Title of the Paper [16 point font]
Proposal of a Classification of Analogies
DAVID ALVARGONZÁLEZ
Department of Philosophy
University of Oviedo Campus de Humanidades, 33011 Oviedo
Spain
dalvar@uniovi.es
Abstract: In this paper, I will propose
a classification of analogies based on
their internal structure. Selecting the
criteria used in that classification first
requires discussing the minimal
constitutive parts of any analogy.
Accordingly, I will discuss the differ-
ences between analogy and similarity
and between analogy and “synalogy,”
and I will stress the importance of the
analogy of operations and procedures.
Finally, I will set forth a classification
of the different types of analogies,
which lends itself to a further under-
standing of the differences between
certain modulations of the general
idea of analogy, such as archetypes,
prototypes, models, simulations,
parables, paradigms, canons, maps,
thought experiments, myths, utopias,
dystopias and fables.
Résumé: Dans cet article, je pro-
poserai une classification des analo-
gies en fonction de leur structure
interne. La sélection des critères
utilisés dans cette classification
nécessite d'abord de discuter des
parties constantes essentielles de toute
analogie. En conséquence, je vais
discuter des différences entre l'analo-
gie et la similitude et entre l'analogie
et la synalogie, et je vais souligner
l'importance de l'analogie des opé-
rations et des procédures. Enfin, je
vais présenter une classification des
différents types d'analogies, qui
permet une meilleure compréhension
des différences entre certaines modu-
lations de l'idée générale d'analogie,
telles que les archétypes, les proto-
types, les modèles, les simulations, les
paraboles, les paradigmes, canons,
cartes, expériences de pensée, mythes,
utopies, dystopies et fables.
Keywords: Analogy, model, myth, simulation, thought experiment, utopia
1. Introduction
Years back, Jorge Luis Borges described the division of animals as
it appeared in a certain Chinese encyclopedia:
Animals (a) belonging to the emperor, (b) embalmed, (c) tame, (d)
sucking pigs, (e) sirens, (f) fabulous, (g) stray dogs, (h) included
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in the present classification, (i) frenzied, (j) innumerable, (k)
drawn with a very fine camelhair brush, (l) et cetera, (m) having
just broken the water pitcher, (n) that from a long way off look
like flies" (Borges 1993, pp. 104).
This whimsical classification differs significantly from the phylo-
genetic taxonomies of animals based on the theory of evolution,
just as there is an epistemic difference between the early alche-
mists’ lists of substances and the current periodic table of ele-
ments: the first being laundry lists and the second coherent, essen-
tial classifications stemming from scientific principles. Classifying
triangles or levers by color or material is extrinsic to geometry and
physics, whereas classifying triangles by relative length of side
(equilateral, isosceles and scalene) and categorizing levers into
three classes by the relative position of their constituent parts are
intrinsic to geometry and physics. When seeking to establish a
classification of internal structure, as occurs with the parts of
triangles (sides, angles) and levers (load, effort and fulcrum) in the
foregoing examples, identifying the relevant parts of the structures
being classified is key. Once the minimal constitutive parts of a
given structure have been correctly detected, it is possible to attain
a certain degree of completeness in the classification. Conversely,
the potency of a structure-based classification may serve to evalu-
ate the suitability of the foregoing constitutive parts. The structure
of this paper rests on the co-implication of these two tasks (classi-
fying and characterizing) as applied to the idea of analogy.
In addition to the overarching goal of coming to a structure-
based classification of analogies, in this paper I will first discuss
the constituent parts of any analogy. In the first section, I contend
that the idea of analogy arises not only from logic, argumentation
theory, linguistics, and perception psychology, but that it is also
necessary to take into account the existence of analogies appearing
in other contexts such as techniques, technologies, arts, religions,
laws, and sciences. The second section deals with the differences
between analogy and similarity. In the third section, I discuss the
difference between analogy and “synalogy.” In the fourth and fifth
sections, I comment on why asymmetry and same-level relation-
ship are constitutive features of any analogy. In the section sixth, I
stress the importance of analogies that compare operations and
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procedures. Finally, in the seventh section, I put forward a pro-
posal for classifying analogies according to their previously dis-
cussed internal structure.
2. The sources of the idea of analogy
By drawing from certain examples, this section looks to show that
a full understanding of the idea of analogy cannot be reached by
only considering the contents of logic, argumentation theory,
linguistics, and perception psychology, and that the existence of
analogies in other contexts, such as in techniques, in the arts, in the
rest of the sciences, in technologies, in religion and in ethical,
political, moral and juridical practice to name but a few, must also
be taken into account. Specifically, analogy cannot be reduced to a
variety of argumentation since there are many circumstances in
which analogies do not have a primarily argumentative function.
The use of analogies to resolve practical problems can be traced
throughout human phylogenies and ontogenesis. Ethologists have
recognized the presence of some kind of analogical behavior and
reasoning among non-human primates (Thompson and Oden 2000;
Oden et al. 2001), while prehistorians and archaeologists have
taken for granted the human use of analogies of relations and
operations to develop and improve on the most primitive pristine
techniques of the Stone Age (Shelley 1999). Furthermore, there is
a widespread and well-grounded agreement among cognitive
psychologists regarding the central role played by analogy in the
learning process of newborns, toddlers, infants, children, adoles-
cents and adults (Gentner and Holyoak 1997).
In historical times, analogy and the proportion between particu-
lar beings and situations were recognized as a way to address
practical problems (in techniques, engineering, law, rhetoric, war,
and policies), and as a tool to assay explanations (in science and
philosophy) and discuss practical issues (in politics, philosophy,
morality and religion). In legal reasoning, the study of cases (usu-
ally actual precedents) has been standard procedure since antiquity
both in common law systems (the stare decisis doctrine) where
prior cases are the primary source of law and analogies are con-
sistently drawn from such cases, and in civil law systems where
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case analogies are necessary to fill the gaps when the issue at stake
is not explicitly dealt with in written law (Weinreb 2005). The
central role of metaphor and allegory in persuasion and rhetoric
seems incontrovertible. In military studies, ancient battles have
frequently been taken as analogues of future confrontations so as
to develop new tactics and strategies and evaluate new war scenar-
ios; the same goes for the implementation of new practical policies
in peacetime.
Equally incontrovertible is the fertility of certain analogical
models and counter-models in the natural sciences. The most well-
known examples of the scientific use of analogies and thought
experiments include Galileo’s discussion of falling bodies, Ste-
vin’s inclined plane, Newton’s bodies projected in lines parallel to
the horizon, Newton’s rotating water bucket, Laplace’s genius,
Maxwell’s demon, impossible thermodynamic “machines,” Poin-
caré’s and Reichenbach’s flatland, Einstein’s chasing a light beam,
Einstein’s trains and elevators, and Schrödinger’s cat, to name but
a few. Reduced to a variety of argumentation, the pragmatic and
material contents of these scientific analogies may go unnoticed.
Indeed, certain analogies and thought experiments have become so
familiar that they have shaped our thinking and significantly struc-
tured our discourse on relevant issues in science (Brown 1991).
Metaphors, allegories, myths, thought experiments, utopias,
parables, fables, models and counter-models have also been fre-
quently used throughout the history of philosophy: Plato’s philo-
sophical myths (the ring of Gyges, the Amazons, Atlantis, the
androgynes, the cave, etc.), Avicenna’s floating man, Buridan’s
ass, Descartes’s evil genius, Leibniz’s mill, Locke’s prince migrat-
ed into the body of a cobbler, Hobbes’ Leviathan, renaissance
utopias, Putnam’s brain-in-a-vat and Twin Earth, Davidson’s
swamp man, Searle’s Chinese room, the Gettier belief argument,
and modern dystopias such as Aldous Huxley’s Brave New World,
may serve as an cursory list of the presence of such procedures in
philosophy. Perelman, among others, has highlighted the critical
role of analogy in the history of Western philosophy (Perelman
1969). Furthermore, as regards the three great religions of the
book, the parables and allegories contained in the holy texts are
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also based on analogies, which serve as a canon of righteous be-
havior (which means righteous operations and procedures).
As illustrated, analogies may be guided by a wide variety of
purposes: they can serve to address practical problems (in tech-
niques, technologies, engineering, law, rhetoric, war, and policies),
to assay theoretical explanations (in science and philosophy), to
structure new phenomena (in science), and to discuss arguments of
varying natures (in politics, philosophy, morality and religion).
The idea of analogy, though, does not boil down to a problem
of formal (or informal) logic or argumentation theory since it cuts
across a wide variety of human activities. The aforementioned
illustrations show that discussing this idea requires that a wide
range of disciplines and human activities be taken into considera-
tion. Acknowledging this fact is of vital importance to understand-
ing the argument for the analogy of operations and procedures that
I will make below in the sixth section and to generalizing certain
findings reached in the theory of argumentation.
3. The difference between analogy and mere similarity
The purpose of this section is to state the differences between
analogy and mere similarity. Attending to this issue is imperative
when discussing the scope of the idea of analogy and the outer
edges of the classification of analogies, as proposed below. As
found in most treatises, the lexical definitions of analogy always
include as their chief feature the comparison and similarity be-
tween two or more elements, and, therefore, may induce a confla-
tion of the two concepts. The word “analogy” comes from the
Latin analogia, which itself comes from the Greek analogia: the
prefix ana- meaning “over” (which is related to the Indo-European
root an meaning “over,” “up”), the word logos meaning ratio, and
the suffix -ia, meaning quality. The etymological structure of the
word, with the root “logos,” already suggests the quality of a ratio
among two or more things or concepts. Sufficient in ordinary
conversational contexts, such lexical and etymological characteri-
zations fall short when trying to understand the structure of the
underlying idea as it has been forged in philosophy.
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Certain cognitive psychologists contend that analogy should be
distinguished from mere similarity since “analogy is a clever,
sophisticated process used in creative discovery, whereas similari-
ty is a brute perceptual process that we share with the entire ani-
mal kingdom” (Gentner and Markman 1997, pp. 45-46). Gentner
and Toupin argue that analogy implies some manner of systema-
ticity and is not “a mere assortment of independent facts” (Gentner
and Toupin 1986, pp. 280). Developed by cognitive scientists, the
higher-level perception theory of analogy states a clear differentia-
tion between perceptual similarity and the higher-level construc-
tion of analogies (Mitchell 1993; Hofstadter 1995). From the
tenets of structure-mapping theory, Gentner, Rattermann, and
Forbus have concluded that similarity-based access to memory
depends on what they call “similarity,” while similarity of a match
(something very close to “analogy”) depends on the degree of
shared higher-order structures, including causal bindings (Gentner
et al. 1993). Irrespective, the perception of similarities between
elements and processes can be understood as a constitutive, albeit
not distinctive, feature of analogies. Analogies imply similarities
between their parts; nevertheless, mere similarity between images,
things or processes may also appear amid non-human animals,
apart from analogical constructions. In the same vein, in research
concerning data analysis, Barbosa and others have argued that
similarity refers to instances within the same class while analogy
involves different classes (Barbosa et al 2007).
In line with those findings I assume that:
1. Similarity, likeness and resemblance and the related antonyms
dissimilarity, unlikeness, and difference are dyadic relationships
grounded on direct perceptions. Consequently, the apprehension of
similarity and difference is present in actu exercito in the behav-
ioral repertoire of a wide range of non-human animals since it is a
capacity humans share with other organisms endowed with a
psychological makeup.
2. Analogy, though, is a more complex relationship implying the
determination of the relevant constituents of certain wholes and
the representation of proportions between them. Consequently,
constructing analogical relationships is a distinctive feature of
human beings endowed with a language of words—a feature that
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might be shared by certain trained-in-captivity great apes (Thomp-
son and Oden 2000). The pragma-dialectical philosophy of Frans
H. van Eemeren defines comparison in terms of relevant similarity
(Eemeren and Garssen 2014, pp. 45-49). In structure-mapping
theory, analogy implies the existence of shared structural relation-
ships in the mapping of the elements of source and target (Gentner
1983).
In analogy, the relationships of similarity between things and
processes are always partial. Were a total similarity to exist be-
tween them, we would speak of univocal terms, which are not
differentiable. An absolute differentiation and lack of any related-
ness is a feature of equivocal terms; analogous terms, for their
part, feature a certain similarity and a certain differentiation, with
some kind of relatedness. Accordingly, analogy could be under-
stood as an intermediate position between univocity and equivoci-
ty. In her meta-psychological theory of analogy, Dedre Gentner
characterizes analogy based on its intermediate place between
literal similarity (something very close to univocity) and anomaly
(which could be seen as a soft version of equivocity) (Gentner
1983, p. 161). Partial likeness is a constitutive feature of analogy
but is also a distinctive quality compared to literal similarity,
univocity, anomaly, and equivocity.
3. The difference between analogy and “synalogy”
The purpose of this section is to argue that certain types of analo-
gies (mainly the so-called analogies of attribution) are not truly
analogies and, consequently, should be excluded from the classifi-
cation of analogies sensu stricto.
In Aquinas, the idea of analogy played an important role since
theological anthropology implied that human beings were, in
certain features, analogous to God (Lyttkens 1952). By means of
analogical arguments, theologians tried to understand both human
nature as made in the image of God, and God’s attributes as de-
duced from those of humans. Inspired by Aristotle and partially
following Aquinas, Thomas de Vio (also known as Cajetan for
having been born in Gaeta, Naples) wrote his famous treatise On
the Analogy of Names (1498), from which I will take the distinc-
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tion of three kinds of analogies, since the structure of his analogy
of attribution is still taken into consideration in certain present-day
studies. The three kinds move from stronger to weaker:
1. The analogy of proper proportionality, which entails propor-
tionality between terms and relations and the symmetric relation-
ship between the analogues.
2. The analogy of improper proportionality or metaphoric propor-
tionality. In this case, the analogy refers only to the terms, and the
relationship between the analogues is not symmetrical: there is a
properly used noun and the other analogues are constructed meta-
phorically based on their relationship to the proper noun.
3. The analogy of attribution, which is the weakest, most improp-
er, non-symmetrical analogy since it implies the existence of a first
analogue or main analogue to which the others refer obliquely,
weakly and indirectly (by symbolic or causal relation). Aquinas
called this situation an “analogy because of diverse attributions”
(De Veritate 21, 4 ad 4 and Principles of Nature Ch. 6, No. 38).
In this case, there is always a main analogue, and the other ana-
logues acquire their meaning through very indirect reference to it.
For instance, an animal can, in the proper sense, be said to be
"healthy" (“a healthy animal”), but it can also be predicated indi-
rectly on urine (“healthy urine”) to mean that it is a sign of health,
on medicine (“healthy medicine”) to signify that it causes health,
and on a diet (“healthy diet”) to show that it preserves health. The
main analogue is the animal’s health, and the other analogues
(urine, medicine, diet) acquire their meaning through it (as signs or
causes of health). The first analogue is intrinsic, whereas the oth-
ers are said to arise by “extrinsic denomination.”
However, in this paper I maintain that Cajetan's analogy of at-
tribution is not a proper analogy governed by relations of similari-
ty, but is rather a relationship constructed through spatial/temporal
or causal contiguity: medicine, urine and diet are called “healthy”
by means of “contagion” with the healthy animal. Analogies nec-
essarily imply certain relations of similarity (not contiguity) and,
consequently, Cajetan's analogy of attribution is not a true analo-
gy. The relationships characterizing Cajetan’s analogies of attribu-
tion (Aristotle’s four causes) imply a “contiguity adjustment.”
Taking cues from Gustavo Bueno, I will call this kind of relation-
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ship “synalogy” taken from the Greek “sinalage” meaning "join-
ing" (Bueno 1999). Examples of synalogies include the key and
the lock, and the sexual organs during reproduction. Hardly novel,
the differences between analogy and synalogy were already at
work in Hume’s philosophy when he distinguished, in his Treatise
on Human Nature, three principles of association: similarity,
contiguity, and cause/effect. Similarity relates to analogy while
contiguity and cause/effect imply synalogy. The opposition be-
tween synalogy and analogy was also acting in Frazer’s distinction
of sympathetic magic into two types: contagious magic, acting by
contiguity, and homoeopathic or imitative magic, acting by simi-
larity, as explained in his famous book The Golden Bough.
The distinction between synalogy and analogy is at work in cer-
tain biological and linguistic distinctions. Evolutionary biologists
clearly distinguish between analogy and homology. When struc-
tures pertaining to organisms of two different species share mor-
phology and perform the same function, they are analogous. If
they share a common ancestry, they are homologous even if they
are morphologically and functionally different, as is the case in the
extremities of whales, horses and monkeys. I understand homolo-
gy as a sort of processual, temporal contiguity. Two analogous
structures may be also homologous (such as the eyes of fishes and
birds), but when two structures perform the same function and
have different ancestries, biologist use the term “homoplasty,” as
with the wings of birds and insects. In linguistics, I contend that
the distinction between metaphor and metonymy is another modu-
lation of the differences between analogy and synalogy. The struc-
ture of metaphors is clearly analogical as I will discuss in section
seven below. In the metonymy, though, a thing or concept is des-
ignated by the name of a different thing with which it shows cer-
tain temporal, spatial or causal contiguity. This occurs when the
content is designed with the name of the continent, the product
with the name of its origin, and the effect by the name of the cause
(and vice versa).
The difference between analogy and synalogy, between similar-
ity and contiguity, affects the relationships between analogates
(the “horizontal” one-to-one correspondence between analogates
to use Juthe’s terminology in Juthe 2016, pp. 83, 109, 431), but it
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does not affect the relationships between their elements (Juthe’s
“vertical” relationship, Juthe 2016, pp. 83, 109, 431). The parts of
each of the analogates can be linked by contiguity (by causality,
supervenience, resultance, genus to species etc.), which can be
compatible with the correspondence by similarity between analo-
gates, with the similarity of their parts, and with the similarity of
the contiguity relationships between their parts. For instance, when
establishing the analogy between a map and the terrain, the map
has its own parts linked by contiguity, as does the terrain, even
though the relationship between the two analogates (the map and
the terrain) is not by causality or contiguity. The terrain does not
cause the map, and does not adjust by contiguity to the map, alt-
hough there is a proportional correspondence between the parts of
the map and the terrain, and between the contiguity relations of
their parts. At this juncture, I follow Holyoak’s definition of anal-
ogy whereby “two situations are analogous if they share a com-
mon pattern of relationships among their constituents even though
the elements themselves differ across the two situations” (Holyoak
2005, p. 117).
Interestingly, the conflation of analogy and synalogy is not a
mere misunderstanding by medieval philosophers, but still occurs
today. Guarini and his team include homology among the relations
of similarity (Guarini et al. 2009, p. 94). André Juthe (2016, pp.
60-62) has proposed a certain correspondence between the medie-
val analogy of attribution and other present-day concepts such as
Sacksteder’s qualitative analogy (Sacksteder 1974), Michalos’
analogy based on analogous properties (Michalos 1969), Hesse’s
analogical types A and B (Hesse 1965 and 1966), Gentner’s and
Markman’s mere appearance matches (Gentner and Markman
1997) and Holyoak’s and Thagard’s attribute mapping (Holyoak
and Thagard 1995). Nevertheless, this correspondence is disputa-
ble since, in the analogy of attribution, the relationship between
the analogates is grounded on causes, ends, and agencies, alt-
hough it is established by contiguity, while in the cases studied by
Juthe, the relationship between analogates is always a one-to-one
correspondence grounded on partial similarity.
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5. Analogy and asymmetry
In what follows, I will argue that asymmetry is a core feature of
any analogy. The idea is not new, as the issue was already dis-
cussed among Thomistic philosophers. As already stated, Cajetan,
following Aquinas (De Veritate, q.2 a11), stated that the most
perfect analogy is the analogy of proper proportionality whereby
there is complete symmetry between the analogues. Cajetan con-
tended that in this kind of symmetric analogy "no analogue is
defined by another, since the definition of one is proportionally the
same as that of another" (Cajetan 1498, 1953, p. 77). In his Meta-
physical Disputations (1596, d. XXVIII, s.3/11), the famous 16th
century Spanish philosopher Francisco Suárez argued that analogy
always implies asymmetry and criticized Cajetan’s analogy of
proper proportionality. According to Suárez, one of the sides of
the analogy has to support the weight of the relationship. Follow-
ing this criticism, I hold that asymmetry is a core feature of true
analogy. Perfect symmetry between the analogues makes it possi-
ble to explain two or more particular cases using the same underly-
ing principles, but this implies a much closer relationship between
the particular cases than mere analogy. The solar system as com-
pared with other multi-planetary systems sharing the universal
principles of gravity, and similar triangles sharing the same pro-
portions serve as illustrations of this symmetrical pattern. In such
cases, the supposed analogues are instead illustrations of a general
law or proportion. In this paper, I hold that asymmetry is a distinc-
tive attribute of analogy. Perfect, symmetric proportionality be-
tween two (or more) different objects or situations is but an ex-
treme or “degenerated” modulation of asymmetric analogy. In this
context, I use the adjective “degenerated” denotatively, not axio-
logically, such as when mathematicians characterize the empty set
as an extreme, “degenerated set” since it has no elements.
J.E. Adler has defended the significance of asymmetry in ana-
logical arguments, saying that the widely admitted difference
between the source and the target of any analogy stands as an
indication of the importance of this feature (Adler 2007). The
distinction made by William R. Brown between “analans” and
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“analandum” also suggests the asymmetric relationship between
the two poles of any analogy (Brown 1989, p. 164).
6. Same-level relationship
In the Aristotelian and scholastic tradition, analogical arguments
are always understood as from particular to particular. When
moving from the universal to the particular, the argument is
deemed deductive. In such cases, the particular may serve as an
example or illustration of the universal, although examples and
illustrations are different from analogical arguments. The deriva-
tion of the universal from particular cases is deemed as an induc-
tive procedure. Aristotle, in his treatise On Sophistical Refutations
(part 15), discusses the cases where no universal is available: “In
cases where there is no term to indicate the universal, still you
should avail yourself of the resemblance of the particulars to suit
your purpose; for resemblance often escapes detection” (174a37-
40). Typical Aristotelian analogies are inspired by the mathemati-
cal proportionality A/B=C/D. Aristotle used the following exam-
ple to illustrate a typical analogy: as is a calm in the sea so is
windlessness in the air (Topics, I, 17, 108a, 7-11). Consequently,
deductive and inductive arguments, although including similarities
between premises and conclusions, are clearly differentiated from
analogical arguments. André Juthe defends the existence of genu-
ine arguments by analogy that are not reducible to any other type
of argument since “their inferences are always from particular to
particular, never from general to particular or from particular to
general” (Juthe 2005, p. 19). Ionel Apostolatu, in looking at cer-
tain dictionaries, concludes that analogy, in its broad sense, im-
plies partial similarity between circumstances, things, and situa-
tions moving from particular to particular (Apostolatu 2012, p.
332). Digging further, Juthe, in two later works, characterizes
analogical arguments as material/pragmatic same-level reasoning
via comparison either from particular to particular or from general
to general. Analogies moving from universal to universal are
common in ethical analogical argumentation (Juthe 2015, p. 383;
2016, p. 125). In this paper, I assume that this material/pragmatic
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same-level relationship between analogates is a core feature of
every analogy (not only of analogical arguments).
7. Analogy of relations and analogy of operations and proce-
dures
In this section, I should like to touch on the nature of the terms and
elements being compared in any analogy. Taking cues from the
multiconstraint theory of Holyoak and Thagard (Holyoak and
Thagard 1995 and 1997) and from Gentner’s structure-mapping
theory (Gentner 1983), I assume that the analogy of individual
predicates or attributes of objects is not sufficient when character-
izing analogies. While analogies do indeed include comparison
between objects and attributes of objects, they also require that the
relationships between those terms and objects be similar (Perel-
man 1969). The analogy between the solar system and the atom
entails similarity between the relationship of the Sun with the
planets and the relationship of the nucleus with electrons (I am
citing this illustration salva veritate), although it also implies
similarity between the nucleus of the atom and the Sun and a
comparison between planets and electrons. In the typical four-term
proportions that underlie metaphors, the comparison is not be-
tween the terms, but rather between the relationships of the first
pair and those of the second. The presence of analogies between
relationships is sometimes obscured by the fact that objects and
situations have a complex structure and, consequently, comparing
certain attributes of complex objects implicitly presupposes com-
paring the relationships between their parts or attributes. The
nature of the compared relationships may be highly diverse involv-
ing causality, spatial or temporal adjustment, equality, congruence,
kinship, correlation, dependence, to cite but a few possibilities.
As stated, analogy of things includes objects and relations be-
tween objects (for instance, situations); however, mention should
also be made of the analogy of operations (for instance, the analo-
gy of procedures and processes). In any given language, there may
be an “analogy of nouns” (as in Cajetan’s treatise), but there may
also be an analogy of relations (the analogy of prepositions) and of
operations (analogy of actions, analogy of verbs).
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Esa Itkonen has proposed a distinction between an analogy un-
derstood as a structure, defined by a static relation between sys-
tems, and an analogy as the dynamic process that produces those
analogical structures (Itkonen 2005). The distinction is most rele-
vant since analogies are human constructions and, consequently,
are always the result of synthetic human procedures. While I
subscribe to Itkonen’s proposal, my argument for the existence of
analogies of procedures implies a different idea: the materials
being compared proportionally in certain analogies are operations
or behaviors of humans and other animals. In such cases, the
analogy’s core may depend on the comparison between operations.
In the oft-quoted analogy between the State and the ship (“the
governor is to the Republic as the helmsman is to the ship”), the
sameness between the two different domains (political and nauti-
cal) can be understood as an analogy of relationships. The rela-
tionship between the governor and the citizens is deemed similar
to the relationship between the helmsman and the seamen. How-
ever, a comparison of the operations involved could also be apro-
pos since the operations performed by the prince of the Republic
in political praxis are, in certain aspects, like the operations of the
helmsman with respect to seamanship. In the analogy between
artificial selection and natural selection, the results of the selective
operations performed by the human breeder (a farmer or a garden-
er) are compared with the results obtained by the operations of
organisms in the wild. In the famous analogy of Thomson’s violin-
ist, the operations of the aborting woman are compared with those
of the woman unplugging the violinist. In those cases, the analogy
implies the relative proportionality between two (or more) differ-
ent courses of operations. The same occurs in the analogies be-
tween two wars separated by many centuries. Operations, proce-
dures and processes are always directed by a certain finality; they
are teleological (either teleonomic, teleoclinical, or teleomorphic)
wholes. Consequently, analogy between operations and processes
implies a discussion of the proportionality between goals and ends,
which does not occur when taking into account the analogy of
relationships alone.
Interestingly, most present-day studies have failed to discuss
the analogy of operations and procedures. In characterizing analo-
Proposal of a Classification of Analogies 123
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gies, Paul Bartha, Dedre Gentner and Kenneth J. Kurtz, Marcello
Guarini, André Juthe and many others do not even mention them
(Bartha 2016, Gentner 1981, Gentner and Kurtz 2006, Guarini
2009, Juthe 2016, p. 62). I suspect certain reasons for this lack of
interest about operations. On one hand, research about analogy
frequently focuses on theoretical reasoning and argumentation and
consequently centers on the analogy of relationships between
analogates. Operations are not directly reflected in sentences and
propositions since their meaning is circumscribed to performance
thereof and, consequently, they may go unnoticed. On the other
hand, cognitive psychologists often understand human behavior
from a computational perspective that gives priority to the analogy
of relationships over the analogy among operations (see, for in-
stance, Gentner et al. 2001).
8. A classification of the different types of analogies based on
their internal structure
I have hitherto defined analogy as an asymmetrical proportionality
stablished among situations, relationships, or operations of relative
similar level. Identifying those constituent parts of any analogy
makes it possible to construct an internal classification based on
three criteria.
The first criterion, arising from the asymmetric relationship be-
tween analogates, could be defined as a “directionality criterion”
whereby the route linking their similar items can be traveled in
two opposite directions. I term the direction from the familiar
source to the less known target “extrapolative” moving from the
most known to the relatively unknown, from the actual to the
possible. In this case, the analogy has an explorative function: the
better-known case (source) serves as a platform from which to
clarify the structure of the less known, unfamiliar case (target). An
illustration of this extrapolative direction of analogies is the analo-
gy between the relatively well-known liquid flow and the unfamil-
iar electric current that was introduced in the 19th century. Alt-
hough people did not then know exactly what an electric current
was, they made an extrapolation and imagined it as a liquid flow
such that voltage was immediately aligned with flow pressure. The
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cases studied by Adler fulfill this explorative function (Adler
2007). In their theories, Ross (Ross 1983, p. 208), Gentner and
Holyoak characterize analogies by reference to this explorative or
extrapolative function and do not take the opposite direction into
separate consideration (Gentner and Holyoak 1997, p. 33).
However, the opposite direction has also been frequented. Wil-
liam R. Brown taking cues from the distinction between explanan-
dum and explanans, as it is used in the philosophy of science,
introduces the words “analandum,” (which is the phenomenon to
be analyzed), and “analans” (which is the phenomenon taken to
analyze the analandum) (Brown 1989, p. 164). I term this direc-
tion “analytical,” and although it may appear paradoxical at first
glance, it has played an important role in the history of analogies.
In such cases, the analans is perhaps still the less known and less
familiar part of the analogy—although it is nevertheless under-
stood as an instrument used to identify and analyze the relevant
constituents of the analanandum since it is supposed to be easier
to manipulate or to understand—perhaps because it is more sche-
matic in certain relevant aspects. When moral philosophers resort
to bizarre analogies and thought experiments such as Thomson’s
violinist (1971) or Parfit’s transmogrifying humans (1984) in order
to discuss real moral problems, they are invoking bizarre situations
(the involuntarily plugged-in violinist or the transmogrified hu-
man) to shed light on a real situation (in this case, abortion). Dan-
cy, Jackson, Smith and Burns, among others, have discussed the
role of analogy in moral deliberation (Dancy 1985, Jackson 1992,
Smith 2002 and Burns 2006).
Although semantical and structural in nature, the directionality
criterion introduced in the foregoing classification of analogies
implies that analogies may serve two general purposes: the explo-
ration of new domains (targets) or the analysis of a familiar do-
main (analandum) by taking cues from other analogous contexts
(analans). In the first case, the analogy is evaluated by taking into
account the fertility of the familiar source so as to organize and
structure the target as appropriate. In the second case, the evalua-
tion looks into the analytical utility of the patterns suggested by
the “artificial” analans. André Juthe has summarized the classifi-
cations proposed by different authors based on the function or
Proposal of a Classification of Analogies 125
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purpose of analogies as used in argumentation (Juthe 2016, p. 32-
37). His predictive and creative functions coordinate with the
proposed exploratory analogies, while classificatory and heuristic
functions can be understood as analytical. An important difference
should be highlighted: Juthe is classifying the purposes of analogi-
cal argumentation, while I am interested in classifying analogies
in any context (logic, techniques, technology, politics, law etc.).
Accordingly, he concludes that the purpose of argumentation is
probative and consequently finds that the various testing proce-
dures are the primary criterion when classifying analogical argu-
ments. (Juthe 2016, p. 69).
The proposed directionality criterion is reminiscent of Bartha’s
classification of analogies based on the direction of the determin-
ing relation. He distinguished four analogical modes: the first two,
“predictive” and “explanatory,” approximately correspond to my
proposal (extrapolative and analytical). He also introduces a “func-
tional” mode linking the analogates in both directions, and a “cor-
relative” mode in the absence of directions (Bartha 2010, pp. 95-
99). I dispense with those last two modes since they fail to meet
the above-proposed criterion of asymmetry between analogates.
Directionality between analogates should not be confused with
other criteria, such as those used in the distinctions between a
posteriori and a priori analogies (Govier 1989, 2002, 2010), induc-
tive versus deductive analogies (Barker 1989), and empirical
versus normative analogies (Langenbucher 1998; Eemeren and
Garssen 2014). These distinctions may be of interest while classi-
fying analogical arguments but are scantly relevant while classify-
ing analogies in general. When taking into consideration certain
analogies (and not just arguments by analogy), their a priori and a
posteriori aspects, their inductive and deductive character, and
their empirical and normative contents are so inextricably con-
nected that such classification criteria are not of much use. An
example may serve to illustrate this claim. In the analogy between
the brain and the computer, both analogates are quite well known
(a priori and a posteriori), both include deductive and inductive
suppositions, and both involve normative and empirical contents.
Consequently, it is not possible to assess whether this analogy is a
priori or a posteriori, inductive or deductive, empirical or norma-
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tive. The same can be said about the majority of the illustrations
presented in table 1 below.
The second criterion of classification depends on the domain
constraints of the analogates. This criterion takes advantage of
André Juthe’s distinction between a same-domain analogy and a
different-domain analogy (Juthe 2005, 2015, and 2016), and it
equally affects the internal structure of analogies. In the same-
domain analogy, the two elements belong to the same domain. The
analogy between a real plane flying in the air and a scale model
plane in a wind tunnel remains in the same domain (aerodynamics)
although the results cannot be automatically transferred from one
scale to the other. In the different-domain analogy, the components
of the analogy belong to wholly different domains. The aforemen-
tioned analogy between liquid flow and electric current may serve
as an example.
Metaphors can be defined as different-domain analogies, as in
Cajetan’s analogy of metaphoric proportionality. In those cases,
there is one name which is used properly and, from its use, certain
other analogues can be constructed in which the name is used
improperly or metaphorically. As an illustration, Cajetan cites the
following example: laughter is to the face as flowers are to the
field and as fortune is to human life. As such, metaphorically one
can say that flowers are the laughter of the field, and fortune is the
laughter of life. In this kind of analogy, as can be seen, the analogy
falls mainly on the terms (laughter = flowers = fortune). The met-
aphor occurs when the terms of two (or more) different domains
are interchanged. Lakoff and Johnson, in their famous book Meta-
phors We Live By, have shown the extensive presence of a wide
variety of metaphors in our daily lives (Lakoff and Johnson 1980).
The etymology of the word “metaphor” is consistent with this
interpretation of metaphors as different-domain analogies, since
the Greek word metaphorá is formed from the suffix “meta-”
meaning “after” or “across,” and the root “phero” meaning “to
carry.” Although metaphors usually imply different-domain analo-
gies, not all different-domain analogies have the structure of meta-
phor as I will show below.
André Juthe has discussed certain previous distinctions that can
be coordinated with his proposal for the difference in domains
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(Juthe 2016, pp. 46-47). These include Santibáñez’s distinction
between analogical argumentation and metaphor (Santibáñez
2010), Weitzenfeld’s and Weingartner’s difference between ho-
meomorphs and paramorphs (Weitzenfeld 1984, Weingartner
1979), Ruiz’s and Luciano’s division of within-domain and cross-
domain analogies (Ruiz and Luciano 2011), Kokinov’s classifica-
tion of intra- and inter-domain analogies (Kokinov 2013), Gars-
sen’s literal versus figurative analogies (Garssen 2009), and
Bowdle’s and Gentner’s differentiation between domain-specific
and cross-domain analogies (Bowdle and Gentner 2005).
In this paper, I will argue that different-domain analogies, in
turn, can be divided into two subtypes based on the ontological
status of the different domains involved. In fact, when evaluating
the domains of a given analogy, two situations may happen. Either
both domains are real, or one of them is real and the other ficti-
tious. In the first case, we do not abandon the real existing world.
For example, the analogy between brains and computers is a dif-
ferent-domain analogy since biology and cybernetics are, in prin-
ciple, different categories, but both domains are real. In the second
case, one of the analogy domains is not real and exists only as
something imagined or “sketched,” as a product of fantasy. Certain
thought experiments with fantastic beings, such as Laplace’s
genius or Maxwell’s demon, may serve as illustrations of analo-
gies having an unreal component.
The last criterion of classification focuses on the elements of
comparison of the analogy, which can be either exclusively rela-
tional or both relational and operational. An analogy can be cen-
tered on domains stated outside the influence of any operational
being. For example, the aforementioned analogies between the real
plane and the scale model or between liquid flow and electric
current focus on comparing certain objects and relations between
objects, and such analogies can be understood as independent from
the operations of subjects (technicians, scientists, etc.). The analo-
gy between artificial and natural selection, and the analogy of
Thomson’s violinist mentioned above serve as illustrations of the
comparison among operations. The analogy between a utopia and
the real world implies analogies between objects and relations;
however, it must involve analogies of human operations since the
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core of the analogy requires a comparison of the individual actions
and operations of people in the imagined world with those in the
real world. In the fields of natural sciences, analogies usually have
a relational nature, while in the field of human and ethological
sciences, operational analogies are frequent since those sciences
need to take into account the behaviors of certain human and non-
human animals.
To summarize:
1. Based on their function, analogies are extrapolative when they
move from a familiar source so as to explore a relatively unknown
target. Conversely, they are analytical if they make use of certain
features of an artificial analans to shed light on the analandum.
2. The analogates domains can be similar or different. When dif-
ferent, they can either both be real, or one of them can be real
(positive) and the other fictitious.
3. In certain cases, comprehending analogies only requires taking
into consideration the similarities between terms and relationships
of the analogates, while in other cases the similarities between the
elements of comparison include the operations of certain involved
subjects.
To conclude this paragraph, the following table lays out the
three criteria and shows the extent to which they may be useful in
understanding the differences and similarities of a wide-ranging
sample of analogies. It includes some of the components of the
resulting types of analogies and makes careful use of the most
suitable words while attending to their lexical structure and ety-
mology.
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TABLE 1: TYPES OF ANALOGIES ACCORDING TO THEIR INTERNAL STRUCTURE
1. DIRECTION
2. DOMAINS
EXTRAPOLATIVE
from source to target
ANALYTICAL
from analans to analandum
SAME-DOMAIN ANALO-
GY
I
source as
archetype or
exemplar
Oken’s
vertebrate
archetype
II
source as
precedent,
prototype
stare decisis
doctrine
qiyas
III
same-domain
model,
morphism
scale model
plane in the
wind tunnel
IV
same-domain
simulation
learning
simulator
DIFFERENT-
DOMAIN
ANALOGY
BOTH
REAL
V
source as
paradigm
liquid
flow/electric
current,
Plato’s line
analogy
VI
source as
canon
artificial
selection/
natural
selection
VII
different-
domain model
mapping,
brain/computer
analogy
VIII
different-
domain
simulation
game
simulation,
parables,
Thomson’s
violinist
ONE REAL
(POSITIVE)
AND
ANOTHER
FICTITIOUS
IX
extrapolative
thought
experiment
in natural
sciences,
myth
Einstein
riding on a
beam of
light,
Plato’s
Timaeus
X
extrapolative
thought
experiments
in social
sciences,
utopia,
soteriological
myths
More’s
Utopia,
Skinner’s
Walden Two
XI
analytical
thought
experiments in
natural sciences,
myth
EPR paradox,
Plato’s myth of
the cave
XII
analytical
thought
experiments
in social
sciences,
myth, fable,
dystopia
Lessing’s
“Three rings
parable”,
Buridan’s ass,
Ethics thought
experiments
3. ELEMENTS OF COM-
PARISON
TERMS &
RELATIONS
ONLY
TERMS,
RELATIONS &
OPERATIONS
TERMS &
RELATIONS
ONLY
TERMS,
RELATIONS &
OPERATIONS
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The first row of Table 1 deals with same-domain analogies
(cells I-IV). As already stated, when extrapolative, analogies move
from a known, familiar source to a less known, unfamiliar terrain.
The first type of analogy establishes the similarity between the
terms and relations of a known set of objects (which I term “arche-
types” from the Greek “arkhe-“ meaning “first,” and “typos”
meaning “model” or “type”) and certain other unfamiliar materials
in the same domain (cell I). Oken’s vertebrate archetype serves as
example since other unknown vertebrates are expected to be simi-
lar to the archetype proposed. In the scholastic theory of the anal-
ogy between God and humans, God’s knowledge is defined as
archetypal since it is the original, while creatures’ knowledge is
ectypal since it is a revealed by God.
I use the word “prototype” (Greek “proto-” meaning “original”
or “primitive”) to refer to the source in an explorative same-
domain analogy when it takes into consideration certain subjects’
operations (cell II). Many modern languages reserve the word
“prototype” in reference to things made operationally by humans.
In the common law system, the use of prior cases in deciding new
ones illustrates this type of analogy. In the US, the Roe v. Wade
decision is the prototype of subsequent decisions about abortions.
Same-domain analogies can be constructed in the opposite di-
rection, from the analans to the analandum. Same-domain models
and simulators can be understood as analans of those types of
analogies (cells III and IV). Experimentation with scale model
planes in wind tunnels frequently enables relations to be estab-
lished between their parts, which subsequently prove to be rele-
vant in the design of real planes. The Latin world “modelus” sug-
gests the “lesser size” or relative “schematic character” of the
analans in the same domain, while the Latin word “simulare”
meaning “imitate” accords with the intentional operational nature
assigned to this type of analogy. In a flight simulator, the subject’s
operations imitate the operations performed in a real plane alt-
hough a simulator makes it possible to analyze situations that
cannot be repeatedly studied in real life (i.e. dangerous threshold
situations) (cell IV).
As can be seen, same-domain analogies deal with certain situa-
tions bordering on what I have called “perfect symmetry” or
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“shared common principles,” and, consequently, they stand at the
frontier of genuine analogies. The fact that both parts of the analo-
gy belong to the same domain contributes to this proximity and
makes it more likely for them to be governed by the principles of
the shared domain (especially if this domain is a scientific one).
Nevertheless, I have included them in the table since I contend that
asymmetric analogies can be made even without leaving a given
domain. Analogies between cases in law demonstrate the existence
of such asymmetry.
Most frequently, analogies imply two different domains; the
difference in domain between the analogates inevitably entails the
asymmetry of their relationship. As already stated, different-
domain analogies may be subdivided into two subtypes, according
to the ontological reality of the domains involved. The second row
(cells V-VIII) refers to situations where both domains are real
albeit different. When a source domain lends its internal organiza-
tion to another different domain in a non-operational context, I
propose calling the source “paradigm” (from the Greek word
“paradeigma” meaning “pattern”) (cell V). The aforementioned
case of liquid flow as the paradigm (pattern) of the electric current
serves as an example of two different, albeit real, scientific do-
mains (fluid dynamics and electromagnetism). In Plato’s analogy
of the divided line (Republic 509d-511e), the source paradigm is
geometrical (the proportionally divided line) whereas the target is
philosophical (epistemological). The analogy’s explorative nature
can be observed in the conjectural nature of the noesis placed in
the last line segment and in the stipulated proportionality between
the various segments. When the extrapolative analogy between
different domains requires reference to operations (either human
or non-human), the familiar source is taken to be a canon of the
target (cell VI). In line with the meaning of the Greek word, “ka-
non” includes the meaning of “rule”; the source acts as the rule in
order to organize or understand the target. As an illustration of this
situation, I propose Darwin’s use of artificial selection (which is
clearly an operational procedure) to understand natural “selection”
mutatis mutandis.
Cells VII and VIII include, respectively, different-domain mod-
els and simulations. The map is analogous to the terrain; both
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domains are real and different, and, at least in so-called “physical
maps,” the analogy is mainly between elements and relationships
between elements both in the terrain and on the map. I hold that
the map, when it is a true map, has an analytical nature (cell VI). I
view game theory simulations as illustrations of different-domain,
analytical, operational analogies (cell VIII) since they act as in-
struments for understanding other real operational situations (auc-
tions, market wars, etc.). Parables also fit into this type of analogy.
The domains (the parable domain and the real case) usually exhibit
differences; the parable is used as an instrument for understanding
the real case (analytical direction), and the context is operational in
both domains.
Finally, the last row comprises different-domain analogies in
which one of the domains is real (positive) and the other is ficti-
tious (cells IX-XII). Due to this ontological gap, asymmetry in
such cases is inevitable. Thought experiments and myths pervade
the cells in this row since the analogies always imply a comparison
between a fictitious domain (be it of myth, fantasy, or merely
imagination) and a real one. Myths and thought experiments can
have an extrapolative nature when they are used to explore un-
known domains. Many of Einstein’s thought experiments with
trains and light beams have this structure, and Plato, in his Timae-
us, makes use of several myths to speculate about the structure of
the unknown cosmos (cell IX). In an operational context, explora-
tory analogies with a fictitious component take the form of utopias
and soteriological, chiliastic myths, such as More’s Utopia and
myths regarding the final state or the end of history (cell X). How-
ever, the unreal domain of certain analogies may also have an
analytical purpose. In the famous EPR paradox, for example, the
imagined situation plays the role of a counterexample designed for
understanding the inner limits of the quantum mechanics. Plato’s
allegory of the cave (Republic 514a-520a) uses the fictitious do-
main of the cave as an instrument to analyze the internal world of
shadows (cell XI). Other myths, such as Plato’s Ring of Gyges
(Republic 360b-d), exemplify situations where the analysis is
performed in an operational context through a fantastic domain. In
this vein, I understand dystopias less as undesired proposals and
more as analytical counterexamples showing the shortcomings and
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contradictions of certain operational projects. Fables also fall
under this category of operational, analytical analogies with an
unreal domain (cell XII).
9. Concluding remarks
In this paper, I have assumed that classifying and characterizing
analogies are two co-implicated tasks. I have defended the claim
that the sources of the general idea of analogy are wider and more
diverse than commonly admitted and do not reduce to logic, argu-
mentation theory, linguistics, or cognitive psychology. According-
ly, I have argued that characterizing and classifying analogies
must take into account the varied contexts where analogies take
place. I have summarized certain arguments for differentiating
analogy and similarity and proposed criteria for differentiating
analogy from synalogy (as it appears in the analogy of attribution,
biological homology, and linguistic metonymy). I have character-
ized analogy by asymmetry and relative same-level relationships
between analogates. In addition, I have stressed the role played by
procedures and operations in the internal structure of certain anal-
ogies since operations and procedures can be proportionally com-
pared. Stemming from this characterization of analogies, I have
proposed classification thereof based on three criteria: (1) relation-
ship directionality, which is an important issue due to the supposed
asymmetry between analogates, (2) analogates’ type of domain
and proximity, which is related to the relative same-level relation-
ship between them, and (3) the different nature of the compared
analogates’ elements (terms, relationships, and operations). The
co-implication between the characterization and the classification
of analogies strongly suggests that the proposed classification will
contribute to an understanding of the internal structure of the
general idea of analogy.
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