The Concept of Model and its Triple History

 

Opening lecture

of the 13^th International Conference on History and Philosophy of Science (organized by the IUHPS/DHS-DLMPS Joint Commission), University of Zurich, 19-22 October 2000; topic: “Scientific Models: Their Historical and Philosophical Relevance”

 

IUHPS = International Union for the History and Philosophy of Science

DHS = Division of History of Science

DLMPS = Division of Logic, Methodology and Philosophy of Science

 

(If you wonder at some wording, please consult the tentative translation key)

 

German translation see: Modellgeschichte ist Kulturgeschichte (Kurzfassung)

 

red = corrections and additions

 

 

Model history is culture history

 

To trace the history of the concept of model is one of the most fascinating ways to pursue culture history. The creation and use of models belong to the elementary occupations of humans.

 

Even contemporary physics is culture historical. Take for instance the concept and idea oft the atom, which is about 2500 years old. Or take the concept "quark" (in the so-called "standard model"), which is taken from the novel "Finnegan’s Wake" by James Joyce.

 

The history of the concept of model is likewise 2500 years long.

 

Arguments around models become rapidly very emotional, no matter whether it concerns model in general or specific contents. The reasons for that become clear by the following explanations.

 

 

The history of a concept is not equal to the history of the named things

 

We must start out of the following facts:

 

1. The history of a concept and the history of the named things are two different kinds (fig. 0). Already the early people and the cavemen built, produced and used models, but we do not know, how they called them.

 

2. The history of the things is not at all easy to determine. It depends on the one hand on the richness and quality of the archaeological or documentary material, on the other hand on the interpretation of the same. And this interpretation constantly changes.

 

3. We have to take seriously whether the author itself speaks of a model or not. Retrospectively we can call "model" all understandings, „philosophies", "systems" or "theories". But neither Ptolemy nor Copernicus, neither Galilee nor Newton, neither Darwin nor Marx, etc. have named their interpretations or sketches "model".

 

4. There are many other concepts, which describe the same meaning or parts of this meaning as the concept of "model", e. g. representation, abstraction or concretion, idea or idealization, illustration, sensualization or view, pattern or scheme, shape and configuration, picture, symbol, sign and icon, metaphor and allegory, analogy and example, fiction and vision, draft and plan etc.

Very popular are also prototype and archetype, paradigm and exemplar.

In scientific language we have since 1600: system and hypothesis, theory, philosophy, treatise and principles, doctrine and teachings, law, rule, formula, etc.

 

 

In the German Zedler’s „Universallexicon“ (1739) we find as synonyms:

„Modell, Modele, Modello, Modulus, Typus, Exemplar, ein Modell, Vorbild, Abdruck, Form, Muster, Leisten, Richtschnur, oder Vorschrifft, darnach man etwas machet ...“

 

Funk & Wagnalls’ „New International Dictionary of the English Language” (1987) lists the following declared synonyms for the noun “model”:

archetype, copy, design, ectype, example, facsimile, image, imitation, mold, original, pattern, prototype, replica, representation, type; and further: idea, ideal.

 

"Collins English Dictionary and Thesaurus" (1993) has many more synonyms, namely:

1. copy, dummy, facsimile, image, imitation, miniature, mock-up, replica, representation

2. archetype, design, epitome, example, exemplar, gauge, ideal, lodestar, mould, norm, original, par, paradigm, paragon, pattern, prototype, standard, type

3. poser, sitter, subject

4. mannequin

5. configuration, design, form, kind, mark, mode, stamp, style, type, variety, version

 

Synonyms for "mould" are here:

1. cast, die, form, matrix, pattern, shape, stamp

2. brand, build, configuration, construction, cut, design, fashion, form, format, frame, kind, line, make, pattern, shape, stamp, structure, style

3. calibre, character, ilk, kidney, kind, nature, quality, sort, stamp, type.

 

5. Language lives in its use. Therefore it would be desirably to study how researchers coin and use certain words in their laboratories and in daily life. The first empirical studies start 1975 and come from Harry M. Collins, well known for his „Golem“-Books (1991, 1993) and Bruno Latour, known for his „Pandora“-Essays (1999). A concise overview is from Karin Knorr-Cetina (1999).

 

6. Some theorists use the model term thoughtless, e. g.:

·        Antje Korsten: Modelling the modelling language. Manchester: University of Manchester 1995.

·        Margaret C. Morrison: Modelling Nature. Between Physics and the Physical World. Philosophia naturalis 38, 1998, 65-85.

 

7. To define a concept we usually use numerous other „heavy" concepts, which need a definition themselves, e. g.: “Model, in logic a system of areas and concepts, in so far as it fulfils the axioms of a fitting formulated theory.”

 

8. All this becomes even more difficult, if you combine two heavy words. Then you have "model ideas" and "idea models" or "system models" and "model systems".

 

9. The same object or phenomenon is differently named in each language, e. g. gr. phantasia; lat. imago; scholast. imaginatio; English: idea; French: idée; German: Einbildung, Vorstellung, and in addition: Phantasie, Imagination.

 

10. So far there is neither a comprehensive theory of knowledge nor a differentiated ontology of models. Most scholars in the 20th century had in view only the relation "image". One of the first who worked out the triple relation “subject-model-original” was Klaus-Dieter Wüstneck (1963). Georg Klaus followed him 1967 in his „Wörterbuch der Kybernetik“. More complicated approaches have been proposed among others by Wilfried Neugebauer (1977) and Bernd Mahr (2008).

 

 

Reflections on the use of models

 

see at length: Reflections on the use of models

 

Since when is there a reflection on the fact that we use models and think in models?

 

Beginnings are already with Xenophanes (540 BC) and Platon.

Just before 1228 Robert Grosseteste outlined a model theory in a letter with respect to architecture.

Briefly after 1300 Duns Scotus developed a conception theory and his pupil William of Ockham the conceptualism. Around 1450 the religious philosopher Cusanus submitted a picture theory and the art theorist Leon Battista Alberti a model theory. Shortly after followed Antonio Averlino, detto Filarete.

Pronounced we find a reflection since the beginning of modern science, for example with Francis Bacon in his doctrine of idols (1620). He distinguishes four kinds of false ideas humans like to form: collective and individual aberrations, public opinion and tradition.

 

The next wave of consciousness starts with the Cambridge philosopher William Whewell (1840) and the American Scientist Charles Sanders Peirce (1868-1903). They were followed since 1875 by the German philosopher Hans Vaihinger, the two Austrian physicists Ernst Mach and Ludwig Boltzmann, the German physicist Heinrich Hertz, the French physicist Henri Poincaré and the Russian physicist Nikolai Alekseevich Umov.

 

Present reflection on model thinking and the use of models begins in the year 1942. Since 1945 this model-movement was so vehement that in 1951 the Viennese physicist Erwin Schrödinger portrayed in his booklet "Science and Humanism" on five pages the "nature of our ‘model'".

 

Since 1957 model thinking and the concept of model are discussed at numerous international symposia. In January 1960 and in August 1994 the IUHPS (International Union for the History and Philosophy of Science) dedicated congresses to the topic “Model” in Utrecht (Leo Apostel et al./ Hans Freudenthal 1961) and Warsaw (William E. Herfel 1995).

 

 

Word history of „modell“, „model“, „modèle“, „modul(e)“, „moule“, „mould“ (fig. 1)

 

see:    Nachschlagewerke für Begriffsgeschichte

 

In German as in all other European languages the words modell, model, modèle, modul(e), moule and mould have to be taken together for linguistic and historical reasons (Randle Cotgrave 1611; Jacob und Wilhelm Grimm 1885; Godefroy 1888, 1902; Walther von Wartburg 1966; Roland Müller 1980, 1983, 1997).

 

The variety of the ways of writing shows up very beautiful in English. In the "Oxford English Dictionary" we read the following forms for model:

"modill, moddell, moddel, modell, modle, modull, modil, modelle, model".

 

It is important to see that particularly in English for two hundred years (until 1750) the way of writing „modell” (with two l) was used. In the German language the contrary took place: until 1800 "Model" (with one l) was still in use e. g. for painter model and architectural model.

 

In all these concepts five fields of meaning interweave.

 

Five fields of meaning in Greek and Latin

 

The first meaning field goes back on the Greek word "metron" (yardstick, measure, boundary) and Latin "modus" (respectively in the reduction form: "modulus"). The primary meaning is measure in a double meaning, as unit (content) and as measuring instrument (yardstick).

 

The second meaning field goes back to the Greek word "typos" (form, sculpture, mould, figuration, type), Latin "forma" (figure, mould, casting; not: type).

 

The third meaning field goes back to the Greek word "paradeigma", Latin "exemplar". It was used for small-scale representations of buildings, ships and machines, and in addition, for the (usually male) painter model. The use of architectural models is known since Herodotus (450 BC).

The word was also used in the abstract. Aristotle criticizes in his "Metaphysics" (991a21) Plato's theory of ideas: "If you say, the ideas are models/or patterns (paradeigmata) and the other participates in them, then these are empty words and poetic metaphors" (viz. also 101a27).

The theoritician of science Thomas S. Kuhn (1962) has forth-fished the word paradigm in the 50's, but in a very special meaning, approximately in the sense of "current opinion"; the culture-anthropologists speak of "belief system".

 

The fourth meaning field is the most diverse. It goes back to the philosophically weighty Greek words "idea" and "eidos" (shape, form, idea, Urbild, picture), "eidolon" (image, deceit picture) and "eikon" (picture). In Latin we have for it "imago" and "effigies" (picture, ideal, image, conception - viz. Lexicon of the Art 1987-94). Also we have the wide variety of meanings for “species” (appearance, picture, idea, classic example, species) and “simulacrum” (image, pattern, doll, silhouette, dream vision, fake, characterization).

 

The fifth meaning field concerns plastic representations in wax. In Plato’s dialogue "Timaios" we find that God creates the human body like a modeller in wax ("keroplastes"). The verbs "keroplasteo" and "proplasso" were used very rarely for the process of forming. Gr. "proplasma" occurs only in the Roman time. For all types of "wax pictures" the Romans frequently used "cera".

 

 

The multiple history of “modulus”

 

40 BC to 1750: "modulus" (lat.): measure, figure, architectural model, small scale representation

 

The Latin word “modulus” is the reduction form of "modus", with the same primary meaning: measure, yardstick. It was not used very much in ancient Rome. It occurs shortly after 40 BC with Horaz and Varro; then it was used by the well-known architect Vitruvius in his "Book on Architecture" (approx. 23 BC) various times, mostly as architectural standard, namely the half column diameter.

The verb „modulor“ for regulating sounds in music and rhetoric was already used by Cicero (55 BC) and Vergilius. Vitruvius used it likewise, as well as „modulus“, also in the realm of music and introduced „modulatio“ for inflection of tone.

 

In his „Two Books on the Water Supply of the City of Rome“ (100 AD) the politician and writer Sextus Julius Frontinus used the word „modulus“ ca. 30 times for standardized pipes used in 25 sizes. Pliny the Elder and Gellius expanded the meaning of „modulus“ to the blood pulse. Then it was the church father Tertullian (approx. 200 AD; he also coined the concept “innovatio”), who expanded the meaning on the small figures of the sculptors, after which a marble sculpture was made for instance.

 

For patterns and paragons, examples and exemplars of all kinds as well as for small-scale devices Old Romans as well as the Middle Ages scholars used always „exemplum“ or „exemplar“.

 

In the national languages we find derivations from “modulus” since the year 1000.

 

We have to note that the Latin "modulus" (like "exemplar") was used until 1750 in the scholarly world, since 1450 (Alberti) particularly for the architectural model, and in addition, for other small-scale representations of real objects.

 

A prominent exponent is Leibniz. Following the description oft the benefits of making “Modulis” for the construction of fortresses he mentions in the year 1669 in his sketch of the “Ars inveniendi” the collections of models, which were very popular in his time: „de Theatro Naturae et Artis seu de Modulis rerum ipsarum conservatoriis" (G. W. Leibniz 1903, 163).

Shortly after he proposed in his “Atlas universalis” a department of objects, which “oculis subjici possunt”: „Mechanica, ubi omnis generis Machinae et moduli" (222-223). And at the same time he praises in detail the making of “exiguis modulis ligneis (aut cereis)” to foster imagination (596).

 

First development: „modulus“ becomes German „Model“/ “Modul“, French “modle”/ "molle"/ ”mole”/ ”moule”, English „mould„, Italian „mòdano„

 

We hear (not testified) that in German the early loan word "Model" was already used in the times of Charlemagne by the religious master builders as architectural measure.

From 1000 it is – accompanied by “Modul” - in freer use, on the one hand in the abstract sense as rule, pattern, form, example, on the other hand as industrial moulds for things like dragnets and bricks, later documents (e. g. contracts), fabrics and embroideries. Also the forms for printing on textiles and all kinds of hollow forms for casting goods and pastries were called “Model”.

 

Quite similarly we have in French: "modle", "molle", "mole" and "moule" (otherwise: patron) and in English: "mould" (otherwise: pattern).

It is nice to see that in English first came the abstract meaning of “mould”, namely “distinctive nature as indicative of origin” (1225), and that it took a hundred years until the meaning became concrete, in the sense of hollow form or “pattern” (1320).

In the 13th century we find in Italian "mòdano" as instrument for the asterisk measurement; only in 16th century it is used as measure, model and mould (otherwise: stampo). Since 1563 also „modanatura“ is used for "profilatura" or „elemento decorativo architettonico“.

 

The respective words are in German „modeln“ (since Minnesang), in English „mold“ or „mould“ and in French „mouler“.

 

„Moulding“ we find in English since 1327, for „ a raised or incised ornamental contour or outline“ in architecture since 1448, and as ornament on wood or metal since 1679.

„Mollage“ we find in French since 1415 (droit des mouleurs du bois), „moulage“ since 1680 (terme de potier). In English „moulage“ appears first in 1886, in German perhaps around 1850.

 

Second development: „modulus“ becomes Italian „mòdulo“, French and English „module“

 

In Italian "mòdulo" appears in the 13th century in the sense of the Vitruvius' column measure. "Module" appears 1547 in French and in 1583 (or 1586) in English. We note that in English “module” is not only used for measure or unit or standard, but also for design, architectural model, image, example.

 

In the strict sense as measure “module” held itself through the times, in techniques (with gear wheels) and in mathematics (logarithms, congruencies, Abel groups, etc.).

 

In the English mathematics “modulus” was introduced by Roger Cotes (1722; in Latin) and Abraham de Moivre (1738). Later „modulus“ was also used in physics as proportionality factor with distortion characteristics (elasticity: Hooke, Young).

 

In the years 1942-48 the famous Swiss architect Le Corbusier developed the "Modulor", an architectural standard, based on a man of 6 feet.

The use of "module" for a standardized construction unit emerges in 1946 in English and expanded rapidly into the other languages.

 

Third development: „modulatio“ becomes Italian „modulazione“, French and English „modulation“

 

It was also Vitruvius who used the verb „modulor“ for regulating sounds and make music, and the variation „modulatio“ twofold: for the calculation of measurements from a standard unit (e. g. Liber 5, Caput 9, 2-3), and for inflection of tone (e. g. 5, 4, 3). Later “modulatio” was used for rhythmical measure and melody.

 

In Italian „modulazione“ appears before 1342 in the sense of „parlare, cantare, suonare armoniosamente; variazione regolata“. The verb is „modulare“ (since before 1492).

 

„Modulation“ we have in French since 1365 and in English since 1398, both in the meaning of „changement d’intensité dans l’émission de la voix“ and „chant d’allégresse, harmonie“ resp. „the action of singing or making music“. Later the meaning was expanded to forming something according to due mesure and proportion.

The respective verbs are „moduler“ (1458) and „moduliser“ (1508) in French, „modulate“ (1557 or 1567) as well as „modulize“ (1605 or 1656) in English.

In German „Modulation“ appears in 1571 for „Akkordfolge, Übergang einer Tonart in eine andere“. The verb „modulieren“ appears at the same time.

 

The use of the English words "modulate" and "modulation" in telecommunication starts 1908. The other languages followed soon.

 

Fourth development: 1355-1417: The complicated birth of the Italian word "modello”

 

The often spread statement, that the vulgarly Latin word "modellus" is precursor for “modello” is not plausible. This word was used in the whole Middle Ages only around 1330 twice as wall crusher, twice as vessel in the household.

 

The Italian word "modello" appears in respect to the construction of the Dome of Florence.

Neither Arnolfo di Cambio the first master builder of the new construction, planned since 1294, nor the artist Giotto submitted a three-dimensional model for the Campanile (around 1334 - viz. Howard Saalman, 1964; Rolf Bernzen 1986; Roland Müller 1988; Andres Lepik, 1994, 27-38). Only under Francesco Talenti two wooden models are mentioned: 1353 for the Campanile, two years later for the choir chapels and a part of the nave.

 

In 1366 the building authority ordered designs for the completion of the cathedral. After short time two drawings and a model from brickwork were available. One of the drawings ran under "desingnum seu modellum". The three-dimensional structure was named "Chiesa piccola" and had to meet a double similarity (similitudo): On the one hand it had to be similar to the drawing, on the other hand the church to be built had to be similar to that model. (Presumably the well-known Fresco in the Spanish chapel of S. Maria Novella in Florence shows this model.)

 

For the time being the construction was not to realize for technical reasons. Fifty years later (1417) Brunelleschi became an advisor, and soon a lot of carpenters were busy producing models for the execution of the dome (Howard Saalman 1980; Rolf Bernzen, 1986, 122-137; Andres Lepik, 1994, 59-89). These were called now for the first time in Italian "modello", "modelo", "modeglio", in Latin "modello" or "modellum". In the year 1420 one was selected. With the help of further models - also for elevators and lifting devices - the construction of the dome was advanced step by step. An engineering master performance.

 

 

Models etc. in the Middle Ages and Renaissance

 

Imagination, analogy, metaphor and representation

 

Important concepts in the Middle Ages were imagination, analogy, metaphor and representation.

 

Phantasia, imaginatio

 

The Ancient Greeks called the modelling process in mind „ phantasia”. Romans used „imago "(almost never: imaginatio, repraesentatio, perceptio). Only Boethius (ca. 500 AD) explained in its „ Consolatio "(V. book): „Imaginatio vero solam sine materia iudicat figuram "(engl.: Imaginative power judges the shape without matter). In medieval philosophy the word „imaginatio " was common, e. g. with Abelard, Hugo of St. Viktor and Thomas Aquinas.

A good overview is given by Murray Wright Bundy (1927) and John Martin Cocking (1991).

Since 1500 imagination and fantasy are frequently described and discussed. In German we have also the words “Einbildungskraft”, “Vorstellung” und “Anschauung”. In English one used „idea”, in French „idée".

 

Analogy

 

Of course the Ancient Greeks already knew analogies. The concept of analogy got attention since the Franciscan and mystic Bonaventura (ca. 1250) and the Dominican Thomas Aquinas (ca. 1270) and is richly discussed up to today particularly in catholic theology.

Artists and scholars in Renaissance used analogies virtuous and often. Since that time the use of analogies is common in science and everyday life. With Kant and Goethe (ca. 1800) the concept of analogy became again interesting.

 

Metaphor

 

Ancient Greeks used also metaphors, i. e. pictures to illustrate an ordinary expression. Scholars in the Middle Ages concentrated on the interpretation of metaphors and the like in the Scripture. Research on metaphors begins only 1878.

Anthologies of beautiful essays on metaphors in history were arranged 1978 by Hayden V. White and 1994 by Frank Rudolf Ankersmit.

 

Repraesentatio

 

New interest in “repraesentatio” showed the specialists for the Middle Ages around 1970. Poor historical knowledge in this respect is found in the publications of Max Wartofsky (1979), Jerry Alan Fodor (1979), Ian Hacking (1983), Allan Paivio (1986), Hilary Putnam (1988), Patrick Suppes (1988), Robert A. Cummins (1989; 1996), R. I. G. Hughes (1997) and Michael A. Forrester (2000).

 

Cerae and Effigies

 

Since the first pilgrimage to Santiago de Compostela (950) the catholic church makes a cult out of votives made in wax (cerae).

The cult of “effigies” with respect to funerals and magic rape or execution is well documented from 1300-1800.

 

Since early 12th century: artistic and anatomical wax models

 

We can assume continuity from Antique to Renaissance workshops using objects of imitation made in clay or from wax, especially to train artistic expression.

A byzantine miniature of the 12th century (“St. Luc. Atelier d’artiste”) shows very well the use of antique masques, a statue and a column as models.

 

Likewise we assume that the first anatomical models have been shaped in the early 14th century in the course of investigating the vascular system. Molten wax was injected into the vessels, forming a cast that was carefully dissected out from the surrounding tissue. Another of the earliest models was created by none other than Leonardo da Vinci, who injected wax into the ventricular septum of the brain to bring out the detailed structures, and carefully recorded his method in his notebooks.

 

And more: Leonardo and Michelangelo used not only extensively the word “modello” but have already made, constructed and used a wide variety of models, not only for buildings of all kinds and for devices but also for artistic purposes, i. e. for drawings and paintings, sculptures and giant sculptures.

 

Since 400: Toys

 

Most toys create model worlds. Toys are well-known since earliest time of antiquity.

Because the medieval education system was rough and undemanding, toys were the same way.

Christmas cribs are mentioned in sermons around 400, rag dolls (simulacra de pannis) in the 8th century, mechanically moved dolls and birds around the year 1000. In the “Hortus Deliciarum" (1175-95) we see two children playing a tournament with knight figures, moving them like jumping Jacks.

Since these times toys were offered on fairs by flying dealers (Antonia Fraser 1966). Toys have survived since 1250: female figures and fable animals from tone, the tin figure of a knight in armament on his horse, a water jug in the shape of a horse.

From 1283 dates a accurate description of chess, games of dice and board games.

Since 1300 we have drawings of hobbyhorse, wind wheel, hand doll play (1338), kite (1405) and paper toys.

 

The first professional peg-doll carver (Dockenmacher) is mentioned in Nuremberg in 1413. The invention of the peep box is attributed to Leon Battista Alberti (1437). First reports of a baby-house (doll’s house) date from 1558, of silver household appliances for children from 1571. A mechanical Christmas crib with music was created 1589 by the Augsburg constructor of automats Hans Schlottheim.

 

Since 600: Beauty of bronze casting

 

From antiquity nearly no bronze statues have survived because they could be easily melted.

Artistic casting experienced a high level already in the dark Middle Ages. It begins in the 7th century with plaques of the Vikings and Langobards, continues with art work of the time of Charlemagne and in the dome of Hildesheim (1015/20), as well as with elaborate fonts out of brass (1118) and bronze (1225) and the lion of Braunschweig (1166) and ends with the first free standing human sculpture, „David" of Donatello (1430), and later “Perseus” of Benvenuto Cellini (1554).

 

The only preserved book describing the technique of casting is from Theophilus Presbyter (around 1123).

 

0-1500: Printing forms

 

In Japan a kind oft printed textiles were known in the first century AD. Real prints on bright, uncoloured linen are known since the 4th century from Egypt and since the 7th century from Europe and the Coptic areas of North Africa; likewise Chinese colour prints on silk.

 

The Gothic picture prints were devotion pictures in woodcut technology. Some prints served also as patterns for embroideries, i. e. they were over-stitched by hand. Beautiful examples have survived since the 13th century.

First documentary records of form cutters, i. e. carvers of the wooden printing models, originate from the year 1397 from Nuremberg and 1398 from Ulm. The models were used both for textile printing as well as for printing block books (popular books with woodcuts and short texts). The ornament stitch developed around 1450.

 

Printing with mobile type characters is said to be practiced around 1000 in China. In Europe Johannes Gutenberg introduced it around 1440.

 

13th-15th century: Baking tins

 

The oldest preserved baking tins (except from antiquity) date from the second half of the 13th century and are from limestone. From the 15th century about 150 models survived in middle Europe, particularly from tone, and also from slate and other stones. Representative, large models up to 40 centimetres in diameter start from 1500. They were usually carved in wood and used for marzipan, gingerbread and honey cake (Swiss: Tirggel).

 

Since 900: Model books and pattern books

 

Because the designations model book and pattern book are usually confounded, we have to differentiate between

·        patterns for craftsmen and women (for book illustrations, ornamentations and architectural parts, later embroideries and laces, furniture and other articles)

·        and samples, in the sense of specimen (first of textiles and silks, later of furniture and ceramics) for trade and sales.

 

Robert W. Scheller (1995) has collected and described with utmost care 28 model books with patterns for illustrations and architecture from 900-1470. The well-known collection by Arthur Lotz (1933) of Renaissance patterns for embroideries and laces follows.

Beautiful examples are from the 11th century the codex of the learned monk Adémar of Chabannes (1025) and from the first half oft the 13th century the album, sketch book or lodge-book by Villard de Honnecourt and the pattern books of Rein and Wolfenbuettel.

 

Around 1300 the Florentine textile industry had worldwide reputation. It is plausible that the practice of showing and dispatching samples (Italian „mostra”) started here. Since 1400 the word for it is in German „Muster” and in French „échantillon".

Soon these samples were put on cardboard according to quality, colour and material (wool, flax, cotton, silk).

 

Since 1300: fashion dolls

 

Already in the 2nd millennium BC there were jointed dolls in Babylon. In the grave of the Egyptian king Tutenchamon a wooden torso was found, presumable used as a tailor’s dummy. In Old Greece they made jointed dolls of clay.

At the courts in the Middle Ages there were tailor’s dummies in the precise sizes of the noblemen and noblewomen so that the tailor could adapt his cloths without bothering them.

 

Since about 1300 lay figures were used by artists in their studios. Also since then fashion dolls of all sizes are used as carriers and ambassadors of the newest fashion.

 

0-1200 To build from models and ideas, but not from drawings?

 

We do not have much information on the efforts of architects, builders and artists since Vitruvius until 1200 AD (Martin Warnke 1976; Günther Binding 1993).

Architectural drawings have been preserved only for the Gothic – since 1230 concerning Reims and Siena, others drawn by Villard de Honnecourt. In general the architect relied on heavenly inspiration – by vision or dream – or archetypical ideas. “In mente conceptum” was a standard formula.

 

A culture historical curiosity are the “models of donors” (Stiftermodelle). We find a least 100 exemplars form the times of the Roman Empire to 1500.

 

Since the 6th century: Pleasure gardens

 

For primeval times gardens are models: images or drafts of “paradise "or images or drafts of the “world”. Derek Clifford (1962, 16) states: „It is a world made to our own measure."

 

Starting from the 7th century we know of generously equipped pond gardens in Japan, sketched after Chinese model and serving as pleasure gardens for wealthy and mostly noble owners. Often they were miniature reproductions of the world at that time.

 

The Sassanide King Chosru I. (or Chosros I.; ca. 570) is said to have had marvelous gardens around his pleasure castles in Persia (Hans Sarkowicz 1998).

 

In the Arab culture (also in Spain under the Moors) we find at the same time the shaping of gardens with flowers, trees and bushes as well as with colored tiles, ponds and fountains. Today still impressing is the garden „Generalife" in Granada, probably put on before 1250 (Germain Bazin 1988).

 

In his “Roman de la Rose”, written around 1230, Guillaume de Lorris describes a dream garden, „the garden of pleasure". His work was finished 40 years later by Jean de Meun. In the 15th century it was richly illustrated several times.

 

Since that time gardens were described again and again by:

·        Jean de Garlande (around 1230)

·        Albertus Magnus (“de Vegetabilibus” 1257)

·        Pietro de Crescenzi (“Ruralia commoda", 1306)

·        Giovanni Bocciaccio in the Third day of the “Decameron" (1348)

·        “Le Ménagier de Paris” (1393)

·        Leon Battista Alberti (“De re aedificatoria”, 1450/60)

·        Francesco Colonna (“Hypnerotomachia Poliphili", 1499).

 

The first German book concerning „Pleasure gardens and planting "appeared 1530 with Egenolff in Strasbourg and with Steiner in Augsburg. Of large impact was the book „Tutti l'opera architecttura” of Sebastiano Serlio (1537-1547).

 

Since 1494 beautifully arranged gardens according certain patterns were called “knot gardens”, since 1579 in French “parterres”.

 

500-1500: Models for thinking and for behavior (fig. 1b)

 

Some important world models, ideas, ideals and behavior models of the Middle Ages – in Europe and the Middle East - were:

 

·        Economics: Feudalism (beginning of 6^th cent.), crop rotation (6^th cent.), fiefdom (Merovingian donation of land; Karl Martell 725), cities (1000), slave trade (Pope Urban II 1095; Henry the Navigator 1441), fairs (12^th cent.), private banks (1163), Franz of Assisi (poverty 1208), household (Walter de Henley 1250; Leon Battista Alberti 1444; also ecology), Thomas von Aquin (ban on interest, theory of work, property theory 1270), money economics replaces pay in kind; public banks (1401), stock exchange (1460/85 Antwerp)

·        Ideal life: Epic („Digenis Akritas” 11^th cent.; „Ruodlieb "1050; „Roland" 1090; „El Cid "1140; „Nibelungen” 1200), „Christian knight" (Bonizo 1090), minne, courtly life (Troubadours since 1100), service (Franz of Assisi 1210), humanism (since 1300: Dante, Petrarca, Boccaccio), „Della vita civile "(Matteo Palmieri 1438), discovery of the individual (Pico della Mirandola 1492)

·        Political procedures: Sovereignty (Manegold 1085), „Domesday Book "(1086 in England: land register and tax book), parliament (1265 in England); „voluntary subjecting contract" (William of Ockham 1330)

·        Instructions for behavior: Benedikt of Nursia (529), Konstantin VII (De „ceremoniis "950), Avicebron (1050), „Regimen sanitatis" (1050), Petrus Alfonsi (1120), Petrus Abaelard (“Ethica" 1136), Johannes of Salisbury (1159), fashion (12^th cent.)

·        World models: apocalypse (999), Bernhard Silvestris (1148), Hildegard of Bingen (1180), Joachim de Fiore (1190), Sacrobosco (1220/30), Robert Grosseteste (metaphysics of light 1250), Konrad of Megenberg (1350), Cusanus („coincidentia oppositorum“ 1438)

·        Science: „House of wisdom" (Bagdad 813), Gerbert (990), nominalism (Roscelin 1092; William of Ockham 1330; Nicolaus d'Autercourt 1347), separation of faith and knowledge (Adelard of Bath and William of Conches, before 1150; Alfredus Anglicus 1217; Siger of Brabant 1270; Johannes Duns Sotus 1300), universities (from 1155: Bologna, Paris, Oxford), experience (Roger Bacon 1268; Petrus Peregrinus 1269), Platonic academy (1459)

·        Thought Models: Chess (500), dialectics (Berengar of Tours 1050), „Sic et non" (Petrus Abaelard 1140), combinatorics (Raymundus Lullus 1303).

 

 

Since 1542: The model concept in French, German and English

 

Since 1542: "modello" arrives in French, German and English

 

Around 1550 the Italian word „modello „came

into French as "modelle" or "modèle",

into German as „Modell" and

into English as "modell" or "model".

Whereby the variety of meaning expanded rapidly into the present-day abundance.

 

The continuous change in the usage shows up very beautiful in English, where since middle oft the 16th century not only the word “model” was used for models of buildings, machines and landscapes, but also “modell”, "moddel" and “module". On the other side the “modulus” of Vitruvius was translated with „module ", "model" and "modulus".

Shakespeare used model more than a dozen times in various meanings, e. g. in the sense of an architect’s set of designs and or of a person that is the likeness or „image” of another, and in different spellings, e .g. “modle” (1597), “model” (1598), “modill” (1604) and “Modell” (1623).

“Mould” was also written as French “moule” and also as “mowle”.

 

In German both "Model" and "Modell" were used for architectural models. The meaning rapidly expanded on patterns and examples. The uncertainty of writing, once with one l, once with two l, continued for a long time.

 

In fashion (French: "à la mode" or "modo") we find already in 1640 in German "models of clothes and shoes". In the other languages this seems to be the case 200 years later.

 

The respective verbs are „modeler“ (French, since 1585: „rendre semblable“) and „modellare“ (Italian, 1598), in English „modelize“ (1605) and „model“ (1625), in German „modellieren“ (see 1739 in Zedlers Lexicon).

 

Starting from 1555: Mental designs or forms as models

 

It is remarkable that at that time already mental designs were marked as models, such as the reformation (“il modello di Martino Lutero” by the monk Giacomo Moronessa 1555), the “new Theorick” of Copernicus (by Thomas Digges 1576), Bacon’s "New Atlantis" (1627), Descartes’ "Discourse" (by himself and Huygens) as well as "The German Principality” of the Cameralist von Seckendorff (1656).

The philosopher Pascal defined model in this sense as: "ouvrage d'esprit ou action morale, dont on peut s'inspirer".

 

Partial rivals of the concept of model

 

After his birth the concept of the model term immediately got in rivalry to numerous other concepts.

Copernicus used neither in his “Commentariolus” (approx. 1515) nor in “De revolutionibus orbium coelestium” (1543) the concepts “system” and “model”. But in the title of his main work we find the word „hypothesis". As early as 1540 Joachim Rheticus spoke of the „systema” of Copernicus. In 1576 Thomas Digges wrote of the models of Ptolome and Copernicus.

 

Since then further persistent partial rivals of the concept of model are „theory" (lat.: theorica), „philosophy" (philosophia), „treatise" (tractatus) and „principles" (principia)

.

Other rivals include in another perspective “representation”, “analogy” and “metaphor” – not forgetting „image“ and „imagery“. Since 1960 these topics have been disputed anew, fewest of all analogy, increasingly metaphor and representation. Concerning the latter the confusion of idea became soon so manifest that since 1990 on had to speak of a “crisis of representation”. In the anglophone countries furthermore evolved a dispute on “imagery” such intensive that from 1980 on a “pictorial turn” or “iconic turn” has been diagnosed. Germany tentatively followed with a “Bildwissenschaft”.

 

Humans as "models"

 

Drawing from a human model was begun again in the Renaissance. In 1270 Cimabue painted the "countess X". Still over 100 years passed until artists dared to paint (1380/1400) from the naked body.

Another three hundred years later the word for it was "modello" (Italian 1672; later also: modella), "modelle" (French 1676), "model" (English 1691) and "Modell" (German 1717).

 

In the years 1953-54 Picasso painted 70 pictures to the topic "the painter and his model".

 

A woman displaying clothes is called "mannequin" since 1850 (in French) and “model” in English since 1904 ( “mannequin” since 1919) .

 

One of the many examples of the so-called "Americanisation" of the German language after the World War II is the substitution of the words “Probierfräulein”, “Fotomodell”, “Vorführmodell”" and "Mannequin" by "Model" since 1968, whereby in the 80's still both forms were used.

 

Model as euphemism for prostitute is used in England since 1963 and soon spread on the continent.

 

 

Starting from 1600: The use of models in science and education

 

Model experiments

 

Since the beginning of modern science, which is at about 1600, not only the concept of model is used more frequently, but one begins also with model experiments.

The clergyman Simon Sturtevant described in 1612 in his patent application "Metallica" the heuristic use of models. The first model experiments in the sciences made the two Dutchmen Simon Stevin and Cornelius Drebbel, the Englishman William Gilbert (1600 with his terrella, a small iron ball as earth), the Italian Galileo Galilei (1638 in the "Discorsi": experiments on the bend of beam) as well as the German Otto von Guericke (1663 attempts with the Magdeburger hemispheres).

 

Since 1600 there were constructed ship models for hydraulic experimenting, first in England, then in Holland, France and Russia.

 

Visual instruction

 

Most important with the model are visuality, manipulating and improvability. No one has this expressed more beautifully than the famous "uomo universale" of the Renaissance, Leon Battista Alberti.

But only in the baroque his ideas were picked up. Campanella placed a reform program for education in his "City of the Sun” (1602 respectively 1623), which is based decisively on the use of models. Bacons "New Atlantis" (written 1624) brings something similar.

The famous pedagogue Jan Comenius emphasized in his "Bohemian Didactics” as well as in his "Great Didactics" (1633-38; published 1657) the character of models as always capable of improvement, and he publicised the visual instruction.

 

At that time there were presumably models with cords and wires, from cardboard or gypsum for geometrical bodies for instruction. They are mentioned in Christian Wolff’s "Mathematical Lexicon„ (1734 - viz. Gerd Fischer 1986). In instructing mathematics it was learned to modelling on the basis of the five Platonic bodies.

 

The use of hydrodynamic analogies

 

The ancient Greeks and the artists and scholars of the Renaissance had already used analogies virtuous. In the course of the "mechanization of the world view" hydrodynamic analogies arose. William Harvey’s discovery of the blood circulation (1616) was inspired by hydrodynamic analogies. Also Descartes was stimulated from the hydraulic engineering arts of his time. Giovanni Borelli (since 1666) used likewise analogies from the hydrostatics; he invented the Iatromathematics or Iatrophysics, a preliminary stage of biophysics.

Whether François Quesnay could be inspired for his model of the economic circulation (1758) of the blood circulation or of hydrodynamics, is disputed. In the physics of electromagnetism since 1820 (Faraday, Gauss, Maxwell) there were used a lot of hydrodynamic analogies.

 

Holistic thinking: The organism as analogy

 

There are also analogies in the other direction. Very popular was the (in fact: idealized) organism as a model for social or economic things, sometimes as well as for the universe.

The English statesman and philosopher Thomas Hobbes compared the State (1651) to a “artificial man”.

Economists and philosophers of the Romantic as Adam Müller (1809) and Franz von Baader (1832) have been inspired by the natural philosophic concept of the organism. The most prominent representative of this kind of thinking was Albert Schäffle. He has tempered the extreme - and therefore wide spread - formulations of his main publication, “Structure and life of the social body” (1875-78) in its second edition (1896). He can be regarded as one of the pioneers of systems sthinking.

 

 

19. century: Reality, visualization and theory in mathematics and science

 

Animals as substitutes for humans

 

Lamettries „L'homme machine "(1748) initiated psychological research on animals, and the animal experiments of the universal scholar Albrecht von Haller (1750) laid the foundation for neurobiology.

Since 1820 François Magendie and others regularly made experiments with animals. Pierre Flourens, professor for comparative anatomy in Paris, removed by exstirpation certain brain parts of pigeons and dogs and observed in consequence a decline in performance (1824).

Already in 1831 the neurologist and physiologist Marshall Hall set up guidelines for experiments with animals. The first investigations into isolated hearts took place 1846. And immediately the first protests against vivisection arouse (Evalyn Westacott 1949).

1998 Kenneth Joel Shapiro came to the conclusion that the investigation into animals does not help understanding of human behavior.

 

Samples as extracts from society

 

William Petty was the first to make a sociograph exploration in 1655-56 and soon founded „political arithmetic". First statistic work originates from the same time around 1660.

But only about 1740 - when the first consequences of the industrialization began to show up - social sciences took serious the conditions of the working poor. Already around 1795 the Englishmen David Davies and Sir Frederick Morton Eden used a kind of questionnaire to explore them.

 

A kind of “social experiments” claiming some representativeness was practiced since 1800 by the so-called utopian socialists Charles Fourier (1804-1836: “Phalanstère”, and thereof inspired 1844-46: Brook Farm Colony in Massachusetts), Robert Owen (1824-27: “New Harmony”) and Louis Blanc (1840: productive cooperatives).

 

Empirical social research has been pioneered by the members of the “Royal Commissions” of 1825, whose efforts culminated in the law for factory inspection of 1833. Their results of research were used still by Marx and Engels.

 

Since 1840 in many countries social enquêtes belong to the agenda.

 

The journalist Henry Mayhew used already 1851 „nondirective interviews". The mining engineer Frédéric Le Play refined 1855 the "observation method".

1895 the Norwegian Anders N. Kiaer presented his idea of a sample based on what he called the "representative method" for the first time to public. Later he used many representative samples as a basis for statistics, especially with regard to income statistics. In England Sir Arthur L Bowley used 1912-14 the procedure of random sampling.

 

1790-1880: American patent models

 

The United States Patent Office represented an early form of Federal support for science. This support enabled scientists, inventors, and entrepreneurs to secure property rights for their innovations. While many of the original thirteen American Colonies had some form of patent law, Thomas Jefferson (among others) influenced the development of the first national patent system in 1790. President George Washington signed the Patent Act of 1790.

Until 1880, to obtain a patent, the inventor submitted to the U.S. Patent Office an application, which consisted of a proper specification, carefully measured drawings, and, in most cases, a physical model of the invention. Well-known examples are the washing machine, septic tank and alarm systems (William and Marlys Ray 1974; American Enterprise 1984; Icons of Invention 1990).

Fire in the Patent Office 1836 and 1877 destroyed more than 80 000 models, but 150 000 remained when the obligation to submit a model was dropped. Today the office demands only a model when the applicant has to show that his inventions works in practice.

Nowadays there are various collections, private or public, of these patent models, e. g. with the Smithsonian Institution or the N. E. C. Group, Inc.

 

Science since 1840

 

Another differentiation of the model concept started approximately 1840. On the one hand, it was used for industrial products manufactured in great quantities (David S. Landes 1968); on the other hand it played a new role in physics.

 

We were told tat the modern model discussion begins 1840 with the investigation of the Cambridge professor William Whewell „The Philosophy of the Inductive Sciences", which was influenced by Kant. At the same time a second wave of visualization began in science. First such concepts were used as picture, illustration, idea, analogy, etc. In 1855 the Scotsman James Clerk Maxwell tried to give a "geometrical model" oft the physical forces. (In German the concept of model in physics appears more than twenty years later, 1879, with the translations of Maxwell's writings.)

 

Real visualizations of the theory by apparatus were built since the 1870’s in particular by the Englishman Oliver Lodge (who later devoted himself to the examination of psychic phenomena) and the Irishman George Francis Fitzgerald. In the autumn 1892 the German Union of Mathematicians organized an exhibition in Munich of such apparatus. The extensive "Catalogue of mathematical and mathematical-physical models, apparatus and instruments" (ed. Walther Dyck 1892) appeared with a preface of Ludwig Boltzmann.

Already in 1893 the French physicist Pierre Duhem made fun of the efforts of his English colleagues, in particular William Thomson. More than a dozen years later he brought an extended version (70 pages) of his essay as Chapter Four in his legendary work "La théorie physique - son objet et sa structure” (1906; German: 1908; Engl. 1914).

 

It was Heinrich Hertz who introduced 1894 the concept of model explicitly in German science with his theory of "dynamic models".

 

Another Scotsman, Archibald Couper, introduced 1858 to chemistry the graphic visualization by the structural formula with valence lines. The German chemist August Kekulé built at the same time atomic models and models of molecules from balls and wires "because of an irresistible need of visualization". Likewise many mathematicians, e.g. Julius Plücker and Ernst Eduard Kummer, started the plastic modelling of complicated mathematical and geometrical curves and bodies. Gerd Fischer (1986) published two rich and beautiful illustrated volumes.

 

 

The case of William Thomson, 1884 vs. 1904

 

How intensive was his search for models?

 

Generations of historians and theorists of science have quoted the following sentences of Sir William Thomson (1892: Baron Kelvin):

„I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand; and that is why I cannot get the electro-magnetic theory… But I want to understand light as well as I can, without introducing things that we understand even less of. That is why I take plain dynamics. I can get a model in plain dynamics, I cannot in electro-magnetics.”

 

These sentences are from the beginning of the last of 20 lectures held by Thomson in October 1884 at Johns Hopkins University in Baltimore. A. S. Hathaway made a record in shorthand. Of this in December the same year a “papyrograph volume” was edited. The careful revision of these texts took Thomson 20 years.

Only 1904 the hardcover edition of the „Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light“ was edited – without the sentences quoted above! Reason for that? Thomson had supplemented most lectures, and more, in the years 1901-03 he wrote Nr. 16-20 totally new.

 

Therefore we can ask if it is fair to quote again and again the shorthand notes and to ignore the final edition of 1904. (The 20 lectures “in their original form” have been edited by Robert Kargon and Peter Achinstein as late as 1987. Here we find the quoted sentences on page 206.)

 

bibliography see:   model: special topics – William Thomson (1892: Baron Kelvin)

 

"Levels" of models in mathematics and science (fig. 2)

 

If we summarize the efforts of mathematicians and scientists in the 19th century we can differentiate six "levels" of their access to the things:

1. As starting point or "objects" we have on the one hand, mathematical ideas or ideals, on the other hand „reality", that means physical and chemical objects and processes

2. The area of the equations and formulas, laws and axioms, which are set up concerning the appearances and structures of the first level

3. The level of the "thought pictures" or hypothetical constructions

4. These "pictures" can be brought to paper as graphic representations

5. The level of the three-dimensional, material visualization of these "pictures".

6. The level of the theories.

 

Unfortunately many renowned physicists give rise to considerable confusion, because the use the word model for things of the level 2 (e.g. axioms or analogies) as well as for things of the levels 3 and 6. One of the first promoters of confusion was Ludwig Boltzmann (since 1890).

 

 

1. Half of 20th century: Nearly silence for model in the science

 

Surprisingly the model term - apart from the "atom model", learning psychology (around 1930) and econometrics - has been a wall flower nearly half a century after 1900. Most authors in physics did not know what to make with it (e. g. Norman Robert Campbell 1920) or they mention briefly the material models of Maxwell, Thomson and Boltzmann (e. g. Paul Volkmann 1910; Abram Cornelius Benjamin 1937).

 

Philipp Frank (1927), James Jeans (1933) and Pascual Jordan (1936) thought about illustrativeness in physics (also Viktor A. Stoff 1969, 287-298).

 

For Hermann Weyl (1927) model belongs into the range of logic. Nevertheless the physicist Percy W. Bridgman meant in the same year (1927, 53):„I believe that the model is a useful and indeed inescapable tool of thought, in that it enables us to think about the unfamiliar in term of the familiar."

 

Mostly theorists tried to replace model by „symbol" (e. g. Abram Cornelius Benjamin) or „icon", "isomorphism" and "analogy" (e. g. Norman Robert Campbell).

 

In 1963 Mary Brenda Hesse constructed literarily a contrast between the ideas of Pierre Duhem (1906) and Campbell (1920). This is not convincing because no such dispute took place.

 

Albert Einstein made use of the word model quite unusual for physics. He stated 1930 ("The world as I see it") in a speech: „I still believe in the possibility of a model of the reality, i. e. a theory which represent the things themselves and not only the probability of their occurrence."

 

 

Visual thinking is very disputed

 

The first half of the 20th century is shaped by a strong contrast. On the one side we have the Wuerzburg School (psychology of thinking) and the Behaviorists as picture destructors, on the other hand we had an eruption of activities and thinking about concerning creativity, which resulted also in exploration of imagination and genius.

 

It is no longer trendy to speak of visual thinking

 

Since 1901 the philosopher and psychologist Oswald Kuelpe and his students in Wuerzburg questioned the theses of symbolic recognition and visual thinking. William Wundt protested furious and a controversy arouse in the years 1907-09, which finally resulted in discrediting of the “introspective” method – despite Wundt was wrong.

In 1913 John Broadus Watson led the death blow for visual thinking by presenting the program of Behaviorism.

Since then to 1960 in certain scientific communities it was not at all trendy to speak of „mental imagery".

Also Analytic Philosophy and later Logical Empirism, which soon controlled the whole Anglo-Saxon area and thought the medium of thinking was language, denied the traditional view that the verbal meaning is deduced of „pictures in the brain".

 

Nevertheless psychological research on imagery and creativity

 

The important books of the two French Théodule Ribot (“L'imagination créatrice” 1900) and Henri Bergson (“L'évolution créatrice"1907) formed the counterweight to the Wuerzburger School and to Watson. They caused a boom of investigations into mental and visual imagery and imagination as well as into creativity, “Schöpferkraft” and genius.

 

Connected with these investigations were often studies of problem solving. The first impulses came again from the Wuerzburger School. Immediately it went internationally with the Englishmen Charles Spearman (1904) and William McDougall (1910), the Germans Karl Buehler (1907/8) and Otto Selz (1913), the Frenchman Henri Poincaré (1908), the American John Dewey (1909) and the Viennese Sigmund Freud (1911).

 

Research on orientation plans in the brain

 

An important experimental investigation into thinking has been submitted by the American psychologist Edna Heidbreder 1924. More than twenty years later (1946; 1947) she published her basic research reports on „concept learning."

 

The American psychologist Edward Chace Tolman studied the behavior of rats in the labyrinth and due to his observations he developed a systematic learning theory. He held the view these animals create themselves a picture of the labyrinth in which they move, a kind of internal map (“cognitive„map"; see 1948), an internal representation of the geometrical relations of important points in the animal’s environment.

 

First reports on „higher mentally processes in animals "and „’insight’ in rats” he published already 1927 and 1930.His huge tome „ Purposive Behavior in Animals and Men "(1932) reached several editions.

 

The English experimental psychologist Frederick Charles Bartlett reported in his book on „remembering" (1932) the influence of social factors on memory. Most of his research he had made already in the First World War (1916; 1921).

Instead of senseless syllables he used „meaningful" material. It showed up that the test subjects not only reproduced them but arranged them in the light of past experiences. That was named by Bartlett „scheme" or „conceptual model".

 

In 1932 Tolman also introduced in the field of psychological research the “intervening variable". Later psychologists spoke of “hypothetical constructs” (Kenneth MacCorquodale, Paul Everett Meehl 1948) and “personal constructs” (George Alexander Kelly 1955).

 

Starting from 1960 upswing of research on imagery

 

Around 1960 a similar paradox situation arouse as at the beginning of the century. On the one hand the so-called “cognitive” approach in psychology, anthropology (Ethnology) and ethologic spread rapidly out, on the other hand research pounced on imagery and mental images and got back to the scene metaphor and analogy.

Important works came from Alan Richardson (1969) and Allan Paivio (1971).

After 1980 there was no holding them. More than 200 studies on imagery and some on “mental representation” were published from 1990 to 2000.

In the year 2000 Michel Denis offered a “state of the art” (2000), and the old masters of linguistic and thinking philosophy Jerry Alan Fodor warned: "The mind doesn't work that way!"

 

Research on metaphor

 

Research of metaphor started with Friedrich Brinkmann (1878) and spread rapidly. But the vast majority remained in the field of theology, rhetoric and literature.

The two most important works were by the psychologist Heinz Werner on the “origins of metaphor (1919) and by Martin Foss: „Symbol and metaphor in human experience" (1949).

 

After a straw fire from 1960 to 1966 it remained again calm. The study of metaphor was initiated only with the anthology of Andrew Ortony (“Metaphor and thought" 1979) and the best-seller of George Lakoff and Mark Johnson „Metaphors we live by "(1980). An abundance of studies of all kinds developed, several hundreds to 2000.

 

Research on analogy

 

Kant and Goethe (around 1800) made the concept of analogy popular. William Stanley Jevons (“The principles of science" 1874) was the first to examine the use of analogy in science.

1902 diagnosed Ernst Mach „similarity and analogy as guidelines of research”. In the previous year Albert Thumb and Karl Marbe had made „experimental investigations into the psychological bases of linguistic analogy formation” in the context of their pioneering work to psychology of thinking at the University of Wuerzburg.

 

All alone stayed studies on analogy by Harald Hoeffding (1905, 1924), Scott Milross Buchanan (1932), S. T. Cargill (1947) and Maurice Dorolle (1949).

In shorter contributions Lothar von Strauss and Torney (1936), Rudolf Seeliger (1948), Werner Theis (1951) and Joseph Turner (1955-56) examined the analogy term in physics.

 

Also from 1960 to 2000 research on analogy remained meagre. Some momentum resulted from the threefold titles by William Hilton Leatherdale „Analogy, model, metaphor"(1974) and by Danielle and George Arthur Mihram “The role of models, metaphors and analogy" (1974).

Public interest was generated following Nancy J. Nersessian (1988), Rome Harré (1988) and Kenneth J. Gilhooly (1990).

 

 

20th century: Models in modern logic, robotics, economics. social sciences, computer science

 

Since 1915: Extension in the modern logic

 

The model concept was expanded once again by the Viennese philosopher Ludwig Wittgenstein (1921) and the German mathematician Hermann Weyl (1927). In the 1930’s logicians as Rudolf Carnap (1934ff), Morris Raphael Cohen and his disciple Ernest Nagel (1934) and Alfred Tarski (1935; 1935/36) saw the model as "fulfilment" of axiomatic systems and formalized theories.

In the “Historical dictionary of philosophy” we read: "In logic 'model' is a system of areas and concepts, in so far as it fills the axioms of an adequately formulated theory.“

 

After World War II model theory expanded further in the logic, semantics and mathematics. One of the first essays in this area, in which the expression „theory of models“ occurs, is from Alfred Tarski (1954/55). A first introduction to this kind of model theory gave Abraham Robinson in 1963.

 

In an appendix to the papers of a symposium, edited by John W. Addison et al. (1965, 442-492) we find a collection of not less than 940 titles in a „Bibliography of the theory of models“.

At a symposium in honour of Alfred Tarski in summer 1971 in Berkeley Robert L. Vaught and Chen Chung Chang told the history of this kind of “Theory of models” since 1915 with vast bibliographies.

 

Since 1920: electrical and electronic robots

 

Inspired of Karel Capeks play "R. U. R." (1920) numerous so-called "robots" were built; they had names as “Occultus” (a robot soldier) "Televox" (a domestic robot), "Eric", "Alpha", "Sabor" or "Elektro”. In the 1930's each fair and each exhibition, particular about it’s appearance, had its own, often larger-than-life robot.

 

In 1938 the American Thomas Ross built the first scientific robot. It was a small machine, learning like a mouse, by trial and error, the way out from a maze.

Since then researchers like to build "life-imitating" machines. Famous are the electronic turtles "Elmer" and “Elsie" of the American-English brain researcher William Grey Walter (1948), the “Homeostat” of the Englishman W. Ross Ashby (1948) and the "machina labyrinthea" of the American R. A. Wallace (1952).

The first complete robot system with sensors and optical pathfinder was developed 1968 at the Stanford Research Institute and was called "Shakey". It was rebuilt 1971 for other tasks.

Numerical controlled industry robots are in use since 1960.

 

Since 1930: mathematical treatment of economic questions

 

Important mathematical treatment of economic questions have been given from the 1930s on – besides Ragnar Frisch and Jan Tinbergen – among others John von Neumann (1938; primary 1932), Michal Kalecki (1935), Victor Edelberg (1936; 1936), James E. Meade (1936), John Richard Hicks (1937), Roy F. Harrod (1939) and Paul A. Samuelson (1939). Already in 1938 economists spoke – besides „Keynes’ model“ - of „Kalecki’s model“, and two years later Nicholas Kaldor proposed an extension of it. Therefore Vittorio Marrama could speak in 1946 of the „Kalecki-Kaldor model“.

In 1948/49 William Jack Baumol plucked to pieces the models of Harrod und Samuelson. John Richard Hicks (1949) made the same with Harrods „Dynamic Theory“; Sidney S. Alexander followed in 1949/50. Oddly enough Baumol in consequence did not speak of the Harrod-Samuelson model, but of the Harrod-Domar model (1952).

Already since 1940 has been spoken of the „Hicksian model“, since 1951 of the „Hicksian IS-LM diagram“, since 1963 oft the „Hicks IS-LM“ and since 1968 of the „Hicksian IS-LM model“. In 1962 it has been extended by Robert Mundell and Marcus Fleming.

 

The notation “econometric model” we first encounter with Victor Edelberg (1936). In 1941 Sami Semsiddin Tekiner did his doctorate at Cornell University on „dynamic economic models“.

In 1944 Leonid Hurwicz spoke of „Haavelmo’s model“, „Koopman’s model“ and „Samuelson’s system“. Since 1941 one speaks of the „Leontief system“, since 1943 of „Leontief’s model“ and since 1950 of „Leontief’s input-output model“.

 

Since 1944: refinements of economic models and new models in other sciences

 

After World War II models in econometrics were refined by Leonid Hurwicz, Tjalling C. Koopmans; Lawrence Robert Klein; Robert W. Solow.

New areas were:

• decision and risk theory (Herbert Alexander Simon, Abraham Wald, Leonard J. Savage; Ward Edwards; Kenneth Joseph Arrow, Robert McDowell Thrall, Clyde H. Coombs)

• game theory (John von Neumann und Oskar Morgenstern, Melvin Dresher, Martin Shubik) and

• portfolio theory (Harry M. Markowitz, James Tobin).

A mathematical treatment of learning psychology has been attempted by William Kaye Estes; Robert R. Bush, Frederick Mosteller.

 

Starting with his dissertation 1950 Patrick Suppes published dozens of contributions concerning models and science in all facets. Anthologies of them appeared in 1979 and 1993.

 

Other pioneers show an international diversity, e g. Ernest Hirschlaff Hutten, Mary Brenda Hesse and Karl Wolfgang Deutsch as well as Evert Willem Beth, John G. Kemeny, Georg Kreisel, Abraham Robinson and Chen Chung Chang.

 

Mathematical-logical „model theory“ has been enlarged by Alfred Tarski (1954-55).

 

Since 1950: Simulation and modelling

 

In the early 1950’s researchers started with simulations on the computer. They tried to introduce mathematical, statistical or stochastic models for the most different processes. In 1958 the AIIE held a first symposium in Baltimore on „system simulation”. Important impulses came from the RAND Corporation in Santa Monica, a think tank, which made also important contributions to "systems analysis".

End of the 1970's a bibliography counted over 6000 titles for "computer simulation" (Per Holst 1979).

Parallel efforts ran to find “mechanical models" for economic, biological and psychological processes (N. F. Morehouse et al. 1950; O. J. M. Smith, H. F. Erdley 1952; Arnold Tustin 1953; Donald E. Broadbent 1957).

 

The concept of "modelling" appears somewhat later, on the one hand in the Russian (and the East German translations), on the other hand in English (Eric John Barker 1954; N. L. Irvine, L. Davis 1955; Herbert A. Simon 1961; Kenneth M. Sayre 1963; Richard F. Reiss 1964; George Jiri Klir, Miroslav Valach 1966; Francis F. Martin 1968).

 

Since 1960: A revolution - Computer Aided Design (CAD)

 

Many traditional and beloved techniques of drafting and designing “models” for buildings, ships or automobiles, electrical circuits or injection molds have been replaced since 1960 by Computer Aided Design (CAD).

This kind of computer use was advanced from US-military research on space travel. Later they made them accessible also for the public.

1964 IBM developed the first CAD Computer, the “System 2250”. A first general introduction in the field gave 1968 Charles Russell Mischke.

 

 

Conclusion

 

„Model Muddle"

 

Despite the programmatic title „Models" the anthology of 18 essays of the philosopher Max W. Wartofsky from the years 1953-1978 is poor. On only one page he mentions the mechanical models of Maxwell and Lord Kelvin, with the criticism of Duhem.

Like many other scholars he does not like the concept “model” and he spoke therefore 1966 of a „model muddle" (1979, 1). His solution reads as follows: „I propose to collapse the distinction between models, theories, analogies, and to take all of these, and more besides, as species of the genus representation; and to take representation in the most direct sense of image or copy.”

That is a collapse of all upright scientific endeavour.

 

An elaborate general theory of models (“Allgemeine Modelltheorie”) was presented 1973 by the German mathematician Herbert Stachowiak. It was widely ignored.

 

In a short contribution on models in physics Brigitte Falkenburg maintains (1997, 28) that empiristic oriented theory of science does not view the concept of models as something independent, “but as a derivative of the formal concept of theory: Models therefore are abstract set-theoretical representations of sentences of an axiomatic theory, which can have themselves concrete empirical representations."

Falkenburg uses another concept of model. It seems to be about phases on the way to complete theories. She thinks basic research in physics consists of „the search for fundamental theories on the basis of incoherent principles and models "(38).

 

Mary S. Morgan and Margaret Morrison report on such research under the formula „Models as Mediators" (1999). But already in the introduction (1999, 8) they admit after intensive discussions with colleagues for 10 years:

„We have very little sense of what a model is in itself and how it is able to function in an autonomous way."

 

What can we rely on today?

 

Models are basic in science and technology

 

Brigitte Falkenburg and Susanne Hauser open their Editorial to their anthology “Model thinking in the sciences" (1997) with the following statement:

"Despite non-uniformness with respect to content and methodology today all sciences of nature as well as of culture have a common ground: Modelling plays a prominent role in them.

Models constitute scientific discovery; apart from hermeneutic methods they are the most important tools to the opening of the object-areas of each single science."

 

Very similar is the statement by Margaret Morrison and Mary S. Morgan (1999, 10):

„Models are one of the critical instruments of modern science. We know that models function in a variety of different ways within the sciences to help us learn not only about theories but also about the world.“

 

For the field of technology George A. Hazelrigg (in Carl W. Hall: Laws and models. 2000, viii) writes:

„A model is an abstraction of reality … It is only through models, and especially inferences of cause and effect, that we gain an understanding of nature … In engineering we use models to combine disparate elements of knowledge and data to make accurate predictions of future events.”

 

 

Selected Bibliography

 

American enterprise: Nineteenth-century patent models. New York: Cooper-Hewitt Museum 1984.

Frank Rudolf Ankersmit: History and Tropology. The rise and fall of metaphor. Berkeley: University of California Press 1994.

Francis Bacon: Neu-Atlantis. In Klaus J. Heinisch (Ed.): Der utopische Staat – Morus: Utopia; Campanella: Sonnenstaat; Bacon: Neu-Atlantis. Reinbek: Rowohlt Taschenbuch Verlag 1960.

Abram Cornelius Benjamin: The logical structure of science. London: Paul, Trench, Trubner 1936.

Rolf Bernzen: Die praktische und theoretische Konstruktion des Modellverfahrens. Ein Beitrag zur Frühgeschichte der neuzeitlichen Wissenschaft. Frankfurt: Peter Lang 1986.

Günther Binding: Baubetrieb im Mittelalter. Darmstadt: Wissenschaftliche Buchgesellschaft 1993.

Percy Williams Bridgman: The Logic of Modern Physics. New York: Macmillan 1927; Neudruck 1960; Reprint Salem N. H.: Ayer 1993;
dt.: Die Logik der heutigen Physik. München : Hueber 1932.

Donald E. Broadbent: A Mechanical Model for Human Attention and Immediate Memory. Psychol. Rev. 64, 1957, 205-215.

Murray Wright Bundy: The theory of imagination in classical and mediaeval thought. Urbana, Ill.: The University of Illinois 1927; Reprints Urbana: Folcroft Libr. 1970, 1976, 1980, resp. Norwood, Pa.: Norwood editions 1976, 1978.

Tommaso Campanella: Sonnenstaat. In Klaus J. Heinisch (Ed.): Der utopische Staat – Morus: Utopia; Campanella: Sonnenstaat; Bacon: Neu-Atlantis. Reinbek: Rowohlt Taschenbuch Verlag 1960.

Norman Robert Campbell: Physics. The Elements. Cambridge 1920 (Chapter VI: Theories, 128-158);
unchanged reprint u. d. T.: Foundations of Science. The Philosophy of Theory and Experiment. New York: Dover 1957, London 1963.

Rudolf Carnap: Logische Syntax der Sprache. Wien: Julius Springer 1934, 2. ed. 1968;
engl.: The Logical Syntax of Language. London/ New York 1937, 2. ed. 1949.

Rudolf Carnap: Philosophy and Logical Syntax. London. 1935.

Chen Chung Chang: Model Theory 1945-1971. In Proceedings of the Tarski Symposium held at the University of California, Berkeley, June 23-30, 1971. Proceedings of symposia in pure mathematics, vol. 25, 1974, 173-186.

John Martin Cocking: Imagination. A study in the history of ideas. London: Routledge 1991.

Morris Raphael Cohen, Ernest Nagel: An Introduction to Logic and Scientific Method. New York 1934 (Chapter 7 is an introduction to logic models).

J. A. Comenius: Böhmische Didaktik. Ed. and introduced by K. Schaller. Paderborn: Schöningh 1970.

J. A. Comenius: Grosse Didaktik. Ed. And introduced by H. Ahrbeck. Berlin: Volk und Wissen 1957.

Michel Denis (Ed.): Imagery, language, and visuo-spatial thinking. Philadelphia: Psychology Press 2000.

Pierre Duhem: L’Ecole anglaise et les Théories physiques. Revue des Questions Scientifiques 34, October 1893, 345-378;
engl.: The English School and Physical Theories: On a Recent Book by W. Thomson. In Pierre Duhem: Essays in History and Philosophy of Science. Indianapolis: Hackett 1996, 50-74.

Pierre Duhem: La théorie physique. Son objet et sa structure. 1906;
dt.: Ziel und Struktur der physikalischen Theorien. Leipzig: Barth 1908; Reprint Hamburg: Meiner 1978, erneut 1998; 4. Kap.: Die abstrakten Theorien und die mechanischen Modelle, 67-136);
engl.: The Aim and Structure of Physical Theory. 1914.

Walther Dyck (Ed.): Katalog mathematischer und mathematisch-physikalischer Modelle, Apparate und Instrumente. München: C. Wolf u. Sohn 1892.

Brigitte Falkenburg, Susanne Hauser (Ed.): Modelldenken in den Wissenschaften. Hamburg: Meiner 1997 (= Dialektik 1997,1).

Gerd Fischer (Ed.): Mathematische Modelle. Aus den Sammlungen von Universitäten und Museen. 2. Bde. Braunschweig: Vieweg 1986.

Michael A. Forrester: Psychology of the image. Sign, representation and discourse. London: Routledge 2000.

Philipp Frank: Über die „Anschaulichkeit“ physikalischer Theorien. Die Naturwissenschaften Bd. 16, 1928, Heft 8, 122ff.

Antonia Fraser: A history of toys. London: Weidenfeld and Nicolson 1966;
dt.: Spielzeug. Die Geschichte des Spielzeugs in aller Welt. Oldenburg und Hamburg: Stalling 1966, erneut 1984.

Hans Freudenthal (Ed.): The Concept and the Role of the Model in Mathematics and Natural and Social Sciences. Proceedings of the Colloquium Sponsored by the Division of Philosophy of Sciences of the International Union of History and Philosophy of Sciences, Organized in Utrecht, January 1960. Dordrecht: Reidel 1961.

Kenneth J. Gilhooly: Representation, reasoning, analogy and decision making. Chichester: Wiley 1990.

Rom Harré: Where models and analogies really count. International Studies in the Philosophy of Science 2, 1988, 118-133.

George A. Hazelrigg: Introduction. In Carl W. Hall: Laws and models. Science, engineering and technology. Boca Raton, Fla.: CRC Press 2000.

William E. Herfel et al.: Theories and Models in Scientific Processes. Proceedings of AFOS ’94 Workshop, August 15-26, Madralin, and IUHPS ’94 Conference, August 27-29, Warszawa. 1995.

Heinrich Hertz: Die Prinzipien der Mechanik in neuem Zusammenhange dargestellt. Gesammelte Werke Bd. 3, hrsg. von P. Lenard und eingeleitet von H. v. Helmholtz. Leipzig: J. A. Barth 1894, Reprint 1963.

Mary Brenda Hesse: Models and Analogies in Science. London, New York: Sheed and Ward 1963;
2. ed. um zwei Kapitel erweitert, Notre Dame, Indiana: University of Notre Dame Press 1966, second printing 1970.

Per Holst: Computer simulation 1951-1976. An index to the literature. London: Mansell 1979.

Icons of Invention. American patent Models. National Museum of American History 1990.

N. L. Irvine, L. Davis: Simulation by Modeling. Proc. (AFIPS) Western Joint Computer. Conf., Vol. 7, 1955, 13-15.

M. Jammer: Die Entwicklung des Modellbegriffes in den physikalischen Wissenschaften. Studium Generale 18, 1965, 166-173.

Sir James Hopwood Jeans: The new background of science. London: Cambridge at the University Press 1933, 2. ed. 1934, Reprint 1959;
dt.: Die neuen Grundlagen der Naturerkenntnis. Stuttgart: Deutsche Verlagsanstalt 1933, 2. ed. 1934.

Pascual Jordan: Anschauliche Quantentheorie. Eine Einführung in die moderne Auffassung der Quantenerscheinungen. Berlin: Springer 1936.

Robert Kargon, Peter Achinstein (Ed.): Kelvin’s Baltimore Lectures and modern theoretical Physics. Historical and Philosophical Perspectives. Cambridge, Mass.: Massachusetts Institute of Technology 1987.

Friedrich Kaulbach: Schema, Bild und Modell nach den Voraussetzungen des Kantischen Denkens. Studium Generale 18, 1965, 464-479.

J. Klir, M. Valach: Cybernetic Modelling. London 1966.

Karin Knorr-Cetina: Epistemic cultures. How the sciences make knowledge. Cambridge, Mass.: Harvard Univ. Press 1999.

Thomas S. Kuhn: The Structure of Scientific Revolutions. The University of Chicago: dt.: Die Struktur wissenschaftlicher Revolutionen. Frankfurt am Main: Suhrkamp 1967, Taschenbauchausgabe 1973.

David S. Landes: The Unbound Prometheus. Technological Change and Industrial Development in Western Europe from 1750 to the Present. Cambridge 1968;
dt.: Der entfesselte Prometheus. Köln: Kiepenheuer & Witsch 1978, als dtv-Taschenbuch 1983 (zur Serienproduktion 288ff).

G. W. Leibniz: Opuscules et fragments inédits. Ed. Louis Couturat. Hildesheim: Olms 1966 (Reprint der Ausgabe Paris 1903).

Lexikon der Kunst, 7 Bde, 1987-1994 (precise information for a lot of concepts as Bozzetto, Effigies, Imagines, Model, Modell, Stifterbildnis, Votivgaben, Wachsbildnerei).

Arthur Lotz: Bibliographie der Modelbücher. Beschreibendes Verzeichnis der Stick- und Spitzenmusterbücher des 16. und 17. Jahrhunderts. Leipzig: Hiersemann 1933, 2. ed. 1963.

Lorenzo Magnani, Nancy J. Nersessian, Paul Thagard (Ed.): Model-Based Reasoning in Scientific Discovery. Papers presented at the International Conference on Model-Based Reasoning in Scientific Discovery, MBR’98, held December 17-19, 1998, in Pavia, Italy. New York: Kluwer Academic/ Plenum Publishers 1999.

Francis F. Martin: Computer Modeling and Simulation. New York: Wiley 1968.

Charles Russell Mischke: An introduction to computer-aided design. Fundamentals of engineering design. Englewood Cliffs: Prentice-Hall 1968.

Mary S. Morgan, Margaret Morrison (Ed.): Models as Mediators. Perspectives on Natural and Social Science. Cambridge: Cambridge University Press 1999.

Roland Müller: Zur Geschichte des Modellbegriffs und des Modelldenkens im Bezugsfeld der Pädagogik. In Herbert Stachowiak (Ed.): Modelle und Modelldenken im Unterricht. Bad Heilbrunn: Klinkhardt (April) 1980, S. 202-224.

Roland Müller: Zur Geschichte des Modelldenkens und des Modellbegriffs. In Herbert Stachowiak (Ed.): Modelle - Konstruktion der Wirklichkeit. München: Fink 1983, S. 17-86.

Roland Müller: Innovatives Lernen am Modell (1988). In Roland Müller: Innovation gewinnt. Kulturgeschichte und Erfolgsrezepte. Zürich: Industrielle Organisation/ Orell Füssli 1997, 127-137.

Roland Müller: Das Modellkonzept in Geschichte und Gegenwart. Lecture at the joint colloquium of history of science at the University of Zurich and the Federal Institute of Technology Zurich, April 2, 1997 (unpublished).

Nancy J. Nersessian. Reasoning from imagery and analogy in scientific concept formation. PSA, 1988, Bd. 1, 41-47.

Allan Paivio: Imagery and verbal processes. New York, London: Holt, Rinehart and Winston 1971, 2. ed. 1979.

Nicole Parrot: Mannequins. Paris: Editions Colona 1981;
dt.: Mannequins. Bern: Edition Erpf 1982;
engl.: Mannequins. London: Academy Editions/ New York: St. Martin's Press 1982, 1983.

William and Marlys Ray: The Art of Invention. Patent Models and Their Makers. Princeton, N. J.: Pyne Press 1974.

Richard F. Reiss (Ed.): Neural Theory and Modelling, Proceedings oft the 1962 OJAI Symposium. Stanford University Press 1964.

Alan Richardson: Mental imagery. London: Routledge & Kegan Paul/ New York: Springer 1969.

Abraham Robinson: Introduction to Model theory and to the Meta-mathematics of Algebra. Amsterdam: North-Holland 1963, 2. ed. 1965.

Howard Saalman: Filippo Brunelleschi. The Cupola of Santa Maria del Fiore. London: Zwimmer 1980.

Hans Jörg Sandkühler (Ed.): Theorien, Modelle und Tatsachen. Konzepte der Philosophie und der Wissenschaften. Frankfurt: Lang 1994 (18 Beiträge des 4. Bremer Wissenschaftsphilosophischen Symposiums, 5.-8. Oktober 1993).

Robert W. Scheller: Exemplum. Model book drawings and the practice of artistic transmission in the middle ages (ca. 900 - ca. 1470) Amsterdam: Amsterdam University Press 1995.

Erwin Schrödinger: Science and Humanism. Cambridge University Press 1951; dt.: Naturwissenschaft und Humanismus. Wien 1951, 32-36.

Kenneth Joel Shapiro: Animal models of human psychology. Critique of science, ethics, and policy. With a foreword by Jane Goodall. Seattle : Hogrefe und Huber 1998.

Herbert A. Simon: Modeling human mental processes. Proc. (AFIPS) Western Joint Computer. Conf., Vol. 19, 1961, 111-120.

Herbert Stachowiak: Allgemeine Modelltheorie. Wien: Springer 1973.

Viktor A. Stoff: Modellierung und Philosophie. Berlin: Akademie-Verlag 1969 (aus .d Russ. Moskau: Nauka 1966).

Patrick Suppes: Models of Data. In Ernest Nagel, Patrick Suppes, Alfred Tarski (Ed.): Logic, Methodology and Philosophy of Science. Proceedings of the 1960 International Congress, Stanford, California: Stanford University Press 1962, 252-261;
dt.: Modelle von Daten. In Wolfgang Balzer, Michael Heidelberger (Ed.): Zur Logik empirischer Theorien. Berlin: de Gruyter 1983, 191-204.

Patrick Suppes: Studies in the methodology and foundations of science. Selected papers from 1951 to 1969. Dordrecht: Reidel 1969.

Patrick Suppes: Models and Methods in the Philosophy of Science: Selected Essays. Synthese Library, vol. 226. Dordrecht: Kluwer 1993.

Alfred Tarski: Der Wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica 1, 1935, 261-405 (original dissertation in Polish, Warsaw 1933);
also engl.: The Concept of Truth in Formalized Languages. In: Logic, Semantics, Metamathematics. Oxford: Clarendon Press 1956, 152-278;
German Reprint in K. Berka, L. Kreiser (Ed.): Logik-Texte. Berlin: Akademie-Verlag 1971, 447-559, 4. Ed. 1986, 445-546.

Alfred Tarski: Grundzüge des Systemenkalküls I/II. Fund. Math. 25/26 (1935/36), 503-526; 283-301;
engl. in: Logic, Semantics, Metamathematics. 1956, 343-383.

Alfred Tarski: Contributions to the theory of models. Indagationes Mathematicae 16 (1954), 572-588; 17 (1955), 56-64.

Edward Chace Tolman: Cognitive maps in rats and men. Psychol. Rev. 55, 1948, 189-208.

Arnold Tustin: The mechanism of economic systems. An approach to the problem of economic stabilisation from the point of view of control-system engineering. London: Heinemann 1953, 2. Aufl. 1957.

Robert L. Vaught: Model Theory before 1945. In Proceedings of the Tarski Symposium held at the University of California, Berkeley, June 23-30, 1971. Proceedings of symposia in pure mathematics, vol. 25, 1974, 153-172.

Paul Volkmann: Erkenntnistheoretische Grundzüge der Naturwissenschaften und ihre Beziehungen zum Geistesleben der Gegenwart. Leipzig: Teubner 1896 (zu den mechanischen Modellen einige Sätze 36f. ferner ein Kapitel „Analogie und Anschauung 147-152);
2. vollständig umgearbeitete und erweiterte ed. 1910 (Abschnitte „Physikalische Analogie“, 87-89, „Mechanische Analogie“, 89-91, und „Mechanische Modelle. Mechanical Illustration“, 94-97).

Martin Warnke: Bau und Überbau. Frankfurt: Syndikat 1976, 2.ed. 1979; als Suhrkamp Taschenbuch Wissenschaft Nr. 468, 1984.

Max W. Wartofsky: Models. Representation and the Scientific Understanding. Dordrecht: Reidel 1979.

Evalyn Westacott: A century of Vivisection and Antivivisection. A study of their effect upon science, medicine and human life during the past hundred years. Ashingdon, Essex: C. W. Daniel 1949.

Hermann Weyl: Philosophie der Mathematik und Naturwissenschaften. Handbuch der Philosophie, Band 2, München und Berlin: Oldenbourg 1927, A1-162.

Hayden V. White: Tropics of discourse. Essays in cultural criticism. Baltimore, Md.: Johns Hopkins University Press 1978, 4. ed. 1990;
German: Auch Klio dichtet oder Die Fiktion des Faktischen. Studien zur Tropologie des historischen Diskurses. Stuttgart: Klett-Cotta 1986, Reprint 1991.

Ludwig Wittgenstein: Tractatus logico-philosophicus (1921/22). Logisch-philosophische Abhandlung. Frankfurt: Suhrkamp, 6. ed. 1969.

Christian Wolff: Mathematisches Lexicon: Gleditsch 1716;
2. ed. als: Vollständiges Mathematisches Lexicon, 1734.

Klaus-Dieter Wüstneck: Zur philosophischen Verallgemeinerung und Bestimmung des Modellbegriffs. Deutsche Zeitschrift für Philosophie 1963, Heft 12.

 

Nachschlagewerke für Begriffsgeschichte

 

see:   Model, Modell: Nachschlagewerke für Begriffsgeschichte