Concept

A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in language or symbology, that denotes all of the objects in a given category or class of entities, interactions, phenomena, or relationships 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. Unlike perceptions, which are particular images of individual objects, concepts cannot be visualized. Because they are not, themselves, individual perceptions, concepts are discursive and result from reason. They can only be thought and designated by a name.

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 dog in English, 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.

The acquisition of concepts is studied in machine learning as supervised classification and unsupervised classification, and in psychology and cognitive science as concept learning and category formation.

A term labels or designates concepts. Several partly or fully distinct concepts may share the same term. These different concepts are easily confused by mistakenly being used interchangeably, which is a fallacy.

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 blood. 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.

Kant

A posteriori concepts

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

A concept is a common feature or characteristic. Kant investigated the way that empirical a posteriori concepts are created.

The logical acts of the understanding by which concepts are generated as to their form are: (1.) comparison, i.e., the likening of mental images to one another in relation to the unity of consciousness; (2.) reflection, i.e., the going back over different mental images, how they can be comprehended in one consciousness; and finally (3.) abstraction or the segregation of everything else by which the mental images differ. … In order to make our mental images into concepts, one must thus be able to compare, reflect, and abstract, for these three logical operations of the understanding are essential and general conditions of generating any concept whatever. For example, I see a fir, a willow, and a linden. In firstly comparing these objects, I notice that they are different from one another in respect of trunk, branches, leaves, and the like; further, however, I reflect only on what they have in common, the trunk, the branches, the leaves themselves, and abstract from their size, shape, and so forth; thus I gain a concept of a tree.

— Logic, §6

Kant's description of the making of a concept has been paraphrased as "…to conceive is essentially to think in abstraction what is common to a plurality of possible instances… ." (H.J. Paton, Kant's Metaphysics of Experience, I, 250)

A priori concepts

Kant called a pure or an 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"). In his On the Will in Nature, "Physiology and Pathology," Schopenhauer said that a concept is "drawn off from previous images ... by putting off their differences. This concept is then no longer intuitively perceptible, but is denoted and fixed merely by words"

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".

Embodied concepts

In Cognitive linguistics, abstract concepts are transformations of concrete concepts derived from embodied experience. The mechanism of transformation is structural mapping, in which properties of two or more source domains are selectively mapped onto a blended space (Fauconnier & Turner, 1995; see conceptual blending). A common class of blends are metaphors.

This theory contrasts with the rationalist view that concepts are perceptions (or recollections, in Plato's term) of an independently existing world of ideas, the empiricist view from Locke (above) that concepts are generalizations of individual experiences. While the perspective is compatible with Jamesian pragmatism (above), the notion of the transformation of embodied concepts through structural mapping makes a distinct contribution to the problem of abstract concept formation.

Concepts in science

Further information: List of concepts in science

Concepts are extremely useful for the development of science. It would be difficult to imagine science without concepts like: energy, force, acceleration, time, charge, or gravity.

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 observations 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.

See also

• Abstraction
• Categorization
• Class (philosophy)
• Concept and object
• Concept learning
• Concept map
• Conceptual art
• Conceptual blending
• Conceptual clustering
• Conceptual framework

• Formal concept analysis
• Hypostatic abstraction
• Idea
• Meme
• Misconception
• Philosophy
• Prescisive abstraction
• Social construction
• Symbol Grounding Problem

References

• The History of Calculus and its Conceptual Development, Carl Benjamin Boyer, Dover Publications, ISBN 486-60509-4
• The Writings of William James, University of Chicago Press, ISBN 0-226-39188-4
• Logic, Immanuel Kant, Dover Publications, ISBN 0-486-25650-2
• A System of Logic, John Stuart Mill, University Press of the Pacific, ISBN 1-4102-0252-6
• Parerga and Paralipomena, Arthur Schopenhauer, Volume I, Oxford University Press, ISBN 0-19-824508-4
• What is Philosophy?, Gilles Deleuze and Félix Guattari
• Kant's Metaphysic of Experience, H.J. Paton, London: Allen & Unwin, 1936
• "Conceptual Integration Networks." Gilles Fauconnier and Mark Turner, 1998. Cognitive Science. Volume 22, number 2 (April-June 1998), pages 133-187.

External links

• Blending and Conceptual Integration