plato's Divided Line) [ edit ] I previously added a link to this paper, which seems clearly relevant, and all-the-more helpful to users because it supplies (1) the complete text of the Divided Line (including the often-neglected section in Book 7 of the Republic), and (2) perhaps the most extensive ...
Meno 's theme is also dealt with in the dialogue Protagoras, where Plato ultimately has Socrates arrive at the opposite conclusion: virtue can be taught. Likewise, while in Protagoras knowledge is uncompromisingly this-worldly, in Meno the theory of recollection points to a link between knowledge and eternal truths.
Plato (c. 428–348 BC), the founder of the Platonic Academy, mentions mathematics in several of his dialogues. [22] While not considered a mathematician, Plato seems to have been influenced by Pythagorean ideas about number and believed that the elements of matter could be broken down into geometric solids. [23]