Analogy 2: Structural Analogy

1. Terminology

Structural analogy connects two complex domains, each articulating an indefinite and unlimited number of objects and relationships between these objects. It combines intra-categorical analogy (a property of objects) with proportional analogy (a property of relations). One could also speak of formal analogy (the areas have the same shape) or borrow the mathematical term “isomorphism”, S. Intra-categorical analogy; Proportion.

The expression “physical analogy” refers to the relationship between two objects when one is a replica of the other. The concept covers different phenomena, such as the relationship between a model and its original, or the relationship between a prototype and the object to be manufactured. The reasoning based on the model or prototype is then applied to the original.

Structural analogy is involved in the two following situations.

(i) A, B, C … are similar ­— To establish if the complex objects or domains A, B, C are similar, one has to compare their components and the relations between them. The conclusion of this investigation will be a claim such as “A, B, C… are similar”; “A, B, are indeed similar, but C is something different”, etc.

One may ask if the 1929 Great depression, the Lost Decade of Japan during the 90s, and the Argentinian Crisis in 2001 share some significant characteristics. The whole purpose of the investigation may be to establish a typology of economic crisis, without — as far as possible — drawing on preconceived ideas of how politicians will use the conclusions of this investigation.

The areas are symmetrical from the viewpoint of the investigation, which does not favor one of the areas over the others, but only focuses on their relationships.

(ii) A is similar to B — A contrario, the importance of the previous situation appears when the series involves the 2008 crisis. Given the actuality of this last crisis, it will certainly be tempting to see if we can “learn lessons” from the previous crises and to apply them to the 2008 case, with the intention of making provisions for the current situation. If the proponent uses the analogy 1929 ~ 2008 to predict a third world war, her opponent can rebut the inference by showing that the domains are not similar, and that it is therefore impossible to rely on the first instance, in 1929, to make inferences about something about what will happen in 20** and after (see farther).

The difference in status between the two areas is expressed in different ways. In his analysis of the metaphor, Richards opposes Tenor and Vehicle (1936); Perelman & Olbrechts-Tyteca speak of Theme and Phore ([1958], p. 501). A simple way to name these domains may be comparing domain / compared domain; or, in view of the analysis of argument, Resource domain / Target domain.

The argument by analogy works on the asymmetry of the compared areas; that is why these two areas will be designated, when necessary by the letters of alphabets, R, as Resource field and Π (capital Greek letter “pi”),   the Problematic field, targeted by the investigation. The field R is the source or the Resource on which the arguer relies to make changes in the Targeted area Π, or to derive from R certain consequences about Π. In other words, the Resource field R is the argument domain and the Targeted field Π is the conclusion domain. The two fields are differentiated from epistemic, psychological, linguistic and argumentative perspectives.

— In epistemic terms, the Resource field is the best-known area; the Target field is the area under exploration.
— In psychological terms, intuition and values operating in the Resource field are put to work in the Target field.
— In linguistic terms, the Resource field is well covered by a stabilized, well-known and easily spoken language; the Target domain is not.
— In practical terms, we know what to do within the Resource field whereas in the Target domain, we do not.

2. Explicative analogy

In the well-known analogy proposed by Ernest Rutherford between the atom and the solar system, the Resource field is the solar system, the Target field is the atom:

the atom is like the solar system.

This is a didactic analogy, intended to provide a first intuitive understanding of the atomic structure, taking advantage of a (supposed) better understanding of the solar system. The asymmetry of the areas is obvious: the Resource field, the solar system, has been known and understood for a long time. The Targeted field, the atom, is new, poorly understood, inaccessible to direct perception, enigmatic.

The explanatory analogy retains some educational merits even when partial. A comparison is not identification, and two systems can be compared simply in order to identify the limits of the comparison, that is, the irreducible specificities of each field, cf. infra, §6.

The analogy has explanatory value in the following situation:

In the world Π, the proposition π is poorly understood. In a world R, there is no debate over r. Π is isomorphic to R (structural, systemic analogy). The position of π in Π is the same as that of r in R. So, the knowledge, images, obligations… attached to r are now transferred to π; π  is now slightly better understood; we know how to do with π.

The analogy relationship integrates the unknown on the basis of the known. As causal explanations, explanations by analogy break the insularity of the facts.

The analogy is an invitation to see and handle the Problem through the Resource. The Resource domain is considered to be a model of the Target domain. The relation of the domain under investigation to the Resource domain is treated like that of the domain of investigation to an abstract representation of this domain. Otto Neurath uses a maritime metaphorical analogy to explain his vision of epistemology:

There is no tabula rasa. We are like sailors at sea, who must rebuild their ship without ever bringing her to a dock to be disassembled and rebuilt it with better items. (Otto Neurath, [Protocol Statement],1932/3.[1])

The analogy can be translated word for word: “There is no ultimate foundation of knowledge from which we could, without any presuppositions, re-build the whole of our present knowledge.” This resource is extremely powerful; the image could also be applied to social life: “There is no ‘good explanation’ (meaning “good discussion of our disagreements”) that permits reconstructing a damaged relationship and re-start from scratch.”

3. Arguments based on structural analogy

In ordinary situations, analogy is used argumentatively, as in the following case:

— In the world Π, we are in a difficult situation; what should we do? Should we accept or reject perspective π?
— But we know for sure what happened in a world R.
Fortunately, Π is isomorphic to R (structural, systemic analogy); if necessary we can argue for that.
The position of π in Π is the same as that of r in R.
So we can act, in world Π, on the basis of the knowledge, images, obligations… attached to r — That is to say, we can now decide about π.

This argumentative operation argues that “if the domains are analogous, so are their corresponding elements and the relations between them”, which may prove true or false under further investigation. The analogy gives us something to think about, but proves nothing; the conclusion projected upon Π may be false or ineffective.

4. From analogy to metaphor and back

A language is attached to the Resource domain. For example, ​​the human body is referred to in a language that may be incomplete and fairly incoherent, but commonly understood, the language of the flow of organic matter, of popular physiology, of good health and sickness, life and death. This language synthetizes and builds a common intuition of the body. Other unfamiliar areas are not equipped with such a dense, effective and functional language. The analogy projects the language of the Resource area, the human body, onto the Problematic field, the society. As a result, the target can be problematized in a familiar, non-controversial language; so that social convulsions can be discussed and a cure found. The analogy is an invitation to see the problem through the lens of the resource; full metaphorization enables us to forget the glasses.

The following apologue is based on the analogy “society is like a body”, as expressed in the metaphorical expression “social body”. Note the explicitness of the vocabulary of analogy in the final commenting section.

The senate decided, therefore, to send as their spokesman Menenius Agrippa, an eloquent man, who was also accepted by the plebs as being himself of plebeian origin. He was admitted into the camp, and it is reported that he simply told them the following fable in primitive and uncouth fashion. ‘In the days when all the parts of the human body were not as now agreeing together, but each member took its own course and spoke its own speech, the other members, indignant at seeing that everything acquired by their care and labour and ministry went to the belly, whilst it, undisturbed in the middle of them all, did nothing but enjoy the pleasures provided for it, entered into a conspiracy; the hands were not to bring food to the mouth, the mouth was not to accept it when offered, the teeth were not to masticate it. Whilst, in their resentment, they were anxious to coerce the belly by starving it, the members themselves wasted away, and the whole body was reduced to the last stage of exhaustion. Then it became evident that the belly rendered no idle service, and the nourishment it received was no greater than that which it bestowed by returning to all parts of the body this blood by which we live and are strong, equally distributed into the veins, after being matured by the digestion of the food.’ By using this comparison, and showing how the internal disaffection amongst the parts of the body resembled the animosity of the plebeians against the patricians, he succeeded in winning over his audience.
Titus Livius, The History of Rome, Vol. 1, Bk 2; between 27 and 9 BC.[2]

The resource does not necessarily preexist its use in an analogy. An analogy can create ex nihilo a self-evident resource, as in the following analogy, proposed by Heisenberg in 1955. The danger mentioned in the first line refers to the cold war era, and the resource term is “a ship built with such a large quantity of steel and iron that its compass, instead of pointing to the North is oriented towards the iron mass of the ship.” Note that, once again, there is no clear-cut frontier between structural analogy and metaphor. Heisenberg refers to the situation he imagines as a metaphor; and in the next line, he uses a construction expressing an analogy: “humanity is in the position of a captain…”.

Another metaphor might make such a danger even clearer. By the seemingly un­limited growth of its material power, humanity is might be compared to a captain whose ship has been built out of such a large quantity of steel and iron that its compass, rather than pointing to the North, orients towards the huge iron mass of the ship. Such a ship would get nowhere. It would be blown off course and led in circles.

But back to the situation of modern physics: we must admit that the danger exists only if the captain does not know that his compass no longer responds to the magnetic force of the earth. By the time he understands this, the danger is already halved. Because the captain who, not wishing to turn around, wants to achieve a known or unknown purpose, will find a way to steer the boat, either by using new modern compass that does not react to the iron mass of the boat, or by steering in relation to the stars as sailors once did. It is true that the visibility of stars does not depend on us, and perhaps today do we see them only rarely. Despite this, our awareness of the limits of our hope in progress supposes the desire not to go in circles, but to achieve a goal. Once recognized, this limit becomes the first fixed point which allows a new orientation.
Werner Heisenberg, [Nature in Contemporary Physics], [1955][3]

5. Structural analogy as an epistemological barrier

Analogy is fertile to stimulate discovery and invention, useful for teaching and popularizing knowledge. Yet it becomes an epistemological obstacle when the proposed explanation by analogy seems so clear and satisfying that it hinders further research:

For example, blood flow like water. Canalized water irrigates the ground, so blood should also irrigate the body. Aristotle was the first to assimilate the distribution of blood from the heart to the body with the irrigation of a garden by canals (De Partes Animalium, III, v, 668 a 13 et 34). Galen did not think otherwise. But to irrigate the soil, it is ultimately to get lost in the soil. And here is exactly the main obstacle to a proper understanding of blood circulation.
Georges Canguilhem, [The Knowledge of Life], 1951.[4]

The systematic rejection of analogy as an instrument for knowledge is grounded in such observations.

6. Refutation of structural analogies

6.1 Vain analogy

In an explanation, the explanation (explanans) must be clearer than the thing to explain (explanandum). Analogical explanation must also satisfy this condition, and if the resource area is even less well known than the area under investigation the analogy does not help in the understanding of things.

The analogy is also vain when used to impress the audience and display the grandstanding of the speaker as familiar with the Resource domain. Gödel’s theorem is used extensively for this purpose (Bouveresse [1999]).

6.2 False analogy

An argument by analogy can be rejected by showing that there are critical differences between the Resource domain and the Target domain, prohibiting the projection of the former upon the latter so that no lesson can be learned from the supposed Resource domain. In the following passage for example, it is argued that the comparison of the 2008 and 1929 crisis is marred by the facts that the present situation in Germany has nothing to do with its situation after 1918 and the coming years. Furthermore, it is argued that there is nothing similar to Hitler and Nazism in the European landscape in 2009:

Jean-François MondotDoes the economic crisis weaken our civilization? We sometimes hear intellectuals and columnists making analogies with the 1929 crisis that led to World War II.

Pascal Boniface — We often make the mistake of thinking that history repeats itself, and so make very risky comparisons. Russia bangs his fist on the table, everybody immediately talks about the Cold War. An economic and financial crisis erupts on Wall Street, and immediately an analogy is drawn with 1929, the suggestion being that Hitler could come to power as a result of these difficulties. Yet the political circumstances are obviously very different, insofar as no great country is now humiliated as Germany was after 1918, leaving it wishing to take revenge. This comparison is easy to make, but it has no basis, neither strategic nor intellectual.
Pascal Boniface, [The clash of civilizations is not inevitable], 2009.[5]

6.3 Partial analogy

Partial analogy (“misanalogy” Shelley, 2002, 2004) is an analogy that has been criticized and recognized as limited. The two domains cannot be equated. Nonetheless, partial analogy still has a pedagogical use, as seen in the case of the analogy between the solar system and the atom (cf. supra §2):

A central body: the sun, the nucleus of the atom.
Peripheral elements: the planets, the electrons.
A central mass much larger than peripheral masses: the mass of the sun is larger than the planets; the mass of the core is larger than that of electrons. —etc.

Differences (analogy breaks):

The nature of the attraction: electrical for the atom, gravitational for the solar system.
There are identical atoms, each solar system is unique.
There may be several electrons in the same orbit, whereas there is only one planet in the same orbit. — etc.
The fact that the limits of analogy are precisely known prohibits any automatic transposition of the knowledge gained in one field into the other field.

6.4 Reversed analogy

A conclusion C1 has been established for a Target resource on the basis of an analogy drawn from the Resource domain R. The opponent argues that the same analogy drawn from the same domain R leads to another conclusion C2 about the same Target domain, that is incompatible with C1 (“disanalogy” Shelley, ibid.). These two contradictory conclusions prohibit the use of the Resource domain to argue in the Target domain.

This is particularly effective because the opponent concedes to playing on her adversary’s home ground. The opponent accepts and examines more closely the analogy advanced by the proponent, in order to neutralize his or her conclusions. This strategy is exploited in the refutation of argumentative metaphors.

Argument: ­­— This area lies at the heart of our discipline.
Refutation: — That’s true. But disciplines also need eyes to see clearly, legs to move in, hands to act, and even a brain to think.
Other refutation — That’s true, but the heart can very well keep beating preserved in a jar.

A supporter of hereditary monarchy speaks against universal suffrage:

Argument:— An elected president, that’s absurd, we do not elect the driver.
Rebuttal: — Nor are there natural born drivers.

Both sides enact the same metaphorical field. This form of rebuttal has the strength of an ad hominem refutation, based on the own beliefs of the speaker: “You are your own refuter”.

Counter-analogy — As with any argument, one can oppose an argumentation by analogy by putting forward a counter-argumentation (an argumentation whose conclusion is incompatible with the original conclusion). This counter-argumentation can be of any kind, including another argument by analogy, taken from another Resource domain; an analogy equilibrates another analogy:

Argument:   — The university is (like) a company, so …
Rebuttal:     — No, it is (like) a daycare, an abbey …

[1] Otto Neurath, “Protokollsätze”. Erkenntnis 3 (1932/3), p. 206. Quoted in A. Beckermann “Zur Inkohärenz und Irrelevanz of Wissensbegriffs”. Zeitschrift für Philosophische Forschung 55, 2001. P. 585.
[2] Trans. by Rev. Canon Roberts; Ed. by Ernest Rhys. J. M. Dent & Sons, Ltd., London, 1905. Quoted from; No pag. (11-08-2017)
[3] Quoted after Werner Heisenberg (1962) La Nature dans la Physique Contemporaine. Paris: Gallimard, 1962. P. 35-36.
[4] Quoted after Georges Canguilhem, La Connaissance de la Vie. Paris: Vrin, 1965. P. 26-27.
[5] Pascal Boniface, “Le clash des civilisations n’est pas inévitable”. Interview by J.-F. Mondot, Les Cahiers de Science et Vie, 2009. / Op-2009-03-04.php3] (09-20-2013)