Invariance principle
Encyclopedia
In cognitive linguistics
Cognitive linguistics
In linguistics, cognitive linguistics refers to the branch of linguistics that interprets language in terms of the concepts, sometimes universal, sometimes specific to a particular tongue, which underlie its forms...

, the invariance principle is a simple attempt to explain similarities and differences between how an idea is understood in "ordinary" usage, and how it is understood when used as a conceptual metaphor
Conceptual metaphor
In cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another, for example, understanding quantity in terms of directionality . A conceptual domain can be any coherent organization of human experience...

.

Kövecses (2002: 102) provides the following examples based on the semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....

 of the English verb
Verb
A verb, from the Latin verbum meaning word, is a word that in syntax conveys an action , or a state of being . In the usual description of English, the basic form, with or without the particle to, is the infinitive...

 to give.
She gave him a book. (source language)

Based on the metaphor CAUSATION IS TRANSFER we get: She gave him a kiss. She gave him a headache.
However, the metaphor does not work in exactly the same way in each case, as seen in: She gave him a headache, and he still has it. *She gave him a kiss, and he still has it.

The invariance principle offers the hypothesis
Hypothesis
A hypothesis is a proposed explanation for a phenomenon. The term derives from the Greek, ὑποτιθέναι – hypotithenai meaning "to put under" or "to suppose". For a hypothesis to be put forward as a scientific hypothesis, the scientific method requires that one can test it...

 that metaphor only maps components of meaning from the source language that remain coherent
Coherence (linguistics)
Coherence in linguistics is what makes a text semantically meaningful.It is especially dealt with in text linguistics. Coherence is achieved through syntactical features such as the use of deictic, anaphoric and cataphoric elements or a logical tense structure, as well as presuppositions and...

 in the target context
Context (language use)
Context is a notion used in the language sciences in two different ways, namely as* verbal context* social context- Verbal context :...

. The components of meaning that remain coherent in the target context retain their "basic structure" in some sense, so this is a form of invariance
Invariance
Invariance is a French magazine edited by Jacques Camatte, published since 1968.It emerged from the Italian left-communist tradition associated with Amadeo Bordiga and it originally bore the subtitle "Invariance of the theory of the proletariat", indicating Bordiga's notion of the unchanging nature...

.

George Lakoff
George Lakoff
George P. Lakoff is an American cognitive linguist and professor of linguistics at the University of California, Berkeley, where he has taught since 1972...

 and Mark Turner
Mark Turner (cognitive scientist)
Mark Turner is a cognitive scientist, linguist, and author. He is Institute Professor and Professor of Cognitive Science at Case Western Reserve University, where he was for two years Dean of the College of Arts and Sciences...

originated the idea under the name invariance hypothesis, later revising and renaming it as the invariance principle. Lakoff (1993: 215) gives the invariance principle as: "Metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain, in a way consistent with the inherent structure of the target domain".
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