Analogy is a
cognitiveIn science, cognition refers to mental processes. These processes include attention, remembering, producing and understanding language, solving problems, and making decisions. Cognition is studied in various disciplines such as psychology, philosophy, linguistics, and computer science...
process of transferring
informationInformation in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
or
meaningIn linguistics, meaning is what is expressed by the writer or speaker, and what is conveyed to the reader or listener, provided that they talk about the same thing . In other words if the object and the name of the object and the concepts in their head are the same...
from a particular subject (the analogue or source) to another particular subject (the target), and a
linguisticLanguage may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...
expression corresponding to such a process. In a narrower sense, analogy is an
inferenceInference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...
or an argument from one particular to another particular, as opposed to
deductionDeductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
,
inductionInductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
, and
abductionAbduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...
, where at least one of the
premisePremise can refer to:* Premise, a claim that is a reason for, or an objection against, some other claim as part of an argument...
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 similarity, as in the
biological notion of analogyAn analogy is a trait or an organ that appears similar in two unrelated organisms. The cladistic term for the same phenomenon is homoplasy, from Greek for same form. Biological anologies are often the result of convergent evolution....
.
Analogy plays a significant role in
problem solvingProblem solving is a mental process and is part of the larger problem process that includes problem finding and problem shaping. Consideredthe most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of...
,
decision makingDecision making can be regarded as the mental processes resulting in the selection of a course of action among several alternative scenarios. Every decision making process produces a final choice. The output can be an action or an opinion of choice.- Overview :Human performance in decision terms...
,
perceptionPerception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...
,
memoryIn psychology, memory is an organism's ability to store, retain, and recall information and experiences. Traditional studies of memory began in the fields of philosophy, including techniques of artificially enhancing memory....
,
creativityCreativity refers to the phenomenon whereby a person creates something new that has some kind of value. What counts as "new" may be in reference to the individual creator, or to the society or domain within which the novelty occurs...
,
emotionEmotion is a complex psychophysiological experience of an individual's state of mind as interacting with biochemical and environmental influences. In humans, emotion fundamentally involves "physiological arousal, expressive behaviors, and conscious experience." Emotion is associated with mood,...
,
explanationAn explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequencesof those facts....
and
communicationCommunication is the activity of conveying meaningful information. Communication requires a sender, a message, and an intended recipient, although the receiver need not be present or aware of the sender's intent to communicate at the time of communication; thus communication can occur across vast...
. It lies behind basic tasks such as the identification of places, objects and people, for example, in
face perceptionFace perception is the process by which the brain and mind understand and interpret the face, particularly the human face.The human face's proportions and expressions are important to identify origin, emotional tendencies, health qualities, and some social information. From birth, faces are...
and
facial recognition systemA facial recognition system is a computer application for automatically identifying or verifying a person from a digital image or a video frame from a video source...
s. It has been argued that analogy is "the core of cognition". Specific analogical language comprises
exemplificationExemplar, in the sense developed by philosopher of science Thomas Kuhn, is a well known usage of a scientific theory.According to Kuhn, scientific practice alternates between periods of normal science and extraordinary/revolutionary science...
,
comparisonComparison, in grammar, is a property of adjectives and adverbs in most languages; it describes systems that distinguish the degree to which the modifier modifies its complement....
s,
metaphorA metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
s,
simileA simile is a figure of speech that directly compares two different things, usually by employing the words "like", "as". Even though both similes and metaphors are forms of comparison, similes indirectly compare the two ideas and allow them to remain distinct in spite of their similarities, whereas...
s,
allegoriesAllegory is a demonstrative form of representation explaining meaning other than the words that are spoken. Allegory communicates its message by means of symbolic figures, actions or symbolic representation...
, and
parableA parable is a succinct story, in prose or verse, which illustrates one or more instructive principles, or lessons, or a normative principle. It differs from a fable in that fables use animals, plants, inanimate objects, and forces of nature as characters, while parables generally feature human...
s, but
not metonymyMetonymy is a figure of speech used in rhetoric in which a thing or concept is not called by its own name, but by the name of something intimately associated with that thing or concept...
. Phrases like
and so on,
and the like,
as if, and the very word
likeIn the English language, the word like has a very flexible range of uses, ranging from conventional to non-standard. It can be used as a noun, verb, adverb, adjective, preposition, particle, conjunction, hedge, interjection, and quotative....
also rely on an analogical understanding by the receiver of a
messageA message in its most general meaning is an object of communication. It is a vessel which provides information. Yet, it can also be this information. Therefore, its meaning is dependent upon the context in which it is used; the term may apply to both the information and its form...
including them. Analogy is important not only in
ordinary languageOrdinary language philosophy is a philosophical school that approaches traditional philosophical problems as rooted in misunderstandings philosophers develop by distorting or forgetting what words actually mean in everyday use....
and
common senseCommon sense is defined by Merriam-Webster as, "sound and prudent judgment based on a simple perception of the situation or facts." Thus, "common sense" equates to the knowledge and experience which most people already have, or which the person using the term believes that they do or should have...
(where
proverbA proverb is a simple and concrete saying popularly known and repeated, which expresses a truth, based on common sense or the practical experience of humanity. They are often metaphorical. A proverb that describes a basic rule of conduct may also be known as a maxim...
s and
idiomIdiom is an expression, word, or phrase that has a figurative meaning that is comprehended in regard to a common use of that expression that is separate from the literal meaning or definition of the words of which it is made...
s give many examples of its application) but also in
scienceScience is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
,
philosophyPhilosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and the
humanitiesThe humanities are academic disciplines that study the human condition, using methods that are primarily analytical, critical, or speculative, as distinguished from the mainly empirical approaches of the natural sciences....
. The concepts of
associationIn psychology and marketing, two concepts or stimuli are associated when the experience of one leads to the effects of another, due to repeated pairing. This is sometimes called Pavlovian association for Ivan Pavlov's pioneering of classical conditioning....
, comparison,
correspondenceIn mathematics and mathematical economics, correspondence is a term with several related but not identical meanings.* In general mathematics, correspondence is an alternative term for a relation between two sets...
,
mathematicalIn mathematics , homology is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group...
and
morphological homologyHomology forms the basis of organization for comparative biology. In 1843, Richard Owen defined homology as "the same organ in different animals under every variety of form and function". Organs as different as a bat's wing, a seal's flipper, a cat's paw and a human hand have a common underlying...
,
homomorphismIn abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός meaning "same" and μορφή meaning "shape".- Definition :The definition of homomorphism depends on the type of algebraic structure under...
,
iconicityIn functional-cognitive linguistics, as well as in semiotics, iconicity is the conceived similarity or analogy between the form of a sign and its meaning, as opposed to arbitrariness.Iconic principles:...
,
isomorphismIn abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
,
metaphorA metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
, resemblance, and similarity are closely related to analogy. In
cognitive linguisticsIn linguistics, cognitive linguistics refers to the branch of linguistics that interprets language in terms of the concepts, sometimes universal, sometimes specific to a particular tongue, which underlie its forms...
, the notion of
conceptual metaphorIn cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another, for example, understanding quantity in terms of directionality . A conceptual domain can be any coherent organization of human experience...
may be equivalent to that of analogy.
Analogy has been studied and discussed since
classical antiquityClassical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome, collectively known as the Greco-Roman world...
by philosophers, scientists and
lawLaw is a system of rules and guidelines which are enforced through social institutions to govern behavior, wherever possible. It shapes politics, economics and society in numerous ways and serves as a social mediator of relations between people. Contract law regulates everything from buying a bus...
yers. The last few decades have shown a renewed interest in analogy, most notably in
cognitive scienceCognitive science is the interdisciplinary scientific study of mind and its processes. It examines what cognition is, what it does and how it works. It includes research on how information is processed , represented, and transformed in behaviour, nervous system or machine...
.
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 cultures and economics tradition speaks of an arrow, homomorphism
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός meaning "same" and μορφή meaning "shape".- Definition :The definition of homomorphism depends on the type of algebraic structure under...
, mappingIn most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.In graph theory, a map is a...
, or morphismIn mathematics, a morphism is an abstraction derived from structure-preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics...
from what is typically the more complex domain or source to what is typically the less complex codomainIn mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall. It is the set in the notation...
or target, using all of these words in the sense of mathematical category theoryCategory theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
.
- The tradition that appears more common in cognitive psychology
Cognitive psychology is a subdiscipline of psychology exploring internal mental processes.It is the study of how people perceive, remember, think, speak, and solve problems.Cognitive psychology differs from previous psychological approaches in two key ways....
, in literary theoryLiterary theory in a strict sense is the systematic study of the nature of literature and of the methods for analyzing literature. However, literary scholarship since the 19th century often includes—in addition to, or even instead of literary theory in the strict sense—considerations of...
, and in specializations within philosophyPhilosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
outside of logicIn philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, 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.
Identity of relation
In ancient
GreekGreek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
the word
αναλογια (
analogia) originally meant
proportionalityIn mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...
, in the mathematical sense, and it was indeed sometimes translated to
LatinLatin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
as
proportio. From there analogy was understood as
identity of relation between any two
ordered pairIn mathematics, an ordered pair is a pair of mathematical objects. In the ordered pair , the object a is called the first entry, and the object b the second entry of the pair...
s, whether of mathematical nature or not.
Kant'sImmanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
Critique of Judgment held to this notion. Kant argued that there can be exactly the same relation between two completely different objects. The same notion of analogy was used in the
USThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
-based
SATThe SAT Reasoning Test is a standardized test for college admissions in the United States. The SAT is owned, published, and developed by the College Board, a nonprofit organization in the United States. It was formerly developed, published, and scored by the Educational Testing Service which still...
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
AristotelianAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
format:
- HAND : PALM : : FOOT : ____
While most competent
EnglishEnglish is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
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. This relation is not apparent in some
lexical definitionThe lexical definition of a term, also known as the dictionary definition, is the meaning of the term in common usage. As its other name implies, this is the sort of definition one is likely to find in the dictionary...
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
abstractionAbstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
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
SATThe SAT Reasoning Test is a standardized test for college admissions in the United States. The SAT is owned, published, and developed by the College Board, a nonprofit organization in the United States. It was formerly developed, published, and scored by the Educational Testing Service which still...
test. The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by 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
PlatoPlato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
and
AristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
actually used a wider notion of analogy. They saw analogy as a
shared abstraction. Analogous objects did not share necessarily a relation, but also an idea, a pattern, a regularity, an attribute, an effect or a function. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as
argumentIn philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
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 AgesThe Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...
saw an increased use and theorization of analogy.
RomanRome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
lawyers had already used analogical reasoning and the Greek word
analogia. Medieval lawyers distinguished
analogia legis and
analogia iuris (see below). In
Islamic logicLogic played an important role in Islamic philosophy .Islamic Logic or mantiq is similar science to what is called Traditional Logic in Western Sciences.- External links :*Routledge Encyclopedia of Philosophy: , Routledge, 1998...
, analogical reasoning was used for the process of
QiyasIn Islamic jurisprudence, qiyās is the process of deductive analogy in which the teachings of the Hadith are compared and contrasted with those of the Qur'an, in order to apply a known injunction to a new circumstance and create a new injunction...
in Islamic
shariaSharia law, is the moral code and religious law of Islam. Sharia is derived from two primary sources of Islamic law: the precepts set forth in the Quran, and the example set by the Islamic prophet Muhammad in the Sunnah. Fiqh jurisprudence interprets and extends the application of sharia to...
law and
fiqhFiqh is Islamic jurisprudence. Fiqh is an expansion of the code of conduct expounded in the Quran, often supplemented by tradition and implemented by the rulings and interpretations of Islamic jurists....
jurisprudence. In
ChristianChristianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...
theologyTheology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
, analogical arguments were accepted in order to explain the attributes of
GodGod is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....
.
AquinasThomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...
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
polysemyPolysemy is the capacity for a sign or signs to have multiple meanings , i.e., a large semantic field.Charles Fillmore and Beryl Atkins’ definition stipulates three elements: the various senses of a polysemous word have a central origin, the links between these senses form a network, and ...
and homonymy).
Thomas CajetanThomas Cajetan , also known as Gaetanus, commonly Tommaso de Vio , was an Italian cardinal. He is perhaps best known among Protestants for his opposition to the teachings of Martin Luther and the Protestant Reformation while he was the Pope's Legate in Wittenberg, and perhaps best known among...
wrote an influential treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved.
James Francis RossJames Francis Ross was an American philosopher. James Ross, a creative thinker in philosophy of religion, law, metaphysics and philosophy of mind, was a member of the Philosophy Department at the University of Pennsylvania from 1962 until his death...
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.
Special case of induction
On the contrary, Ibn Taymiyya, Francis Bacon and later
John Stuart MillJohn Stuart Mill was a British philosopher, economist and civil servant. An influential contributor to social theory, political theory, and political economy, his conception of liberty justified the freedom of the individual in opposition to unlimited state control. He was a proponent of...
argued that analogy is simply
a special case of induction. In their view analogy is an inductive inference from common known attributes to another
probableProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
common attribute, which is known only about the source of the analogy, in the following form:
Premises
- a is C, D, E, F, G
- b is C, D, E, F
Conclusion
- b is probably G.
Alternative conclusion
- every C, D, E, F is probably G.
This view does not accept analogy as an autonomous mode of thought or inference,
reducingIn philosophy, reduction is the process by which one object, property, concept, theory, etc., is shown to be explicable in terms of another, lower level, entity...
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
deductionDeductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
stating as a
premisePremise can refer to:* Premise, a claim that is a reason for, or an objection against, some other claim as part of an argument...
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
trueTruth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
universal premise to replace the analogical premises. And analogy is not only an argument, but also a distinct cognitive process.
Shared structure
Contemporary cognitive scientists use a wide notion of analogy,
extensionallyIn any of several studies that treat the use of signs - for example, in linguistics, logic, mathematics, semantics, and semiotics - the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of...
close to that of Plato and Aristotle, but framed by Gentner's (1983)
structure mapping theory. The same idea of
mappingIn most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.In graph theory, a map is a...
between source and target is used by
conceptual metaphorIn cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another, for example, understanding quantity in terms of directionality . A conceptual domain can be any coherent organization of human experience...
and
conceptual blendingConceptual Blending is a general theory of cognition. According to this theory, elements and vital relations from diverse scenarios are "blended" in a subconscious process known as Conceptual Blending, which is assumed to be ubiquitous to everyday thought and language...
theorists. Structure mapping theory concerns both
psychologyPsychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
and
computer scienceComputer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
. According to this view, analogy depends on the
mappingIn most of mathematics and in some related technical fields, the term mapping, usually shortened to map, is either a synonym for function, or denotes a particular kind of function which is important in that branch, or denotes something conceptually similar to a function.In graph theory, a map is a...
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
psychologyPsychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as
metaphorA metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
and similarity.
Keith HolyoakKeith James Holyoak is a researcher in cognitive psychology and cognitive science, working on human thinking and reasoning. Holyoak's work focuses on the role of analogy in thinking...
and Paul Thagard (1997) developed their
multiconstraint theory within structure mapping theory. They defend that the "
coherenceCoherence theory of truth regards truth as coherence with some specified set of sentences, propositions or beliefs. There is no single coherence theory of truth, but rather an assortment of perspectives that are commonly collected under this title...
" of an analogy depends on structural consistency,
semantic similaritySemantic similarity or semantic relatedness is a concept whereby a set of documents or terms within term lists are assigned a metric based on the likeness of their meaning / semantic content....
and purpose. Structural consistency is maximal when the analogy is an
isomorphismIn abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
, 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. Hummel and Holyoak (2005) recast the multiconstraint theory within a
neural networkThe term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...
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).
Mark T. 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. Empirical evidence shows that human analogical mapping performance is influenced by information presentation order.
High-level perception
Douglas HofstadterDouglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
and his team challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between
perceptionPerception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...
, 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
representationsKnowledge representation is an area of artificial intelligence research aimed at representing knowledge in symbols to facilitate inferencing from those knowledge elements, creating new elements of knowledge...
by selecting relevant information from low-level
stimuliIn physiology, a stimulus is a detectable change in the internal or external environment. The ability of an organism or organ to respond to external stimuli is called sensitivity....
. 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.
Analogy and Complexity
Antoine Cornuéjols has presented analogy as a
principle of economy and
computational complexity.
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
St and a missing part
Rt. We assume that we can isolate a situation of the source
Ss, which corresponds to a situation of target
St, and the result of the source
Rs, which correspond to the result of the target
Rt. With
Bs, the relation between
Ss and
Rs, we want
Bt, the relation between
St and
Rt.
If the source and target are completely known:
Using
Kolmogorov complexityIn algorithmic information theory , the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object...
K(x), defined as the size of the smallest description of
x and Solomonoff's approach to
inductionAround 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols...
, Rissanen (89),
WallaceProfessor Christopher Stewart Wallace was an Australian computer scientist notable for having devised:...
& Boulton (68) proposed the principle of
Minimum description lengthThe minimum description length principle is a formalization of Occam's Razor in which the best hypothesis for a given set of data is the one that leads to the best compression of the data. MDL was introduced by Jorma Rissanen in 1978...
. This principle leads to minimize the complexity
K(target| Source) of producing the target from the source.
This is unattractive in Artificial Intelligence, as it requires a computation over abstract Turing machines. Suppose that
Ms and
Mt 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:
- K(Ms) + K(Ss|Ms) + K(Bs|Ms) + K(Mt|Ms) + K(St|Mt) + K(Bt|Mt) (1).
If the target is completely unknown:
All models and descriptions
Ms,
Mt,
Bs,
Ss, and
St leading to the minimization of:
- K(Ms) + K(Ss|Ms) + K(Bs|Ms) + K(Mt|Ms) + K(St|Mt) (2)
are also those who allow to obtain the relationship
Bt, and thus the most satisfactory
Rt for formula (1).
The analogical hypothesis, which solves an analogy between a source case and a target case, has two parts:
- 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.
- 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.
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:
- K(Ms) + K(Bs|Ms) + K(Mt|Ms) (3).
Logic
Logicians analyze how analogical reasoning is used in
arguments from analogyArgument from Analogy is a special type of inductive argument, whereby perceived similarities are used as a basis to infer some further similarity that has yet to be observed. Analogical reasoning is one of the most common methods by which human beings attempt to understand the world and make...
.
Rhetoric
- An analogy can be a spoken or textual
Writing is the representation of language in a textual medium through the use of a set of signs or symbols . It is distinguished from illustration, such as cave drawing and painting, and non-symbolic preservation of language via non-textual media, such as magnetic tape audio.Writing most likely...
comparison between two words (or sets of words) to highlight some form of semanticSemantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
similarity between them. Such analogies can be used to strengthen politicalPolitics is a process by which groups of people make collective decisions. The term is generally applied to the art or science of running governmental or state affairs, including behavior within civil governments, but also applies to institutions, fields, and special interest groups such as the...
and philosophicalPhilosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
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.
Linguistics
- An analogy can be the linguistic
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
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 EnglishEnglish is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
verbA verb, from the Latin verbum meaning word, is a word that in syntax conveys an action , or a state of being . In the usual description of English, the basic form, with or without the particle to, is the infinitive...
help once had the preteriteThe preterite is the grammatical tense expressing actions that took place or were completed in the past...
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 levelingIn linguistics, morphological leveling is the generalization of an inflection across a paradigm or between words. For example, the extension of the form is to persons such as I is and they is in some dialects of English is leveling, by analogy with a more frequent form, as is the reanalysis of...
. However, irregular forms can sometimes be created by analogy; one example is the American EnglishAmerican English is a set of dialects of the English language used mostly in the United States. Approximately two-thirds of the world's native speakers of English live in the United States....
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
Hardware is a general term for equipment such as keys, locks, hinges, latches, handles, wire, chains, plumbing supplies, tools, utensils, cutlery and machine parts. Household hardware is typically sold in hardware stores....
; other analogous neologisms such as firmwareIn electronic systems and computing, firmware is a term often used to denote the fixed, usually rather small, programs and/or data structures that internally control various electronic devices...
and vaporwareVaporware is a term in the computer industry that describes a product, typically computer hardware or software, that is announced to the general public but is never actually released nor officially canceled. Vaporware is also a term sometimes used to describe events that are announced or predicted,...
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
Generative linguistics is a school of thought within linguistics that makes use of the concept of a generative grammar. The term "generative grammar" is used in different ways by different people, and the term "generative linguistics" therefore has a range of different, though overlapping,...
for explaining productiveIn linguistics, productivity is the degree to which native speakers use a particular grammatical process, especially in word formation. Since use to produce novel structures is the clearest proof of usage of a grammatical process, the evidence most often appealed to as establishing productivity is...
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.
In science
Analogues 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 behaviours of similar systems. For instance, an analogy commonly
used in electronics textbooks compares electrical circuits to hydraulics. Another example is the
analog earAn analog ear or analog cochlea is a model of the ear or of the cochlea based on an electrical, electronic or mechanical analog...
based on electrical, electronic or mechanical devices.
Mathematics
Some types of analogies can have a precise mathematical formulation through the concept of
isomorphismIn abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a
bijectionA bijection is a function giving an exact pairing of the elements of two sets. A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements...
between them which preserves some or all of the relevant structure. For example,
and
are isomorphic as vector spaces, but the complex numbers,
, have more structure than
does –
is a
fieldIn abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...
as well as a
vector spaceA vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...
.
Category theoryCategory theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
takes the idea of mathematical analogy much further with the concept of
functorIn category theory, a branch of mathematics, a functor is a special type of mapping between categories. Functors can be thought of as homomorphisms between categories, or morphisms when in the category of small categories....
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 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
anatomyAnatomy is a branch of biology and medicine that is the consideration of the structure of living things. It is a general term that includes human anatomy, animal anatomy , and plant anatomy...
, two anatomical structures are considered to be
analogous when they serve similar
functionA role or a social role is a set of connected behaviours, rights and obligations as conceptualised by actors in a social situation. It is an expected or free or continuously changing behaviour and may have a given individual social status or social position...
s but are not
evolutionEvolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...
arily related, such as the legs of
vertebrateVertebrates are animals that are members of the subphylum Vertebrata . Vertebrates are the largest group of chordates, with currently about 58,000 species described. Vertebrates include the jawless fishes, bony fishes, sharks and rays, amphibians, reptiles, mammals, and birds...
s and the legs of
insectInsects are a class of living creatures within the arthropods that have a chitinous exoskeleton, a three-part body , three pairs of jointed legs, compound eyes, and two antennae...
s. Analogous structures are the result of
convergent evolutionConvergent evolution describes the acquisition of the same biological trait in unrelated lineages.The wing is a classic example of convergent evolution in action. Although their last common ancestor did not have wings, both birds and bats do, and are capable of powered flight. The wings are...
and should be contrasted with
homologousHomology forms the basis of organization for comparative biology. In 1843, Richard Owen defined homology as "the same organ in different animals under every variety of form and function". Organs as different as a bat's wing, a seal's flipper, a cat's paw and a human hand have a common underlying...
structures.
Engineering
Often a physical
prototypeA prototype is an early sample or model built to test a concept or process or to act as a thing to be replicated or learned from.The word prototype derives from the Greek πρωτότυπον , "primitive form", neutral of πρωτότυπος , "original, primitive", from πρῶτος , "first" and τύπος ,...
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
MONIACThe MONIAC also known as the Phillips Hydraulic Computer and the Financephalograph, was created in 1949 by the New Zealand economist Bill Phillips to model the national economic processes of the United Kingdom, while Phillips was a student at the London School of Economics , The MONIAC was an...
(an
analog computerAn analog computer is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved...
) used the flow of water in its pipes as an analog to the flow of money in an economy.
Morality
Analogical reasoning plays a very important part in
moralityMorality is the differentiation among intentions, decisions, and actions between those that are good and bad . A moral code is a system of morality and a moral is any one practice or teaching within a moral code...
. 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 particularismMoral particularism is the view that there are no moral principles and that moral judgement can be found only as one decides particular cases, either real or imagined. This stands in stark contrast to other prominent moral theories, such as deontology or utilitarianism...
accepts analogical moral reasoning, rejecting both deduction and induction, since only the former can do without moral principles.
Law
In
lawLaw is a system of rules and guidelines which are enforced through social institutions to govern behavior, wherever possible. It shapes politics, economics and society in numerous ways and serves as a social mediator of relations between people. Contract law regulates everything from buying a bus...
, 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
precedentIn common law legal systems, a precedent or authority is a principle or rule established in a legal case that a court or other judicial body may apply when deciding subsequent cases with similar issues or facts...
case lawIn law, case law is the set of reported judicial decisions of selected appellate courts and other courts of first instance which make new interpretations of the law and, therefore, can be cited as precedents in a process known as stare decisis...
.
Analogies from codes and statutes
In
civil lawCivil law is a legal system inspired by Roman law and whose primary feature is that laws are codified into collections, as compared to common law systems that gives great precedential weight to common law on the principle that it is unfair to treat similar facts differently on different...
systems, where the preeminent source of law is
legal codeA legal code is a body of law written by a governmental body, such as a U.S. state, a Canadian Province or German Bundesland or a municipality...
s and
statuteA statute is a formal written enactment of a legislative authority that governs a state, city, or county. Typically, statutes command or prohibit something, or declare policy. The word is often used to distinguish law made by legislative bodies from case law, decided by courts, and regulations...
s, a
lacunaIn law, a non liquet is a situation where there is no applicable law. Non liquet translates into English from Latin as "it is not clear." According to Cicero, the term was applied during the Roman Republic to a verdict of "not proven" where the guilt or innocence of the accused was "not clear." ...
(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
legislatorA legislator is a person who writes and passes laws, especially someone who is a member of a legislature. Legislators are usually politicians and are often elected by the people...
'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
authoritiesThe word Authority is derived mainly from the Latin word auctoritas, meaning invention, advice, opinion, influence, or command. In English, the word 'authority' can be used to mean power given by the state or by academic knowledge of an area .-Authority in Philosophy:In...
.
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.
In teaching strategies
Teaching the process of thinking by analogy is one of the main themes of
The Private Eye ProjectThe Private Eye Project is a research based educational program created by Kerry Ruef in 1988. Founded in both inquiry-based learning and active learning approaches, it is designed to accelerate student learning by the development of critical thinking skills, creativity, literacy, and scientific...
.
See also
- List of thinking-related topics
- Conceptual metaphor
In cognitive linguistics, conceptual metaphor, or cognitive metaphor, refers to the understanding of one idea, or conceptual domain, in terms of another, for example, understanding quantity in terms of directionality . A conceptual domain can be any coherent organization of human experience...
- Conceptual blending
Conceptual Blending is a general theory of cognition. According to this theory, elements and vital relations from diverse scenarios are "blended" in a subconscious process known as Conceptual Blending, which is assumed to be ubiquitous to everyday thought and language...
- False analogy
-The Argument from Analogy:The process of analogical inference involves noting the shared properties of two or more things, and from this basis infering that they also share some further property...
- Portal: thinking
- Metaphor
A metaphor is a literary figure of speech that uses an image, story or tangible thing to represent a less tangible thing or some intangible quality or idea; e.g., "Her eyes were glistening jewels." Metaphor may also be used for any rhetorical figures of speech that achieve their effects via...
- Simile
A simile is a figure of speech that directly compares two different things, usually by employing the words "like", "as". Even though both similes and metaphors are forms of comparison, similes indirectly compare the two ideas and allow them to remain distinct in spite of their similarities, whereas...
- Hypocatastasis
Hypocatastasis is a figure of speech that declares or implies a resemblance, representation or comparison. It differs from a metaphor, because in a metaphor the two nouns are both named and given; while, in hypocatastasis, only one is named and the other is implied, or as it were, is put down...
- Allegory
Allegory is a demonstrative form of representation explaining meaning other than the words that are spoken. Allegory communicates its message by means of symbolic figures, actions or symbolic representation...
- Argumentum e contrario
In logic, an argumentum e contrario denotes any proposition that is argued to be correct because it is not proven by a certain case. It the opposite of the analogy. Arguments e contrario are often used in the legal system, as a way to solve problems not currently covered by a certain system of laws...
- Parable
A parable is a succinct story, in prose or verse, which illustrates one or more instructive principles, or lessons, or a normative principle. It differs from a fable in that fables use animals, plants, inanimate objects, and forces of nature as characters, while parables generally feature human...
External links