The parable of lines is a well-known parable of ancient philosophy . It comes from the Greek philosopher Plato (428 / 427-348 / 347 BC), who at the end of the sixth book of his dialogue Politeia has it told by his teacher Socrates . Immediately beforehand, Socrates recited the parable of the sun . At the beginning of the seventh book there is the allegory of the cave , the last of the three famous parables in the Politeia . All three parables illustrate statements from Plato's ontology and epistemology .
Specifically, Platonic ideas are presented in the three parables. The “platonic” Socrates, who appears here as a speaker and tells the parables, is a literary figure. His position cannot therefore be equated with that of the historical Socrates.
In the parable of lines, the entire recognizable reality is compared with a vertical line. The line is divided into four unequal sections, which stand for four modes of knowledge and the objects of knowledge assigned to them. There is a hierarchical order between them. The modes of knowledge are ordered according to their reliability, the objects of knowledge according to their rank. The two main sections of the line correspond to the areas of the sensually perceptible (below) and the purely spiritual (above).
In the sixth book of the Politeia , Socrates explains to his interlocutors Glaukon and Adeimantos , the two brothers of Plato, the ethical and intellectual requirements that one must meet in order to be qualified for the philosophical study of the highest realm of knowledge and at the same time for political leadership tasks. Whoever fulfills the necessary requirements has to strive for the knowledge of the “ good ”, because the good is the highest-ranking object of knowledge and ultimately the goal of all philosophical endeavors. In the Platonic doctrine of ideas , the idea of the good is the supreme principle. But it is difficult to grasp because of its transcendence . In the allegory of the sun, Socrates compared the good with the sun: just as in the realm of the visible the sun as the source of light is the all-dominating power, so in the intelligible (spiritual) world there is good as the source of truth and knowledge. Glaukon asks for further explanation, whereupon Socrates begins with the representation of the line parable.
The starting point is the division of total reality, already illustrated in the parable of the sun, into two analogously structured areas, the visible (accessible to sensory perception) and the spiritual (only accessible to the striving for knowledge). Glaukon is to imagine a vertical line divided into two unequal main sections. The main sections represent the two areas of reality. The whole line is commonly referred to as AB in the research literature, with A being the lower end point and B the upper end point; point C divides the line into the two main sections AC (below, sensory world) and CB (above, spiritual world). Each of the two main sections is divided in the same proportion as the whole line. This creates four sections, two for the sensory world (AD and DC) and two for the spiritual world (CE and EB). The result is the proportion AC: CB = AD: DC = CE: EB.
The system is structured in such a way that from the lowest section of the line to the top, the clarity with which the respective objects can be detected increases. This corresponds to an increase in the objective truth content of the knowledge that can be achieved in each case and the certainty that the knower attains. The different modes of knowledge that correspond to the sections of the line are determined by the quality of the objects.
First major section of the line
The first main section (AC) corresponds to the world of things that can be perceived by the senses. Different types of objects of sensory perception are assigned to its two subsections. The objects of perception are characterized by their instability.
The first subsection (AD) is the world of indistinct images that nature itself creates: shadows and reflections on water surfaces and on smooth and shiny surfaces. The second subsection (DC) is the world of real things, the body, the images of which appear in the first subsection. Here are real animals, plants and objects that are looked at directly, with far clearer, more unambiguous sensory impressions than when looking at the shadows and mirror images.
From an epistemological point of view, the first main section corresponds to my opinion ( dóxa ), the possibly correct, but insufficiently justified, conceptions. Opinion comes in two forms: Assumption ( eikasía ), which is assigned to subsection AD, and holding to be true ( pístis ), which corresponds to subsection DC.
Eikasia as the lowest mode of knowledge is directed towards shadows and mirror images, objects whose perception only allows guesswork, since the objects that cast a shadow or are reflected are outside the field of vision. It does not emerge from the text whether Plato is assuming here that the presumptive person is not aware of the representativeness of what he has perceived, but rather considers this to be the whole of reality, or whether it is meant that the presumptive person provides information about their causes from the shadows and mirror images , the three-dimensional objects. An example of the latter would be a moving shadow that indicates the presence of an invisible human or animal.
The pistis as “holding true” is trust in the sensory world and the correctness of the information supplied by the sense organs. It is based on a direct perception of real three-dimensional objects as they are presented to the senses. Therefore their value is higher than that of the Eikasia, for here knowledge can be obtained which is more truthful.
Second main section of the line
The second main section (CB) represents the spiritual world. Its subdivision into the two subsections CE and EB is analogous to that of the first main section. In the spiritual realm, all objects of knowledge are perfect and absolutely immutable. In this way it differs fundamentally from the world of the senses, the area of becoming, in which everything is changing.
The conceptual thinking of mathematicians ( diánoia )
The way of knowing of conceptual thinking (Dianoia) corresponds to the first subsection (CE). Objects of mathematics are named as their objects, especially ideal geometrical figures. The insight that can be obtained through Dianoia requires justification through evidence. It leads to the certainty of understanding and is a prerequisite for arriving at the ideas as basic principles.
Mathematicians assume that their concepts (such as geometrical figures or types of angles) are known and base their proofs on them as if they knew about them. However, they do not explain their terms and are unable to give an account of themselves or others about what the things they refer to are in reality. Since they do not check their presuppositions, they do not go back to the "beginning" (a principle) and gain no knowledge of it; their starting points are only assumptions from which they advance to inferences.
In addition, mathematicians use visual images of the objects they are thinking about. You draw, although the objects are completely withdrawn from your efforts of sensual perception; they look at the visible geometrical shapes, but think of the ideas that are inadequately represented by these shapes. For example, they draw a diagonal as a visible line, with which they create a reference to the familiar world of experience, even though the ideal diagonal they are concerned with is not visual. They do not know the things that mathematics is about because they are only dealing with images of these things. Thus, their approach is inappropriate to the very nature of what they are dealing with. They rely without justification on alleged evidence, on assumptions that have not been questioned. The conceptual thinking of mathematicians therefore does not count towards the insight into reason, but rather stands as a middle thing between it and the mere opinion that comes about when evaluating sensory impressions. The mathematical subject area is indeed intellectual and therefore basically accessible to knowledge, but mathematicians have no real knowledge about it.
With these statements, Plato does not want to criticize contemporary mathematicians insofar as they work as such, but only show from a philosophical point of view the limits of what mathematics can achieve for the knowledge of reality within the framework of its possibilities.
The insight into reason ( nóēsis )
Plato assigns the Noesis (insight into reason), the highest mode of knowledge, to the highest line segment (EB). Elsewhere, however, he uses the term noesis in a broader sense for the totality of the knowledge of spiritual objects, i.e. for the entire upper main section of the line, and calls the knowledge product of the uppermost subsection (EB) "knowledge" ( epistḗmē ). In the research literature, “noesis” is usually understood in a narrower sense, referring only to the top subsection of the line.
In contrast to Dianoia, noesis (in the narrower sense) does not need any aids from sensual perception, but takes place exclusively within the purely spiritual realm and reaches the real beginning, without any preconditions, which it then makes the foundation. In this way it gains a firm footing. Plato describes this procedure as "dialectical". He understands dialectics not to be a specific subject knowledge, not a science alongside other sciences, but rather the method of investigation of philosophy, which from his point of view only meets the criteria of scientific nature. The dialectician is able to recognize methodological and other deficits in mathematics and to make correct statements about the status of mathematical subjects. The task of dialectics is to grasp the objective conceptual contents, the ideas, in their essence and overall context.
Like Dianoia, the Noesis is initially based on presuppositions, but then rises from this starting point to something without presuppositions, which does not require any justification. Once this highest level is reached, the initial requirements become superfluous. The lack of presuppositions in turn becomes the starting point for the - now correctly founded - knowledge of all subordinate areas of knowledge, the totality of what can be known. The ascent to the highest level of the knowable is thus followed by a descent.
The lack of presuppositions, which is the presupposition for everything else and from which everything else is derived, is the highest principle, which in the parable of the sun was equated with the idea of the good. With this the discussion returns to its starting point: The parable of lines serves to explain the parable of the sun. With the allegory of the cave presented below, the train of thought should be further deepened.
Plato thus represents the concept of a universal science that anchors and thus combines all branches of research in a single principle. This universal science is supposed to lead back fields as diverse as mathematics and ethics to a common root and thereby unite them. The theory of ideas forms the background: The objects of mathematics, like those of ethics, are ideas and as such ontologically dependent on the highest idea, the idea of the good.
Ancient and early modern times
The allegory of lines received relatively little attention in Middle Platonism . Plutarch briefly summarized the content and discussed the question of why the sections of the line are unequal and which of the two main sections is the larger (information on this is missing in the parable). Alcinous discussed this in his Didaskalikos , an introduction to Platonic philosophy.
The reception of the parable was much more intense among the neo-Platonists of late antiquity . Iamblichos interpreted it in his work "The science of mathematics in general" ( De communi mathematica scientia ), Calcidius gave it again in detail in his commentary on Plato's dialogue Timaeus , Syrianos and Proklos dealt with it in their commentaries on Politeia and Asklepios von Tralleis explained it in his commentary on the metaphysics of Aristotle .
In the 16th century, the philosopher Francesco Patrizi used the allegory of lines as part of his Aristotle criticism. He tried to prove the superiority of the Platonic philosophy over the Aristotelian and explained his understanding of the analytical method of Plato, which Aristotle ignored, using quotations from the parable of the lines.
In the 19th century, the interpretation of the parable in Plato research was mostly viewed as relatively unproblematic. An intense debate did not begin until the 1920s.
A research discussion concerns the question of whether the first main section of the line expresses a real, continuous gain in knowledge when moving from bottom to top, i.e. has an independent function, or whether it only serves as a preparatory illustration of what is presented in the second main section.
The question of whether the four sections of the line and the types of knowledge assigned to them correspond to the phases of ascent in the allegory of the cave has long been controversial. A match is considered plausible by many researchers, but some see no analogy between the cave and the lower part of the line.
Another ambiguity concerns the status of the subjects of mathematics. According to one hypothesis, they have their own ontological status in relation to the ideas and therefore they are assigned their own section on the line, the knowledge of ideas is reserved for the uppermost section. Another research opinion is that the entire upper main section of the line is about idea recognition; Dianoia and Noesis are just two different ways of accessing the world of ideas.
Due to the proportionality (AC: CB = AD: DC = CE: EB), the two middle subsections of the line must be of the same length. This fact is not mentioned in the illustration of the parable. It is disputed whether this is a coincidence or whether there is a meaning behind it.
According to one interpretation of the line equation, advocated by some researchers, there are not four modes of knowledge, but only three: perceptual, mathematical and dialectical knowledge. Theodor Ebert is one of the proponents of this interpretation . He thinks that the modes of knowledge are linked to one another and not, as the erroneous idea of levels of knowledge and reality suggests, separated from one another on the basis of an ontological difference between their objects. The distinction between archetype and copy is to be understood as functional, not ontological. The assumption that the parable of lines illustrates levels of knowledge and reality goes back to a misunderstanding by Aristotle, which the later Platonists would have subscribed to in this regard. According to the conviction of Ebert and some other historians of philosophy, Plato did not advocate a dualistic metaphysics with ontological separation ( chorismos ) between the intelligible and sensually perceptible world. The traditional, common counter-conception, which continues to dominate research, is based on two ontologically different areas or "worlds". The ontological differences are emphasized by Rafael Ferber , who uses the term “two-worlds theory”, Michael Erler , who also characterizes Plato's ontology as a “doctrine of two worlds ” and notes that Aristotle speaks “not without reason of a chorism”, and Thomas Alexander Szlezák .
Wolfgang M. Ueding tried to reconstruct the line parable as a musical diagram.
Text editions and translations
- Otto Apelt , Karl Bormann : Plato: The State. About the just (= Philosophical Library , Vol. 80). 11th, revised edition, Meiner, Hamburg 1989, ISBN 3-7873-0930-6 , pp. 264–267 (translation only)
- John Burnet (Ed.): Platonis opera , Vol. 4, Clarendon Press, Oxford 1902 (critical edition without translation; often reprinted)
- Heinrich Dörrie , Matthias Baltes (ed.): The Platonism in antiquity , Volume 4: The philosophical teaching of Platonism . Frommann-Holzboog, Stuttgart-Bad Cannstatt 1996, ISBN 3-7728-1156-6 , pp. 84–97 (source texts with translation) and pp. 332–355 (commentary)
- Gunther Eigler (Ed.): Plato: Politeia. The state (= Plato: works in eight volumes , vol. 4). 2nd edition, Wissenschaftliche Buchgesellschaft, Darmstadt 1990, ISBN 3-534-11280-6 , pp. 544–553, 612–615 (critical edition; edited by Dietrich Kurz, Greek text by Émile Chambry, German translation by Friedrich Schleiermacher )
- Rüdiger Rufener (Ed.): Plato: The State. Politeia . Artemis & Winkler, Düsseldorf / Zurich 2000, ISBN 3-7608-1717-3 , pp. 556–565, 622–625 (Greek text based on the edition by Émile Chambry without the critical apparatus, German translation by Rüdiger Rufener, introduction and explanations by Thomas Alexander Szlezák)
- Wilhelm Wiegand: The State, Book VI-X . In: Platon: Complete Works , Volume 2, Lambert Schneider, Heidelberg without a year (around 1950), pp. 205–407, here: 245–248, 277 f. (only translation)
- Michael Bordt : Plato . Herder, Freiburg im Breisgau 1999, ISBN 3-451-04761-6 , pp. 93-127
- Rafael Ferber : Plato's idea of the good . 2nd edition, Academia Verlag, Sankt Augustin 1989, ISBN 3-88345-559-8 , pp. 80-114
- Christoph Quarch : Being and soul. Plato's philosophy of ideas as the metaphysics of vitality. Interpretations of Phaedo and Politeia . Lit Verlag, Münster 1998, ISBN 3-8258-3996-6 , pp. 39-57
- Yvon Lafrance: Pour interpréter Plato . Volume 1: La Ligne en République VI, 509d-511e. Bilan analytique des études (1804–1984). Les Belles Lettres, Paris 1986, ISBN 2-89007-633-4 (extensive bibliography with summaries of the contents of the cited publications)
- ↑ Plato, Politeia 505a-509d.
- ↑ Plato, Politeia 511d8: The line has a “top” part. See Egil A. Wyller : Der late Platon , Hamburg 1970, p. 16; Heinrich Dörrie, Matthias Baltes: Platonism in antiquity , vol. 4, Stuttgart-Bad Cannstatt 1994, p. 333, note 6.
- ↑ Plato, Politeia 509d.
- ↑ Plato, Politeia 509e – 510a.
- ↑ This is the interpretation of Wolfgang Wieland : Plato and the forms of knowledge , 2nd, extended edition, Göttingen 1999, p. 205 f.
- ↑ Theodor Ebert: Opinion and knowledge in Plato's philosophy , Berlin 1974, p. 175 f.
- ↑ Wolfgang Wieland: Plato and the forms of knowledge , 2nd, extended edition, Göttingen 1999, pp. 204–206. On the relationship between Eikasia and Pistis, see Vassilis Karasmanis: Plato's Republic: The Line and the Cave . In: Apeiron Vol. 21 No. 3, 1988, pp. 147-171, here: 165-168.
- ↑ Plato, Politeia 510c-511b.
- ↑ Plato, Politeia 511c-d. See also Wolfgang Wieland: Platon und die Formen des Wissens , 2nd, extended edition, Göttingen 1999, pp. 208–216; Jürgen Mittelstraß : The dialectic and its scientific preparatory exercises (Book VI 510b – 511e and Book VII 521c – 539d). In: Otfried Höffe (Ed.): Platon: Politeia , 3rd edition, Berlin 2011, pp. 175–191, here: 182–186.
- ↑ Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, p. 91 f.
- ↑ Plato, Politeia 511d-e.
- ↑ Plato, Politeia 533e-534a.
- ↑ Jürgen Mittelstraß: The dialectic and its scientific preparatory exercises (Book VI 510b – 511e and Book VII 521c – 539d). In: Otfried Höffe (Ed.): Platon: Politeia , 3rd edition, Berlin 2011, pp. 175–191, here: 182–186.
- ↑ Plato, Politeia 510b, 511b-d; see. 533c-e. See Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, pp. 99–111.
- ↑ Plato does not explicitly establish the identity of the “ unprecedented ” ( anhypótheton ) of the allegory of lines with the “good” of the allegory of the sun and has been disputed in individual research. According to the prevailing research opinion, however, it arises from the context of the parables. For the reason, see Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, p. 97 f.
- ↑ To trace the fundamentals of mathematics back to the idea of the good, see Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, p. 98 f .; Hans Krämer : The idea of the good. Parable of the sun and lines (Book VI 504a – 511e) . In: Otfried Höffe (Ed.): Platon: Politeia , 3rd edition, Berlin 2011, pp. 135–153, here: 147–151.
- ↑ Plutarch, Quaestiones Platonicae 3; see Heinrich Dörrie, Matthias Baltes: Der Platonismus in der Antike , Vol. 4, Stuttgart-Bad Cannstatt 1994, pp. 88–91, 342 f.
- ↑ Alkinous, Didaskalikos 7, ed. by John Whittaker and Pierre Louis: Alcinoos: Enseignement des doctrines de Platon , 2nd edition, Paris 2002, p. 18 f.
- ↑ See Heinrich Dörrie, Matthias Baltes: Der Platonismus in der Antike , Vol. 4, Stuttgart-Bad Cannstatt 1994, pp. 344–355.
- ↑ Mihaela Girardi-Karšulin: Petrić's interpretation of the allegory of lines . In: Damir Barbarić (ed.): Plato on the good and justice , Würzburg 2005, pp. 203-209.
- ^ Theodor Ebert: Opinion and knowledge in Plato's philosophy , Berlin 1974, pp. 152–159 (research overview); Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, p. 112 f .; Vassilis Karasmanis: Plato's Republic: The Line and the Cave . In: Apeiron Vol. 21 No. 3, 1988, pp. 147-171, here: 157 f. Further literature from Yvon Lafrance: Pour interpréter Platon , Volume 1, Paris 1986, No. I 4, I 7, I 15, I 16, I 17, I 18, I 24, I 27, I 68, I 80, I 83 , I 123, I 141, I 146.
- ↑ See also Michael Erler: Platon (= Hellmut Flashar (Hrsg.): Grundriss der Geschichte der Philosophie . Die Philosophie der Antike , Volume 2/2), Basel 2007, pp. 400, 402; Wilhelm Blum: cave parables , Bielefeld 2004, pp. 51–53; Oswald Utermöhlen: The importance of the theory of ideas for the Platonic Politeia , Heidelberg 1967, pp. 33–51, 69, 78; Christoph Quarch: Sein und Seele , Münster 1998, pp. 58–60; Thomas Alexander Szlezák: The allegory of the cave (Book VII 514a – 521b and 539d – 541b) . In: Otfried Höffe (Ed.): Platon: Politeia , 3rd edition, Berlin 2011, pp. 155–173, here: 160–162; Hans Lier: On the structure of the Platonic allegory of the cave . In: Hermes 99, 1971, pp. 209-216; John Malcolm: The Line and the Cave . In: Phronesis 7, 1962, pp. 38-45; John S. Morrison: Two Unresolved Difficulties in the Line and the Cave . In: Phronesis 22, 1977, pp. 212-231; Ronald Godfrey Tanner: ΔΙΑΝΟΙΑ and Plato's Cave . In: The Classical Quarterly 20, 1970, pp. 81-91; Vassilis Karasmanis: Plato's Republic: The Line and the Cave . In: Apeiron Vol. 21 No. 3, 1988, pp. 147-171; Karl Bormann: On Plato, Politeia 514 b 8–515 a 3 . In: Archive for the History of Philosophy 43, 1961, pp. 1–14, here: 5–14; Miguel A. Lizano-Ordovás: 'Eikasia' and 'Pistis' in Plato's allegory of the cave . In: Journal for Philosophical Research 49, 1995, pp. 378–397.
- ↑ Thomas Alexander Szlezák: The allegory of the cave (Book VII 514a – 521b and 539d – 541b) . In: Otfried Höffe (Ed.): Platon: Politeia , 3rd edition, Berlin 2011, pp. 155–173, here: 161 f .; Konrad Gaiser : Plato's unwritten teaching , 2nd edition, Stuttgart 1968, pp. 89–95; Heinrich Dörrie, Matthias Baltes: Platonism in antiquity , Vol. 4, Stuttgart-Bad Cannstatt 1994, pp. 334-340; John A. Brentlinger: The Divided Line and Plato's 'Theory of Intermediates' . In: Phronesis 8, 1963, pp. 146-166.
- ↑ Wolfgang Wieland: Plato and the forms of knowledge , 2nd, extended edition, Göttingen 1999, pp. 207 f., 212, 215; Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, p. 92; Theodor Ebert: Opinion and knowledge in Plato's philosophy , Berlin 1974, p. 183 and note 120 and p. 186; Vassilis Karasmanis: Plato's Republic: The Line and the Cave . In: Apeiron Vol. 21 No. 3, 1988, pp. 147-171, here: 155-157.
- ^ Heinrich Dörrie, Matthias Baltes: The Platonism in antiquity , Vol. 4, Stuttgart-Bad Cannstatt 1994, p. 337 f. and note 3; Pierre Aubenque : De l'égalité des segment intermédiaires dans la Ligne de la République . In: Marie-Odile Goulet-Cazé u. a. (Ed.): Sophies maietores, “Chercheurs de sagesse”. Hommage à Jean Pépin , Paris 1992, pp. 37-44; Hans Krämer: The idea of the good. Parable of the sun and lines (Book VI 504a – 511e) . In: Otfried Höffe (Ed.): Platon: Politeia , 3rd edition, Berlin 2011, pp. 135–153, here: p. 145, note 18.
- ^ Yvon Lafrance: Pour interpréter Platon , Volume 1, Paris 1986, No. I 4, I 5, I 24, I 41, I 56, I 150. Cf. Pierre Aubenque: De l'égalité des segments intermédiaires dans la Ligne de la République . In: Marie-Odile Goulet-Cazé u. a. (Ed.): Sophies maietores, “Chercheurs de sagesse”. Hommage à Jean Pépin , Paris 1992, pp. 37–44, here: p. 43 and note 16.
- ^ Theodor Ebert: Opinion and knowledge in Plato's philosophy , Berlin 1974, pp. 181–193. John N. Findlay also turned against the “two-world notion” and Aristotle's accusation of chorism based on it : Plato: The Written and Unwritten Doctrines , London 1974, pp. XI f., 32–40, Pierre Aubenque : De l'égalité des intermédiaires dans la Ligne de la République . In: Marie-Odile Goulet-Cazé u. a. (Ed.): Sophies maietores, “Chercheurs de sagesse”. Hommage à Jean Pépin , Paris 1992, pp. 37–44, here: 44 and Christoph Quarch: Sein und Seele , Münster 1998, pp. 42, 55–57, 132–149. In this sense, Richard Lewis Nettleship expressed himself in the 19th century : Lectures on the Republic of Plato , London 1963 (reprint; first publication 1897), pp. 238-240.
- ↑ Rafael Ferber: Plato's idea of the good , 2nd edition, Sankt Augustin 1989, pp. 19–48; Michael Erler: Platon (= Hellmut Flashar (Hrsg.): Outline of the history of philosophy. The philosophy of antiquity , Vol. 2/2), Basel 2007, pp. 390, 393; Thomas Alexander Szlezák: The idea of the good in Plato's Politeia , Sankt Augustin 2003, pp. 95–97.
- ↑ Wolfgang M. Ueding: The proportionality of the means or the mean-moderation of the ratios: The diagram as a theme and method of philosophy using the example of Plato or some examples of Plato. In: Petra Gehring et al. (Ed.): Diagram and Philosophy , Amsterdam 1992, pp. 13–49, here: 28–44.