Concepts are expected to be useful in dealing with reality.A concept is basically the main idea. Generally speaking, concepts are taken (a) to be acquired dispositions to recognize perceived objects as being of a certain ontological kind, and at the same time (b) to understand what this kind or that kind of object is like, and consequently (c) to perceive a number of perceived particulars as being the same in kind and to discriminate between them and other sensible particulars that are different in kind. In addition, concepts are acquired dispositions to understand what certain kinds of objects are like both (a) when the objects, though perceptible, are not actually perceived, and (b) also when they are not perceptible at all, as is the case with all the conceptual constructs we 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, which is 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 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.).
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… .
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.
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.
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'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.
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, 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.
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.
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 Gödel 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.