Editing Analogy (section)

== 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 system]]s. [[Douglas Hofstadter|Hofstadter]] has argued that analogy is "the core of cognition".<ref name="Analogy as the Core of Cognition"/>

An analogy is not a [[figure of speech]] but a kind of thought. Specific analogical language uses [[wikt:exemplar|exemplification]], [[Comparison (grammar)|comparisons]], [[metaphor]]s, [[simile]]s, [[allegory|allegories]], and [[parable]]s, 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 philosophy|ordinary language]] and [[common sense]] (where [[proverb]]s and [[idiom]]s give many examples of its application) but also in [[science]], [[philosophy]], [[law]] and the [[humanities]].

The concepts of [[association (psychology)|association]], comparison, correspondence, [[homology (mathematics)|mathematical]] and [[homology (biology)|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 (e.g., experiments on rats when results are applied to humans).

Analogy has been studied and discussed since [[classical antiquity]] by philosophers, scientists, theologists and [[law]]yers. The last few decades have shown a renewed interest in analogy, most notably in [[cognitive science]].

=== Development ===
* [[Aristotle]] identified analogy in works such as [[Metaphysics]] and [[Nicomachean Ethics]]<ref>{{cite journal |last1=Hesse |first1=Mary |title=Aristotle's Logic of Analogy |journal=The Philosophical Quarterly |date=October 1965 |volume=15 |issue=61 |pages=328–340 |doi=10.2307/2218258 |jstor=2218258 |url=https://www.jstor.org/stable/2218258 |access-date=11 June 2023}}</ref>
* [[Rome|Roman]] lawyers used analogical reasoning and the Greek word ''analogia''. {{citation needed|date=September 2023}}
* In [[Logic in Islamic philosophy|Islamic logic]], analogical reasoning was used for the process of [[qiyas]] in Islamic [[sharia]] law and [[fiqh]] jurisprudence. {{citation needed|date=September 2023}}
* Medieval lawyers distinguished ''[[analogia legis]]'' and ''[[analogia iuris]]'' (see below). 
* The [[Middle Ages]] saw an increased use and theorization of analogy.  
* In [[Christianity|Christian]] [[scholasticism|scholastic]] [[theology]], analogical arguments were accepted in order to explain the attributes of [[God]]. 
** [[Thomas Aquinas|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 (see the contemporary distinction between [[polysemy]] and [[homonymy]]). {{citation needed|date=September 2023}}
** [[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:<ref>{{cite web |last1=Strumia |first1=Alberto |title=Analogy |url=https://inters.org/analogy |website=Interdisciplinary Encyclogpedia of Religion and Science |publisher=Pontifical University of the Holy Cross |access-date=11 June 2023}}</ref>

* Analogy of attribution (''analogia attributionis'') or improper proportionality, e.g., "This food is healthy."
* Analogy of proportionality (''analogia proportionalitatis'') 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."<ref>{{cite journal |last1=Tabaczek |first1=Mariusz |title=htA Trace of Similarity within Even Greater Dissimilarity |journal=Forum Philosophicum |date=November 2018 |volume=23 |issue=1 |pages=95–132 |doi=10.5840/forphil20182314 |url=https://www.researchgate.net/publication/335001068 |access-date=11 June 2023|doi-access=free }}</ref>
* [[Metaphor]], e.g., steely determination.

=== Identity of relation ===

In ancient [[Greek language|Greek]] the word ''αναλογια'' (''analogia'') originally meant [[Proportionality (mathematics)|proportionality]], in the mathematical sense, and it was indeed sometimes translated to [[Latin]] as ''proportio''.{{citation needed|date=May 2020}} Analogy was understood as identity of relation between any two [[ordered pair]]s, 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.<ref>{{cite web |url=http://www.amstat.org/publications/jse/v11n2/martin.html |title=Journal of Statistics Education, V11N2: Martin |access-date=2012-12-10 |url-status=live |archive-url=https://web.archive.org/web/20130307062856/http://www.amstat.org/publications/jse/v11n2/martin.html |archive-date=2013-03-07 }},
Michael A. Martin, ''The Use of Analogies and Heuristics in Teaching Introductory Statistical Methods''</ref> 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 [[United States|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 [[Aristotle|Aristotelian]] format: HAND : PALM : : FOOT : ____ While most competent [[English language|English]] 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 as ''hand'' and ''palm'', and between ''foot'' and ''sole''. This relation is not apparent in some [[lexical definition]]s 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''.

[[Immanuel Kant|Kant's]] ''[[Critique of Judgment]]'' held to this notion of analogy, arguing that there can be exactly the same [[Logic of relatives|relation]] between two completely different objects.

===Shared abstraction===

[[Image:Crepuscular rays8 - NOAA.jpg|thumb|300px|In several [[culture]]s,{{which|date=December 2012}} the [[Sun]] is the source of an analogy to [[God]].]]
Greek philosophers such as [[Plato]] and [[Aristotle]] used a wider notion of analogy. They saw analogy as a shared abstraction.<ref name="Shelley">Shelley 2003</ref> 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 as [[argument]]s, 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'' (1982), the first substantive examination of the topic since Cajetan's ''De Nominum Analogia'',{{Dubious|date=June 2023}} 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===
[[Ibn Taymiyya]],<ref name="Hallaq-94-5">{{Cite journal|title=The Logic of Legal Reasoning in Religious and Non-Religious Cultures: The Case of Islamic Law and the Common Law|last=Hallaq|first=Wael B.|journal=Cleveland State Law Review|volume=34|year=1985–1986|pages=79–96 [93–5]}}</ref><ref name=Mas>{{Cite journal  | author = Ruth Mas  | title = Qiyas: A Study in Islamic Logic  | journal = Folia Orientalia  | volume = 34  | pages = 113–128  | year = 1998  | url = http://www.colorado.edu/ReligiousStudies/faculty/mas/LOGIC.pdf  | issn = 0015-5675  | url-status = live  | archive-url = https://web.archive.org/web/20080708225858/http://www.colorado.edu/ReligiousStudies/faculty/mas/LOGIC.pdf  | archive-date = 2008-07-08  }}</ref><ref name="Sowa">{{Cite conference  | author1 = John F. Sowa  | author2 = Arun K. Majumdar  | title = Analogical reasoning  | book-title = Conceptual Structures for Knowledge Creation and Communication, Proceedings of ICCS 2003  | publisher = Springer-Verlag  | year = 2003  | location = Berlin  | url = http://www.jfsowa.com/pubs/analog.htm  | url-status = live  | archive-url = https://web.archive.org/web/20100405103529/http://www.jfsowa.com/pubs/analog.htm  | archive-date = 2010-04-05  | author1-link = John F. Sowa }}, pp. 16–36</ref> [[Francis Bacon (philosopher)|Francis Bacon]] and later [[John Stuart Mill]] argued that analogy is simply a special case of induction.<ref name="Shelley"/> In their view, analogy is an [[induction (philosophy)|inductive]] inference from common known attributes to another [[probability|probable]] common attribute, which is known about only in the source of the analogy, in the following form:
;Premises
:''a'' is C, D, E, F, G
: ''b'' is C, D, E, F
;Conclusion
: ''b'' is probably G.

===Shared structure===
[[Image:Latimeria chalumnae01.jpg|thumb|left|300px|According to Shelley (2003), the study of the [[coelacanth]] drew heavily on analogies from other fish.]]
Contemporary cognitive scientists use a wide notion of analogy, [[Extension (semantics)|extensionally]] close to that of Plato and Aristotle, but framed by Gentner's (1983) [[structure-mapping theory]].<ref>See [[Dedre Gentner]] et al. 2001</ref> The same idea of [[Map (mathematics)|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 (see below). Some studies extended the approach to specific subjects, such as [[metaphor]] and similarity.<ref>See Gentner et al. 2001 and [http://groups.psych.northwestern.edu/gentner/publications2.htm Gentner's publication page] {{webarchive|url=https://web.archive.org/web/20100614055322/http://groups.psych.northwestern.edu/gentner/publications2.htm |date=2010-06-14 }}.</ref>