# Analogy: Wikis

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# Encyclopedia

Analogy is a cognitive process of transferring information 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 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.

Niels Bohr's model of the atom made an analogy between the atom and the solar system.

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".[1] Specific 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, 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 lawyers. The last few decades have shown a renewed interest in analogy, most notable in cognitive science.

## Usage of the terms source and target

With respect to the terms source and target there are two distinct traditions of usage:

• The logical and mathematical tradition speaks of an arrow, homomorphism, mapping, or morphism from what is typically the more complex domain or source to what is typically the less complex codomain or target, using all of these words in the sense of mathematical category theory.
• The tradition that appears to be more common in cognitive psychology, literary theory, and specializations within philosophy outside of logic, speaks of a mapping from what is typically the more familiar area of experience, the source, to what is typically the more problematic area of experience, the target.

## Models and theories

### 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 : ____

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.

Recently a computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test. [2] 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

In several cultures, the sun is the source of an analogy to God.

Greek philosophers such as Plato and Aristotle actually used a wider notion of analogy. They saw analogy as a shared abstraction.[3] 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 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. Medieval lawyers distinguished analogia legis and analogia iuris (see below). In Islamic logic, analogical reasoning was used for the process of qiyas. 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.

### Special case of induction

On the contrary, Bacon and later Mill argued that analogy is simply a special case of induction.[3] In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form:

Premises
a is C, D, E, F, 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 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 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 universal premise to replace the analogical premises.[4] And analogy is not only an argument, but also a distinct cognitive process.

### Shared structure

According to Shelley (2003), the study of the coelacanth drew heavily on analogies from other fish.

Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by the structure mapping theory.[5] 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.[6]

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.[3] 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[7] challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between perception, including high-level perception, and analogical thought. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans make representations by selecting relevant information from low-level stimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers et al. conclude that analogy is high-level perception. Forbus et al. (1998) claim that this is only a metaphor. It has been argued (Morrison and Dietrich 1995) that Hofstadter's and Gentner's groups do not defend opposite views, but are instead dealing with different aspects of analogy.

## Applications and types

### In language

#### 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). Analogies are sometimes used to persuade those that cannot detect the flawed or non-existent arguments.

#### 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.) This is called leveling. However, irregular forms can sometimes be created by analogy; one example is the American English past tense form of dive: dove, formed on analogy with words such as drive: drove.
• Neologisms can also be formed by analogy with existing words. A good example is software, formed by analogy with hardware; other analogous neologisms such as firmware and vaporware have followed. Another example is the humorous term underwhelm, formed by analogy with overwhelm.
• Analogy is often presented as an alternative mechanism to generative rules for explaining productive formation of structures such as words. Others argue that in fact they are the same mechanism, that rules are analogies that have become entrenched as standard parts of the linguistic system, whereas clearer cases of analogy have simply not (yet) done so (e.g. Langacker 1987.445-447). This view has obvious resonances with the current views of analogy in cognitive science which are discussed above.

### In science

Analogues are often used in theoretical and applied sciences in the form of models or simulations which can be considered as strong analogies. Other much weaker analogies assist in understanding and describing functional behaviours of similar systems. For instance, an analogy commonly used in electronics textbooks compares electrical circuits to hydraulics. Another example is the analog ear based on electrical, electronic or mechanical devices.

#### Mathematics

Some types of analogies can have a precise mathematical formulation through the concept of isomorphism. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a bijection between them which preserves some or all of the relevant structure. For example, $\Bbb{R}^2$ and $\Bbb{C}$ are isomorphic as vector spaces, but the complex numbers, $\Bbb{C}$, have more structure than $\Bbb{R}^2$ does - $\Bbb{C}$ is a field as well as a vector space.

Category theory takes the idea of mathematical analogy much further with the concept of functors. Given two categories C and D a functor F from C to D can be thought of as an analogy between C and D, because F has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the compositional structure of the two categories is preserved. This is similar to the structure mapping theory of analogy of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.

#### Anatomy

In anatomy, two anatomical structures are considered to be analogous when they serve similar functions but are not 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.

#### 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.

### In normative matters

#### Morality

Analogical reasoning plays a very important part in morality. This may be in part because morality is supposed to be impartial and fair. If it is wrong to do something in a situation A, and situation B is analogous to A in all relevant features, then it is also wrong to perform that action in situation B. Moral particularism accepts analogical moral reasoning, rejecting both deduction and induction, since only the former can do without moral principles.

#### Law

In law, analogy is used to resolve issues on which there is no previous authority. A distinction has to be made between analogous reasoning from written law and analogy to precedent case law.

##### Analogies from codes and statutes

In civil law systems, where the preeminent source of law is legal 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 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.

##### 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.

## References

1. ^ Hofstadter in Gentner et al. 2001.
2. ^ Turney 2006
3. ^ a b c Shelley 2003
4. ^ See Juthe 2005
5. ^ See Dedre Gentner et al. 2001
6. ^ See Gentner et al. 2001 and Gentner's publication page.
7. ^ See Chalmers et al. 1991

# 1911 encyclopedia

Up to date as of January 14, 2010

### From LoveToKnow 1911

ANALOGY (Gr. avaXoyia, proportion), a term signifying, (I) in general, resemblance which falls short of absolute similarity or identity. Thus by analogy, the word "loud," originally applied to sounds, is used of garments which obtrude themselves on the attention; all metaphor is thus a kind of analogy. (2) Euclid used the term for proportionate equality; but in mathematics it is now obsolete except in the phrase, "Napier's Analogies" in spherical trigonometry (see Napier, John). (3) In grammar, it signifies similarity in the dominant characteristics of a language, derivation, orthography and so on. (4) In logic, it is used of arguments by inference from resemblances between known particulars to other particulars which are not observed. Under the name of "example" (7rapaSErry�a) the process is explained by Aristotle (Prior Anal. ii. 4) as an inference which differs from induction in having a particular, not a general, conclusion; i.e. if A is demonstrably like B in certain respects, it may be assumed to be like it in another, though the latter is not demonstrated. Kant and his followers state the distinction otherwise, i.e. induction argues from the possession of an attribute by many members of a class that all members of the class possess it, while analogy argues that, because A has some of B's qualities, it must have them all (cf. Sir Wm. Hamilton, Lectures on Logic, ii. 165-174, for a slight modification of this view). J. S. Mill very properly rejects this artificial distinction, which is in practice no distinction at all; he regards induction and analogy as generically the same, though differing in the demonstrative validity of their evidence, i.e. induction proceeds on the basis of scientific, causal connexion, while analogy, in absence of proof, temporarily accepts a probable hypothesis. In this sense, analogy may obviously have a universal conclusion. This type of inference is of the greatest value in physical science, which has frequently and quite legitimately used such conclusions until a negative instance has disproved or further evidence confirmed them (for a list of typical cases see T. Fowler's edition of Bacon's Nov. Org. Aph. ii. 27 note). The value of such inferences depends on the nature of the resemblances on which they are based and on that of the differences which they disregard. If the resemblances are small and unimportant and the differences great and fundamental, the argument is known as "False Analogy." The subject is dealt with in Francis Bacon's Novum Organum, especially ii. 27 (see T. H. Fowler's notes) under the head of Instantiae conformes sive proportionatae. Strictly the argument by analogy is based on similarity of relations between things, not on the similarity of things, though it is, in general, extended to cover the latter. See works on Logic, e.g. J. S. Mill, T. H. Fowler, W. S. Jevons. For Butler's Analogy and its method see Butler, Joseph.

The term was used in a special sense by Kant in his phrase, "Analogies of Experience," the third and most important group in his classification of the a priori elements of knowledge. By it he understood the fundamental laws of pure natural science under the three heads, substantiality, causality, reciprocity (see F. Paulsen, I. Kant, Eng. trans. 1902, pp. 188 ff.).

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# Bible wiki

Up to date as of January 23, 2010

### From BibleWiki

A philosophical term used to designate, first, a property of things; secondly, a process of reasoning. We have here to consider its meaning and use:
I. In physical and natural sciences; II. In metaphysics and scholastic philosophy; III. In theodicy; IV. In relation to the mysteries of faith.

## I. ANALOGY IN PHYSICAL AND NATURAL SCIENCES

As a property, analogy means a certain similarity mixed with difference. This similarity may be founded entirely or chiefly upon a conception of the mind; in this sense we say that there is analogy between the light of the sun and the light of the mind, between a lion and a courageous man, between an organism and society. This kind of analogy is the source of metaphor. The similarity may be founded on the real existence of similar properties in objects of different species, genera, or classes; those organs, for instance, are analogous, which, belonging to beings of different species or genera, and differing in structure, fulfil the same physiological functions or have the same connections. As a process of reasoning, analogy consists in concluding from some analogical properties or similarity under certain aspects to other analogical properties or similarity under other aspects. It was by such a process that Franklin passed from the analogy between the effects of lightning and the effects of electricity to the identity of their cause; Cuvier, from the analogy between certain organs of fossils and these organs in actual species to the analogy of the whole organism; that we infer from the analogy between the organs and external actions of animals and our own, the existence of consciousness in them. Analogical reasoning is a combination of inductive and deductive reasoning based on the principle that "analogical properties considered as similar involve similar consequences". It is evident that analogical reasoning, as to its value, depends on the value of the analogical property on which it rests. Based on a mere conception of the mind, it may suggest, but it does not prove; it cannot give conclusions, but only comparisons. Based on real properties, it is more or less conclusive according to the number and significance of the similar properties and according to the fewness and insignificance of the dissimilar properties. From a strictly logical point of view, analogical reasoning can furnish only probable conclusions and hypotheses. Such is the case for most of the theories in physical and natural sciences, which remain hypothetical so long as they are merely the result of analogy and have not been verified directly or indirectly.

## II. ANALOGY IN METAPHYSICS AND SCHOLASTIC PHILOSOPHY

Analogy in metaphysics and Scholastic philosophy was carefully studied by the Schoolmen, especially by the Pseudo-Dionysius, Albertus Magnus, and St. Thomas. It also may be considered either as a property or as a process of reasoning. As a metaphysical property, analogy is not a mere likeness between diverse objects, but a proportion or relation of object to object. It is, therefore, neither a merely equivocal or verbal coincidence, nor a fully univocal participation in a common concept; but it partakes of the one and the other. (Cf. St. Thomas, Summa Theol., I, Q. xiii, a. 5, 10; also, Q. vii, De potentiâ, a. 7.) We may distinguish two kinds of analogy:

• Two objects can be said to be analogous on account of a relation which they have not to each other, but to a third object: e.g., there is analogy between a remedy and the appearance of a person, in virtue of which these two objects are said to be healthy. This is based upon the relation which each of them has to the person's health, the former as a cause, the latter as a sign. This may be called indirect analogy.
• Two objects again are analogous on account of a relation which they have not to a third object, but to each other. Remedy, nourishment, and external appearance are termed healthy on account of the direct relation they bear to the health of the person. Here health is the basis of the analogy, and is an example of what the Schoolmen call summum analogatum (Cf. St. Thomas, ib.)

This second sort of analogy is twofold. Two things are related by a direct proportion of degree, distance, or measure: e.g., 6 is in direct proportion to 3, of which it is the double; or the healthiness of a remedy is directly related to, and directly measured by, the health which it produces. This analogy is called analogy of proportion. Or, the two objects are related one to the other not by a direct proportion, but by means of another and intermediary relation: for instance, 6 and 4 are analogous in this sense that 6 is the double of 3 as 4 is of 2, or 6:4::3:2. The analogy between corporal and intellectual vision is of this sort, because intelligence is to the mind what the eye is to the body. This kind of analogy is based on the proportion of proportion; it is called analogy of proportionality. (Cf. St. Thomas, Q. ii, De verit., a. 11; Q. xxiii, De verit., a. 7, ad 9<sup.am</sup>).

## III. ANALOGY AS A METHOD IN THEODICY

As human knowledge proceeds from the data of the senses directed and interpreted by reason, it is evident that man cannot arrive at a perfect knowledge of the nature of God which is essentially spiritual and infinite. Yet the various elements of perfection, dependence, limitation, etc., which exist in all finite beings, while they enable us to prove the existence of God, furnish us also with a certain knowledge of His nature. For dependent beings must ultimately rest on something non-dependent, relative beings on that which is non-relative, and, even if this non-dependent and non-relative Being cannot be conceived directly in itself, it is necessarily conceived to some extent through the beings which depend on it and are related to it. It is not an Unknown or Unknowable. It can be known in different ways. We remark in finite things a manifold dependence. These things are produced; they are produced according to a certain plan and in view of a certain end. We must conclude that they have a cause which possesses in itself a power of efficiency, exemplarity, and finality, with all the elements which such a power requires: intelligence, will, personality, etc. This way of reasoning is called by the Schoolmen "the way of causality" (via causalitatis). (Cf. Pseudo-Dion., De Div. Nom., c. i, sect. 6, in P. G., III, 595; also, St. Thomas, Summa Theol., I, Q. iii, a. 3; Q. xiii, a. 12.) When we reason from the effects to the First, or Ultimate, Cause, we eliminate from it all the defects, imperfections, and limitations which are in its effects just because they are effects, as change, limitation, time, and space. This way of reasoning is "the way of negation or remotion" (via negationis, remotionis). (Cf. Pseudo-Dion., ibid.; also, St. Thomas, Summa Theol., I, QQ. iii-xiii, a. 1; C. Gent., lib. I, c. xiv.) Finally, it is easily understood that the perfections affirmed, in these two ways, of God, as First and Perfect Cause, cannot be attributed to Him in the same sense that they have in finite beings, but only in an absolutely excellent or supereminent way (via eminentiae, excellentiae). (Cf. Pseudo-Dion., Div. Nom., c. i, sect. 41, in P.G., III, 516, 590; c. ii, sect. 3, 8, in P.G., III, 646, 689; St. Thomas, ibid.)

## IV. ANALOGY IN THE KNOWLEDGE OF THE MYSTERIES OF FAITH

The Fathers of the Church always emphasized the inability of the human reason to discover or even to represent adequately the mysteries of faith, and insisted on the necessity of analogical conceptions in their representations and expressions. St. Thomas, after the Pseudo-Dionysius and Albertus Magnus, has given the theory of analogy so applied to the mysteries of faith. (Cf. St. Thomas, Summa, Theol., I, Q. i, a. 9; Q. xxii, a. 1; In Librum Boëthii De Trinitate Expositio.) The Vatican Council set forth the Catholic doctrine on the point. (Cf. Const., Dei Filius, cap. iv; cf. also Conc. Coloniense, 1860.) (1) Before Revelation, analogy is unable to discover the mysteries, since reason can know of God only what is manifested of Him and is in necessary causal relation with Him in created things. (2) In Revelation, analogy is necessary, since God cannot reveal the mysteries to men except through conceptions intelligible to the human mind, and therefore analogical. (3) After Revelation, analogy is useful to give us certain knowledge of the mysteries, either by comparison with natural things and truths, or by consideration of the mysteries in relation with one another and with the destiny of man.

Portions of this entry are taken from The Catholic Encyclopedia, 1907.

# Simple English

Analogy in a more simple understanding is a similar structure to a given structure or the use of a similar example or model to explain something.

To be more precise one can say that it is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ÁáÀà

## Other websites and references

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