Analogy (from Ancient Greek αναλογια, “reasoning from one point to another”) is a cognitive process involving comparison whereby the information concerning one element is linked to another element through observed similarities. Analogy is related to “iconicity” (both involve parallels of form/meaning): the strong drive language users have to describe their world through signs that have some natural connection with the object the sign refers to. Analogy is concerned with (1) similarities between observable properties (material or horizontal analogy) and (2) causal similarities, i.e., the relations between a material property and a function of that property (vertical analogy). It enables language learning, is involved in language change, and helps in seeking explanations in science (including linguistics) through the spotting of parallels, e.g., the discovery of sound waves on the basis of water waves. Analogy is omnipresent in language but its working through speakers in language use and language change can only be captured after the fact; there are no fixed “rules” to “predict” analogy. It plays an important role in streamlining (“oiling”) the “machinery” (i.e., the “rules” or “patterns”) of language: without analogy, languages may develop too many exceptions, caused by internal changes elsewhere in the system or external factors, such as contact. The cognitive ability people have to analogize is the concern of cognitive scientists. In linguistics proper, a distinction is often made between this ability and the mechanism of analogy, which is concerned with the effects it has on language output, with specific patterns and constraints. This more narrow approach bears most fruit on the morpho-phonological level, where formal similarities play an important role. As soon as higher lexical and grammatical levels are involved, similarities become looser, more associative, making it more difficult to constrain the workings of analogy. Some linguists make a distinction between proportional and non-proportional analogy: the former is seen as more systematic, more concerned with form, and the result of interference from a productive morphological system (as in analogical extension/leveling), while the latter concerns innovations in individual items and constructions, with meaning playing a large(r) role. In morphological studies, analogy is usually seen as strictly proportional, making use of the formula A : B :: C : D, with more sporadic forms of analogy excluded as being non-proportional. Linguists interested in analogy on higher levels (syntax, lexis, semantics), also consider analogy to be proportional but in a less strict sense; here too there is symmetry between the forms and functions of source and target. For example, in the metaphorical use of foot, when there is a symmetry in meaning between referent A (“bottom part of a human body”) and B (“bottom part of a mountain”), this may result in a new formal symmetry between the signs: thus C foot leads to the new use of foot in D (just like work: worked leads to help: helped (replacing earlier holp).