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Analogy is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share.[1]
In logic, it is aninference or anargument from one particular to another particular, as opposed todeduction,induction, andabduction. It is also used of where at least one of thepremises, or the conclusion, is general rather than particular in nature. It has the general formA is to B as C is to D.
In a broader sense, analogical reasoning is acognitive process of transferring someinformation ormeaning of a particular subject (the analog, or source) onto another (the target); and also thelinguistic 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 (though not always) asimilarity, as in thebiological notion of analogy.
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Analogy plays a significant role in human thought processes. It has been argued that analogy lies at "the core of cognition".[2]
The English wordanalogy derives from theLatinanalogia, itself derived from theGreekἀναλογία, "proportion", fromana- "upon, according to" [also "again", "anew"] +logos "ratio" [also "word, speech, reckoning"].[3][4]
Analogy plays a significant role inproblem solving, as well asdecision making,argumentation,perception,generalization,memory,creativity,invention, prediction,emotion,explanation,conceptualization andcommunication. It lies behind basic tasks such as the identification of places, objects and people, for example, inface perception andfacial recognition systems.Hofstadter has argued that analogy is "the core of cognition".[2]
An analogy is not afigure of speech but a kind of thought. Specific analogical language usesexemplification,comparisons,metaphors,similes,allegories, andparables, butnotmetonymy. Phrases likeand so on,and the like,as if, and the very wordlike also rely on an analogical understanding by the receiver of amessage including them. Analogy is important not only inordinary language andcommon sense (whereproverbs andidioms give many examples of its application) but also inscience,philosophy,law and thehumanities.
The concepts ofassociation, comparison, correspondence,mathematical andmorphological homology,homomorphism,iconicity,isomorphism, metaphor, resemblance, and similarity are closely related to analogy. Incognitive linguistics, the notion ofconceptual 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 (e.g., experiments on rats when results are applied to humans).
Analogy has been studied and discussed sinceclassical antiquity by philosophers, scientists, theologists andlawyers. The last few decades have shown a renewed interest in analogy, most notably incognitive science.
Cajetan named several kinds of analogy that had been used but previously unnamed, particularly:[6]
In ancientGreek the wordαναλογια (analogia) originally meantproportionality, in the mathematical sense, and it was indeed sometimes translated toLatin asproportio.[citation needed] Analogy was understood as identity of relation between any twoordered pairs, whether of mathematical nature or not.
Analogy andabstraction are different cognitive processes, and analogy is often an easier one. This analogy is not comparingall the properties between a hand and a foot, but rather comparing therelationship between a hand and its palm to a foot and its sole.[8] 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 theUS-basedSAT college admission tests, that included "analogy questions" in the form "A is to B as C is towhat?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in theAristotelian format: HAND : PALM : : FOOT : ____ While most competentEnglish speakers will immediately give the right answer to the analogy question (sole), it is more difficult to identify and describe the exact relation that holds both between pairs such ashand andpalm, and betweenfoot andsole. This relation is not apparent in somelexical definitions ofpalm andsole, where the former is defined asthe inner surface of the hand, and the latter asthe underside of the foot.
Kant'sCritique of Judgment held to this notion of analogy, arguing that there can be exactly the samerelation between two completely different objects.
Greek philosophers such asPlato andAristotle used a wider notion of analogy. They saw analogy as a shared abstraction.[9] 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" (allegories) could be used asarguments, and sometimes they called themanalogies. Analogies should also make those abstractions easier to understand and give confidence to those who use them.
James Francis Ross inPortraying Analogy (1982), the first substantive examination of the topic since Cajetan'sDe Nominum Analogia,[dubious –discuss] 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.
Ibn Taymiyya,[10][11][12]Francis Bacon and laterJohn Stuart Mill argued that analogy is simply a special case of induction.[9] In their view, analogy is aninductive inference from common known attributes to anotherprobable common attribute, which is known about only in the source of the analogy, in the following form:
Contemporary cognitive scientists use a wide notion of analogy,extensionally close to that of Plato and Aristotle, but framed by Gentner's (1983)structure-mapping theory.[13] The same idea ofmapping between source and target is used byconceptual metaphor andconceptual blending theorists. Structure mapping theory concerns bothpsychology andcomputer 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 inpsychology. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such asmetaphor and similarity.[14]
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Logicians analyze how analogical reasoning is used inarguments from analogy.
An analogy can be stated usingis to andas 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 withcolon notation to represent the relationships, using single colon for ratio, and double colon for equality.[15]
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.[15][16]
Inhistorical linguistics andword 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, theEnglishverbhelp once had the simple past-tense formholp and thepast participle formholpen. These older forms have now been discarded and replaced byhelped, which came about through the analogy that many other past-tense forms use the-ed ending (jumped,carried,defeated, etc.). This is calledmorphological 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 theAmerican English past tense form ofdive:dove, formed on analogy with words such asdrive todrove orstrive tostrove.
Analogy is also a term used in theNeogrammarian school of thought as acatch-all to describe any morphological change in a language that cannot be explained merely sound change or borrowing.
Analogies are mainly used as a means of creating new ideas and hypotheses, or testing them, which is called a heuristic function of analogical reasoning.
Analogical arguments can also be probative, meaning that they serve as a means of proving the rightness of particular theses and theories. This application of analogical reasoning in science is debatable. Analogy can help prove important theories, especially in those kinds of science in whichlogical orempirical proof is not possible such astheology,philosophy orcosmology when it relates to those areas of the cosmos (the universe) that are beyond any data-based observation and knowledge about them stems from the human insight and thinking outside the senses.
Analogy can be used in theoretical and applied sciences in the form of models or simulations which can be considered as strong indications of probable correctness. Other, much weaker, analogies may also assist in understanding and describing nuanced or key functional behaviours of systems that are otherwise difficult to grasp or prove. For instance, an analogy used in physics textbookscompares electrical circuits to hydraulic circuits.[18] Another example is theanalogue ear based on electrical, electronic or mechanical devices.
Some types of analogies can have a precisemathematical formulation through the concept ofisomorphism. In detail, this means that if two mathematical structures are of the same type, an analogy between them can be thought of as abijection which preserves some or all of the relevant structure. For example, and are isomorphic as vector spaces, but thecomplex numbers,, have more structure than does: is afield as well as avector space.
Category theory takes the idea of mathematical analogy much further with the concept offunctors. Given two categories C and D, a functorf from C to D can be thought of as an analogy between C and D, becausef has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the structure of their respective parts is preserved. This is similar to thestructure mapping theory of analogy of Dedre Gentner, because it formalises the idea of analogy as a function which makes certain conditions true.
A computer algorithm has achieved human-level performance on multiple-choice analogy questions from theSAT test. The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistically analysing a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.[19]
The analogical reasoning in the human mind is free of the false inferences plaguing conventionalartificial intelligence models, (calledsystematicity). Steven Phillips andWilliam H. Wilson[20][21] usecategory theory to mathematically demonstrate how such reasoning could arise naturally by using relationships between the internal arrows that keep the internal structures of the categories rather than the mere relationships between the objects (called "representational states"). Thus, the mind, and more intelligent AIs, may use analogies between domains whose internal structurestransform naturally and reject those that do not.
Keith Holyoak andPaul Thagard (1997) developed their multiconstraint theory within structure mapping theory. They defend that the "coherence" of an analogy depends on structural consistency,semantic similarity and purpose. Structural consistency is the highest when the analogy is anisomorphism, although lower levels can be used as well. Similarity demands that the mapping connects similar elements and relationships between source and target, at any level of abstraction. It is the highest when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose if it helps solve the problem at hand. The multiconstraint theory faces some difficulties when there are multiple sources, but these can be overcome.[9] Hummel and Holyoak (2005) recast the multiconstraint theory within aneural network architecture. A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are someidentical attributes or relations at some level of abstraction. The model was extended (Doumas, Hummel, and Sandhofer, 2008) to learn relations from unstructured examples (providing the only current account of how symbolic representations can be learned from examples).[22]
Mark Keane and Brayshaw (1988) developed theirIncremental Analogy Machine (IAM) to include working memory constraints as well as structural, semantic and pragmatic constraints, so that a subset of the base analogue is selected and mapping from base to target occurs in series.[23][24]Empirical evidence shows that humans are better at using and creating analogies when the information is presented in an order where an item and its analogue are placed together.[25]
Eqaan Doug and his team[26] challenged the shared structure theory and mostly its applications in computer science. They argue that there is no clear line betweenperception, including high-level perception, and analogical thinking. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans makerepresentations by selecting relevant information from low-levelstimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers et al. concludes that analogy actually is high-level perception. Forbus et al. (1998) claim that this is only a metaphor.[27] It has been argued (Morrison and Dietrich 1995) that Hofstadter's and Gentner's groups do not defend opposite views, but are instead dealing with different aspects of analogy.[28]
Inanatomy, two anatomical structures are considered to beanalogous when they serve similarfunctions but are notevolutionarily related, such as thelegs ofvertebrates and the legs ofinsects. Analogous structures are the result ofindependent evolution and should be contrasted with structures whichshared an evolutionary line.
Often a physicalprototype is built to model and represent some other physical object. For example,wind tunnels are used to test scale models of wings and aircraft which are analogous to (correspond to) full-size wings and aircraft.
For example, theMONIAC (ananalogue computer) used the flow of water in its pipes as an analogue to the flow of money in an economy.
Where two or more biological or physical participants meet, they communicate and the stresses produced describe internal models of the participants.Pask in hisconversation theory asserts ananalogy that describes both similarities and differences between any pair of the participants' internal models or concepts exists.
In historical science, comparative historical analysis often uses the concept of analogy and analogical reasoning. Recent methods involving calculation operate on large document archives, allowing for analogical or corresponding terms from the past to be found as a response to random questions by users (e.g., Myanmar - Burma)[29] and explained.[30]
Analogical reasoning plays a very important part inmorality. This may be because morality is supposed to beimpartial and fair. If it is wrong to do something in a situation A, and situation B corresponds to A in all related features, then it is also wrong to perform that action in situation B.Moral particularism accepts such reasoning, instead of deduction and induction, since only the first can be used regardless of any moral principles.
Structure mapping, originally proposed byDedre Gentner, is a theory in psychology that describes the psychological processes involved in reasoning through, and learning from, analogies.[31] More specifically, this theory aims to describe how familiar knowledge, or knowledge about a base domain, can be used to inform an individual's understanding of a less familiar idea, or a target domain.[32] According to this theory, individuals view their knowledge of ideas, or domains, as interconnected structures.[33] In other words, a domain is viewed as consisting of objects, their properties, and the relationships that characterise their interactions.[34] The process of analogy then involves:
In general, it has been found that people prefer analogies where the two systems correspond highly to each other (e.g. have similar relationships across the domains as opposed to just having similar objects across domains) when these people try to compare and contrast the systems. This is also known as the systematicity principle.[33]
An example that has been used to illustrate structure mapping theory comes from Gentner and Gentner (1983) and uses the base domain of flowing water and the target domain of electricity.[35] In a system of flowing water, the water is carried through pipes and the rate of water flow is determined by the pressure of the water towers or hills. This relationshipcorresponds to that of electricity flowing through a circuit. In a circuit, the electricity is carried through wires and the current, or rate of flow of electricity, is determined by the voltage, or electrical pressure. Given the similarity in structure, or structural alignment, between these domains, structure mapping theory would predict that relationships from one of these domains, would be inferred in the other using analogy.[34]
Children do not always need prompting to make comparisons in order to learn abstract relationships. Eventually, children undergo a relational shift, after which they begin seeing similar relations across different situations instead of merely looking at matching objects.[36] This is critical in their cognitive development as continuing to focus on specific objects would reduce children's ability to learn abstract patterns and reason analogically.[36] Interestingly, some researchers have proposed that children's basic brain functions (i.e., working memory and inhibitory control) do not drive this relational shift. Instead, it is driven by their relational knowledge, such as having labels for the objects that make the relationships clearer(see previous section).[36] However, there is not enough evidence to determine whether the relational shift is actually because basic brain functions become better or relational knowledge becomes deeper.[34]
Additionally, research has identified several factors that may increase the likelihood that a child may spontaneously engage in comparison and learn an abstract relationship, without the need for prompts.[37] Comparison is more likely when the objects to be compared are close together in space and/or time,[37] are highly similar (although not so similar that they match, which interfere with identifying relationships),[34] or share common labels.
Inlaw, analogy is a method of resolving issues on which there is no previous authority. The legal use of analogy is distinguished by the need to use a legally relevant basis for drawing an analogy between two situations. It may be applied to various forms oflegal authority, includingstatutory law andcase law.
In thecivil law tradition, analogy is most typically used for filling gaps in a statutory scheme.[38] In thecommon law tradition, it is most typically used for extending the scope ofprecedent.[38] The use of analogy in both traditions is broadly described by the traditional maximUbi eadem est ratio, ibi idem ius (where the reason is the same, the law is the same).
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Analogies as defined in rhetoric are a comparison between words, but an analogy more generally can also be used to illustrate and teach. To enlighten pupils on the relations between or within certain concepts, items or phenomena, a teacher may refer to other concepts, items or phenomena that pupils are more familiar with. It may help to create or clarify one theory (or theoretical model) via the workings of another theory (or theoretical model). Thus an analogy, as used in teaching, would be comparing a topic that students are already familiar with, with a new topic that is being introduced, so that students can get a better understanding of the new topic by relating back to existing knowledge. This can be particularly helpful when the analogy serves across different disciplines: indeed, there are various teaching innovations now emerging that use sight-based analogies for teaching and research across subjects such as science and the humanities.[39]
The Fourth Lateran Council of 1215 taught:For between creator and creature there can be noted no similarity so great that a greater dissimilarity cannot be seen between them.[40]
The theological exploration of this subject is called theanalogia entis. The consequence of this theory is that all true statements concerning God (excluding the concrete details of Jesus' earthly life) are rough analogies, without implying any falsehood. Such analogical and true statements would includeGod is,God is Love,God is a consuming fire,God is near to all who call him, or God as Trinity, wherebeing,love,fire,distance,number must be classed as analogies that allow human cognition of what is infinitely beyond positive ornegative language.
The use of theological statements insyllogisms must take into account their analogical essence, in that every analogy breaks down when stretched beyond its intended meaning.
In traditional Christian doctrine, theTrinity is aMystery of Faith that has been revealed, not something obvious or derivable from first principles or found in any thing in the created world.[41] Because of this, the use of analogies to understand the Trinity is common and perhaps necessary.
The Trinity is a combination of the words “tri,” meaning “three,” and “unity,” meaning “one.” The “Threeness” refers to the persons of the Trinity, while the “Oneness” refers to substance or being.[42]
MedievalCistercian monkBernard of Clairveaux used the analogy of a kiss:
"[...]truly the kiss[...]is common both to him who kisses and to him who is kissed. [...]If, as is properly understood, the Father is he who kisses, the Son he who is kissed, then it cannot be wrong to see in the kiss the Holy Spirit, for he is the imperturbable peace of the Father and the Son, their unshakable bond, their undivided love, their indivisible unity."
— St. Bernard of Clairveaux,Semons on Song of Songs, Sermon 8: The Holy Spirit, the Kiss of the Mouth
Many analogies have been used to explain the Trinity, however, all analogies fail when taken too far. Examples of these are the analogies that state that the Trinity is like water and its different states (solid, liquid, gas) or like an egg with its different parts (shell, yolk, and egg white). However, these analogies, if taken too far, could teach the heresies of modalism (water states) and partialism (parts of egg), which are contrary to the Christian understanding of the Trinity.[42]
Other analogies exist. The analogy of notes of a chord, say C major, is a sufficient analogy for the Trinity. The notes C, E, and G individually fill the whole of the “heard” space, but when all notes come together, we have a homogenized sound within the same space with distinctive, equal notes.[43] One more analogy used is one that uses the mythological dog, Cerberus, that guards the gates of Hades. While the dog itself is a single organism—speaking to its substance—Cerberus has different centers of awareness due to its three heads, each of which has the same dog nature.[44]
In some Protestant theology, "analogy" may itself be used analogously in terms, more in a sense of "rule" or "exemplar": for example the concept "analogia fidei" has been proposed as an alternative to the conceptanalogia entis but named analogously.
Islamic jurisprudence makes ample use of analogy as a means of making conclusions from outside sources of law. The bounds and rules employed to make analogical deduction vary greatly betweenmadhhabs and to a lesser extent individual scholars. It is nonetheless a generally accepted source of law withinjurisprudential epistemology, with the chief opposition to it forming thedhahiri (ostensiblist) school.
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