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Jump to navigationJump to searchNew page: Image:lighterstill.jpg '''Analogy''' is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (th...
[[Image:lighterstill.jpg]]
'''Analogy''' is both the cognitive process of transferring [[information]] from a particular subject (the analogue or source) to another particular subject (the target), and a [[language|linguistic]] expression corresponding to such a process. In a narrower sense, analogy is an [[inference]] or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises 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 similarity, as in the biological notion of analogy.
Analogy plays a significant role in problem solving, decision making, [[perception]], [[memory]], [[creativity]], [[emotion]], and [[communication]]. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception. It has been argued that analogy is "the core of cognition" ([[Douglas Hofstadter|Hofstadter]] in Gentner et al. 2001). <br>
Specific analogical language comprises exemplification, 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]] and common sense, where proverbs and [[idiom]]s give many examples of its application, but also in [[science]], [[philosophy]] and the [[humanities]]. The concepts of association, comparison, correspondence, [[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 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 notable in [[cognitive science]].
==Usage of the terms ''source'' and ''target''==
With respect to the terms ''source'' and ''target'' there are two distinct traditions of usage:
* The logical and mathematical tradition speaks of an ''arrow'', ''[[homomorphism]]'', ''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.
* The tradition that appears to be more common in [[cognitive psychology]], [[literary theory]], and specializations within [[philosophy]] outside of [[logic]], speaks of a 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''.
==Models and theories of analogy==
===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''. 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 Aristotelian format:
:HAND : PALM : : FOOT : ____
It is worth noting that while most competent [[English language|English]] speakers will immediately give the right answer to the analogy question (''sole''), it is quite more difficult to identify and describe the exact relation that holds both between ''hand'' and ''palm'', and between ''foot'' and ''sole''. This relation is not apparent in some lexical definitions of ''palm'' and ''sole'', where the former is defined as ''the inner surface of the hand'', and the latter as ''the underside of the foot''. Analogy and abstraction are different cognitive processes, and analogy is often an easier one.
Recently a computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test (Turney 2006). 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.
===Shared abstraction===
Greek philosophers such as [[Plato]] and [[Aristotle]] actually used a wider notion of analogy. They saw analogy as a '''shared abstraction''' (Shelley 2003). Analogous objects did not share necessarily a relation, but also an [[idea]], a [[pattern]], a [[regularity]], an [[attribute]], an [[effect]] or a [[function (philosophy)|function]]. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as valid [[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.
The [[Middle Ages]] 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 Islamic philosophy, analogical reasoning was used for the process of [[qiyas]]. 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 latter 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.
===Special case of induction===
On the contrary, [[Francis Bacon (philosopher)|Bacon]] and later [[John Stuart Mill|Mill]] argued that analogy be simply '''a special case of induction''' (see Shelley 2003). In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form:
;Premises
:''a'' is C, D, E, F and G.
: ''b'' is C, D, E and F.
;Conclusion
: ''b'' is probably G.
;Alternative conclusion
: every C, D, E and F is probably G.
This view does not accept analogy as an autonomous mode of thought or inference, 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.
===Hidden deduction===
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:
;Premises
: ''a'' is analogous to ''b''.
: ''b'' is F.
;Conclusion
: ''a'' is plausibly F.
We should have:
;Hidden universal premise
:all Gs are plausibly Fs.
;Hidden singular premise
: ''a'' is G.
;Conclusion
: ''a'' is plausibly F.
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 (see Juthe 2005). And analogy is not only an argument, but also a distinct cognitive process.
===Shared structure===
Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by the '''structure mapping theory''' (See [[Dedre Gentner]] et al. 2001). The same idea of mapping between source and target is used by [[conceptual metaphor]] 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 (see Gentner et al. 2001 and Gentner's publication page).
[[Keith Holyoak]] and [[Paul Thagard]] (1997) developed their '''multiconstraint theory''' within structure mapping theory. They defend that the "[[coherence]]" of an analogy depends on structural consistency, semantic similarity and [[purpose]]. Structural consistency is 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 (Shelley 2003). 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. [[Human]] analogy does not, or at least not apparently.
===High-level perception===
[[Douglas Hofstadter]] and his team (see Chalmers et al. 1991) 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 representations by selecting relevant information from low-level 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.
==Applications and types of analogy==
===Rhetoric===
*An analogy can be a spoken or textual comparison between two words (or sets of words) to highlight some form of semantic similarity between them. Such analogies can be used to strengthen [[Political Science|political]] and [[Philosophy|philosophical]] arguments, even when the semantic similarity is weak or non-existent (if crafted carefully for the audience).
===Linguistics===
*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 Verb-''ed'' rule.) This is called ''morphological leveling.'' However, irregular forms can sometimes be created by analogy; one example is the [[American]] [[English]] past tense form of ''dive'': ''dove'', formed on analogy with words such as ''drive'': ''drove''.
*[[Neologisms]] can also be formed by analogy with existing words. A good example is ''[[software]]'', formed by analogy with ''[[hardware]]''; other analogous neologisms such as ''[[firmware]]'' and ''[[vaporware]]'' have followed. Another example is the humorous term ''underwhelm'', formed by analogy with ''overwhelm''.
*Analogy is often presented as an alternative mechanism to generative ''rules'' for explaining 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.
===Science===
Analogs are often used in theoretical and applied sciences in the form of models or simulations
which can be considered as strong analogies. Other much weaker analogies assist in understanding
and describing functional behaviors of similar systems. For instance, an analogy commonly
used in electronics textbooks compares electrical circuits to hydraulics. Another example is the [[analog ear]] based on electrical, electronic or mechanical devices.
===Mathematics===
Some types of analogies can have a precise [[Mathematics|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.
Category theory takes the idea of mathematical analogy much further with the concept of functors. 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 structure mapping theory of analogy of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.
===Anatomy===
In [[anatomy]], two anatomical structures are considered to be ''analogous'' when they serve similar functions but are not related, such as the [[Leg (anatomy)|legs]] of [[vertebrate]]s and the legs of insects. Analogous structures are the result of convergent [[evolution]] and should be contrasted with [[homology (biology)|homologous]] structures.
===Morality===
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.
===Law===
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.
====Analogies from codes and statutes====
In [[civil law]] systems, where the preeminent source of law is legal codess and statutes, a 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]].
====Analogies from precedent case law====
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.
=== 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 act as an analog to full-size wings and aircraft.
For example, the MONIAC Computer (an analog computer) used the flow of water in its pipes as an analog to the flow of money in an economy.
==See also==
* [[Metaphor]]
* [[Allegory]]
==External links and references==
* [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-09 ''Dictionary of the History of Ideas:''] Analogy in Early Greek Thought.
* [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.
* [http://plato.stanford.edu/entries/analogy-medieval/ ''Stanford Encyclopedia of Philosophy'':] Medieval Theories of Analogy.
*[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.
*[http://www.coe.uga.edu/twa/ Shawn Glynn’s publications page], all on teaching with analogies and some available for download.
*[http://reasoninglab.psych.ucla.edu/KeithPublications.htm Keith Holyoak's publications page], many on analogy and available for download.
* 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].
* Forbus, K. et al. (1998). [http://www.psych.northwestern.edu/psych/people/faculty/gentner/newpdfpapers/ForbusGentner98.pdf Analogy just looks like high-level perception].
* 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
* 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.
* 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.
* 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.
* Holyoak, K.J., and Thagard, P. (1997). [http://cogsci.uwaterloo.ca/Articles/Pages/Analog.Mind.html The Analogical Mind].
*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]
* Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company.
* 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.
* Lamond, G. (2006). [http://plato.stanford.edu/entries/legal-reas-prec/ Precedent and Analogy in Legal Reasoning], in [[Stanford Encyclopedia of Philosophy]].
*Langacker, Ronald W. (1987). Foundations of Cognitive grammar. Vol. I, Theoretical prerequisites. Stanford: Stanford University Press.
* Little, J. (2000). Analogy in Science: Where Do We Go From Here? Rhetoric Society Quarterly, 30, 69-92.
* Little, J. (2008). The Role of Analogy in George Gamow's Derivation of Drop Energy. Technical Communication Quarterly, 17, 1-19.
* Morrison, C., and Dietrich, E. (1995). [http://eksl.cs.umass.edu/~clayton/publications/CogSci95/SM-v-HLP.pdf Structure-Mapping vs. High-level Perception].
* Shelley, C. (2003). Multiple analogies in Science and Philosophy. Amsterdam/Philadelphia: John Benjamins Publishing Company.
* 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.
* Turney, P.D. (2006). [http://arxiv.org/abs/cs.CL/0608100 Similarity of semantic relations]. Computational Linguistics, 32 (3), 379-416.
Applications and examples
* [http://student.dei.uc.pt/~racosta/jmapper jMapper - Java Library for Analogy/Metaphor Generation]
[[Category:Philosophy]]
[[Category:Languages and Literature]]
[[Category:Linguistics]]
'''Analogy''' is both the cognitive process of transferring [[information]] from a particular subject (the analogue or source) to another particular subject (the target), and a [[language|linguistic]] expression corresponding to such a process. In a narrower sense, analogy is an [[inference]] or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises 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 similarity, as in the biological notion of analogy.
Analogy plays a significant role in problem solving, decision making, [[perception]], [[memory]], [[creativity]], [[emotion]], and [[communication]]. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception. It has been argued that analogy is "the core of cognition" ([[Douglas Hofstadter|Hofstadter]] in Gentner et al. 2001). <br>
Specific analogical language comprises exemplification, 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]] and common sense, where proverbs and [[idiom]]s give many examples of its application, but also in [[science]], [[philosophy]] and the [[humanities]]. The concepts of association, comparison, correspondence, [[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 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 notable in [[cognitive science]].
==Usage of the terms ''source'' and ''target''==
With respect to the terms ''source'' and ''target'' there are two distinct traditions of usage:
* The logical and mathematical tradition speaks of an ''arrow'', ''[[homomorphism]]'', ''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.
* The tradition that appears to be more common in [[cognitive psychology]], [[literary theory]], and specializations within [[philosophy]] outside of [[logic]], speaks of a 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''.
==Models and theories of analogy==
===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''. 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 Aristotelian format:
:HAND : PALM : : FOOT : ____
It is worth noting that while most competent [[English language|English]] speakers will immediately give the right answer to the analogy question (''sole''), it is quite more difficult to identify and describe the exact relation that holds both between ''hand'' and ''palm'', and between ''foot'' and ''sole''. This relation is not apparent in some lexical definitions of ''palm'' and ''sole'', where the former is defined as ''the inner surface of the hand'', and the latter as ''the underside of the foot''. Analogy and abstraction are different cognitive processes, and analogy is often an easier one.
Recently a computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test (Turney 2006). 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.
===Shared abstraction===
Greek philosophers such as [[Plato]] and [[Aristotle]] actually used a wider notion of analogy. They saw analogy as a '''shared abstraction''' (Shelley 2003). Analogous objects did not share necessarily a relation, but also an [[idea]], a [[pattern]], a [[regularity]], an [[attribute]], an [[effect]] or a [[function (philosophy)|function]]. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as valid [[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.
The [[Middle Ages]] 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 Islamic philosophy, analogical reasoning was used for the process of [[qiyas]]. 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 latter 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.
===Special case of induction===
On the contrary, [[Francis Bacon (philosopher)|Bacon]] and later [[John Stuart Mill|Mill]] argued that analogy be simply '''a special case of induction''' (see Shelley 2003). In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form:
;Premises
:''a'' is C, D, E, F and G.
: ''b'' is C, D, E and F.
;Conclusion
: ''b'' is probably G.
;Alternative conclusion
: every C, D, E and F is probably G.
This view does not accept analogy as an autonomous mode of thought or inference, 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.
===Hidden deduction===
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:
;Premises
: ''a'' is analogous to ''b''.
: ''b'' is F.
;Conclusion
: ''a'' is plausibly F.
We should have:
;Hidden universal premise
:all Gs are plausibly Fs.
;Hidden singular premise
: ''a'' is G.
;Conclusion
: ''a'' is plausibly F.
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 (see Juthe 2005). And analogy is not only an argument, but also a distinct cognitive process.
===Shared structure===
Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by the '''structure mapping theory''' (See [[Dedre Gentner]] et al. 2001). The same idea of mapping between source and target is used by [[conceptual metaphor]] 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 (see Gentner et al. 2001 and Gentner's publication page).
[[Keith Holyoak]] and [[Paul Thagard]] (1997) developed their '''multiconstraint theory''' within structure mapping theory. They defend that the "[[coherence]]" of an analogy depends on structural consistency, semantic similarity and [[purpose]]. Structural consistency is 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 (Shelley 2003). 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. [[Human]] analogy does not, or at least not apparently.
===High-level perception===
[[Douglas Hofstadter]] and his team (see Chalmers et al. 1991) 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 representations by selecting relevant information from low-level 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.
==Applications and types of analogy==
===Rhetoric===
*An analogy can be a spoken or textual comparison between two words (or sets of words) to highlight some form of semantic similarity between them. Such analogies can be used to strengthen [[Political Science|political]] and [[Philosophy|philosophical]] arguments, even when the semantic similarity is weak or non-existent (if crafted carefully for the audience).
===Linguistics===
*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 Verb-''ed'' rule.) This is called ''morphological leveling.'' However, irregular forms can sometimes be created by analogy; one example is the [[American]] [[English]] past tense form of ''dive'': ''dove'', formed on analogy with words such as ''drive'': ''drove''.
*[[Neologisms]] can also be formed by analogy with existing words. A good example is ''[[software]]'', formed by analogy with ''[[hardware]]''; other analogous neologisms such as ''[[firmware]]'' and ''[[vaporware]]'' have followed. Another example is the humorous term ''underwhelm'', formed by analogy with ''overwhelm''.
*Analogy is often presented as an alternative mechanism to generative ''rules'' for explaining 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.
===Science===
Analogs are often used in theoretical and applied sciences in the form of models or simulations
which can be considered as strong analogies. Other much weaker analogies assist in understanding
and describing functional behaviors of similar systems. For instance, an analogy commonly
used in electronics textbooks compares electrical circuits to hydraulics. Another example is the [[analog ear]] based on electrical, electronic or mechanical devices.
===Mathematics===
Some types of analogies can have a precise [[Mathematics|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.
Category theory takes the idea of mathematical analogy much further with the concept of functors. 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 structure mapping theory of analogy of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.
===Anatomy===
In [[anatomy]], two anatomical structures are considered to be ''analogous'' when they serve similar functions but are not related, such as the [[Leg (anatomy)|legs]] of [[vertebrate]]s and the legs of insects. Analogous structures are the result of convergent [[evolution]] and should be contrasted with [[homology (biology)|homologous]] structures.
===Morality===
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.
===Law===
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.
====Analogies from codes and statutes====
In [[civil law]] systems, where the preeminent source of law is legal codess and statutes, a 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]].
====Analogies from precedent case law====
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.
=== 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 act as an analog to full-size wings and aircraft.
For example, the MONIAC Computer (an analog computer) used the flow of water in its pipes as an analog to the flow of money in an economy.
==See also==
* [[Metaphor]]
* [[Allegory]]
==External links and references==
* [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-09 ''Dictionary of the History of Ideas:''] Analogy in Early Greek Thought.
* [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.
* [http://plato.stanford.edu/entries/analogy-medieval/ ''Stanford Encyclopedia of Philosophy'':] Medieval Theories of Analogy.
*[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.
*[http://www.coe.uga.edu/twa/ Shawn Glynn’s publications page], all on teaching with analogies and some available for download.
*[http://reasoninglab.psych.ucla.edu/KeithPublications.htm Keith Holyoak's publications page], many on analogy and available for download.
* 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].
* Forbus, K. et al. (1998). [http://www.psych.northwestern.edu/psych/people/faculty/gentner/newpdfpapers/ForbusGentner98.pdf Analogy just looks like high-level perception].
* 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
* 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.
* 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.
* 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.
* Holyoak, K.J., and Thagard, P. (1997). [http://cogsci.uwaterloo.ca/Articles/Pages/Analog.Mind.html The Analogical Mind].
*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]
* Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company.
* 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.
* Lamond, G. (2006). [http://plato.stanford.edu/entries/legal-reas-prec/ Precedent and Analogy in Legal Reasoning], in [[Stanford Encyclopedia of Philosophy]].
*Langacker, Ronald W. (1987). Foundations of Cognitive grammar. Vol. I, Theoretical prerequisites. Stanford: Stanford University Press.
* Little, J. (2000). Analogy in Science: Where Do We Go From Here? Rhetoric Society Quarterly, 30, 69-92.
* Little, J. (2008). The Role of Analogy in George Gamow's Derivation of Drop Energy. Technical Communication Quarterly, 17, 1-19.
* Morrison, C., and Dietrich, E. (1995). [http://eksl.cs.umass.edu/~clayton/publications/CogSci95/SM-v-HLP.pdf Structure-Mapping vs. High-level Perception].
* Shelley, C. (2003). Multiple analogies in Science and Philosophy. Amsterdam/Philadelphia: John Benjamins Publishing Company.
* 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.
* Turney, P.D. (2006). [http://arxiv.org/abs/cs.CL/0608100 Similarity of semantic relations]. Computational Linguistics, 32 (3), 379-416.
Applications and examples
* [http://student.dei.uc.pt/~racosta/jmapper jMapper - Java Library for Analogy/Metaphor Generation]
[[Category:Philosophy]]
[[Category:Languages and Literature]]
[[Category:Linguistics]]
