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This idea and detailed examination of the underlying processes was first explored in detail by George Lakoff and Mark Johnson in Metaphors we live by
A conceptual metaphor consists of two conceptual domains, in which one domain is understood in terms of another. Metaphorical linguistic expressions are words or other linguistic expressions that come from the language or terminology of the more concrete conceptual domain. Conceptual metaphors underlie the metaphorical expressions. They tend to be pre-linguistic and make basic assumptions regarding space, time, moving, counting, controlling, and other core elements of human experience.
Source domain: the conceptual domain from which we draw metaphorical expressions.
Target domain: the conceptual domain that we try to understand.
Conceptual metaphors typically employ a more abstract concept as target and a more concrete or physical concept as their source. For instance, metaphors such as 'the days (the more abstract or target concept) ahead' or 'giving my time' rely on more concrete concepts, thus expressing time as a (more concrete) path into physical space or as a substance (that can be handled and offered as a gift). Different conceptual metaphors tend to be invoked when the speaker is trying to make a case for a certain point of view or course of action. For instance, we associate 'the days ahead' more with leadership, and 'giving my time' more with bargaining (if time is a substance, clearly, it should be traded for things of substance, and this metaphor makes that more obvious than the path metaphor). Selection of such metaphors tends to be directed by a subconscious or implicit purpose, in the mind of s/he who chooses them.
The principle of unidirectionality states that the metaphorical process typically goes from the more concrete to the more abstract but not the other way around. Accordingly, abstract concepts are understood in terms of prototype concrete processes. An extreme version of this view is expressed in the cognitive science of mathematics, where it is proposed that mathematics itself, the most widely accepted means of abstraction in the human community, reflects a cognitive bias unique to humans, and prototype processes, e.g. counting, moving along a path, that are understood by all human beings through their experiences.
A mapping is the systematic set of correspondences that exist between constituent elements of the source and the target domain. Many elements of target concepts come from source domains and are not preexisting. To know a conceptual metaphor is to know the set of mappings that applies to a given source-target pairing.
This knowledge is presumed to be largely unconscious and to emerge in language acquisition. Quine and others influential in the recent philosophy of mathematics have argued that each natural human language reflects an assumed ontology which makes certain conceptual metaphors easy to employ, and others more difficult or complex, and thereby less convincing. If so, each natural language becomes one 'mapping' from the concrete experience of early human life to the more abstract and socially-prescribed 'source domain' of culture. A consequence of this would be great difficulty in learning a new natural language in adult life, which does seem to be the case.
Some basic conceptual metaphors discussed in Lakoff, Johnson, 1980, are:
Each of these invokes certain assumptions about concrete experience and requires the reader or listener to apply them to the much more abstract concepts of love or organizing in order to understand the sentence in which the conceptual metaphor is used.
There are numerous ways in which this process of assuming and applying metaphors have been said to manipulate human perception and communication, especially in mass media and in public policy: