Analogy of the Divided Line

The line is a well known parable parable of ancient philosophy. It comes from the Greek philosopher Plato ( 428/427-348/347 BC), who can tell it from his teacher Socrates at the end of the sixth book of his dialogue Politeia. Immediately before Socrates has argued the sun parable. At the beginning of the seventh book, the Allegory of the Cave, the last of the three famous parables in the Republic follows. All three parables illustrate statements of Plato's ontology and epistemology.

In the three parables specifically Platonic thought is carried forward. The " Platonic " Socrates, who appears here as a speaker and tells the parables, is a fictional figure figure. His position therefore can not be equated with that of the historical Socrates.

In the parable of the entire line of recognizable reality is compared to a vertical line presented. The line is divided into four unequal sections that represent four ways of knowing and their associated objects of knowledge. There is a hierarchical order between them. The ways of knowing are ordered by their reliability, the objects of knowledge according to their rank. The two main sections of the line correspond to the areas of the sensible ( below) and the purely spiritual (above).

• 2.1 Ancient and Early Modern Times
• 2.2 Modern research debates

Content

In the sixth book of the Republic, Socrates explains his interlocutors, Glaucon and Adeimantus, the two brothers of Plato, the ethical and intellectual demands, which you must meet in order to be qualified for the philosophical study of the highest knowledge area and at the same time for political leadership. Those who fulfill the necessary conditions, has to strive for the realization of the "good ", because the good is the highest-ranking object of knowledge, and ultimately the goal of all philosophical aspirations. In the Platonic doctrine of ideas, the idea of ​​the Good is the supreme principle. But it is difficult to capture because of its transcendence. In the solar parable Socrates has compared the good with the sun: As in the case of the visible sun is the source of light, the all-conquering power, so there is in the intelligible ( spiritual ) world good as a source of truth and knowledge. Glaucon asks for further explanation, to which Socrates begins with the presentation of the line parable.

The starting point is the illustrated already in the solar parable dividing the total reality into two similarly structured regions, the visible ( accessible to sensory perception ) and the spiritual (only the cognitive effort accessible ). Glaucon to imagine a vertical line, which is divided into two unequal main sections. The main sections are for the two spheres of reality. The whole line is in the research literature commonly referred to as AB, where A is the lower, the upper end point B; the point C divides the line into two main sections AC (bottom, meaning the world) and CB (upper, spiritual world ). Each of the two main sections divided in the same proportion as the whole line. So come into four sections, two for the physical world (AD and DC) and two for the spiritual world (CE and EB). This gives the proportion AC: CB = AD: DC = CE: EB.

The system is structured so that the lowermost portion of the line to the top, the clarity with which the respective objects may be detected increases. This corresponds to an increase of the objective truth content of the respective accessible knowledge and the confidence that obtained the knower. The different ways of knowing which correspond to the sections of the line are determined by the quality of the objects.

First main section of the line

The first main section ( AC) corresponds to the world of sensible things. His two subsections are associated with different kinds of objects of sense perception. The objects of perception are characterized by their instability.

The first sub- section (AD) is the world of blurry images, which generates the nature itself: Shadows and reflections on water surfaces and on smooth and shiny surfaces. The second sub- section ( DC) is the world of real things, the body whose pictures appear in the first subsection. Here are real animals, plants and objects that are viewed directly, with far crisper, clearer sensations arise as when looking at the shadows and mirror images.

Under epistemological aspect, the first main section corresponds to my (doxa ), the possibly correct but not sufficient based views. Meaning it comes in two forms: conjecture ( Eikasia ), is associated with the sub-section AD, and holding true ( pistis ), which corresponds to the subsection, DC.

The Eikasia as the lowest cognition depends on the shadows and mirror images, objects, their perception allows only guess as any objects that throw or reflected, out of view of a shadow are. The text is not clear whether Plato assumed here that the presumable the representational quality of what he perceived is not aware but this holds for all of reality, or whether it is meant that the presumable the shadows and reflections about their causes, the three-dimensional objects, takes. An example of the latter would be a moving shadow indicates the presence of non-visible human or animal.

The Pistis as " to accept as true " is the confidence in the world of the senses and the accuracy of the information provided by the sensory organs. It is based on direct perception of real three-dimensional objects, as these present themselves to the senses. Therefore, its value is higher than that of the Eikasia, because knowledge can be gained here, the truth of which is larger.

Second main section of the line

The second main section ( CB ) represents the spiritual world dar. Its division into two subsections CE and EB is the first main portion analog. In the spiritual realm, all objects of knowledge are completely and absolutely unchangeable. This makes it fundamentally different from the physical world, the realm of becoming, in which everything is changing.

The conceptual thinking of mathematicians ( Dianoia )

The cognition of conceptual thinking ( Dianoia ) corresponds to the first subsection (CE). As their objects the objects of mathematics are called, especially ideal geometric figures. The achievable by Dianoia insight needs to be substantiated by proof. It leads to understanding and certainty is essential that you get to the ideas as fundamental principles.

The mathematicians set their terms ahead (such as geometrical figures or angle types ) to be known and put it their evidence based programs, as if they knew about it. They clarify their terms but not on and are unable to give any account of themselves and others, what are the things they designate, in reality. Since they do not check their conditions, they do not go to the "beginning" back ( a principle ) and get over him no knowledge; their starting points are just assumptions from which they proceed to conclusions.

In addition, the mathematicians use visible images of objects, they think about. They are distinguished, although the objects of their efforts are entirely deprived of sensory perception; they look at the visible geometric shapes, but think of the ideas that are represented inadequately by these figures. For example, they draw a diagonal line as visible, so they make a reference to the familiar experience of the world, although the ideal diagonal, at issue them, is not vivid. You know the things that mathematics is not because they have to do only with images of those things. Thus, their approach to the actual nature of that with which they deal, not appropriate. They are based on rechtfertigungslos alleged evidence on unquestioned assumptions. The conceptual thinking of mathematicians so does not count for rational insight, but is used as something between her and the mere opinion, which is used in the evaluation of sensory impressions about. The mathematical subject matter is indeed spiritually and therefore in principle accessible to the knowledge, but the mathematicians have no real knowledge of him.

With these findings, Plato does not want to criticize the contemporary mathematicians as far as they work as such, but only from a philosophical point of view to show the limits of what it can do mathematics within their means for the cognition of reality.

The rational insight ( noesis )

Plato assigns the Noesis ( rational insight ), the highest kind of knowledge, the top line section (EB). However Elsewhere he uses the term noesis in a broader sense, for all the knowledge of spiritual objects, ie for the whole upper main section of the line, and calls the product knowledge of the uppermost sub-section ( EB) "knowledge" ( episteme ). In the research literature " Noesis " is usually understood in a narrow sense and based only on the uppermost sub-section of the line.

The Noesis ( in the narrow sense ) is required, in contrast to Dianoia no aid from the sensuous intuition, but takes place exclusively within the purely spiritual region and reaches the unconditional real beginning, she then makes the foundation. So it gains a firm footing, this procedure referred to Plato as " dialectical ". Under dialectic he does not understand a specific subject knowledge, no science among other sciences, but the investigation method of philosophy that meets the criteria of the scientific method alone in his view. The dialectician is to recognize the situation, methodological and other shortcomings of mathematics and to make accurate statements about the status of mathematical objects. The object of the dialectic is to capture the objective concept levels, the ideas in their nature and context.

Although the noesis goes as the first Dianoia of conditions, but then rises from this base on the requirement lots that needs no justification. Is this highest level is reached, the initial conditions are superfluous. The prerequisite lots will then in turn the starting point for the - now correctly informed - knowledge of all subordinate fields of knowledge, the totality of what can be known. On the climb to the top level of the knowable thus follows a descent.

The prerequisite lots, which is a prerequisite for everything else and from which everything else is derived, is the highest principle, which was equated in the sun parable with the idea of good. This completes the discussion returns to its starting point: the line parable for explaining the sun parable. The allegory of the cave then set out the reasoning should be further deepened.

Thus Plato represents the concept of a universal science that anchors all branches of research in a single principle, and so summarizing. This universal science is to lead back to various areas such as mathematics and ethics to a common root and thus unite. The background is the theory of Ideas: The objects of mathematics, like the ideas of ethics and as such ontologically dependent on the highest idea, the idea of ​​the good.

Reception

Ancient and Early Modern Times

In Mittelplatonismus the line parable found relatively little attention. Plutarch summarized the content together and just discussed the question why the sections of the line are unequal and which of the two main sections of the larger is ( are lacking in the parable data). Alcinous went in his Didaskalikos, an introduction to the Platonic philosophy, a fact.

Much more intense was the reception of the parable in the late ancient Neoplatonists. Iamblichus interpreted it in his book " The Science of mathematics in general" ( De communi mathematica scientia ), Calcidius there were in his commentary on Plato's Timaeus in detail again, Syrianos Proclus and treated it in their commentaries on Politeia and Asclepius of Tralles explained it in his commentary on the metaphysics of Aristotle.

In the 16th century the philosopher Francesco Patrizi drew the line parable approach in the context of his critique of Aristotle. He tried the superiority of the Platonic philosophy of the Aristotelian evidence and explained it on the basis of quotations from the line parable his understanding of the analytical method of Plato, who had ignored Aristotle.

Modern research debates

In the 19th century, the interpretation of the parable of Plato Research was usually regarded as relatively unproblematic. An intense debate began in the twenties of the 20th century.

A research discussion concerns the question whether the first main section of the line a real, continuous gain in knowledge as proceeding from bottom to top expresses, so it has an independent function, or whether it is only the preliminary illustration of the second main section set forth.

It has long been controversial is the question of whether the four sections of the line and their associated knowledge types correspond to the ascent phase in the allegory of the cave. A match is considered by many researchers as a plausible, but some see no analogy between the cave and the lower part of the line.

Another uncertainty concerns the status of the objects of mathematics. According to one hypothesis, they have assigned its own ontological status and therefore them is on the line in a separate section towards the ideas, the idea of ​​knowledge remains the top portion reserved. According to another opinion research it comes to knowledge of Ideas in the entire main section of the line; Dianoia and noesis are just two different methods of approaching the world of ideas.

Due to the connection (AC: CB = AD: DC = CE: EB ), the middle two sub-sections of the line have the same length. This fact is not mentioned in the presentation of the parable. It is disputed whether this is a coincidence or whether this is hiding a meaning.

After one represented by some researchers interpretation of the line parable is not about the four modes of knowledge, but only three: sensing, mathematical and dialectical knowledge. Among the proponents of this interpretation Theodor Ebert heard. He thinks the modes of knowledge were chained together and not, as the erroneous notion of knowledge and reality levels Besage, due to an ontological difference of their objects divorced from each other. The distinction between original and copy is functional, not ontological understanding. The assumption that the line parable illustrative of knowledge and reality levels, go back to a misunderstanding of Aristotle, which the later Platonists would have connected in this regard. After the conviction of Ebert and many other historians philosophy Plato took no dualistic metaphysics with ontological separation ( chorismos ) between intelligible and of sensible world. The traditional, popular opposing view that will continue to dominate in the research, going from two ontologically diverse areas or "worlds" from. The ontological difference emphasize, among other things Rafael Ferber, who uses the term " two-world theory," Michael Erler, of Plato's ontology also characterized as " doctrine of two worlds " and remarks, Aristotle speak " not without reason from a chorismos " and Thomas Alexander Szlezák.

Text editions and translations

• Otto Apelt: Plato: The state ( = Otto Apelt (ed.): Plato: All dialogs, Vol 5). Meiner, Hamburg 1988, ISBN 3-7873-0920-9, pp. 265-268, 297-298 (reprint of the 3rd edition Leipzig 1923; translation only )
• John Burnet (ed.): Platonis opera, Vol 4, Clarendon Press, Oxford 1902 ( critical edition without translation, and often reprinted )
• Heinrich Dorrie / Matthias Baltes ( Eds.): The Platonism in antiquity, Volume 4: The philosophical doctrine of Platonism. From man - Holzboog, Stuttgart-Bad Cannstatt 1996, ISBN 3-7728-1156-6, pp. 84-97 ( source texts with translation ) and p 332-355 (comment)
• Gunther Eigler (ed.): Plato 's Politeia. The state ( = Plato works in eight volumes, Volume 4). 2nd edition, University Press, Darmstadt 1990, ISBN 3-534-11280-6, pp. 544-553, 612-615 ( critical edition, edited by Dietrich short, Greek text by Émile Chambry, German translation by Friedrich Schleiermacher )
• Rüdiger Rufener (ed.): Plato: the state. Politeia. Artemis & Winkler, Dusseldorf and Zurich 2000, ISBN 3-7608-1717-3, pp. 556-565, 622-625 (Greek text after the issuance of Émile Chambry without the critical apparatus, German translation by Rüdiger Rufener, introduction and notes by Thomas Alexander Szlezák )
• Wilhelm Wiegand: The State, Book VI -X. In: Plato: Complete Works, Volume 2, Lambert Schneider, Heidelberg without year ( 1950 ), pp. 205-407, here: 245-248, 277 f (only translation )