Editing Analogy (section)

==Applications and types==
{{Excessive examples|section|date=April 2023}}

=== Logic ===
Logicians analyze how analogical reasoning is used in [[Argument from analogy|arguments from analogy]].

{{anchor|Analogy symbolism}}<!--Redirect target-->
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 (punctuation)#Mathematics and logic|colon notation]] to represent the relationships, using single colon for ratio, and double colon for equality.<ref name="REA-1994">{{cite book |author=Research and Education Association |editor1-last=Fogiel |editor1-first=M |title=Verbal Tutor for the SAT |chapter-url=https://books.google.com/books?id=A17t-PP5xkgC&pg=PA84 |access-date=25 January 2018 |date=June 1994 |publisher=Research & Education Assoc. |location=Piscataway, New Jersey |isbn=978-0-87891-963-5 |pages=84–86 |chapter=2. Analogies |oclc=32747316}}</ref>

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.<ref name="REA-1994" /><ref name="Schwartz-2007">{{cite book |last1=Schwartz |first1=Linda |last2=Heidrich |first2=Stanley H.  |last3=Heidrich |first3=Delana S.  |title=Power Practice: Analogies and Idioms, eBook |url=https://books.google.com/books?id=PaWURypwLcUC&pg=PA4 |access-date=25 January 2018 |date=1 January 2007 |publisher=Creative Teaching Press |location=Huntington Beach, Calif. |isbn=978-1-59198-953-0 |pages=4– |oclc=232131611}}</ref>

=== Linguistics ===
<!-- This section is linked from [[Comparative method]] --><!-- This section is linked from [[Comparative method]] -->
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 language|English]] [[verb]] ''[[wiktionary:help|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 (''jumped'', ''carried'', ''defeated'', etc.). 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 [[Comparison of American and British English#Verb morphology|American English]] past tense form of ''[[wiktionary:dive|dive]]'': ''dove'', formed on analogy with words such as ''drive'' to ''drove'' or ''strive'' to ''strove''.
* [[Neologisms]] (new words) can also be formed by analogy with existing words. A good example is ''[[software]]'', formed by analogy with ''[[computer hardware|hardware]]''; other analogous neologisms such as ''[[firmware]]'' and ''[[vaporware|vapourware]]'' have followed. Another example is the humorous<ref>{{Cite web|url=http://www.oxforddictionaries.com/us/definition/american_english/underwhelm|title=underwhelm - definition of underwhelm in English {{!}} Oxford Dictionaries|website=Oxford Dictionaries {{!}} English|access-date=2017-04-07|url-status=dead|archive-url=https://web.archive.org/web/20160816122000/http://www.oxforddictionaries.com/us/definition/american_english/underwhelm|archive-date=2016-08-16}}</ref> term ''underwhelm'', formed by analogy with ''overwhelm''.
* Some people present analogy as an alternative to [[generative linguistics|generative ''rules'']] for explaining the [[Productive (linguistics)|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 (yet) done so (e.g. Langacker 1987.445–447). 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 [[Umbrella term|catch-all]] to describe any morphological change in a language that cannot be explained merely sound change or borrowing.

===Science===
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 which [[logical proof|logical]] or [[empirical]] proof is not possible such as [[theology]], [[philosophy]] or [[cosmology]] 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 textbooks [[Hydraulic analogy|compares electrical circuits to hydraulic circuits.]]<ref>Going with the flow: Using analogies to explain electric circuits. Mark D. Walker and David Garlovsky. School Science Review, 97, no. 361 (2016): 51-58.https://www.academia.edu/33380466/Going_with_the_flow_Using_analogies_to_explain_electric_circuits_Going_with_the_flow_Using_analogies_to_explain_electric_circuits</ref> Another example is the [[analog ear|analogue ear]] based on electrical, electronic or mechanical devices.

====Mathematics====
Some types of analogies can have a precise [[mathematical]] formulation through the concept of [[isomorphism]]. In detail, this means that if two mathematical structures are of the same type, an analogy between them can be thought of as a [[bijection]] which preserves some or all of the relevant structure. For example, <math> \mathbb{R}^2 </math> and <math> \mathbb{C} </math> are isomorphic as vector spaces, but the [[complex numbers]], <math> \mathbb{C} </math>, have more structure than <math> \mathbb{R}^2 </math> does: <math> \mathbb{C} </math> is a [[Field (mathematics)|field]] as well as a [[vector space]].

[[Category theory]] takes the idea of mathematical analogy much further with the concept of [[functor]]s. Given two categories C and D, a functor ''f'' from C to D can be thought of as an analogy between C and D, because ''f'' 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 the [[#Shared structure|structure mapping theory of analogy]] of Dedre Gentner, because it formalises the idea of analogy as a function which makes certain conditions true.

====Artificial intelligence====
{{Further |case-based reasoning}}
{{Further |structure-mapping theory}}

A computer algorithm has achieved human-level performance on multiple-choice analogy questions from the [[SAT]] 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.<ref>Turney 2006</ref>

The analogical reasoning in the human mind is free of the false inferences plaguing conventional [[artificial intelligence]] models, (called ''systematicity''). Steven Phillips and [[William H. Wilson]]<ref>{{Cite journal | last1 =  Phillips | first1 = Steven  | last2 = Wilson | first2 =  William H.  | date = July 2010  | title = Categorial Compositionality: A Category Theory Explanation for the Systematicity of Human Cognition | journal = PLOS Computational Biology  | volume = 6 | issue = 7 | pages =  e1000858| doi = 10.1371/journal.pcbi.1000858 | pmid = 20661306  | pmc = 2908697  | bibcode =2010PLSCB...6E0858P | doi-access = free }}</ref><ref>{{Cite journal | last1 =  Phillips | first1 = Steven  | last2 =  Wilson | first2 =  William H. | date = August 2011  | title = Categorial Compositionality II: Universal Constructions and a General Theory of (Quasi-)Systematicity in Human Cognition | journal = PLOS Computational Biology  | volume = 7 | issue = 8 | pages =  e1002102| doi = 10.1371/journal.pcbi.1002102 | pmid=21857816 | pmc=3154512| bibcode =2011PLSCB...7E2102P | doi-access = free }}</ref> use [[category 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 structures [[natural transformation|transform naturally]] and reject those that do not.

[[Keith Holyoak]] and [[Paul Thagard]] (1997) developed their multiconstraint theory within structure mapping theory. They defend that the "[[coherence theory of truth|coherence]]" of an analogy depends on structural consistency, [[semantic similarity]] and purpose. Structural consistency is the highest when the analogy is an [[isomorphism]], 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.<ref name="Shelley"/> Hummel and Holyoak (2005) recast the multiconstraint theory within a [[Artificial neural network|neural 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 some ''identical'' 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).<ref>Doumas, Hummel, and Sandhofer, 2008</ref>

[[Mark Keane (cognitive scientist)|Mark Keane]] and Brayshaw (1988) developed their ''Incremental 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.<ref>Keane, M.T. and Brayshaw, M. (1988). The Incremental Analogical Machine: a computational model of analogy. In [[Derek H. Sleeman|D. H. Sleeman]] (Ed). European working session on learning. (pp.53–62). London: Pitman.</ref><ref>{{Cite journal | last1 = Keane | first1 = M.T. Ledgeway | last2 = Duff | first2 = S | year = 1994 | title = Constraints on analogical mapping: a comparison of three models | url =http://www.tara.tcd.ie/bitstream/2262/12939/1/TCD-CS-93-24.pdf | journal = Cognitive Science | volume = 18 | issue = 3| pages =  387–438| doi=10.1016/0364-0213(94)90015-9| doi-access = free }}</ref> [[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.<ref>{{Cite journal | last1 = Keane | first1 = M.T. | year = 1997 | title = What makes an analogy difficult? The effects of order and causal structure in analogical mapping | journal = Journal of Experimental Psychology: Learning, Memory, and Cognition | volume = 23 | issue = 4| pages = 946–967 | doi=10.1037/0278-7393.23.4.946| pmid = 9231438 }}</ref>

Eqaan Doug and his team<ref>See Chalmers et al. 1991</ref> challenged the shared structure theory and mostly its applications in computer science. They argue that there is no clear line between [[perception]], 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 make [[Knowledge representation|representations]] by selecting relevant information from low-level [[stimulus (physiology)|stimuli]]. 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.<ref>Forbus et al., 1998</ref> 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.<ref>Morrison and Dietrich, 1995</ref>

====Anatomy====
{{See also|Analogy (biology)}}
In [[anatomy]], two anatomical structures are considered to be ''analogous'' when they serve similar [[role|functions]] but are not [[evolution]]arily related, such as the [[Leg (anatomy)|legs]] of [[vertebrate]]s and the legs of [[insect]]s. Analogous structures are the result of [[convergent evolution|independent evolution]] and should be contrasted with structures which [[Homology (biology)|shared an evolutionary line.]]

==== Engineering ====

Often a physical [[prototype]] 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, the [[Phillips Machine|MONIAC]] (an [[analog computer|analogue computer]]) used the flow of water in its pipes as an analogue to the flow of money in an economy.

==== Cybernetics ====

Where two or more biological or physical participants meet, they communicate and the stresses produced describe internal models of the participants. [[Gordon Pask|Pask]] in his [[conversation theory]] asserts an [[Conversation theory#Analogy|analogy]] that describes both similarities and differences between any pair of the participants' internal models or concepts exists.

==== History====

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)<ref>Zhang, Y., Jatowt, A., Bhowmick, S., & Tanaka, K. (2015, July). Omnia mutantur, nihil interit: Connecting past with present by finding corresponding terms across time. In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers) (pp. 645-655). [https://aclanthology.org/P15-1063.pdf pdf]</ref> and explained.<ref>Zhang, Yating, Adam Jatowt, and Katsumi Tanaka. "Towards understanding word embeddings: Automatically explaining similarity of terms." In 2016 IEEE international conference on big data (big data), pp. 823-832. IEEE, 2016. [https://ieeexplore.ieee.org/abstract/document/7840675 pdf]</ref>

=== Morality ===
Analogical reasoning plays a very important part in [[morality]]. This may be because morality is supposed to be [[impartiality|impartial]] 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.

=== Psychology ===

==== Structure mapping theory ====
{{Main |Structure-mapping theory}}
Structure mapping, originally proposed by [[Dedre Gentner]], is a theory in psychology that describes the psychological processes involved in reasoning through, and learning from, analogies.<ref>{{Cite journal|last=Gentner|first=Dedre|date=April 1983|title=Structure-Mapping: A Theoretical Framework for Analogy*|journal=Cognitive Science|language=en|volume=7|issue=2|pages=155–170|doi=10.1207/s15516709cog0702_3|s2cid=5371492 |doi-access=free}}</ref> 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.<ref name=":0">{{Citation|last=Gentner|first=Dedre|title=Analogical Reasoning, Psychology of|date=2006|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/0470018860.s00473|encyclopedia=Encyclopedia of Cognitive Science|publisher=American Cancer Society|language=en|doi=10.1002/0470018860.s00473|isbn=978-0-470-01886-6|access-date=2020-12-09}}</ref> According to this theory, individuals view their knowledge of ideas, or domains, as interconnected structures.<ref name=":1">{{Cite journal|last1=Gentner|first1=D.|last2=Gunn|first2=V.|date=June 2001|title=Structural alignment facilitates the noticing of differences|journal=Memory & Cognition|volume=29|issue=4|pages=565–577|doi=10.3758/bf03200458|issn=0090-502X|pmid=11504005|s2cid=1745309|doi-access=free}}</ref> In other words, a domain is viewed as consisting of objects, their properties, and the relationships that characterise their interactions.<ref name=":2">{{Cite web|last1=Gentner|first1=Dedre|last2=Smith|first2=Linsey A.|editor1-first=Daniel|editor1-last=Reisberg|date=2013-03-11|title=Analogical Learning and Reasoning|url=https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780195376746.001.0001/oxfordhb-9780195376746-e-42|access-date=2020-12-09|website=The Oxford Handbook of Cognitive Psychology|language=en|doi=10.1093/oxfordhb/9780195376746.001.0001|isbn=9780195376746}}</ref> The process of analogy then involves:

# Recognising similar structures between the base and target domains.
# Finding deeper similarities by mapping other relationships of a base domain to the target domain.
# Cross-checking those findings against existing knowledge of the target domain.<ref name=":0" /><ref name=":2" />

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.<ref name=":1" />

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.<ref name=":3">{{Cite book|last1=Gentner|first1=Dedre|url=https://www.taylorfrancis.com/books/e/9781315802725|title=Mental Models|last2=Stevens|first2=Albert L.|date=2014-01-14|publisher=Psychology Press|isbn=978-1-315-80272-5|language=en|doi=10.4324/9781315802725}}</ref> 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 relationship [[Hydraulic analogy|corresponds 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.<ref name=":2" />

===== Children =====
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.<ref name=":5">{{Citation|last1=Hespos|first1=Susan J.|title=Structure-Mapping Processes Enable Infants' Learning Across Domains Including Language|date=2020|url=https://doi.org/10.1007/978-3-030-35594-4_5|work=Language and Concept Acquisition from Infancy Through Childhood: Learning from Multiple Exemplars|pages=79–104|editor-last=Childers|editor-first=Jane B.|place=Cham|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-030-35594-4_5|isbn=978-3-030-35594-4|access-date=2020-12-09|last2=Anderson|first2=Erin|last3=Gentner|first3=Dedre| s2cid=213450124 }}</ref> 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.<ref name=":5" /> 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).<ref name=":5" /> 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.<ref name=":2" />

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.<ref name=":6">{{Cite journal|last1=Gentner|first1=Dedre|last2=Hoyos|first2=Christian|date=2017|title=Analogy and Abstraction|journal=Topics in Cognitive Science|language=en|volume=9|issue=3|pages=672–693|doi=10.1111/tops.12278|pmid=28621480|issn=1756-8765|doi-access=free}}</ref> Comparison is more likely when the objects to be compared are close together in space and/or time,<ref name=":6" /> are highly similar (although not so similar that they match, which interfere with identifying relationships),<ref name=":2" /> or share common labels.

===Law===
{{main|Analogy (law)}}

In [[law]], 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 of [[Sources of law|legal authority]], including [[statutory law]] and [[case law]].

In the [[civil law (legal system)|civil law]] tradition, analogy is most typically used for filling gaps in a statutory scheme.<ref name="langenbucher">{{Cite journal | author-last = Langenbucher | author-first = Katja | title = Argument by Analogy In European Law | journal = The Cambridge Law Journal | volume = 57 | issue = 3 | year = 1998 | pages = 481–521 | doi = 10.1017/S0008197398003031 }}</ref> In the [[common law (legal system)|common law]] tradition, it is most typically used for extending the scope of [[precedent]].<ref name="langenbucher"/> The use of analogy in both traditions is broadly described by the traditional maxim {{lang|la|Ubi eadem est ratio, ibi idem ius}} (where the reason is the same, the law is the same).

===Teaching strategies===
{{original research|section|date=April 2023}}
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.<ref name="Petrucci">{{cite journal |last1=Petrucci |first1=Mario |title=Scientific Visualizations: Bridge-Building between the Sciences and the Humanities via Visual Analogy |journal=Interdisciplinary Science Reviews |date=December 2011 |volume=36 |issue=4 |pages=276–300 |doi=10.1179/030801811X13160755918561 |url=https://www.yumpu.com/en/document/read/39959333/scientific-visualizations-bridge-building-between-mario-petrucci/18 |access-date=15 February 2025}}</ref>

===Religion===
====Catholicism====
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.''<ref>[http://www.papalencyclicals.net/councils/ecum12-2.htm#2 Fourth Lateran Council of 1215]</ref>

The theological exploration of this subject is called the ''[[analogia 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 include ''God is'', ''God is Love'', ''God is a consuming fire'', ''God is near to all who call him'', or God as Trinity, where ''being'', ''love'', ''fire'', ''distance'', ''number'' must be classed as analogies that allow human cognition of what is infinitely beyond positive or [[Via negativa|negative]] language.

The use of theological statements in [[syllogism]]s must take into account their analogical essence, in that every analogy breaks down when stretched beyond its intended meaning.

====Doctrine of the Trinity====
In traditional Christian doctrine, the [[Trinity]] is a [[Mystery of faith#Theological term|Mystery of Faith]] that has been revealed, not something obvious or derivable from first principles or found in any thing in the created world.<ref>{{CCC|237}}</ref> 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.<ref name="Zondervan">{{cite book |last1=Copan |first1=Paul |title=Dictionary of Christianity and Science |date=2017 |publisher=Zondervan |isbn=978-0-310-49605-2 |pages=664}}</ref>

Medieval [[Cistercian]] monk [[Bernard of Clairveaux]] used the analogy of a kiss:

{{Blockquote|"[...]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."|source=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.<ref name="Zondervan"/>

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.<ref>{{cite book |last1=Begbie |first1=Jeremy |title=Hearing God in C Major |date=2000 |publisher=Baker}}</ref> 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.<ref>{{cite book |last1=Moreland |first1=J. P. |last2=Craig |first2=William L. |title=Philosophical Foundations for the Christian Worldview |date=2003 |publisher=IVP Academic |location=Downers Grove, IL}}</ref>

====Protestantism====
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 concept ''[[Analogia entis#Protestant treatments|analogia entis]]'' but named analogously.

==== Islam ====
{{Further|Qiyas}}
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 between [[madhhab]]s and to a lesser extent individual scholars. It is nonetheless a generally accepted source of law within [[Usul Al-Fiqh|jurisprudential epistemology]], with the chief opposition to it forming the [[Zahiri|dhahiri]] (ostensiblist) school.