Beings are categorized, named and defined on the basis of their shared characteristics (what bring them together?), and their specificities (what differentiate them from beings of another nature?).
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 characterizes what Lévi-Strauss calls “the science of the concrete”, a fundamental science shared by all humans (1962], chap. 1), and the basis of ordinary argumentation.

From the point of view of argumentation, the system “categorization – definition – classification – syllogism” defines logic as an “art of thinking” in natural language. Until the development of mathematics with their application to 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 allowing them to be grouped in 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 the modern age.[1]

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

Suzan is a human.
Humans are animals
Humans are rational.
The horse neighs (meaning: horses neigh)
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, “man”.
— “Humans are rational” predicates a difference, “rational” of a species, “man”. 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 defining difference between man and other animals.
— “Horses neigh”: in its generic interpretation, this statement attaches to the species “horse”, a property, “— neighs”. The 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, one can tell a human from any other being. Essentialist philosophy reproaches such definitions based on properties for saying nothing of what is, in essence, a human being.
— “This horse suffers” predicates an accident upon an individual. The accident belongs only to individuals, not to species or genus. The horse cannot be characterized, at any level, as “a suffering animal”; a particular horse can suffer or not, depending on the circumstances, it cannot, however, be a mammal or not.

The famous Aristotelian definition of man, that is human being, is built on this basis:

[ Humans_specie ] _definiendum ARE [reasonable_difference animals_genus] _definiens

The definition of a being by its species, its specific difference and its genus makes it possible to position 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 objects (in the same genus), and disassociated from individual that are closest to them, that is, individuals belonging 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”.

A wrong analysis of the kind of predication is at the origin of definition mistakes, leading to a wrong categorization. Suppose that the statement “some clouds are grey” and “all sparrows are grey” are true. This color is an accidental property of clouds, whereas it is a common characteristic shared by all sparrows, but not exclusively: elephants are also grey. The property, “being grey”, although shared by clouds, sparrows and elephants, does not allow them to be classified within the same natural genus. At most, we can say that, in term of their color, indeed, some clouds are like sparrows, S. Intra-Categorical Analogy; Metaphor.

2. Classifications of natural kinds

This “classificatory thinking” gives impressive results in the classification of natural entities. Every 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 includes a number of orders; an order includes families; a family includes several genera; and a genus includes several species characterizing individuals. producing the following pattern of nested succession:

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

The above series of categories constitute a seven-level taxonomy. Depending on the complexity of the kingdom considered, other intermediary levels must be introduced, for example: Kingdom => Division => Class => Order, etc.

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

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

3. Syllogistic reasoning on natural taxonomies

Scientific classifications obey the laws of set theory.

Definitions are organized in taxonomies according to their generality. The tree-structure of the system of categories allows for valid syllogistic inferences. A taxonomic space defines a syllogistic space. This coupling between classification and syllogism is a fundamental instrument of ordinary argumentation; Reasoning means here moving in a controlled manner from one branch to the other in a “Porphyrian tree”.

A well-constructed taxonomy relies on definitions and authorizes inferences based on the nature of things: “— is a Labrador” implies “— is a dog”, and both also imply “—is a mammal” S. 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 sub-genus 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 [reasonable_difference animals_genus]_definiens
one can construct the valid syllogism:

all H are A	Human are animals
all H are R	Human are reasonable
SO, some A are R	SO, some animals are reasonable

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 a E1, or a E2 or … or a 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 belong to all the species included within its scope. If “being a mammal” is defined as “being a vertebrate, warm-blooded, having a constant temperature, with pulmonary respiration, nursing the cubs” then all of these properties can be attributed to every mammal, regardless of their differences, that is, regardless of the species they belong to.

3. Ordinary classifications and natural reasoning

According to 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 designated primarily by the name of their “basic” category, characterized by its frequency or its perceptual, cognitive or cultural salience. Non-specialists first identify an animal as a dog, not as a mammal or a labrador.

The concepts of hyponym and hypernym are used in semantics to refer to pairs of terms in a hierarchic relationship. The hyponym relationship corresponds to the genus to species relation “rose is a hyponym of flower, all roses are flowers”. The hypernym relationship corresponds to the species to genus relation, “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, where 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 meaning relationships 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.
Socio-linguistic categories are said to be fuzzy and poorly defined; they are actually evolving categories, in a process of permanent de-stabilization and re-stabilization under the pressure of historical evolution of things, language change, and conversational necessities. They are debatable 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 refers to itself as a « classification », (h). It reveals the requirements of the Aristotelian classification by proper characters and specific differences; the interest 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 distant 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 camelhair brush, (l) et cetera, (m) having just broken a water pitcher, (n) that from a long way off look like flies.
(*) Warehouse
Jorge Luis Borges, ‘The Analytical Language of John Wilkins’ [3].

Needless to say, this presentation 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: Non-fiction, 1922–1986, Penguin, London, 1999.

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