Analogy
Analogy is either the
cognitive process of transferring
information from a particular subject (the
analogue or source) to another particular subject (the target), or a
linguistic expression corresponding to such a process. In a narrower sense, analogy is an
inference or an
argument from a particular to another particular, as opposed to
deduction,
induction, and
abduction, where at least one of the
premises or the conclusion is general. The word
analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a
similarity, as in the
biological notion of analogy.
Analogy plays a significant role in
problem solving,
decision making,
perception,
memory,
creativity,
emotion,
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 systems. It has been argued that analogy is "the core of cognition" (
Hofstadter in Gentner et al. 2001). Specifically analogical language comprises
exemplification,
comparisons,
metaphors,
similes,
allegories, and
parables, but
not metonymy. Phrases like
and so on,
and the like,
as if, and the very word
like also rely on an analogical understanding by the receiver of a
message including them. Analogy is important not only in
ordinary language and
common sense, where
proverbs and
idioms give many examples of its application, but also in
science,
philosophy and the
humanities. The concepts of
association,
comparison,
correspondence,
homomorphism,
iconicity,
isomorphism,
mathematical homology,
metaphor,
morphological homology,
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
lawyers. The last few decades have shown a renewed interest in analogy, most notable in
cognitive science.
With respect to the terms
source and
target, there are two distinct traditions of usage:
* The logical and mathematical tradition speaks of an
arrow,
homomorphism,
mapping, or
morphism from what is typically the more complex
domain or
source to what is typically the less complex
codomain or
target, using all of these words in the sense of mathematical
category theory.
* The tradition that appears to be more common in
cognitive psychology,
literary theory, and specializations within
philosophy outside of
logic, speaks of a mapping from what is typically the more familiar area of experience, the
source, to what is typically the more problematic area of experience, the
target.
Identity of relation
In ancient
Greek 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 pairs, 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::HAND : PALM : : FOOT : ____It is worth noting that while most competent
English speakers will immediately give the right answer to the analogy question (
sole), it is quite more difficult to identify and describe the exact relation that holds both between
hand and
palm, and between
foot and
sole. This relation is not apparent in some
lexical definitions of
palm and
sole, where the former is defined as
the inner surface of the hand, and the latter as
the underside of the foot. Analogy and
abstraction are different cognitive processes, and analogy is often an easier one.
Shared abstraction
Greek philosophers such as
Plato and
Aristotle actually used a wider notion of analogy. They saw analogy as a
shared abstraction (Shelley 2003). Analogous objects did not share necessarily a relation, but also an
idea, a
pattern, a
regularity, an
attribute, an
effect or a
function. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as valid
arguments, 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. Mediaeval lawyers distinguished
analogia legis and
analogia iuris (see below). In
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 influent treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved.
Special case of induction
On the contrary,
Bacon and later
Mill argued that analogy be simply
a special case of induction (see Shelley 2003). In their view analogy is an
inductive inference from common known attributes to another
probable common attribute, which is known only about the source of the analogy, in the following form:
Premisesa is C, D, E, F and G.:
b is C, D, E and F.
Conclusion:
b is probably G.
Alternative conclusion: every C, D, E and F is probably G.
This view does not accept analogy as an autonomous mode of thought or inference,
reducing it to induction. However, autonomous analogical arguments are still useful in science, philosophy and the humanities (see below), which makes this reduction philosophically uninteresting. Moreover, induction tries to achieve general conclusions, while analogy looks for particular ones.
Hidden deduction
The opposite move could also be tried,
reducing analogy to deduction. It is argued that every analogical argument is partially superfluous and can be rendered as a
deduction stating as a
premise a (previously hidden) universal proposition which applied both to the source and the target. In this view, instead of an argument with the form:
Premises:
a is analogous to
b.:
b is F.
Conclusion:
a is plausibly F.We should have:
Hidden universal premise:all
a‘s are plausibly Fs.
Hidden singular premise:
a is F.
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 universal premise to replace the analogical premises (see Juthe 2005). And analogy is not only an argument, but also a distinct cognitive process.
Shared structure
Contemporary cognitive scientists use a wide notion of analogy,
extensionally close to that of Plato and Aristotle, but framed by the
structure mapping theory (See
Dedre Gentner et. al. 2001). The same idea of
mapping between source and target is used by
conceptual metaphor theorists. Structure mapping theory concerns both
psychology and
computer science.
According to this view, analogy depends on the
mapping or alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target.
Structure mapping theory has been applied and has found considerable confirmation in
psychology. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as
metaphor and
similarity (see Gentner et. al. 2001 and Gentner's publication page).
Keith Holyoak and
Paul Thagard (1997) developed their
multiconstraint theory within structure mapping theory. They defend that the "
coherence" of an analogy depends on structural consistency,
semantic similarity and
purpose. Structural consistency is maximal when the analogy is an
isomorphism, although lower levels are admitted. Similarity demands that the mapping connects similar elements and relations of source and target, at any level of abstraction. It is maximal when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose insofar as it helps solve the problem at hand. The multiconstraint theory faces some difficulties when there are multiple sources, but these can be overcome (Shelley 2003). Hummel and Holyoak (2005) recast the multiconstraint theory within a
neural network architecture.
A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are some
identical attributes or relations at some level of abstraction.
Human analogy does not, or at least not apparently.
High-level perception
Douglas Hofstadter and his team (see Chalmers et. al 1991) challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between
perception, including high-level perception, and analogical thought. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans make
representations 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.
Rhetoric
*An analogy can be a
spoken or
textual comparison between two words (or sets of words) to highlight some form of
semantic similarity between them. Such analogies can be used to strengthen
political and
philosophical arguments, even when the semantic similarity is weak or non-existent (if crafted carefully for the audience).
Linguistics
*An analogy can be the
linguistic process that reduces word forms perceived as irregular by remaking them in the shape of more common forms that are governed by rules. For example, the
English verb help once had the
preterite holp and the past participle
holpen. These
obsolete forms have been discarded and replaced by
helped by the power of analogy (or by widened application of the
productive Verb-
ed rule.) However, irregular forms can sometimes be created by analogy; one example is the
American English past tense form of
dive:
dove, formed on analogy with words such as
drive:
drove (though this may also be a survival of an archaic form instead/as well).
*
Neologisms can also be formed by analogy with existing words. A good example is
software, formed by analogy with
hardware; other analogous neologisms such as
firmware and
vaporware have followed. Another example is the humorous term
underwhelm, formed by analogy with
overwhelm.
Analogy is often presented as an alternative mechanism to
generative rules for explaining
productive formation of structures such as words. Others argue that in fact they are the same mechanism, that rules are analogies that have become entrenched as standard parts of the linguistic system, whereas clearer cases of analogy have simply not (yet) done so (e.g. Langacker 1987.445-447). This view has obvious resonances with the current views of analogy in cognitive science which are discussed above.
Mathematics
Some types of analogies can have a precise
mathematical formulation through the concept of
isomorphism.
Artificial intelligence
See
case-based reasoningAnatomy
See also: Analogy (biology)In
anatomy, two anatomical structures are considered to be
analogous when they serve similar
functions but are not
evolutionarily related, such as the
legs of
vertebrates and the legs of
insects. Analogous structures are the result of
convergent evolution and should be contrasted with
homologous structures.
Law
In
law, analogy is used to resolve issues on which there is no previous authority. A distinction has to be made between analogous reasoning from written law and analogy to
precedent case law.
Analogies from codes and statutes
In
civil law systems, where the preeminent source of law are
legal codes and
statutes, a
lacuna (a gap) arises when a specific issue is not explicitly dealt with in written law. Judges will try to identify a provision whose purpose applies to the case at hand. That process can reach a high degree of sophistication, as judges sometimes not only look at 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.
Analogies from precedent case law
By contrast, in
common law systems, where precedent cases are the primary source of law, analogies to codes and statutes are rare (since those are not seen as a coherent system, but as incursions into the common law). Analogies are thus usually drawn from precedent cases: The judge finds that the facts of another case are similar to the one at hand to an extent that the analogous application of the rule established in the previous case is justified.
Engineering
Often a physical
prototype is built to model and represent some other physical object. For example,
wind tunnels are used to test scale models of wings and aircraft, which act as an analog to full-size wings and aircraft.
For example, the
MONIAC (an
analog computer) used the flow of water in its pipes as an analog to the flow of money in an economy.
*
List of thinking-related topics*
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.
*
Keith Holyoak's publications page, many on analogy and available for download.
* Chalmers, D.J. et. al. (1991). Chalmers, D.J., French, R.M., Hofstadter, D.,
High-Level Perception, Representation, and Analogy.
* Forbus, K. et. al. (1998).
Analogy just looks like high-level perception.
* Gentner, D., Holyoak, K.J., Kokinov, B. (Eds.) (2001).
The Analogical Mind: Perspectives from Cognitive Science. Cambridge, MA, MIT Press, ISBN 0262571390
* Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company.
* Juthe, A. (2005).
"Argument by Analogy", in Argumentation (2005) 19: 1â€"27.
* Holland, J.H., Holyoak, K.J., Nisbett, R.E., and Thagard, P. (1986).
Induction: Processes of Inference, Learning, and Discovery. Cambridge, MA, MIT Press, ISBN 0262081609.
* Holyoak, K.J., and Thagard, P. (1995).
Mental Leaps: Analogy in Creative Thought. Cambridge, MA, MIT Press, ISBN 0262581442.
* Holyoak, K.J., and Thagard, P. (1997).
The Analogical Mind.
*Hummel, J.E., and Holyoak, K.J. (2005).
Relational Reasoning in a Neurally Plausible Cognitive Architecture* Lamond, G. (2006).
Precedent and Analogy in Legal Reasoning, in
Stanford Encyclopedia of Philosophy.
*Langacker, Ronald W. (1987). Foundations of Cognitive grammar. Vol. I, Theoretical prerequisites. Stanford: Stanford University Press.
* Morrison, C., and Dietrich, E. (1995).
Structure-Mapping vs. High-level Perception.
* Shelley, C. (2003). Multiple analogies in Science and Philosophy. Amsterdam/Philadelphia: John Benjamins Publishing Company.
