Concepts arise as abstractions or generalisations from experience; from the result of a transformation of existing ideas; or from innate properties.[unreliable source?] A concept is instantiated (reified) by all of its actual or potential instances, whether these are things in the real world or other ideas.
Concepts are studied as components of human cognition in the cognitive science disciplines of linguistics, psychology and philosophy, where an ongoing debate asks whether all cognition must occur through concepts. Concepts are used as formal tools or models in mathematics, computer science, databases and artificial intelligence where they are sometimes called classes, schema or categories. In informal use the word concept often just means any idea, but formally it involves the abstraction component. Concepts are sometimes known by other names in everyday language such as "kinds", "types" or "sorts", as in "an oak is a kind of tree", or "this object is a kind of tree".
In metaphysics, and especially ontology, a concept is a fundamental category of existence. In contemporary philosophy, there are at least three prevailing ways to understand what a concept is:[See talk page]
Concepts can be organized into a hierarchy, higher levels of which are termed "superordinate" and lower levels termed "subordinate". Additionally, there is the "basic" or "middle" level at which people will most readily categorize a concept. For example, a basic-level concept would be "chair", with its superordinate, "furniture", and its subordinate, "easy chair".
In addition to the mind-body problem, philosophers since David Hume have also sought to understand the nature of thought. Thought is understood to be built up out of concepts, and so philosophers (and increasingly cognitive psychologists) seek to understand the nature and structure of concepts.
The study of concepts depends on the perspective one takes, and today, the predominant (though not exclusive) perspective taken by many philosophers and most cognitive psychologists is understood to be the Representational Theory of Mind. Within the RTM framework, the structural position of concepts can be understood as follows: Concepts serve as the building blocks of what are called mental representations (colloquially understood as ideas in the mind). Mental representations, in turn, are the building blocks of what are called propositional attitudes (colloquially understood as the stances or perspectives we take towards ideas, be it "believing", "doubting", "wondering", "accepting", etc). And these propositional attitudes, in turn, are the building blocks of our understanding of thoughts that populate everyday life, as well as folk psychology. In this way, we have an analysis that ties our common everyday understanding of thoughts down to the scientific and philosophical understanding of concepts. 
A central question in the study of concepts is the question of what concepts are. Philosophers construe this question as one about the ontology of concepts - what they are really like. The ontology of concepts determines the answer to other questions, such as how to integrate concepts into a wider theory of the mind, what functions are allowed or disallowed by a concept's ontology, etc. There are two main views of the ontology of concepts: (1) Concepts are abstract objects, and (2) concepts are mental representations. 
There is debate as to the relationship between concepts and natural language. However, it is necessary at least to begin by understanding that the concept "dog" is philosophically distinct from the things in the world grouped by this concept - or the reference class or extension. Concepts that can be equated to a single word are called "lexical concepts".
In the simplest terms, a concept is a name or label that regards or treats an abstraction as if it had concrete or material existence, such as a person, a place, or a thing. It may represent a natural object that exists in the real world like a tree, an animal, a stone, etc. It may also name an artificial (man-made) object like a chair, computer, house, etc. Abstract ideas and knowledge domains such as freedom, equality, science, happiness, etc., are also symbolized by concepts. It is important to realize that a concept is merely a symbol, a representation of the abstraction. The word is not to be mistaken for the thing. For example, the word "moon" (a concept) is not the large, bright, shape-changing object up in the sky, but only represents that celestial object. Concepts are created (named) to describe, explain and capture reality as it is known and understood.
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. He held that the account of the concept as an abstraction of experience is only partly correct. He called those concepts that result from 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:
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.
- comparison, i.e., the likening of mental images to one another in relation to the unity of consciousness;
- reflection, i.e., the going back over different mental images, how they can be comprehended in one consciousness; and finally
- abstraction or the segregation of everything else by which the mental images differ ...-- Logic, §6
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, the notion of the transformation of embodied concepts through structural mapping makes a distinct contribution to the problem of concept formation.
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 lay 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 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.
Can two people ever come to learn exactly the same concept? If person A has seen 100 trees and person B has seen a different 100 trees, they will not always generalize the same set of features in their concept of trees. The two concepts are sometimes written as TREE_A and TREE_B to emphasise their difference. If A and B have these different concepts, and intend them by their use of the English word, "tree", then how can they ever have a meaningful debate to decide the truth of a statement about "trees"? A statement that is true of TREE_A may be false of TREE_B, and the two parties will talk past one another. Concept theorists suggest that this is the root of many, especially political, disagreements in the world, and that more productive resolutions should be found by the participants exploring each other's different concepts and trying to locate the conceptual source of the disagreement.
The situation becomes even more complex when reasoning about other people's beliefs. For example, is the statement "George Bush thinks conservatism is bad" true or false? Bush presumably possesses some concept in his own mind, CONSERVATISM_BUSH, but the reasoner (eg. ones self) does not have access to this exact concept. If the reasoner is a liberal, it is likely that their concept CONSERVATISM_REASONER will be defined differently to that of Bush. It is likely that it will contain many properties which are bad. The reasoner can conclude that "CONSERVATISM_REASONER is bad", and might even have reason to believe that if this version of the concept was explained to Bush, then Bush would also think it is bad. But the reasoner has no access to Bush's own concept and can therefore assign no deep truth value to statements about it. They might have heard Bush say "conservatism is good" and thus have evidence that "Bush thinks CONSERVATISM_BUSH is good", but this is only a weak statement about the Fregean sense of the concept and not its (deep) referent. Concept theorists again suggest that this type of confusion could help to resolve many real-world, especially political, disagreements.
In a physicalist theory of mind, a concept is a mental representation, which the brain uses to denote a class of things in the world. This is to say that it is literally, a symbol or group of symbols together made from the physical material of the brain. Concepts are mental representations that allow us to draw appropriate inferences about the type of entities we encounter in our everyday lives. Concepts do not encompass all mental representations, but are merely a subset of them. The use of concepts is necessary to cognitive processes such as categorization, memory, decision making, learning, and inference.
Concepts are thought to be stored in long term cortical memory, in contrast to episodic memory of the particular objects and events which they abstract, which are stored in hippocampus. Evidence for this separation comes from hippocampal damaged patients such as patient HM. The abstraction from the day's hippocampal events and objects into cortical concepts is often considered to be the computation underlying (some stages of) sleep and dreaming. Many people (beginning with Aristotle) report memories of dreams which appear to mix the day's events with analogous or related historical concepts and memories, and suggest that they were being sorted or organised into more abstract concepts. ("Sort" is itself another word for concept, and "sorting" thus means to organise into concepts.)
The classical theory of concepts, also referred to as the empiricist theory of concepts, is the oldest theory about the structure of concepts (it can be traced back to Aristotle), and was prominently held until the 1970s. The classical theory of concepts says that concepts have a definitional structure. Adequate definitions of the kind required by this theory usually take the form of a list of features. These features must have two important qualities to provide a comprehensive definition. Features entailed by the definition of a concept must be both necessary and sufficient for membership in the class of things covered by a particular concept. A feature is considered necessary if every member of the denoted class has that feature. A feature is considered sufficient if something has all the parts required by the definition. For example, the classic example bachelor is said to be defined by unmarried and man. An entity is a bachelor (by this definition) if and only if it is both unmarried and a man. To check whether something is a member of the class, you compare its qualities to the features in the definition. Another key part of this theory is that it obeys the law of the excluded middle, which means that there are no partial members of a class, you are either in or out.
The classical theory persisted for so long unquestioned because it seemed intuitively correct and has great explanatory power. It can explain how concepts would be acquired, how we use them to categorize and how we use the structure of a concept to determine its referent class. In fact, for many years it was one of the major activities in philosophy - concept analysis. Concept analysis is the act of trying to articulate the necessary and sufficient conditions for the membership in the referent class of a concept. For example, Shoemaker's classic "Time Without Change" explored whether the concept of the flow of time can include flows where no changes take place, though change is usually taken as a definition of time.
Given that most later theories of concepts were born out of the rejection of some or all of the classical theory, it seems appropriate to give an account of what might be wrong with this theory. In the 20th century, philosophers such as Wittgenstein and Rosch argued against the classical theory. There are six primary arguments summarized as follows:
Prototype theory came out of problems with the classical view of conceptual structure. Prototype theory says that concepts specify properties that members of a class tend to possess, rather than must possess.Wittgenstein, Rosch, Mervis, Berlin, Anglin, and Posner are a few of the key proponents and creators of this theory. Wittgenstein describes the relationship between members of a class as family resemblances. There are not necessarily any necessary conditions for membership, a dog can still be a dog with only three legs. This view is particularly supported by psychological experimental evidence for prototypicality effects. Participants willingly and consistently rate objects in categories like 'vegetable' or 'furniture' as more or less typical of that class. It seems that our categories are fuzzy psychologically, and so this structure has explanatory power. We can judge an item's membership to the referent class of a concept by comparing it to the typical member - the most central member of the concept. If it is similar enough in the relevant ways, it will be cognitively admitted as a member of the relevant class of entities. Rosch suggests that every category is represented by a central exemplar which embodies all or the maximum possible number of features of a given category. According to Lech, Gunturkun, and Suchan explain that categorization involves many areas of the brain, some of these are; visual association areas, prefrontal cortex, basal ganglia, and temporal lobe.
Theory-theory is a reaction to the previous two theories and develops them further. This theory postulates that categorization by concepts is something like scientific theorizing. Concepts are not learned in isolation, but rather are learned as a part of our experiences with the world around us. In this sense, concepts' structure relies on their relationships to other concepts as mandated by a particular mental theory about the state of the world. How this is supposed to work is a little less clear than in the previous two theories, but is still a prominent and notable theory. This is supposed to explain some of the issues of ignorance and error that come up in prototype and classical theories as concepts that are structured around each other seem to account for errors such as whale as a fish (this misconception came from an incorrect theory about what a whale is like, combining with our theory of what a fish is). When we learn that a whale is not a fish, we are recognizing that whales don't in fact fit the theory we had about what makes something a fish. In this sense, the Theory-Theory of concepts is responding to some of the issues of prototype theory and classic theory.
According to the theory of ideasthesia (or "sensing concepts"), activation of a concept may be the main mechanism responsible for creation of phenomenal experiences. Therefore, understanding how the brain processes concepts may be central to solving the mystery of how conscious experiences (or qualia) emerge within a physical system e.g., the sourness of the sour taste of lemon. This question is also known as the hard problem of consciousness. Research on ideasthesia emerged from research on synesthesia where it was noted that a synesthetic experience requires first an activation of a concept of the inducer. Later research expanded these results into everyday perception.
There is a lot of discussion on the most effective theory in concepts. Another theory is semantic pointers, which use perceptual and motor representations and these representations are like symbols.
The term "concept" is traced back to 1554-60 (Latin conceptum - "something conceived"), but what is today termed "the classical theory of concepts" is the theory of Aristotle on the definition of terms.