CLASSIFICATION

Beings are categorized, named and defined on the basis of their common characteristics (what brings them together?), and their specific characteristics (what distinguishes them from beings of other kinds?).
A classification is a set of definitions organized according to their degree of generality, increasing (down-top) or decreasing (top-down).

Categorization and the organization of categories into classifications characterize what Lévi-Strauss calls “the science of the concrete”, a fundamental science shared by all human beings (1962], ch. 1), and the basis of ordinary argumentation.

From the point of view of argumentation, the system “categorization – definition – classification – syllogism” defines logic as the “art of thinking” in natural language. Until the development of mathematics with its application to the experimental sciences and the emergence of formal logic, the theory of definition and classification served as an introduction to logical reasoning, that is, to scientific reasoning.

1. Fundamental predicates and essentialist definition

Fundamental predicates are also called « fundamental categories ». The theory of categories comes from Aristotle’s Categories and Topics, where he assigns to science the task of giving correct definitions of beings, i.e. definitions that allow them to be grouped into well-made classifications. Reconstructed by Porphyry (c.234 – c.305, in the Isagoge (« Introduction to the Categories of Aristotle »), and transmitted in the Middle Ages mainly by Boethius (c.480-525), this « Aristotelian methodology of definition » (de Pater, 1965) constituted the fundamental intellectual equipment of science until modern times.[1]

Aristotle distinguishes five basic types of predicates (predicables, categories): genus, species, difference, proper, accident. The exact logico-metaphysical status of these terms is disputed, but their function is clear, it is to give a logical-semantic structure to statements such as the following ones

Suzan is a human being
Humans are animals
Humans are rational
The horse whinnies
The (this) horse suffers.

The analysis in terms of categories assigns the following structures to these assertions:

— “Suzan is a human” predicates the species, “man”, of the individual, Suzan.
— “Humans are animals” predicates a genus, “animal” of a species, “human”.
— “Humans are rational” predicates a difference, “rational” of a species, “human”. Human and horse are two species belonging to the same genus animal; unlike the horse and other animals, man is endowed with reason, which is the classical defining difference between man and other animals.
— “Horses whinny”: in its generic interpretation, this statement attaches to the species “horse”, a quality, “— whinnying”. The specific property is a non-essential characteristic of a species; that is (all) horses neigh, and only horses neigh.
The definition of man as a “featherless biped” is extensionally valid; on this basis, a human being can be distinguishedfrom any other being. Essentialist philosophy charges that such property-based definitions say nothing about what is, in essence, a human being.
— “This horse is suffering” attributes an accident to an individual. The accident belongs only to the individual, not to the species or genus. The horse cannot be characterized, at any level, as “a suffering animal”; a particular horse may or may not suffer, depending on the circumstances, but it cannot be a mammal or not.

The famous Aristotelian definition of man, that is human being, is based on these categories

[ Humans_specie ] _definiendum ARE [rational_difference animals_genus] _definiens

The definition of a being by its species, its specific difference and its genus makes it possible to place it correctly in the classification to which it belongs.
An object is known when it has been successfully defined and classified. Then, it is associated with identical individuals (in the same genus), and disassociated from individuals that are closest to them, that is, individuals that belong to the same genus but to different species. This knowledge is not attached to it as a particular individual; this is what is meant by the expression “there is no science of the contingent”.

An incorrect analysis of the nature of predication is at the origin of definitional errors that, lead to incorrect categorization. Suppose that the statements “some clouds are gray” and “all sparrows are gray” are true. This color is an incidental property of clouds, whereas it is a common but not exclusive property of all sparrows: elephants are also grey. The property, “being grey”, although shared by clouds, sparrows and elephants, does not allow them to be placed within the same natural genus. At most, we can say that some clouds are indeed like sparrows in term of their color, S. Intra-Categorical Analogy; Metaphor.

2. Classifications of natural kinds

This “classificatory thinking” gives impressive results in the classification of natural entities. Each entity is classified at its proper level, in a global, comprehensive hierarchy, on the basis of its common and specific properties. At the very top of this great pyramid of classification, are the plant, animal and mineral kingdoms. Such a kingdom contains a number of orders; an order contains families; a family contains several genera; and a genus contains several species that characterize individuals. producing the following pattern of nested succession:

Kingdom => Order => Family => Genus => Species :: {Individuals}

The above series of categories form a seven-level taxonomy. Depending on the complexity of the kingdom under consideration other intermediate levels may need to be introduced, such as Kingdom => Division => Class => Order, etc.

A species is a group of individuals. It is the basic unit of taxonomy. In the animal kingdom, the individuals that make up a species come from the same, or similar, parents, and they can interbreed [2].

As a domain of knowledge, taxonomy requires a well-developed denominative language, that is transparent to the specialist. Latin names are used for this purpose. For example, the fairy ring mushroom (Fr. mousseron), iis scientifically known as Marasmius Oreades. This name corresponds to the following taxonomy: Genus: marasmius; Family: marasmiaceae; Order: Agaricales; Species: Oreades.

3. Syllogistic reasoning about natural taxonomies

Scientific classifications obey the laws of set theory.

Definitions are organized in taxonomies according to their generality. The tree structure of the of the categoriy system allows valid syllogistic reasoning. A taxonomic space defines a syllogistic space. This coupling of classification and syllogism is a fundamental tool of ordinary reasoning; reasoning here means moving in a controlled way from one branch to another in a “Porphyrian tree”.

A well-constructed taxonomy relies on definitions and allows inferences based on the nature of things: “— is a Labrador” implies “— is a dog”, and both also imply “—is a mammal” see Definitions and Argument. Hence the syllogism:

Labradors are dogs, dogs are mammals, SO Labradors are mammals

All L are D	Labradors are dogs	Labrador is a species of genus1, dogs
All D are M	Dogs are mammals	Genus_1 is a subgenus of genus2, mammals
All Ls are M	So, Labradors are mammals	Labrador is a sub (subspecies) of genus2 mammals

From the definition « humans_definiendum are [rational_difference animals_genus]_definiens« 
one can construct the valid syllogism:

all H are A	Humans are animals
all H are R	Humans are rational
SO, some A are R	SO, some animals are rational

Conversely, if the genus C includes the species E1, E2, … En, then we immediately infer the truth of the disjunction:

“to be a C” implies “to be either an E1, or an E2 or … or an En”
“X is a mammal” means “X is either a human, or a rat, … or a whale”.

Other implications are based on the fact that the genus is characterized by a set of properties that are common to all the species included within its scope. If “to be a mammal” is defined as “to be a vertebrate, to be warm-blooded, to have a constant temperature, to have pulmonary respiration, to nurse the youn” then all of these characteristics can be attributed to all mammals, regardless of their differences, that is, regardless of the species they belong to.

3. Common classifications and natural reasoning

According to the psychological and linguistic theories of the prototype, common classifications have three levels:

superordinate category:	“— is a mammal”
basic category:	“ — is a dog”
subordinate category:	« — is a Labrador”.

Beings are identified and names primarily by the name of their “basic” category, which is characterized by its frequency or its perceptual, cognitive or cultural salience. Non-experts first identify an animal as a dog, not as a mammal or a Labrador.

The terms hyponym and hypernym are used in semantics to refer to pairs of terms in a hierarchical relationship. The hyponym relationship is analogous to the genus-species relationship “rose is a hyponym of flower, all roses are flowers”. The hypernym relationship corresponds to the species-genus relation,ship “flower is hypernym of rose, some flowers are roses”.

Scientific categorization determines the exact position of an individual or of a class of entities in a taxonomy, in which the terms have been given an essentialist definition from which it is possible to argue syllogistically.
Linguistic nomination-categorization assigns to an individual its current name and the definition associated with that name. This operation could be considered to be the basic argumentative technique, fundamental for all types of argumentation. The simple and stable system of scientific-Aristotelian categories is replaced by the infinitely complex system of semantic relations in a given language.
Syllogistic reasoning remains possible on the islands of stability corresponding to semantic agreements, i.e. hyponyms/hypernyms hierarchies.

Since linguistic categories can be destabilized and revised, a pari arguments and arguments from the opposites play a predominant role in ordinary speech, especially in argumentative situations.
Sociolinguistic categories are said to be fuzzy and ill-defined; they are in fact evolving categories, in a process of permanent destabilization and re-stabilization under the pressure of historical evolution of things, language change, and conversational necessities. They are contestable and adjustable; a pari argument and argument from the opposites play a predominant role in ordinary speech, especially in argumentative situations.

4. A non-Aristotelian “classification”

The following passage by Jorge Luis Borges calls itself as a « classification », (h). It reveals the requirements of the Aristotelian classification through common characterisstics and specific differences; the value of a theory of definition; and above all the renunciation of free association and subjectivity.

These ambiguities, redundancies, and deficiencies recall those attributed by Dr. Franz Kuhn to a certain Chinese Encyclopaedia called the Heavenly Emporium (*) of Benevolent Knowledge. In its remote pages it is written that animals are divided into: (a) belonging to the Emperor, (b) embalmed, (c) tame, (d) suckling pigs, (e) sirens, (f) fabulous, (g) stray dogs, (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camel-hair brush, (l) et cetera, (m) which have just broken a water jug, (n) which from afar off look like flies.
(*) Warehouse
Jorge Luis Borges, ‘The Analytical Language of John Wilkins’ [3].

Needless to say, this account has little to do with the reality of the classification methods actually used in ancient or contemporary China.

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[1] In this book, the word category is used only in the sense defined in the entry Categorization – nomination, and not with the Aristotelian sense of « predicate, predicable or fundamental category ».

[2] From Jacques Brosse, Lexicon, in Atlas des arbustes, arbrisseaux et lianes, de France et d’Europe occidentale, Paris, Bordas, 1983 [Atlas of shrubs, bushes and lianas of France and Western Europe].

[3] Jorge Luis Borges. El idioma analÍtico de John Wilkins. In La Nación. 8 February 1942.
Translated and republished by Eliot Weinberger as “John Wilkins’ Analytical Language,” p. 229–232 in Jorge Luis Borges.The Total Library: Nonfiction, 1922–1986, Penguin, London, 1999.

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