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| | These issues need to be addressed if you are to cure your infection for good. Yeasts such as Candida albicans are called opportunistic pathogens, which means they can only cause a yeast infection when the body's immune system is weakened for some reason and conditions then become favourable for the yeasts to overgrown and invade the tissues. Insert the applicator into the vagina and depress the plunger. If you want to know a lot more about this treatment, you really should study on. However, these bacteria killers do not harm the candida. <br><br>There are numerous solutions to treat your yeast infections which means you are not to worry. Numerous people say yes and that it can't be beat when it comes to a yeast infection home remedy. ________________________________________________________________. This is why you can feel so much worse than when you first start on your yeast treatment program. The tiny blood vessels under the skin break easily and leak fluid into the skin - because of this a bruise will appear. <br><br>It is always wise that besides hearing the advice of health care professionals you do some serious researching of your own, after all, you are the most interested in curing your condition and the one that knows exactly all your symptoms. Fill your tub and add one cup of oatmeal engrossed. Wear panties made of breathable materials such as cotton or at least panties with cotton crotch (preferably white). This could cause the immune system to be weaker than normal and as a result less able to neutralize infections. There are a number of triggers for yeast infections, ranging from antibiotics to pregnancy to stress, but there are some things you can do to help reduce the risk of getting a yeast infection such as keeping the genital area cool and dry by wearing cotton underwear and loose-fitting clothes, and changing out of wet or damp clothes as soon as possible. <br><br>Also spots with white patches on the foreskin and the shaft of the penis may be another indication. Because of this, it is difficult for post partum women who have undergone a cesarean operation to get back into shape. Diflucan can also result in allergic reactions, though such instances are pretty rare. Yeast thrives in moist and warm areas of the body like in the genitals, buttocks, armpits and within skin folds. And that your timing of supplements can influence how effective they are. <br><br>So it is vital that your partner be treated as well as you. Every time that I have ever gotten a reacurring yeast infection I have always been able to cure it with hydrogen peroxide. First, the yogurt we are talking about here is natural, sugar-free yogurt with no added fruit or other non-natural additives. But it is always better to consult your doctor in case you. Some patients may experience pseudomembranous colitis (a severe intestinal disorder).<br><br>Should you loved this information and you would love to receive details regarding [http://www.naturalcureyeastinfection.info/sitemap/ how to treat yeast infection at home] assure visit our webpage. |
| {{original research|date=March 2013}}
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| {{tone|date=March 2013}}
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| '''Analogy''' (from [[Greek language|Greek]] ἀναλογία, ''analogia'', "proportion"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.po0057%3Aentry%3Da%29nalogi%2Fa ἀναλογία],
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| Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref><ref>[http://www.etymonline.com/index.php?term=analogy analogy], Online Etymology Dictionary</ref>) is a [[cognition|cognitive]] process of transferring [[information]] or [[Meaning (linguistics)|meaning]] from a particular subject (the analogue or source) to another particular subject (the target), or a [[language|linguistic]] expression corresponding to such a process. In a narrower sense, analogy is an [[inference]] or an [[Logical argument|argument]] from one particular to another particular, as opposed to [[deductive reasoning|deduction]], [[inductive reasoning|induction]], and [[abductive reasoning|abduction]], where at least one of the [[premise]]s or the conclusion is general. The word ''analogy'' can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a [[:wikt:similarity|similarity]], as in the [[analogy (biology)|biological notion of analogy]].
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| [[Image:Bohr atom model English.svg|thumb|200px|right|[[Niels Bohr]]'s model of the [[atom]] made an analogy between the atom and the [[solar system]].]]
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| Analogy plays a significant role in [[problem solving]] such as, [[decision making]], [[perception]], [[memory]], [[creativity]], [[emotion]], [[explanation]] 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. It has been argued that analogy is "the core of cognition".<ref>[[Douglas Hofstadter|Hofstadter]] in Gentner et al. 2001.</ref> Specific analogical language comprises [[wikt:exemplar|exemplification]], [[Comparison (grammar)|comparison]]s, [[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]] and the [[humanities]]. The concepts of [[association (psychology)|association]], comparison, [[correspondence (mathematics)|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.
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| Analogy has been studied and discussed since [[classical antiquity]] by philosophers, scientists and [[law]]yers. The last few decades have shown a renewed interest in analogy, most notably in [[cognitive science]].
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| ==Usage of the terms "source" and "target"==
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| With respect to the terms ''source'' and ''target'' there are two distinct traditions of usage:
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| * The logical and cultures and economics tradition speaks of an ''arrow'', ''[[homomorphism]]'', ''[[Map (mathematics)|mapping]]'', or ''[[morphism]]'' from what is typically the more complex ''domain'' or ''source'' to what is typically the less complex ''[[codomain]]'' or ''target'', using all of these words in the sense of mathematical [[category theory]].
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| * The tradition that appears{{Or|date=September 2011}} more common in [[cognitive psychology]], in [[literary theory]], and in specializations within [[philosophy]] outside of [[logic]], speaks of a [[Conceptual metaphor#Mappings|mapping]] from what is typically the more familiar area of experience, the ''source'', to what is typically the more problematic area of experience, the ''target''.
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| ==Models and theories==
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| ===Identity of relation===
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| {{Original research|section|date=July 2009}}
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| 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''. From there analogy was understood as '''identity of relation''' between any two [[ordered pair]]s, whether of mathematical nature or not. [[Immanuel Kant|Kant's]] ''[[Critique of Judgment]]'' held to this notion. Kant argued that there can be exactly the same [[Logic of relatives|relation]] between two completely different objects. The same notion of analogy was used in the [[United States|US]]-based [[SAT]] 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:
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| :HAND : PALM : : FOOT : ____
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| 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 ''hand'' and ''palm'', and between ''foot'' and ''sole''{{Citation needed|date=July 2009}}{{Or|date=July 2009}}. 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''. Analogy and [[abstraction]] are different cognitive processes, and analogy is often an easier one.
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| It's important to note that the above 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>[http://www.amstat.org/publications/jse/v11n2/martin.html],
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| 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 is focusing on their similarity in having an inner surface.
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| Recently a computer algorithm has achieved human-level performance on multiple-choice analogy questions from the [[SAT]] test.<ref>Turney 2006</ref> The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistical analysis of a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.
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| ===Shared abstraction===
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| [[Image:Crepuscular rays8 - NOAA.jpg|thumb|right|300px|In several [[culture]]s{{which|date=December 2012}}, the [[sun]] is the source of an analogy to [[God]].]]
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| Greek philosophers such as [[Plato]] and [[Aristotle]] actually 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 the ones using them.
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| The [[Middle Age]] saw an increased use and theorization of analogy. [[Rome|Roman]] lawyers had already used analogical reasoning and the Greek word ''analogia''. Medieval lawyers distinguished ''analogia legis'' and ''analogia iuris'' (see below). In [[Logic in Islamic philosophy|Islamic logic]], analogical reasoning was used for the process of qiyas in Islamic [[sharia]] law and [[fight]] jurisprudence. In [[Christianity|Christian]] [[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]]). [[Thomas Cajetan]] wrote an influential treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved. [[James Francis Ross]] in ''Portraying Analogy'' (1982), 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.
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| ===Special case of induction===
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| On the contrary, [[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]|postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}</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}}</ref><ref name="Sowa">{{Cite conference | author1 = [[John F. Sowa]] | author2 = Arun K. Majumdar | title = Analogical reasoning | booktitle = 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 | accessdate = }}, 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 only about the source of the analogy, in the following form:
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| ;Premises
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| :''a'' is C, D, E, F, G
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| : ''b'' is C, D, E, F
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| ;Conclusion
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| : ''b'' is probably G.
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| This view does not accept analogy as an autonomous mode of thought or inference, [[reduction (philosophy)|reducing]] it to induction. However, autonomous analogical arguments are still useful in science, philosophy and the humanities (see below), which makes this reduction philosophically uninteresting. Moreover, induction tries to achieve general conclusions, while analogy looks for particular ones.
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| ===Hidden deduction===
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| The opposite move could also be tried, '''reducing analogy to deduction'''. It is argued that every analogical argument is partially superfluous and can be rendered as a [[Deductive reasoning|deduction]] stating as a [[premise]] a (previously hidden) universal proposition which applied both to the source and the target. In this view, instead of an argument with the form:
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| ;Premises
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| : ''a'' is analogous to ''b''.
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| : ''b'' is F.
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| ;Conclusion
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| : ''a'' is plausibly F.
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| We should have:
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| ;Hidden universal premise
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| :all Gs are plausibly Fs.
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| ;Hidden singular premise
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| : ''a'' is G.
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| ;Conclusion
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| : ''a'' is plausibly F.
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| This would mean that premises referring the source and the analogical relation are themselves superfluous. However, it is not always possible to find a plausibly [[truth|true]] universal premise to replace the analogical premises.<ref>See Juthe 2005</ref> And analogy is not only an argument, but also a distinct cognitive process.
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| ===Shared structure===
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| [[Image:Latimeria chalumnae01.jpg|thumb|left|300px|According to Shelley (2003), the study of the [[coelacanth]] drew heavily on analogies from other fish.]]
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| 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 [[Map (mathematics)|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].</ref>
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| [[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 maximal when the analogy is an [[isomorphism]], although lower levels are admitted. Similarity demands that the mapping connects similar elements and relations of source and target, at any level of abstraction. It is maximal when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose insofar as 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 [[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, & Sandhofer, 2008) to learn relations from unstructured examples (providing the only current account of how symbolic representations can be learned from examples).
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| [[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 analog is selected and mapping from base to target occurs in a serial manner.<ref>Keane, M.T. and Brayshaw, M. (1988). The Incremental Analogical Machine: a computational model of analogy. In D. 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 = | journal = Cognitive Science | volume = 18 | issue = | pages = 287–334 }}</ref> [[Empirical evidence]] shows that human analogical mapping performance is influenced by information presentation order.<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 | url = | journal = Journal of Experimental Psychology: Learning, Memory and Cognition | volume = 123 | issue = | pages = 946–967 }}</ref>
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| ===High-level perception===
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| [[Douglas Hofstadter]] 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 line between [[perception]], including high-level perception, and analogical thought. 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. conclude that analogy '''''is''''' high-level perception. Forbus et al. (1998) claim that this is only a metaphor. 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.
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| ===Analogy and Complexity===
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| Antoine Cornuéjols<ref>Cornuéjols, A. (1996). [http://www.lri.fr/~antoine/Papers/JFA96-final-osX.pdf Analogie, principe d’économie et complexité algorithmique]. In ''Actes des 11èmes Journées Françaises de l’Apprentissage''. Sète.</ref> has presented analogy as a ''principle of economy'' and ''computational complexity''.
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| Reasoning by analogy is a process of, from a given pair ''(x,f(x))'', extrapolating the function ''f''. In the standard modeling, analogical reasoning involves two "objects": the ''source'' and the ''target''. The target is supposed to be incomplete and in need for a complete description using the source. The target has an existing part ''S<sub>t</sub>'' and a missing part ''R<sub>t</sub>''. We assume that we can isolate a situation of the source ''S<sub>s</sub>'', which corresponds to a situation of target ''S<sub>t</sub>'', and the result of the source ''R<sub>s</sub>'', which correspond to the result of the target ''R<sub>t</sub>''. With ''B<sub>s</sub>'', the relation between ''S<sub>s</sub>'' and ''R<sub>s</sub>'', we want ''B<sub>t</sub>'', the relation between ''S<sub>t</sub>'' and ''R<sub>t</sub>''.
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| '''''If the source and target are completely known:'''''
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| Using [[Kolmogorov complexity]] ''K(x)'', defined as the size of the smallest description of ''x'' and [[Solomonoff]]'s approach to [[inductive inference|induction]], Rissanen (89),<ref>Rissanen J. (1989) : ''Stochastical Complexity and Statistical Inquiry''. World Scientific
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| Publishing Company, 1989.</ref> [[Chris Wallace (computer scientist)|Wallace]] & Boulton (68) proposed the principle of [[Minimum description length]]. This principle leads to minimize the complexity ''K(target| Source)'' of producing the target from the source.
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| This is unattractive in Artificial Intelligence, as it requires a computation over abstract Turing machines. Suppose that ''M<sub>s</sub>'' and ''M<sub>t</sub>'' are local theories of the source and the target, available to the observer. The best analogy between a source case a and target case is the analogy that minimizes:
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| :''K(M<sub>s</sub>) + K(S<sub>s</sub>|M<sub>s</sub>) + K(B<sub>s</sub>|M<sub>s</sub>) + K(M<sub>t</sub>|M<sub>s</sub>) + K(S<sub>t</sub>|M<sub>t</sub>) + K(B<sub>t</sub>|M<sub>t</sub>)'' (1).
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| '''''If the target is completely unknown:'''''
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| All models and descriptions ''M<sub>s</sub>'', ''M<sub>t</sub>'', ''B<sub>s</sub>'', ''S<sub>s</sub>'', and ''S<sub>t</sub>'' leading to the minimization of:
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| :''K(M<sub>s</sub>) + K(S<sub>s</sub>|M<sub>s</sub>) + K(B<sub>s</sub>|M<sub>s</sub>) + K(M<sub>t</sub>|M<sub>s</sub>) + K(S<sub>t</sub>|M<sub>t</sub>)'' (2)
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| are also those who allow to obtain the relationship ''B<sub>t</sub>'', and thus the most satisfactory ''R<sub>t</sub>'' for formula (1).
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| The analogical hypothesis, which solves an analogy between a source case and a target case, has two parts:
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| * Analogy, like induction, is a ''principle of economy''. The best analogy between two cases is the one which minimizes the amount of information necessary for the derivation of the source from the target (1). Its most fundamental measure is the computational complexity theory.
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| * When solving or completing a target case with a source case, the parameters which minimize (2) are postulated to minimize (1), and thus, produce the best response.
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| However, a ''cognitive agent'' may simply reduce the amount of information necessary for the interpretation of the source and the target, without taking into account the cost of data replication. So, it may prefer to the minimization of (2) the minimization of the following simplified formula:
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| :''K(M<sub>s</sub>) + K(B<sub>s</sub>|M<sub>s</sub>) + K(M<sub>t</sub>|M<sub>s</sub>)
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| ==Applications and types==
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| ===In language===
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| ====Logic====
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| Logicians analyze how analogical reasoning is used in [[Argument from Analogy|arguments from analogy]].
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| ====Rhetoric====
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| *An analogy can be a [[speech communication|spoken]] or [[Writing|textual]] comparison between two words (or sets of words) to highlight some form of [[semantics|semantic]] similarity between them. Such analogies can be used to strengthen [[Politics|political]] and [[Philosophy|philosophical]] [[Logical argument|arguments]], even when the semantic similarity is weak or non-existent (if crafted carefully for the audience). Analogies are sometimes used to persuade those that cannot detect the flawed or non-existent arguments.
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| ====Linguistics====<!-- This section is linked from [[Comparative method]] -->
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| * An analogy can be the [[linguistics|linguistic]] process that reduces word forms perceived as irregular by remaking them in the shape of more common forms that are governed by rules. For example, the [[English language|English]] [[verb]] ''[[wiktionary:help|help]]'' once had the [[preterite]] ''holp'' and the past participle ''holpen''. These [[obsolete]] forms have been discarded and replaced by ''helped'' by the power of analogy (or by widened application of the [[productive (linguistics)|productive]] Verb-''ed'' rule.) This is called ''[[Morphological leveling|leveling]].'' However, irregular forms can sometimes be created by analogy; 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'': ''drove''.
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| * [[Neologisms]] 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]]'' have followed. Another example is the humorous{{Citation needed|date=November 2012}} term ''underwhelm'', formed by analogy with ''overwhelm''.
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| * Analogy is often presented as an alternative mechanism to [[generative linguistics|generative ''rules'']] for explaining [[productivity (linguistics)|productive]] formation of structures such as words. Others argue that in fact they are the same mechanism, that rules are analogies that have become entrenched as 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 has obvious resonances with the current views of analogy in cognitive science which are discussed above.
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| ===In science===
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| Analogues are often used in theoretical and applied sciences in the form of models or simulations
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| which can be considered as strong analogies. Other much weaker analogies assist in understanding
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| and describing functional behaviours of similar systems. For instance, an analogy commonly
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| used in electronics textbooks compares electrical circuits to hydraulics. Another example is the [[analog ear]] based on electrical, electronic or mechanical devices.
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| ====Mathematics====
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| Some types of analogies can have a precise [[mathematical]] formulation through the concept of [[isomorphism]]. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a [[bijection]] between them which preserves some or all of the relevant structure. For example, <math> \Bbb{R}^2 </math> and <math> \Bbb{C} </math> are isomorphic as vector spaces, but the [[complex numbers]], <math> \Bbb{C} </math>, have more structure than <math> \Bbb{R}^2 </math> does: <math> \Bbb{C} </math> is a [[Field (mathematics)|field]] as well as a [[vector space]].
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| [[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 compositional structure of the two categories is preserved. This is similar to the [[Analogy#Shared structure|structure mapping theory of analogy]] of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.
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| ====Artificial intelligence====
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| Steven Phillips1 and William H. Wilson <ref>http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000858</ref><ref>http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1002102</ref> uses [[category theory]] to mathematically demonstrate how the analogical reasoning in the human mind, that is free of the spurious inferences that plague conventional artificial intelligence models, (called [[systematicity]]), could arise naturally from the use of 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 may use analogies between domains whose internal structures fit according with a [[natural transformation]] and reject those that do not.
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| see also [[Structure mapping engine]].
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| See also [[case-based reasoning]].
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| ====Anatomy====
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| {{See also|Analogy (biology)}}
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| In [[anatomy]], two anatomical structures are considered to be ''analogous'' when they serve similar [[role|function]]s 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]] and should be contrasted with [[homology (biology)|homologous]] structures.
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| ==== Engineering ====
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| 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 act as an analog to full-size wings and aircraft.
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| For example, the [[MONIAC Computer|MONIAC]] (an [[analog computer]]) used the flow of water in its pipes as an analog to the flow of money in an economy.
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| ==== Cybernetics ====
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| Where there is dependence and hence interaction between a pair or more of biological or physical participants communication occurs and the stresses produced describe internal models inside the participants. [[Gordon Pask|Pask]] in his [[Conversation Theory]] asserts there exists an [[Conversation Theory#Conversation|analogy]] exhibiting both similarities and differences between any pair of the participants' internal models or concepts.
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| ===In normative matters===
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| ====Morality====
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| Analogical reasoning plays a very important part in [[morality]]. This may be in part because morality is supposed to be impartial and fair. If it is wrong to do something in a situation A, and situation B is analogous to A in all relevant features, then it is also wrong to perform that action in situation B. [[Moral particularism]] accepts analogical moral reasoning, rejecting both deduction and induction, since only the former can do without moral principles.
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| ====Law====<!-- This section is linked from [[Communist crime]] -->
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| In [[law]], analogy is used to resolve issues on which there is no previous authority. A distinction has to be made between analogous reasoning from written law and analogy to [[precedent]] [[case law]].
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| =====Analogies from codes and statutes=====
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| In [[civil law (legal system)|civil law]] systems, where the preeminent source of law is [[legal code]]s and [[statute]]s, a [[Non liquet|lacuna]] (a gap) arises when a specific issue is not explicitly dealt with in written law. Judges will try to identify a provision whose purpose applies to the case at hand. That process can reach a high degree of sophistication, as judges sometimes not only look at a specific provision to fill lacunae (gaps), but at several provisions (from which an underlying purpose can be inferred) or at general principles of the law to identify the [[legislator]]'s [[value judgement]] from which the analogy is drawn. Besides the not very frequent filling of lacunae, analogy is very commonly used between different provisions in order to achieve substantial coherence. Analogy from previous judicial decisions is also common, although these decisions are not binding [[authority|authorities]].
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| =====Analogies from precedent case law=====
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| By contrast, in common law systems, where precedent cases are the primary source of law, analogies to codes and statutes are rare (since those are not seen as a coherent system, but as incursions into the common law). Analogies are thus usually drawn from precedent cases: The judge finds that the facts of another case are similar to the one at hand to an extent that the analogous application of the rule established in the previous case is justified.
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| ====In gender science====
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| In the 19th century, there was increased attention to differences in gender.{{citation needed|date=December 2012}} Scientists started to use an analogy between race and gender to explain gender differences. In gender, the female represents a lower race than the male. Researchers record the data of women's bodies for analysis. Nancy Leys Stepan believes that the analogy is so crucial in science that it shapes and influences scientific study. In her article "Race and Gender: The Role of Analogy in Science",<ref>{{cite journal | title = Race and Gender: The Role of Analogy in Science | journal = Isis | date = Jun., 1986 | first = Nancy Leys | last = Stepan | volume = 77 | issue = 2 | pages = 261–277 | jstor = 232652 | url = http://www.jstor.org/stable/232652 | accessdate = 2012-12-30}}</ref> she states "The analogy guided research, generated new hypotheses, and helped disseminate new, usually technical vocabularies. The analogy defined what was problematic about these social groups, what aspects of them needed further investigation, and which kinds of measurements and what data would be significant for scientific inquiry."
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| ===In teaching strategies===
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| Analogies as defined in rhetoric, are a comparison between words, but an analogy can be used in teaching as well. 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 topic and relate back to previous knowledge. Shawn Glynn, a professor in the department of educational psychology and instructional technology at the University of Georgia,<ref>University of Georgia. Curriculum Vitae of Shawn M. Glynn. 2012. 16 October 2013</ref> developed a theory on teaching with analogies and developed steps to explain the process of teaching with this method. The steps for teaching with analogies are as follows: Step one is introducing the new topic that is about to be taught and giving some general knowledge on the subject. Step two is reviewing the concept that the students already know to ensure they have the proper knowledge to assess the similarities between the two concepts. Step three is finding relevant features within the analogy of the two concepts. Step four is finding similarities between the two concepts so students are able to compare and contrast them in order to understand. Step five is indicating where the analogy breaks down between the two concepts. And finally, step six is drawing a conclusion about the analogy and comparison of the new material with the already learned material. Typically this method is used to learn topics in science.<ref>Glynn, Shawn M. Teaching with Analogies. 2008.</ref>
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| In 1989, Kerry Ruef, a teacher began an entire program, which she titled [[The Private Eye Project]]. It is a method of teaching that revolves around using analogies in the classroom to better explain topics. She thought of the idea to use analogies as a part of curriculum because she was observing objects once and she said, "my mind was noting what else each object reminded me of..." This led her to teach with the question, "what does [the subject or topic] remind you of?" The idea of comparing subjects and concepts led to the development of The Private Eye Project as a method of teaching.<ref>Johnson, Katie. Educational Leadership: Exploring the World with the Private Eye. September 1995. 16 October 2013 .</ref> The program is designed to build critical thinking skills with analogies as one of the main themes revolving around it. While Glynn focuses on using analogies to teach science, The Private Eye Project can be used for any subject including writing, math, art, social studies, and invention. It is now used by thousands of schools around the country.<ref>The Private Eye Project. The Private Eye Project. 2013.</ref>
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| There are also various pedagogic innovations now emerging that use visual analogies for cross-disciplinary teaching and research, for instance between science and the humanities.<ref name=Petrucci>{{Cite journal | author = Mario Petrucci | title = Crosstalk, Mutation, Chaos: bridge-building between the sciences and literary studies using Visual Analogy | url = http://www.mariopetrucci.com/Visualizations.htm}}</ref>
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| ==See also==
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| * [[Conceptual metaphor]]
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| * [[Conceptual blending]]
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| * [[Argument from analogy]]
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| * [[False analogy]]
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| * [[Metaphor]]
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| * [[Simile]]
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| * [[Hypocatastasis]]
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| * [[Allegory]]
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| * [[Argumentum e contrario]]
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| * [[Parable]]
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| ==Notes==
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| {{Reflist|2}}
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| ==References==
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| * Cajetan, Tommaso De Vio, (1498), ''De Nominum Analogia'', P.N. Zammit (ed.), 1934, ''The Analogy of Names'', Koren, Henry J. and Bushinski, Edward A (trans.), 1953, Pittsburgh: Duquesne University Press.
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| * Chalmers, D.J. et al. (1991). Chalmers, D.J., French, R.M., Hofstadter, D., [http://consc.net/papers/highlevel.pdf High-Level Perception, Representation, and Analogy].
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| * Coelho, Ivo (2010). "Analogy." [[ACPI Encyclopedia of Philosophy]]. Ed. Johnson J. Puthenpurackal. Bangalore: ATC. 1:64-68.
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| * Cornuéjols, A. (1996). [http://www.lri.fr/~antoine/Papers/JFA96-final-osX.pdf Analogie, principe d’économie et complexité algorithmique]. In ''Actes des 11èmes Journées Françaises de l’Apprentissage''. Sète.
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| * Doumas, L. A. A., Hummel, J.E., and Sandhofer, C. (2008). [http://internal.psychology.illinois.edu/~jehummel/pubs/DORA_PR_2008.pdf A Theory of the Discovery and Predication of Relational Concepts.] Psychological Review, 115, 1-43.
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| * Gentner, D. (1983). [http://groups.psych.northwestern.edu/gentner/papers/Gentner83.pdf Structure-mapping: A theoretical framework for analogy.] Cognitive Science, 7, 155–170. (Reprinted in A. Collins & E. E. Smith (Eds.), Readings in cognitive science: A perspective from psychology and artificial intelligence. Palo Alto, CA: Kaufmann).
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| * Forbus, K. et al. (1998). [http://www.psych.northwestern.edu/psych/people/faculty/gentner/newpdfpapers/ForbusGentner98.pdf Analogy just looks like high-level perception].
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| * Gentner, D., Holyoak, K.J., Kokinov, B. (Eds.) (2001). [http://cognet.mit.edu/library/books/view?isbn=0262571390 The Analogical Mind: Perspectives from Cognitive Science.] Cambridge, MA, MIT Press, ISBN 0-262-57139-0
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| * Hofstadter, D. (2001). [http://prelectur.stanford.edu/lecturers/hofstadter/analogy.html Analogy as the Core of Cognition], in [[Dedre Gentner]], [[Keith Holyoak]], and [[Boicho Kokinov]] (eds.) The Analogical Mind: Perspectives from Cognitive Science, Cambridge, MA: The MIT Press/[[Bradford Book]], 2001, pp. 499–538.
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| * Holland, J.H., Holyoak, K.J., Nisbett, R.E., and Thagard, P. (1986). [http://cognet.mit.edu/library/books/view?isbn=0262580969 Induction: Processes of Inference, Learning, and Discovery]. Cambridge, MA, MIT Press, ISBN 0-262-58096-9.
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| * Holyoak, K.J., and Thagard, P. (1995). [http://cognet.mit.edu/library/books/view?isbn=0262581442 Mental Leaps: Analogy in Creative Thought]. Cambridge, MA, MIT Press, ISBN 0-262-58144-2.
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| * Holyoak, K.J., and Thagard, P. (1997). [http://cogsci.uwaterloo.ca/Articles/Pages/Analog.Mind.html The Analogical Mind].
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| *Hummel, J.E., and Holyoak, K.J. (2005). [http://reasoninglab.psych.ucla.edu/KH%20pdfs/hummel&holyoak_cdips_2005.pdf Relational Reasoning in a Neurally Plausible Cognitive Architecture]
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| * Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company.
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| * Juthe, A. (2005). [http://www.cs.hut.fi/Opinnot/T-93.850/2005/Papers/juthe2005-analogy.pdf "Argument by Analogy"], in Argumentation (2005) 19: 1–27.
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| * {{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 = | journal = Cognitive Science | volume = 18 | issue = | pages = 287–334 }}
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| * {{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 | url = | journal = Journal of Experimental Psychology: Learning, Memory and Cognition | volume = 123 | issue = | pages = 946–967 }}
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| * Kokinov, B. (1994). [http://nbu.bg/cogs/personal/kokinov/ambr94.pdf "A hybrid model of reasoning by analogy."]
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| * Kokinov, B. and Petrov, A. (2001). [http://nbu.bg/cogs/personal/kokinov/Analogy&Memory(2002).pdf "Integration of Memory and Reasoning in Analogy-Making."]
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| * Lamond, G. (2006). [http://plato.stanford.edu/entries/legal-reas-prec/ Precedent and Analogy in Legal Reasoning], in [[Stanford Encyclopedia of Philosophy]].
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| *Langacker, Ronald W. (1987). Foundations of Cognitive grammar. Vol. I, Theoretical prerequisites. Stanford: Stanford University Press.
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| * Little, J. (2000). Analogy in Science: Where Do We Go From Here? ''Rhetoric Society Quarterly'', 30, 69–92.
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| * Little, J. (2008). The Role of Analogy in George Gamow's Derivation of Drop Energy. ''Technical Communication Quarterly'', 17, 1–19.
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| * Morrison, C., and Dietrich, E. (1995). [http://eksl.cs.umass.edu/~clayton/publications/CogSci95/SM-v-HLP.pdf Structure-Mapping vs. High-level Perception].
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| * Ross, J.F., (1982), ''[[Portraying Analogy]]''. Cambridge: Cambridge University Press.
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| * {{Cite journal | doi = 10.2307/2024008 | last1 = Ross | first1 = J.F. | year = 1970 | title = Analogy and The Resolution of Some Cognitivity Problems | jstor = 2024008 | journal = The Journal of Philosophy | volume = 67 | issue = 20| pages = 725–746 |month=October}}
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| * {{Cite journal | last1 = Ross | first1 = J.F. | year = 1961 | title = Analogy as a Rule of Meaning for Religious Language | url = | journal = International Philosophical Quarterly | volume = 1 | issue = 3| pages = 468–502 |month=September}}
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| * Ross, J.F., (1958), ''A Critical Analysis of the Theory of Analogy of St Thomas Aquinas'', (Ann Arbor, MI: University Microfilms Inc).
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| * Shelley, C. (2003). Multiple analogies in Science and Philosophy. Amsterdam/Philadelphia: John Benjamins Publishing Company.
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| * Turney, P.D., and Littman, M.L. (2005). [http://arxiv.org/abs/cs.LG/0508103 Corpus-based learning of analogies and semantic relations]. ''Machine Learning'', 60 (1–3), 251–278.
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| * Turney, P.D. (2006). [http://arxiv.org/abs/cs.CL/0608100 Similarity of semantic relations]. ''Computational Linguistics'', 32 (3), 379–416.
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| * Cornuéjols, A. (1996). [http://www.lri.fr/~antoine/Papers/JFA96-final-osX.pdf Analogy, principle of economy and computational complexity].
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| ==External links==
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| {{Wiktionary|analogy}}
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| * [http://plato.stanford.edu/entries/reasoning-analogy/ ''Stanford Encyclopedia of Philosophy''] "Analogy and Analogical Reasoning", by Paul Bartha.
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| * [http://plato.stanford.edu/entries/analogy-medieval/ ''Stanford Encyclopedia of Philosophy''] "Medieval Theories of Analogy", by E. Jennifer Ashworth.
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| * [http://plato.stanford.edu/entries/legal-reas-prec/ ''Stanford Encyclopedia of Philosophy''] "Precedent and Analogy in Legal Reasoning", by Grant Lamond.
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| * [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-09 ''Dictionary of the History of Ideas''] Analogy in Early Greek Thought.
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| * [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-10 ''Dictionary of the History of Ideas''] Analogy in Patristic and Medieval Thought.
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| *[http://www.psych.northwestern.edu/psych/people/faculty/gentner/publications2.htm Dedre Gentner's publications page], most of them on analogy and available for download.
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| *[http://www.coe.uga.edu/twa/ Shawn Glynn’s publications page], all on teaching with analogies and some available for download.
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| *[http://reasoninglab.psych.ucla.edu/KeithPublications.htm Keith Holyoak's publications page], many on analogy and available for download.
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| *[http://nbu.bg/cogs/personal/kokinov/index.html Boicho Kokinov's publications page], most of them on analogy and available for download.
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| *[http://www.the-private-eye.com/html/resources/handout.html The Private Eye Project's publications page], all on teaching with analogies (and thinking by analogy) and some available for download.
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| *[http://student.dei.uc.pt/~racosta/jmapper jMapper – Java Library for Analogy/Metaphor Generation]
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| *[http://sites.google.com/site/abimepublications/home Analogy games] – Analogy used as the basis for a cultural game
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| [[Category:Philosophical arguments]]
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| [[Category:Semantics]]
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| [[Category:Conceptual models]]
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| [[Category:Analogy]]
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