Analogy
Encyclopedia
Analogy is a cognitive
process of transferring information
or meaning
from a particular subject (the analogue or source) to another particular subject (the target), and a 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 premise
s or the conclusion is general. The word analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a similarity, as in the biological notion of analogy
.
Analogy plays a significant role in problem solving
, decision making
, perception
, memory
, creativity
, emotion
, explanation
and communication
. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception
and facial recognition system
s. It has been argued that analogy is "the core of cognition". Specific analogical language comprises exemplification
, comparison
s, metaphor
s, simile
s, 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 proverb
s and idiom
s give many examples of its application) but also in science
, philosophy
and the humanities
. The concepts of association
, comparison, correspondence
, mathematical
and morphological homology
, homomorphism
, iconicity
, isomorphism
, metaphor
, resemblance, and similarity are closely related to analogy. In cognitive linguistics
, the notion of conceptual metaphor
may be equivalent to that of analogy.
Analogy has been studied and discussed since classical antiquity
by philosophers, scientists and law
yers. The last few decades have shown a renewed interest in analogy, most notably in cognitive science
.
the word αναλογια (analogia) originally meant 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. Kant's
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 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:
While most competent English
speakers will immediately give the right answer to the analogy question (sole), it is more difficult to identify and describe the exact relation that holds both between hand and palm, and between foot and sole. This relation is not apparent in some lexical definition
s of palm and sole, where the former is defined as the inner surface of the hand, and the latter as the underside of the foot. Analogy and abstraction
are different cognitive processes, and analogy is often an easier one.
Recently a computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT
test. The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistical analysis of a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.
Greek philosophers such as Plato
and Aristotle
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 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. Roman
lawyers had already used analogical reasoning and the Greek word analogia. Medieval lawyers distinguished analogia legis and analogia iuris (see below). In Islamic logic
, analogical reasoning was used for the process of Qiyas
in Islamic sharia
law and fiqh
jurisprudence. In Christian
theology
, analogical arguments were accepted in order to explain the attributes of God
. 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. James Francis Ross
in Portraying Analogy (1982), the first substantive examination of the topic since Cajetan's De Nominum Analogia, demonstrated that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent.
argued that analogy is simply a special case of induction. 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
Conclusion
Alternative conclusion
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.
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
Conclusion
We should have:
Hidden universal premise
Hidden singular premise
Conclusion
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 true
universal premise to replace the analogical premises. And analogy is not only an argument, but also a distinct cognitive process.
Contemporary cognitive scientists use a wide notion of analogy, extensionally
close to that of Plato and Aristotle, but framed by Gentner's (1983) structure mapping theory. The same idea of mapping
between source and target is used by conceptual metaphor
and conceptual blending
theorists. Structure mapping theory concerns both psychology
and computer science
. According to this view, analogy depends on the mapping
or alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target. Structure mapping theory has been applied and has found considerable confirmation in psychology
. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as metaphor
and similarity.
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. Hummel and Holyoak (2005) recast the multiconstraint theory within a neural network
architecture. A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are some identical attributes or relations at some level of abstraction. The model was extended (Doumas, Hummel, & Sandhofer, 2008) to learn relations from unstructured examples (providing the only current account of how symbolic representations can be learned from examples).
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.
and his team 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.
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 complexity
K(x), defined as the size of the smallest description of x and Solomonoff's approach to induction
, Rissanen (89), Wallace
& Boulton (68) proposed the principle of Minimum description length
. This principle leads to minimize the complexity K(target| Source) of producing the target from the source.
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:
If the target is completely unknown:
All models and descriptions Ms, Mt, Bs, Ss, and St leading to the minimization of:
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:
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:
.
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 ear
based on electrical, electronic or mechanical devices.
. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a bijection
between them which preserves some or all of the relevant structure. For example,
and 
are isomorphic as vector spaces, but the complex numbers, 
, have more structure than 
does – 
is a field
as well as a vector space
.
Category theory
takes the idea of mathematical analogy much further with the concept of functor
s. Given two categories C and D, a functor F from C to D can be thought of as an analogy between C and D, because F has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the 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.
, two anatomical structures are considered to be analogous when they serve similar function
s but are not evolution
arily related, such as the legs of vertebrate
s and the legs of insect
s. Analogous structures are the result of convergent evolution
and should be contrasted with homologous
structures.
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
(an analog computer
) used the flow of water in its pipes as an analog to the flow of money in an economy.
. 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.
, 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
.
In civil law
systems, where the preeminent source of law is legal code
s and statute
s, 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 authorities
.
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.
.
Cognition
In 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 information
Information
Information 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 meaning
Meaning (linguistics)
In 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 linguistic
Language
Language 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 inference
Inference
Inference 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 deduction
Deductive reasoning
Deductive 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...
, induction
Inductive reasoning
Inductive 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 abduction
Abductive reasoning
Abduction 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 premise
Premise
Premise 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 analogy
Analogy (biology)
An 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....
.
Problem solving
Problem 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 making
Decision making
Decision 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...
, perception
Perception
Perception 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...
, memory
Memory
In 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....
, creativity
Creativity
Creativity 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...
, emotion
Emotion
Emotion 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,...
, explanation
Explanation
An explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequencesof those facts....
and communication
Communication
Communication 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 perception
Face perception
Face 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 system
Facial recognition system
A 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 exemplification
Exemplar
Exemplar, 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...
, comparison
Comparison (grammar)
Comparison, 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, metaphor
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...
s, simile
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...
s, allegories
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...
, and parable
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...
s, but not metonymy
Metonymy
Metonymy 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 like
Like
In 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 message
Message
A 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 language
Ordinary language philosophy
Ordinary 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 sense
Common sense
Common 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 proverb
Proverb
A 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 idiom
Idiom
Idiom 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 science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
, philosophy
Philosophy
Philosophy 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 humanities
Humanities
The 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 association
Association (psychology)
In 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, correspondence
Correspondence (mathematics)
In 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...
, mathematical
Homology (mathematics)
In 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 homology
Homology (biology)
Homology 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...
, homomorphism
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...
, iconicity
Iconicity
In 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:...
, isomorphism
Isomorphism
In 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...
, metaphor
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...
, resemblance, and similarity are closely related to analogy. In cognitive linguistics
Cognitive linguistics
In 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 metaphor
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...
may be equivalent to that of analogy.
Analogy has been studied and discussed since classical antiquity
Classical antiquity
Classical 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 law
Law
Law 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 science
Cognitive science
Cognitive 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, homomorphismHomomorphismIn 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...
, mappingMap (mathematics)In 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 morphismMorphismIn 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 codomainCodomainIn 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 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 psychologyCognitive psychologyCognitive 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 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 philosophyPhilosophyPhilosophy 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 logicLogicIn 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 language
Greek 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 proportionality
Proportionality (mathematics)
In 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 Latin
Latin
Latin 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 pair
Ordered pair
In 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's
Immanuel Kant
Immanuel 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 US
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
-based SAT
SAT
The 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 Aristotelian
Aristotle
Aristotle 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 English
English language
English 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 definition
Lexical definition
The 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 abstraction
Abstraction
Abstraction 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 SAT
SAT
The 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
Plato
Plato , 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 Aristotle
Aristotle
Aristotle 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 argument
Argument
In 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 Ages
Middle Ages
The 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. Roman
Rome
Rome 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 logic
Logic in Islamic philosophy
Logic 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 Qiyas
Qiyas
In 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 sharia
Sharia
Sharia 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 fiqh
Fiqh
Fiqh 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 Christian
Christianity
Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...
theology
Theology
Theology 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 God
God
God 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....
. Aquinas
Thomas Aquinas
Thomas 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 polysemy
Polysemy
Polysemy 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 Cajetan
Thomas Cajetan
Thomas 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 Ross
James Francis Ross
James 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
John 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 probable
Probability
Probability 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, reducing
Reduction (philosophy)
In 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
Deductive 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 premise
Premise
Premise 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 true
Truth
Truth 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
Extension (semantics)
In 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 mapping
Map (mathematics)
In 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 metaphor
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...
and conceptual blending
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...
theorists. Structure mapping theory concerns both psychology
Psychology
Psychology 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 science
Computer science
Computer 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 mapping
Map (mathematics)
In 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 psychology
Psychology
Psychology 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 metaphor
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...
and similarity.
Keith Holyoak
Keith Holyoak
Keith 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 "coherence
Coherence theory of truth
Coherence 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 similarity
Semantic similarity
Semantic 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 isomorphism
Isomorphism
In 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 network
Neural network
The 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 Hofstadter
Douglas 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 perception
Perception
Perception 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 representations
Knowledge representation
Knowledge 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 stimuli
Stimulus (physiology)
In 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 complexity
Kolmogorov complexity
In 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 induction
Inductive inference
Around 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), Wallace
Chris Wallace (computer scientist)
Professor Christopher Stewart Wallace was an Australian computer scientist notable for having devised:...
& Boulton (68) proposed the principle of Minimum description length
Minimum description length
The 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
Argument 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 textualWritingWriting 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 semanticSemanticsSemantics 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 politicalPoliticsPolitics 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 philosophicalPhilosophyPhilosophy 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 linguisticLinguisticsLinguistics 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 languageEnglish 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...
verbVerbA 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 preteritePreteriteThe 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 levelingMorphological 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 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 hardwareHardwareHardware 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 firmwareFirmwareIn 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 vaporwareVaporwareVaporware 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 rulesGenerative linguisticsGenerative 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 productiveProductivity (linguistics)In 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 simulationswhich 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 ear
Analog ear
An 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 isomorphismIsomorphism
In 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 bijection
Bijection
A 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 fieldField (mathematics)
In 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 space
Vector space
A 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 theory
Category theory
Category 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 functor
Functor
In 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
Anatomy 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 function
Role
A 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 evolution
Evolution
Evolution 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 vertebrate
Vertebrate
Vertebrates 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 insect
Insect
Insects 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 evolution
Convergent evolution
Convergent 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 homologous
Homology (biology)
Homology 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 prototypePrototype
A 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 MONIAC
MONIAC Computer
The 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 computer
Analog computer
An 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
Morality 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 particularism
Moral particularism
Moral 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
Law 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 precedent
Precedent
In 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 law
Case law
In 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 law
Civil law (legal system)
Civil 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 code
Legal code
A 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 statute
Statute
A 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 lacuna
Non liquet
In 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 legislator
Legislator
A 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 authorities
Authority
The 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
The 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 metaphorConceptual 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...
- Conceptual blendingConceptual 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...
- False analogyFalse 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
- MetaphorMetaphorA 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...
- SimileSimileA 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...
- HypocatastasisHypocatastasisHypocatastasis 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...
- AllegoryAllegoryAllegory 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 contrarioArgumentum e contrarioIn 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...
- ParableParableA 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
- Dictionary of the History of Ideas: Analogy in Early Greek Thought.
- Dictionary of the History of Ideas: Analogy in Patristic and Medieval Thought.
- Stanford Encyclopedia of Philosophy: Medieval Theories of Analogy.
- Dedre Gentner's publications page, most of them on analogy and available for download.
- Shawn Glynn’s publications page, all on teaching with analogies and some available for download.
- Keith Holyoak's publications page, many on analogy and available for download.
- Boicho Kokinov's publications page, most of them on analogy and available for download.
- The Private Eye Project's publications page, all on teaching with analogies (and thinking by analogy) and some available for download.
- jMapper – Java Library for Analogy/Metaphor Generation
- Analogy games: Analogy used as the basis for a cultural game