Reflections on the use of models

 

see in German:        Zur Geschichte des Modelldenkens und des Modellbegriffs – paragraph 3: Von dem Bewusstsein davon, dass wir in Modellen denken

                                   Modellgeschichte ist Kulturgeschichte

Vom Bewusstsein, dass wir Modelle verwenden

2. Hälfte des 20. Jahrhunderts: Explosion der Modell-Literatur

 

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Old Greece: Xenophanes und Platon

1077-1092

1120-1160

1228-1235

High Middle Ages und Renaissance: Scholastics and theorists of art

1500-1700: Theological and scientific zeal

19th century

20th century

 

 

Old Greece: Xenophanes und Platon

 

The reflection on the fact that we use models and think in terms of models starts in Old Greece with Xenophanes (540 BC) and Plato (370 BC – see also chap. I: Archetype, idea – Plato on the view of the craft).

 

 

 

1077-1092

 

Some scholars see the beginning of semiotics with Anselm of Canterbury (1077). In 1092 he urged Roscelin of Compiègne to revoke his extreme nominalism. This is the start of the debate on the nature of „universals“, concepts, mental entities, and the like, which continues till today.

 

 

1120-1160

 

Some further hints on reflections on the use of models we find in the first handbook for the artistic goldsmith and metalworker by Theophilus Presbyter („Diversarium artium schedula“, ca. 1123), in the „Didascalicon“ of Hugo of St. Victor (before 1125 or 1128/33) and in Abaelard’s conceptualism (ca. 1140).

On „imagery“ theorized Hugo, Abaelard and John of Salisbury („Metalogicon“, 1159).

 

 

1228-1235

 

Just before 1228 Robert Grosseteste outlined a model theory in a letter with respect to architecture („imaginare in mente artificis ... utpote in mente architecti“ – Günther Binding 1993, 20-21, 181-182).

Marvelous pattern books are preserved from the monks of Rein (1213) and in the library of Wolfenbüttel (1230). Villard de Honnecourt’s sketchbook (model-book) is dated 1235.

 

 

High Middle Ages und Renaissance: Scholastics and theorists of art

 

Briefly after 1300 Duns Scotus developed a conception theory (Reinhold Messner 1942; Etienne Gilson 1952; G. Scheltens 1965; Martin M. Tweedale 1990, 1999; Giovanni Pizzo 1998).

Scotus’ pupil William of Ockham refined the conceptualism by the concept of fiction („figmentum“) (Josef Reiners 1910; Erich Hochstetter 1926; Sebastian J. Day 1947; Wolfgang Stegmüller 1956/57; G. Leff 1975; Elisabeth Leinfellner 1986; Jan P. Beckmann 1996; Jürgen Goldstein 1998). According to Ockham our imaginations are not representations of objects, but signs („signa“) we relate to these objects.

 

Around 1450 the religious philosopher Cusanus submitted a picture theory (Norbert Henke 1969; Norbert Herold 1986: Hubert Benz 1999), and the art theoretician Leon Battista Alberti (see Fig. 37 and 38) developed a model theory. Shortly after followed Antonio Averlino, detto Filarete, and Franceso di Giorgio Martini (see Fig. 39).

 

 

1500-1700: Theological and scientific zeal

 

Many theologicians in the 16th und 17th century spoke of „false ideas“. Catholics (e. g. Giacomo Moronessa 1555) accused the members of the Reformed Church of heresy, the puritans (William Perkins 1607, John Sheffield 1659, John Owsen 1682) conversely the adepts of the Pope.

 

We find a pronounced degree of reflection since the beginning of modern science, for example with the doctrine of idols of Francis Bacon in his “Novum Organon” (1620). He distinguishes four kinds of false ideas humans like to form (Reinhard Gammel 1983; Edmund Siegl 1983):

·        collective aberrations

·        individual aberrations

·        public opinion and

·        tradition.

 

Some kinds of reflection – mainly on visual instruction and use of experimental mental models - show also the two utopias of Tommaso Campanella (1602; published 1623) and Francis Bacon (1624), the “Heuretica” of the clergyman Simon Sturtevant (1612) as well as the main didactic works of Jan Amos Comenius (1628-1638), the reflections of the philosopher René Descartes and of the physicist Galileo Galilei (1638).

Bacon and Galilei are considered also as promotors of empiricism, Descartes as defensor of rationalism.

 

 

19th Century

 

1840-1895: First studies of induction, sign and symbol, fiction and images

 

The next wave of consciousness starts with the Cambridge philosopher William Whewell („The Philosophy of the Inductive Sciences“, 1840) and the American Scientist Charles Sanders Peirce (since 1868).

 

At the same time when Charles Sanders Peirce was developing his theory of sign, Hans Vaihinger wrote in 1873-1878 his „system of the theoretical, practical and religious fictions of mankind“ (German 1911; English 1924), based on the conjunction „as if“ already used by Immanuel Kant and the concept of „fiction“ used by Friedrich Nietzsche. The book was published not before 1911. Since the concept of model was not broadly used in contemporary science Vaihinger named models „schematic fictions“ (Thomas Conrad 1983; Klaus Ceynowa 1993; Andrea Wels 1997).

 

Vaihinger has been followed since 1883 by

·       the two Austrian physicists Ernst Mach („The Science of Mechanics“; German 1883; English 1893; “Erkenntnis und Irrtum”; German 1905; English 1976 – see Fig. 42, 43, 44 and 45) and Ludwig Boltzmann („On the Methods of Theoretical Physics“, German, 1892; English 1974),

·       the German physicist Heinrich Hertz („The Principles of Mechanics“, German 1891-94; English 1899 – see Fig. 46 and 47),

·       the Russian physicist Nikolai Alekseevich Umov.

 

The trilogy on fundamental questions of science by the French physicist Henri Poincaré (1902-08) had a remakable influence on scientific theorizing. Because he was an educated engineer he took also in account the practical problems and needs of researchers (Tobias Dantzig 1954; Jerzy Giedymin 1982; Corinna Mette 1985).

 

19th century: Other philosophical trends and reflections

 

As some centuries ago with nominalism, around 1830-60 revolutionary trends in the pilosophy of knowledge arouse: positivism (Comte, 1830-42) and materialism (Moleschott, Vogt and Büchner, 1852-55). In reaction to them not only the widely distributed philosophy of life, vitalism and organizism gained new life but also Neo-Kantianism (Otto Liebmann, 1865; Friedrich Albert Lange, 1866).

 

Reflection on analogy starts with Laurenz Lersch (1838), Ludwig Merz (1842), Richard Owen (1843), Christian Friedrich Ludwig Wurm (1848), Heinrich Hess (1851), Janus Hoppe (1873) and William Stanley Jevons („The principles of science“ 1874).

Reflection on metaphor starts around the same time (1844) with Johann Jakob Langbehn and Johann Guthe.

 

Different approaches to catch the secret of creativity concentrate on the unconsciousness (Carl Gustav Carus, 1846; Edward von Hartmann, 1869), on „genius and madness“ (Jacques-Joseph Moreau de Tours,1859; Cesare Lombroso, 1864) and on the scientific use of imagination (Ernest Royer, 1867; John Tyndall, 1870).

 

In 1874 the philosopher and psychologist Franz Brentano showed that psychological phenomena are characterized by intentionality, i. e. they tend to an object.

 

Reflections on the use of mental models of prehistoric man start with Edward B. Tylor’s „Primitive Culture“ (1871) and on the construction and use of material models with Lazarus Geiger (1871) and Ernst Kapp (“Grundlinien einer Philosophie der Technik”, 1877).

 

 

20th century

 

First half of 20th century: Nearly silence for model in the science

 

Surprisingly the model term - apart from the "atom model" and model in learning psychology (around 1930) and econometrics - has been a wall flower nearly half a century after 1900. Most authors 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 or specified the term model by „symbol" (e. g. Abram Cornelius Benjamin, 1937) or by „icon", "isomorphism" and "analogy" (e. g. Norman Robert Campbell, 1920).

 

Logical Empirism - as coined by Alfred Tarski; Rudolf Carnap; Morris Raphael Cohen and Ernest Nagel in the 1930s - saw models as side phenomenon of science. Hence theories, syntactically seen, were reconstructed as non-interpreted calculuses of axiomatic systems

 

In 1963 Mary Brenda Hesse in her booklet „Models and Analogies in Science“ tried to construct a divergence between the adherents of Pierre Duhem (1906) and Norman Robert Campbell (1920), but there is no such (viz. Kurt Hübner 1971).

 

Therefore dozens of other scholars made valuable contributions to this theme:

Josef Clemens Kreibig (1909), Paul Volkmann (1910), Moritz Schlick (1918), Alfred North Whitehead (1919; 1920; 1926), Ludwig Wittgenstein (1921), Charlie Dunbar Broad (1923), Ernst Cassirer (1923; 1950), Henry Jackson Watt (1925), Edwin Arthur Burtt (1925), Percy William Bridgman (1927), Joshua Craven Gregory (1927), Hermann Weyl (1927), Charles William Morris (1927; 1938; 1946), Hugo Dingler (1928; 1938; 1951), Herbert Feigl (1929), Aloys Wenzl (1929; 1935; 1954), Hans Reichenbach (1931; 1938; 1944), Philipp Frank (1932; 1946; 1949) and Cyril Edwin Mitchinson Joad (1932), later Abram Cornelius Benjamin (1936; 1937), Lizzie Susan Stebbing (1937; 1941) and William Heriot Watson (1938; 1963).

 

Since 1942: Reflection on the construction and use of models

 

Modern-day reflection on thinking in models and the use of models lies mostly in the hands (brains!) of Americans and British and some Germans.

 

It begins with the German physicist Jürg Johannesson (1942) und the Scotch experimental psychologist Kenneth James William Craik (1943). Concerning Craik we read in a study on mental models: “The idea that people rely on mental models can be traced back to Kenneth Craik’s suggestion in 1943 that the mind constructs ‘small-scale models’ of reality that it uses to anticipate events.”

 

It follows a jointly written paper of the Mexican physiologist Arturo Rosenblueth and the American mathematician Norbert Wiener (1945) as well as a book of Anton Fischer (1947), physician in Budapest.

Also in 1945 the American Albert Gailord Hart thought about „Model-Building“ and fiscal policy, and the Englishman Arthur Percy Rollett reflected on mathematical models and constructions.

In 1953 the Lithuanian born Gregor Sebba wrote on the construction of theoretical models since the Old Greeks in physics and since Adam Smith in economics.

 

In the five years 1945-49 we have already 80 publications (articles and books) on models.

 

This impetus 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'.

 

Seminal articles in scientific journals

 

Seminal articles are found in fourteen scientific journals:

·        Economic Journal (since 1940)

·        Econometrica (1944)

·        American Economic Review (1945)

·        Review of Economic Studies (1945)

·        Philosophy of Science (1945)

·        Synthese (1948)

·        Journal of Symbolic Logic (1948)

·        Psychological Review (1948)

·        Public Opinion Quarterly (1950)

·        Journal of Personality (1951)

·        Psychometrika (1951)

·        British Journal of the Philosophy of Science (1952)

·        American Psychologist (1957) and

·        Philosophia naturalis (1957).

 

1948 and 1965 „model” got some populartiy by special issues of the German journal „Studium generale“.

 

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

 

After World War II models in econometrics (developed since 1930) 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).

 

1947-1955: The first scientific books with the word „model“ in their titles

 

Among the first scientific books with the word „model“ in their titles are the dissertations of Clifford Dixon Firestone (1947), Marjorie Hall Harrison (1947) and Detlef Schmidt (1949).

 

The next model-titles mostly got several editions, e. g.:

·        “Statistical Inference in Dynamic Economic Models”, ed. by Tjalling C. Koopmans (1950)

·        “Le modulor” of Le Corbusier (1950)

·        „Mathematical Models” by Henry Martyn Cundy and A. P. Rollett (1951)

·        “Dimensional Analysis and Theory of Models” by Henry Louis Langhaar (1951)

·        “Theoretical Models and Personality Theory”, ed. by David Krech und George Stuart Klein (1952)

·        „Das ‚physikalische Modell’ und die ‚metaphysische Wirklichkeit’“ of Erwin Nickel (1952)

·        “Modelling Geography” by Eric John Barker (1954)

·        “Stochastic Models for Learning” by Robert R. Bush and Frederick Mosteller (1955)

·        “An Econometric Model of the United States 1929-1952” by Lawrence R. Klein and A. S. Goldberger (1955).

 

1951-1956: Influential works of philosophy of science and of new approaches

 

For dealing with models more influential were at first of:

·        Herbert Feigl and May Brodbeck the 800page “Readings in the philosophy of science“ (1953)

·        Richard Bevan Braithwaite „Scientific Explanation“ (1953)

·        Stephen Toulmin „The Philosophy of Science“ (1953)

·        Nelson Goodman „Fact, Fiction and Forecast“ (1954)

·        Mary Brenda Hesse “Science and the human imagination” (1954)

·        Marjorie Hope Nicolson “Science and imagination” (1956)

·        Ernest Hirschlaff Hutten “The language of modern physics” (1956)

·        Alfred Jules Ayer “The Problem of Knowledge” (1956).

 

Especially important for the social sciences were:

·        Kenneth Joseph Arrow „Social choice and individual values“ (1951)

·        Daniel Lerner and Harold Dwight Lasswell with their  344pages anthology “The Policy Sciences” (1951)

·        Talcott Parsons and Edward A. Shils with their 500pages anthology “Toward a General Theory of Action” (1951)

·        Lawrence Robert Klein “A textbook of econometrics” (1953)

·        Arnold Tustin “The mechanism of economic systems” (1953)

·        Frank Harary and Robert Zane Norman “Graph theory as a mathematical model in social science” (1953)

·        Paul Felix Lazarsfeld with his 444pages anthology “Mathematical Thinking in the Social Sciences” (1954)

·        Leonard Dupee White with his 500pages anthology “The State of the Social Sciences” (1956)

·        Talcott Parsons and Neil J. Smelser “Economy and society” (1956)

·        Jerome Seymour Bruner et al. “A study of thinking” (1956)

 

In the area of decision making we have the very important works of:

·        John Charles Chenoweth McKinsey “Introduction to the theory of games” (1952)

·        Paul Everett Meehl “Clinical versus statistical prediction” (1954)

·        Robert MacDowell Thrall et al. the 300pages anthology “Decision Processes” (1954)

·        Leonard Jimmie Savage “The Foundations of Statistics” (1954)

·        David Blackwell and Meyer A. Girshick: “Theory of games and statistical decisions” (1954)

·        John Davis Williams “The compleat strategyst” (1954)

·        John Cohen and Mark Hansel “Risk and Gambling” (1956).

 

In the area of cybernetics and information theory we have for instance:

·        William Ross Ashby “Design for a brain” (1952)

·        Louis Couffignal “Les machines à penser” (1952)

·        Pierre de Latil „La pensée artificielle“ (1952)

·        Albert Ducrocq “ Appareils et cerveaux électroniques“ (1952)

·        John Diebold “Automation” (1952)

·        Stanford Goldman “Information Theory” (1953)

·        David Arthur Bell “Information theory and its engineering applications” (1953)

·        William Grey Walter “The living brain” (1953)

·        Georges Théodule Guilbaud “La Cybernétique” (1954)

·        Hsue Shen Tsien “Engineering cybernetics” (1954)

·        Richard Wagner „Probleme und Beispiele biologischer Regelung“ (1954)

·        Winfried Oppelt: “Kleines Handbuch technischer Regelvorgänge“ (1954)

·        Colin Cherry “Kybernetik” (1954)

·        Albert Ducrocq “Découverte de la cybernétique” (1955)

·        Vitold Belevitch “Langage des machines et langage humain“ (1956)

·        Léon Brillouin “Science and information theory” (1956)

·        Horst Mittelstaedt with his congress papers “Regelungsvorgänge in der Biologie” (1956)

·        Colin Cherry with his 400pages anthology “Information Theory” (1956)

·        William Ross Ashby “An Introduction to Cybernetics” (1956)

·        Ludwig von Bertalanffy and Anatol Rapaport with their „Yearbooks of the Society of General Systems Research: General Systems“ (1956ff).

 

1957-63: The first symposia and fundamental books

 

In the years 1957-63 thinking in models and the concept of model were discussed at various international symposia in USA and in Europe:

1957:  Cornell University, Ithaca, N. Y. (Alfred Tarski et al. 1957)

            Amsterdam (Arend Heyting 1959)

            Symposium on Sociological Theory (Llewellyn Gross 1959)

1959:  Stanford (Kenneth J. Arrow et al. 1960)

Bristol (J. W. L. Beament 1960)

Warschau („Infinitistic methods“ 1961)

1960:  Utrecht (Leo Apostel et al. 1960; Hans Freudenthal 1961)

            London (Colin Cherry 1961)

            Berlin (Friedrich Jung et al. 1961)

            Stanford (Ernest Nagel et al. 1962)

1961.  Los Angeles (Austin Curwood Hoggatt et al. 1963)

1962:  OJAY, Stanford (Richard F. Reiss 1964)

1963:  Berkeley (John W. Addison et al. 1965)

 

The most preprints or anthologies of congress papers were extensive cited.

 

Fundamental books got attention:

·        Earl Francis Beach (“Economic Models” 1957)

·        Herbert Alexander Simon („Models of Man“ 1957)

·        Robert Duncan Luce und Howard Raiffa (“Games and Decisions” 1957)

·        Colin Cherry (“On human communication” 1957)

·        Norwood Russell Hanson („Patterns of discovery“ 1958)

·        Frank Honywill George („Automation, cybernetics and society“ 1959)

·        Rom Harré („An introduction to the logic of the sciences” 1960)

·        Ernest Nagel („The Structure of Science” 1961)

·        Max Black („Models and Metaphors” 1962)

·        John G. Kemeny and James Laurie Snell („Mathematical Models in the Social Sciences” 1962)

·        Thomas S. Kuhn („The Structure of Scientific Revolutions” 1962)

·        Mary Brenda Hesse („Models and Analogies in Science” 1963; revised 1966).

 

Second half of the 20th century: Explosion of model publications

 

We can see the rapid expansion of the concept of model from the explosion of publications with respect to model, modelling, model experiments, etc.

In the Deutsche Bibliothek in Frankfurt we have – mostly German titles – per year:

1950:     30

1960:     50

1970:   350

1980:   700

1990: 1100

2000: 1950

2004: 2300.

 

In 10 years from 1990-1999 more than 17 000 titles on model were published, in the five years from 2000-2004 around 12 000.

The joint online-catalogue of the British Libraries (COPAC) registered for 1990-1999 more than 16 000 English titles (but with al lot of doubles).

 

1964-1979: A lot of confusion arises

 

In the 1960s starts an explosion of model-books. And a lot of confusion arises because scholars use also analogy, metaphor, representation, or symbol, theory and realism.

 

Important monographs in this period are of

Viktor A. Stoff (1966), Peter Achinstein (1968), Rom Harré (1970), May Brodbeck (1972), Mario August Bunge (1973), Herbert Stachowiak (1973), William Hilton Leatherdale (1974), Gerald Holton (1979) and Ronald Nelson Giere (1979).

In addition we have the dissertations of Klaus-Dieter Wüstneck (1966) and Frederick Roy Suppe (1967).

 

1980-89: Construction and consequences of models

 

Since 1980 models are seen more than before as important elements of scientific practice. It is studied how models are constructed and what consequences the use of models has for other philosophical questions, for instance in the debates on realism and reductionism.

Important works are:

·        Bas C. van Fraassen: The Scientific Image. 1980.

·        Hilary Putnam: Reason, Truth and History. 1981.

·        Nancy Cartwright: How the Laws of Physics Lie. 1983.

·        Ian Hacking: Representing and Intervening. 1983.

·        Ronald Nelson Giere: Explaining Science. 1988.

·        Frederick Roy Suppe: The Semantic Conception of Theories and Scientific Realism. 1989.

 

For the first time – with exception of Max Jammer (1965) – we find the historical dimension of models (Roland Müller 1983; Rolf Bernzen 1986).

 

1990-2006: Important series of lectures and symposia

 

After a long break model is to be treated in series of lectures and symposia.

Important series of lectures on reality, representation and model were organized by Hans Jörg Sandkühler 1993-2003 at the University of Bremen.

In August 1994 the IUHPS (International Union for the History and Philosophy of Science) devoted a congress to “model” at Warsaw (William E. Herfel 1995).

Important contributions were made by:

·        An interdisciplinary series of lectures at the Freien Universität Berlin in 1992 on „contemporary models of thinking“ (Sybille Krämer 1994)

·        A workshop of the Santa Fe Institute Studies in the Sciences of Complexity (George A. Cowan, David Pines, David Meltzer 1994)

·        A colloquium at the Technischen Universität Berlin in June 1996 (Brigitte Falkenburg, Wolfgang Muschik 1998)

·        Congresses oft the Philosophy of Science Association (PSA) in Fall 1996 in Cleveland (Lindley Darden 1997) and in Fall 1988 in Kansas City (Don A. Howard 2000)

·        An international conference in Cortona in September 1997 (Rosaria Conte et al. 1997)

·        Various reunions of historians and philosophers of science from Canada and USA, UK, the Netherlands and Germany in the years 1990-1996, resulting in an anthology, edited by Mary S. Morgan and Margaret Morrison (1999)

·        Several international congresses at the University of Pavia since 1998 on „model-based reasoning“, in 2006 in China (Lorenzo Magnani et al. 1999, 2002, 2002, 2004, 2006, 2006, 2007).

 

October 19.-22. 2000 there was held a DHS-DLMPS Joint Conference of the IUHPS (organized by Erwin Neuenschwander) at the University of Zürich.

 

At the congress of the Philosophy of Science Association (PSA), November 2.-4. 2000 in Vancouver a session (chair: Margaret Morrison, University of Toronto) dealt with „Scientific Modeling“, an other (chair: Paul Teller, University of California, Davis) dealt with „Models and Analogy“ (Jeffrey A. Barrett, J. McKenzie Alexander  2002).

.

 

Also at the next congresses of the PSA in 2002 in Milwaukee (Sandra D. Mitchell 2003, 2004), in 2004 in Austin (Miriam Solomon 2005, 2006), in 2006 in Vancouver (Cristina Bicchieri, Jason McKenzie Alexander, 2007) and in 2008 in Pittsburgh various lectures dealt with models.

 

In addition in September 2003 at the Universität Bielefeld a colloquium “’Models’ in the Philosophy of Science” was held at the “Fünften Internationalen Kongress der Gesellschaft für Analytische Philosophie” (Christian Nimtz, Ansgar Beckermann 2005).

 

 

bibliographies

 

Modell: einzelne Sachgebiete – model: special topics

Modellgeschichte ist Kulturgeschichte

Model: The 66 most important publications from 6 centuries