Diairesis (, "division") is a form of Categorization 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 syllogism. He makes clear, however, that definition by diaresis does not in itself prove anything.
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
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 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
Forerunners of Plato
Opinions 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,
[(german) Hans Leisegang: Denkformen, Walter de Gruyter, Berlin 1951, p. 220] like one from musicology,
[(german) Hermann Koller: Die dihäretische Methode, in: Glotta Vol. 39, Vandenhoeck & Ruprecht, Göttingen 1961, p. 23] one from pre-scientific and everyday divisions
[(german) Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 111, online: [1] ] and one from medicine.
[(german) Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 116] About forerunners in the field of philosophy there are as well different opinions. Under consideration are
Prodicus,
[(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)] Democritus,
Leucippus,
[(german) Julius Stenzel: Studien zur Entwicklung der platonischen Dialektik von Sokrates zu Aristoteles, 2. edition 1931, Nachdruck: Teubner, Stuttgart 1961, p. 112] and the
sophism.
[(german) Artur v. Fragstein: Die Diairesis bei Aristoteles, Adolf M. Hakkert, Amsterdam 1967, p. 80] It was even suggested that Plato says that he himself found the new method,
[(german) Margot Fleischer: Hermeneutische Anthropologie – Platon, Aristoteles, Walter de Gruyter, Berlin 1976, p. 143] which shows that it is possible that Plato had no forerunners at all.
[Richard Robinson: Plato's Earlier Dialectic, Oxford University Press, Oxford 1953, p. 89]
Later exponents of the method of diairesis
The platonic method of division is found to be applied at the first steps of classifying biology, namely in the zoology of
Aristotle[(german) Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 123] and in the botany of
Theophrastus.
[Hans Herter: Platons Naturkunde, in: Rheinisches Museum für Philologie Vol. 121, 1978, p. 115] 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.)
[Keith Dickson: 'Stephanus the Philosopher and Physician, Commentary on Galen's Therapeutics to Glaucon', Leiden:Brill, 1998] Philosophically relevant methodical divisions or statements about the method of
diairesis can be found in members of the Platonic Academy (especially
Speusippus[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] 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.
[(german) Hans Leisegang: Denkformen, Walter de Gruyter, Berlin 1951, p. 252]
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