Analogy

Analogy is a comparison or correspondence between two things because of a third element that they are considered to share.
Logically, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction. It is also used where at least one of the premises, or the conclusion, is general rather than particular in nature. It has the general form A is to B as C is to D.
In a broader sense, analogical reasoning is a cognitive process of transferring some information or meaning of a particular subject onto another ; and also the linguistic expression corresponding to such a process. The term analogy can also refer to the relation between the source and the target themselves, which is often a similarity, as in the biological notion of analogy.
Image:Bohr atom model.svg|thumb|200px|right|Ernest Rutherford's model of the atom made an analogy between the atom and the Solar System.
Analogy plays a significant role in human thought processes. It has been argued that analogy lies at "the core of cognition".

Etymology

The English word analogy derives from the Latin analogia, itself derived from the Greek ἀναλογία, "proportion", from ana- "upon, according to" + logos "ratio" .

Models and theories

Analogy plays a significant role in problem solving, as well as decision making, argumentation, perception, generalization, memory, creativity, invention, prediction, emotion, explanation, conceptualization and communication. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception and facial recognition systems. Hofstadter has argued that analogy is "the core of cognition".
An analogy is not a figure of speech but a kind of thought. Specific analogical language uses exemplification, comparisons, metaphors, similes, allegories, and parables, but not metonymy. Phrases like and so on, and the like, as if, and the very word like also rely on an analogical understanding by the receiver of a message including them. Analogy is important not only in ordinary language and common sense but also in science, philosophy, law and the humanities.
The concepts of association, comparison, correspondence, mathematical and morphological homology, homomorphism, iconicity, isomorphism, metaphor, resemblance, and similarity are closely related to analogy. In cognitive linguistics, the notion of conceptual metaphor may be equivalent to that of analogy. Analogy is also a basis for any comparative arguments as well as experiments whose results are transmitted to objects that have been not under examination.
Analogy has been studied and discussed since classical antiquity by philosophers, scientists, theologists and lawyers. The last few decades have shown a renewed interest in analogy, most notably in cognitive science.

Development

Archytas, a contemporary of Plato, described three kinds of analogy: mathematical, harmonic, and geometric: the last being the true analogy
Aristotle identified analogy in works such as Metaphysics and Nicomachean Ethics
Roman lawyers used analogical reasoning and the Greek word analogia.
In Islamic logic, analogical reasoning was used for the process of qiyas in Islamic sharia law and fiqh jurisprudence.
Medieval lawyers distinguished analogia legis and analogia iuris.
The Middle Ages saw an increased use and theorization of analogy.
In Christian scholastic theology, analogical arguments were accepted in order to explain the attributes of God.
* Aquinas made a distinction between equivocal, univocal and analogical terms, the last being those like healthy that have different but related meanings. Not only a person can be "healthy", but also the food that is good for health.
* Thomas Cajetan wrote an influential treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved.

Cajetan named several kinds of analogy that had been used but previously unnamed, particularly:

Analogy of attribution or improper proportionality, e.g., "This food is healthy."
Analogy of proportionality or proper proportionality, e.g., "2 is to 1 as 4 is to 2", or "the goodness of humans is relative to their essence as the goodness of God is relative to God's essence."
Metaphor, e.g., steely determination.
Identity of relation

In ancient Greek the word αναλογια originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as proportio. Analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not.
Analogy and abstraction are different cognitive processes, and analogy is often an easier one. This analogy is not comparing all the properties between a hand and a foot, but rather comparing the relationship between a hand and its palm to a foot and its sole. While a hand and a foot have many dissimilarities, the analogy focuses on their similarity in having an inner surface.
The same notion of analogy was used in the US-based SAT college admission tests, that included "analogy questions" in the form "A is to B as C is to what?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in the Aristotelian format: HAND : PALM : : FOOT : ____ While most competent English speakers will immediately give the right answer to the analogy question, it is more difficult to identify and describe the exact relation that holds both between pairs such as hand and palm, and between foot and sole. This relation is not apparent in some lexical definitions of palm and sole, where the former is defined as the inner surface of the hand, and the latter as the underside of the foot.
Kant's Critique of Judgment held to this notion of analogy, arguing that there can be exactly the same relation between two completely different objects.

Shared abstraction

Greek philosophers such as Plato and Aristotle used a wider notion of analogy. They saw analogy as a shared abstraction. Analogous objects did not share necessarily a relation, but also an idea, a pattern, a regularity, an attribute, an effect or a philosophy. These authors also accepted that comparisons, metaphors and "images" could be used as arguments, and sometimes they called them analogies. Analogies should also make those abstractions easier to understand and give confidence to those who use them.
James Francis Ross in Portraying Analogy, the first substantive examination of the topic since Cajetan's De Nominum Analogia, demonstrated that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent.

Special case of induction

, Francis Bacon and later John Stuart Mill argued that analogy is simply a special case of induction. In their view, analogy is an inductive inference from common known attributes to another probable common attribute, which is known about only in the source of the analogy, in the following form:
;Premises
;Conclusion

Shared structure

Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by Gentner's structure-mapping theory. The same idea of mapping between source and target is used by conceptual metaphor and conceptual blending theorists. Structure mapping theory concerns both psychology and computer science. According to this view, analogy depends on the mapping or alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target. Structure mapping theory has been applied and has found considerable confirmation in psychology. It has had reasonable success in computer science and artificial intelligence. Some studies extended the approach to specific subjects, such as metaphor and similarity.

Applications and types

[Logic]

analyze how analogical reasoning is used in arguments from analogy.
An analogy can be stated using is to and as when representing the analogous relationship between two pairs of expressions, for example, "Smile is to mouth, as wink is to eye." In the field of mathematics and logic, this can be formalized with colon notation to represent the relationships, using single colon for ratio, and double colon for equality.
In the field of testing, the colon notation of ratios and equality is often borrowed, so that the example above might be rendered, "Smile : mouth :: wink : eye" and pronounced the same way.

Linguistics

In historical linguistics and word formation, analogy is the process that alters words-forms perceived as breaking rules or ignoring general patterns to more typical forms that follow them. For example, the English verb help once had the simple past-tense form holp and the past participle form holpen. These older forms have now been discarded and replaced by helped, which came about through the analogy that many other past-tense forms use the -ed ending. This is called morphological leveling. Analogies do not always lead to words shifting to fit rules; sometimes, they can also leading to the breaking of rules; one example is the American English past tense form of dive: dove, formed on analogy with words such as drive to drove or strive to strove.

Neologisms can also be formed by analogy with existing words. A good example is software, formed by analogy with hardware; other analogous neologisms such as firmware and vapourware have followed. Another example is the humorous term underwhelm, formed by analogy with overwhelm.
Some people present analogy as an alternative to generative rules for explaining the productive formation of structures such as words. Others argue that they are in fact the same and that rules are analogies that have essentially become standard parts of the linguistic system, whereas clearer cases of analogy have simply not done so. This view agrees with the current views of analogy in cognitive science which are discussed above.

Analogy is also a term used in the Neogrammarian school of thought as a catch-all to describe any morphological change in a language that cannot be explained merely sound change or borrowing.