# Dihairesis

Plato's definition of the term "angling"

The Dihairesis ( classification of terms , Greek  διαίρεσις ) is a form and method of classification used in ancient logic , which makes it possible to order concepts in a system and to define concepts . A simple example of a dihairesis would be to subdivide the term "furniture" into the sub-terms "tables", "armchairs", etc.

In Plato, the Dihairesis is a logical method with which a term can be determined by dividing a more general term into (at least two) sub-terms until one can give a definition of the term sought. In addition to defining a term, it also results in a hierarchical structure of general and subordinate concepts.

The founder of Dihairesis was Plato , who in the 4th century BC BC was also the first to give instructions for performing a dihairesis. Later ancient logicians (such as Aristotle ) also commented on the dihairetic classification of terms, and similar methods were soon used in other sciences, such as in ancient biology to classify plants. Today other classification methods play an important role in the various sciences. The Dihairesis has only historical significance. Their treatment today is limited to the specialist literature on the history of philosophy.

## translation

The Greek word διαίρεσις (dihaíresis) can be translated as 'division' or 'separation'. The Greek dihaíresis is a noun of the verb dihairéin ('take apart, separate, (two) divide, distinguish'), which is composed of hairéin ('take') and the prefix diá ('apart'). The Romans translated the Greek word divisio . The English translation is division .

## example

The starting point of the Dihairesis method is the question of the definition of any term, for example: What is a fishing rod? In order to find the definition of the angler, one first creates a generic term: The angler exercises a skill. Then the generic term is divided into types: There are acquiring and manufacturing arts. Then the term sought is subordinated to one of the two types of the generic term: The anglers practice an acquisition craft. Now the species itself is further subdivided into its subspecies until the lowest, indivisible species (the atomon eidos ) is reached. From the two lowest types ( harpoon fishing and angling ) and their generic term (wounding fishing) , the exact definition of the term sought can now be formed: Angling is the artistry of wounding fish with a hook, during the day, for the purpose of acquisition.

## Plato

Plato

### Origin of the method

It is not known whether conceptual divisions were deliberately set up before Plato. The different assumptions about possible precursors go back to Homer (8th century BC). However, it is more plausible that Plato adopted the Dihairesis method from ancient science. It has been claimed that Dihairesis played a role in mathematics even before Plato's time; other assumptions see the original application in musicology or medicine . Forerunners within philosophy were also considered, namely Prodikos von Keos , the Sophists, as well as Democritus and Leucippus . According to a completely different hypothesis, Plato ascribes the finding of the classification to himself, which would mean that there are no forerunners. And finally, a simple transfer of simple and everyday classifications into the logic was also considered.

From a philosophical perspective, Plato's Dihairesis, with its orderly system of terms, is probably a reaction to the arbitrary, often deliberately misleading conceptual acrobatics of the sophists, whose views and methods were criticized and opposed by Socrates and Plato.

### Meaning of Dihairesis in Plato's philosophy

The theory of Dihairesis and its applications can be found above all in the Platonic dialogues Sophistes , Politikos , Philebos and Phaedrus , further applications, among others, in the dialogues Nomoi and Timaeus .

#### The three platonic methods

With Richard Robinson, one can distinguish three essential methods within the Platonic dialectic that lead to knowledge. First , the Socratic refutation method named after Socrates in the early dialogues, which leads to insight into one's own ignorance. Second, the method of hypothesis in the middle dialogues, which tests hypotheses, and third, the method of dihairesis in the late dialogues. In the early dialogues, in which Socrates is the main actor, the search is mostly for the definition of a term with which the essence of what is designated is to be grasped clearly and completely (for example, What is the pious? ). In the late dialogues, the Dihairesis method was a means of answering similar questions of definition. With it you get from the question What is angling? For definition Angling is the skill of wounding hunting fish with a hook during the day for the purpose of acquisition .

cultivated fruits
(as opposed to wild fruits)
Dried fruits
 Grain vegetables

Tree fruits
 fruit that is difficult to preserve long-life fruit (e.g. figs, nuts)

The classification of fruits according to Plato in Critias as an example of a biological classification

#### Interpretations

Some modern philosophers (especially Julius Stenzel ) claim that with the introduction of the Dihairesis method, Plato began to distance himself from some aspects of his earlier doctrine of ideas and to adapt this doctrine to a new level of knowledge. For example, in an earlier phase of the development of the doctrine of ideas, terms (mostly of an ethical nature) were equated with one another (e.g. the beautiful is the good ). The lack of differentiation in such statements caused Plato to introduce subsumption by means of the Dihairesis, which defines a systematic order of concepts. Many interpreters also suspect that the Dihairesis shows a general tendency of Plato to turn increasingly to the empirical. Within the early doctrine of ideas there was still an irreconcilable separation ( chorismos ) between the true world of being (the world of ideas) and the world of becoming (the empirically given world ) , which was discredited as a mere appearance , which would only be overcome with the application of the conceptual classification. The ideas are now no longer exclusively located in the transcendent area beyond the sensually perceptible things, as the definition of the angler shows. This hypothesis of a development of the Platonic philosophy is, however, not approved by all researchers. Among other things, it is opposed to the view that Plato never intended a strict separation of ideas from the realm of the empirical world (he himself ironically ironizes this position). Rather, one must imagine the ideas as the basis of every knowledge woven into every access to the world.

#### Theory of Dihairesis

The principle of division is a basic logical phenomenon , but there is controversial debate as to whether Plato's method of Dihairesis is also of high relevance for logic.

• The purpose and result of the classification is either a definition or a classification . The classification results either in a definition of a single term or in a classification of a plurality of terms in a system, that is, of all species and subspecies of a genus. In the pseudoplatonic (wrongly attributed to Plato) script Horoi , the term "definition" is defined: "Definition (horos) : explanation (logos) from the difference (diaphora) and the closest genus (genos synkeimenon) ". The definition of woman would be accordingly: "A woman is a person (closest genus) whose gender is not male (difference)."
• Classification criterion : A genus is always divided into different types according to a certain classification or difference criterion (diaphora) . “Man” and “woman” differ in terms of their “gender”. "Bipedes" differ from "quadrupeds" with regard to the criterion "number of legs".
• Separating and summarizing: The counterpart to the method of division or division (dihairesis) is the reverse method of combining (synagogue) concepts.
Left picture: the "Tree of Porphyrios" according to Petrus Hispanus (13th century). Right picture: the "Tree of Porphyrios" in a modern representation.
• Rules for the correct classification: Plato gives numerous rules for the implementation of a correct concept classification. However, he does not always adhere to it exactly, possibly because he sees the Dihairesis more as a skill ( téchne ) , not as a rigidly defined and strictly followed method.
• Dichotomy and enumeration : Plato expressly prefers the division of the genus into two species over the division into more than two species. The two types are usually opposite to each other ( dichotomy ), e.g. B. Even numbers and odd numbers . If a certain classification comprises more than two elements, one can speak of an enumeration (e.g. Socrates, Plato, Aristotle, Jimi Hendrix etc. are people ).
• End of classification:
• The top end of the Platonic Dihairesis is controversial. The five "highest genera" (megista gene) listed by Plato do not necessarily have to be understood as generic terms of a hierarchical system of terms.
• At the lower end of the classification, according to Plato, there is a term that can no longer be subdivided or subdivided (atomon eidos) , which therefore has no sub-terms. Firstly, what exactly this indivisible concept is (a concept, an idea or an extensional class of individual elements) and, secondly, what falls under this indivisible concept (the non-conceptual sensually perceivable objects or an indefinite manifold) is disputed.

Dihairesis was only illustrated in diagrams and lists at a later time; in Plato it occurs exclusively in the context of dialogues. Today Dihairesis is usually illustrated by conceptual pyramids such as the tree of Porphyrios , which is a graphic that goes back to Boethius (6th century). Attempts were also made to visualize lines, areas and brackets. There are only rudimentary attempts to transform the Dihairesis into usable formulas, to translate them into formal logical languages.

Many individual questions concerning Dihairesis, on which Plato did not or only hinted at, are still controversial today. James A. Philip provides a list of these open questions.

### Quotes and passages

“But because they are not used to classifying what they are looking at according to species, they lump together these very different things into one and consider them to be similar; in the same way they do the opposite in that they do not separate other things from one another after a proper division, since whoever first notices the similarity between many should not let go until he has seen all the differences in the same, just so many they are based on concepts, and again, when the manifold dissimilarities have appeared in a majority, one should not be able to shy away and cease until one has included all related within one similitude and dealt under the essence of a species. "

- Plato : Politikos 285
A dihairetic structure visualized with brackets (from the encyclopedia by Denis Diderot and D'Alembert )

" Gast : Since we have now admitted that the concepts behave in the same way with the intention of mixing, it is not necessary to speak to a science to determine who wants to correctly show which concepts agree with which and which do not record, tape? And again, whether there are those that hold them together in general that they are able to mix? And again in the separations, whether others are consistently the cause of the separation?
Theaetetos: How should it not need a science and perhaps the greatest!
Guest: And what, Theaetetos, should we call them? Or have we, with Zeus, got into the science of free men without noticing it? And may well have first found the philosopher by searching for the sophist?
Theaetetos: What do you mean?
Gast: Do we not want to say that this is part of dialectical science? The division according to genre, so that one does not consider the same term to be another, or another for the same?
Theaetetos: We want to say that.
Guest: Anyone who knows how to do this properly will notice a concept through many individually separated from each other spread out in all directions, and externally embraced many different from one another, and again consistently linked one with only one of many, and finite many completely separated from one another. This then means to what extent each can enter into community and to what extent not knowing how to differentiate according to type.
Theaetetos: In all ways, certainly.
Gast: But I hope you will not instruct this dialectical business to anyone other than the pure and right philosophizing one?
Theaetetus: How should one instruct someone else?
Guest: In this area around we will find the philosopher both now and afterwards, if we look for him. "

- Plato : Sophistes 253

Considerations on the method of Dihairesis can be found primarily in the dialogues of Philebos (16c – 17a) and in three passages of Phaedrus (265c – 266c, 273d – 273e, 277b), applications mainly in the dialogues of Sophistes and Politikus, but also in Philebos (Division of letters 18b-18d and division of musical intervals 17d). The definition of what a fisherman is is found in Sophists 218e-221b, six different definitions of the sophist in Sophists 221b-231e, and a seventh definition of the sophist in Sophists 235b-236e and 264c-268d. Further concrete applications of Diahiresis are the first definition of politician in Politikos 258b – 267c and the definition of weaving in Politikos 279c – 283b.

## reception

### Antiquity

About the time of Plato there are three traditional collections of definitions whose unknown authors can be assigned to the environment of the Platonic Academy : that of Pseudo-Aristotle , that of Pseudo-Andronicus and the pseudo-Platonic Horoi . In the academy, but also in other philosophically interested circles, there were collections of classifications and definitions that were widespread in different versions and arrangements up to late antiquity.

The successor of Plato as scholarch (head of the academy) was Speusippus . Only fragments of his writings have survived, but some work titles have come down that clearly refer to the method of Dihairesis: Dihairesis and assumptions about similarities , About examples of genera and species , Definitions . The fragments of his work Homoia (Similarities) contain zoological and botanical definitions, such as the meadow herb, the cuckoo fish or the spindle animal. Apparently Speusippos tried to organize and classify the totality of the things known at his time according to species and genre by systematically applying the dihairetic method practiced in the academy to all areas of knowledge. In the parts of Homoia that have not been preserved , he probably included the areas of the inanimate, the spiritual and material products of man and mathematics through definition and classification in his all-encompassing system of subdivisions. With this he probably wanted to summarize the collective work of the academy systematically.

The surviving list of the writings of Speusippus' successor Xenocrates , which are lost today , also suggests that he dealt with Dihairesis.

#### Aristotle and the Peripatetic School

Aristotle

Aristotle was the first occidental author to write a systematic textbook on logic . In modern research on the history of logic , one sees Plato's theory of Dihairesis, which is scattered over many dialogues, as an important preliminary stage of the Aristotelian Organon in many respects . Aristotle, however, expresses himself extremely critical of the Dihairesis method on several occasions. According to some interpreters, his criticism is essentially not directed against the Dihairesis as a method of classification, but against the, in his view, unjustified claim that this is a method of proof. In any case, as a mere division of concepts, it differs essentially from Aristotle's syllogistic, which deals with inferences from given sentences to new sentences.

In other passages, Aristotle certainly admits that Dihairesis was also useful. In addition, he sets up innumerable classifications and that both his theory of categories and his syllogistics refer to the Dihairesis as a predecessor. The latter can be seen from the fact that the Aristotelian inference logic is a conceptual logic that presupposes or constructs a hierarchically ordered system of concepts. The following conclusion (left) is based, for example, on the following hierarchy of terms (right):

 All human beings are mortal beings All Greeks are human It follows: All Greeks are mortal beings
Mortal beings
People
 Greeks Egyptians, Romans, etc.

Animals, plants

Illustration of the logical inference with the help of quantity diagrams
##### Critique of Dihairesis

Aristotle's criticism of Dihairesis consists primarily in the fact that he regards it as a “weak conclusion”. It does not prove statements, but simply postulates them. In doing so, she takes the topmost of the three terms in the end as the middle term . If one wants to prove a definition, then, according to Aristotle, this is not possible by means of the Dihairesis method; rather, definitions achieved through the division of terms are unproven assertions.

##### The definition
Genus, species difference, species and individual according to Aristotle's categories
 Second substance genus (living being) species-forming difference Two-legged, gifted with reason neighing one- footed quadruped Second substance: kind of human Second substance: kind of horse Individuation First substance: Socrates First substance: Plato First substance: bucephalos

The Aristotelian definition, which refers to Dihairesis, became famous. Species terms are defined by specifying the genus and the species- forming difference . An example of a definition would be: "Man is (in contrast to animals) a living being gifted with reason."

“Some of that which always lives in a single thing extends to other things. [...] If you really investigate an entire area, you have to separate the genus down to the first, indivisible, lowest species, [...] then you have to try to find the definitions of these species. "

- Aristotle : Analytica posteriora 2.13
##### First and Second Substance

Aristotle differentiates first substances, by which he means for example certain people like "Socrates" or "Plato", from second substances, by which he means species and generic terms, such as "human" or "living being". Second substances, one could say general terms, can be predicted from the first substances, one could say from certain objects.

##### terminology

Plato had not adhered to a consistent terminology with regard to the terms “genus” and “species”; only Aristotle used the word genos for “genus” and eidos for “species” throughout .

##### Zoology, botany and music theory

Aristotle used procedures similar to the dihairestic method in his work Historia animalium for zoological classification. According to some researchers, the Dihairesis is at the beginning of the classifying biology, others speak of essential differences between the Dihairesis and the classifications in the Historia animalium . It was assumed, for example, that although Aristotle first adopted the method of the academics for zoological classifications, in his later major biological works he had advanced to a more complex empirical system.

Theophrast took over the approach of his teacher Aristotle for his botany. The music theorist Aristoxenus , also a student of Aristotle, used Dihairesis to classify the intervals and rhythms.

#### Parodies

Some modern scholars insinuate that Plato could not possibly have meant all the Dihairese appearing in his dialogues seriously. Accordingly, some have straightforward ridiculous features; Even ancient writers made fun of Plato's classifications of terms. Dialog Politikos is defined on the search for the definition of the statesman implicitly man. The definition is based on purely physical characteristics (something similar can be found in Aristotle's zoology) and ultimately states that humans are unfeathered bipeds. In Diogenes Laertios there is a passage in which it is reported in which way the Cynic Diogenes of Sinope is said to have made fun of this definition.

Since Plato was applauded with his definition that man is a bipedal, featherless living being, Diogenes plucked a rooster, carried it into class and shouted:“ This is Plato's man. ”That is why the definition was added“ broad-nosed ”. "

- Diogenes Laertios

From a comedy by the poet Epicrates , who wrote in the first half of the 4th century BC. Was active during Plato's lifetime, a passage has been preserved in which Dihairesis and Plato and his students are parodied .

This 19th century painting by an unknown author shows Diogenes of Sinope bringing a plucked rooster past Plato.

Person A : How about Plato, Speusippus and Menedemus?
what' subjects is your investigation now?
Person B: I saw the crowd of lads ... at
the academy's practice area , heard speeches,
unspeakable, meaningless: definitions about nature.
They divided the nature of the animals,
the species of the trees, the vegetable genera.
They also checked the pumpkin, which kind it was probably ...
First, everyone stood in silence,
bent down, meditated ...
Suddenly someone said: A round vegetable!
The other: herb! The third ': a tree. -
Hearing this, a doctor from Sicily let
himself be heard with a fart: They are crazy!
Person A: You got really angry? And don't yell now:
This is an insult! Because it is not fitting
to express oneself like that in the classroom !
Person B: No, that doesn't
bother the boys at all, and Plato, who stood by, said
very gently and without anger: Try
to define again from the beginning:
What is a pumpkin? - And they further divided ... "

- Epicrates

#### Hellenism and the Roman Empire

Example of a Middle Platonic division: The universe in Philon of Alexandria (1st century)
The cosmos
Beings
(alive)
Plants
(soulless)
wild
 ...
cultivated
 ...
Animals
(animated)
unreasonable
Birds
 ...
Aquatic animals
 ...
Land animals
 ...
sensible
mortal
 Men Women
immortal
 ...
Matter
(inanimate)
The heaviness
and density
earth
Mainland
 ...
Islands
 ...
water
Rivers
 ...
Seas
 ...
The light
and thin
air  Fire

Methodical classifications relevant to the history of philosophy or statements about the method of classification can also be found in several important philosophical schools of Hellenism and the Roman Empire up to late antiquity .

The Stoic Chrysippus (3rd century BC) differentiates the Dihairesis (as a division of a genus into its species) from an “Antidihairesis” (as a division of the genus into contradicting opposites), a “Hypodihairesis” (as a further division of a species) and a completely new kind of division, division (merismos) as a division of attributes according to the substances in which they occur.

The method of the dihairetic division came about in the 2nd century BC primarily through the mediation of the logic of the Stoics. To the knowledge of the Roman jurists, including Publius Mucius Scaevola , Marcus Junius Brutus , Manius Manilius and above all Quintus Mucius Scaevola . This was used to create a legal classifications especially the Termini genus (genus) of the broader term output and type (species) for the obtained after the division of generic terms. A later application of Dihairesis by a Roman jurist can be found in the Institutiones of Gaius from the 2nd century AD. Each main section of this work begins with a supreme distinction (summa divisio) , in which elementary terms are subdivided, such as the term people (personae) into free (liberi) and slaves (sciavi) .

Cicero (1st century BC) understands the definition as a statement (oratio) that determines its object in its what-being. For Cicero, a definition is either a division (partitio) or a division (divisio) . The division splits a perceptible object in its organic parts, such as the human body in the head, shoulders, hands, legs, etc. The division, however, does not share objects, but concepts, namely one genus (genus) in their types (formae) .

Middle Platonists of the 1st to 3rd centuries such as Alcinous , Maximos of Tire and Philon of Alexandria divided the totality into the different kinds of matter and living beings. The Stoic Seneca (1st century) was also influenced by these dihaireses .

Dihairesis also played a role in Neo-Platonism (from the 3rd century). In the work of Plotinus , the founder of Neoplatonism, it is only mentioned incidentally, but with his illustration of Dihairesis , Plotin's pupil Porphyry gained great importance for the further history of reception. In addition, in his influential Isagoge , Porphyry deals extensively with five terms (the predicables ) that can be viewed as central terms in the theory of Dihairesis: genus, species, difference, proprium and accidental.

The academician Damascius , who worked in the 5th and 6th centuries , wrote a commentary on Plato's Dialogue Philebos, in which he specifies twelve tasks in Dihairesis. Only four of them can be directly related to Plato's Philebos, the remaining eight go beyond Plato's statements.

In Boethius (6th century) at the end of antiquity one finds a kind of summary of the previous teachings of classification. His writing De divisione was later available to medieval logicians and philosophers and thus formed a bridge between antiquity and the Middle Ages. Boethius deals with the benefits that classifications can have, the different types of classification and the methodology of classification. The two basic types of division are, according to his presentation, the “division according to accidents(divisio per accidens) , that is, according to merely secondary characteristics, and the more important “division per se(division secundum se) . The "division in itself" is in turn divided into the division of a genus into its species (divisio generis in species) , the division of a whole into its parts (divisio totius in partes) and the division of different meanings of a word (divisio vocis in significationes) . Although Boethius thought Neoplatonic as a philosopher, he nowhere refers to dialogues of Plato in De divisione , but refers to Aristotle and refers to the Aristotelian Andronikos of Rhodes , who wrote a treatise on the division. His work, which is entirely Aristotelian influenced, is mainly based on the portrayal of Porphyry in his now lost commentary on Plato's dialogue with Sophistes ; Porphyrios had used an Aristotelian source.

### middle Ages

In medieval logic, the method of divisio (division, subdivision) was widespread. Historically, it is the late result of a further development of the original Platonic Dihairesis, but it differs in some respects from Plato's method, which was only indirectly known in the Middle Ages - thanks to the mediation of Aristotle, Cicero, Porphyrios and Boethius. The authors of medieval sums , in which the entire knowledge of a subject was processed into a system, used the method of deriving from a principle by means of the divisio . This is how “concept pyramids” emerged, for example in representations of the science systematics and / or the systematics of transcendental concepts. Systems with such classifications can be found in the 12th century with Dominicus Gundisalvi , in the 13th century with Thomas Aquinas , Bonaventure and Johannes Duns Scotus .

 Philosophy (or science) Concerning objects that man did not create Concerning objects that man has created theology mathematics physics politics Economy ethics
The division of philosophy (as the epitome of all sciences) according to Dominicus Gundisalvi

### Modern times

There are no representatives of Dihairesis in modern times, but there are dozen, often very different, attempts at interpretation. Modern exploration began in 1888 with extensive work by Franz Lukas. A study by Julius Stenzel published in 1917 was groundbreaking for later research. In his work Experience and Judgment , Edmund Husserl referred to the connection between synthesis and Dihairesis in order to characterize the analytical-synthetic structure of a predicative judgment based on the Aristotelian theory of definitions with the question: “What is the type of connection between these two members (i.e. the term S and the term p), which have always been differentiated in the judgment, to what extent is the judgment Synthesis and Diairesis in one? "In 1928, Hans Leisegang had Dihairesis as a main representative of a certain way of thinking, he says a" form of thinking ", tried to identify. According to Leisegang, it is the hierarchical “concept pyramid” way of thinking. In 2001, Karen Gloy distinguished five different types of rationality , one of which she called the “dihairetic type of rationality”. This is the predominant one in the Western cultural area and, together with mathematical rationality, has formed the paradigm of our understanding of science since ancient times.

#### Modern logic

Class A (e.g. the class of fishermen) is subsumed under class B (hunters).

While questions of division play a role in modern logic, modern logicians and the historians of philosophy who deal with the history of logic very rarely make explicit reference to Plato's Dihairesis.

The diairesis touched questions of propositional logic and the circuit logic . You can easily read statements from a term pyramid. A predicate is basically a higher term (generic term), a subject is basically a lower term (species term). A conclusion , as formulated for the first time by Aristotle, relates three (by means of classification) hierarchically structured terms: subject, predicate, middle term . This shows the (at least historical) importance of the Dihairesis for every type of system.

While Aristotle systematized the higher and lower order of concepts in his syllogistics, modern classical logic goes a step further. The Aristotelian syllogistics is now considered to be a mere subsystem of the predicate logic that has emerged since 1879 . The class logic that emerged since 1847 (as well as set theory since 1874 ) for its part offers an extremely precise and comprehensive formal treatment of the scope of the term , i.e. H. the superordinate and subordinate order of terms (or of “classes” and “sets”). In modern class logic, for example, one writes for the natural language expression “the class of the hunters” in one (of the many) invented artificial languages : (in words: “those who are”, where stands for the hunters). To express, for example, that Socrates is a human being, one can write, whereby Socrates stands for the individual, for the class of people and for an element of . Whether a purely extensional class logic can fully describe the Platonic Dihairesis is controversial. ${\ displaystyle f (x)}$${\ displaystyle x}$${\ displaystyle f}$${\ displaystyle f}$${\ displaystyle a \ in K}$${\ displaystyle a}$${\ displaystyle K}$${\ displaystyle \ in}$

#### Criticism and Defense of Dihairesis

In modern times, the objection to Plato's Dihairesis is that in order to be able to divide a term into sub-terms at all, one needs prior knowledge of this structure, and that the classifications do not follow any specific rule, but are arbitrary. Karen Gloy problematized the relationship between the purely logically dividing system and reality (also: ontological system) as well as the internal structure of the reality-related logical-dihairetic system. She also pointed to the historical change in the criteria according to which subject areas such as plants or animals are systematically classified. In addition, modern critics have generally questioned the value and usefulness of Dihairesis. It was thought to have no philosophical relevance and, because of its simplicity, for the youngest students of the Platonic Academy. A main proponent of this view is Gilbert Ryle , whose criticism of the value of Dihairesis shows in places a polemical character. Another supporter of this view is John R. Trevaskis. However, the group of representatives of the contrary opinion is more numerous. They take Dihairesis seriously and defend it, sometimes even expressing admiration. This group includes Carl Prantl , Joseph Maria Bocheński , Franz Lukas, Julius Stenzel, Julius ME Moravcsik, James A. Philip and John Lloyd Ackrill .

## literature

Lexicon article

• Fritz-Peter Hager: Dihairesis . In: Joachim Ritter u. a. (Ed.): Historical dictionary of philosophy . Vol. 2, Schwabe, Basel 1972, Col. 242-244
• Michael Schramm: Dihairesis . In: Christian Schäfer (Ed.): Platon-Lexikon. Term dictionary on Plato and the Platonic tradition . Wissenschaftliche Buchgesellschaft, Darmstadt 2007, pp. 92–95
• Matthias Gatzemeier : Dihairesis . In: Jürgen Mittelstraß (Hrsg.): Encyclopedia Philosophy and Philosophy of Science . Vol. 1, Metzler, Mannheim 1980, p. 482.
• Niko Strobach: Dialectic / Dihairesis . In: Christoph Horn , Jörn Müller, Joachim Söder (Hrsg.): Platon-Handbuch. Life - work - effect . Metzler, Stuttgart 2009, pp. 258-263.
• Hartmut Westermann: Dihairesis . In: Christoph Horn, Christof Rapp (Hrsg.): Dictionary of ancient philosophy . CH Beck, Munich 2002, Col. 110-112.

Overview of the history of reception

• Hans Leisegang: Denkformen , Walter de Gruyter, Berlin 1951 (reprint of the 1928 edition), pp. 215–284
• Paul Michel : Branches, curly brackets, decimal places. Potency and limits of the taxonomic classification system from Plato to Theodor Zwinger to Melvil Dewey . In: Paul Michel, Madeleine Herren, Martin Rüesch (Ed.): General knowledge and society. Files from the international congress on knowledge transfer and encyclopedic ordering systems, from September 18 to 21, 2003 in Prangins , Shaker Verlag , 2007, pp. 105–144, here: pp. 111–115 ( online , PDF; 3.9 MB)
• Peter Kolb: Platons Sophistes , Königshausen & Neumann, Würzburg 1997, pp. 202–213
• Margarita Kranz: The knowledge of the philosopher , dissertation Tübingen 1986, pp. 132-135

Investigations

• Franz Lukas: The method of division in Plato . Halle (Saale) 1888 ( online )
• Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle . 2nd edition, Teubner, Stuttgart 1961 (reprint of the Leipzig 1931 edition)
• James A. Philip: Platonic Diairesis . In: Transactions and Proceedings of the American Philological Association , Vol. 97, 1966, pp. 335-358
• Artur von Fragstein : The Diairesis with Aristotle . Adolf M. Hakkert, Amsterdam 1967

## Footnotes

1. Plato, Sophist 218e-221b.
2. ^ Henry George Liddell , Robert Scott : A Greek-English Lexicon , 9th Edition, Clarendon Press, Oxford 1940, p. 395 ( online ).
3. This example comes from Plato's dialogue Sophistes : Plato, Sophistes 218e – 221b.
4. ^ Hans Leisegang: Denkformen , Walter de Gruyter, Berlin 1951, p. 220.
5. Hermann Koller: The diheretic method . In: Glotta Vol. 39, 1961, pp. 6–21, here: p. 23.
6. Hans Herter : Plato's natural history . In: Rheinisches Museum für Philologie Vol. 121, 1978, pp. 103-131, here: p. 116 ( online , PDF; 6.6 MB).
7. Michael Schramm: Dihairesis . In: Christian Schäfer (Ed.): Platon-Lexikon. Term dictionary on Plato and the Platonic tradition . Wissenschaftliche Buchgesellschaft, Darmstadt 2007, pp. 92–95, here: p. 92; John Lloyd Ackrill: In Defense of Platonic Division . In: John L. Ackrill: Essays on Plato and Aristotle , Clarendon Press, Oxford 1997, pp. 3–109, here: p. 105.
8. ^ Artur von Fragstein: Die Diairesis in Aristoteles , Hakkert, Amsterdam 1967, p. 80.
9. Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , 2nd edition, Leipzig 1931, reprint: Teubner, Stuttgart 1961, p. 112.
10. Plato, Sophistes 267; see Margot Fleischer: Hermeneutische Anthropologie. Plato, Aristoteles , de Gruyter, Berlin 1976, p. 143.
11. ^ Richard Robinson: Plato's Earlier Dialectic , Oxford University Press, Oxford 1953, p. 89.
12. Hans Herter: Plato's natural history (PDF; 6.6 MB) . In: Rheinisches Museum für Philologie Vol. 121, 1978, pp. 103-131, here: p. 111.
13. Kurt Walter Zeidler: Outline of the transcendental logic , Junghans, Cuxhaven 1992, p. 127.
14. For example, the stemma of the types of movement, obtained dihairetically; see Christian Pietsch: The Dihairesis of the Movement in Plato, Nomoi X 893b1–894c9 . In: Rheinisches Museum für Philologie 146, 2003, pp. 303–327.
15. ^ Richard Robinson: Plato's Earlier Dialectic , Oxford University Press, Oxford 1953, p. 65.
16. Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , 2nd edition, Leipzig 1931, reprint: Teubner, Stuttgart 1961, pp. 42 f., 53.
17. Plato, Critias 115a – 115b; Scheme according to Hans Herter: Plato's natural history (PDF; 6.6 MB) . In: Rheinisches Museum für Philologie Vol. 121, 1978, pp. 103-131, here: pp. 109-111.
18. Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , 2nd edition, Leipzig 1931, reprint: Teubner, Stuttgart 1961, pp. 25–44; See also Friedrich Kümmel: Plato and Hegel on the ontological foundation of the circle in knowledge (PDF; 228 kB) , Max Niemeyer, Tübingen 1968, excerpt: first part. The Platonic Dihairesis and its ontological presuppositions . Second chapter: The dialectic as division and connection of concepts , pp. 74-101 (accessed on January 2, 2011).
19. Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , 2nd edition, Leipzig 1931, reprint: Teubner, Stuttgart 1961, pp. 1, 7 f., 46 f.
20. E.g. Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , 2nd edition, Leipzig 1931, reprint: Teubner, Stuttgart 1961, pp. 19 f., 54–58. Friedrich Kümmel goes further than Stenzel: Plato and Hegel on the ontological foundation of the circle in knowledge , Max Niemeyer, Tübingen 1968, pp. 87, 95.
21. ^ Plato, Sophistes 246.
22. On the dihairetic logic of Plato see also: Walter Cavini: Naming and Argument. Diaeretic Logic in Plato's Statesman . In: Christopher Rowe (Ed.): Reading the Statesman. Proceedings of the III. Symposium Platonicum . Vol. 4 of the International Plato studies . Academia Verlag, Sankt Augustin 1995, pp. 123-138.
23. ^ Pseudo-Plato: Definitions . In: Karlheinz Hülser (Ed.): Platon: Complete Works in Ten Volumes , Insel-Verlag, Frankfurt am Main 1991, Vol. 10, pp. 446 f .; see. Plato, Politicus 285a.
24. Plato, Phaedrus 265d, also Sophistes 253d; 226a; Nomoi 626d; Philebos 16d.
25. ^ Illustration of the tree according to Peter Schroeder-Heister: arbor porphyriana . In: Jürgen Mittelstraß (Ed.): Encyclopedia Philosophy and Philosophy of Science , 2nd edition, Vol. 1: A – B, Stuttgart 2005, p. 192 f.
26. Franz Lukas offers a catalog of all the rules listed in Plato: The method of division in Plato , Halle (Saale) 1888, pp. 109 and 287–290.
27. James A. Philip: Platonic Diairesis . In: Transactions and Proceedings of the American Philological Association , Vol. 97, 1966, pp. 335-358, here: p. 348.
28. James A. Philip: Platonic Diairesis . In: Transactions and Proceedings of the American Philological Association , Vol. 97, 1966, pp. 335-358, here: pp. 342, 350, 357 f.
29. Plato, Politicus 287c.
30. Plato, Sophistes 254. The following genres are involved: being or being (on) , identity or equality (tauton) , difference (heteron) , movement or change (kinesis) , rest or persistence (stasis) .
31. James A. Philip: The "Megista Gene" of the "Sophistes" . In: Phoenix Vol. 23 No. 1, 1969, pp. 89-103, here: p. 89.
32. One of the most important passages on this is Plato, Philebos 16. In connection with Dihairesis cf. Karsten Friis Johansen : The One and The Many . In: Classica et Mediaevalia . Vol. 18, 1957, pp. 1-35.
33. ^ Antony C. Lloyd: Plato's Description of Division . In: Reginald E. Allen (ed.): Studies in Plato's Metaphysics , Routledge and Kegan Paul, London 1965, pp. 219–230, here: p. 221.
34. Konrad Gaiser : Plato's unwritten teaching , Klett-Cotta, Stuttgart 1963, pp. 125–128.
35. Kenneth M. Sayre: Plato's analytic method . University of Chicago Press, Chicago and London 1969, pp. 216-223.
36. James A. Philip: Platonic Diairesis . In: Transactions and Proceedings of the American Philological Association , Vol. 97, 1966, pp. 335-358, here: p. 337.
37. For the assignment see Heinz Gerd Ingenkamp: Investigations on the pseudoplatonic definitions , Otto Harrassowitz, Wiesbaden 1967, p. 109 and Hans Günter Zekl (ed.): Aristoteles: Organon , Vol. 2: Categories, Hermeneutik , Hamburg 1998, p. LXIV -LXVII.
38. ^ Edition: Hermann Mutschmann (Ed.): Divisiones quae vulgo dicuntur Aristoteleae , Leipzig 1907, pp. 42–66. Translation: Hans Günter Zekl (Ed.): Aristoteles: Organon , Vol. 2: Categories, Hermeneutics , Hamburg 1998, pp. 189–231. Detailed commentary: Cristina Rossitto: Aristotele ed altri: Divisioni , Padova 1984, pp. 121–391.
39. Heinz Gerd Ingenkamp: Investigations on the pseudoplatonic definitions , Otto Harrassowitz, Wiesbaden 1967, p. 106
40. ^ Edition: John Burnet (ed.): Platonis opera , Vol. 5, Oxford 1907 (section Horoi ); Translation: Hans Günter Zekl (Ed.): Aristoteles: Organon , Vol. 2: Categories, Hermeneutics , Hamburg 1998, pp. 233–245.
41. ^ Paul Moraux: Aristotelianism among the Greeks , Vol. 2, Berlin 1984, pp. 681-683.
42. See Malcolm Wilson: Speusippos on Knowledge and Division . In: Wolfgang Kullmann, Sabine Föllinger (ed.): Aristotelian biology . Franz Steiner Verlag, Stuttgart 1997 and Andrea Falcon: Aristotle, Speusippus and the Method of Division . In: The Classical Quarterly . Vol. 50, No. 2, 2000
43. Diogenes Laertios, On the Lives and Teachings of Famous Philosophers 6.4.
44. Some fragments are translated by Wilhelm Nestle: Die Sokratiker , Scientia, Aalen 1968 (reprint of the Jena 1922 edition), p. 195. A critical edition of the fragments with commentary is offered by Leonardo Tarán: Speusippus of Athens , Leiden 1981.
45. Hans Krämer : Speusipp . In: Hellmut Flashar (ed.): Outline of the history of philosophy . The philosophy of antiquity , Vol. 3: Older Academy - Aristoteles - Peripatos , 2nd edition, Schwabe, Basel 2004, pp. 13–31, here: pp. 18–20.
46. Diogenes Laertios: About the life and teachings of famous philosophers 6 : 11-14.
47. ^ For example, Joseph Maria Bocheński: Formal Logic , 5th edition, Karl Alber, Freiburg / Munich 1996, p. 46; Klaus Oehler : The historical place where formal logic emerged . In: Ancient Philosophy and Byzantine Middle Ages. Essays on the history of Greek thought , CH Beck, Munich 1969, pp. 48–65, here: pp. 51 f .; William Kneale , Martha Kneale : The Development of Logic , Clarendon Press, Oxford 1962, p. 10. Julius ME Moravcsik opposed a close connection between dihairesis and syllogistics: Logic Before Aristotle: Development or Birth? In: Dov M. Gabbay, John Woods (Ed.): Handbook of the History of Logic , Vol. 1: Greek, Indian and Arabic Logic , Elsevier, Amsterdam u. a. 2004, pp. 1–26, here: pp. 18–20.
48. ^ Christian Pietsch: dihairesis / specifying subdivision . In: Otfried Höffe (Hrsg.): Aristoteles-Lexikon (= Kröner's pocket edition . Volume 459). Kröner, Stuttgart 2005, ISBN 3-520-45901-9 , p. 128 f. On the position of Aristotle, see David M. Balme: Aristotle's use of division and differentiae . In: Allan Gotthelf, James G. Lennox (eds.): Philosophical issues in Aristotle's biology , Cambridge 1987, pp. 69-89; Allan Gotthelf: Division and Explanation in Aristotle's Parts of Animals . In: Hans-Christian Günther, Antonios Rengakos (ed.): Contributions to ancient philosophy , Stuttgart 1997, pp. 215–229; Pierre Pellegrin: Division et syllogisme chez Aristote. In: Revue Philosophique de la France et de l'Étranger 171, 1981, pp. 169-187; Christian Pietsch: Finding principles in Aristoteles , Stuttgart 1992, pp. 78-139.
49. Aristotle, Analytica posteriora 2.13; Topik 6,5,6; De partibus animalium 1, 2, 3 and Metaphysics 1037b – c.
50. Examples in Artur von Fragstein: Die Diairesis in Aristoteles , Hakkert, Amsterdam 1967, pp. 86, 108–155.
51. ^ Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , 2nd edition, Leipzig 1931, reprint: Teubner, Stuttgart 1961, p. 96; Artur von Fragstein: Die Diairesis in Aristoteles , Hakkert, Amsterdam 1967, p. 86; Harold Cherniss : Aristotle's Criticism of Plato and the Academy . Vol. 1, Johns Hopkins Press, Baltimore 1944.
52. Aristotle, Analytica priora 1.31 and Analytica posteriora 2.5. It should be noted that the writings of Plato do not suggest that the Dihairesis should represent a conclusion at all.
53. Hans Leisegang: Denkformen , de Gruyter, Berlin 1951, p. 223 f.
54. Cf. Niko Strobach: Dialektik / Dihairesis . In: Christoph Horn, Jörn Müller, Joachim Söder (Hrsg.): Platon-Handbuch. Life - work - effect . Metzler, Stuttgart 2009, pp. 258-263, here: p. 259; Fritz-Peter Hager: Dihairesis . In: Joachim Ritter u. a. (Ed.): Historical dictionary of philosophy . Vol. 2, Schwabe, Basel 1972, Sp. 242-244, here: 243.
55. Aristotle, Topik 103b15-16.
56. Aristotle, categories 2a ff.
57. ^ Edition: David M. Balme (Ed.): Aristotle: Historia animalium , Vol. 1: Books I – X: Text , Cambridge 2002; Translation: Paul Gohlke: Aristoteles: Tierkunde , 2nd edition, Paderborn 1957 (Aristoteles: Die Lehrschriften Vol. 8,1). See Geoffrey Ernest Richard Lloyd: The Development of Aristotle's Theory of the Classification of Animals . In: Phronesis , Vol. 6, 1961, pp. 59-81 and Wolfgang Kullmann, Sabine Föllinger (Ed.): Aristotelische Biologie . Franz Steiner, Stuttgart 1997.
58. Hans Herter: Plato's natural history (PDF; 6.6 MB) . In: Rheinisches Museum für Philologie , Vol. 121, 1978, pp. 103-131, here: p. 123.
59. ^ Geoffrey Ernest Richard Lloyd: The Development of Aristotle's Theory of the Classification of Animals . In: Phronesis , Vol. 6, 1961, pp. 59-81, here: p. 80.
60. Hans Herter: Plato's natural history (PDF; 6.6 MB) . In: Rheinisches Museum für Philologie , Vol. 121, 1978, pp. 103-131, here: p. 115; Reinhold Strömberg: Theophrastea. Studies on botanical concept formation . Dissertation Gothenburg 1937.
61. Diogenes Laertios, On the Lives and Teachings of Famous Philosophers 6.40.
62. The extract from the work of Epicrates has come down to us through a fragment by Athenaeus (II 59c – f). The German rendering is based on Hans Günther Zekl: Aristoteles: Organon , Bd. 1, Meiner, Hamburg 1997, pp. XXIII f. An alternative translation is offered by Claus Friedrich: Athenaios: The Scholarly Meal. Book I – VI , Part 1: Book I – III , Stuttgart 1998, pp. 104f. See Heinz-Günther Nesselrath : Die Attische Mittlere Komödie , Berlin 1990, p. 277.
63. ^ After Hans Leisegang: Denkformen , Walter de Gruyter, Berlin 1951, p. 243.
64. Diogenes Laertios VII, 61 f. (= Chrysippos, Stoicorum Veterum Fragmenta II, 215.1-10). See also: Fritz-Peter Hager: Dihairesis . In: Joachim Ritter u. a. (Ed.): Historical dictionary of philosophy . Vol. 2, Schwabe, Basel 1972, Sp. 242-244, here: 243.
65. ^ Gaius, Institutiones I, 9-12
66. Cf. (Italian) Mario Talamanca: Lo schema genus-species nelle sistematiche dei giuristi romani . In: Colloquio Italo-Francese La filosofia greca e il diritto romano . Rome 1973 and (Italian) M. Bretone: Storia del diritto romano . Laterza 1987, p. 184 ff.
67. Cicero, Topica 5–8 and 22 ( English and Latin ); see also Hartmut Westermann: difference, more specific . In: Joachim Ritter u. a. (Ed.): Historical dictionary of philosophy . Vol. 11, Schwabe, Basel 2001, col. 313-325, here: p. 315.
68. Philon of Alexandria, Who is the Heir of the Divine Things n. 27, § 133-140
69. Seneca, An Lucilius epist. 58, § 8
70. ^ Fritz-Peter Hager: Dihairesis . In: Joachim Ritter u. a. (Ed.): Historical dictionary of philosophy . Vol. 2, Schwabe, Basel 1972, Sp. 242-244, here: 243.
71. Plotinus enneads III 1,3,9-25.
72. ^ Angela Long: La divisione nel commento di Damascio al Filebo di Platone . In: John M. Dillon , Luc Brisson (eds.): Plato's Philebus. Selected Papers from the eight Symposium Platonicum , Academia, Sankt Augustin 2010, pp. 369–375, here: p. 372. See also: C. Terezis: The Ontological Relation 'One-Many' according to the Neoplatonist Damascius . In: Bochum philosophical yearbook for antiquity and the Middle Ages , number 1, 1996, pp. 23–37.
73. Boethius, De divisione 877b-878d; see also Gerhard Otte: Logical classification techniques in the glossators of Roman law . In: Johannes Fried (ed.): Dialectics and rhetoric in the early and high Middle Ages . Oldenbourg, Munich 1997, pp. 157–170, here: p. 160.
74. For details see Paul Moraux: Der Aristotelismus bei den Greeks , Vol. 1, Berlin 1973, pp. 120–128.
75. Hans Leisegang: Denkformen , Walter de Gruyter, Berlin 1951, p. 252.
76. Hans Leisegang: Denkformen , Walter de Gruyter, Berlin 1951, pp. 253-258.
77. Dominicus Gundissalinus: De divisione philosophiae , ed. and commented on by Ludwig Baur, Münster 1903, pp. 188–190.
78. Franz Lukas: The method of division in Plato , Halle (Saale) 1888.
79. Julius Stenzel: Studies on the development of the Platonic dialectic from Socrates to Aristotle , Breslau 1917.
80. Edmund Husserl: Experience and judgment. Investigations into the genealogy of logic. Elaborated and edited. by Ludwig Landgrebe, Academia, Prague 1939, § 2, p. 5
81. ^ Hans Leisegang: Denkformen , Walter de Gruyter, Berlin 1951
82. ^ Karen Gloy: Vernunft und das Andere der Vernunft , Alber, Freiburg and Munich 2001, 67–114.
83. Karen Gloy: Vernunft und das Andere der Vernunft , Alber, Freiburg and Munich 2001, 67.
84. ^ Kurt Walter Zeidler: Outline of the transcendental logic , Junghans, Cuxhaven 1992, p. 128 f.
85. Cf. the section Judgment and Conclusion on the Basis of the Dihairetic Rationality Concept in Karen Gloy: Vernunft und das Andere der Vernunft , Alber, Freiburg and Munich 2001, 105–110.
86. See Julius ME Moravcsik: Plato's Method of Division . In: Julius ME Moravcsik (ed.): Patterns in Plato's Thought , Reidel, Dordrecht 1973, pp. 158–181 and S. Marc Cohen: Plato's Method of Division . In: Julius ME Moravcsik (Ed.): Patterns in Plato's Thought , Reidel, Dordrecht 1973.
87. ^ Stefano Minardi: On Some Aspects of Platonic Division . In: Mind Vol. 92, 1983, pp. 417-423, here: p. 418. Cf. also Martin Heidegger : Platon. Sophistes. In: Martin Heidegger: Complete Edition , Vol. 19, Vittorio Klostermann, Frankfurt am Main 1992.
88. ^ For example, Gilbert Ryle: Plato's Progress , Cambridge University Press, Cambridge 1966, p. 136.
89. ^ Karen Gloy: Vernunft und das Andere der Vernunft , Alber, Freiburg and Munich 2001, 82–89.
90. ^ Karen Gloy: Vernunft und das Andere der Vernunft , Alber, Freiburg and Munich 2001, 94-102.
91. Gilbert Ryle: Plato's Progress , Cambridge University Press, Cambridge 1966, pp. 135-141.
92. John R. Trevaskis: Division and Its Relation to Dialectic and Ontology in Plato . In: Phronesis , Vol. 12, 1967, pp. 118–129, here: p. 128. Cf. also John R. Trevaskis: Classification in the “Philebus” . In: Phronesis , Vol. 5, 1960.
93. ^ Carl Prantl: History of Logic in the Occident . Vol. 1. Hirzel, Leipzig 1855, pp. 80ff.
94. ^ Joseph Maria Bocheński: Formal Logic , Karl Alber, Freiburg / Munich 1956, pp. 42–46
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