A concept is a constituent of thought or generalized idea, that designates common properties and characteristics abstracted from a number of instances. While ideas, perceptions, and "representations" have psychological implications, concepts have logical implications.
Human beings understand the world by applying concepts and expressing them with language. Theories of concepts are thus closely tied to the philosophy of language, philosophy of mind, cognitive science, and psychology, as well as ontology and epistemology.
A vast array of accounts attempt to explain the nature of concepts. According to classical accounts, a concept denotes all of the entities, phenomena, and/or relations in a given category or class by using definitions. Concepts are abstract in that they omit the differences of the things in their extension, treating the members of the extension as if they were identical. Classical concepts are universal in that they apply equally to everything 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.
Concepts are important in understanding reality. Generally speaking, concepts are taken to be:
In addition, concepts are acquired dispositions to understand what certain kinds of objects are like both when the objects, though perceptible, are not actually perceived, and also when they are not perceptible at all, as is the case with all the conceptual constructs people employ in physics, mathematics, and metaphysics. The impetus to have a theory of concepts that is ontologically useful has been so strong that it has pushed forward accounts that understand a concept to have a deep connection with reality.
On some accounts, there may be agents (perhaps some animals) which don't think about, but rather use relatively basic concepts (such as demonstrative and perceptual concepts for things in their perceptual field), even though it is generally assumed that they do not think in symbols. On other accounts, mastery of symbolic thought (in particular, language) is a prerequisite for conceptual thought.
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.
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, constituting a fallacy. Also, the concepts of term and concept are often confused, although the two are not the same.
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. In the philosophy of Kant, any purely empirical theory dealing with the acquisition of concepts is referred to as a noogony.
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 Chihuahuas.
In the same tradition as Locke, 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 realized 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.).
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." Nietzsche, who was heavily influenced by Schopenhauer, wrote, "Every concept originates through our equating what is unequal. No leaf ever wholly equals another, and the concept 'leaf' is formed through an arbitrary abstraction from these individual differences, through forgetting the distinctions… " ("On Truth and Lie in an Extra—Moral Sense," The Portable Nietzsche, p. 46).
By contrast to the above philosophers, Immanuel Kant held that the account of the concept as an abstraction of experience is only partly correct. He called those concepts that result of abstraction "a posteriori concepts" (meaning concepts that arise out of experience). 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). In his discussion of Kant, Christopher Janaway wrote: "… generic concepts are formed by abstraction from more than one species."
Kant declared that human minds possess pure or a priori concepts. Instead of being abstracted from individual perceptions, like empirical concepts, they originate in the mind itself. He called these concepts categories, in the sense of the word that means predicate, attribute, characteristic, or quality. But these pure categories are predicates of things in general, not of a particular thing. According to Kant, there are 12 categories that constitute the understanding of phenomenal objects. Each category is that one predicate which is common to multiple empirical concepts. In order to explain how an a priori concept can relate to individual phenomena, in a manner analogous to an a posteriori concept, Kant employed the technical concept of the schema.
It seems intuitively obvious that concepts must have some kind of structure. Up until recently, the dominant view of conceptual structure was a containment model, associated with the classical view of concepts. According to this model, a concept is endowed with certain necessary and sufficient conditions in their description which unequivocally determine an extension. The containment model allows for no degrees; a thing is either in, or out, of the concept's extension. By contrast, the inferential model understands conceptual structure to be determined in a graded manner, according to the tendency of the concept to be used in certain kinds of inferences. As a result, concepts do not have a kind of structure that is in terms of necessary and sufficient conditions; all conditions are contingent (Margolis: 5).
However, some theorists claim that primitive concepts lack any structure at all. For instance, Jerry Fodor presents his Asymmetric Dependence Theory as a way of showing how a primitive concept's content is determined by a reliable relationship between the information in mental contents and the world. These sorts of claims are referred to as "atomistic," because the primitive concept is treated as if it were a genuine atom.
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' 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.
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). 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, in that it denies the existence of any such realm. It also contrasts with the empiricist view that concepts are abstract generalizations of individual experiences, because the contingent and bodily experience is preserved in a concept, and not abstracted away. 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 concept formation.
A long and well-established tradition in philosophy posits that philosophy itself is nothing more than conceptual analysis. This view has its proponents in contemporary literature as well as historical. 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 a 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."
Concepts are vital to the development of scientific knowledge. For example, it would be difficult to imagine physics without concepts like: Energy, force, or acceleration. Concepts help to integrate apparently unrelated observations and phenomena into viable hypothesis and theories, the basic ingredients of science. The concept map is a tool that is used to help researchers visualize the inter-relationships between various concepts.
Although the mainstream literature in cognitive science regards the concept as a kind of mental particular, it has been suggested by some theorists that concepts are real things (Margolis: 8). In the most radical form, the realist about concepts attempts to show that the supposedly mental processes are not mental at all; rather, they are abstract entities, which are just as real as any mundane object.
Plato was the starkest proponent of the realist thesis of universal concepts. By his view, concepts (and ideas in general) are innate ideas that were instantiations of a transcendental world of pure forms that laid behind the veil of the physical world. In this way, universals were explained as transcendent objects. Needless to say, this form of realism was tied deeply with Plato's ontological projects. This remark on Plato is not of merely historical interest. For example, the view that numbers are Platonic objects was revived by Kurt Godel as a result of certain puzzles that he took to arise from the phenomenological accounts.
Gottlob Frege, founder of the analytic tradition in philosophy, famously argued for the analysis of language in terms of sense and reference. For him, the sense of an expression in language describes a certain state of affairs in the world, namely, the way that some object is presented. Since many commentators view the notion of sense as identical to the notion of concept, and Frege regards senses as the linguistic representations of states of affairs in the world, it seems to follow that we may understand concepts as the manner in which we grasp the world. Accordingly, concepts (as senses) have an ontological status (Morgolis: 7)
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.
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