EVALUATION SUMMARY REPORT - Eironeia

Marie-Curie Intra-European Fellowships Call: FP7-PEOPLE-IEF-2008
EVALUATION SUMMARY REPORT
Proposal Nr : 235273 Acronym : Symbols of genesis
Scientist in
Charge Name :
Jean Dhombres
Instrument : FP7-PEOPLE-IEF-2008 Scientific Panel: SOC
Title :
Symbols of their own genesis.
Foundations of a Dynamics of the Representation
Overall score (Threshold : 70) 62
Has the proposal passed all numerical thresholds? No
1. Scientific quality of the project (Weight 25/ Threshold 3) Mark (out of 5)
One strength of the proposal is its wide range across topics and disciplines, documenting an
erudite talent for making deep, innovative, and resonant connections among ideas. Another
strength is the practical concern for applied consequences in education and therapy. The host
institution is also of good quality as is the host supervisor. However, despite these apparent
strengths the proposal was too densely written. For instance, the proposal borrows unexplicated
technical language from all the relevant disciplines making the proposal almost impossible to
understand. Thus it was not clear from the proposal that it included a research methodology, for
example, and too much evidence was supplied in the form of anecdotes that are impossible to
evaluate. The proposal did not explain how the host scholar's expertise would benefit the project
and no effort was made to connect the research project to other possibly parallel developments
in the fields discussed-- work in Cognitive Linguistics, contemporary work in the vein of
Piagetian theory, and work on impredicativity in cognitive science, are examples.
2. Training activities (Weight 15 / Threshold 3) Mark (out of 5)
The choice of the host scholar is good, but the training section is weak. In fact, it is not clear
what training is proposed. Rather, the proposal is to support the candidate in the publication of
his theory because “the time has come for my theory to have an important impact on the current
scientific and educational community.” Even with the stated goal, the proposal could have
explained how, and with what training, the host and host institution would play a role in
realizing this goal. What scientific, scholarly, or practical training would enhance the success of
the candidate in realizing his goal, and in emerging as a mature scholar.
3. Quality of the researcher (Weight 25 / Threshold 4) Mark (out of 5)
The candidate has a few publications and shows evidence of leadership, independent thinking,
creativity, innovation, and a voracious capacity to acquire new knowledge.
4. Implementation (Weight 15 / No Threshold) Mark (out of 5)
A timeline of publications and meetings is provided but no information about how these
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Marie-Curie Intra-European Fellowships Call: FP7-PEOPLE-IEF-2008
meetings would be implemented. While the available infrastructure of the host institution is of
high quality, the proposal lacks specific information concerning the quality of infrastructure /
facilities and international collaborations of host, and lacks information concerning the practical
arrangements for the implementation and management of the scientific project. The absence of
this crucial information greatly reduces the credibility of the project, as proposed. Instead of a
detailed discussion of implementation, the proposal presents a timeline, and claims about what
will be written.
5. Impact (Weight 20 / No Threshold) Mark (out of 5)
If the success in education, claimed possible in the proposal, were realized, then children would
benefit greatly, but it remains uncertain, from the proposal, whether this impact would be
realized. A weakness of the proposal, in this regard, is the over-reliance on anecdotal claims to
make the case, no objective evidence is discussed and no plan for obtaining this evidence is
presented. If the success were realized, however, the contribution to European excellence would
be near term.
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To:
Dear co-ordinator
EUROPEAN COMMISSION
RESEARCH DIRECTORATE GENERAL
Marie Curie Actions – Fellowships
Brussels,
D/556428
21/08/2008
eduardo caianiello
Via Valle Cupa 54/56
01100 Viterbo
Italy (IT)
7th Framework Programme – acknowledgement of receipt of proposal
Thank you for submitting your proposal Symbols of genesis
Symbols of their own genesis. Foundations of a Dynamics of the Representation
under the call FP7-PEOPLE-IEF-2008
which has been recorded as having arrived on 13/08/2008 16:21:38
Your proposal has been given the following reference number:
Proposal reference number: FP7- 235273
Please make sure that you quote this reference number in all future correspondence related to this
proposal. Also make sure that all of your partners are aware of this reference number.
Your proposal will be checked for eligibility, including confirmation of the time and date of arrival. All eligible
proposals will go forward for evaluation. Guidance on when the Commission will decide on successful proposals
for funding can be found in the original call for proposals. You will be notified as soon as possible after this of
whether your proposal has been successful or not.
Disclaimer: Please note that this acknowledgement of receipt letter may in no way be taken to prejudge the
Commission's check of eligibility criteria nor the outcome of the evaluation process related to this call for
proposals.
On behalf of the Commission, I would like to thank you for your interest in the 7th Framework Programme.
Yours sincerely,
Commission européenne, B-1049 Bruxelles / Europese Commissie, B-1049 Brussel - Belgium. Telephone: (32-2)299 11 11.
Office: SDME 1/78. Telephone: direct line (32-2)2988020.
Karim Berkouk

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“Symbols of their own genesis. Foundation of the Dynamics of Representation”
And if someone truly spoke to children about numbers?…
Marie Curie Actions
People
Intra-European European Fellowships for Career Development
Call identifier FP7 FP7-PEOPLE-IEF-2008
Proposal coordinator : Eduardo Caianiello (Eironeia, Italie)
Scientist in charge : Jean Dhombres (Institut Alexandre Koyré, Paris)
Host organisation : Ecole des hautes Etudes en Sciences Sociales (Paris)

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Keywords
Evolutionary theory of the Mind, Dynamics of Representation, Genesis of Symbol, Logicism,
Genetic Epistemology, Boolean mind, A n =A , Hamiltonian Algebra as the Science of Pure Time,
Wittgenstein’s Tautology and Linguistic game, Cantor’s Projection, Dedekind’s Gedankenwelt, School
Phobia, Blocks in Learning, Headache, Literacy/Numeracy skills, Knowledge Society.
Abstract
The goal of the present project is to provide fundamental tools for a novel « powerfully
explicative » learning theory, and it corresponds to the wish of Mr.H Koizumi: «the educational science is
still at the Lynnaeus stage – it can draw a list of good examples to follow, classify and clarify effective
pedagogical methods – and it is waiting for the Darwin who will provide it with a powerfully explicative
learning theory», in such a way that my project has direct applications in Pedagogy, Pedagogy of science and
educational politics on one hand and in Neurosciences and Psychiatry on the other.
I) My thesis is that the dynamical analysis of the representational field from the inside
of which we can observe the genesis of Mathematics, shows that A) «from without» a unitary subjective and
evolutionary force is as much the root of the Gestaltic apparition of conventional symbols (a,b,c…1,2,3) to
human consciousness, as all mathematical transformations human understanding will be able to generate
thanks to these symbolic tools; B) «from within» the same laws which underlie the genesis and the symbolic
development of Mathematics, are the genetic seed of the Mind itself; C) these laws are in fact the educational
laws for school learning.
This theory is a “transdisciplinary” enhancement of the Piagetian Genetic Epistemology. I provide a unitary
dynamic/vectorial model of mental development which is more powerful and more coherent than Piaget’s
S(A)R model. I do this using A) the Boolean notion of the «index law» A n ×A =A , that formally explains the
Gestaltic transformation of the object A in the symbol “A” when a child learns to read at the end of the
temporal process At1×At2×At3×…Atn = “A” ; B) the Wittgenstein’s dynamical notion of «tautology» as the
dynamical field in which «bipolar functions with a sense» take form, inside of what I call the linguistic
game of school.
II) On this basis, I have already established a very efficient method of intervention in
the didactical field for the Pedagogy of sciences, and in the educational/therapeutical field of
mental/emotional obstacles for learning and for preventing headache.
As a teacher, my problem was the following: are we able to really give pupils the «social
maturity that allows them to distance themselves from social pressures» [OECD2000, DeSeCo - Definition
and Selection of Competencies]. Through my experience, the answer I can give to this question is a definite
no. In our age, all western boys and girls, men and women, rich and poor… are equal when faced with
social pressure. We are all equally poor in Time, even if Europe tells us continuously that we are rich
enough, and that the time is right to start thinking differently about human life, citizenship and «social
cohesion» [Lisbon European Council 23 and 24 March 2000. Presidency Conclusions].
Thus, something more radical has to be done: we must be able to scientifically show that this
«distance from social pressure», which is fairly crucial for a real mental then social cohesion, lies at the core
of every scientific truth as such. The age of science has lost the time of science, but time does not come to
science from the outside. Time is, on the contrary, at the deep heart of every scientific truth, and time is
essentially the time of genesis, during which the human mind must truly and gradually grow up, by acquiring
patience, tolerance, wisdom, and the courage to exist.
III) Finally, after 11 years of relentless research, my genetic theory of the mind, symbols
and education is now a coherent and complete whole. It only needs to take on its exteriorized form, in
order to give a public and rigorous systematization to my already effective practical methods, and the chance
to be universally understood and applied. I therefore urge the European Union to provide me with the means
to dedicate two years in which to funnel my energy into this final phase of exteriorization/systematization,
and I have no doubt that the impact of my work will live up to my expectations.

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B1 - SCIENTIFICAL AND TECHNOLOGICAL QUALITY 3
The “continuity hypothesis” of Jean Piaget, and its application. 5
[A] An overview of the six steps of the “practical” period of an infant’s intelligence. 5
[B] An overview on the “non-operational” and “verbal” period of an infant’s intelligence. 7
FIRST ELEMENT - A more-than-Piagetian vector of human evolution 8
SECOND ELEMENT – The gift of the synchretical world of mathematics. 11
THIRD ELEMENT - From the crystallization/cohesion of A to the inter-action between A and A 11
BACK TO SCHOOL. From the Piagetian A =A×B to the Boolean A×A =A 13
to Dedekind/Wittgenstein’s “I am someone”. 13
The “completeness” of my educational project. 14
Educational and therapeutical consequences 15
B2 TRAINING OBJECTIVES 16
HOST EXPERTISE 17
B3 - RESEARCHER 18
Philosopher and official delegate of AIC (Italian Headache Association) 18
Teacher of children suffering from school-phobias and Kung Fu/Yoga researcher 19
Eironeia 20
B4 IMPLEMENTATION 23
B5 IMPACT 24
B6. ETHICAL ISSUES. 25
In the Age of Knowledge, in search of the lost Time of Science 25
Dialogue between a teacher and a young European citizen 25
Opportune igitur hodie mentem curis omnibus exsolvi, 26
securum mihi otium procuravi… (Descartes - Meditatio Prima) 26
Works Cited 27
REFEREES – At the end of the document.

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B1 -- SCIIENTIIFIICAL AND TECHNOLOGIICAL QUALIITY
Outline the research objectives against the background of the state of the art, and the results hoped for.
Give a clear description of the state-of-the-art of the research topic.
« Educational science is still at the Lynnaeus stage – she can draw a list of good examples
to follow, classify and clarify effective pedagogical methods – and she is waiting for the Darwin who
will provide her with a powerfully explicative learning theory. » [H.Koizumi- OCDE2002/207]
The challenge of my research program Symbols of their own genesis… is to provide the
fundamental tools for a new « powerfully explicative learning theory», having direct applications in the areas
of pedagogy, pedagogy of science and educational politics on the one hand, and of neurosciences and
psychiatry on the other. In fact, I am not as radical as M.H.Koizumi in what concerns the present
epistemological condition of the science of education, but I am even more radical than him with regards to
science education. This document will show the way in which the profound need for a renewed «preparation
of the child for science» (according to Mary Boole Everest’s expression) has, during the last 8 years of my
life, generated a new educational theory on human evolution in my Gedankenwelt.
Actually, in the field of educational science we do not merely have «lists of good examples» at our
disposal, because during the XX th Century an unitary dynamical/evolutionary model of the human mind has
been thought up and realized by Jean Piaget. Rigorously speaking then, my research program is the
Piagetian program of an educational theory capable of linking together all the stages of the cognitive
development of man. I am stimulated by the same goal of completeness that has been the highest but most
inaccessible peak that the great project of logicism – the philosophical and scientifical root of Piagetian
epistemology – has had the courage to conceive.
Now concerning the epistemological weakness of Piagetian logicism, there is nothing better than
the words of M.Grattan-Guinnes to describe the “state of the art” of its educational consequences:
Educational aspects [of Logicism], especially Piaget. - The Swiss educational psychologist
Jean Piaget (1896-1982) came eventually to the borders of logicism […] The influence of Principia
Mathématica came through Piaget's belief that rationality resembles mathematical reasoning, which in turn
was captured by (mathematical) logic. But such a position is hardly credible, especially for the creative
sides of mathematics itself. Later his work played a role in the 'new mathematics' educational idiocy of
the 1960s onwards. Around that time (1973) Quine told me that when he had heard that set theory was being
used in mathematical education, he had thought that he was being told a joke. […]
As with all philosophical schools, logicism paid no attention within arithmetic to 'goes-into'
integers. They arise in contexts such as the Euclidean algorithm: for example, 7 goes into 23 thrice, with 2
over. Words like 'thrice' show that a special vocabulary applies to these integers, which are neither
cardinals nor ordinals; and the mention of Euclid shows that their history is long. Yet they usually escape
the attention of mathematicians and philosophers — and, despite their heuristic utility, educators also.
[I.G.Guinnes]
A personal remark made by a child «prepared for science» by this educational program.
I am 40 years old, and I have been submerged by the wave of “modern mathematics”. I didn’t
understand “modern” mathematics – it is impossible to really understand it: no child has understood it – but
I loved mathematics so much, and up till now, my entire life has been spent on building up a new kind of
transmission of scientific knowledge to new generations.
As we shall see, I fully agree with Grattan-Guinnes on the question of the «creative side of
mathematics» and on the heuristic and educational weight of « these integers, which are neither cardinals nor
ordinals». Notwithstanding, I pose the question: can we simply give up the Piagetian/logicist «great project»
[C.Mangione]? Has the Europe of Knowledge the right to do so?
In fact, according to Mr Guinnes, there is a close relationship between the «hard credibility» of
the Piagetian position, and the inner educational gap of its logicist root, whereas concerning the logicist
program as such, the scholar simply declares that we are in «another epoch»:

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Kurt Gödel, in his incompletability theorem of 1931 showed that the assumption of consistency and
completeness intuitively made by Russell (and by most mathematicians and logicians of that time) could not be
sustained in the form intended. No authoritative position either within or outside logicism emerged. After
1931 many of the main questions had to be reframed, and another epoch began. [I.G.Guinnes]
In my opinion, from an historical point of view, the epoch that began after 1931 was neither a
«reframing» nor a really scientific epoch at all: it was essentially the age of preparation for the Second World
War, during which (1936) Kurt Gödel’s teacher Moritz Schlick, was murdered by a proto-nazi: an event that
engendered the first mental breakdown of Schlick’s pupil. En revanche, from a philosophical point of view,
I think that the Piagetian position – that is to say, the logicist Weltanschauung in terms of the possible
foundation of a fully rational life – must be trusted by any science that aims to grasp the roots of human
evolution. Immanuel Kant would say that the logico/mathematical roots of our mental life must be thinkable:
doch [sie] wenigstens müssen denken können [KrV, II° Preface]
To summarise: the «state of the art” of my research-topic» is that
(1) «Educational science is still at the Linneaus-stage» with the exception of the Piagetian
equation S(A)R - Stimulus/Assimilation/Reponse – that is intended to give an unitary
mathematical/dynamical model for all the evolutionary transformation in the universe. (2) Regarding the
foundation of science «no authoritative position either within or outside logicism» has crowned the logicist
research program. The Gödelian breakdown of any Russellian intuition of what comprises “completeness”
has been the breakdown of any completeness ambition. (3) Science education is now escaping from the
epoch of “modern mathemathics”, and a lot of international global drives such as EFA (UNESCO 2000)
PISA/CERI (OECD 2000/2007) and UE (“Knowledge Society” Lisbon 2000) are in search of a new
methodical approach to give 7 billion men/women a scientific education in harmony with our globalised
planet.
If relevant, provide information on interdisciplinary / multidisciplinary and/or inter-sectorial aspects of
the proposal.
My transdisciplinary “dimensional equation” and my “middle term”.
Dynamics of Representation =
[Cognitive psychology] × [Logic/Mathematics] × [Genetic Epistemology] × [Philosophy (of Mind)]
I state that my theory is more powerful than Piagetian genetic epistemology, and that only a deep educational
misunderstanding around man and child can generate the false idea of an impossible completeness of
science, which was the core of the logicist project.
Now to set down a new synthesis between the genetic/psychlogical perspective on the mind and
and the logico/mathematical idea of the foundation of science, my research method must be rigorously
transdisciplinary, in the sense that Koizumi contributes to this notion, and that OCDE fully adopts it:
« The concepts of interdisciplinarity and multidisciplinarity are situated on a plane, a twodimensional
space, but the concept of transdisciplinarity occupies a three-dimensional space ».
This three-dimensional space is the fruit of a vectorial fusion between existing disciplines:
«The classical Newton dynamics, for instance, were created by combining the concepts that
explained the movement of astronomic objects and the falling on earth of an object, an apple according to the
tradition ».
In fact, such a new fusion needs to be realized by means of an old/new middle term acting as its
catalyser, and such a catalyser is necessarily a very simple phenomenon, (the censer of Galileo, the apple of
Newton…) whose appearance is imperative: it must have the strength of Galileo’s inclined plane, and an
ability to pierce without hesitation an unexplored yet evident dimension of the world and of the disciplines to
be fused.
My research finds this transdiciplinary catalyser in a
fact as evident as the apple of Newton: the birth of
mathematical evidence in a child’s consciousness. On this
basis, I arrive at a genetic theory of the conventional symbol

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(“A”) as the only possible horizon of the apparition of a categorical truth such as “A=A”. My
“Newtonian/fusioning” theory is: “the same force reveals its action as the symbol A… [= the
earthly/symbolic A-apple orbits the perceptive earth onto which it falls] and as the truth A=A [the
celestial/categorical A=A-truth, falls down on the rational earth it orbits around].”
In my PhD thesis – Le fait génétique des mathématiques et la puissance dynamique du mental
humain – I claim that a mind does exist, that is: the birth of scientific evidence in the human consciousness
is the cinematic phenomenon that results from the continuous and unitary application of a dynamical vector
of projection (German «Projection» in the Cantorian/Wittgensteinian sense of the expression) that I call Yod
(as an hommage to the Aleph of Georg Cantor), whereas the present project aims to develop the results of
this first existential position, in the direction of a Galileian type of dynamics of representational
transformations inside the vectorial space of Mind.
Research methodology. For each objective explain the methodological approach that will be employed
in the project and justify it in relation to the overall project objectives.
The “continuity hypothesis” of Jean Piaget, and its application.
L'activité fonctionnelle de la raison (l'ipse intellectus qui ne vient pas de l'expérience) est
évidemment liée à l'«hérédité générale» de l'organisation vitale elle-même [...] Du simple réflexe à
l'intelligence la plus systématique, un même fonctionnement nous paraît se prolonger au travers de tous
les stades , établissant ainsi une continuité entière entre des structures de plus en plus complexes. [NI] si les
structures dont use la pensée varient d'un stade à l'autre et, a fortiori, d'un systeme mental à un autre, la
pensee demeure constamment identique à elle-même du point de vue fonctionnel.[CR]
This is Piaget’s “continuity hypothesis”. Let us now consider the concrete action of this
hypothesis in what concerns the first two steps of its application in Piaget’s research program: [(A)
Naissance de l’Intelligence… - (B) Genèse du Nombre… ]
[A] An overview of the six steps of the “practical” period of an infant’s intelligence.
(In bold: the behavioral evidence from which the different phases of Piagetian observations begin).
I. (BIRTH) SCREAMSTORM→CALMNESS - At birth, the infant explodes in an accelerative
storm of screams, until a perfect calmness suddenly appears in the infant’s body/face when the desired
situation (i.e. suckling) is reached. The logico/dynamic structure of this mechanism shows that an oriented
totality of meaning is in action from the beginning of human life [«Simple Reflex» - «Dynamogenesis of the
reflex-field»]
II. SMILE and CONTEMPLATION - The global field of the reflex expands its perimeter «wave after
wave» by always «incorporating» new objects, either by transforming them into signals of others objects that
it finds inside of its action (the associationist mechanism of Signalwirkung is actually the result of an active
intervention of the psychological subject as a whole on its practical world), or by contemplating them for the
sake of contemplation (i.e the infant looks silently at something, for a long time) [«Primary Circular
Reactions»].
III. CONCENTRATED ATTENTION - The infant is clearly interested in the new unexpected
phenomena of the world around it. The sensorial frameworks of perception and actions are stimulated by an
autonomous force of expansion/incorporation, with the consequence that an «assimilation scheme» (i.e.
vision) that naturally «tends to assimilate the entire [exterior] world around it» also assimilates other
schemes (i.e. touch) that it finds within the interior world of the subject. [«Secondary Circular Reactions»].
IV. EXPRESSED INTENTION - The infant clearly conceives a goal in its mind before acting on a
perceived interesting reality. This phenomenon entails an enhancement of the reciprocal (=non objectual)
interaction between assimilation schemes. A mental space first appears, where a sign exists before its object,
and the presence of this new space allows a new internal mobility of mind. [«Coordination of Secondary
Reactions» – First Representational Inversion: representation before action - Practical phase of the
Concept.]
V. ACTIVE EXPERIMENTATION – To achieve its intentional goal, the infant conceives new
means that do not form part of the interesting situation to preserve/repeat. In the internal space of its mind –

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where it now combines purely semantical realities – it is able to transform an old goal (=a practical scheme
of action as a whole) into new means, and vice-versa. The infant is then able to conceive a semantical system
organized into a hierarchy in its mind: the mobility of the latter now becomes a practical reversibility
[«Tertiary Circular Reactions» - Second Representational Inversion: goals become means submitted to other
goals. Practical phase of Judgement ]
VI. MENTAL CREATION – The infant’s mind finally appears, as a space of a virtual action where
new goals are continuously created by means of a mental combination power that uses its inner apparatus of
purely semantic entities as a potentially infinite set of symbols that do not need to converge onto a concrete
external action to be the elements of that inner effectual action that we call operation. [«Invention of New
Means Through Mental Combination» - Third representational inversion: the possible before the real -
Practical phase of Reasoning].
The dynamic description of this progressive “biological” endogeneration of new schemes from step I
to step VI is:
Chaque schème, en tant que totalité, est gros d'une série de schèmes virtuellement contenus en lui,
toute totalité organisée étant ainsi, non pas composée de totalités d'échelle inférieure, mais source
possible de telles formations [NI].
I state that a « possible source» is a metaphysical/modal error. A seed is not a “possible source
of a formed plant”: it is, on the contrary, the real and actual source of a possible plant, so as soon as the
plant is born, its root are the real and actual source of this real and actual plant, of which this root is a part
of. Similarly, in the vectorial modelization of a given accelerated movement happening in t=1 and
beginning from quietness, the first = 1° instant of this given movement, in which v=0, is not the condition of
“possible movement”, but a real and actual movement, which is a part of this real and actual given
movement = 1.
The Cantor/Dedekind [=sets/class theory] model of the same process is:
Grâce à la complication progressive des schèmes, l’enfant renouvèle sans cesse ses actes par assimilation
reproductrice et généralisatrice, et il dépasse le simple exercice réflexe pour découvrir la réaction
circulaire et constituer ainsi ses premières habitudes. Un tel processus est évidemment susceptible
d'extension illimitée. Après l'avoir appliqué à son propre corps , le sujet l'utilisera tôt ou tard pour
s'adapter aux phénomènes imprévus du monde extérieur, d'où les conduites d'exploration,
d'expérimentation, etc.[NI]
Here it is quite evident that the strictly set theory notion of Abbildung≡application orients the
Piagetian modelization of the behavior of a 1-2 year-old child which is certainly not yet “unlimited” . I say
then that the only possible “unlimited” human behavior is the symbolically unlimited mathematical
management of symbols: Piaget is here projecting on a child’s mind/body whose “mathematical movement”
is = 0, the formally unlimited space of possibilities that will appear during his adult mathematical life. Now
when the psychologist studies the birth of mathematics in a human mind, he cannot avoid this projection:
and here I am only stressing that this is a vectorial projection from an after to a before. On the basis of the
Piagetian continuity hypothesis we must then say that the suckling activity of a child that will become a
mathematician is an actual and real “mathematical movement” whose velocity is=0, and that it is the actual
and real source (seed/root) of the future mathematician.
According to Piaget [EG], the functional expression of this unitary and global inner isomorphism of
[not only] human life is the formula «S(A)R» where S=stimulus, R=response and A=assimilation, that is the
«fundamental [incorporating] operation»[NI], common to all forms of life in the universe, in their
evolutionary interaction with the world around them. I stress in this case that Piaget calls this primary
cosmological fact a «fundamental operation», whereas in the Piagetian formal system S(A)R it is not an
operation but the symbolic model of all possible operations.
As aforementioned, the primary observational evidence on which Piaget has based his
developmental theory are Calmness - Contemplation - Attention - Intention - Experimentation -
Creation. All the observations that Piaget makes on his children are secondary types of observational
evidence, generated inside of this cardinal sequence of quite ordinary primary human evidence that is
universally recognizable and accepted. Now Piaget’s “continuity hypothesis” is that «thought remains

constantly the same and identical to itself self from a functional point of view»: there is then no doubt that the
sequence I.Calmness→VI.Creation
→VI.Creation is the primary behavioral [= phenomenal] counterpart of the functional
isomorphism of thought which for Piaget unif unifies the totality of the phenomena of [not only] human life. The
behavioral calmness of an adult after an explosion of rage is then “functionally” the same calmness of an
infant, and so is “contemplation”, “attention” etc. We must consequently affirm that the S(A)R
contemplation of a 1 month old infant that observes an oscillating toy placed above its cradle, is the same
S(A)R contemplation as that of Galileo Galilei when observing his famous us oscillating censer.
Now within this functionally homogeneous horizon, the main concern of Piaget is to stress that at the
end of every step of these 6 phases, the moment comes for the mental activity of the child «to grasp
something on the exterior of its given field» [NI] at this very moment. Piaget asks then « «how can this
cognitive enhancement be possible? possible?» and the answer to this how is his dynamical/set set theory theory/functionalist -
in a word: structuralist - description of the internal mechanism of a psyc psychological hological empowerment, by which
«the ego is delivered from itself»[CR]. self»[CR]. Finally then, there is no reason for the subject to go forth: the
dynamical power of its self-improvement
improvement on the occasion of experience, express a primary fact - the fact of
life - and the sequence of structures described by Piaget is a pure cinematic juxtaposition of mathematical
forms that reveal this transformational fact.
[B] An overview on the “non “non-operational” and “verbal” period of an infant’s intelligence.
(In what concerns the three steps of the notion of numbers and continuous/discrete quantities).
VII. STABILITY and CERTAINTY about the non-conservation of numberss
and physical quantity.
(eventually, ASTONISHMENT before an unexpected result)
SIM (5). «Il y a la même chose d'eau dans les
verres [A1 et A2] n'est-ce ce pas? — Oui. «Regarde. Maintenant
Madeleine eine verse le sirop rouge dans lle
verre là (L1)— Il y a
plus de rouge parce que c'est plus haut. — Il y a plus à boire,
ou on dirait seulement? — Il y a plus à boire.
BA (4,9) ne croit pas l’équivalence nécessaire
lorsque l’on altère la disposition de l’une des collections qu’il
vient de mettre en correspondance. Il suffit, par exemple, de
coucher sur le grand côté [A] un rectangle de 12 jetons
qu’il a construit en hauteur [L] pour qu’il ne le croie plus
équivalent au modèle (dressé)
7
ZU (4) « Est-ce ce qu'il y a assez d'œufs pour ces
coquetiers? — Oui. - Mets-les les toi toi-même, pour voir. — (Il les met et paraît très surpris qu'il en manque.)
VIII. INSTABILITY and OSCILLATION around the non-conservation conservation of number numbers and
continuous/discrete quantities
EDI (5) « Tu dois prendre autant de sirop ici (L) qu’il y en a là (A). — (II verse la même hauteur.)
— C’est la même chose à boire? — Edi: [6] Oui. — Tout à fait? — Non. — Pourquoi pas? — Ça (A)
c’est un plus gros verre. — Qu’est Qu’est-ce qu’il faut faire pour avoir la même chose? — Rajouter (il remplit L).
— C’est juste? — Non. —Qui Qui en a plus? — Moi (il enlève le surplus). … Non, c’est la maman qui a plus
(A). — (Il rajoute, joute, enlève à nouveau, etc., sans parvenir à se satisfaire.)
IX. STABILITY and A PRIORI CERTAINTY about the conservation of numbers and physical
quantity. The child «n’a n’a plus à réfléchir pour s’assurer de la conservation des quantités totales: il en est
certain a priori. »
LIN (6) constate l’égalité de AA1
et A2. « Si je verse (A1) en (L)? — Ce sera toujours la même
chose. — Et si je verse (L) en (G) ? — Encore la même chose. Vraiment? — Bien sûr, parce qu’ici, dans le
petit (= le mince = L), il y a plus
The primary observational evidence upon which Piaget bases his theory of the genesis of
numbers/physical quantity, is this triadic sequence i.Certainty-Astonishment → ii.Doubt ii.Doubt-Oscillation→
iii.A priori certainty. . Inside this continuous cognitive triplet, the main concern of Piaget is (as in the case
of the six steps of practical intelligence) to stress the necessary active existence of an under underlying subjective
structure that only can explain a sequence of transformation that is:

1) Perfectly unnecessary (=simply factual) at step i→ii (perceptive certainty of non--conservation)
C’est ’est une question de jugement et non point de perception que nous cherchons à résoudre. Notre
problème n’est pas de découvrir pourquoi cette perception est trompeuse, mais pourquoi les sujets d’un
certain niveau se fient à elle sans plus, tandis que d’autres la corrigent et la complètent par l’intelligence
[GN]
2) Totally unaware of its own genesis at the step ii→ iii (a priori certainty of conservation)
Or, au moment où l’enfant découvre cette invariance, il l’affirme comme une chose si simple et si
évidente qu’elle parait indépendante de toute multiplication des relations […] Il y aurait ainsi conservation par
simple identification logique, sans interven intervention d’aucune mathématique. A une telle simplification du
processus génétique on sera toujours en droit d’opposer, no nous semble-t-il, il, la question sui suivante qui resterait
alors sans solution: pourquoi faut faut-il que l’enfant parvienne au troisième stade pour déc découvrir cette
identification?[GN]
Here I say that :
As in the case of the transitions I→VI, Piaget does not give a causal answer
concerning the transition VII→VIII VIII→IX.
1. “Why does the human uman mind break the ccircle
of perceptive and «synchretical» certainty of the first
childhood to go towards the age of doubt?”. The Piagetian way of answering this question is
cinematical one: this fact (the fact of mental life) reveals the birth of a multiplicative=mathematical structure
within human cognition, whose «solidified» or «crystallized» symbolic form is
[GN], and in order to reach this mathematical «power of equalisation» the child must pass through a
transitional phase (phase II) of doubt and oscillation.
2. “Why [we claim that] is the a priori certainty of numerical conservation not a simple and ungenerated
item of «logical identification»”? The Piagetian way of answering this question is: because for
there is no obvious identity at all. Then the numerical/quantitative identity A×L=L×A
genetic process whose cinematical inner structure is that of a decrystallisation→
perceptive/synchretical certainty «ܣ ↑ ℎ ௟
← ܮ ≠ ܣ ௚
causal answer to his double «why?»
«synchretical» certainty of the first
this question is again only a
(the fact of mental life) reveals the birth of a multiplicative=mathematical structure
« ܣ ↑ ℎ
↔ ܮ » … to the a priori certainty «
௟
← ܮ = ܣ ௚
↔ ܮ »
«power of equalisation» the child must pass through a
[we claim that] is the a priori certainty of numerical conservation not a simple and ungenerated
item of «logical identification»”? The Piagetian way of answering this question is: because for Zu and Edi
A×L=L×A is the result of a
→crystallisation from the
« ܣ ↑ ℎ ௟
← ܮ = ܣ ௚
↔ ܮ ».
௚
FIRST ELEMENT - A more-than-Piagetian Piagetian vector of human evolution
Now I claim that the cinematical evolutionary transition {ܣ ↑ ℎ ௟ ௚
← ܮ ≠ ܣ ↔ ܮ}→{ܣ ↑ ℎ ௟
← ܮ = ܣ
↔ ܮ} – that has not been questioned by anybody in the present or previous scientific community – has the
dynamical identity of a vector, , and this is the first element at the core of my project. The path of human
evolution that leads from the stabilisation stabilisation-event accelerative screamstorm→calmness calmness (step 0/I) to the
stabilisation-event oscillating-uncer uncertainty→a priori-certainty (step VIII/IX) ) has the dynamical/vectorial
identity of a force, , and the metaphysical status of an unnecessary fact.
௚
Let us consider the universal form of mental evolution {ܣ ↑ ℎ ௟ ௚
← ܮ ≠ ܣ ↔ ܮ}→{ܣ ↑ ℎ ௟
← ܮ = ܣ
↔ ܮ} in Piaget’s perspective on the history of science:
« Toute connaissance, qu’elle soit d’ordre scientifique ou relève du simple sens commun, suppose
un système, explicite ou implicite, de principes de conservation. Dans le do domaine maine des sciences expérimentales,
il n’est pas besoin de rappeler comment l’introduction de la conservation du mouvement rectiligne et
uniforme (principe d’inertie) a rendu possible le développement de la physique moderne, ni comment le
postulat de la conservation du poids a permis à Lavoisier d’opposer une chimie rationnelle à l’alchimie
qualitative.»[GN]
Now Lavoisier’s intervention in the human world of the XVIII
the transition from the non-conserva
conservative/rational world of Lin:
th Century was as unnecessary as
conservative/synchretical world of Sim to the
« Sans doute, si l’on érige en principe la possibilité pour un liquide de se
dilater ou de se concentrer sans permanence aucune, il n’y a là [SIM] aucune
contradiction » [GN].
Here on the right a steam engine can be seen, which perfectly
realizes Lavoisier’s ier’s postulate of conservation, while perceptively confirming
8

Sim’s certainty of non-conservation
conservation.
Let us say that Sim’s recipient A is water tank A
(where L1 is evidently > L). According to Sim’s expression, «
A1 to boiler L1, but because of a « non
Lavoisier’s principle of conservation has thus been thought of within a perfectly non
where no man or child has any kind of problem when confronted with the evident and universal fact of
conservation.
I claim then that the classic Pia
biological and mental evolution is
Galileian postulate of a «conservation principle» within cognitive sciences [in GN]
recognize what the Mechanics of the XVII
dynamics = the mathematical presence of a force inside the new experimental (Galileian/Newtonian)
evidence. Similarly, on the experimental, mathematical and cinematic basis of Sim’s/Lavoisier’s unnecessar
sequence {ܣ ↑ ℎ ௟
← ܮ ≠ ܣ ௚
↔ ܮ}→{ܣ
of his «mathematics» as an active, spontaneous
Finally, when we consider the
from the beginning, and we cannot avoid grasping the phenomena that we meet inside this observational
perimeter with mathematical tools
mathematizing activity. In the present case, the cinemati
screamstorm→calmness→perceptive certainty {
certainty {࡭ ↑ ࢎ ࢒
← ࡸ = ࡭ ࢍ
Let us say that Sim’s recipient A is water tank A1, while Lavoisier’s recipient L is the boil
). According to Sim’s expression, « the same thing of water» passes to t
non-contradictory » dilatation, in t2 there is «more red» in L
isier’s principle of conservation has thus been thought of within a perfectly non
where no man or child has any kind of problem when confronted with the evident and universal fact of
I claim then that the classic Piagetian opposition to any idea of a «force of organisation» underlying
biological and mental evolution is nothing more than an ideological and cultural attitude
Galileian postulate of a «conservation principle» within cognitive sciences [in GN]
recognize what the Mechanics of the XVII
↔ ࡸ } is
applied by the projection-subject Yod
th Century had already called the “mathematical forces” of new
dynamics = the mathematical presence of a force inside the new experimental (Galileian/Newtonian)
evidence. Similarly, on the experimental, mathematical and cinematic basis of Sim’s/Lavoisier’s unnecessar
ܣ ↑ ℎ ௟
← ܮ = ܣ ௚
↔ ܮ} Piaget should have recognized the genetic presence
of his «mathematics» as an active, spontaneous mental force.
Finally, when we consider the birth of mathematical thinking, we are inside
, and we cannot avoid grasping the phenomena that we meet inside this observational
mathematical tools. Mathematics obliges us to mathematize the beginning of our
mathematizing activity. In the present case, the cinemati
perceptive certainty {࡭ ↑ ࢎ ࢒
← ࡸ ≠ ࡭ ࢍ
recipient L is the boiler L1
the same thing of water» passes to t1 from tank
there is «more red» in L1 than in A1.
isier’s principle of conservation has thus been thought of within a perfectly non-contradictory world,
where no man or child has any kind of problem when confronted with the evident and universal fact of nongetian
opposition to any idea of a «force of organisation» underlying
cultural attitude, whereas his
formally obliged him to
had already called the “mathematical forces” of new
dynamics = the mathematical presence of a force inside the new experimental (Galileian/Newtonian)
evidence. Similarly, on the experimental, mathematical and cinematic basis of Sim’s/Lavoisier’s unnecessary
Piaget should have recognized the genetic presence
inside mathematical thinking
, and we cannot avoid grasping the phenomena that we meet inside this observational
to mathematize the beginning of our
mathematizing activity. In the present case, the cinematic transformation
↔ ࡸ} → oscillating doubt → a priori
– mathematically speaking – a vector, , that I call the projection vector,
Yod.
Let uss now look at the heuristical power of this new tool.
From childhood to adulthood. From the oscillating Edi to the oscillating Sagredo.
Sagredo is Salviati’s friend/pupil in Galilei’s Dialogues on two world systems, where he represents the
transition (=decrystallization/crystallization) phase between the old “qualitative” (=synchretical/perceptive)
Simplicio physics and the new mathematichal (=operational/reversible) Salviati dynamics.
SALVIATI - Will you now conf confess that the impetus of that
which descends by plain CA, having arrived at point A, may be equal to the
impetus acquired by the other in point B, after the descent by the
perpendicular CB? SAGREDO SAGREDO. I resolutely believe so:[…] SALVIATI .
But on the inclining ng plane CA it would descend, but with a gentler motion
than by the perpendicular CB? SSAGREDO.
I may confidently answer in
the affirmative, … yet nevertheless, vertheless, if this is so, how can the cadent by
the inclination after reaching point A, have as much impetus, that is, the
same degree of velocity, that the cadent by the perpendicular shall have in
point B? These hese two Propositions seem contradictory
contradictory…
Here the Piagetian isomorphism childhood → adulthood is formally evident: the transition from
the oscillating mental condition of Sagredo to the crystallized condition of Salviati’s mind is rigorously
expressed by the same Edi→Lin formula formula: {ۯ ↑ ܐ ܔ
← ۺ ≠ ۯ ܏
↔ ۺ}→ {ۯ ↑ ܐ ܔ
evident: the transition from
the oscillating mental condition of Sagredo to the crystallized condition of Salviati’s mind is rigorously
܏
← ۺ = ۯ ↔ ۺ }.
Furthermore, the doubt that Sagredo had concerns the same geometrical transformation as the
doubt that Edi had. It is then a case of Piagetian «decalage»: from the perceptive oscillation of Edi to the
projective condition of Sagredo. Now we can easily say that the difficulty concerning this geometrical
transformation concerns all the ages and objects of our cognition (see the coins of BA here above):
JACQUELINE, , à 1; 3 (12), est
assise dans son parc, c'est-à-dire
dans une
enceinte carrée dont les quatre côtés sont formés
de barreaux verticaux reliés en leur base et en
leur sommet par une barre horizontale. Les
9

10
barreaux sont distants de 6 cm. Je place en dehors du parc, et parallèlement au côté devant lequel se trouve
Jacqueline, un bâton de 20 em. occupant ainsi la longueur dde
e 3 intervalles environ entre les barreaux. Nous
appellerons ces trois intervalles a, b et c, l'intervalle b correspondant donc à la partie médiane du bâton et les
intervalles a et c aux parties extrêmes. Le problème est de faire passer ce bâton de l'extér l'extérieur à l'Intérieur
du parc. Le bâton est posé à terre parallèlement au côté du cadre en face duquel Jacqueline est assise. Dix
essais lui ont suffi pour résoudre le problème . Jacqueline saisit le bâton en B. Elle le lève horizontalement et
l'applique ainsi [۴ሬ⃗] ૚ contre les barreaux barreaux. Elle tire de toutes ses forces [۴ሬ⃗] ૛ puis le déplace sans système, le
relève et le passe tout à coup par hasard [۴ሬ⃗] ૜ sans avoir compris comment. Elle prend cette fois le bâton en A,
l'applique horizontalement contre les barreaux et tire tant qu'elle peut [۴ሬ⃗] ૛].
Elle le redresse ensuite
systématiquement, mais le bâton, touchant le sol par son extrémité inférieure, demeure oblique. Elle tire à
nouveau très fort [۴ሬ⃗], ૛ , puis renonce. Elle commence encore par tirer horizontalem
horizontalement, puis le relève, tire
à nouveau et enfin l'incline de manière à le passer correctement. Elle l'a saisi ces deux fois en B. Jacqueline
saisit le bâton en C, le tire horizontalement puis le relève. Mais elle le redresse tant qu'il dépasse le cadre par
en haut et reste accroché par le bas. Elle le secoue alors et finit par le
passer par hasard.
Itt is clear from Jaqueline’s example that the continuous
application of the same force [۴ ሬ ૚ି૛૛ሬ⃗]
should have been sufficient for the
infant to find the “way out” (as in the purely mechanical engine here on the
right), but this is not so: the infant is perfectly able to increase the
“modulus” of its force (she «pulled with all her strength”), but she finds an
essential difficulty in its re-orientation. orientation.
Finally, we are discovering here an universal isomorphism between the perceptive and the
projective difficulty in «equalizing» the ( (↔) horizontal (→) and vertical (↑) ) orientation of a given
phenomenon.
I claim that this isomorphism reveals to
us the non-commutative commutative inner structure of our
operational mental space, , that is shown by the non-
commutative [= genetic because endowed with an
absolute cognitive beginning ning] relationship between
the projective space of trigonometry – where
inside of the absolutely vertical rectangle L
“there is a greater” angle angle-amplitude than in the
horizontal rectangle A – and the perceptive space of euclidean geometry, , where RRL
and RA are rigorously
equivalent, and that we must necessarily grasp before their [= ITS!] ] rotation can make the sinus/cosinus
relationship appear before our projective/[tauto
projective/[tauto-]logical imagination.
I am thus claiming that the trigonometrical way to look at euclidean angles is the final
reapparition – at the projective level, with a « décalage» – of the child’s vision of the absolute and
«synchretic» orientation of its perceptual uni-verse.
From adulthood to childhood. From the mathematical certainty of the adult Georg Cantor (or
Galilei) to the synchretical certainty of the little Zu:
This image is evidence of another formally perfect isomorphism between the perceptive condition
of a child that verbally organizes a «synchretical» set of things by saying that there is the same number of
eggs and egg-cups and the projective condition of an adult that symbolically organizes an unlimited set of
symbols, by saying that there is the same number of natural numbers and odd numbers. [My objection to
the objection of Bever/Dehaene & CC.
. to the sense and truthfulness of this Piagetian experience is that the
infant’s practical choice of 7 bonbons (between 7 and 4) is not the he purely perceptual /verbal grasp of 7 and 4
objects: we do not eat perceptions or symbols). ]

11
SECOND ELEMENT – The gift of the synchretical world of mathematics.
Now this rather Piagetian isomorphism is at the same time my first perfectly anti anti-Piagetian (or
more-than-Piagetian) Piagetian) isomorphism, that I discovered on the basis of my vector of the cognitive Yod-
continuity.
Piaget did not comment on this fundamental «décalage» that leads us in perfect continuity from the
perceptive synchretical world of childhood ( (-) to the projective mathematical world of adult adulthood (-) by
passing through the transitional phase of an ordinary operational mind, that, as it is able to grasp ordinary
and symbolic evidence (+), is totally unmindful of its genesis and totally unaware of its scientific destination.
And this is the second element at the core of my project.
… And this is finally my more more-than-Piagetian Piagetian representation of the cognitive vector of mental
evolution: (I) ZU: age of synchretical/magical evidenc evidence; (II-III) III) LIN/Simplicio: age of
ordinary/unmindful/dogmatic evidence; (IV) Galilei/Cantor: age of critical/mathematical and magical
evidence.
The strictly unnecessary character of this progression of steps, shows that the cibernetical idea of
feed-back and homeostatical equilibrium [Piaget MG] is incorrect: the human mind goes forth, and the only
inner equilibrium that it regognizes and accepts is its continuous and irreversible activity of creation. The
birth of science is the first irreversible beginning of an operation that is always reversible = freedom of
science is a gift that noone can take away from man man. We must have a formal and epistemological tool to
think of this kind of dynamical synthesis (irreversible beginning × rreversible
eversible operation = definitive gift), and
my entire project aims to construct this new tool, to pass it on to new generations.
The symbols + and – mean the opposite cognitive polarity of the different phases of this global
transformation, from the synchretical retical and for us unbelievable and marvellous (–) certainty of children, to the
mathematical and for us unbelievable believable and mmarvellous
(–) certainty of all the great thinkers that created that
unnecessary and impossible object that we call science.
THIRD ELEMENT - From the crystallization/cohesion of A to the inter inter-action action between A and A
Where do symbols come into all of this? Let us go back to step VIII→IX (from the doubt that Edi
had to the certainty of Lin). I said that this is a transition to a totally unmindful condition: the condition (+)
of the age of «concrete operations» when the child reaches, at the same time, an a priori certainty about
perceptive transformations of thingss
around him, and an a priori certainty about a new kind of thing: these
graphical thingss that we call “letters” and “numbers” “numbers”, , that can now reveal to his consciousness the
phenomenon (+) of mathematical evidence 7=7≠4. What is evidently unmindful in this phenomenon? The
Gestaltic estaltic impossibility to perceive these graphical objects as something other than letters and numbers. So
as no man can go back with his memory to the age in which his mother spoke to him in a language that
wasn’t yet his “mother-tongue”, tongue”, no man can go ba back ck with his perception to the moment in which the
sensorial presence of 7 was not yet the immediate perception of the number seven.
Now I claim that the irreversibility of this perceptual evidence (that obliges us to read A when we
perceive A) is the signn that the force that engenders this gestaltic crystallization leading to the final internal
cohesion of A, , is the same force that underlies the event of that interaction between A and A that we
perceive as the symbolic evidence A=A A=A.. This is the third element at the core of my project.
I will now present two lines of evidence to support this affirmation “ “the the same force reveals its action
as symbol A and truth A=A”.

12
If the force of mathematical evidence has a negative polarity, then only symbols can express it.
From 0 to 1, if the force of the evidence of {1,2,3,4,5,6,7}≠{1,3,5,7 } is =1, then either the
Galileian/Cantorian expression {1,2,3,4,5,6,7…}={1,3,5,7 …} is necessarily false = impossible = a simple
mistake, or the evidence of its truth is –1. Now this kind of negative evidence (such as x 0 =1, that is the
fundamental chassis of mathematics) can exist only inside the world of purely symbolical entities. I claim
then that the negative polarity of mathematical evidence is the immediate manifestation of an essential
propriety of symbols.
If the force of mathematical evidence is not hypothetical but categorical, then it is strictly
representational = symbolical (only symbols can represent an «impossible outcome»)
The a priori certainty that 7=7≠4 is not the same as the a priori certainty that Lin showed in terms of
the same volumes of liquid in the large and long vase having to be equal, because the modality of these two
certainties is quite the opposite. No child and no man will ever be astonished – not even for an instant – by
the expression 2+2=7, because this is nothing more than a mistake. This means that 7≠4 is a categorical truth
that only symbols can reveal. On the contrary, we can create astonishment and amusement (= the
Piaget’s/Claparede’s «prise de conscience») in a 7 year-old child like LIN, by organizing a magic show in
which the quantity of the liquid changes when we transfer it from the large vase to the long one. This modal
transformation in a child’s experience of the world at the moment in which he grasps the symbolical
evidence of mathematics for the first time, has not been stressed by Piaget or by the post-Piagetian research
on an infant’s grasp of “numerosity”. (See my [IPM])
Infants could clearly see the nature of the arithmetical operation being performed, but could not
see the result of the operation. Infants look at unexpected events longer [the “impossible outcome” 1+1] than
they do expected ones… […] (Winn)
Now here «1+1» means «a single item was shown… a second identical item was brought in the
display area », while «1+1=1» means «after the above sequence of events was concluded, the screen was
rotated downwards to reveal 1 item in the display case » [Winn] . It is then incorrect to say that in this way
the infant can clearly see « the nature of the arithmetical operation», because this series of events is not the
arithmetical operation 1+1=x, or 1×2=x : it is just the description of a 3-step experience, realized by means of
1 puppet, 1 other puppet, 1 display case and 1 screen… The mathematical evidence is neither the simple
numerosity of post-Piagetian psychology, nor the numerical quantity of Piaget, nor this hypothetical evidence
that makes an «occlusion event» the occasion of astonishment () and then of science. In contrast
to the simple quantity/numerosity “2” of a given set of items, the result 2 of 1+1 is perceived as
mathematical evidence only when the object/result 1 is pre-judged as impossible, that is, crossed out as an
error.
In summary: in the way that only symbols can reveal to the human mind an «unlimited number of
possibilities», similarly, only symbols can really represent an « impossible outcome». Reciprocally, things
can only be real-and-then astonishing, but never impossible. I claim that the categorical aspect of
mathematical evidence is the immediate manifestation of an essential propriety of symbols.
Nevertheless, this modal aspect of a symbol is a strictly dynamic one. It is just this apparition of
the categorical evidence of symbols that allows the final transition to science just by making ... the
impossble happen, because only the same symbol that forbids 7 to be = 4 can allow the human mind to
penetrate a very astonishing world of things where Part 1,3,5,7… can be equal to the Whole 1,2,3,4,5,6,7…
Also in this case we have an internally homogeneous sequence of astonishment1 (Winn’s infants) →
astonishment2 (ZU and his Cantorian egg-cups) → astonishment3 (Lin and our magic trick) →
astonishment4 (Cantor and his «I see it, but I don’t believe it»). It is then evident that this vectorial sequence
represents a purely representationl trip inside the human mind, that incessantly trasforms and enhances
its vision of what is possile, real, and impossible. The dynamical field in which man realizes this transmodal
navigation is the vectorial space of Mind: the land of my Dynamics of Representation.
SYNTHETICALLY, MENTAL ACTIVITY IS A FORCE BECAUSE OF THE THREE ELEMENTS THAT
MAKE UP ITS INNER EXPERIMENTAL MANIFESTATION:

13
First Element – I. Formally: a vector - The unity of the two parts of Piaget’s equalization
formula {ۯ ↑ ܐ ܔ
← ۺ ≠ ۯ ܏
↔ ۺ}→{ۯ ↑ ܐ ܔ
← ۺ = ۯ ܏
↔ ۺ} is formally a vector. (It could express for example the
condensation inside a gas nebula of a solid body that at a given moment begins to turn around itself by
preserving its rotational mass, or “moment”. This metaphore of «solidification» is incessantly used by
Piaget). II. Metaphysically: an active transformational factor. - As Piaget incessantly stresses, nothing
obliges our mind to «solidify» itself around a conservation principle. Then, the simple Principle of Sufficient
Reason obliges us to recognize the intervention of an active factor of transformation from within our mental
apparatus.
Second Element – Trigonometrically: a period - A force as we know and conceive it, must be
1) unitary and continuous; 2) submitted to a cyclic = trigonometric law of internal periodicity: minimum
0°, maximum 90°, minimum 180°. All the forces that we recognise in the Cosmos are submitted to this kind
of internal transformation, and for this reason the dynamical space of vectors is not an isotropic space. Now
this kind of periodicity is a main feature of Piagetian décalages as I have shown.
Third Element – Structurally: bi-polar - A force as we know and conceive it is necessarily a
bipolar reality. Now {1,2,3,4,5,6,7}≠{1,3,5,7 } is an orientative evidence = 1, and this means that 2+2=7 is
impossible but necessarily is. I say then that the evidence of 2+2=7 is = 0, as in the case of velocity =0, must
be something if a uniformly accelerated movement exists. On the other hand, this evidence=0 of the
mathematically impossible 4=7 is the internal limit that separates the two opposite lines of evidence
{1,2,3,4,5,6,7}≠{1,3,5,7} and {1,2,3,4,5,6,7...}={1,3,5,7 ...}. I say then that the evidence of
{1,2,3,4,5,6,7...}={1,3,5,7 ...} = – 1
BACK TO SCHOOL. From the Piagetian A =A×B to the Boolean A×A =A
to Dedekind/Wittgenstein’s “I am someone”.
I have claimed that the mental force that engenders the internal cohesion of A is the same force that
underlies the event of the interaction between A and A, that we perceive as the symbolical evidence A=A.
Now to grasp the dynamical laws that underly this force, the Piagetian vision of the mathematical
structure of the mind is too weak. Piaget makes use of the commutative algebra of groups, in which the
ultimate analytical object is the monomial multiplication A×B (=B×A) that in Piaget’s perspective represents
the internal structure of any conceivable name such as “A” or “B”. Now we are asking how can the graphical
object A become a symbol capable of revealing the logical, strictly symbolical evidence A=A? From the
Piagetian point of view, we should then write (A×A) ↔ (A=A) that is A×A=A, which is the Boolean logical
«special [index ] law » A 2 =A.
Let us imagine that the logical Boolean operation of «election» occurring in time (as Boole [ILT]
and W.R.Hamilton have done). During this time, it occurs that a child learns to read the perceptual object
(graphema) A as the symbolical object (letter) A, by perceivingA ௧భ (ೀಿ ಴ಶ) × A ௧మ (೅ೈ ಺಴ಶ) × A ௧య (೅ಹ ೃ಺಴ಶ) ×
…. × A ௧೙ = "ۯ". Here it is quite evident that the temporal process that leads to the gestaltic apparition =
election of A as a symbol (eventually stressed by W.Koeler in 1929) is constituted by n applications of the
same child’s A-attention, that is A n =A. Now G.Boole explicitly did not focus his attention on this time of
crystallisation of symbols (as I will do however) but he states very clearly that the «mental operation» of
«attention» that leads to the «election» of A is not a «grouping operation».
I. The symbols of Logic are subject to the special law, x 2 = x. Now of the symbols of Number there are
but two, viz. 0 and 1, which are subject to the same formal law. We know that 0 2 = 0, and that 1 2 = 1; and the
equation x 2 = x, considered as algebraic, has no other roots than 0 and 1.Hence, instead of determining the
measure of formal agreement of the symbols of Logic with those of Number generally, it is more
immediately suggested to us to compare them with symbols of quantity admitting only of the values 0 and 1.
[G.Boole ILT] II. From the nature of the operation which the symbols x, y, z, are conceived to
represent, we shall designate them as elective symbols. […] It will not be necessary that we should here
enter into the analysis of that mental operation which we have represented by the elective symbol. It is not
an act of Abstraction according to the common acceptation of that term, because we never lose sight of the
concrete, but it may probably be referred to an exercise of the faculties of Comparison and Attention. Our
present concern is rather with the laws of combination and of succession, by which its results are governed,
and of these it will suffice to notice the following. 1st. The result of an act of election is independent of the
grouping or classification of the subject....» [G.Boole MAL]

14
Dynamics of Representation must essentially penetrate the mental space from which A appears as
an «elective» symbol to the mind of a child that learns to read. Piaget has rejected the idea of a simple, nonmultiplicative
«logical identification » because a purely ideological anti-Bergsonian attitude prohibited him
to grasp the inner core of a dynamic = temporal, novel interpretation of logical identity [The laws of such an
Algebra will be identical to the laws of an Algebra of Logic. The difference in interpretation alone will
divide them.ILT)]. Boole’s mental operation of «election» is then the right answer to the Piagetian
«fundamental operation of assimilation» S(A)R, because no «multiplicative» function of «assimilation» will
ever be strong enough to justify the simple presence of the «elective symbols» S, R, A that make it up,
whereas the Boolean mind is defined by its «index law»-prerogative «x n = x » that is like the [tauto-]logical
Unity (in Boole’s system 1=Universe) of a pre-multiplicative base of all arithmetical multi-plications.
As regards my vectorial model of cognitive progression, the author that provides me with the
formal tools to face the question is Ludwig Wittgenstein:
[TLP 6] If we are given the general form according to which propositions are constructed, then with it we
are also given the general form according to which one proposition can be generated out of another by
means of an operation. Therefore the general form of an operation is then [ xത ܰ(x) തതത ]’(ߟ̅) , which is the most
general form of transition from one proposition to another. 6.02 And this is how we arrive at numbers. […].
We write the seriesݔ, ߗ ᇱ ݔ, ߗ ᇱ ߗ ᇱ ݔ, ߗ ᇱ ߗ ᇱ ߗ ᇱ ݔ, …, in the following way: ߗ଴ᇲ ݔ, ߗ଴ାଵᇲ ߗ଴ାଵାଵᇲ ݔ,
ߗ଴ାଵାଵାଵᇲ ݔ… And I give the following definitions : 0+1= 1 Def., 0+1+1 =2 Def, 0+1+1+1 =3 Def,(and so on).
This model of a numerical progression of operations that is generated from within the inner
cohesion of the proposition, comes to Wittgenstein from his idea of tautology as the dynamical field of the
vectorial treatment of bi-polar «functions-with-a-sense»[NB]. For Wittgenstein, the time in which the
Tatsache A×A=A happens as a determining «logical place» in the «logical space» of «my World», is the
dynamical time of application of the same […] proposition [… : “this is A”. Now this
proposition – that is the application of a child’s mental force on the perceptual object A (B, C…) – is
necessarily a natural language proposition, that can be “Abgebildet” only within the «linguistic game» of
School (in the sense of Wittgenstein’s Philosophical Investigations): a language-game that can be played
only with the free and active participation of a child that clearly understands what school is, and what
learning to read is.
These Boolean/Wittgensteinian
tools will then allow me to overcome all the
difficulties that can arise from my
educational notion of the cognitive vector of
evidence, whose structure is innerly
articulated in the two Boolean dimensions
«from within» [= underlying projection of Yod-dynamics] / «from without» [=phenomenal apparition of Acinematics].
The “completeness” of my educational project.
We have seen that since the seventies, several cognitive development psychologists have given the
definitive anti-Piagetian demonstration that a 4 month-old infant seizes and “preserves” the number. Hence
Piaget is wrong: when a child speaks about numbers, we can trust him, because he is truly speaking about
numbers.
On the other hand, on the basis of the Russellian idea of what the logical completeness of
arithmetic is, Gödel shows that Peano’s numbers do not generate real demonstrative truths about numbers:
then if a given natural number [or a given so-called Gödel “encoded” number] is apparently demonstrating
the autarchic perfection of numbers, he is not truly speaking. We may then ask: “how can we trust
numbers after Gödel has shown that when they speak about the completeness of their system they are surely
lying?” ... but we won’t, because even children know that numbers don’t speak about anything at all.
Men – children – speak about numbers! And this fact – the fact that ( “
man always arithmetize”: the Aristotelian quotation on Dedekind [WSZ]) is the fundamental fact that the
great enterprise of what we now call “logicism” has taken into account since at least 2500 years ago.
Then if Peano’s axiomatisation is submitted to Gödel’s prohibition – that is, if Peano pretends that his
numbers can speak, (as Michelangelo did with his Moses) – this is not the case for Richard Dedekind’s
foundation of the first set, from which number 1 is generated by a man (or a child) that says: “I am
someone”.

15
§5- 66. Theorem. There exist infinite systems. Proof. My own realm of thoughts (Gedankenwelt), i.
e., the totality S of all things, which can be objects of my thought is infinite. For if s signifies an element of S, then
is the thought s' that s can be object of my thought, itself an element of S. If we regard this as the image (s) of the
element s, then the application (Abbildung) of S has the property that the image S' is a part of S; and S' is
certainly proper part of S, because there are elements in S (e. g., my own ego) which are different from such thought
s', and therefore are not contained in S'. 71. […] Definition. A system N is said to be simply infinite when there
exists a similar transformation of N in itself such that N appears as chain of an element not contained in (N)
We call this element, which we shall denote in what follows by the symbol 1, the base-element of N and say the
simply infinite system N is set in order by this transformation .
Wittgenstein will say:
[5.621→5.641] The world and life are one. [Die Welt und das Leben sind Eins] - 5.63 I am my world.
(The microcosm) - 5.631 There is no such thing as the subject that thinks or entertains ideas. If I wrote a book called
“The World as I found it”. If I should have to include a report on my body, and should have to say which parts were
subordinate to my will, and which were not, etc., this being a method of isolating the subject, or rather of showing
that in an important sense there is no subject; for it alone could not be mentioned in that book. […] Thus there
really is a sense in which philosophy can talk about the self in a non-psychological way. What brings the self
into philosophy is the fact that the world is my world The philosophical self is not the human being, not the
human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the
world not a part of it. [TLP]
I must stop my presentation here. At this point, my post-doctoral research program Symbols of
their own genesis begins, with this first penetration into the deep roots of Logicism. I am finally in a
position to experimentally penetrate this space of «Comparison and Attention» from which our force of
projection is able to give birth to the «elective» = unnecessary and conventional symbols of science, that is,
to the unlimited space of our freedom, that only School and Education can give to Humanity.
Educational and therapeutical consequences
Describe any novel concepts, approaches or methods that will be employed. When any novel methods
or techniques are proposed, explain their advantages and disadvantages.
From an educational point of view (as well as from a neurophysiologic and psychiatric one: see
my [SEO]). My perspective has enormous consequences on the way in which the teacher can speak to his
pupils about the magical and marvellous world of science.
With children - I demonstrate that the «synchretic» force of a child’s mind, is here and now,
the deep real and actual root of the highest scientific peaks. A teacher must then speak to pupils not only
about the positive evidence of the world, but also about the negative evidence of what no adult will ever be
able to explain, but about what he can certainly speak of: with calmness, while smiling, and with
attention… to the contemplative silence of a child (= to the actual and real root of men), that never expects
the complete certainty of Truth from adults, but that understands very well if someone is truly speaking to
him.
With adults – If the synchretical perception of the world does not disappear from the human mind
but reappears in adulthood to express its power in the highest mathematical proceedings, the same thing must
also be said for the case of the destiny of the “cohesion” force A ௧భ × A ௧మ × A ௧య × …. × A ௧೙ = "ۯ" in a
person that can already read. In this case, it is evident that the mathematical operation A×A=A 2 does not
achieve the same mental activity as the logical operation A×A =A, but it is also clear that both the
operational inter-actions between already-existing symbols “A×A=A 2 ” and “A×A=A”, belong to the same
cognitive phase, that comes after the phase of pre-operational cristallisation A×A×A…×A =A, leading our
mind to the first perception of A as “A”.
Now if this symbolising crystallisation-force does not disappear, in which kind of mental activity
can we use it, when we can already read? The OECD educational program SeDeCo [OECD2000] answers
this question:
La réflexion implique des processus mentaux relativement complexes : le sujet de la réflexion
doit devenir son objet. Par exemple, chez un individu qui s’est appliqué à maîtriser une technique mentale
donnée, la pratique réflexive lui permet de réfléchir à cette technique, de l’assimiler, de la mettre en rapport

16
avec d’autres aspects de son vécu et de la modifier ou de l’adapter. Chez les individus qui recourent à la pratique
réflexive, de tels processus de réflexion conduisent à des applications ou à l’action 1 .
This is the most important «key skill» that the OECD’s DeSeCo program speaks about: the
meditation on an already acquired symbolic/mental skill. In fact, it is easy to understand that if we ask
someone to reflect on an expression such as A=A they can already read and understand, as if they were a
child that cannot yet read at all, we are suggesting to him to meditate the meaning of what he is doing and
reading. Now “doing” and “reading” are events, as is “operating”, because for human beings every
“evidence” is an event: every “operation” necessarily is performed in an individual time, as every symbol
necessarily “occurs” = happens in an individual mental life. Then, when a man is obliged to reflect on the
operations he is performing, his mind finally re-establishes contact with the innerly historical and eventdriven
nature of his internal world: and this is making sense. We must thus never forget that A ௧భ × A ௧మ ×
A ௧య × …. × A ௧೙ = "ۯ" is the tale of an history: the individual history of a child that contemplates his first
school-book… and that suddenly becomes perfectly unmindful, when the finally crystallized perception of
“A” first appears. But…A=A can save our mind, because it obliges us to face the shock of A 0 =1. So, when
for the first time this child, that is now an astonished man or woman, asks himself/herself “what is
happening?!” … this event can be the beginning of a new-and-old tale, that will be, at the same time, the
universal history of science and the individual history of all human beings that have decided to listen to this
inner voice 2 . We know that all great mathematicians have had this kind of interior very troubling experience
of symbolic and experimental evidences. All men that really face the negative and “paradoxical” evidence of
{1,2,3,4,5,6,7…}={1,3,5,7…} or of a movement without movement (such as mv) are shocked by these
totally unexpected apparitions… and if they decide to take their time to reflect on the meaning of this
troubling apparition, during this time their mind will acquire more and more the «athletic vigour» that
George Boole speaks about : «To supersede the employment of common reason, or to subject it to the rigour
of technical forms, would be the last desire of one who knows the value of that intellectual toil and warfare
which imparts on the mind an athletic vigour, and teaches it to contend with difficulties and to rely upon
itself in emergencies. [MAL]» So, the magical teaching of children by George Boole’s wife – Mary
Everest – gives us a pre-existing vision and tradition of this kind of scientifical education to science, and I
have applied my renewed, enhanced and transciplinary Piagetian/Boolean method in my pedagogical
center “EIRONEIA” for at least 5 years, with great success in my battle against school phobia and
cognitive/emotional blocks in learning…
On the other hand, with adults that love the time of scientific meditation, I have trained the mind
of my pupils with these shocking evidences that Plato called «awakening truths - » [Rep.VII]. Such
a pre-operational and negative practice of science calls the human mind to a new, deeper and conscious
way to awaken human life and man’s tale of its own history.
B2 Trraiiniing Objjeeccttiiveess
The two years anticipated for the completion of my project will essentially be dedicated to pure
and full-time research. All the public meetings and public seminars that I intend to organize and which I will
participate in will be scientific events that will allow me to improve my scientific abilities and to realize my
research program, thus strengthening my position as a non-formal educator. The Alexandre Koyré center in
Paris and the EHESS are the choice institutes for carrying out and concluding my research. Moreover, M.
Jean Dhombres’s expertise in this field is universally recognized and appreciated. He is not only a
mathematician, an historian of mathematics and an epistemologist, but also an expert on the cultural and
historical question of the pedagogy of science, in all ages of our mathematized world. Furthermore, the goal
of my program is the mathematization of the cognitive development of man, and this is one of the main
areas of interest of the Koyré Institute and of M. Dhombres. In addition, I will spend these two years of my
research endeavouring to enhance my skills within the EHESS/Eironeia scientific and human perimeter, and
to diffuse my results in order to affirm the European existence of Eironeia and to pave the way for its
international future.
1 The only objection I have with the words of OECD, is that the reflexive application of our crystallization force on an already crystallized symbol is
psychologically more complex (=harder), whereas it is logically and dynamically more simple, because A×A=A is more simple than A×B=C.
2 OECD [2000] would say: «reflectiveness implies the use of metacognitive skills (thinking about thinking, creative abilities and taking a critical
stance. It is not just about how individuals think, but also about how they construct experience more generally, including their thoughts, feelings
and social relations…».

17
Hosstt eexpeerrttiissee
Host expertise in training experienced researchers in the field and capacity to provide
mentoring/tutoring. Give a short outline of the host's expertise in mentoring/tutoring researchers -
Mr. JEAN DHOMBRES is a very important and universally recognized scientific figure in the
field of my research program, as are the EHESS and Koyré host institutes.
CURRICULUM VITAE Directeur émérite de recherche au CNRS, Jean Dhombres est
mathématicien (doctorat d’Etat par une thèse en analyse fonctionnelle soutenue à l’Université Paris VI),
professeur de mathématiques à l’Université de Nantes jusqu’en 1988. Il est alors devenu directeur d’études à
l’EHESS (intitulé de la direction d’études : histoire des sciences exactes) et directeur de recherche au CNRS.
Ses recherches en mathématiques ont porté en analyse fonctionnelle sur les opérateurs de moyenne et
d’espérance conditionnelle et sur les équations fonctionnelles les caractérisant. Ses recherches en histoire des
sciences ont porté sur de nombreux aspects de l’histoire des sciences mathématiques : histoire
institutionnelle (Ecole polytechnique, Ecole Normale, Académie des Sciences, expédition d’Egypte), histoire
culturelle (la science de la Révolution à la Restauration, science baroque du XVIIe siècle en Europe), histoire
conceptuelle (fondation des nombres réels depuis la théorie des proportions, concept de fonction, équations
fonctionnelles), histoire individuelle (biographies de Fourier, Carnot, Grégoire de Saint-Vincent, Gergonne),
histoire des textes (édition des leçons de l’École normale de l’an III). Il réunit les deux domaines,
mathématiques et histoire, en préparant une histoire des équations fonctionnelles jusqu’à nos jours, et par
ailleurs prépare une Histoire des sciences mathématiques en 3 volumes, dont un premier volume, La
mathématique du monde, devrait paraître chez Fayard en 2008. Il prépare une édition synoptique, comportant
la traduction en français, des Leçons sur le calcul différentiel et le calcul intégral de Jean Bernoulli (1691), la
confrontant à l’Analyse des Infiniment petits de Guillaume de l’Hôpital (1696). Il prépare une édition du
livre V de l’Opus Geometricum de Grégoire de Saint-Vincent, une anthologie de textes d’enseignement des
mathématiques du XVIIIe siècle, une édition critique du Traité de géométrie analytique d’Auguste Comte, et
un catalogue de lettres de Lebesgue.
A relevant seminar. Séminaire 2006/2007 - Épistémologies de la mise en mathématiques
La mise en mathématique n’en a pas moins toujours été une question faisant jouer des arguments
sur la nature de ce qui est mathématisable et de ce qui ne l’est pas. La mathématisation est un des lieux
majeurs de l’épistémologie depuis Aristote, qui la jugeait presque toujours impossible, auquel répondit
pourtant et par exemple Archimède dans l’Antiquité, et Galilée à l’aube des temps modernes. Ceci vaut
toujours pendant la période scientiste à la fin du XIXe siècle, et la multiplication des lois empiriques, alors
même que la mathématique ne se définissait plus comme science des quantités, ou science de la mesure. La
pensée structuraliste et la révolution logique ont donné au XXe siècle ses objets formels à la mathématique,
la dégageant enfin d’être une logique in concreto, cela n’a pas amoindri les questions épistémologiques de la
modélisation en physique, en biologie, en sciences humaines, et bien sûr en économie…
Some relevant publications. L’aventure épistémologique de la mathématisation des
Lumières éclairée par les images de marine de l’Encyclopédie méthodique, in L’Encyclopédie méthodique
(1782-1832) Droz, Genève, 2006, - La mise à jour des mathématiques par les professeurs royaux, in
Histoire du Collège de France, t. 1, La création 1530-1560, Fayard, 2006, -L’enjeu épistémologique d’une
mesure du savoir mathématique, in P.Hummel et F.Gabriel (éd.), La mesure du savoir. Etudes sur
l’appréciation et l’évaluation des savoirs, Philologicum, Paris, 2007. - Les professeurs royaux de
mathématiques au XVIe siècle - Les mathématiciens en France sous l’Occupation allemande (1940-
1944) - Histoire de l’enseignement mathématique et questions actuelles de cet enseignement éclairées
par l’histoire.- Le mouvement des mathématiques modernes - HISTOIRE D’UNE PENSEE : LA
CAUSALITE Histoire du concept de fonction comme une des mathématisations de la causalité - La
parabole chez Galilée et le principe d’inertie - Le premier travail de Laplace sur le principe d’inertie -
Analyse de la propagation de la chaleur par Fourier - Le scientisme et la physique mathématique -Histoire
de la notion de potentiel comme remplaçant la notion de force - La question de la cosmographie en
place de la cosmologie - Actualité et obsolescence du débat Panofski/Koyré - La représentation des
mathématiques - Imagerie pour les mathématiques.

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B3 -- RESEARCHER
Tout projet innovateur se trouve à un moment dans la position de « K » cherchant à
atteindre le Château. De telles difficultés ne doivent cependant pas faire baisser les bras. Et comme le
disait Lao-Tseu : « le chemin, c’est le but »… [OCDE 2007]
Philosopher and official delegate of AIC (Italian Headache Association)
I was born in Rome on October the 4 th 1967.
In July 1986 – I obtained my high school diploma (Classical Literature).
In July 1997 – I graduated (mark awarded: summa cum laude) in Philosophy (History of
Science) at the University of Rome, La Sapienza. My thesis was on the Scientific Revolution of the XVII th
century, and its evolution/reception/vulgarization during the French enlightenment, and was entitled:
«Voltaire, Newton and the scientific Revolution at the age of French enlightenment».
It took me 10 years to graduate, largely due to an excruciating and incessant [vasomotory/Horton]
headache, which broke the continuity of my exterior progress. I even became an official representative of
the Italian Association for Headaches (AIC) and in 1998 I participated in a national television program –
«Check Up» – where I spoke about this terrible syndrome. This is in fact the second very important fact
about me, besides my philosophical and [then] pedagogical vocation. As a philosopher/historian, a teacher
specialized in scholar phobia and as someone tormented by headaches, my studies have always been
motivated by the deep desire to know why the mind/body life of human beings can cyclically forbid
them to go forth.
During these years I began a theoretical collaboration with Professor Pierluigi Scapicchio
(neurologist and psychiatrist, President of the Italian Psychiatric Society – see reference) who was very
interested in my mode of conceiving the dynamic and evolutionary mind/body relationship, that I studied
from both an individual (neuropsychological) and social (historical) point of view.
In September 1998 – I went to Paris where I attended the Ecole des hautes Etudes en Sciences
Sociales (EHESS) to carry out my PhD in Histoire et Civilisation, under the supervision of Mr.Chaussinand
Nogaret. The object of my research was strictly epistemological and methodological, and it determined (as x,
the unknown) the third synthetic dimension where the conceptual product [History]×[Science] took form. I
think that if we want to scientifically understand the birth of science in human history, we must, as
historians, have a scientific method available: then, the Science of History and the History of Science
necessarily appear (are created) simultaneously. Indeed, this is the case for French scientific storiography
during the XVIII th century. Bossuet, Montesquieu and Voltaire are hence the main subjects in my DEA
mémoire «La création de l’histoire moderne chez Voltaire ».
In June 1999 – I obtained my DEA (mark awarded: très bien) and received a lot of praise for
my methodology: «Eduardo Caianiello is an exceptional subject, who is certainly promised to the
elaboration of a primary work that will renew our perception of enlightenment’s thought» [M.Nogaret,
EHESS] «E.Caianiello totally renews our idea of enlightenment…(M.Gérard Jorland, EHESS)».
«Caianiello’s approach is not only original but also a very promising one» (M.Heinz Wismann, EHESS)».
In October 1999, I was awarded a scholarship from La Sapienza for a year of foreign
research, when I finally began my doctorate studies at the EHESS. The subject of my thesis was:
«Archaïsme et modernité, l’histoire à l’époque des lumières», whose epistemological goal was more
general and deeper: my two notions of «archaïsme» and «modernité» already signify the two formal
polarities of a unitary and meta-historical concept of mental evolution, as the piagetian «egocentrism» and
«operational rationality» do (cf. Piaget’s Psichogenèse et histoire des sciences), but I was not logically
satisfied with this way of “naturalizing” human history .
In Spring 2000, I discovered my own (kantian) method, and I wrote a long essay on the
unsatisfactory epistemological structure of social sciences’s notion of evolution: «Le progrès de la
civilisation et la condition actuelle de l’épistémologie de l’histoire». In this essay, I showed that it is
impossible to “naturalize” human history without losing any formal possibility to speak about a “social
transformation”: the ethical/juridical, that is the irreducible human notion of “evolution” (=civilization) is at
the core of every historical transformation as such. As historians and as human beings we are obliged to
ideally presuppose the historical vector of a practical reason as a pre-existing whole. It is evidently a kantian
way to think about the formal relationship between the material and the mental side of human (social and
individual) phenomena, and it is also the way in which we can think about a real action of mind on body.
This essay has been highly commended: M. Alexis Philonenko affirms: «This document is a
serious contribution to the epistemology of history. […] The research has an interdisciplinary inspiration.

19
For example, the work of the sociologist Marcel Mauss is analysed in depth, and a set of thought structures
that until now were unknown finally appears[…] One of the most important results of this research is that it
engenders an history of history. Where we see a discontinuity, E.Caianiello shows a continuous transition.[..]
We can also see the formal self-limitation of Caianiello’s project: he won’t lose himself on endless paths, but
he will focus his attention on the concrete reversals that entail the dialectic’s strategies on the one hand, and
on the elaboration of historical categories on the other hand».
Thanks to this essay on «history of history», I became the official foreign EHESS candidate for
the «Chancellerie des Universités de Paris»’s scholarship.
Notwithstanding, this was also my point of no return.
I know that my novel method is the most appropriate one to use in order to give an operational
description of the fundamental structures of the material/mental evolution of man and of its stoppage
mechanisms. Consequently, I know that I have discovered a method of intervention for my headaches, and
this has been the case: I have been completely cured for 9 years. Dr Mara Bonciani – Director of the
Headache center of Florence (where I was hospitalized twice every year) and President of AIC – was
astounded when she saw that I had defeated my Horton pathology: «I found Eduardo Caianiello in perfect
health ». Nevertheless, I am clearly aware of the insufficiency of my theoretical/methodological tools,
and of the large amount of time and work that I would need to get on level with my new operational goals.
M.Philonenko is right when she speaks about my focus on «the concrete reversals that entail the dialectic’s
strategies», but my intention is not only to elaborate new «historical categories» in science, but also a new
mathematized history↔historicized mathematics. In other words, I would like the epistemological product
[History × History] to become a mathematical Abbildung H=f(H) or H=H(h), whose innerly non commutative
nature allows us to think about a real historical human action on history. (The result of all this is my Yodvector
ܲሬ⃗ = {A×A×…×A→ “A”} ).
Furthermore, I was 33 years old, and old enough, I felt, to decide to try out my new understanding
in the field. I hence resign from the EHESS and will be back when my operational methodology is ready to
be conveyed to the scientific community.
Research results including patents, publications, teaching etc.,
taking into account the level of experience
Teacher of children suffering from school-phobias and Kung Fu/Yoga researcher
Since then, I have been working without respite, from both the theoretical and the practical points
of view. I trained as a pedagogue expert in schooling difficulties, aiming to manage mental blocks in the
dynamic/cognitive evolution of the boys and girls I was taking care of.
In addition, I also practiced my new comprehension of the energetic mind/body circuit on myself.
I became a Kung-Fu/Yoga researcher (now I am a Kung-Fu teacher), and I studied many oriental texts –
Indian, Chinese, Tibetan and Japanese scientific traditions – to understand the way in which oriental science
practically and conceptually manages the dynamic relationship between the evolution and homeostatic
stabilisation of living/mental systems.
2000-2003 – As a teacher, I marked the perimeter of my theoretical research on the field.
Now this “field” is not at all an anodyne one.
2001 In the Suburbs of Paris – I was a history/geography teacher in a Parisian high school,
called «Votre Ecole chez Vous» (“Your school at your home”) due to the fact that the students are very sick
children that cannot go to school, primarily for psychological reasons. My destination was the Parisian
banlieue, and I was really shocked by the amount of pain and mental/social paralysis that I had to battle with.
My kungfu/yoga activities helped me to retain my stability, but not the schooling stability of my pupils (I
showed great hospitality to one of the students, whereas during the same period, another one of them – a 17
year old girl – tried to commit suicide). I then understood that the pedagogical tools which teachers normally
have at their disposal are far from sufficient. A pupil’s mental pain is an irreducible school pain: a
psychiatrist will never be able to autonomously manage the latter, and ordinary teachers even less so.
2002 – A teacher, not a kung-fu adept. - Meanwhile, I continued to study scientific kungfu/yoga
traditions, and I met several teachers. I began a theoretical/practical collaboration with Sensei Kenji
Tokitsu (I wrote in the «Tokitsu-Ryu» review, that can be found on the web) and I produced many theoretical
results. Finally M. Tokitsu asked me to help him open a new kind of martial arts school in Italy. We tried to
put this joint project into effect… but I realized that our goals were actually rather different: Sensei Tokitsu
is essentially a Kung-Fu adept, whereas I am a philosopher, a researcher and a pedagogue. My goal is a

20
scientific/educational one, not a martial one. [In 2004, , as the creator of EIRONEIA – I became the technical
Director of the «Nanpei Nanpei Shaolin KungFu Association Association» – in Viterbo (Italy), thanks to Master Alessandro
Parapetti. My aim was to contact tact Chinese experts in oriental traditional medicine and this placement
resulted in my current scientific and pedagogical collaboration with Mr. Zhao Min Hua - professor of
traditional Chinese medicine at the University of Beijing, and Kung Kung-Fu master.]
2003 – In the rich center of Paris Paris. I became a specialized tutor («precepteur») in the rich center
of Paris, where the mental blocks of my pupils were rigorously equal to those in the infamous suburbs. The
fear of texts, school, teachers, the BAC (!!!)… the same terror can be found everywhere: no parents, no
socioeconomical conditions, no personal history can explain such an universal, unitary and clearly distilled
phenomenon. Boys and girls, rich and poor, children and adults…finally the human mind can produce an
authentic paralysis when it is a question of school. Now “ “school”: is a question of what what? There is no doubt
that: the pupil paralyses his mind in front of a) the text b) the introspective movement that any act of
interpretation necessarily entails. Thankfully I am a good teacher, so I’m in condition to grasp this
experimental evidence: when I speak to explain my lesson, the pupil is quiet and attentive…but when it is
time for him/her to access the text and/or his/her own thoughts to interpret either the text or to explain his
comprehension of my words, his/her entire being falls down in a kind of hypnoïd condition from which he
can typically produce a destructive hunger against… me, that is to say, the teacher. And what is a teacher? A
teacher is the human being that allows ≡ obliges you to go forth towards your own personal, mental,
emotional…and ultimately, human evolution.
My educational theory on the human mind is then finally created: 1) the greatest form of energy
that the human body/mind can produce follows the dynamic (vectorial) direction of its natural=mental
human evolution; ; 2) the most essential task to realize in this evolutionary vector is an interpretation task.
Now, the hypnoïd condition of my paralyzed pupils in front of the interior and/or exterior
symbolic forms to which they must give a meaning, is clearly as difficult to fight as my headaches had been.
Then there is no reason why I cannot win again.
Independent thinking and leadership qualities - Match between een the fellow's profile and project.
Eironeia
2003/6 – I decided to go back to Italy, to create my own pedagogical center of non-formal
education, EIRONEIA, Scuola di Filosofia (www.eironeia.eu
www.eironeia.eu). I obtained funding as
a young entrepreneur by the public agency Sviluppotalia, , who greatly valued the
originality and the boldness of my idea. «From the first moment I met Eduardo
Caianiello, I thought that Eironeia should be born. It was a great idea, and a new
way to conceive at once enterprise, education, and philosophy… » [Francesca
Pistoia, Sviluppoitalia
Sviluppoitalia]
I worked hard over these three years. A group of mature students (from
30-40 40 years old) became a team of collaborators, and my pedagogical activ activity ity was the same as before: blocks
in learning of any kind. I worked in synergy with school professors, psychiatrists, families…and I made
political institutions aware of my actions.
Two professors from La Sapienza (Professor Marco Borioni and Professo Professor Paolo Vinci: «
Eironeia is a need of current age») ») accepted my students and my programs. Our pedagogical engagement
obtained the institutional recognition of our social utility, and in 1996 we obtained recognition and a prize

21
for being a “Social Enterprise” ” from the regional agency Filas, and from the
Provincia di Viterbo.
Eironeia is not only a specialized educational center: it is a global pedagogical, cultural and
scientific answer to the unitary educational problem that is the problem of our unified
and our globalized planet. In other words: Eironeia is the
microcosm of an entire educational type of politics politics.
Why? Because my life has finally convinced me that
without the simultaneous and synergic help of all tthe
positive forces of our world, a teacher will never be
strong enough to make a child (or adult) that is terrorized by school, go forth towards texts and towards his
inner [interpretation of] the world, that is towards his future life. [Here on the right:
appeal to «Youth», to win the battle against PANIC PANIC]
I am very pragmatic and my actions as an entrepreneur have been very coherent with my
educational vision.
1. EIRONEIA, Scuola di Filosofia
trademark, with three logos: the school (the logo here above),
the physical activities, and the publishing house (here on the
right).
Why is it represented in this way? Because my rich
and-poor/old-and-young pupils were terrorized by
symbols - remember their hypnoïd condition in front of a mathematical or literary text?
charmed by market symbols. Then a school symbol must have the ability to
2. Our headquarters in Viterbo are 800 years old, situated in a ma
of UNESCO’s World Heritage :
® Filas, and from the Regione Lazio and the
Eironeia is not only a specialized educational center: it is a global pedagogical, cultural and
oblem of our unified Europe of Knowledge
strong enough to make a child (or adult) that is terrorized by school, go forth towards texts and towards his
: The official European
and my actions as an entrepreneur have been very coherent with my
is a registered
trademark, with three logos: the school (the logo here above),
the physical activities, and the publishing house (here on the
Why is it represented in this way? Because my richyoung
pupils were terrorized by school
remember their hypnoïd condition in front of a mathematical or literary text? – as much as they are
Then a school symbol must have the ability to charm.
Our headquarters in Viterbo are 800 years old, situated in a marvelous rvelous medieval district that is part
« “Quartiere di S.Pellegrino
S.Pellegrino" " is a beautiful and rare example of a typical district from 1200. It is
characterized by towers, houses with little mullioned windows with two lights, shady yyards
ards and narrow streets. For a long
period, the district was inhabited by workers and farmers. Recently it has come to life again, thanks to antique shops
and artistic manifestations. [From http://whc. http://whc.UNESCO.org/en/tentativelists/1157/»
Why these millenary nary headquarters? Because learning time must not be market time time. This is
Eironeia’s answer to Carol Bellamy’s words:
« The fifth essential part of education in the
new century is that in a world more and more fraught with
conflict, violence, and instability, the school can be a
sanctuary, a child-friendly friendly place where children can find a
zone of peace and a sense of normalcy that is so important
for their well-being [Dakar Dakar 2000 2000]»
3. As you can see, Eironeia is a cultural activity center
(we have had a school of chess). ). Among the activities are the
cycles of films (Epos pros Epos) ) that I consider a great
didactical tool. Here to the right, the poster of the cycle «The
women’s war» can be seen. This has been prized by the
Regione Lazio and Rome’s municipality ality.
In summary: : the pedagogical, cultural and political reality of Eironeia is thought to be the
convergence-perimeter perimeter of all human energies that, according to my vision, are necessary to give man the
force to move towards symbols (= to his truly human roots and destination), and to give symbols the
concrete= historical possibility to nourish human life. In other words: Eironeia is aimed at materializing what
I now call the innerly genetic=educational nature of the human mind.

22
2006 - From Franz Kafka and Lao-Tseu to Marie Curie
During these years I never halted my research activities. Finally, in Autumn 2006 my dynamic
and genetic theory on the mind attained its definitive exterior form. The moment had arrived to go back to
EHESS, to realize my thesis, entitled «Le fait génétique des mathématiques et la puissance dynamique de
l’esprit t humain». M. Jean Dhombres was happy to be my new directeur d’etudes.
Now, this was not just a need for my research, but indeed a rigorous necessity.
The path of informal education is a very difficult one. The system of formal education is an
extremely closed system, and all forms of international appeal to a formal/informal collaboration are very
very hard to be heard by formal systems:
[Carol Bellamy – Education For All - Dakar 2000] - We must also ensure that every school and
community has a mechanism in place to seek out and find excluded and at-risk children and get them into
school. Where needed, we must develop more flexible, "informal," targeted approaches to education for
these children. And we must recognise that getting the last 5 to 30 per cent of children into school is likely to
require more innovative approaches - and be more expensive - than the first 70 to 95 per cent. - [EFA –
Action Framework] Strategies III. Faire en sorte que la société civile s'investisse activement dans la
formulation, la mise en œuvre et le suivi de stratégies de développement de l'éducation - 45 Pour atteindre les
six objectifs exposés ci-dessus, il faut une approche diversifiée qui dépasse de loin le cadre des systèmes
formels d'éducation…
As I have shown, I actively put forward Eironeia’s «instances de dialogue systematique [EFA
53]» to political and educational institutions…but there is nothing better than the words of the OECD on the
difficulties faced by a non-formal and «transdisciplinary» teacher/researcher when he proposes a new vision
of education to the old intra-national school, even if it is the same vision that is proposed by the most
important inter-national organization in the world:
Kafka - Franz Kafka, dans « Le Château », en décrivant les vains efforts du protagoniste pour
atteindreses objectifs nous dit tout le désespoir que peut ressentir l’individu face à une machine
bureaucratique sourde et aveugle. […]Qu’il s’agisse de simples incompréhensions, d’inerties mentales
diverses et variées, du refus catégorique de remettre en cause certaines « vérités », de réflexes corporatistes de
défense des positions acquises, ou de lourdeur bureaucratique, les obstacles qui se dressent devant tout effort
transdisciplinaire visant à l’émergence d’un nouveau champ, ou visant plus modestement à jeter une lumière
nouvelle sur les questions éducatives, ne manquent pas. Si un scepticisme constructif de bon aloi ne peut certes
jamais nuire, tout projet innovateur se trouve à un moment dans la position de « K » cherchant à atteindre le
Château. De telles difficultés ne doivent cependant pas faire baisser les bras. Et comme le disait Lao-Tseu : « le
chemin, c’est le but »… [OCDE 2007 Naissance d’une nouvelle science de l’apprentissage,p.32]
I can only confirm that the creation of a new educational reality that aims to fight against school
phobia, thus suggesting another – meditative and reflexive – method of education to the scientific
community … is quite a kafkian experience.
I want anyway to stress something very important…perhaps the most important thing to stress.
Our globalized western world is here and now the place of violent institutional
dialectics: intra-national education fights against the new inter-national drives, and in
the case of that intra-inter-national reality called “Europe”, Europe fights against
itself. I have accepted this situation with an unconditioned kantian faith, which is my
Vernunftglauben, because if the Europe of nations fights against the Europe of its eurocosmopolitan
citizens, this institutional war is a great victory of Peace, that is the
beginning of a real new world.
Furthermore, every teacher knows what a spectacle a child can make of himself when he does not
want to go to school, because life for him is also a kafkian and terrific thing to live and think. I fought until
my theory was ready to be conveyed, and I went back to Paris, to get real help from the European
scientific and political community.
2007-2008 Paris×Viterbo = Europe – In 2007-2008, Eironeia and my team allowed me to lead a
bi-polar existence, and gave my mind (I am soon to be 40 years old!) the inner solidity to establish my new
scientific contacts. M. Jean Dhombres really appreciated my work, and in June 2007 he invited me to the

23
international meeting in Peiresq « Humanismes, mathématiques, positivismes ». There I met Dr. Hamdi
Mlika (PhD in Philosphy of Mathematics - Vice President of the Groupe d'Etudes et de Recherches
Epistémologiques, Paris) who greatly praised and publicized all my Eironeia/philosophical work. Thanks to
this publicity, Mme Angèle Marietti (President of the Groupe…) came into contact with my work and in
March 2008 she published my work entitled « Infant’s prolegomena to any future metaphysics: the sense of
numerical identity, the numerical identity of sense.» in Dogma.
In addition, in June 2008, Mme Angèle Marietti offered me the chance to attend my first public
conference «Proust, Poincaré, Piaget et la genèse du symbole mathématique et littéraire », at the Maison
Auguste Comte, in the framework of the Groupe de recherches épistémologiques et historiques. (The Youtube
of this conference can be seen on my website). At this conference, I spoke about the unitary root of the
literary and mathematical symbol: the proustian and the galileian notions of Pure Time do not only have a
«family similarity», because a deep isomorphism unifies literacy and numeracy skills in the same genetical
source, that a unified science of human evolution can experimentally grasp.
Publications
1. Plorr-Morr. A proposito di Aristotele [La Ragione Possibile, 1992]
2. A proposito di “Sopravvivere al Millennio” [Bollettino della Società Italiana di Psichiatria,1995]
3. A proposito di “Istruzioni sull’uso del Lupo” [Almanacchi nuovi,1995]
4. A proposito di “Istinti. Antiche vie verso il comportamento umano” [Bollettino della Società
Italiana di Psichiatria, 1996]
5. Popper et Laing contra Freud: voci della contemporaneità [Psichiatri Oggi, 2002]
6. Sisifo e l'eterna omeostasi della psichiatria attuale [Il Nuovo Baretti, 2004]
7. Les prolégomènes de l’enfant à toute métaphysique future: le sens d l'identité numérique, l'identité
numérique du sens [2008, Dogma]
Languages known – Italian (mother tongue) French, English, German, Ancient Greek, Latin.
Computing – Office 2007 – XHTML
B4 IImplleemeenttattiion
Provide a work plan that includes the goals that can help assess the progress of the project.
In what follows, I will often say «I will publish it». This means that I will elaborate a paper in
order to publish it, and I will find a way to bring it to publication.
I Step
Until
spring2009
II Step
(Spring 2009)
III Step
Springsummer
2009
1. I work on Time and Mathematical Operations. I finish my current essay on Time
and Simultaneity in Poincaré’s notion of Esprit” – that is part of my Phd thesis (as is
the essay Les prolégomènes... is ). I will publish it.
2. I obtain my PhD on «The genetic fact of mathematics, and the dynamic power
of the human mind», in which I affirm the unrepetent existence of a mental power of
projection at the roots of human educational evolution, that we can call a force, and I
will publish it.
I will organize the international meeting in Viterbo’s headquarters of Eironeia on
«Symbol of their own genesis» in which I will explain the general plan of my «Dynamics
of representation». This will be the first of a systematic Lazio/Italy/Europe/Unesco
scientific rendez-vous (a meeting every year) on the mind, learning and educational
politics.
I work on Mind and Begin.
1. I work on Boole’s notions of the mind, election, and symbol 1 as «the Universe
we are speaking about», from which all election must begin. I will publish an article
about it.
2. I work A) on Dedekind’s notions of Gedankenwelt, Ich and « symbol 1, as the
base-element » of the first «abgebildet» endless set; B) on Wittgenstein’s notion of «Ich
bin Mein Welt» and the dynamic nature of the tautology inside of this Mein Welt’s field;
C) On Gödel’s not encodable number 1. - On this basis, I propose the notion of an
absolute operatory beginning within the natural language. I will publish an article
about it.

Following
Steps
24
I will work on the Mind’s genetic beginning in the intersubjective world of natural
language, that is of our world of human beings that speak to each other, in order to show
that the action of leading someone to education is a totally free action that depends only
on the absolute beginning of our choice.
I cannot honestly describe step by step all the phases of a research project spanning
two years with the same precision as I did for the first three steps, but I can give three
assessment criteria: A) at the end of these two years my work will be finished and
published; B) for every step there will be a publication; C) the institutional world will be
widely informed about and engaged in all that I propose to do and all that I discover.
B5 IImpacctt
Describe which measures are foreseen to help the researcher to acquire professional maturity. Which
impact this will have on the prospects of reaching and/or reinforcing a position of professional
maturity, diversity and independence.
In what concerns the
«measures foreseen». -
1. As I have already shown, the
Italian local and regional
institutions are much in favour of
the diffusion of Eironeia’s
international educational action.
Here on the right, one can see my
European program which aims to
create leadership skills in the new
European and non-European generations. My project for the future (for after these 2 years of research) is a
“DeSeCo” international education institute to teach freedom in scientific research.
2. I am now organizing an international meeting in April 2009 at Eironeia’s main headquarters in
Viterbo, which will revolve around my subject of research: «Symbols of their own genesis».
M. Jean Dhombres (History of Mathematics, EHESS, Paris) – Mme Angèle Kremer-Marietti
(Philosophy, Groupe d'Etudes et de Recherches Epistémologiques, Paris) M. Bruno D’amore
(Didactics of Mathematics, Università di Bologna) - M. Pierluigi Scapicchio (Neuropsychiatrist
Università Cattolica di Roma) – and M. Zhao Min Hua (Traditional Chinese medicine, Beijing
University) have already accepted my invitation.
3. Generally speaking, I know the time has come for my theory to have an important impact on the
current scientific and educational community. My professors at EHESS and La Sapienza were convinced that
my epistemological and historical research would «completely renew our idea of the enlightenment», that I
would give «a serious contribution to the epistemology of history», and that Eironeia is an important «answer
to a central question of our age»…But to give something really concrete and operational to our renewed
scientific enlightenment – this is the current «Age of Knowledge» – eight years of relentless studies and
solitary meditation had to pass by. The result is that I now know that my theory is coherent and complete,
and it only needs to take on its exteriorized form. Then, if the European Union gives me the means with
which to dedicate all my energies to this final phase of exteriorization, I have no doubt that the impact of my
work will live up to my expectations.

25
B6. . Etthiiccall IIssssueess. .
The impact of the research, not only in terms of scientific advancement, but also in terms of human
dignity and social and cultural impact.
In the Age of Knowledge, in search of the lost Time of Science
Let us imagine a dialogue that could take place between a teacher and a quite ordinary
(middle/upper class) European highschool/university pupil, who is anxious because he/she cannot grasp an
apparently trivial physical notion, as for example the mechanical concept of the isochronism of pendulum
oscillation. “I don’t understand… - the pupil says to the teacher - … if frequency is f = f (l) [l=pendulum
thread], if the rapidity of the translation of the pendulum depends only on the thread’s length…this means
that the oscillation movement is totally independent from the space of the oscillation…because… … I mean…
the length of the thread is not the space of the oscillation… Is that not so?”.
As a teacher, I am pleased about the fact that this pupil has doubts, because I know that his mind
is feeling a deep, subtle, and necessarily not-yet conscious difficulty in grasping the notion of a
transformation whose velocity takes no place in space, but in time. I know that on the basis of this new
dynamical insight, he will be able to really grasp the enigmatic notions of an “instantaneous velocity” ( speed
without a space-extension) or of a “quantity of movement” mv (a movement that can exist in a quiet masscondition)
and so on…In fact, this child is facing a negative and an awakening scientific fact: a very
important moment that necessarily manifests itself in a troubling “I don’t undersand… at all!.”
I try then to convince him that he has got time and that he can take his time to understand… as
Socrates, Descartes, Gaileo, Foucault, Marie Curie did… Notwithstanding, even if I am the teacher, my
pupil strongly refuses to calm his mind, to be patient and wise…. NO: he pretends to understand, because he
has to apply the FORMULA and to pass his examination etc.
I try then to persuade him with a social and historical argument.
Dialogue between a teacher and a young European citizen
- Listen to me kid: you’re a lucky human being… because you are a Western and European
citizen, and your great country «…is experiencing its best macro-economic outlook in a generation. […] The
Euro has been successfully introduced … the internal market is largely complete and is yielding tangible
benefits for consumers and businesses alike. – And that is not all! : – The forthcoming expansion will create
new opportunities for growth and employment…the Union possesses a generally well-educated workforce
– like yourselves! – as well as social protection systems able to provide, beyond their intrinsic value, the
stable framework required for managing the structural changes involved in moving towards a
knowledge-based society [EUP]» ... Do you understand me young man? We are rich enough to take our
time to understand, and to acquire the knowledge that will make of us well-educated people! The time for
people to take their time has come: «…with the improved current economical situation, the time is right to
undertake both economic and social reforms as part of a positive strategy which combines competitiveness
and social cohesion – …and «social cohesion» depends on personal, that is, mental cohesion… – […] An
overall strategy aimed at preparing the transition to a knowledge-based economy and society through
improved policies for the information society, modernizing the European social model, investing in people
and combating social exclusion… [EUP]».
- I don’t understand… what does “take your time”mean,…to do what? Why does personal
cohesion depend on time?
- Because we are speaking of the time needed to create a new Knowledge horizon. Do you
know that «the European Commission has proposed that 2009 will be the 'European Year of Creativity and
Innovation'» ?... «…both are essential elements for the future success of Europe and its long-term economic
competitiveness. The European Year aims to raise public awareness, spread information and promote
public debate on creativity and the capacity for innovation. It should also stimulate research into how to
develop creativity and innovative attitudes [EUC]. In most OECD countries, value is placed on flexibility,
entrepreneurship and personal responsibility. Not only are individuals expected to be adaptable, but also
innovative, creative, self-directed and self-motivated. [OECD2000]»”
- But…I don’t understand… how can the time of scientific doubt and uncertainty engender a
new «creative and innovative» attitude?

26
- Because the time of science is intrinsically a long, patient time, necessary to acquire freedom
of thought and to accept the responsibility and the risk to think about one’s own life : «At the centre of the
framework of key skills is the ability of individuals to think for themselves as an expression of moral
and intellectual maturity, and to take responsibility for their learning and for their actions. [OECD
2000]»…in other words: in order to take your time to reflect on Galileo’s time, you must decide that your life
is your life, that your brain is your brain, and that your eyes are made to look at the real world around you:
a real pendulum is not a void graphical formula: symbols have a genesis, a life, an history… and this is the
only possible way to acquire your personal cohesion.
- You mean I must meditate on physical formulas?
- Yes.
- But… How?
- First of all, as you are doing right now:here and now you are having doubts, that is thinking,
about your own thoughts, and this is reflectiveness, which « implies the use of metacognitive skills (thinking
about thinking), creative abilities and taking a critical stance. It is not just about how individuals think, but
also about how they construct experiences more generally, including their thoughts, feelings and social
relations. This requires individuals to reach a level of social maturity that allows them to distance
themselves from social pressures, take different perspectives, make independent judgements and take
responsibility for their actions. [OECD2000]»
- But this is philosophy, not physics!
- Oh no my young man! This is simply citizens education.
- What do you mean by “citizen”?
- Do you know John Amos Comenius?
- ?
- John Amos Comenius was a great European teacher, contemporaneous with the first
scientifical apparition of your enigmatic pendulum. He has been called the “teacher of nations”, because he
was encouraged by a very deep faith in the universal destination of all educational actions.
- What else?
- Your country – Europe – has traced a great educational horizon in the name of Comenius
around you, and within this horizon, teachers and pupils are now meditating about a new kind of awakened
and self-aware citizen. For example the « Comenius 2.1 Project SEDEC: whose goals are to contribute to
education in science and to raise awareness of European citizenship through the development of teaching and
training methodologies and materials…». This is because science is not only a question of anodyne symbolic
concatenations that allow anxious pupils to pass their examinations. Science is essentially an ethical and
then political question of time, patience, responsibility, and ability to act on human life and to nourish the
human… that is, the cosmopolitan, freedom of Man.
Opportune igitur hodie mentem curis omnibus exsolvi,
securum mihi otium procuravi… (Descartes - Meditatio Prima)
Now the question is: will such a rich-but/then-anxious nationally-educated pupil listen to my
pedagogical suggestion? Will he take his time to calm his mind, and to meditate the «European (= universal)
dimension» of what he is doing? Will he think of himself as a citizen of the same Cosmos where Galileo has
had the time to meditate on Time? This was my problem: am I able to really give an anxious
suburban/lower/middle/upper/class young/old intra/inter-national citizen the «social maturity that allows
him to distance themselves from social pressures»? My answer (the answer of my experience) has been:
no. In the present age all western boys and girls, men and women… are equal in terms of social pressure.
We are all equally poor in Time, even if Europe continually tells us: we are rich enough, the time has come
to think differently about human life.
Thus something more radical has to be done: we must be able to scientifically show that this
«distance from social pressure» – is at the core of every scientific truth as such. The age of science has lost
the time of science, but time doesn’t come to science from the outside. Time is, on the contrary, the deep
heart of every scientific truth, and this time is essentially the time of a genesis, during which the human mind
must truly and gradually grow up, by acquiring patience, tolerance, wisdom, and a courageous freedom to
exist notwithstanding its essentially and quite democratically universal, mortal nature.
This then becomes the real ethical and cosmopolitan issue of my Research Program: Symbols of
their own genesis – Foundation of the Dynamics of Representation.

27
Informed Consent . Does the proposal involve children? Does the proposal involve patients or persons not able to give
consent? Does the proposal involve adult healthy volunteers?Does the proposal involve Human Genetic Material?
Does the proposal involve Human biological samples?Does the proposal involve Human data collection?Research on
Human embryo/foetus. Does the proposal involve Human Embryos? Does the proposal involve Human Foetal Tissue /
Cells?Does the proposal involve Human Embryonic Stem Cells?Privacy. Does the proposal involve processing of genetic
information or personal data (eg. health, sexual lifestyle, ethnicity, political opinion, religious or philosophical conviction)
Does the proposal involve tracking the location or observation of people? Research on Animals. Does the proposal
involve research on animals? Are those animals transgenic small laboratory animals?Are those animals transgenic farm
animals? Are those animals cloning farm animals? Are those animals non-human primates? Research Involving
Developing Countries. Use of local resources (genetic, animal, plant etc). Benefit to local community (capacity building
i.e. access to healthcare, education etc). Dual Use. Research having potential military / terrorist application
I CONFIRM THAT NONE OF THE ABOVE ISSUES APPLY TO MY PROPOSAL
Works Cited
Boole,G. [MAL] The mathematical Analysis of Logic, Cambridge 1847; [ILT] An investigation of the Laws oh thought,
Cambridge 1854
Bever ,T.G & Meeler,J. “Cognitiv capacity of very young children”, Science, 158 (1967)
Barone,F., Logica formale e logica trascendentale, Torino: 1965
Caianiello, E. [IPM]“Infant’s prolegomena to any future metaphysics: the sense of numerical identity, the numerical
identity of sense”, Dogma, Mars 2008.; [SEO] “Sisifo e l’eterna omeostasi della psichiatria attuale”, Il Nuovo Baretti ,
(April 2004).
Cantor,G. Beiträge zur Begründung der transfiniten Mengenlehre, Berlin : 1895
Dehaene, S. La bosse des maths, Paris : 1997
Dedekind,R.[WSZ], Was sind und was sollen di Zahlen? Berlin : 1888
EUROPEAN COMMISSION – [EUC] Proposal for a Decision of the European Parliament And of the Council
concerning the European Year of creativity and Innovation (2009)
EUROPEAN PARLIAMENT [EUP] Lisbon European Council 23 and 24 March 2000. Presidency
Conclusions
Everest Boole, M., The preparation of child for science, Oxford:1904
Galilei,G. Dialogues on two world systems, Chicago: 1953
Grattan Guinness, I., The search for mathematical roots, Princeton 2000
Hamilton,W.R., Theory of conjugate functions, or algebraic couples; with a preliminary and elementary essay on
Algebra as the science of Pure Time, London: 1837
Kant,I., Kritik der Reinen Vernunft, Berlin 1787
W.Koeler, Die Gestaltpsychologie, Berlin 1929
Mangione, C. Logica e fondamenti della matematica, in L.Geymonat, Storia del pensiero filosofico e scientifico, vol.
VI, Milano: 1972
OECD [2000] DeSeCo. La Définition et la sélection des Compétence.; [2002] Comprendre le cerveau. Vers une
nouvelle science de l’apprentissage ; [2003] Cadre d’évaluation de PISA 2003 – Connaissances et compétences en
mathématiques, lecture, science et résolution de problèmes ; [2005/2006] L’Education à l’OCDE [2006] Assessing
Scientific, Reading and Mathematical Literacy. A Framework for PISA 2006 [2007] Comprendre le cerveau. Naissance
d’une science de l’apprentissage. [2008] Teaching, Learning and Assessment for Adults: Improving Foundation Skills
Piaget J. [NI] La naissance de l’intelligence chez l’enfant, Neuchâtel-Paris : 1936 ; [CR] La construction du réel chez
l’enfant, Neuchâtel-Paris 1937 ; [GN] La genèse du nombre chez l’enfant, Neuchâtel-Paris 1941; [FS] La formation
du symbole chez l'enfant, Neuchâtel 1945. [EG] L’épistemologie genetique, Paris : 1970 ; [MG] “Le mécanisme du
développement mental et les lois du groupement des opérations ”, Archives de Psychol, 1941
Plato, Republic, Oxford
UNESCO [1990] World declaration on Education for All and framework for action to meet basic learning needs
adopted by the world conference on education for all meeting basic learning needs . Jomtien, 1990
[2000] a) Education For All: Meeting Our Collective Commitments. Dakar, Senegal, 26-28 April 2000 ; b) Action
Framework ; c) Living Literacy.
Winn,K. “Addition and soustraction by human infants” Nature, 358, (1992)
Wittgenstein,L. [NB] Notebooks 1914-1916, London 1961 [TLP] Tractatus Logico-Philosophicus, London: 1922; [PI]
Philosophical Investigations, London:1953
YES

Jean Dhombres
Directeur de recherche au CNRS Directeur d'études à l'EHESS
Centre Alexandre Koyré Groupe de Recherches sur les Savoirs
Histoire des sciences et des techniques 10 Rue Monsieur le Prince,
27 rue Damesme, 75 013 Paris 75 006 Paris
tél: 01 45 65 42 53 tél: 01 53 10 54 67/ou 66
Fax 01 45 81 16 47
Jean.Dhombres@damesme.cnrs.fr gers@ehess.fr
I hereby professor Jean Dhombres, from EHESS (Paris) do accept to be « participant number 1 » for the
project registered as FP7-People-IEF-2008, and entitled “Symbols of their own genesis. Foundation of a
Dynamics of Representation”. The call identification is 03 CO74 of march 2008, and the project is submitted
by M.Eduardo Caianiello. Normally, E.Caianiello is finishing his PHD thesis at EHESS, and intends to submit it
before the end of present year.

Direction et Administration :
Muséum National d'Histoire Naturelle, Pavillon Chevreul
57 rue Cuvier, 75231 PARIS Cedex 05
Tél. : 33 01 43 36 70 69 - Fax 33 01 43 3134 49
Ce 10.août 2008
Centre Alexandre KOYRE
Histoire des Sciences et des Techniques
EHESS - CNRS (UMR 8560) - MNHN
Secrétariat Scientifique et Chercheurs :
27 rue Damesme, 75013 PARIS
Tél. : 33 0145 65 97 42 ou / 97 46
Fax : 33 01 45 8116 47
Les conditions d'apprentissage des sciences, en particulier des sciences
mathématiques, que ce soient les conditions sociales, mentales, émotionnelles ou
organisationnelles au sein même des savoirs, ont fait l'objet de très nombreuses études. La
didactique des sciences et particulièrement la didactique des mathématiques, a en effet fait des
progrès considérables depuis son lancement véritable par Piaget dans les années 50 du XXe
siècle, et la mise en œuvre d'une expérimentation par Guy Brousseau dans les années 70, sans
compter les nombreuses approches sociologiques. Dans la plupart des travaux, que ce soit
reconnu ouvertement, ou resté implicite, un rôle important est dévolu à la notion générale
d'obstacle épistémologique, telle que mise en avant par Gaston Bachelard pour rendre compte
de l'histoire des sciences en général, et de l'innovation humaine en particulier. Ces travaux, il
faut le souligner, avaient tous une légitime prétention théorique, avec le souci de parvenir à
une théorie de la connaissance par sa transmission.
Le présent projet tente une réflexion aussi radicale, partant aussi bien de la philosophie
analytique que de la phénoménologie, en s'attaquant d'une façon originale au problème de la
représentation des objets, ou des idées mathématiques. L'originalité tient à une perception
dynamique du champ des représentations mathématiques, et à une double vision interne et
externe, dont il s'explique très bien dans le projet qui est soumis, et pour lequel il demande
une subvention lui permettant de pouvoir travailler pendant deux années. Cette perception
dynamique lui fait mettre de côté les aspects sociaux, pour pouvoir les situer au plus près des
significations des symboles et de leur appropriation par le sujet apprenant.
Eduardo Caianiello, qui déploie une énergie farouche et impressionnante laquelle attire
forcément la sympathie, est certainement à même de réaliser le programme qu'il décrit. Je le
soutiens d'autant plus volontiers qu'il est inscrit pour une thèse sous ma direction à l'Ecole des
Hautes Etudes en Sciences Sociales, dont le titre original est : Le fait génétique de
mathématiques et la puissance dynamique du mental humain. Dans son travail de thèse, il
manifeste une curiosité tous azimuts, allant voir de près les exemples historiques en
mathématiques que je lui soumets, acceptant de remettre en question ses analyses, les affinant
en les modifiant au besoin. C'est cette curiosité intellectuelle, fruit d'un long travail passé et de
nombreuses difficultés résolues, qui fait que sa demande d'un soutien mérite vraiment d'être
étudiée et validée.
Jean Dhombres
Directeur d'études à l'EHESS

Referee Jean Dhombres.
English
The conditions of learning the Sciences, in particular the Mathematical Sciences, which deal with social,
mental, emotional or organizational conditions within the context of knowledge, have been the object of
numerous studies. The teaching of Sciences, and in particular the teaching of Mathematics, has in fact made
considerable progress since its effective launch by Piaget in the 1950’s, and by the experiment put into effect by
Guy Brousseau in the 1970’s; without considering the numerous sociological approaches. In the majority of
studies, whether they be openly recognized or whether they remain implicit, an important role is attributed to the
general notion of an epistemological obstacle, that has been proposed by Gaston Bachelard to explain the history
of Sciences in general, and human innovation in particular. It must be underlined that all these studies had a
legitimate theoretical claim to the problem of arriving at a theory of knowledge through its transmission.
The present project makes an attempt at a similarly radical thought, beginning from analytical
philosophy as much as from phenomenology, and confronting the problem of representation of objects, or of
mathematical ideas in a completely original way. The originality lies in the dynamic perception of the field of
mathematical representations, and in a double vision, both internal and external, which is well explained in the
proposed project and for which Eduardo Caianiello asks for funding to allow him to work for two years. This
dynamic perception causes him to put the social aspects to one side, so that he can place them closer to the
meaning of symbols and to their appropriation by the subject of learning.
Eduardo Ciananiello, who exudes an explosive and impressive amount of energy, means that he is well
liked, and that he is certainly able to realize the project that he describes. I support him willingly as he is
registered for a thesis entitled ‘The genetic fact of Mathematics and the dynamic power of the human mind’ under
my guidance at the ' Ecole des Hautes Etudes en Sciences Sociales’. In his thesis he shows an immense curiosity,
enabling him to deal closely with historical and mathematical examples which I propose to him. He also accepts
that he may have to question his analyses, analyzing them and modifying them if needs be.
It is this intellectual curiosity, fruit of lengthy past studies and numerous resolved difficulties, which
makes his request for funding truly worthy of being studied and heard.
Italiano
Le condizioni di apprendimento delle scienze, in particolare delle scienze matematiche, che si tratti delle
condizioni sociali, mentali, emozionali o organizzative nel seno stesso dei saperi, sono state l'oggetto di
numerosissimi studi. La didattica delle scienze, e particolarmente la didattica della matematica, ha in effetti fatto
progressi considerevoli dal suo lancio effettivo da parte di Piaget dagli anni '50 del XX secolo, e la messa in opera
di una sperimentazione da parte di Guy Brousseau negli anni '70; senza contare i numerosi approcci sociologici.
Nella maggior parte dei lavori, che questo sia riconosciuto apertamente o resti implicito, un ruolo importante è
attribuito alla nozione generale di ostacolo epistemologico, quale è stata proposta da Gaston Bachelard per render
conto della storia delle scienze in generale, e dell'innovazione umana in particolare. Questi lavori, bisogna
sottolinearlo, avevano tutti una legittima pretesa teorica, nella preoccupazione di pervenire a una teoria della
conoscenza attraverso la sua trasmissione.
Il progetto presente tenta una riflessione altrettanto radicale, a partire tanto dalla filosofia analitica che dalla
fenomenologia, e affrontando in modo del tutto originale il problema della rappresentazione degli oggetti, o delle
idee matematiche. L'originalità sta nella percezione dinamica del campo delle rappresentazioni matematiche, e in
una doppia visione, interna e esterna, che è ben spiegata nel progetto proposto, e per il quale Eduardo Caianiello
richiede una sovvenzione che gli permetta di poter lavorare per due anni. Questa percezione dinamica gli fa
mettere da parte gli aspetti sociali, per poterli situare più vicino alle significazioni dei simboli e alla loro
appropriazione da parte del soggetto dell'apprendimento.
Eduardo Ciananiello, che dispiega un’energia esplosiva e impressionante che necessariamente attira la
simpatia, è certamente in grado di realizzare il programma che descrive. Io lo sostengo tanto più volentieri in
quanto è iscritto per una tesi sotto la mia direzione all' Ecole des Hautes Etudes en Sciences Sociales, e di cui il
titolo originale è Il fatto genetico della matematica e la potenza dinamica della mente umana. Nel suo lavoro di
tesi, egli manifesta una curiosità a trecentosessanta gradi, per cui si occupa sempre da vicino degli esempi storici
e matematici che io gli propongo, e accetta di rimettere in questione le sue analisi, analizzandole e
all'occorrenza modficandole.
È questa curiosità intellettuale, frutto di un lungo lavoro passato e di numerose difficoltà risolte, a far sì che
la sua richiesta di un sostegno meriti veramente di essere studiata e ascoltata.

Bologna, 5 luglio 2008
Sono diversi anni che da un’angolazione centrata sulla didattica della matematica seguo
le ricerche razionalistiche di Eduardo Caianiello che persegue con sempre maggiore convinzione e
successo il progetto di un rinnovamento radicale nei modi della trasmissione del sapere scientifico (
e non solo) in un mondo e un’epoca che di un tale rinnovamento hanno un bisogno veramente
vitale.
Eduardo ha avuto otto anni fa il coraggio di abbandonare il percorso canonico della
carriera accademica – nonostante gli indubbi successi che riscuoteva – per poter seguire senza
riserve, e assumendosi tutti i rischi del caso, il cammino teorico e pratico che gli veniva via via
indicato dalle sue intuizioni teoriche e dalle sue esperienze didattico/pedagogiche sul campo.
Il nocciolo dell’impresa scientifica di Eduardo Caianiello è nella sua idea genetica e
dinamica del rapporto che la mente umana istituisce tra sé stessa e i simboli convenzionali della
matematica, analizzando le leggi che reggono i processi della sua stessa nascita. L’idea è insomma
che uno sguardo dinamico sulla fonte comune di quelle forme cinematiche che chiamiamo
“pensiero algoritmico” ci consente di potere osservare non solo dei movimenti di simbolizzazione in
atto, ma anche i processi genetici che hanno portato quegli stessi movimenti alla piena e diretta
coscienza di sé stessi nel momento in cui la nostra mente pone in essere un’ [auto]trasformazione
“matematica”. Si tratta cioè di un’ indagine analoga a quella che consente di osservare oggi al
telescopio la condizione iniziale del nostro universo, e di ricostruire così l’intero processo della sua
formazione, di cui noi stessi che osserviamo siamo uno dei risultati finali.
Questa genetica che si collega agli aspetti percettivi del grafema matematico, richiama
la dinamogesi dei simboli che la compongono (“Ogni simbolo è un nuovo simbolo” direbbe Ludwig
Wittgenstein), e questa dinamogenesi si produce – secondo l’idea di Eduardo Caianiello –
all’interno di uno spazio della Rappresentazione entro il quale alla nostra mente è dato di osservare
l’evento/processo della sua stessa nascita. Per questo, la stessa disciplina che si occupa della genesi
dei simboli, in essi vedendo i simboli della loro propria genesi, offre infine le basi di partenza di una
Dinamica della Rappresentazione.

Su queste basi, rilevo un interesse certo di questa prospettiva tanto nel dominio della
didattica che in quello della psicologia clinica. Una buona didattica deve essere capace di deautomatizzare
gli schemi mentali degli allievi, facendo in modo che le forme apprese siano sempre
l’occasione di un movimento sperimentale nuovo e creativo, mentre una nuova luce viene gettata
sulla fonte del blocco fobico scolare così diffuso.
Il programma di ricerca “Simboli della propria genesi. Fondamenti di una Dinamica
della Rappresentazione” offre dunque delle prospettive estremamente fertili e preziose a partire
da un orizzonte già pienamente strutturato e maturo, mentre un quadro di finanziamenti come
“People” intitolato a Marie Curie non può vedere in Eduardo Caianiello che l’espressione esemplare
di quel pieno e coraggioso impegno personale e individuale che è da sempre il motore del
progresso della scienza e della civiltà.
dr dr prof dr PhD Bruno D’Amore
Docente di Didattica della Matematica
Direttore della rivista “La matematica e la sua didattica”
Direttore scientifico del Convegno Nazionale “Incontri con la Matematica”,
Responsabile scientifico degli accordi con le università di Colombia
telef univ: ++39)0512094446 / fax: (++39)0512094490
telef. privato: (++39)051505616 / cell: (++39)3356463896
e-mail: damore@dm.unibo.it www.dm.unibo.it/rsddm

TRANSLATION (D’AMORE)
Since several years I’ve been following, from a point of view centered on the
didactics of mathematics, the rationalist researches of Eduardo Caianiello, who’s leading his
project of a radical renovation in the methods of (not only) scientific knowledge transmission,
with always stronger conviction and success.
Height years ago, Eduardo has had the courage to quit the canonical way of
academicals career – notwithstanding the success he was getting – to unconditionally follow
the theoretical and practical path that his scientific intuition and his didactico/pedagogical
experiences on field suggested him to follow.
The core of scientific enterprise of Eduardo Caianiello is in his dynamic and genetic
vision of the relationship that human understandig establishes between itself and the
conventional symbols of mathemathics, in which our mind has the possibility to grasp the
laws of its own birth.
The idea is that a dynamic undersatinding of the common root of these cinematic
forms that we call “algorthmic thought”, allows us to observe not only an actual movement
of symbolisation, but also the genetic process that has brought this movement to a direct
self-awarness, when our mind realizes a “mathematical” self-transformation. It is then the
same method as that which permits us to observe here and now through the telescope, the
initial condition of our universe, and to describe the total process of its formation, of which
we, the actual observers, are one of the final effects.
This genetic transformation is also observable in the perceptive aspects of
mathematical graphema, because it recalls the dynamogenesis of the symbols that compose
mathematical evidence (“every symbol is a new symbol” would say Ludwig Wittgenstein).
Now this dynamogenesis takes form – accordingly to Caianiello’s perspective – inside of a
space of the Representation, that is then the final horizon in which our mind can observe the
event of its own first apparition.
For this reason, the same science that is concerned with the genesis of symbols,
and that sees them as the symbols of their own genesis, builds up the foundations of a
Dynamics of the Representation.
On this ground, I find this perspective really interesting as in the field of the
didactics as in that of clinic psychology. A good didactic program must be able to deautomatizing
the mental schemas of the students, so that the forms they learn will always be
the occasion for a new and creative experimental movement; furthermore, a new light is
thrown on the root of the so diffused school phobia.
From a scientific point of view then, the research program “Symbols of their own
genesis. Foundation of a Dynamics of Representation” offers a really fruitful perspective, on
the basis of a fully ripe and structured conceptual framework, while from the human point of
view the European program “People”, entitled to the memory of Marie Curie, finds in
Eduardo Caianiello the perfect expression of that complete and courageous personal
engagement that since always is at the core of scientific and historical progress.

Prof. Dott. Pierluigi Scapicchio
Psichiatra
Via Venanzio Fortunato, 12
00136 Roma - Italy
Rome, 12/8/2008
I first met Eduardo Caianiello in 1995, and I immediately realized that this young undergraduate thinker would
have an important future in the scientific community.
I found Mr. Caianiello’s s simultaneous philosophical, historical and formal formal approach to the the relationship
relationship
between the material and the mental dimension of human life extremely interesting. His historical and cultural insight
convinced him that the cyclical rhythm rhythm of the main neurological phenomena had had to to be be explained explained with with the the strictly
strictly
logical/cognitive tools of an enhanced science of the mind. This was due to tthe
he fact that the essentially pedagogical
perspective on the ethical question: «how can man be an an active active agent in his material history?» has always always been
been
concurrent with the scientific question: «how can the mind actively intervene on on the the body?».
In 1995/1996, 96, I published the first two interdisciplinary interdisciplinary reviews by Mr. Caianiello Caianiello on on this this subject: subject: the the first
first
review discussed the book written by the psychoanalyst G.Jervis «Surviving Surviving until the Millenium Millenium», while the second
discussed the book written by the psychiatrist psychia A.Balestrieri «Instincts. Instincts. Ancient ways to human behavior». behavior I must say that
for me, the most astonishing aspect of these 13 years of relentless research has been - besides the fact that Mr. Caianiello
has been an effective “active agent” against his aawful
Horton headache! - the perseverance of this philosopher. When he
resigned from the EHESS in 2000, Mr. Caianiello told me that it it was was only only a temporary decision, decision, to «re-meditate «re the
methodological question» and to «obtain more powerful formal tools» … I confess that on this occasion I feared that he
could lose the way back to his – for me – quite apparent vocation in research. But I was proven wrong: Mr. Caianiello
never stops studying.
In 2003, I published Mr. Caianiello’s Caianiello «Voices of the current age: Popper opper and Laing contra Freud», Freud and in
2004 I much enjoyed reading his «Sisyphus Sisyphus and the the Eternal Eternal Homeostasis Homeostasis of of current current Psychiatry», Psychiatry concerning the
epistemological condition of modern psychiatry, where the roots of Mr. Mr. Caianiello’s current current results results were were in in fact f
established. Moreover, during these years, I have followed Mr. Caianiello Caianiello’ss theoretical and pedagogical research on
mathematical and physical matters, so that I now know that the PhD-Thesis PhD «The The genetic fact of mathematics… » and the
research-program «Symbols Symbols of their own genesis… genesis…» » are really the final answer to his old ethical/scientific (that is,
pedagogical) question on man’s possibility to act on his life and world.
Mr. Caianiello’s s idea idea of an evolutionary evolutionary vector vector of human cognition cognition sets the “Min “Mind” as the profound orienting
identity (→) →) of a dynamical system that at any given moment moment manifests itself on its own surface as as the “commutative”
“commutative”
mind↔body interaction. It is quite a simple simple idea idea that unifies unifies all all human phenomena under the the experimental conc concept of
«representation», that Mr. Caianiello has found in the educational/cognitive field of of symbolic/mathematical symbolic/mathematical learning.
This new conceptual framework thus opens a coherent horizon to really «re-meditate» «re meditate» the cardinal neurophysiologic and
psychiatric notions otions of “homeostasis”, “homeostasis”, “oscillation” and “stability”… Furthermore, what what Mr. Caianiello affirms about the
relationship between the the «absolute «absolute beginning» beginning» entailed entailed by every symbolic operation, and the the roots roots of psychological
school-phobia and neurophysiologic brain brain-obsolescence, obsolescence, deserves the greatest attention by the scientific and educational
community. I would be extremely delighted if our old-and-new old new Europe would give this precious opportunity to such a
pure researcher to “resume career”, in a world where pperhaps
erhaps nothing is more important than this kind of fidelity and
abnegation to scientific and pedagogical life.
Professor of Neurology and Geriatric Psychiatry
UNIVERSITÀ CATTOLICA DEL SACRO CUORE di ROMA
Past President of the Società Italiana di Psichiatria.
National Coordinator of Research on the relationship between between depression depression and and Alzheimer’s Alzheimer’s disease
Italian Interdisciplinary Network of Alzheimer Disease (ITINAD)
President of the Associazione Italiana di Psicogeriatria

Referee Pierluigi Scapicchio
Italiano
Conobbi Eduardo Caianiello per la prima volta nel 1995, e capii immediatamente che questo giovane pensatore non
ancora laureato avrebbe avuto un futuro importante nella comunità scientifica.
Trovavo estremamente interessante il suo approccio allo stesso tempo filosofico, storico, e formale al rapporto tra la
dimensione materiale e mentale della vita umana: la sua sensibilità storica e culturale lo aveva convinto che il ritmo ciclico dei
principali fenomeni neurologici deve essere spiegato con gli strumenti strettamente logico/cognitivi di una potenziata scienza
della mente, e questo era dovuto al fatto che la prospettiva essenzialmente pedagogica sulla questione etica: “come un uomo
può essere un agente attivo nella sua storia materiale?” è per lui sempre stata concentrica alla a questione scientifica: “come la
mente umana può attivamente intervenire sul corpo?”. Così, nel 1995/1996, ho pubblicato i primi due articoli interdisciplinari
del Sig. Caianiello: il primo trattava del libro dello psichiatra A. Balestrieri «Istinti. Antiche vie al comportamento umano», il
secondo del saggio dello psicoanalista Giovanni Jervis «Sopravvivere al millennio».
Devo dire che per me, l’aspetto più sorprendente di questi 13 anni di ininterrotte ricerche è stato – oltre al fatto che il
Sig. Caianiello è stato un effettivo «agente attivo» contro la sua terribile emicrania ! – la perseveranza di questo filosofo.
Quando lasciò l’ EHESS nel 2000, Eduardo mi disse che era solo una decisione temporanea, per “rimeditare la questione
metodologica” e per “ottenere strumenti formali più potenti” … e confesso che in questa occasione temetti che potesse perdere
la via del ritorno alla sua – per me – del tutto ovvia vocazione alla ricerca.
Ma mi ero sbagliato: il Sig. Caianiello non smette mai di studiare. Nel 2003, ho pubblicato il suo «Voci della
contemporaneità: Popper e Laing contra Freud», e nel 2004 ho apprezzato molto il suo «Sisifo e l’ Eterna omeostasi della
Psichiatria contemporanea» , sulla la condizione epistemologica della psichiatria attuale, dove erano già presenti le radici dei
suoi attuali risultati teorici. Infine, durante questi anni, ho seguito la su ricerca teorica e pedagogica sui fondamenti della
Matematica e della Fisica, sicché ora so che la tesi di PhD «Il fatto genetico della matematica …» e il programma di ricerca
«Simboli della propria genesi …» sono realmente la sua risposta finale alla iniziale questione etico/scientifica (cioè,
pedagogica) sulla possibilità dell’uomo di agire sulla sua vita e sul suo mondo.
L’idea del Sig. Caianiello di un vettore evolutivo della cognizione umana pone la “Mente” come l’ orientante identità
profonda (→) di un sistema dinamico che ad ogni istante dato manifesta sé stesso sulla sua propria superficie come l’interazione
commutativa mente ↔ corpo. È un’idea semplice, che unifica tutti i fenomeni dell’umano sotto il concetto sperimentale di
«rappresentazione», che il Sig. Caianiello rinviene nel campo educativo/cognitivo dell’apprendimento simbolico/matematico.
Questa nuova struttura concettuale apre dunque un orizzonte coerente per effettivamente “ri-meditare” le nozioni
neurofisiologiche e psichiatriche di “omeostasi”, “oscillazione”, “ stabilità” … Ulteriormente, ciò che il Sig. Caianiello afferma
circa la relazione tra l’ “inizio assoluto” implicato da ogni operazione simbolica, e le radici della fobia-scolare e dell’
invecchiamento neurofisiologico del cervello, è degno della più grande attenzione da parte della comunità scientifica e
educativa.
Sarei dunque estremamente felice se la nostra vecchia-e-nuova Europa desse questa preziosa opportunità a un tale puro
ricercatore, in un mondo dove niente forse è più importante che questo tipo di fedeltà e abnegazione alla vita scientifica e
pedagogica.

Maison d'Auguste Comte
Association Internationale
ociation interna 10, rue Monsieur-le Prince
75006 Paris
01.43.26.08.56 (tel)
01.43.54.82.71 (fax)
augustecomte@wanadoo.fr
Angèle Kremer-Marietti,
Présidente du Groupe d’Études et de Recherches Épistémologiques,
01 70 07 23 02
angele.marietti@numericable.com
Paris , le 13 juillet 2008
Je ne connaissais pas avant cette année Monsieur Eduardo Caianiello dont j’ai publié
dans ma revue électronique DOGMA (numéro de mars 2008) un article fort bien documenté,
« Les prolégomènes de l’enfant à toute métaphysique future : le sens de l’identité numérique,
l’identité numérique du sens », dont l’orientation cognitiviste est nettement marquée.
J’ai ensuite donné l’occasion à Monsieur Eduardo Caianiello de venir, le 7 juin 2008,
présenter et développer ses idées à mon Groupe d’Études et de Recherches Épistémologiques,
au cours d’une conférence intitulée « Poincaré, Piaget, Marcel Proust et la genèse du symbole
mathématique et littéraire ».
Je m’intéresse aux travaux de Monsieur Eduardo Caianiello car ils partent du point de
vue de la représentation pour expliquer les processus du symbolisme intervenant dans la
phénoménologie de la cognition – ce qui est mon point de vue dans la perpective d’une
« philosophie comme science du symbolique » à laquelle je travaille personnellement depuis
plusieurs années.
J’apprécie donc le projet général formulé par Monsieur Eduardo Caianiello d’une
théorie qu’il conçoit, en ce qui le concerne, comme devant être génétique et qui devrait lui
permettre d’enchaîner toutes les phases de la cognition humaine. Son propos se rattache
explicitement à Kant, Piaget et Wittgenstein, ce dont je ne puis que l’approuver.
Angèle Kremer-Marietti

Referee Marietti
English
I met Mr.Eduardo Caianiello this year, when I published his highly and exhaustively
informative essay «Infant's prolegomena to any future metaphysics: the sense of numerical identity,
the numerical identity of sense» in my electronic review DOGMA (March 2008). In this study, Mr.
Caianiello’s cognitivist orientation is clearly expressed.
Afterwards, on June the 7th 2008, I invited Mr. Caianiello to present at and to develop his
theories with my Groupe d'Études et de Recherches Épistémologiques, in a conference entitled «
Poincaré, Piaget, Marcel Proust and the genesis of the mathematical and literary symbol ».
I am very interested in Mr. Caianiello's work, because it comes about as the result of a point
of view on representation, to explain the process of symbolism that intervenes in the
phenomenology of cognition, and this is also my point of view in the perspective of a philosophy like
the science of symbolism, on which I have been working for many years.
I thus appreciate the general project proposed by Mr. Caianiello of a theory that, according
to his vision, must be genetic, and would allow him to link together all the steps of human cognition.
Mr.Caianiello’s intent is explicitly linked to Kant, Piaget, and Wittgenstein, and this is an additional
reason for me to give him my complete approval.
Italiano
Non conoscevo prima di quest’anno Eduardo Caianiello, di cui ho pubblicato nella
mia rivista elettronica DOGMA (numero di marzo 2008) un articolo molto ben documentato,
“I prolegomeni del bambino ad ogni metafisica futura : il senso dell’identità numerica,
l’identità numerica del senso ”, il cui orientamento cognitivista è nettamente pronunciato.
Ho in seguito dato l’occasione a Eduardo Caianiello di venire, il 7 giugno 2008, a
presentare e sviluppare le sue idee al mio Gruppo di Studi Epistemologici, nel corso di una
conferenza intitolata “Poincaré, Piaget, Marcel Proust e la genesi del simbolo matematico e
letterario ”.
Mi interesso ai lavori di Eduardo Caianiello perché essi partono dal punto di vista
della rappresentazione per spiegare i processi del simbolismo intervenendo nella
fenomenologia della cognizione – ciò che è il mio punto di vista nella prospettiva di una
filosofia come scienza del simbolico alla quale lavoro personalmente da più anni.
Apprezzo dunque il progetto generale formulato da Eduardo Caianiello di una
teoria che egli concepisce, in ciò che lo concerne, come necessariamente genetica e che
dovrebbe permettergli di concatenare tutte le fasi della cognizione umana. Il suo proposito si
ricollega esplicitamente a Kant, Piaget e Wittgenstein, ciò che io non posso che approvare.
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