Diairesis ( grc, διαίρεσις, diaíresis, "division") is a form of

classification Classification is a process related to categorization, the process in which ideas and objects are recognized, differentiated and understood. Classification is the grouping of related facts into classes. It may also refer to: Business, organizat ...

used in

ancient Ancient history is a time period from the History of writing, beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian language, Sumerian c ...

(especially

Platonic Plato's influence on Western culture was so profound that several different concepts are linked by being called Platonic or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole. It ...

)

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

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 Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...

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. Apart from this definition, the procedure also results in a

taxonomy Taxonomy is the practice and science of categorization or classification. A taxonomy (or taxonomical classification) is a scheme of classification, especially a hierarchical classification, in which things are organized into groups or types. ...

of other concepts, ordered according to a general–specific relation. The founder of diairesis as a method was

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...

. 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 Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

Plato's method of definition

Diairesis is Plato's later method of

definition A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitio ...

based on division, developed in the

Platonic dialogues Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...

'' Phaedrus'', ''

Sophist A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ' ...

'', ''

Statesman A statesman or stateswoman typically is a politician who has had a long and respected political career at the national or international level. Statesman or Statesmen may also refer to: Newspapers United States * ''The Statesman'' (Oregon), a n ...

'', and ''

Philebus The ''Philebus'' (; occasionally given as ''Philebos''; Greek: ) is a Socratic dialogue written in the 4th century BC by Plato. Besides Socrates (the main speaker) the other interlocutors are Philebus and Protarchus. Philebus, who advocates the ...

''. Further applications are found in the ''

Laws Law is a set of rules that are created and are law enforcement, enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. ...

'' and ''

Timaeus Timaeus (or Timaios) is a Greek name. It may refer to: * ''Timaeus'' (dialogue), a Socratic dialogue by Plato *Timaeus of Locri, 5th-century BC Pythagorean philosopher, appearing in Plato's dialogue *Timaeus (historian) (c. 345 BC-c. 250 BC), Greek ...

''. 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 Merism ( la, merismus, grc-gre, μερισμός, merismós) is a rhetorical device (or figure of speech) in which a combination of two ''contrasting parts'' of the whole refer to the whole. For example, in order to say that someone "searched e ...

: 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 In philosophy, techne (; , ) is a term that refers to making or doing, which in turn is derived from the Proto-Indo-European root "Teks-" meaning "to weave," also "to fabricate". As an activity, ''technē'' is concrete, variable, and context-dep ...

'', 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 Homer (; grc, Ὅμηρος , ''Hómēros'') (born ) was a Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Homer is considered one of the ...

. Also an adoption from the fields of mathematics has been considered, like one from musicology, one from pre-scientific and everyday divisions and one from medicine. About forerunners in the field of philosophy there are as well different opinions. Under consideration are

Prodicus of Ceos Prodicus of Ceos (; grc-gre, Πρόδικος ὁ Κεῖος, ''Pródikos ho Keios''; c. 465 BC – c. 395 BC) was a Greek philosopher, and part of the first generation of Sophists. He came to Athens as ambassador from Ceos, and became known as ...

Democritus Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. No ...

Leucippus Leucippus (; el, Λεύκιππος, ''Leúkippos''; fl. 5th century BCE) is a pre-Socratic Greek philosopher who has been credited as the first philosopher to develop a theory of atomism. Leucippus' reputation, even in antiquity, was obscured ...

, and the

sophists A sophist ( el, σοφιστής, sophistes) was a teacher in ancient Greece in the fifth and fourth centuries BC. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics, and mathematics. They taught ' ...

. It was even suggested that Plato says that he himself found the new method, which shows that it is possible that Plato had no forerunners at all.

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

and in the botany of

Theophrastus Theophrastus (; grc-gre, Θεόφραστος ; c. 371c. 287 BC), a Greek philosopher and the successor to Aristotle in the Peripatetic school. He was a native of Eresos in Lesbos.Gavin Hardy and Laurence Totelin, ''Ancient Botany'', Routledge ...

. Diairesis is central to

Galen Aelius Galenus or Claudius Galenus ( el, Κλαύδιος Γαληνός; September 129 – c. AD 216), often Anglicized as Galen () or Galen of Pergamon, was a Greek physician, surgeon and philosopher in the Roman Empire. Considered to be one of ...

'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 edicalsects 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.) Philosophically relevant methodical divisions or statements about the method of ''diairesis'' can be found at exponents of the Platonic Academy (especially

Speusippus Speusippus (; grc-gre, Σπεύσιππος; c. 408 – 339/8 BC) was an ancient Greek philosopher. Speusippus was Plato's nephew by his sister Potone. After Plato's death, c. 348 BC, Speusippus inherited the Academy, near age 60, and remained ...

and

Xenocrates Xenocrates (; el, Ξενοκράτης; c. 396/5314/3 BC) of Chalcedon was a Greek philosopher, mathematician, and leader (scholarch) of the Platonic Academy from 339/8 to 314/3 BC. His teachings followed those of Plato, which he attempted to d ...

), exponents of the

Peripatetic school The Peripatetic school was a school of philosophy in Ancient Greece. Its teachings derived from its founder, Aristotle (384–322 BC), and ''peripatetic'' is an adjective ascribed to his followers. The school dates from around 335 BC when Aristo ...

(especially

Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...

), at the

Stoicism Stoicism is a school of Hellenistic philosophy founded by Zeno of Citium in Athens in the early 3rd century Common Era, BCE. It is a philosophy of personal virtue ethics informed by its system of logic and its views on the natural world, asser ...

(especially

Chrysippus Chrysippus of Soli (; grc-gre, Χρύσιππος ὁ Σολεύς, ; ) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of the Stoic philosopher Cleanthes. When Clean ...

), at the

Middle Platonism Middle Platonism is the modern name given to a stage in the development of Platonic philosophy, lasting from about 90 BC – when Antiochus of Ascalon rejected the scepticism of the new Academy – until the development of neoplatonism u ...

(especially

Alcinous In Greek mythology, Alcinous (; Ancient Greek: Ἀλκίνους or Ἀλκίνοος ''Alkínoös'' means "mighty mind") was a son of Nausithous and brother of Rhexenor. After the latter's death, he married his brother's daughter Arete who bore ...

Maximus of Tyre Maximus of Tyre ( el, Μάξιμος Τύριος; fl. late 2nd century AD), also known as Cassius Maximus Tyrius, was a Greek rhetorician and philosopher who lived in the time of the Antonines and Commodus, and who belongs to the trend of the Sec ...

Philo Philo of Alexandria (; grc, Φίλων, Phílōn; he, יְדִידְיָה, Yəḏīḏyāh (Jedediah); ), also called Philo Judaeus, was a Hellenistic Jewish philosopher who lived in Alexandria, in the Roman province of Egypt. Philo's deplo ...

) and at the

Neoplatonism Neoplatonism is a strand of Platonism, Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and Hellenistic religion, religion. The term does not encapsulate a set of ideas as much as a chain of ...

(especially

Plotinus Plotinus (; grc-gre, Πλωτῖνος, ''Plōtînos''; – 270 CE) was a philosopher in the Hellenistic philosophy, Hellenistic tradition, born and raised in Roman Egypt. Plotinus is regarded by modern scholarship as the founder of Neop ...

, 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

References

External links

* {{Authority control Classification systems Concepts in ancient Greek epistemology Concepts in ancient Greek ethics Concepts in ancient Greek philosophy of mind Concepts in logic Definition History of logic Philosophical methodology Platonism Rhetorical techniques Stoicism Theories in ancient Greek philosophy