Diairesis (Ancient Greek: διαίρεσις, romanized: diaíresis, "division") is a form of classification used in ancient (especially Platonic) logic that serves to systematize concepts and come to definitions. When defining a concept using diairesis, one starts with a broad concept, then divides this into two or more specific sub-concepts, and this procedure is repeated until a definition of the desired concept is reached. Aristotle makes extensive use of diaresis in categorization as basis for syllogizing. He makes clear, however, that definition by diaresis does not in itself prove anything.[1] Apart from this definition, the procedure also results in a taxonomy of other concepts, ordered according to a general–specific relation.
The founder of diairesis as a method was Plato. Later ancient logicians (including Aristotle) and practitioners of other ancient sciences have employed diairetic modes of classification, e.g., to classify plants in ancient biology.
Plato's method of definition
editDiairesis 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 eliminated until a suitable definition is discovered.
A complementary term is merismos (cf. English merism: parsing or the distinguishing of parts, as opposed to diairesis, which is the division of a genus into its parts).
For example, in the Sophist (§235B), the Eleatic Stranger is examining illusions, which consist of words and "visual objects." By using diairesis, he divides visual objects, by which it becomes clear he means works of art, into two categories: eikastikē technē, the art of making likenesses or eikones; and phantastikē technē, the art of creating illusionary appearances. The Stranger is much more fond of the former; the latter is only created to produce an appearance of beauty.
The method of diairesis in the history of philosophy
editForerunners of Plato
editOpinions about possible forerunners of Platonic diairesis are varying; they even reach back until Homer. Also an adoption from the fields of mathematics has been considered,[3] like one from musicology,[4] one from pre-scientific and everyday divisions[5] and one from medicine.[6] About forerunners in the field of philosophy there are as well different opinions. Under consideration are Prodicus of Ceos,[7][8] Democritus, Leucippus,[9] and the sophists.[10] It was even suggested that Plato says that he himself found the new method,[11] which shows that it is possible that Plato had no forerunners at all.[12]
Later exponents of the method of diairesis
editThe platonic method of division is found to be applied at the first steps of classifying biology, namely in the zoology of Aristotle[13] and in the botany of Theophrastus.[14] Diairesis is central to Galen's therapeutics; see for example 'Therapeutics to Glaucon' 1 (XI, 4 K), where Galen, attributing the method to Plato, asserts that 'the errors of the [medical] sects and whatever mistakes the majority of physicians make in the care of the sick have incompetent division as their principal and major cause' (tr. Dickson.)[15] Philosophically relevant methodical divisions or statements about the method of diairesis can be found in members of the Platonic Academy (especially Speusippus[16] and Xenocrates), of the Peripatetic school (especially Aristotle, Aristoxenus, Theophrastus), of Stoicism (especially Chrysippus), of Middle Platonism (especially Alcinous, Maximus of Tyre, Philo) and of Neoplatonism (especially Plotinus, Porphyry). In medieval times the so-called method of divisio was a common method.[17]
References
edit- ^ Shorey, Paul (January 1924). "The Origin of the Syllogism". Classical Philology. 19 (1): 1–19. doi:10.1086/360550. ISSN 0009-837X. S2CID 162227302.
- ^ Pietsch, Christian (2003). "Die Dihairesis der Bewegung in Platon, Nomoi X 893b1–894c9" (PDF). Rheinisches Museum für Philologie. 146: 303–327. JSTOR 41234713.
- ^ (german) Hans Leisegang: Denkformen, Walter de Gruyter, Berlin 1951, p. 220
- ^ (german) Hermann Koller: Die dihäretische Methode, in: Glotta Vol. 39, Vandenhoeck & Ruprecht, Göttingen 1961, p. 23
- ^ (german) Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 111, online: [1] Archived 2009-09-28 at the Wayback Machine
- ^ (german) Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 116
- ^ (german) Christian Schäfer (editor): Platon-Lexikon, Wissenschaftliche Buchgesellschaft Darmstadt 2007, p. 92
- ^ John Lloyd Ackrill: In Defense of Platonic Division, in: Essays on Plato and Aristotle, Clarendon Press, Oxford 1997, p. 105; Devin Henry: A Sharp Eye for Kinds: Collection and Division in Plato's Late Dialogues. In Michael Frede, James V. Allen, Eyjólfur Kjalar Emilsson, Wolfgang-Rainer Mann & Benjamin Morison (eds.), Oxford Studies in Ancient Philosophy. Oxford University Press. pp. 229–255 (2011)
- ^ (german) Julius Stenzel: Studien zur Entwicklung der platonischen Dialektik von Sokrates zu Aristoteles, 2. edition 1931, Nachdruck: Teubner, Stuttgart 1961, p. 112
- ^ (german) Artur v. Fragstein: Die Diairesis bei Aristoteles, Adolf M. Hakkert, Amsterdam 1967, p. 80
- ^ (german) Margot Fleischer: Hermeneutische Anthropologie – Platon, Aristoteles, Walter de Gruyter, Berlin 1976, p. 143
- ^ Richard Robinson: Plato's Earlier Dialectic, Oxford University Press, Oxford 1953, p. 89
- ^ (german) Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 123
- ^ Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 115
- ^ Keith Dickson: 'Stephanus the Philosopher and Physician, Commentary on Galen's Therapeutics to Glaucon', Leiden:Brill, 1998
- ^ See John Dillon (1998). "Speusippus." In E. Craig (Ed.), Routledge Encyclopedia of Philosophy. London: Routledge. Retrieved October 10, 2007, from http://www.rep.routledge.com/article/A111SECT3[permanent dead link]
- ^ (german) Hans Leisegang: Denkformen, Walter de Gruyter, Berlin 1951, p. 252
External links
edit- Gill, Mary Louise. "Method and Metaphysics in Plato's Sophist and Statesman". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.