Analogía (del griego ἀναλογία, analogia , "proporción", de ana- "sobre, según" [también "contra", "de nuevo"] + logos "relación" [también "palabra, habla, cálculo"] [1] [ 2] ) es un proceso cognitivo de transferir información o significado de un sujeto en particular (el análogo o fuente) a otro (el objetivo), o una expresión lingüística correspondiente a dicho proceso. En un sentido más estricto, la analogía es una inferencia o un argumento de un particular a otro particular, en oposición a la deducción ,inducción y abducción , en las que al menos una de las premisas , o la conclusión, es de naturaleza general más que particular. El término analogía también puede referirse a la relación entre la fuente y el objetivo mismos, que a menudo (aunque no siempre) es una similitud , como en la noción biológica de analogía .
La analogía juega un papel importante en la resolución de problemas , así como en la toma de decisiones , argumentación , percepción , generalización , memoria , creatividad , invención , predicción, emoción , explicación , conceptualización y comunicación . Se encuentra detrás de tareas básicas como la identificación de lugares, objetos y personas, por ejemplo, en los sistemas de percepción y reconocimiento facial . Se ha argumentado que la analogía es "el núcleo de la cognición". [3] El lenguaje analógico específico comprende ejemplificación , comparaciones , metáforas , símiles , alegorías y parábolas , pero no metonimia . Frases como, y así sucesivamente , y cosas por el estilo , como si , y la misma palabra como también se basan en una comprensión analógica por parte del receptor de un mensaje que las incluye. La analogía es importante no solo en el lenguaje ordinario y el sentido común (donde los proverbios y modismos dan muchos ejemplos de su aplicación) sino también en la ciencia , la filosofía , el derecho y las humanidades . Los conceptos de asociación , comparación, correspondencia, homología matemática y morfológica , homomorfismo , iconicidad , isomorfismo , metáfora , semejanza y similitud están estrechamente relacionados con la analogía. En lingüística cognitiva , la noción de metáfora conceptual puede ser equivalente a la de analogía. La analogía también es una base para cualquier argumento comparativo, así como para experimentos cuyos resultados se transmiten a objetos que no han sido examinados (por ejemplo, experimentos en ratas cuando los resultados se aplican a humanos).
La analogía ha sido estudiada y discutida desde la antigüedad clásica por filósofos, científicos, teólogos y abogados . Las últimas décadas han mostrado un interés renovado en la analogía, sobre todo en la ciencia cognitiva .
Uso de los términos "fuente" y "destino"
Con respecto a los términos fuente y destino, existen dos tradiciones de uso distintas:
- La tradición de la lógica y las culturas y la economía habla de una flecha , homomorfismo , mapeo o morfismo desde lo que suele ser el dominio o fuente más complejo hasta lo que suele ser el codominio o el objetivo menos complejo , utilizando todas estas palabras en el sentido de categoría matemática. teoría .
- La tradición en psicología cognitiva , en teoría literaria y en especializaciones dentro de la filosofía fuera de la lógica , habla de un mapeo desde lo que es típicamente el área de experiencia más familiar, la fuente , a lo que es típicamente el área de experiencia más problemática, el objetivo. .
Modelos y teorías
Identidad de la relación
En la antigua Grecia la palabra αναλογια ( analogia ) originalmente significaba proporcionalidad , en el sentido matemático, y de hecho se traduce a veces a América como proportio . [ cita requerida ] A partir de ahí, la analogía se entendió como la identidad de relación entre dos pares ordenados , ya sea de naturaleza matemática o no. La Crítica del juicio de Kant se aferró a esta noción. Kant argumentó que puede haber exactamente la misma relación entre dos objetos completamente diferentes. La misma noción de analogía se utilizó en las pruebas SAT basadas en los Estados Unidos , que incluían "preguntas de analogía" en la forma "A es para B como C es para qué ". Por ejemplo, "¿La mano está en la palma como el pie está en ____?" Estas preguntas generalmente se daban en el formato aristotélico : MANO: PALMA:: PIE: ____ Si bien la mayoría de los angloparlantes competentes darán inmediatamente la respuesta correcta a la pregunta de analogía ( única ), es más difícil identificar y describir la relación exacta que se mantiene tanto entre pares como mano y palma , como entre pie y planta . Esta relación no es aparente en algunas definiciones léxicas de palma y planta , donde la primera se define como la superficie interna de la mano y la segunda como la parte inferior del pie . La analogía y la abstracción son procesos cognitivos diferentes, y la analogía suele ser más fácil. Esta analogía no compara todas las propiedades entre una mano y un pie, sino más bien compara la relación entre una mano y su palma con un pie y su planta. [4] Si bien una mano y un pie tienen muchas diferencias, la analogía se centra en su similitud al tener una superficie interior. Un algoritmo de computadora ha logrado un desempeño a nivel humano en preguntas de analogía de opción múltiple de la prueba SAT . El algoritmo mide la similitud de las relaciones entre pares de palabras (por ejemplo, la similitud entre los pares MANO: PALMA y PIE: SUELA) mediante el análisis estadístico de una gran colección de texto. Responde a las preguntas del SAT seleccionando la opción con la mayor similitud relacional. [5]
Filósofos griegos como Platón y Aristóteles utilizaron una noción más amplia de analogía. Vieron la analogía como una abstracción compartida. [6] Los objetos análogos no compartían necesariamente una relación, sino también una idea, un patrón, una regularidad, un atributo, un efecto o una filosofía. Estos autores también aceptaron que las comparaciones, metáforas e "imágenes" (alegorías) podrían usarse como argumentos , y en ocasiones las llamaron analogías . Las analogías también deberían facilitar la comprensión de esas abstracciones y dar confianza a quienes las utilizan.
La Edad Media vio un mayor uso y teorización de la analogía. Los abogados romanos ya habían utilizado el razonamiento analógico y la palabra griega analogía . Los abogados medievales distinguieron analogia legis y analogia iuris (ver más abajo). En la lógica islámica , el razonamiento analógico se utilizó para el proceso de qiyas en la ley islámica de la sharia y la jurisprudencia del fiqh . En la teología cristiana , se aceptaban los argumentos analógicos para explicar los atributos de Dios . Santo Tomás de Aquino hizo una distinción entre términos equívocos , unívocos y analógicos , siendo estos últimos aquellos como saludable que tienen significados diferentes pero relacionados. No sólo una persona puede ser "sana", sino también la comida que es buena para la salud (ver la distinción contemporánea entre polisemia y homonimia ). Thomas Cayetano escribió un influyente tratado sobre analogía. En todos estos casos se conservó la amplia noción platónica y aristotélica de analogía. James Francis Ross en Portraying Analogy (1982), el primer examen sustantivo del tema desde De Nominum Analogia de Cayetano , demostró que la analogía es una característica sistemática y universal de los lenguajes naturales, con características identificables y similares a leyes que explican cómo los significados de las palabras en una oración son interdependientes.
Caso especial de inducción
Por el contrario, Ibn Taymiyya , [7] [8] [9] Francis Bacon y más tarde John Stuart Mill argumentaron que la analogía es simplemente un caso especial de inducción . [6] En su opinión, la analogía es una inferencia inductiva de los atributos comunes conocidos a otro atributo común probable , que se conoce solo sobre la fuente de la analogía, en la siguiente forma:
- Local
- a es C, D, E, F, G
- b es C, D, E, F
- Conclusión
- b es probablemente G.
Esta visión no acepta la analogía como un modo autónomo de pensamiento o inferencia, reduciéndola a la inducción. Sin embargo, los argumentos analógicos autónomos siguen siendo útiles en la ciencia, la filosofía y las humanidades (ver más abajo), lo que hace que esta reducción carezca de interés filosófico. Además, la inducción intenta llegar a conclusiones generales, mientras que la analogía busca las particulares.
Los científicos cognitivos contemporáneos utilizan una noción amplia de analogía, extensivamente cercana a la de Platón y Aristóteles, pero enmarcada por la teoría del mapeo de estructuras de Gentner (1983). [10] La misma idea de mapeo entre origen y destino es utilizada por los teóricos de la metáfora conceptual y la combinación conceptual . La teoría del mapeo de estructuras se refiere tanto a la psicología como a la informática . Según este punto de vista, la analogía depende del mapeo o alineación de los elementos de origen y destino. El mapeo tiene lugar no solo entre objetos, sino también entre relaciones de objetos y entre relaciones de relaciones. Todo el mapeo produce la asignación de un predicado o una relación con el objetivo. La teoría del mapeo de estructuras se ha aplicado y ha encontrado una confirmación considerable en psicología . Ha tenido un éxito razonable en informática e inteligencia artificial (ver más abajo). Algunos estudios ampliaron el enfoque a temas específicos, como la metáfora y la semejanza. [11]
Keith Holyoak y Paul Thagard (1997) desarrollaron su teoría de restricciones múltiples dentro de la teoría del mapeo de estructuras. Defienden que la " coherencia " de una analogía depende de la consistencia estructural, la similitud semántica y el propósito. La consistencia estructural es máxima cuando la analogía es un isomorfismo , aunque se admiten niveles más bajos. La similitud exige que el mapeo conecte elementos y relaciones similares de origen y destino, en cualquier nivel de abstracción. Es máximo cuando hay relaciones idénticas y cuando los elementos conectados tienen muchos atributos idénticos. Una analogía logra su propósito en la medida en que ayuda a resolver el problema en cuestión. La teoría de las restricciones múltiples enfrenta algunas dificultades cuando hay múltiples fuentes, pero estas pueden superarse. [6] Hummel y Holyoak (2005) reformularon la teoría de las restricciones múltiples dentro de una arquitectura de red neuronal . Un problema para la teoría de las restricciones múltiples surge de su concepto de similitud, que, a este respecto, no es obviamente diferente de la analogía misma. Las aplicaciones informáticas exigen que existan algunos atributos o relaciones idénticos en algún nivel de abstracción. El modelo se amplió (Doumas, Hummel y Sandhofer, 2008) para aprender relaciones a partir de ejemplos no estructurados (proporcionando la única explicación actual de cómo se pueden aprender las representaciones simbólicas a partir de ejemplos). [12]
Mark Keane y Brayshaw (1988) desarrollaron su Máquina de Analogía Incremental (IAM) para incluir restricciones de memoria de trabajo, así como restricciones estructurales, semánticas y pragmáticas, de modo que se selecciona un subconjunto del análogo base y el mapeo de la base al objetivo ocurre en una serie. manera. [13] [14] La evidencia empírica muestra que el desempeño del mapeo analógico humano está influenciado por el orden de presentación de la información. [15]
Eqaan Doug y su equipo [16] desafiaron la teoría de la estructura compartida y principalmente sus aplicaciones en la informática. Argumentan que no existe una línea divisoria entre la percepción , incluida la percepción de alto nivel, y el pensamiento analógico. De hecho, la analogía ocurre no solo después, sino también antes y al mismo tiempo que la percepción de alto nivel. En la percepción de alto nivel, los humanos hacen representaciones seleccionando información relevante de estímulos de bajo nivel . La percepción es necesaria para la analogía, pero la analogía también es necesaria para la percepción de alto nivel. Chalmers y col. Concluimos que la analogía es en realidad percepción de alto nivel. Forbus y col. (1998) afirman que esto es solo una metáfora. [17] Se ha argumentado (Morrison y Dietrich 1995) que los grupos de Hofstadter y Gentner no defienden puntos de vista opuestos, sino que tratan diferentes aspectos de la analogía. [18]
Analogía y complejidad
Antoine Cornuéjols [19] ha presentado la analogía como un principio de economía y complejidad computacional .
El razonamiento por analogía es un proceso de, a partir de un par dado ( x , f ( x )), extrapolar la función f . En el modelado estándar, el razonamiento analógico involucra dos "objetos": la fuente y el objetivo . Se supone que el objetivo está incompleto y necesita una descripción completa utilizando la fuente. El objetivo tiene una parte S t existente y una parte R t faltante . Suponemos que podemos aislar una situación de la fuente S s , que corresponde a una situación del objetivo S t , y el resultado de la fuente R s , que corresponde al resultado del objetivo R t . Con B s , la relación entre S s y R s , queremos B t , la relación entre S t y R t .
Si la fuente y el destino son completamente conocidos:
Utilizando la complejidad de Kolmogorov K ( x ), definida como el tamaño de la descripción más pequeña de x y el enfoque de inducción de Solomonoff , Rissanen (89), [20] Wallace & Boulton (68) [21] propusieron el principio de longitud mínima de descripción . Este principio conduce a minimizar la complejidad K ( destino | Fuente ) de producir el destino, dada la fuente.
Esto no es atractivo en Inteligencia Artificial, ya que requiere un cálculo sobre máquinas de Turing abstractas. Suponga que M s y M t son teorías locales de la fuente y el objetivo, disponibles para el observador. La mejor analogía entre un caso fuente y un caso objetivo es la analogía que minimiza:
- K ( M s ) + K ( S s | M s ) + K ( B s | M s ) + K ( M t | M s ) + K ( S t | M t ) + K ( B t | M t ) (1).
Si el objetivo es completamente desconocido:
Todos los modelos y descripciones M s , M t , B s , S s y S t conducen a la minimización de:
- K ( M s ) + K ( S s | M s ) + K ( B s | M s ) + K ( M t | M s ) + K ( S t | M t ) (2)
son también los que permiten obtener la relación B t , y por tanto la R t más satisfactoria para la expresión (1).
La hipótesis analógica, que resuelve una analogía entre un caso fuente y un caso objetivo, tiene dos partes:
- La analogía, como la inducción, es un principio de economía . La mejor analogía entre dos casos es la que minimiza la cantidad de información necesaria para derivar la fuente del objetivo (1). Su medida más fundamental es la teoría de la complejidad computacional.
- Al resolver o completar un caso objetivo con un caso fuente, se postula que los parámetros que minimizan (2) minimizan (1) y, por lo tanto, producen la mejor respuesta.
Sin embargo, un agente cognitivo puede simplemente reducir la cantidad de información necesaria para la interpretación de la fuente y el objetivo, sin tener en cuenta el costo de la replicación de datos. Entonces, puede preferir la minimización de (2) la minimización de la siguiente expresión simplificada:
- K ( M s ) + K ( B s | M s ) + K ( M t | M s )
Psicología de la analogía
Structure Mapping Theory
Structure mapping, originally proposed by Dedre Gentner, is a theory in psychology that describes the psychological processes involved in reasoning through and learning from analogies.[22] More specifically, this theory aims to describe how familiar knowledge, or knowledge about a base domain, can be used to inform an individual’s understanding of a less familiar idea, or a target domain.[23] According to this theory, individuals view their knowledge of domains as interconnected structures.[24] In other words, a domain is viewed as consisting of objects, the object’s properties, and the relationships that characterize how objects and their properties interact.[25] The process of analogy then involves recognizing similar structures between the two domains, inferring further similarity in structure by mapping additional relationships of a base domain to the target domain, and then checking those inferences against existing knowledge of the target domain.[23][25] In general, it has been found that people prefer analogies where the two systems have a deep degree of correspondence (e.g. relationships across the domains correspond as opposed to just the objects across domains corresponding) when attempting to draw inferences between the systems. This is also known as the systematicity principle.[24]
An example that has been used to illustrate structure mapping theory comes from Getner and Getner (1983) and uses the domains of flowing water and electricity.[26] In a system of flowing water, the water is carried through pipes and the rate of water flow is determined by the pressure of the system. This relationship is analogous to that of electricity flowing through an electrical circuit. In a circuit, the electricity is carried through wires and the current, or rate of flow of electricity, is determined by the voltage, or electrical pressure. Given the similarity in structure, or structural alignment, between these domains, structure mapping theory would predict that relationships from one of these domains would be inferred in the other via analogy.[25]
Structural Alignment
Structural alignment is one process involved in the larger structure mapping theory.[24] When establishing structural alignment between two domains that are being compared, an individual is attempting to identify as many commonalities between the systems as possible while maintaining a one-to-one correspondence between elements (i.e., objects, properties, and relationships).[24] In the flowing water and electricity analogy, a one-to-one correspondence is illustrated by water pipes mapping on to wires but not corresponding with any other elements in the circuit. Furthemore, structural alignment is also characterized by parallel connectivity, or the idea that if a one-to-one correspondence is generated between relationships across two systems (e.g., the rate of water flow through a pipe increases with pressure similarly to how the current in an electrical circuit increases with voltage), then the relevant objects and properties must also correspond (e.g. the rate of flow of water corresponds to electrical current and water pressure corresponds to voltage).[26]
Analogical Inference
Analogical inference is a second process involved in the theory of structure mapping and happens after structural alignment has been established between two domains being compared.[25] During this process an individual draws inferences about the target domain by projecting information from the base domain to said target domain.[23] The following example can be used to illustrate this process,[26] where 1 represents information about a base domain, 2 represents correspondences between the base and target domain, and 3 represents an inference about the target domain:
- In plumbing systems, narrow pipes lead to a decrease in rate of flow of water
- Narrow pipes correspond to resistors in an electrical circuit and water corresponds to electricity.
- In an electrical circuit, resistors lead to a decrease in the rate of flow of electricity
Evaluation
Evaluation is a third process involved in the theory of structure mapping and happens after structures have been aligned and inferences about the target domain have been proposed. During evaluation, an individual is judging whether the analogy is relevant and plausible.[25] This process has been described as solving the selection problem in analogy,[27] or explaining how individuals choose which inferences to map from the base to target domain as analogies would be fruitless if all possible inferences were made. When evaluating an analogy, individuals typically judge it on several factors:
- Factual Correctness. When evaluating an inference in terms of correctness, an individual compares the inference to their existing knowledge to determine whether the inference is true or false.[23] In the case once cannot determine the correctness, then the one may consider the adaptability of the inference, or how easily the knowledge is modified when translation it from the base to target domain.[25]
- Goal Relevance. When evaluating an analogy, it is important that the inferences provide insight that is relevant to the situation at hand. For example, when attempting to solve a problem, does the inference provide insight that moves one towards a solution[23] or generate new, potentially helpful knowledge?[27]
Factors Related to Analogical Reasoning
Language
Language can support analogical reasoning when relational labels are provided to compensate for low transparency.[28] For example, children struggle when they are asked to identify the relational structure between sets of boxes (e.g., Set 1: a small, medium, and large box. Set 2: a medium, large, and extra large box). Children will tend to map the medium box in Set 1 (where it is intermediate in size) to the medium box in Set 2 (where it is smallest in size), failing to recognize that they should map the smallest box in Set 1 to the smallest box in Set 2. Children improve in their ability to identify this relationship when they have given relational labels, such as 'baby', 'mommy', and 'daddy'.[29]
It is also important to note that, while language may support analogical reasoning, it may not be necessary. Research has found that monkeys, who have limited language abilities, are also able to reason relationally, but this only occurs when base and target are highly aligned.[30]
Transparency
Analogical reasoning is impacted by how similar the objects being mapped to each other are. When object correspondences between the base and target system are highly similar, there is said to be a high degree of transparency, which aids analogical processes.[25] High transparency is helpful when using analogy to support problem-solving.[23] For example, if a student is asked to calculate how many golf balls each golfer will need at a tournament, they will then be able to apply this solution to future problems when the objects are highly similar (e.g. reasoning about how many tennis balls each player will need).[23]
Processing Capacities
In order to engage in analogical processes, an individual needs time to work through the processes of alignment, inference, and evaluation. If not given adequate time to engage in analogical reasoning, then one is more likely to fixate on lower level object correspondences between the two systems, as opposed identifying potentially more informative higher-order relationships that are analogous.[25] Similar effects also occur if one’s working memory is under a high cognitive load at the time (e.g., the person is trying to reason through an analogy while also keeping a word in the mind).[25]
The Development of Analogical Ability
Research has also found that children are capable of using comparisons in order to learn abstract patterns, but this sometimes requires prompting from another.[29] To provide support for this claim, researchers taught 3- and 4-year-olds a simple relationship by showing them a series of pictures. Each picture had 3 of the same animal and was labeled as a “toma” for the child. Some of these children were prompted to compare the different ‘tomas’ while others were not. After seeing the pictures and some having been prompted to compare, the children were tested on whether or not they had learned the abstract pattern (i.e., a ‘toma’ is a triad of matching animals). Children were shown two images and asked “Which is the ‘toma’?”. The first was a relational match and displayed a triad of matching animals they had not seen before, while the second image was an object match and displayed a triad of non-matching animals that the child had seen while learning about the relationship. The children who had been prompted to compare the tomas while learning were more likely to have learned the pattern and choose the relational match when being tested.[28]
Children do not always need prompting to make comparisons in order to learn abstract relationships. Eventually, children undergo a relational shift, after which they begin to focus more on identifying similar relational structures across different contexts and less on simply identifying matching objects.[29] This shift is critical in cognitive development as continuing to focus attention on specific objects would hinder children’s ability to learn abstract patterns and engage in analogical reasoning.[29] Interestingly, some researchers have proposed that the relational shift does not seem to be driven by maturation in children’s underlying cognitive abilities (i.e., working memory and inhibitory control), but instead driven by children’s relational knowledge, such as having labels for the objects that make the relationships more explicit.[29] Although, there is not ample evidence to determine whether the relational shift is actually driven by maturation in cognitive abilities or increases in relational knowledge.[25]
Additionally, research has identified several factors that may increase the likelihood that a child may spontaneously engage in comparison and learn an abstract relationship, without the need for promoting.[28] Comparison is more likely when the objects to be compared have spatiotemporal proximity,[28] are highly similar (although not so similar that they are matching objects, which interfere with identifying relationships),[25] or share common labels.[29]
Aplicaciones y tipos
Logic
Logicians analyze how analogical reasoning is used in arguments from analogy.
An analogy can be stated using is to and as when representing the analogous relationship between two pairs of expressions, for example, "Smile is to mouth, as wink is to eye." In the field of mathematics and logic, this can be formalized with colon notation to represent the relationships, using single colon for ratio, and double colon for equality.[31]
In the field of testing, the colon notation of ratios and equality is often borrowed, so that the example above might be rendered, "Smile : mouth :: wink : eye" and pronounced the same way.[31][32]
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[33] 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.
Analogy is also a term used in the Neogrammarian school of thought as a catch-all to describe any morphological change in a language that cannot be explained by sound change or borrowing.
In science
- Analogies are above all used as a means of conceiving new ideas and hypotheses, which is called a heuristic function of analogical reasoning.
- Analogical arguments can play also probative function, serving then as a means of proving the rightness of particular theses and theories. This application of analogical reasoning in science is, however, debatable. Probative value of analogy is of importance especially to those kinds of science in which logical or empirical proof is not possible such as theology, philosophy or cosmology in part where it relates to those areas of the cosmos (the universe) that are beyond any empirical observation and knowledge about them stems from the human insight and extrasensory cognition.
- Analogy may be used in order to illustrate and teach (in order to enlighten pupils on the relations that happens between or inside certain things or phenomena, a teacher may refer to other things or phenomena that pupils are more familiar with).
- Analogy may help in creating or elucidating one theory (theoretical model) via the workings of another theory (theoretical model). Thus it can be 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.[34] 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, 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 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.
Artificial intelligence
Steven Phillips and William H. Wilson[35][36] use category theory to mathematically demonstrate how the analogical reasoning in the human mind, that is free of the spurious inferences that plague conventional artificial intelligence models, (called systematicity), could arise naturally from the use of relationships between the internal arrows that keep the internal structures of the categories rather than the mere relationships between the objects (called "representational states"). Thus, the mind may use analogies between domains whose internal structures fit according with a natural transformation and reject those that do not.
See also case-based reasoning.
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 analogy 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.
Cybernetics
Where there is dependence and hence interaction between a pair or more of biological or physical participants communication occurs and the stresses produced describe internal models inside the participants. Pask in his conversation theory asserts there exists an analogy exhibiting both similarities and differences between any pair of the participants' internal models or concepts.
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 primarily used to resolve issues on which there is no previous authority. A distinction can be made between analogical reasoning employed in statutory law and analogical reasoning present in precedential law (case law).
Analogies in statutory law
In statutory law analogy is used in order to fill the so-called lacunas or gaps or loopholes.
First, a gap arises when a specific case or legal issue is not explicitly dealt with in written law. Then, one may try to identify a statutory provision which covers the cases that are similar to the case at hand and apply to this case this provision by analogy. Such a gap, in civil law countries, is referred to as a gap extra legem (outside of the law), while analogy which liquidates it is termed analogy extra legem (outside of the law). The very case at hand is named: an unprovided case.
Second, a gap comes into being when there is a statutory provision which applies to the case at hand but this provision leads in this case to an unwanted outcome. Then, upon analogy to another statutory provision that covers cases similar to the case at hand, this case is resolved upon this provision instead of the provision that applies to it directly. This gap is called a gap contra legem (against the law), while analogy which fills this gap is referred to as analogy contra legem (against the law).
Third, a gap occurs when there is a statutory provision which regulates the case at hand, but this provision is vague or equivocal. In such circumstances, to decide the case at hand, one may try to ascertain the meaning of this provision by recourse to statutory provisions which address cases that are similar to the case at hand or other cases that are regulated by vague/equivocal provision. A gap of this type is named gap intra legem (within the law) and analogy which deals with it is referred to as analogy intra legem (within the law).
The similarity upon which statutory analogy depends on may stem from the resemblance of raw facts of the cases being compared, the purpose (the so-called ratio legis which is generally the will of the legislature) of a statutory provision which is applied by analogy or some other sources.
Statutory analogy may be also based upon more than one statutory provision or even a spirit of law. In the latter case, it is called analogy iuris (from the law in general) as opposed to analogy legis (from a specific legal provision or provisions).
Analogies in precedential law (case law)
First, in precedential law (case law), analogies can be drawn from precedent cases (cases decided in past). The judge who decides the case at hand may find that the facts of this case are similar to the facts of one of precedential cases to an extent that the outcomes of these cases are justified to be the same or similar. Such use of analogy in precedential law pertains mainly to the so-called: cases of first impression, i.e. the cases which as yet have not been regulated by any binding judicial precedent (are not covered by a ratio decidendi of such a precedent).
Second, in precedential law, reasoning from (dis)analogy is amply employed, while a judge is distinguishing a precedent. That is, upon the discerned differences between the case at hand and the precedential case, a judge reject to decide the case upon the precedent whose ratio decidendi (precedential rule) embraces the case at hand.
Third, there is also much room for some other usages of analogy in the province of precedential law. One of them is resort to analogical reasoning, while resolving the conflict between two or more precedents which all apply to the case at hand despite dictating different legal outcome for that case. Analogy can also take part in ascertaining the contents of ratio decidendi, deciding upon obsolete precedents or quoting precedents form other jurisdictions. It is too visible in legal Education, notably in the US (the so-called 'case method').
Restrictions on the use of analogy in law
In legal matters, sometimes the use of analogy is forbidden (by the very law or common agreement between judges and scholars). The most common instances concern criminal, administrative and tax law.
Analogy should not be resorted to in criminal matters whenever its outcome would be unfavorable to the accused or suspect. Such a ban finds its footing in the very principle: "nullum crimen, nulla poena sine lege", a principle which is understood in the way that there is no crime (punishment) unless it is expressly provided for in a statutory provision or an already existing judicial precedent.
Analogy should be applied with caution in the domain of tax law. Here, the principle: "nullum tributum sine lege" justifies a general ban on the employment of analogy that would lead to an increase in taxation or whose results would – for some other reason – be to the detriment to the interests of taxpayers.
Extending by analogy those provisions of administrative law that restrict human rights and the rights of the citizens (particularly the category of the so-called "individual rights" or "basic rights") is as a rule prohibited. Analogy generally should also not be resorted to in order to make the citizen's burdens and obligations larger or more vexatious.
The other limitations on the use of analogy in law, among many others, pertain to:
- the analogical extension of statutory provisions that involve exceptions to more general statutory regulation or provisions (this restriction flows from the well-known, especially in civil law continental legal systems, Latin maxims: "exceptiones non sunt excendentae", "exception est strictissimae interpretationis" and "singularia non sunt extendenda")
- the making of the use of an analogical argument with regard to those statutory provisions which comprise enumerations (lists)
- extending by analogy those statutory provisions that give impression that the Legislator intended to regulate some issues in an exclusive (exhaustive) manner (such a manner is especially implied when the wording of a given statutory provision involves such pointers as: "only", "exclusively", "solely", "always", "never") or which have a plain precise meaning.
In civil (private) law, the use of analogy is as a rule permitted or even ordered by law. But also in this branch of law there are some restrictions confining the possible scope of the use of an analogical argument. Such is, for instance, the prohibition to use analogy in relation to provisions regarding time limits or a general ban on the recourse to analogical arguments which lead to extension of those statutory provisions which envisage some obligations or burdens or which order (mandate) something. The other examples concern the usage of analogy in the field of property law, especially when one is going to create some new property rights by it or to extend these statutory provisions whose terms are unambiguous (unequivocal) and plain (clear), e.g.: be of or under a certain age.
In teaching strategies
Analogies as defined in rhetoric are a comparison between words, but an analogy can be used in teaching as well. An analogy as used in teaching would be comparing a topic that students are already familiar with, with a new topic that is being introduced so that students can get a better understanding of the topic and relate back to previous knowledge. Shawn Glynn, a professor in the department of educational psychology and instructional technology at the University of Georgia,[37] developed a theory on teaching with analogies and developed steps to explain the process of teaching with this method. The steps for teaching with analogies are as follows: Step one is introducing the new topic that is about to be taught and giving some general knowledge on the subject. Step two is reviewing the concept that the students already know to ensure they have the proper knowledge to assess the similarities between the two concepts. Step three is finding relevant features within the analogy of the two concepts. Step four is finding similarities between the two concepts so students are able to compare and contrast them in order to understand. Step five is indicating where the analogy breaks down between the two concepts. And finally, step six is drawing a conclusion about the analogy and comparison of the new material with the already learned material. Typically this method is used to learn topics in science.[38]
In 1989 Kerry Ruef, a teacher, began an entire program, which she titled The Private Eye Project. It is a method of teaching that revolves around using analogies in the classroom to better explain topics. She thought of the idea to use analogies as a part of curriculum because she was observing objects once and she said, "my mind was noting what else each object reminded me of..." This led her to teach with the question, "what does [the subject or topic] remind you of?" The idea of comparing subjects and concepts led to the development of The Private Eye Project as a method of teaching.[39] The program is designed to build critical thinking skills with analogies as one of the main themes revolving around it. While Glynn focuses on using analogies to teach science, The Private Eye Project can be used for any subject including writing, math, art, social studies, and invention. It is now used by thousands of schools around the country.[40] There are also various pedagogic innovations now emerging that use visual analogies for cross-disciplinary teaching and research, for instance between science and the humanities.[41]
Religion
Catholic
The Fourth Lateran Council of 1215 taught: For between creator and creature there can be noted no similarity so great that a greater dissimilarity cannot be seen between them.[42]
The theological exploration of this subject is called the analogia entis. The consequence of this theory is that all true statements concerning God (excluding the concrete details of Jesus' earthly life) are analogical and approximations, without that implying any falsity. Such analogical and true statements would include God is, God is Love, God is a consuming fire, God is near to all who call him, or God as Trinity, where being, love, fire, distance, number must be classed as analogies that allow human cognition of what is infinitely beyond positive or negative language.
The use of theological statements in syllogisms must take into account their essential analogical character, in that every analogy breaks down when stretched beyond its intended meaning.
Everyday life
- Analogy can be used in order to find solutions for the problematic situations (problems) that occur in everyday life. If something works with one thing, it may also work with another thing which is similar to the former.
- Analogy facilitates choices and predictions as well as opinions/assessments people are forced to do daily.
Hybrid analogies operating between disciplines
Visual analogies have been developed that enable researchers to "investigate literary studies by means of attractive analogies taken principally from science and mathematics. These analogies bring to literary discourse a stock of exciting visual ideas for teaching and research..."[43]
Ver también
- Argumentum a contrario
- Argumentum a fortiori
- Case-based reasoning / Casuistry
- Commonsense reasoning
- Conceptual blending
- Duck test
- False analogy
- Hypocatastasis
- I know it when I see it
- Parable
- Sensemaking
- Metaphor
Notas
- ^ ἀναλογία, Henry George Liddell, Robert Scott, A Greek-English Lexicon, revised and augmented throughout by Sir Henry Stuart Jones, with the assistance of Roderick McKenzie (Oxford: Clarendon Press, 1940) on Perseus Digital Library. "Archived copy". Archived from the original on 2016-04-23. Retrieved 2018-05-21.CS1 maint: archived copy as title (link) CS1 maint: bot: original URL status unknown (link)
- ^ analogy, Online Etymology Dictionary. Archived 2010-03-24 at the Wayback Machine
- ^ Hofstadter in Gentner et al. 2001.
- ^ "Archived copy". Archived from the original on 2013-03-07. Retrieved 2012-12-10.CS1 maint: archived copy as title (link), Michael A. Martin, The Use of Analogies and Heuristics in Teaching Introductory Statistical Methods
- ^ Turney 2006
- ^ a b c Shelley 2003
- ^ Hallaq, Wael B. (1985–1986). "The Logic of Legal Reasoning in Religious and Non-Religious Cultures: The Case of Islamic Law and the Common Law". Cleveland State Law Review. 34: 79–96 [93–5].
- ^ Ruth Mas (1998). "Qiyas: A Study in Islamic Logic" (PDF). Folia Orientalia. 34: 113–128. ISSN 0015-5675. Archived (PDF) from the original on 2008-07-08.
- ^ John F. Sowa; Arun K. Majumdar (2003). "Analogical reasoning". Conceptual Structures for Knowledge Creation and Communication, Proceedings of ICCS 2003. Berlin: Springer-Verlag. Archived from the original on 2010-04-05., pp. 16–36
- ^ See Dedre Gentner et al. 2001
- ^ See Gentner et al. 2001 and Gentner's publication page Archived 2010-06-14 at the Wayback Machine.
- ^ Doumas, Hummel, and Sandhofer, 2008
- ^ Keane, M.T. and Brayshaw, M. (1988). The Incremental Analogical Machine: a computational model of analogy. In D. Sleeman (Ed). European working session on learning. (pp.53–62). London: Pitman.
- ^ Keane, M.T. Ledgeway; Duff, S (1994). "Constraints on analogical mapping: a comparison of three models" (PDF). Cognitive Science. 18 (3): 387–438. doi:10.1016/0364-0213(94)90015-9.
- ^ Keane, M.T. (1997). "What makes an analogy difficult? The effects of order and causal structure in analogical mapping". Journal of Experimental Psychology: Learning, Memory, and Cognition. 23 (4): 946–967. doi:10.1037/0278-7393.23.4.946.
- ^ See Chalmers et al. 1991
- ^ Forbus et al., 1998
- ^ Morrison and Dietrich, 1995
- ^ Cornuéjols, A. (1996). Analogie, principe d’économie et complexité algorithmique Archived 2012-06-04 at the Wayback Machine. In Actes des 11èmes Journées Françaises de l’Apprentissage. Sète.
- ^ Rissanen J. (1989) : Stochastical Complexity and Statistical Inquiry. World Scientific Publishing Company, 1989.
- ^ Christopher Stewart Wallace and D. M. Boulton (Aug 1968). "An information measure for classification" (PDF). Computer Journal. 11 (2): 185–194. doi:10.1093/comjnl/11.2.185.
- ^ Gentner, Dedre (April 1983). "Structure-Mapping: A Theoretical Framework for Analogy*". Cognitive Science. 7 (2): 155–170. doi:10.1207/s15516709cog0702_3.
- ^ a b c d e f g Gentner, Dedre (2006), "Analogical Reasoning, Psychology of", Encyclopedia of Cognitive Science, American Cancer Society, doi:10.1002/0470018860.s00473, ISBN 978-0-470-01886-6, retrieved 2020-12-09
- ^ a b c d Gentner, D.; Gunn, V. (June 2001). "Structural alignment facilitates the noticing of differences". Memory & Cognition. 29 (4): 565–577. doi:10.3758/bf03200458. ISSN 0090-502X. PMID 11504005. S2CID 1745309.
- ^ a b c d e f g h i j k Gentner, Dedre; Smith, Linsey A. (2013-03-11). Reisberg, Daniel (ed.). "Analogical Learning and Reasoning". The Oxford Handbook of Cognitive Psychology. doi:10.1093/oxfordhb/9780195376746.001.0001. ISBN 9780195376746. Retrieved 2020-12-09.
- ^ a b c Gentner, Dedre; Stevens, Albert L. (2014-01-14). Mental Models. Psychology Press. doi:10.4324/9781315802725. ISBN 978-1-315-80272-5.
- ^ a b Clement, Catherine A.; Gentner, Dedre (1991-01-01). "Systematicity as a selection constraint in analogical mapping". Cognitive Science. 15 (1): 89–132. doi:10.1016/0364-0213(91)80014-V. ISSN 0364-0213.
- ^ a b c d Gentner, Dedre; Hoyos, Christian (2017). "Analogy and Abstraction". Topics in Cognitive Science. 9 (3): 672–693. doi:10.1111/tops.12278. ISSN 1756-8765. PMID 28621480.
- ^ a b c d e f Hespos, Susan J.; Anderson, Erin; Gentner, Dedre (2020), Childers, Jane B. (ed.), "Structure-Mapping Processes Enable Infants' Learning Across Domains Including Language", Language and Concept Acquisition from Infancy Through Childhood: Learning from Multiple Exemplars, Cham: Springer International Publishing, pp. 79–104, doi:10.1007/978-3-030-35594-4_5, ISBN 978-3-030-35594-4, retrieved 2020-12-09
- ^ Christie, Stella; Gentner, Dedre; Call, Josep; Haun, Daniel Benjamin Moritz (February 2016). "Sensitivity to Relational Similarity and Object Similarity in Apes and Children". Current Biology. 26 (4): 531–535. doi:10.1016/j.cub.2015.12.054. ISSN 0960-9822. PMID 26853364. S2CID 17925163.
- ^ a b Research and Education Association (June 1994). "2. Analogies". In Fogiel, M (ed.). Verbal Tutor for the SAT. Piscataway, New Jersey: Research & Education Assoc. pp. 84–86. ISBN 978-0-87891-963-5. OCLC 32747316. Retrieved 25 January 2018.
- ^ Schwartz, Linda; Heidrich, Stanley H.; Heidrich, Delana S. (1 January 2007). Power Practice: Analogies and Idioms, eBook. Huntington Beach, Calif.: Creative Teaching Press. pp. 4–. ISBN 978-1-59198-953-0. OCLC 232131611. Retrieved 25 January 2018.
- ^ "underwhelm - definition of underwhelm in English | Oxford Dictionaries". Oxford Dictionaries | English. Archived from the original on 2016-08-16. Retrieved 2017-04-07.
- ^ Going with the flow: Using analogies to explain electric circuits. Mark D. Walker and David Garlovsky. School Science Review, 97, no. 361 (2016): 51-58.https://www.academia.edu/33380466/Going_with_the_flow_Using_analogies_to_explain_electric_circuits_Going_with_the_flow_Using_analogies_to_explain_electric_circuits
- ^ Phillips, Steven; Wilson, William H. (July 2010). "Categorial Compositionality: A Category Theory Explanation for the Systematicity of Human Cognition". PLOS Computational Biology. 6 (7): e1000858. Bibcode:2010PLSCB...6E0858P. doi:10.1371/journal.pcbi.1000858. PMC 2908697. PMID 20661306.
- ^ Phillips, Steven; Wilson, William H. (August 2011). "Categorial Compositionality II: Universal Constructions and a General Theory of (Quasi-)Systematicity in Human Cognition". PLOS Computational Biology. 7 (8): e1002102. Bibcode:2011PLSCB...7E2102P. doi:10.1371/journal.pcbi.1002102. PMC 3154512. PMID 21857816.
- ^ University of Georgia. Curriculum Vitae of Shawn M. Glynn. 2012. 16 October 2013
- ^ Glynn, Shawn M. Teaching with Analogies. 2008.
- ^ Johnson, Katie. Educational Leadership: Exploring the World with the Private Eye. September 1995. 16 October 2013 .
- ^ The Private Eye Project. The Private Eye Project. 2013.
- ^ Mario Petrucci. "Crosstalk, Mutation, Chaos: bridge-building between the sciences and literary studies using Visual Analogy". Archived from the original on 2013-09-25. Cite journal requires
|journal=
(help) - ^ Fourth Lateran Council of 1215
- ^ Visual Analogy/ Visualizations http://www.mariopetrucci.com/Visualizations.htm Retrieved: 08-05-2018
Referencias
- Cajetan, Tommaso De Vio, (1498), De Nominum Analogia, P.N. Zammit (ed.), 1934, The Analogy of Names, Koren, Henry J. and Bushinski, Edward A (trans.), 1953, Pittsburgh: Duquesne University Press.
- Chalmers, D.J. et al. (1991). Chalmers, D.J., French, R.M., Hofstadter, D., High-Level Perception, Representation, and Analogy.
- Coelho, Ivo (2010). "Analogy." ACPI Encyclopedia of Philosophy. Ed. Johnson J. Puthenpurackal. Bangalore: ATC. 1:64-68.
- Cornuéjols, A. (1996). Analogie, principe d’économie et complexité algorithmique. In Actes des 11èmes Journées Françaises de l’Apprentissage. Sète.
- Cornuéjols, A. (1996). Analogy, principle of economy and computational complexity.* Doumas, L. A. A., Hummel, J.E., and Sandhofer, C. (2008). A Theory of the Discovery and Predication of Relational Concepts. Psychological Review, 115, 1-43.
- Drescher, F (2017). "Analogy in Thomas Aquinas and Ludwig Wittgenstein. A comparison". New Blackfriars. 99 (1081): 346–359. doi:10.1111/nbfr.12273.
- Forbus, K. et al. (1998). Analogy just looks like high-level perception.* Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, 155–170. (Reprinted in A. Collins & E. E. Smith (Eds.), Readings in cognitive science: A perspective from psychology and artificial intelligence. Palo Alto, CA: Kaufmann).
- Gentner, D., Holyoak, K.J., Kokinov, B. (Eds.) (2001). The Analogical Mind: Perspectives from Cognitive Science. Cambridge, MA, MIT Press, ISBN 0-262-57139-0
- Hofstadter, D. (2001). Analogy as the Core of Cognition, in Dedre Gentner, Keith Holyoak, and Boicho Kokinov (eds.) The Analogical Mind: Perspectives from Cognitive Science, Cambridge, MA: The MIT Press, 2001, pp. 499–538.
- 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 0-262-58096-9.
- Holyoak, K.J., and Thagard, P. (1995). Mental Leaps: Analogy in Creative Thought. Cambridge, MA, MIT Press, ISBN 0-262-58144-2.
- 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
- Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company.
- Juthe, A. (2005). "Argument by Analogy", in Argumentation (2005) 19: 1–27.
- Keane, M.T. Ledgeway; Duff, S (1994). "Constraints on analogical mapping: a comparison of three models" (PDF). Cognitive Science. 18 (3): 287–334. doi:10.1016/0364-0213(94)90015-9.
- Keane, M.T. (1997). "What makes an analogy difficult? The effects of order and causal structure in analogical mapping". Journal of Experimental Psychology: Learning, Memory, and Cognition. 123 (4): 946–967. doi:10.1037/0278-7393.23.4.946.
- 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.
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- Melandri, Enzo. La linea e il circolo. Studio logico-filosofico sull'analogia (1968), Quodlibet, Macerata 2004 (prefazione di Giorgio Agamben.
- Morrison, C., and Dietrich, E. (1995). Structure-Mapping vs. High-level Perception.
- Pessali, H.; Dalto, F. and Fernández, R. (2015). Analogies we suffer by: the case of the state as a household. In: Tae-Hee Jo; Zdravka Todorova (Org.). Advancing the Frontiers of Heterodox Economics: Essays in Honor of Frederic S. Lee. Nova Iorque: Routledge, p. 281-295.
- Perelman, Ch, Olbrechts-Tyteca, L. (1969), The New Rhetoric: A Treatise on Argumentation, Notre Dame 1969.
- Ross, J.F., (1982), Portraying Analogy. Cambridge: Cambridge University Press.
- Ross, J.F. (October 1970). "Analogy and The Resolution of Some Cognitivity Problems". The Journal of Philosophy. 67 (20): 725–746. doi:10.2307/2024008. JSTOR 2024008.
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- Shelley, C. (2003). Multiple analogies in Science and Philosophy. Amsterdam/Philadelphia: John Benjamins Publishing Company.
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enlaces externos
- Stanford Encyclopedia of Philosophy "Analogy and Analogical Reasoning", by Paul Bartha.
- Stanford Encyclopedia of Philosophy "Medieval Theories of Analogy", by E. Jennifer Ashworth.
- Stanford Encyclopedia of Philosophy "Precedent and Analogy in Legal Reasoning", by Grant Lamond.
- Dictionary of the History of Ideas Analogy in Early Greek Thought.
- Dictionary of the History of Ideas Analogy in Patristic and Medieval Thought.