Theory of categories


In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities. A distinction between such categories, in making the categories or applying them, is called an ontological distinction. Various systems of classification have been proposed; these often include categories for substances, properties, relations, states of affairs, or events. A representative question within the theory of categories might be, for example, that which asks: "Are universals prior to particulars?"

Early development

The process of abstraction required to discover the number and names of the categories of being has been undertaken by many philosophers since and including Aristotle, and involves the careful inspection of each concept to ensure that there is no higher category or categories under which that concept could be subsumed. The scholars of the twelfth and thirteenth centuries developed Aristotle's ideas. For example, Gilbert of Poitiers divides Aristotle's ten categories into two sets, primary and secondary, according to whether they inhere in the subject or not:
Furthermore, following Porphyry’s likening of the classificatory hierarchy to a tree, they concluded that the major classes could be subdivided to form subclasses; for example, Substance could be divided into Genus and Species, and Quality could be subdivided into Property and Accident, depending on whether the property was necessary or contingent.
An alternative line of development was taken by the second-century Neoplatonic philosopher Plotinus, who, by a process of repeated abstraction, reduced Aristotle's list of ten categories to five: Substance, Relation, Quantity, Motion and Quality. Plotinus further suggested that the latter three categories of his list—namely, Quantity, Motion, and Quality—correspond to three different kinds of relation and that these three categories could therefore be subsumed under the category of Relation. This was to lead to the supposition that there were only two categories at the top of the hierarchical tree: Substance and Relation. Many supposed that relations only exist in the mind. Substance and Relation, then, are closely commutative with Matter and Mind—this is expressed most clearly in the dualism of René Descartes.

Vaisheshika

Stoic

Aristotle

One of Aristotle’s early interests lay in the classification of the natural world: how, for example, the genus "animal" could be first divided into "two-footed animal" and then into "wingless, two-footed animal". He realized that the distinctions were being made according to the qualities the animal possesses, the quantity of its parts, and the kind of motion that it exhibits. Aristotle stated, in his work on the Categories, that—to fully complete, e.g., the proposition "this animal is ..."—there were ten kinds of predicate where:
"... each signifies either substance or quantity or quality or relation or where or when or being-in-a-position or having or acting or being acted upon".
He realized that predicates could be simple or complex. The simple kinds consist of a subject and a predicate linked together by the "categorical" or inherent type of relation. For Aristotle, the more complex kinds were limited to propositions wherein the predicate is compounded of two of the above categories; for example, "this is a horse running". More complex kinds of proposition were only discovered after Aristotle by the Stoic philosopher Chrysippus, who developed the "hypothetical" and "disjunctive" types of syllogism; these were terms that were to be developed through the Middle Ages, and which were to reappear in Kant's system of categories.
Category came into use with Aristotle's essay Categories, in which he discussed univocal and equivocal terms, predication, and ten categories:
  • Substance, essence – examples of primary substance: this man, this horse; secondary substance : man, horse
  • Quantity, discrete or continuous – examples: two cubits long, number, space, time.
  • Quality – examples: white, black, grammatical, hot, sweet, curved, straight.
  • Relation – examples: double, half, large, master, knowledge.
  • Place – examples: in a marketplace, in the Lyceum
  • Time – examples: yesterday, last year
  • Position, posture, attitude – examples: sitting, lying, standing
  • State, condition – examples: shod, armed
  • Action – examples: to lance, to heat, to cool
  • Affection, passion – examples: to be lanced, to be heated, to be cooled

    Plotinus

, in writing his Enneads around AD 250, recorded that "Philosophy at a very early age investigated the number and character of the existents ... some found ten, others less ... to some the genera were the first principles, to others only a generic classification of existents." He realized that some categories were reducible to others, writing: "Why are not Beauty, Goodness and the virtues, Knowledge and Intelligence included among the primary genera?" He concluded that such transcendental categories, and even the categories of Aristotle, were in some way posterior to the three Eleatic categories first recorded in Plato's dialogue Parmenides, which comprised the following three coupled terms:
  • Unity/Plurality
  • Motion/Stability
  • Identity/Difference
Plotinus called these "the hearth of reality", deriving from them not only the three categories of Quantity, Motion, and Quality, but also what came to be known as "the three moments of the Neoplatonic world process":
  • First, there existed the "One", and "the origin of things is a contemplation" of this "One";
  • The Second "is certainly an activity ... a secondary phase ... life streaming from life ... energy running through the universe";
  • The Third is some kind of Intelligence, concerning which he wrote: "Activity is prior to Intellection ... and self-knowledge."
Plotinus likened the three to the center, the radii, and the circumference of a circle, and clearly thought that the principles underlying the categories were the first principles of creation. "From a single root all being multiplies." Similar ideas were to be introduced into Early Christian thought by, for example, Gregory of Nazianzus who summed it up saying "Therefore, Unity, having from all eternity arrived by motion at duality, came to rest in Trinity."

Modern development

Kant and Hegel accused the Aristotelian table of categories of being 'rhapsodic', derived arbitrarily and in bulk from experience, without any systematic necessity.
The early modern dualism, which has been described above, of Mind and Matter or Subject and Relation, as reflected in the writings of Descartes underwent a substantial revision in the late 18th century. The first objections to this stance were formulated in the eighteenth century by Immanuel Kant who realised that we can say nothing about Substance except through the relation of the subject to other things.
For example: in the sentence "this is a house", the substantive subject "house" only gains meaning in relation to human use patterns or to other similar houses. The category of Substance disappears from Kant's tables, and under the heading of Relation, Kant lists inter alia the three relationship types of Disjunction, Causality and Inherence. The three older concepts of Quantity, Motion and Quality, as Peirce discovered, could be subsumed under these three broader headings in that Quantity relates to the subject through the relation of Disjunction; Motion relates to the subject through the relation of Causality; and Quality relates to the subject through the relation of Inherence. Sets of three continued to play an important part in the nineteenth century development of the categories, most notably in G.W.F. Hegel's extensive tabulation of categories, and in C.S. Peirce's categories set out in his work on the logic of relations. One of Peirce's contributions was to call the three primary categories Firstness, Secondness and Thirdness which both emphasizes their general nature, and avoids the confusion of having the same name for both the category itself and for a concept within that category.
In a separate development, and building on the notion of primary and secondary categories introduced by the Scholastics, Kant introduced the idea that secondary or "derivative" categories could be derived from the primary categories through the combination of one primary category with another. This would result in the formation of three secondary categories: the first, "Community" was an example that Kant gave of such a derivative category; the second, "Modality", introduced by Kant, was a term which Hegel, in developing Kant's dialectical method, showed could also be seen as a derivative category; and the third, "Spirit" or "Will" were terms that Hegel and Schopenhauer were developing separately for use in their own systems. Karl Jaspers in the twentieth century, in his development of existential categories, brought the three together, allowing for differences in terminology, as Substantiality, Communication and Will. This pattern of three primary and three secondary categories was used most notably in the nineteenth century by Peter Mark Roget to form the six headings of his Thesaurus of English Words and Phrases. The headings used were the three objective categories of Abstract Relation, Space and Matter and the three subjective categories of Intellect, Feeling and Volition, and he found that under these six headings all the words of the English language, and hence any possible predicate, could be assembled.