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In cognitive linguistics, relating conceptual domains
In cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another. An example of this is the understanding of quantity in terms of directionality (e. g. "the price of peace is rising") or the understanding of time in terms of money (e. g. "I spent time at work today"). A conceptual domain can be any mental organization of human experience. The regularity with which different languages employ the same metaphors, often perceptually based, has led to the hypothesis that the mapping between conceptual domains corresponds to neural mappings in the brain. This theory gained wide attention in the 1990s and early 2000s, although some researchers question its empirical accuracy. The conceptual metaphor theory proposed by George Lakoff and his colleagues arose from linguistics but became of interest to cognitive scientists due to its claims about the mind and the brain. The empirical evidence for the theory has been mixed to negative. While it is generally agreed that metaphors form an important part of human verbal conceptualization, there is little support for the more specific claims that are relevant to this particular theory of metaphor comprehension. Crucially, Lakoff asserts that human thinking works effortlessly thanks to metaphorical thinking, but psychological research has found that metaphors are actually more difficult to process than non metaphoric expressions. Furthermore, when metaphors lose their novelty and become conventionalized, they eventually lose their status of being metaphors and become processed like ordinary words (a process called grammaticalization). Therefore, the role of the conceptual metaphor in organizing human thinking is more limited than what was claimed by the linguists. In Psychology, Raymond W. Gibbs, Jr., has investigated conceptual metaphor and embodiment through a number of psychological experiments. Other cognitive scientists, for example Gilles Fauconnier, study subjects similar to conceptual metaphor under the labels "analogy", "conceptual blending" and "ideasthesia". Conceptual metaphors are useful for understanding complex ideas in simple terms and therefore are frequently used to give insight to abstract theories and models. For example, the conceptual metaphor of viewing communication as a conduit is one large theory explained with a metaphor. So not only is our everyday communication shaped by the language of conceptual metaphors, but so is the very way we understand scholarly theories. These metaphors are prevalent in communication and we do not just use them in language; we actually perceive and act in accordance with the metaphors.

In the Western philosophical tradition, Aristotle is often situated as the first commentator on the nature of metaphor, writing in the Poetics, "A 'metaphorical term' involves the transferred use of a term that properly belongs to something else," and elsewhere in the Rhetoric he says that metaphors make learning pleasant; "To learn easily is naturally pleasant to all people, and words signify something, so whatever words create knowledge in us are the pleasantest." Aristotle's writings on metaphor constitute a "substitution view" of metaphor, wherein a metaphor is simply a decorative word or phrase substituted for a more ordinary one. This has been sometimes called the "Traditional View of Metaphor" and at other times the "Classical Theory of Metaphor". Later in the first century A. D., the Roman rhetorician Quintilian builds upon Aristotle's earlier work of metaphor by focusing more on the comparative function of metaphorical language. In his work Institutio Oratoria, Quintilian states," In totum autem metaphora brevior est similitudo" or "on the whole, metaphor is a shorter form of simile". Other philosophers throughout history have lent their perspectives to the discussion of metaphor as well. Friedrich Nietzsche for example, claimed that language as a whole did not portray reality but instead made a series of bold metaphors. Nietzsche believed that each step of cognition, the transfer of real world information to nerve stimuli, the culmination of nerve stimuli into mental images, the translation of mental images to words, was metaphorical. Modern interpretations of these early theories have also been intensely debated. Janet Soskice, Professor of Philosophical Theology at the University of Cambridge, writes in summary that "it is certain that we shall taste the freshness of their insights only if we free them from the obligation to answer questions that were never theirs to ask". later concede that Aristotle was working within a different philosophical framework from what we engage with today and that critical interpretations should take this in to account.

In his 2007 book The Stuff of Thought, cognitive scientist Steven Pinker lays out several useful classifications for the study of conceptual metaphor. Pinker first contrasts two perspectives on metaphor, what he calls the killjoy theory and the messianic theory. The killjoy theory categorizes metaphors as "dead", that is it asserts that modern day speakers are not aware of the comparison made between source and target domains in the everyday metaphors they use. For example, many are not cognizant that the phrase "to come to a head" refers to the accumulation of pus in a pimple. In contrast, the messianic theory correlates more closely with Lakoff and Johnson's idea of a conceptual metaphor. This view states that users of metaphors are aware of how the metaphor maps onto the domains and use them to relate shared perceptual experiences to more complex thoughts. Another important distinction made by Pinker is that between literary, or poetic metaphors, and conceptual, or generative metaphors. Poetic metaphors are used for a variety of reasons but ultimately highlight similarities or incongruencies in an expressive manner. Pinker's example of this being the classic Shakespearian line "Juliet is the sun". These metaphors can often appear convoluted or unclear without deeper context. Conceptual metaphors result from some inherent relation between two domains. These metaphors, so innate they are considered cliche, are interestingly able to generate infinite new metaphors. In 2007, Pragglejaz Group came up with a methodology for identifying metaphorical expressions as a response to these criticisms.

The conduit metaphor is a dominant class of figurative expressions used when discussing communication itself (metalanguage). It operates whenever people speak or write as if they "insert" their mental contents (feelings, meanings, thoughts, concepts, etc.) into "containers" (words, phrases, sentences, etc.) whose contents are then "extracted" by listeners and readers. Thus, language is viewed as a "conduit" conveying mental content between people. Defined and described by linguist Michael J. Reddy, PhD, his proposal of this conceptual metaphor refocused debate within and outside the linguistic community on the importance of metaphorical language.

George Lakoff makes similar claims on the overlap of conceptual metaphors, culture, and society in his book Moral Politics and his later book on framing, Don't Think of an Elephant!. Lakoff claims that the public political arena in America reflects a basic conceptual metaphor of 'the family.' Accordingly, people understand political leaders in terms of 'strict father' and 'nurturant mother' roles. Two basic views of political economy arise from this desire to see the nation state act 'more like a father' or 'more like a mother.' He further amplified these views in his latest book, The Political Mind. Urban theorist and ethicist Jane Jacobs made this distinction in less gender driven terms by differentiating between a 'Guardian Ethic' and a 'Trader Ethic'. She states that guarding and trading are two concrete activities that human beings must learn to apply metaphorically to all choices in later life. In a society where guarding children is the primary female duty and trading in a market economy is the primary male duty, Lakoff posits that children assign the 'guardian' and 'trader' roles to their mothers and fathers, respectively.

Lakoff, Johnson, and Pinker are among the many cognitive scientists that devote a significant amount of time to current events and political theory, suggesting that respected linguists and theorists of conceptual metaphor may tend to channel their theories into political realms. Critics of this ethics driven approach to language tend to accept that idioms reflect underlying conceptual metaphors, but that actual grammar, and the more basic cross cultural concepts of scientific method and mathematical practice tend to minimize the impact of metaphors. Such critics tend to see Lakoff and Jacobs as 'left wing figures,' and would not accept their politics as any kind of crusade against an ontology embedded in language and culture, but rather, as an idiosyncratic pastime, not part of the science of linguistics nor of much use. And others further, such as Deleuze and Guattari, Michel Foucault and, more recently, Manuel de Landa would criticize both of these two positions for mutually constituting the same old ontological ideology that would try to separate two parts of a whole that is greater than the sum of its parts. Lakoff's 1987 work, Women, Fire, and Dangerous Things, answered some of these criticisms before they were even made: he explores the effects of cognitive metaphors (both culturally specific and human universal) on the grammar per se of several languages, and the evidence of the limitations of the classical logical positivist or Anglo American School philosophical concept of the category usually used to explain or describe the scientific method. Lakoff's reliance on empirical scientific evidence, i. e. specifically falsifiable predictions, in the 1987 work and in Philosophy in the Flesh (1999) suggests that the cognitive metaphor position has no objections to the scientific method, but instead considers the scientific method a finely developed reasoning system used to discover phenomena which are subsequently understood in terms of new conceptual metaphors (such as the metaphor of fluid motion for conducted electricity, which is described in terms of "current" "flowing" against "impedance," or the gravitational metaphor for static electric phenomena, or the "planetary orbit" model of the atomic nucleus and electrons, as used by Niels Bohr). Further, partly in response to such criticisms, Lakoff and Rafael E. Núñez, in 2000, proposed a cognitive science of mathematics that would explain mathematics as a consequence of, not an alternative to, the human reliance on conceptual metaphor to understand abstraction in terms of basic experiential concretes.

Teaching thinking by analogy (metaphor) is one of the main themes of The Private Eye Project. The idea of encouraging use of conceptual metaphors can also be seen in other educational programs touting the cultivation of "critical thinking skills". The work of political scientist Rūta Kazlauskaitė examines metaphorical models in school history knowledge of the controversial Polish Lithuanian past. On the basis of Lakoff and Johnson's conceptual metaphor theory, she shows how the implicit metaphorical models of everyday experience, which inform the abstract conceptualization of the past, truth, objectivity, knowledge, and multiperspectivity in the school textbooks, obstruct an understanding of the divergent narratives of past experience.

There is some evidence that an understanding of underlying conceptual metaphors can aid the retention of vocabulary for people learning a foreign language. To improve learners' awareness of conceptual metaphor, one monolingual learner's dictionary, the Macmillan English Dictionary has introduced 50 or so 'metaphor boxes' covering the most salient Lakoffian metaphors in English. For example, the dictionary entry for conversation includes a box with the heading: 'A conversation is like a journey, with the speakers going from one place to another', followed by vocabulary items (words and phrases) which embody this metaphorical schema. Language teaching experts are beginning to explore the relevance of conceptual metaphor to how learners learn and what teachers do in the classroom.

A current study showed a natural tendency to systematically map an abstract dimension, such as social status, in our closest and non linguistic relatives, the chimpanzees. In detail, discrimination performances between familiar conspecific faces were systematically modulated by the spatial location and the social status of the presented individuals, leading to discrimination facilitation or deterioration. High ranked individuals presented at spatially higher position and low ranked individuals presented at lower position led to discrimination facilitation, while high ranked individuals at lower positions and low ranked individuals at higher position led to discrimination deterioration. This suggests that this tendency had already evolved in the common ancestors of humans and chimpanzees and is not uniquely human, but describes a conceptual metaphorical mapping that predates language.