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Encyclopedia > The divided line of Plato

Plato, in The Republic Book VI (509d-513e), uses the literary device of a divided line to teach his basic views about four levels of existence (especially "the intelligible" world of the forms, universals, and "the visible" world we see around us) and the corresponding ways we come to know what exists. Plato ( Greek: Πλάτων, Plátōn, wide, broad-shouldered) (c. ... The Republic is an influential dialogue by Plato, written in the first half of the 4th century BC. This Socratic dialogue mainly is about political philosophy and ethics. ... Universals (used as a noun) are either properties, relations, or types, but not classes. ...

The Divided Line
The Divided Line

Plato asks us to imagine a line divided into two parts. The larger part (segment CE) represents the intelligible world and the smaller (segment AC), the visible world. Then, he says, imagine each part of the line further divided. As it turns out, the divisions in the segment for the intelligible world represent higher (DE) and lower (CD) forms, respectively. Moreover, the divisions in the segment for the visible world represent ordinary visible objects (BC), on the one hand, and their shadows, reflections, and other representations (AB), on the other. The Divided Line--simple image, self-created File links The following pages link to this file: The divided line of Plato Categories: GFDL images ...


It is important to note that the line segments are said to be unequal: the proportions of their lengths is said to represent "their comparative clearness and obscurity" and their comparative "reality and truth," as well as whether we have knowledge or instead mere opinion of the objects. It can be shown with simple mathematics that any line divided in the way Plato describes that the two middle sections, BC and CD, are necessarily the same length. Hence, we are said to have relatively clear knowledge of something that is more real and "true" when we attend to ordinary perceptual objects like rocks and trees; by comparison, if we merely attend to their shadows and reflections, we have relatively obscure opinion of something not quite real.


Plato uses this familiar relationship, between ordinary objects and their representations or images, in order to illustrate the relationship between the visual world as a whole (visual objects and their images) and the world of forms as a whole. The former is made up of a series of passing, particular reflections of the latter, which is eternal, more real and "true." Moreover, the knowledge that we have of the forms--when indeed we do have it--is of a higher order than knowledge of the mere particulars in the perceptual world.


Consider next the difference between the two parts of the intelligible world, represented by segments CD and DE. Plato's discussion of this is apt to seem obscure. The basic idea is that the lower forms (represented by CD) are the real items of which the ordinary particular objects around us are merely reflections or images. The higher forms, by contrast--of which the so-called Form of the Good is the "highest"--are known only by what has come to be called a priori reasoning, so that strictly speaking, knowledge of them does not depend upon experience of particulars or even on ideas (forms) of perceptually-known particulars. Plato describes The Form of the Good in his book, The Republic, using Socrates as his mouth piece. ... A priori is a Latin phrase meaning from the former or less literally before experience. In much of the modern Western tradition, the term a priori is considered to mean propositional knowledge that can be had without, or prior to, experience. ...


This can be explained a bit further. In geometry and arithmetic, we often use particular figures to fix our ideas and make demonstrations clear. Moreover, in these sciences, we make certain postulates and draw conclusions that are only as trustworthy as the postulates. By contrast, the intelligible is "that which the reason itself," rather than image-assisted imagination, lays hold of by the power of dialectic, treating its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings, and springboards so to speak, to enable it to rise to that which requires no assumption and is the starting point of all, and after attaining to that again taking hold of the first dependencies from it, so to proceed downward to the conclusion, making no use whatever of any object of sense but only of pure ideas moving on through ideas to ideas and ending with ideas. (511b-c) For the algebra software named Axiom, see Axiom computer algebra system. ...


What all this might mean is essentially to ask, "What are the details of Plato's rationalism?" The reference to and idolization of "pure ideas," as well as deduction as it were without assumptions (or with one grand assumption or principle, as The Form of the Good is sometimes portrayed), is something reflected again and again in later rationalists. The above text finds later echoes in Descartes' interest in pure, a priori deduction and Kant's transcendental arguments. Rationalism, also known as the rationalist movement, is a philosophical doctrine that asserts that the truth can best be discovered by reason and factual analysis, rather than faith, dogma or religious teaching. ... For other things named Descartes, see Descartes (disambiguation). ... Immanuel Kant (22 April 1724 – 12 February 1804), was a German philosopher from Königsberg (now Kaliningrad) in East Prussia. ...


Plato explicitly names four sorts of cognition associated with each level of being:

[A]nswering to these four sections, assume these four affections occurring in the soul--intellection or reason (noesis) for the highest, understanding (dianoia) for the second, belief (pistis) for the third, and for the last, picture thinking or conjecture (eikasia)--and arrange them in a proportion, considering that they participate in clearness and precision in the same degree as their objects partake of truth and reality. (511d-e)

Not too much weight should be put on the English (or Greek) meanings of the words here, however. Any significant meaning that these words have, when used as technical terms for Plato, needs to be informed by the metaphysical and epistemological edifice that supports them.


The metaphor of the divided line immediately follows another Platonic metaphor, that of the sun: see Plato's metaphor of the sun. It is immediately followed by the famous allegory of the cave. Plato, in The Republic (507b-509c), uses the sun as a metaphor for the source of intellectual illumination, which he held to be The Form of the Good, which is sometimes interpreted as Platos notion of God. ... Illustration of Platos cave Platos allegory of the cave is perhaps the best-known of his many metaphors, allegories, and myths. ...


  Results from FactBites:
 
Plato's Analogy of the Divided Line (9749 words)
Plato is here contrasting the epistemic and psychological states that accompany and result from two kinds of reasoning, one which occurs in the visible section of the line, the other in the intelligible.
Plato would thus be committed to the view that the objects of noêsis or epistêmê [ta noêta] are necessarily different from those of dianoia [ta dianoêta]; that both are necessarily different from those of pistis [ta pista]; and that all three are necessarily different from those of eikasia [ta eikasta].
The ideas that in the divided line analogy Plato is presenting a "scale of reality," that he is contrasting the "intelligible world" and the "sphere of appearances," and that "the line is the vertical course leading to the real world," are common enough.
Plato - Academic Kids (1739 words)
Plato founded one of the earliest known organized schools in Western civilization when he was 40 years old on a plot of land in the Grove of Academe.
Plato's thought is often compared with that of his most famous student, Aristotle, whose reputation during the western Middle Ages so completely eclipsed that of Plato that the Scholastic philosophers referred to Aristotle as "the Philosopher." However, in the Byzantine Empire the study of Plato continued.
Plato's original writings were essentially lost to western civilization until they were brought from Constantinople in the century before its fall.
  More results at FactBites »

 
 

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