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TA 73 (Glasersfeld)


Old and new radical constructivism

By Paul Braffort

Summer 2004



Ernst von Glasersfeld’s TA 73 is certainly one of the clearest and more concise expositions of modern radical constructivism. So my purpose here is only to offer some complementary historical and bibliographical information about scholars who brought similar ideas during the twentieth century, but who are insufficiently known by the North American (and even European) Academy. I would also suggest – after others – that recent development in science and technology could very well open new avenues in the old problematic of representation. In this domain, I am certainly more a witness than an actor, but I was fortunate enough to witness many interesting events.


In 1952, at Raymond Queneau’s suggestion, I bought Il Linguaggio con la tabella di Ceccatieff by Silvio Ceccato, which appeared together with Ernst von Glasersfeld’s English translation: Language and the table of Ceccatieff. This book was n°1135 of an already famous series : Actualités scientifiques et industrielles, published by Hermann & Cie, 6 rue de la Sorbonne, Paris. The owner of this publishing company was Freymann, a most remarkable man, a Mexican, Ghandi’s adept, who eventually decided to leave Tibet and settle in Paris with the mission of producing books who could have no chance of finding another publisher! He produced indeed many fundamental works in Science, Technology, Epistemology, etc.. Among them was Norbert Wiener’s Cybernetics, or control and communication in the animal and the machine (1949, A.S.I. n°1053) as well as the famous Bourbaki’s Eléments de Mathématique. Queneau had been introduced to Freymann in 1951 by François Le Lionnais, and then to Ceccato (1) and he contributed, with Vittorio Somenzi, to Freymann’s acceptation of Silvio’s very unusual work..

I was fascinated by Ceccato’s book as soon as I read in Glasersfeld’s translation and I was very keen to meet him. I found the opportunity in June 1956 at the Congrès International de Cybernétique, in Namur (Belgium) (2). We soon became friends and after I joined EURATOM in 1959, a common research program in Computational Linguistic was started with Ceccato’s Centro di Cibernetica e di Attivita Linguistiche in Milan. I succeeded in organizing a colloquium in Brussels, in February 1961 (with a rather grandiose title: Seminaire Leibniz!) and this is how I became Silvio Ceccato’s second French editor, and probably Ernst von Glasersfeld’s first one! (3)


Among their precursors, Ceccato and Glasersfeld often mention Giambattista Vico and Jean Piaget (Ceccato also quotes Hugo Dingler and Percy Bridgman). To those great thinkers I would like to add now Georges Matisse, another remarkable scholar who contributed to many publications and colloquia between the two world wars. He attended the famous Congrès International de Philosophie Scientifique, Paris 1935, organised by Carnap with Bridgman, Enriques, Russell, etc., and published many interesting books (including n°361, n°467, n°962 and n°1162 of the Actualités scientifiques et industrielles). Most of his books may still be found in academic libraries in Canada and the U.S. (and ordered from the major used book networks) but, strangely enough, this author has been completely forgotten, even in France. Probably unknown to Ceccato (but I mentioned him in my Namur talk that Silvio Ceccato has probably read), he cannot be considered as a precursor as such, but his works are without any doubt those of a solid constructivist and I think he deserves to be quoted here.

Georges Matisse (1874-1961) (no relation with the painter) graduated in biophysics (Paris, 1918), but soon enlarged his fields of interest to mathematics, physics and epistemology. His career culminated when he published, between 1938 and 1958, a series of three three-volume series of books. The first triple, La philosophie de la Nature (1938), contains 1. Identité du Monde et de la connaissance ; 2. La primauté du phénomène dans la connaissance ; 3. L’arrangement de l’Univers par l’esprit. The second one is Le Rameau vivant du monde (1947-1949) and the last one, L’Incohérence universelle (1953-1956), includes: 1. Les logiques du réel et les lois de la nature, 2. Le principe d’émergence et le compartimentage du déterminisme, 3. Le mirage de l’ordre. Such titles are very significant of the author’s epistemological convictions. It should be noted that all these books were published by a major academic collection: the Presses Universitaires de France in their Bibliothèque de philosophie contemporaine and were praised by Gaston Bachelard and Louis Rougier. Many pages could be quoted, but I will restrict myself to the following, taken from the last triple (4):
On s’est parfois étonné d’une « mystérieuse harmonie » du monde et de la pensée. En admettant qu’elle existe réellement en toutes choses – ce qui est loin d’être – il n’y aurait là qu’un ajustement de la pensée de l’homme à l’expérience sensible et intellectuelle, une adaptation de l’esprit au milieu où il se développe et qui le façonne.. One could hardly be clearer! ! Recently, I had a first opportunity of calling again attention on Matisse’s personality (5) and I plan to complete my work in the near future.


In 1961, David Hirschberg and I succeeded in organising, under the sponsorship of the IBM European Education Centre in Blaricum (The Netherlands), two seminars devoted to Logic, Linguistics and Computers (6). Both Silvio Ceccato and Luitzen E. J. Brouwer (who lived in Blaricum) attended the first one. I don’t know if they had a discussion at this occasion, but Silvio knew Brouwer and quotes him at least once (7). Other major scientists were present at Blaricum (including mathematician Claude Berge, logicians Evert Beth and Hao Wang, engineer Enrico Maretti, etc.).
One of the greatest topologists of his time, Brouwer (1881-1966) was also the initiator of Logical Intuitionism At first sight his philosophical position seems very far from Ceccato’s. The title of his first paper was Life, Art and Mysticism (1905), which could impress unfavourably rational minds, but on page 40, you can already read: “Language, the slave of the illusion of reality, cannot be an instrument of truth... “ And in his thesis On the foundation of mathematics (1907) among a series of striking statements (under the general heading “SUMMARIZING“), he says :

     [...] (2) The first act of construction has two distinct things thought together (also according to Cantor, Vortrag auf...); F.Meyer (Verharadl...) says that one thing is sufficient, because the  circumstance  that I think of it may be  added as  a second thing;  this is false, for exactly this adding (i.e. setting it while the former is retained)  presupposes the intuition of two­icity; only afterwards this simplest mathematical system is projected on the first thing and the ego which thinks the thing." (8), p.179.

Forty years later, he maintains:

Mathematics comes into being, when the two-ity created by a move of time is diverted of all quality by the subject, and when the remaining empty form of the common substratum of all two-ities, as basic intuition of mathematics,  is  left  to  an  unlimited unfolding,...(loc. cit., p.482)

In his last important paper: "Points and spaces", Brouwer makes his point even more clearly when he says (his underlining):

The first act of intuitionism completely separates mathematics from mathematical language, in particular from the phenomena of language which are described by theoretical logic. It recognises that mathematics is a languageless activity of the mind having its origin in the basic phenomenon of a move of time, which is the falling apart of a life moment into two  distinct things, one of which gives way to the other, but is retained by memory. If the two-ity  thus born is  diverted of all quality  there remains the common substratum of all two-ities,  the mental creation of the empty two-ity. This empty two-ity and the two unities of which it is composed, constitute the basic mathematical systems. And the basic operation of  mathematical construction is the mental creation of the two-icity of two mathematical systems previously acquired and the consideration of this two-icity as a new mathematical system. (p. 523).

In slightly different terms, Ceccato and other members of the Scuola operativa italiana say almost the same thing. As a matter of fact such a similitude can even be formalised as a true isomorphism and extended to some of Polish logician Leon Chwistek’s work. These correspondences were established with my research group in Orsay in the mid-seventies and published, after revision, in 1986 (8).

From 1987 on, the Society of Methodological-Operative Culture was established as a follow-up of the Scuola Operativa Italiana and publishes an excellent periodical: I Quaderni di Methodologia with contributions by Vaccarino, Accame, Glasersfeld, etc. In his recent and excellent book (9) Felice Accame, who chairs the Society of Methodological-Operative Culture, among many important remarks, also points out the close relationship between Brouwer’s and Ceccato’s conceptions.


Gerrit Mannoury (1867-1954), a great figure of Dutch culture, is superbly ignored today in the Netherlands (and elsewhere), the same way Matisse is ignored in France (and elsewhere). But recently Pieter Wisse discovered, in a second-hand bookshop, Mannoury’s major work: Handbook of Analytical Significs (10) and realized that his own work was going in the direction Mannoury had taken many years before and decided to acknowledge that coincidence and promote a revival of Significs.

A former mentor, and then friend of Brouwer, Mannoury, together with van Eedem, van Dantzig, and others, gave a new extension to Lady Victoria Welby’s Significs (11), and organized an informal but influential group discussing questions of semiotics, psychology, mathematics, pedagogy, etc. From his little book Die signifischen grundlagen der Mathematik (12), I pick only two significant fragments from the French translation (also found in a second-hand bookshop):

Un mot n’a de signification que dans la mesure où il est un acte.(p. 12) Mais tout ce dont on affuble encore les mathématiques, leur caractère absolu et leur exactitude parfaite, leur généralité et leur autonomie, tout ceci (qu’on me pardonne l’expression), tout ceci n’est que superstition ! (p. 56).

Born in 1952, Pieter Wisse has already published a number of books and articles on Information management and dynamics. He has written an excellent review of Mannoury’s work, his contribution to the Significs circle, his friendship and partnership with Brouwer, etc. (13). At some point, he thinks that Mannoury is not going far enough in his criticism of the traditional point of view and then, in support of his statement, quotes ... Ernst Von Glasersfeld (p. 13)!


It should not come as a surprise that, in the first commentaries to TA73, some emphasis is put on “cybernetic” metaphors used by Glasersfeld such as “program” or “memory” (cf. <C2> (Cull), <C3> (Adams), <C11> (Geelan)). For we should remember that, after his 1946 first meeting with Vittorio Somenzi, Ceccato discovers Wiener, Ashby, Grey-Walter, going back, even, to La Mettrie and Samuel Butler. In the early forties, already, Ceccato offered “Un contributo alle ricerche sul fare dell’uomo”(cf. (7), vol.1, p. 53) and in 1955 comes his Namur contribution (cf. (2)). The closing chapter of (7), vol.2, p. 639 is entitled: “LA MACCHINA”, and ends up with an enthusiast “Benedetta macchina!” In June 1956, Leonardo Sinisgalli, the great Italian mathematician, poet and designer, editor of Civiltà delle macchine, published Ceccato’s joint paper with Enrico Maretti: Adamo II. Therefrom comes an active involvement, in “Mechanical Translation” research programs with EURATOM and the American Air Force, of the “Centro di Cibernetica e di Attivutà Linguistiche” with Maretti and Glasersfeld. During the following fifty years, much has been achieved in this field (and other chapters of “Artificial Intelligence” research. But not enough to satisfy Ceccato (and Glasersfeld) who finally turned to Didactics and Epistemology.

Important technical progress, however, had been made in a domain we could name “Representation of representation”. Natural (or mathematical and logical) language description was augmented by means of graphs, diagram, stemmas, and networks. Ceccato’s “polyphonic” notation (as well as his use of the Leibnizian – and Hilbertian – vinculum) has been extremely useful, as Giuseppe Vaccarino has shown in his monumental recent work (14). But it is only very recently that authors have been able, thanks to new and efficient text processing software, to draft their own graphics (as well as their own mathematical formulae) and insert them in regular text.

Soon colour capabilities were added to graphic processing ones, and then dynamic management of images. New avenues were opening for more faithful techniques of representation through “actors” way of programming or object-oriented languages. In 1991 Pierre Lévy announced (15) a new concept called Idéographie dynamique which he described as a non-verbal language (he uses “ciné-langage“) built on what he calls GI (générateur d’idéogrammes) and MS (metteur en scène) as a kind of image-driven hypertext. Most of the ideas propound in his book are very appealing and it is interesting to note his interest in Ochanine’s “operative image”. I quote him now :

“La distinction entre l’image « cognitive » et l’image « opérative » peut-être illustrée par la différence entre une carte d’état-major, avec les milliers d’informations détaillées qu’elle comporte, et un tracé d’itinéraire, suffisant pour parvenir au but qu’on s’est fixé.“ (p. 145-146) (Glasersfeld’s metaphor is not far, here!).

Unfortunately this exciting project never concretised. More recently, widely advertised claims by Stephen Wolfram of “A New Kind of Science” failed to convince.

Still, I think Operativism (or Constructivism) should look further in the dynamic modes of expression. We have now the capacity of implementing information-processing models of linguistic (or cognitive) activities. Research in sign-languages processing already show how images, motion and meaning can be entangled (16). Sure we must remember important lessons of the past (and sometimes rediscover them), but great deal of work stands in front of us.



(1)     Raymond Queneau : Journaux 1914-1965. Gallimard 1996, p.775 & p.1093.

(2)     This congress had been sponsored by the UNESCO from Le Lionnais’s initiative. Silvio’s talk was entitled: La machine qui pense et qui parle (p.288 of the proceedings). Two contributions of mine had been accepted: too: Cybernétique et physiologie généralisée (p.101), and L’information dans les mathématiques pures et dans les machines (p. 248).

(3) Ernst von Glasersfeld : Operational Semantics. Analysis of Meaning in Terms of Operations. Rapport Euratom EUR/C-15/2196/61 f, p.6.

(4) L’incohérence universelle : 1. Les logiques du réel et les lois de la nature. Presses Universitaires de France, 1953, p.220.

(5) Paul Braffort : Un autre Matisse : Georges, in Deuxième colloque des Invalides (11 décembre 1998), Du Lérot, éditeur, 1999. This text may be found on my site:

(6) Computer Programming and Formal Systems, North Holland, 1963.

(7) Un tecnico fra i filosofi, vol. 2: Come non filosofare, Marsilio,1966, p.310.

(8) Brouwer, Chwistek, Ceccato et l’univers des dichômes, 1986-2003 (downloadable from my site.

(9) La funzione ideologica delle teorie della cognoscenza, Spirali, 2002, p. 28.

(10) Handboek der Analytische Signifika, Kroonder, (2 columes), 1947-1948.

(11) Victoria Welby (1837-1912) : Sense, Meaning, and Interpretation. Mind 1896, pp. 24-37, 131-150.

(12) Les fondements psycholinguistiques des mathématiques, Editions du Griffon, 1947.

(13) Pieter Wisse : Mannoury’s significs or a philosophy of communal individualism (accessible on.Wisse’s site:

(14) Giuseppe Vaccarino: I fondamenti della semantica. Vol. 1: Le operazione mentali. E Book 4, 2002.

(15) Pierre Lévy: l’idéographie dynamique. Vers une imagination artificielle. La découverte, 1991.

(16) Annelies. Braffort, A. Choisier, C. Collet, and al.: Toward an annotation software for video of Sign Language, including image processing tools and signing space modelling in: 4th International Conference on Language Resources and Evaluation, LREC 2004, Lisbonne, Portugal.

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