Concepts

A concept is an abstract, idea, notion, or entity that serves to designate a category or class of entities, events, phenomena or relations between them. Concepts are abstract in that they omit the differences of the things in their extension, treating them as if they were identical. They are universal in that they apply equally to every thing in their extension. Concepts are also the basic elements of propositions, much the same way a word is the basic semantic element of a sentence.

Concepts may relate to supernatural, say the concept of God or may be subjective: they may refer to facts of this world, as processed by man's means of cognition or to the personal beliefs. (The foregoing is a brief indication; for a full discussion see Introduction to Objectivist Epistemology.)

Concepts are bearers of meaning, as opposed to agents of meaning. A single concept can be expressed by any number of languages. The concept of dog can be expressed as Hund in German, as chien in French, and perro in Spanish. The fact that concepts are in some sense independent of language makes translation possible - words in various languages have identical meaning, because they express one and the same concept.

Locke
John Locke's description of a general idea corresponds to a description of a concept. According to Locke, a general idea is created by abstracting, drawing away, or removing the common characteristic or characteristics from several particular ideas. This common characteristic is that which is similar to all of the different individuals. For example, the abstract general idea or concept that is designated by the word "red" is that characteristic which is common to apples, cherries, and fire engines. The abstract general idea or concept that is signified by the word "dog" is the collection of those characteristics which are common to Airedales, Collies, and Terriers.

A posteriori Concepts
According to Immanuel Kant, an empirical or a posteriori concept is a general representation (Vorstellung) or general mental picture of that which is common to several specific perceived objects. (Logic, I, 1., §1, Note 1)

A concept is a common feature or characteristic.

A priori Concepts
Kant called a pure or a priori concept a category. There are 12 categories that constitute the understanding of phenomenal objects. Each category is that which is common to multiple empirical concepts.

Schopenhauer
For Schopenhauer, empirical concepts "...are mere abstractions from what is known through intuitive perception, and they have arisen from our arbitrarily thinking away or dropping of some qualities and our retention of others." (Parerga and Paralipomena, Vol. I, "Sketch of a History of the Ideal and the Real").

John Stuart Mill's Conceptions
John Stuart Mill stated that general conceptions are formed through abstraction. A general conception is the common element among the many images of members of a class. "...[W]hen we form a set of phenomena into a class, that is, when we compare them with one another to ascertain in what they agree, some general conception is implied in this mental operation" (A System of Logic, Book IV, Ch. II).

Mill did not believe that concepts exist in the mind before the act of abstraction. "It is not a law of our intellect, that, in comparing things with each other and taking note of their agreement, we merely recognize as realised in the outward world something that we already had in our minds. The conception originally found its way to us as the result of such a comparison. It was obtained (in metaphysical phrase) by abstraction from individual things" (Ibid.).

William James's Truth
A concept may be abstracted from several perceptions, but that is only its origin. In regard to its meaning or its truth, William James proposed his Pragmatic Rule. This rule states that the meaning of a concept may always be found in some particular difference in the course of human experience which its being true will make (Some Problems of Philosophy, "Percept and Concept -- The Import of Concepts"). In order to understand the meaning of the concept and to discuss its importance, a concept may be tested by asking, "What sensible difference to anybody will its truth make?" There is only one criterion of a concept's meaning and only one test of its truth. That criterion or test is its consequences for human behavior.

In this way, James bypassed the controversy between Rationalists and Empiricists regarding the origin of concepts. Instead of solving their dispute, he ignored it. The Rationalists had asserted that concepts are a revelation of Reason. Concepts are a glimpse of a different world, one which contains timeless truths in areas such as logic, mathematics, ethics, and aesthetics. By pure thought, humans can discover the relations that really exist among the parts of that divine world. On the other hand, the Empiricists claimed that concepts were merely a distillation or abstraction from perceptions of the world of experience. Therefore, the significance of concepts depends solely on the perceptions that are its references. James's Pragmatic Rule does not connect the meaning of a concept with its origin. Instead, it relates the meaning to a concept's purpose, that is, its function, use, or result.

Gilles Deleuze's definition of Philosophy
According to Deleuze and Guattari's What Is Philosophy? (1991), philosophy is the activity of creating concepts. This creative activity differs from previous definitions of philosophy as simple reasoning, communication or contemplation of Universals. Concepts are specific to philosophy: science has got "percepts", and art "affects". A concept is always signed: thus, Descartes' Cogito or Kant's "transcendental". It is a singularity, not an universal, and connects itself with others concepts, on a "plane of immanence" traced by a particular philosophy. Concepts can jump from one plane of immanence to another, combining with other concepts and therefore engaging in a "becoming-Other".

Ayn Rand
The Ayn Rand Institute has disseminated the following information on Ayn Rand's understanding of human concept formation.

"According to Objectivism, concepts are derived from and do refer to the facts of reality.

The mind at birth (as Aristotle first stated) is tabula rasa; there are no innate ideas. The senses are man's primary means of contact with reality; they give him the precondition of all subsequent knowledge, the evidence that something is. What the something is he discovers on the conceptual level of awareness.

Conceptualization is man's method of organizing sensory material. To form a concept, one isolates two or more similar concretes from the rest of one's perceptual field, and integrates them into a single mental unit, symbolized by a word. A concept subsumes an unlimited number of instances: the concretes one isolated, and all others (past, present, and future) which are similar to them.

Similarity is the key to this process. The mind can retain the characteristics of similar concretes without specifying their measurements, which vary from case to case. 'A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.' The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.

Concepts in Sciences
Concepts are extremely useful for the development of science. It would be difficult to imagine science without the concepts like: energy, force, acceleration, time, charge, gravity, field ( The list can be almost endless). Some illustrative examples of concepts in physical science are: absorption, acid, acceleration, activation, activity, adsorption, atmosphere, alkali, amorphous, angular, anisotropy aromatic, atom, azeotrope, ballast, bandwidth, base, baryons, bond, body, capacitance, catalyst, choke, circuit, color, conductor, covalent, crystalline, coherent, concentration, degree (angle), degree (temperature), density, dielectric, diploid, direction, dipole, dissociation,  distance,  ductile, electron, electronegativity, elastic, element, energy, enthalpy, entropy, equilibrium, experiment, field, induction, torque, velocity, wave.

Similarly, there are concepts in biological sciences, for example, animal, biome, chromosome, death, egg, fertile,  gene, growth, gymnosperm, heredity, hybrid, life, living being, organ, organism, ovule, plant, prokaryote, soil, vascular, zygote and there are concepts in social sciences viz. capital, commodity, finance, geist, psyche, society, wealth community etc.

Concepts help to integrate apparently unrelated obsevations and phenomena into viable hypothesis and theories, the basic ingredients of science. But, somehow this nature of these concepts is rarely emphasized when they are introduced in school. The result is that many students feel confused. Many people have realized this and have introduced a term concept map that helps students to learn the inter-relationships between various concepts.

Concepts in Mathematics
According to Carl Benjamin Boyer, in the introduction to his The History of the Calculus and its Conceptual Development, concepts in calculus do not refer to perceptions. As long as the concepts are useful and mutually compatible, they are accepted on their own. For example, the concepts of the derivative and the integral are not considered to refer to spatial or temporal perceptions of the external world of experience. Neither are they related in any way to mysterious limits in which quantities are on the verge of nascence or evanescence, that is, coming into or going out of appearance or existence. The abstract concepts are now considered to be totally autonomous, even though they originated from the process of abstracting or taking away qualities from perceptions until only the common, essential attributes remained.