The theory of categories lies at the heart of taxonomies. In turn, taxonomies represent a series of coordinated scientific definitions.
Correctly articulated in taxonomies, such definitions mirror valid syllogistic reasoning.
The world organized in a taxonomy represents the deep structure of reality; reading the taxonomy is a reasoned voyage through this world. Until the development of mathematics and their application to experimental sciences in the modern period, and the emergence of formal logic at the end of the nineteenth century, the theory of categories served as an introduction to logical reasoning, that is, to scientific reasoning.
From the point of view of argumentation, this traditional system (category-taxonomy-syllogism) defines logic as an “art of thinking” in natural language. It is the basis for reasoning from categorization and nomination, and definition or analogy either in the explicit form of arguments bearing these names, or implicitly present in other forms of arguments.
The theory of categories was developed by Aristotle in the Topics, re-constructed by Porphyry (c. 234 – c. 305 AD) in the Isagoge, “Introduction”, and transmitted in Latin to the Middle Ages, mainly by Boethius (c. 480-525).
1. Taxonomies
The category system provides the rules for the construction of correct taxonomies. A taxonomy is a reasoned hierarchized classification of beings, a nested system, represented by an arborescence. The position of an entity in a taxonomy corresponds to its definition, and its definition determines its place in the taxonomy to which it belongs.
This “classificatory thinking” has produced 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 genuses; and a genus includes several species chanracterizing individuals. producing the following pattern of nested succession:
Kingdom => Order => Family => Genus => Species :: {Individuals}
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.
The above series of categories creates 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.
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, or mousseron, for example, is known scientifically as marasmius oreades. This name corresponds to the following taxonomy: Genus: marasmius; Family: marasmiaceae; Order: Agaricales; etc.
The simplest taxonomy includes the following 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 an 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”.
2. Categories
In the Aristotelian system, the goal of science is to build stable taxonomies of entities according to their common properties and specific differences. The fundamental intellectual problem is how to correctly categorize an individual and hierarchize the various categories of individuals. This task leads to more or less convincing results depending on the kind of entities considered. We already have meaningful taxonomies of mushrooms, for example, whilst we continue to lack a taxonomy of affect, emotions and moods — and we must ask whether building such a taxonomy is possible at all.
Aristotelian theory of categories provides the tools needed to build definitions for situating terms in taxonomies. It distinguishes between five categories: genus-specie-difference-property-accident. The exact logical-metaphysical status of these concepts is disputed, but the problem is clear: which logical-semantic structure can we give to statements like the following?
Suzan is a human.
Humans are animals
Humans are rational.
The horse neighs (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 attached 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.
Suppose that the statement “some clouds are grey” and “all sparrows are grey” are true. Color is an accidental property of clouds, whereas it is a common characteristic shared by all sparrows, but not exclusively: elephants are also grey. This property, “being grey” cannot serve as a basis for clouds and sparrows to be classed within the same natural genus. At most, we can say that, in term of their color, indeed, some clouds are like sparrows. If one argues that clouds and sparrows belong to the same category, due to this common property, the analogy would be deemed as misleading, S. Analogy (2) Intra-Categorical Analogy; Metaphor.
An object is known when it has been successfully defined, that is, classified. It is associated with identical objects in the same category, and disassociated from objects belonging to different categories. 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”.
3. Syllogistic arguments and natural taxonomies
Predicates 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: to reason means here to move 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 genus_1, dogs |
| All D are M | Dogs are mammals | Genus_1 is a sub-genus of genus_2, mammals |
| All L are M | So, Labradors are mammals | Labrador is a sub (subspecies) of genus_2 mammals |
From the definition
humansdefiniendum are [reasonabledifference animalsgenus]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 | O, 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.
4. Arguments destabilizing socio-linguistic categories
Scientific categorization determines the exact position of a particular 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 a current name and the category covered by that name. This operation could be considered to be the basic argumentative technique. The simple and stable system of scientific-Aristotelian categories is replaced by the infinitely complex system of meaning relationships in a given language. The argument can no more proceed by syllogism on essentialist definitions, but must operate by derivations out of the heterogeneous elements assembled in a linguistic definition.
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 and language change. They are debatable and adjustable, S. A pari; Analogy (II).