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2020-3637-AJHA 1 Jean Piaget’s Genetic Epistemology as a Theory of 1 Knowledge Based on Epigenesis 2 3 4 This article aims to highlight Jean Piaget’s theory of knowledge and insert it in 5 this universe from Ancient Greece where, in Plato, we already find his seminal 6 idea: knowledge is acquired in successive and ascensional moments 7 (dialektikê), starting from an opinion about the sensible world (doxa) towards 8 the épistêmê of the intelligible world, that of Ideas or concepts. Piaget’s Theory 9 of Knowledge, we believe, was determined by four moments: 1) his research 10 as a malacologist under the guidance of Godet and Raymond. 2) the 11 acquaintance with Kant’s philosophy at age 21. 3) his internship at the 12 Binet/Simon laboratory. 4) his studies on the Lymnaea Stagnalis. His core idea: 13 it is possible for human beings to attain the necessary and universal 14 knowledge due to the exchange processes of their organisms with the 15 environment, which give rise to the epigenetic ontogenesis of their specific 16 organic mental structures for the act of knowing. It starts with actions in the 17 world from birth, around two years of age will be represented and organized 18 in sets linked to empirical experience until the brain may perform the 19 operations of the Abelian Group. The physiological construction ends here, and 20 the logico-mathematical knowledge becomes possible. 21 22 Keywords: Theory of Knowledge-Genetic Epistemology-Epigenesis. 23 24 25 Introduction 26 27 The title of this article may be surprising to many, since Jean Piaget 28 has always been considered a genius in psychology. In reality, however, 29 Piaget was a biologist/zoologist who dedicated himself to epistemology. 30 Apart from his interest in biology/zoology, Piaget was always 31 interested in the education of human beings, in parallel with the 32 construction of Genetic Epistemology. Piaget expressed his interest in 33 education at the beginning of his career and subsequently dedicated to 34 it about 400 out of the 20.000 pages he wrote on epigenetic ontogenetic 35 evolution of rationality, which allowed for scientific knowledge, and 36 whose objective was to create a tertium between Darwin and Lamarck. 37 (Ramozzi-Chiarottino, Z et allii, 2017). 38 In this work we aim to demonstrate that Jean Piaget achieved his 39 youth dream (1918) by creating a Theory of Knowledge based on 40 Biology and, in addition, show that it is inserted in the History of 41
Transcript
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1

Jean Piaget’s Genetic Epistemology as a Theory of 1

Knowledge Based on Epigenesis 2

3

4

This article aims to highlight Jean Piaget’s theory of knowledge and insert it in 5

this universe from Ancient Greece where, in Plato, we already find his seminal 6

idea: knowledge is acquired in successive and ascensional moments 7

(dialektikê), starting from an opinion about the sensible world (doxa) towards 8

the épistêmê of the intelligible world, that of Ideas or concepts. Piaget’s Theory 9

of Knowledge, we believe, was determined by four moments: 1) his research 10

as a malacologist under the guidance of Godet and Raymond. 2) the 11

acquaintance with Kant’s philosophy at age 21. 3) his internship at the 12

Binet/Simon laboratory. 4) his studies on the Lymnaea Stagnalis. His core idea: 13

it is possible for human beings to attain the necessary and universal 14

knowledge due to the exchange processes of their organisms with the 15

environment, which give rise to the epigenetic ontogenesis of their specific 16

organic mental structures for the act of knowing. It starts with actions in the 17

world from birth, around two years of age will be represented and organized 18

in sets linked to empirical experience until the brain may perform the 19

operations of the Abelian Group. The physiological construction ends here, and 20

the logico-mathematical knowledge becomes possible. 21

22

Keywords: Theory of Knowledge-Genetic Epistemology-Epigenesis. 23

24

25

Introduction 26

27

The title of this article may be surprising to many, since Jean Piaget 28

has always been considered a genius in psychology. In reality, however, 29

Piaget was a biologist/zoologist who dedicated himself to epistemology. 30

Apart from his interest in biology/zoology, Piaget was always 31

interested in the education of human beings, in parallel with the 32

construction of Genetic Epistemology. Piaget expressed his interest in 33

education at the beginning of his career and subsequently dedicated to 34

it about 400 out of the 20.000 pages he wrote on epigenetic ontogenetic 35

evolution of rationality, which allowed for scientific knowledge, and 36

whose objective was to create a tertium between Darwin and Lamarck. 37

(Ramozzi-Chiarottino, Z et allii, 2017). 38

In this work we aim to demonstrate that Jean Piaget achieved his 39

youth dream (1918) by creating a Theory of Knowledge based on 40

Biology and, in addition, show that it is inserted in the History of 41

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Philosophy which arose in Ancient Greece and has reached our days. A 1

classical Theory of Knowledge and at the same time an absolutely 2

contemporary one insofar as Biology is par excellence the theme of 3

Knowledge in our century. 4

5

6

Methodology 7

8

The Method of this article consisted in: a) identifying a gnosiology 9

that seeks the origin and nature of the human faculty of knowing in 10

Jean Piaget’s work; and b) positioning it in its due place in Western 11

Philosophy's history. 12

13

14

Prolegomena 15

16

Let us begin this article by returning to a classic question posed at 17

the dawn of Philosophy: “Is it possible for humans to attain Knowledge 18

(épistêmê)? If so, does Knowledge come to us through the senses in 19

contact with experience, or is it the prerogative of pure Reason?” 20

The philosophies of Parmenides of Elea and Heraclitus of Ephesus 21

are the icons of the answer to that question in the History of Ideas. The 22

former asserted: “Being Is, no-Being does not exist”, therefore “Being” has 23

always existed; it will be eternal and not subject to transformation, for if 24

it had started on a day or should come to end on day or should undergo 25

changes, it could only be transformed into “Non-Being”, but “Non-26

Being” does not exist. Heraclitus, for believing only in the information 27

coming from the senses, stated: “Nothing ever is, but everything is 28

becoming.” The opposition between knowledge that is pure reason, or 29

pure logic (before the science of logic was first created by Aristotle), and 30

the knowledge that comes to us through the senses is very clear, as 31

Heraclitus put it: No man ever steps in the same river twice. The opposition 32

between reflection and pure evidences of the senses is clear, a dilemma 33

that persists even today, albeit with different wording (Granger, 1992). 34

Parmenides and Heraclitus have survived only, as is known, in 35

their Fragments, with all the difficulties of their reconstruction. We only 36

have the fragments of Parmenides, and it was precisely the interest in 37

his logic which led me to the Philosophy course at the age of 16; 38

decades later I was given a great present - his Fragments, (1997). Here 39

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are some examples of the reflections by the genious of the philosopher: 1

B3 – (…) “For thinking and being are the same.” (Descartes reached the 2

same conclusion 2000 years later, as the unquestionable knowledge of 3

Reason: “Je pense, je suis”). Let us continue with Parmenides in fragment 4

B4 – “Look as the things afar that by the thinking become present” (words 5

that will be repeated by Immanuel Kant when explaining imagination 6

as a priori form of sensibility) – (…) B6 –It is absolutely necessary that the 7

Being, speaking and thinking exist, nothingness does’not existe this is what I 8

bid you to ponder. Keep a distance from this way of inquiry and also from the 9

one upon which mortals, who know nothing, wander (…) and in whose eyes 10

being and non-being are the same (…) 11

12

Plato overcame this dichotomy by showing us that knowledge is 13

achieved through Dialogue, whose ascensional dialectic movement 14

derives from the sensitive multiplicity from our empirical 15

experience toward the intelligible world, of the Ideas or concepts as 16

intelligible unities. 17

18

Curiously and unexpectedly, in Plato’s Dialogues we can find 19

Piaget’s seminal idea: knowledge is acquired in successive and 20

ascensional moments (dialektikê), starting from an opinion about the 21

sensible world (doxa) towards the épistêmê of the Ideas World. The 22

visible world is a matter of opinion and it is nothing more than an 23

image (éïkôn) of the intelligible world, an imitation of eternal essences. 24

Plato in his mythical and poetic language described a reality 25

demonstrated two thousand or so years later by Jean Piaget. He states 26

that the human capacity to knowledge evolves in a dialectical process, 27

passing from the simple ability to act in the sensitive multiplicity of the 28

empirical world to achieve scientific knowledge made up of concepts as 29

intelligible unities. That accomplishement will be possible only after 30

dialectical evolution of Reason itself as Plato describes. For Piaget 31

knowledge and Reason evolve undefinitely. Some will say that Plato’s 32

Eternal Truths, Essences or Ideas, as indicated by the expression itself, 33

are immutable. Nevertheless, Plato’s Dialogues allow the understanding 34

of dialectical inquire will never completely attain the essences. The 35

dream of attaining absolute knowledge always eludes us as Ideas will 36

never show their real splendor to anyone... Thus, in mythical language, 37

Plato discloses to us his conception of knowledge: for him, knowledge 38

will always evolve… 39

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On the other hand, Dialectics overcomes the dichotomy between 1

the senses and Reason in spite of all knowledge begins with experience, 2

an starter of reminiscences of the World of Ideas; the place and time 3

where the souls lived before their reincarnation. Socrates states in 4

Menon: “ah! How I miss the world of Ideas!” For he had contemplated 5

them better than anyone else, and precisely for that reason his soul once 6

incarnated chose to be a philosopher. Thus, only through Reason can 7

one reach the intelligible world and the episteme, as already mentioned. 8

Or, this ascensional movement will emerge in the epigenetic Piagetian 9

ontogenesis of mental structures towards the acquisition of logical - 10

mathematical knowledge, which can always evolve without ever 11

reaching an end. 12

13

Many centuries later… 14

15

For Descartes, the founder of modern Rationalism, Je pense, je suis is 16

the foundation of his entire philosophy, as the first unquestionable 17

knowledge of Reason, which never passed through the senses. (Ad. & 18

Tan., v. VII, p. 30/32). [It is well known that he removed the word 19

“therefore”, “donc”, so that his statement would not be confused with 20

the conclusion of a medieval syllogism.] This statement stems from “the 21

inspection of the spirit” through which he arrives at a truth without 22

relying on metaphysics or religion. In his view, the senses perceives the 23

sensible world, but this information only becomes Knowledge after 24

“being metabolized” by esprits animaux in the brain (in his original texts 25

that is exactly the word he uses: cerebro, brain). Thought and res extensa 26

or body, are for him “two modes of the same substance”, (cogitatio & 27

extension sumi etiam possunt pro modis substantiae; (Ad & Tan., V. VIII, p. 28

31): however, they had been settled in the philosophical debate since 29

the 18th century such as body and soul, a dualism that contradicts his 30

own claims. On page 41 of the same volume VIII, one can read in a 31

Descartes’ text, translated by us: “everything we perceive through our 32

senses concerns the strict union the soul keeps with the body”. A careful 33

reading of Descartes’ original texts in Latin and Old French displays the 34

farce of a Cartesian dualism. Jean Piaget (1965, p. 72) thus writes: Some 35

think that it was precisely the creation of Analytical Geometry that 36

determined in Descartes’ Philosophy the permanent theme of the 37

relations between understanding and the res extensa, “both inseparable 38

and fundamentally different concurrently”. Piaget demonstrates the 39

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concomitant evolution of the body and Reason, “both inseparable and 1

fundamentally different,” by explaining the epigenetic ontogenesis of 2

mathematical logical thinking in his Genetic Epistemology. 3

Descartes was contradicted by David Hume’s skepticism. The 4

dichotomy initiated by Parmenides and Heraclitus reappears. In 5

addition to placing sensitive experience as the only source of 6

knowledge, Hume, the father of Modern Empiricism, deconstructs the 7

logical link or the physical necessity of the causal relations accepted in 8

his time. 9

Let us remember that Hume’s statements are subsequent to the 10

discoveries and inventions of Copernicus, Galileo, Kepler and Newton. 11

The scientists were interested in explaining the physical world, but their 12

metaphysical convictions loomed above everything and harmonized 13

with their discoveries. Kepler concludes his works with a prayer: “I give 14

Thee thanks, O Lord, for letting me know a small part of the Universe Thou 15

hast created” (apud Werner Heisenberg, 1962, p. 82/97). 16

Immanuel Kant, says Cassirer, came to disrupt this harmony by 17

denying Metaphysics the place it occupied until then asking himself: “Is 18

Metaphysics possible?” And within what limits? What was an 19

indisputable foundation of truth until then becomes a disputable one 20

and analyzed with critical arguments. According to Kant, this is about a 21

revolution in the realms of knowledge, as analogous to the Copernican 22

revolution in Astronomy. Kant does not address himself the question 23

whether knowledge is possible since Mathematics and Physics, for him, 24

are already necessary and universal knowledge; nevertheless, he 25

inquires how they are possible. 26

Cassirer states that with Kant, Logic and dialectics are no longer a 27

simple organon of the knowledge of reality, but also encompasses them 28

in all their fullness and wholeness… “Thus, the orbit of philosophical 29

thought seemed to be complete for the first time after having achieved its goal, 30

the identity between reality and Reason (Cassirer, 1948, p. 10/11). Cassirer 31

proceeds: “Such was the point he believed he had reached in “Hegel’s Science 32

of Logic” (Wissenchaft der Logik, 1812). What Hegel condemned in Kant’s 33

logic and the ones that preceded it was their inability to overcome the purely 34

“formal” point of view, which made them adhere to mere abstraction and 35

reflection. According to Hegel, paving this way does not enable us to leave the 36

circle of subjectivism. It is necessary for the spirit to breathe life into the 37

“skeleton” of logic, to give it nerves and “muscles”. This is precisely what the 38

dialectical method promises, and what only this method is able to deliver.” 39

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Jean Piaget’s Theory of Knowledge 1

2

Jean Piaget’s Genetic Epistemology fulfilled Hegel’s aspirations, as 3

Cassirer understood them, and through a dialectical method, for on 4

explaining the epigenetic ontogenesis of specific organic mental 5

structures for the act of knowing, for the first time in the history of 6

ideas, breathed life in the skeleton of Logic giving it nerves and muscles, thus 7

creating his Theory of Knowledge dreamed of since his adolescence 8

(Piaget, 1918). 9

Piaget’s Theory of Knowledge, in our view, can only be understood 10

if we bear in mind the four moments of his life which determined it: 11

12

1) Firstly, he started his career as a zoologist when he was still a 13

child under the guidance of malacologist Paul Godet and then 14

under the orientation of logician Arnold Reymond. Piaget states 15

that studying under A. Reymond made it possible for him to 16

understand the link of the biological forms to the logical 17

structures in such a perspective that there was no more conflict 18

between them, but instead a close union between organic forms 19

and those of intelligence, i.e., the logical and mathematical 20

thinking. Furthermore, upon studying biometrics Piaget arrives 21

at the conclusion that a qualitative biology remains verbal and 22

that the problem of forms and structures in biology need logical 23

and mathematical models for a true explanation. Afterwards he 24

will proceed to the University. 25

2) The acquaintance of Piaget with Immanuel Kant’s Philosophy at 26

age 21, and the idea of explaining it in the light of Biology as he 27

tells us in an autobiographical text (Piaget, 1960 p. 58/59). Piaget 28

states that he makes three discoveries that modify his naïve 29

biologism: “the first discovery is that if we start with Le Dantec, on 30

the duality of functions, named assimilation and imitation by him; 31

whereas I would say assimilation and accommodation. Knowledge is 32

not merely imitation as he believed in his empiricism, but, in fact, an 33

assimilation to the structures of the subject and the organism. It was 34

gently moving from Le Dantec on to an evolutionary Kantianism.” 35

36

In transposing Kant’s theory into Biology, Piaget will answer that 37

Mathematics and Physics are attainable for humans due to the 38

epigenetic ontogenesis of the logical mathematical thinking. This 39

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ontogenesis, we shall see, consists of a constant process of assimilation 1

and accommodation of the organism and is built in the event of 2

disturbances and requests from the environment, to which it adapts 3

and then becomes unbalanced again due to the capacity of the brain to 4

perceive new stimuli and so expand its world. Initially, these stimuli 5

are present in the environment only, but they are also within the scope 6

of abstract and formal representations of this empirical world. 7

The explanation of this ontogenesis will constitute his Theory of 8

Knowledge based on Biology, dreamed of since adolescence as 9

mentioned previously. 10

Kant tells us that “all knowledge begins with experience, but it does not 11

derive from it,” (1787/1950, p. 31) because, according to him, experience 12

is structured and explained by the categories of Understanding 13

(Verstand) that correspond to those a priori of Pure Reason (Vernunft) 14

and thanks to which, even it is made possible. Understanding connects 15

directly with experience, and Pure Reason is constituted by mental 16

units of the multiple parts, the concepts as formal possibilities of all 17

attainable knowledge. Thus, according to Kant, knowledge would not 18

exist without a priori categories of Reason and the imaginative capacity 19

of humans, (Einbildungskraft) responsible for the “necessary unity of a 20

phenomena-based synthesis” in consciousness. In his view, knowledge is 21

an elaboration of an active thought of the matter of intuition, according 22

to a priori principles, i. e., the application of these principles to sensitive 23

data, which results in their subordination to the forms of consciousness 24

“which knows”, that is, incorporating the result of all intuition and, let 25

us say, of perception, in a unified and systematic set – knowledge. “The 26

requirement that proves itself to be the proper principle of Reason in its logical 27

use is to find, for the conditioned knowledge of understanding, the 28

unconditioned that must lead to unity.” (apud Eisler, R. 1994/1930, p. 888). 29

That would be the condition of all attainable knowledge. 30

For Piaget, knowledge begins with an action which has already 31

been a consequence of an endogenous process, whose primary source is 32

the brain, and therefore it does not derive from it. For Kant, Reason is 33

abstract, whereas in Piaget’s view, it is organic. 34

Piaget also believes in a priori as a condition of all attainable 35

knowledge, but not previously chronologically given; in fact, fully 36

constructed. His conviction that every moment of epigenetic evolution 37

is necessary for the construction of the one that succeeds it, that is, 38

every moment is a priori condition of the next moment. Piaget 39

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understands that the construction of the epistemic subject, dialectically 1

constructed (organism and environment) is richer than Kant’s epistemic 2

subject, ready from the start. (1965, p. 82). 3

4

3) The third decisive moment in Piaget’s life for the construction of 5

his Theory of Knowledge was his internship at the Binet and 6

Simon Laboratory. Then and there he discovered a logic 7

underlying children’s actions: inclusion, addition, multiplication 8

of classes, fitting of transitive asymmetric relations etc., whose 9

model was Couturat’s classical logic he had studied at a very 10

young age. This logic, he realizes, foreshadowed a Logic of 11

Classes and Relations and it was not a matter of abstractions or 12

chimeras, “I saw them being constructed.” (1960, p. 60). A second 13

fundamental finding was that the logic underlying a child’s 14

behavior evolves. Would this logical enrichment come from 15

experience or would it just be a development of inherited 16

possibilities? Or both? 17

18

At the beginning of his internship, Piaget believed that language 19

disclosed the logic of thought; later on he will observe that such logic is 20

present, though underlying actions, organizing them and allowing for 21

findings. Piaget then had the idea of studying children’s behavior from 22

the day of their birth, so he set out to study his first daughter Jacqueline 23

born in 1925, and then carried on with his other two children: Lucienne 24

and Laurent. For more than 10 years of observation he collected data to 25

make his hypotheses precise; he realized that in all kinds of behavior, 26

both in the one that seeks an immediate aim and as in any type of game, 27

children’s actions are not structured randomly but they obey true 28

logical systems that determine their behavior without their being aware 29

of them. Similarly, there are laws ruling our endocrine system without 30

our being aware of them at the level of consciousness. 31

32

4) The fourth decisive moment for the construction of Piaget’s 33

Theory of Knowledge was the research conducted with the 34

lymnaea stagnalis, from 1927 to 1965, (80,000 individuals), 35

published in the 1929 and 1965 Reports, i. e., that research took 36

place in parallel with his observations of his children’s behavior. 37

Why did this work that referred to phylogenesis occur to him at 38

the moment he was busy with ontogenesis? His life story does 39

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not give us a clue, however, we have a hypothesis: in 1926, the 1

Viennese biologist and zoologist, Paul Kammerer, who 2

conducted extensive research with the midwife toad with the 3

intent to demonstrate the inheritance of acquired traits, one of 4

Lamarck’s fundamental ideas, had been accused of fraud and 5

degraded by the neo-Darwinian “scientific community.” 6

Outraged by the accusation and being sure of his honesty, 7

Kammerer commits suicide. Would Piaget not want to pay 8

tribute to the biologist, and as he a zoologist, in order to restore 9

his image by conducting research similar to his own with the 10

Limnaea Stagnalis and confirming his findings? The fact of the 11

matter is that Piaget conducted an investigation which started in 12

1927 and lasted 37 years, with all the refinements of the scientific 13

method. Because the waters of the small pond of Lago in which 14

he conducted it had dried up, he had to interrupt it before 15

detailing his ultimate evidence. (Piaget, 1929, 1965). 16

17

It is absolutely necessary to state that in this article we will not be 18

discussing the concept of epigenesis at the present moment, past or 19

future. Here we will simply adopt Waddington’s concept, as 20

understood by Piaget. 21

22

The end of his research conducted with the lymnaea stagnalis, from 23

1927 to 1965 with 80,000 individuals, was published in the 1965 Report. 24

The first of which had come to light in 1929. The scope of Piaget’s work 25

was to observe snails to verify whether they presented random mutations 26

or not, and also to verify the possibility of the transmission of acquired 27

traits. He had already dreamed of creating a tertium between Lamarck 28

and Darwin at that time (1929, p. 454) since there was a revival of 29

Darwinism back then with his idea of “randomness”, which seemed to 30

contradict everything he had observed as a zoologist. On the other 31

hand, on the same page, 454, he reveals his fascination for Lamarck’s 32

theme, the inheritance of acquired traits. 33

Next we will set out to reproduce, ipsis litteris, some report excerpts 34

published by Piaget in December 1965 on the Lymnaea stagnalis, var. 35

lacustris raised in a small pond on the Vaudois Plateau, (Piaget, 1965). 36

The paragraphs that will be transcribed in this article are the ones we 37

deem most significant for his Theory of Knowledge. 38

His text starts as follows: 39

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Everyone knows that the Lymnaea Stagnalis are bred in the Swiss Great 1

Lakes and in Scandinavia, and that they are a lacustris variety, whose 2

globular shape seems to be linked to water turbulence. In places exposed to 3

waves and on a rocky terrain, every wave causes the animal to adhere to 4

the ground; hence during its growth there is an increase in the opening of 5

its shell and an effort on the animal muscle, which tends to make its spiral 6

smaller, i. e., it contracts. 7

8

In 1929, Piaget had confirmed such statement with a statistical 9

analysis of these variations due to water turbulence, in nature itself, 10

through the environmental changes in the course of the lymnaea’s 11

growth. 12

Piaget states: 13

14

We especially sought to demonstrate that the globular shapes found in the 15

most exposed places of the Neuchâtel and Boden Lakes corresponded to a 16

contracted breed which lived long in aquariums and we named them breed 17

V. A less contracted breed (IV) lives in the same lakes and also in the 18

Leman Lake, besides breeds III, II, and I with greater elongations and that 19

are found in calm waters. 20

This fact raises an interesting question as to whether breed V is 21

constituted independently of any influence of the environment, according 22

to the interpretation of classic mutationists, (the ones who carried on the 23

work of De Vries) about 30 or 40 years ago, why does it not take place 24

elsewhere? (except in turbulent waters?) Nothing would prevent them 25

from keeping their contraction in calm waters where I had transported 26

them. 27

28

Since he started to make his catalogues, says he, he has never 29

observed anything other than the maintenance of the contracted spiral. 30

It was at that time that Guyènot told him, says Piaget: 31

32

“It is not out of the question that mutations for the “contracted” 33

(lymnaea) to appear in various places at random, unrelated to the 34

environment, but for unknown reasons such as oxygen insufficiency, or a 35

harmful effect of the humic acid, they are removed from the calm waters 36

and do not prevail except in the great lakes and more precisely in turbulent 37

waters.” 38

39

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It was then that Piaget decided to begin his experiments with the 1

Lymnaea Stagnalis, according to a rigorous scientific Method and with 2

no deadline for their conclusion. His research lasted 37 years and was 3

discontinued because the pond used for the research had dried up. 4

In July of 1928, on the edge of Plateau Vaudois (Jodillon, at an 5

approximate altitude of 700 m), he placed a “boudin” of breed V eggs 6

(derived from the sixth generation bred in aquariums). The pond there 7

contained just the Lymnaea Peregra. Piaget states: 8

9

In September we were able to collect 20 adult specimens already with a 10

1.39 contraction index (ratio between the longest opening length and the 11

height of the shell, whereas the breed V index is on average 1.43 in the 12

aquarium (the average lacustris index is 1.37 -1.50 and that of the species 13

type is 1.78). From then onwards we carried out periodic observations 14

(prevelement periodique) until 1943, i. e., up to the date the pond dried up. 15

But we managed to keep 527 specimens collected within 15 years, alive or 16

dead, still with their epidermis preserved and that seems to be enough to 17

allow for an opinion, for out of 270 collected specimens in 1943 the average 18

rate of contraction was always 1.39! It then seemed useful to publish the 19

results of that small Lymnaea Stagnalis transplant experiment. 20

21

A first point to examine is the relationship between the individuals that 22

were reared in the pond in Jordillon and those that were reared in 23

aquariums. Let us remember that in the latter, the individuals reared in 24

the aquarium, breed V, came from a scattered population around the Port 25

of Hauterive (Lake Neuchâtel) with an average contraction rate of 1.35. 26

Aquarium breeding provided us with 575 specimens in six generations 27

with an average of 1.43 contraction index; the first and last quartiles were 28

1.385 and 1.495. In contrast, the 527 individuals from Jordillon provided 29

an average of 1.39, a first quartile of 1.34 and a third one of 1.44. Here is 30

the distribution of these two populations, and adding, by comparison, 420 31

specimens of the parent population of Hauterive Monruz; 1.35 on average, 32

first quartile at 1.32 and third at 1.39. 33

Thus, we verified the essential fact that the population bred in the Jordillon 34

and multiplied there for 15 years had not lost any of the contractions as 35

those of its predecessors in aquariums. In contrast, they presented a 36

sharper contraction, in-between the preceding one and that of the parent 37

population living in the lake: the 1.39 average is, in fact, located between 38

the averages of 1.43 and 1.35. If the Jordillon population is a little more 39

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contracted than that of Lake Hauterive, it is naturally because in that 1

parent station there is a certain phenotypic contraction due to the waves, 2

which could be added to the genotypic contraction, whereas the calm 3

waters of the Jordillon ignore that factor. In contrast, if the water 4

turbulence effect does not occur in this pond, there will be another factor to 5

favor the contraction, which is that of the movements within the specific 6

area in which they were found, besides the absence there of the natural 7

plants of the lake. 8

9

Even the elongated shapes when they are forced to move in the autumn 10

contract, slightly, a little more. 11

12

In the case of breed V phenotypes, this agitation factor in the container in 13

which they were located may have had a certain role, added to that of 14

genotypic contraction. That would explain why the population of the 15

Jordillon has become slightly more contracted than that of the aquariums. 16

In fact, we gathered at the Jordillon around 1938 a number of individuals 17

whose shape displayed the widest opening with a specimen reaching up to 18

34.5 mm in maximum shell width to a height of 37.8 mm. This case did 19

not occur in the aquarium. 20

21

In fact, a genotype as such, even in its “pure” lineage, is never directly 22

observed since it is always incarnated in living forms in a given 23

environment and accompanied by seasonal or phenotypic variations: the 24

genotype is simply what is common to all phenotypes of the same breed, 25

and if we know that there is a breed V, it follows that in “pure” lineages 26

and in identical conditions (aquariums of the same shapes and dimensions) 27

it differs from breed I to IV. 28

29

Another hypothesis to explain the apparently great location for the 30

individuals with breed V genotypes consists of assuming that contracted 31

mutations arise anywhere, where, in fact, they would always be dominated 32

on the occasion of their growth by individuals of elongated shapes. 33

However, we were able to show that the growth of breeds I and V (joined, 34

therefore crossbred) does not lead to dominance, but to the first generation 35

of intermediaries with the possibility of further segregation. If breed V 36

arose anywhere, its development should therefore at least lead in 37

the event of crossbreeding to remarkable deviations of the 38

contraction rates in calm waters, which was not observed. 39

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1

After the Jordillon experiment it seems to us, therefore, even more difficult 2

than before to explain (these facts) without resorting to the influence of the 3

environment as breed V is produced only in turbulent places of the 4

Great Lakes since it also could live anywhere. (…) 5

6

This tells us that the problem data raised by our Lymnaea are as follows: 7

8

1) The phenotypic contraction is easily accounted for in nature by a 9

kinetogenesis on the basis of the agitation versus substrate complex. 10

2) In lacustrine stations where this phenotypic contraction is maximum 11

and only in them do we find a genotype (breed V) oriented in the same 12

direction. 13

3) This hereditary modification could take place anywhere since nothing 14

prevents a contracted form from living in calm waters, but nowhere did 15

we find such event. From the probabilistic point of view, could we then 16

admit that the appearance of contracted genotypes occurs by chance only at 17

the points where a maximum phenotypic contraction results from water 18

agitation by kinetogenesis or is there a causal link between these 19

phenotypic and genotypic contractions? 20

21

Here is a special case of countless situations in which an initially non-22

hereditary variation then seems to settle. However, what is interesting 23

about this special case is that it all seems to happen in a merely mechanical 24

domain as that of animal movements in the course of its growth, and the 25

repercussions of this motricity on the shape of the animal; the apparent 26

effect of the environment on the hereditary form simply impacts the most. 27

28

In our 1929 article we were hoping for the advent of a theoretical position 29

that could constitute a “tertium” among the ideas of Lamarck, who 30

explained it all by means of the environment, but not verifying it 31

experimentally, and the classical mutationism of which he only had 32

notions about random atomistic variations unrelated to the environment 33

and their selection subsequent to the event, due to the death or survival of 34

the organisms bearing such variations. Now it seems that we are in the 35

process of reaching a compromising position today (1965) due to 36

population genetics and Waddington’s impacting work. Situating our 37

problem in such perspectives may prove to be interesting. 38

39

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I – The genome currently no longer seems to be considered a collection of 1

discontinuous or atomic elements acting in isolation, but as an organized 2

and, above all, functional system so that the gene does not act alone and 3

that there are, in addition to the structural genes, regulatory (or modifier) 4

genes. Moreover, we have distinguished the mutation units, the 5

recombination units and those of function or cistrons. This system is in 6

continuous active availability since the true mutations (distinct from 7

irrecoverable deficiencies) have a constant rate on average “n” for direct 8

mutations, “v” for reverse mutations, a variable dynamic balance and 9

constitutes a kind of scanning or spontaneous and combinatorial 10

production of all possibilities compatible with the system. In addition, 11

genomes are systems with different forms of balances, imbalances and 12

rebalancing of unfavorable mutations (cf. classical experiment by 13

Dobzhansky and Spasski). 14

15

It is pointless to remember that the synthetic activity of genes in the course 16

of their ontogenetic development staggered in space and time due to games 17

of activations and inhibitions, and whose complex mechanisms we have 18

just begun to catch a glimpse of. 19

20

II – Selection, on the other hand, is no longer conceived of today as a mere 21

absolute screening of the fittest, but a set of processes that modify the 22

proportions conceived in the genome as a probability of life or adaptation. 23

Selection that finally reaches both the regulatory and the structural genes 24

depends on two generally combined factors: 25

26

1 - Indirect factors (also called external or eliminating factors). 27

28

2 – Direct factors (often called internal factors) such as longevity, vigor, 29

plasticity*, etc. depending both on the environment and the organism. 30

31

Above all, as Waddington insisted, selection does not occur in the genes 32

directly, but rather exclusively in phenotypes as an interaction between 33

the genome and the environment. From such a point of view, selection is a 34

choice of the most “capable of responding to the environment.” 35

36

Selection, therefore, constitutes a modification of genetic balance 37

proceeding in a manner comparable to those in which the action of an 38

external factor on the organism was previously conceived, but substituting 39

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the simple causal action for a probabilistic action on the proportions of a 1

multi-unit. In other words, the character that is joined or removed is no 2

longer conceived as an expression of a disjunction or an absolute 3

withdrawal, but as a result of a change of proportions in an 4

organized system. That is why we do not speak of a new mutation 5

anymore, but of a new rebalancing that modifies the genetic system in its 6

entirety. (In fact, it is necessary to reverse the possible emergence or 7

discovery of new genes since their number varies according to groups) 8

III) It follows that we can distinguish two kinds of possible actions of the 9

environment on the genetic system that, in fact, are linked to each other in 10

a continuous manner. Let us suppose a genetic system G that includes, in 11

relation to a medium M modified to M’, three groups of elements 12

(structural, regulatory, etc.): A, etc., neutral; B, etc. favorable and C, etc. 13

unfavorable. The two types of possible actions of the M’ medium are then 14

as follows, assuming that: 15

16

I – Selection in the indirect sense (II of I) eliminates the phenotypes in 17

which C predominates over B and favors those of inverse proportion, that 18

is to say; it eliminates individuals of developed characters c (out of C, etc.) 19

and underdeveloped characters b (out of B, etc.) and favors individuals of 20

inverse characters. 21

22

2- This death or survival of the phenotypes (adaptive values w from 0 to 1) 23

is only a moment of arrival at any given state, of a continuous growth of 24

individuals, and this could already give rise to the same process, but in a 25

more direct way (…) and so forth; there exist several other possibilities for 26

combining these factors. 27

28

What we call “reaction norm” or adaptive norm of a genotype or 29

population is the set of phenotypes that can be produced in the occupied 30

environments depending on the variation of one of the factors of that 31

environment (see figure 1). In the case where the medium restrains M’, it 32

is very distant from others at the end of the reaction norm. 33

34

This displacement difference can result from two processes acting 35

independently or jointly: 1) the first process is the selection by elimination, 36

the phenotypes of character C and not favorable (spiral elongation) are 37

eliminated. Those of characters B (contraction) are favorable, and the 38

growths among a certain number of bearers of this contraction result in a 39

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displacement of the norm because in a normal situation they are lost in a 1

mass of variations of all sorts, hence a weak proportion of character B 2

whereas in a selection by elimination, the proportions change and 3

character B becomes pregnant. 4

5

Throughout the animal growth (…), the actions of the C genes are 6

blocked by medium resistance and the actions of B genes are favored. As 7

the morphogenetic action of genes constitutes a continuous functional 8

process (DNA action on RNA in its various forms and hence on proteins), 9

systematic resistance and reinforcement due to the environment cannot 10

but require successive and contiguous rebalancing (proche-en-proche) 11

about which we do not know how far they date back toward the genome: a 12

“genetic” response in Waddington’s sense can then be produced to pass 13

through a type of a “doorway” for genetic assimilation towards 14

consolidation. Genetic rebalancing can be translated into reorganization 15

and a new response. 16

17

The difference between these two possible processes (1 and 2) is that in 1 18

there is pre-formation of the new characters that appear, and in 2 the 19

rebalancing can be translated into reorganization and a new response. Our 20

lymnaea stagnalis example provides some evidence in favor of solution 2: 21

in fact, at the moment when the contracted breed V can live in the “étants” 22

as in the Jordillon and not only in the lakes; and that breed III still 23

elongated, produces enough individual variations in the lakes; contractions 24

to live under turbulent waters, but without maintaining its contraction in 25

an aquarium. 26

27

It is common to keep a somewhat radical opposition between the synthetic 28

activity of the genome intervening within the epigenetic system, therefore 29

susceptible to variations and the interaction with the environment, and the 30

structure of the invariant genome as in this second example. However, if 31

we simultaneously exclude an integral pre-formation of the variations that 32

reappeared and an entirely random mode of formation; all that there 33

remains for us to do is to appeal to this process 3, without which the notion 34

of response loses its meaning (…) 35

36

The aim of this transposition experiment was to show that the contracted 37

genotype of the lymnaea stagnalis, which were constituted only in the most 38

exposed places to the waves of the Neuchâtel and Constance Lakes, could 39

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survive in calm waters and preserve their contraction “character”. Thus, the 1

following hypothesis falls apart: that such genotypes of breed V could appear 2

anywhere at random, but they would be eliminated in the “marais” or in the 3

small lagoons for several reasons excluding their survival in such 4

environments. 5

6

Piaget who says that, “without referring to the acquired characters in 7

the Lamarckian sense, or the recent studies (1960s) of the action of the RNA on 8

the DNA,” sought to interpret the phenomena he observed with breed 9

V, which advocate in favor of the existence of hereditary variations that 10

followed the phenotypes contracted by the influence of the 11

environment; and that later on the same breed may well live in calm 12

waters preserving their characters, as a phenocopy (phénocopie) (or 13

copy of the phenotype by the genotype). We must now clarify that we 14

shall be discussing the term phenocopy later on, which is not entirely in 15

accordance with Piaget’s explanations, for all through the explanations 16

he provides us, he states that it is not about a “copy” of the phenotype. 17

He must have used this term for lack of a more suitable one within the 18

French language. We shall propose a neologism that could express 19

perfectly well, in English, what Piaget meant concerning the phenotype 20

and its relationship to the genotype: pheno-endogenous requirements, 21

instead of phenocopy, i. e., endogenous requirements of the phenotype. 22

Immediately after using that word which indicates a concept, Piaget 23

continues the report, explaining it and saying that: 24

25

“if the environment engenders a common phenotype, there is no reason for 26

endogenous reconstruction, on the contrary; if the exogenous variation is 27

the source of a more or less profound imbalance, it can affect the regulatory 28

genes corresponding to the modified regions of the organism. There is, 29

then, a repercussion of the imbalance thus created, indicating through a 30

feedback the existence of a disturbance in the syntheses commanded by the 31

genome (…) In this specific case where the phenotype has disturbed the 32

balance of the internal environment; it is the latter that will constitute the 33

selection instruments: there will then be an “organic selection” in 34

Baldwin’s sense and it is then normal for the endogenous variation to end 35

up resembling the phenotype, since it was forced by internal selections to 36

mold itself in the framework modified by the phenotype. In most cases, 37

phenotypes are closely linked to behavior, and in the case of plants, to so-38

called reactive variations, the transition from exogenous to endogenous 39

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thus appears to constitute a general process that occurs in all domains of 1

life.” 2

3

Here is a reference to his research with albino cypresses which, due to 4

having their seeds transplanted from low altitudes to high altitudes, had 5

the length and width of their leaves changed in the generations following 6

the initially altered phenotype. 7

8

In these two cases observed by Piaget, he understands that the phenotypic 9

variation shows a result that reveals not only a threat to the environment, 10

but also a process in which the organism tends to “expand its environment 11

and increase its powers; and in both cases, the final genotype achieves a 12

balance the phenotype only sought” (1974, p. 37). 13

14

In this same work of 1974, Piaget upon narrating his research 15

completed and published in the Report we have transcribed on the 16

Lymnaea, along with the research he had already conducted with 17

humans until 1965, and reported in: The Origin of Intelligence in Children 18

(1936), The Construction of Reality in the Child (1937) and Play, Dreams and 19

Imitation in Childhood, (1942), (in addition to another twenty or thirty 20

studies with children that followed until the publication of the Report 21

transcribed here; cf. Bibliography) comments on p. 39: “Now, how can we 22

not be surprise with the convergence between this biological law that seems 23

general and the work of the forms, even the higher forms of intelligence, whose 24

new constructions rest on information taken not from objects as such, but from 25

actions or the coordination of actions that the subject exerts over objects, which 26

is not the same thing at all, as we will insist later on (…)”. 27

Now, the elaboration of such operating structures on this cognitive 28

terrain has its onset in the actions that are internalized as operations, 29

but performed by mental structures with their capacity to represent, 30

and it is preceded by trials and errors of an empirical nature, as if these 31

corresponded to the initial phenotypic responses and to the operations 32

as the functioning of specific organic mental structures for the act of 33

knowing, such as endogenous, genotypic responses. 34

In the case of a purely biological, concrete “phenocopy”, it is then 35

about a change in the phenotype that can lead to a modification in the 36

genome, which could be accounted for by its own reorganization in 37

response to the information or requirements of the phenotype. With the 38

regard to intelligence, “endogenous” must be understood as a set of 39

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organic structures that are formed from within operations in the 1

environment. 2

Let us synthesize this process that Piaget and Waddington will call 3

– Ontogenetic Epigenesis. This will have its beginning with empirical 4

experience, with the actions of a subject upon the environment to know 5

the world. How does knowledge of the world begin? With the 6

establishment of relationships between objects, never at random, but 7

always displaying the logic presented by Piaget when he observed the 8

boys from the Binet & Simon Laboratory, and who were later observed 9

in several parts of the world by his research assistants, including the 10

members of our Laboratory at USP (University of São Paulo). All these 11

observable logical relations can be called phenotypic and remain 12

unconscious up to 5-6 years of age and then become conscious and 13

verbalized, but still in actions with objects. 14

The important thing is that these logical relationships insensibly 15

passed into the boys’ consciousness and on to their speech, but in what 16

way? Introjected and being represented by their image-making faculty, 17

humans can think about them. Piaget understands this movement as 18

“reflechissante” (that means something that is reflected as an image at a 19

higher level than that of the action that will allow for the rise of 20

deduction.) abstraction. Once aware of these logical relationships, it can 21

be said that the children are in the concrete operational stage, that is, 22

they already know how to operate even if only on objects. This stage 23

will be demonstrated by the formal model of groupings that will precede 24

the coming of human Reason into the structure of the Abelian Group. 25

This stage is explained by the formal model of the INRC Group, in 26

Piaget’s theory. 27

What is the relevance of this coming to the so defined “operational 28

stage”, in Piaget’s Theory? This new capacity means that new organic 29

mental structures specific to the act of knowing have been completed in 30

the organism, and will also determine progress in adaptation. This new 31

equilibrium level is transient because it simultaneously means brain 32

progress that increases the capacity of the individual to perceive new 33

stimuli in the environment, and new relations to be established therein, 34

in a dialectic process: organism x environment, which will determine 35

imbalances and rebalances. The endogenous, organic construction of 36

mental structures here constitutes the genotype which we referred to in 37

the purely organic phenocopy, since the phenotypic information of the 38

logic underlying the actions in empirical experience passes through 39

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reflechissantes abstractions causing the evolution of the functioning of the 1

mental structures in the establishment of logical relations, performed in 2

empirical experience, but it will evolve into logical and mathematical 3

relations independent of objects, according to Jean Piaget. Thus we 4

could observe Maria Gabriella, age 9, verbalizing the following 5

reasoning: (…) “if there is only ‘yes’ and ‘no’, if I say no to ‘no’ I’m saying 6

yes.” (…) this thought occurred to Gabriella spontaneously, it is as if we 7

were watching live the moment of arrival at abstract thinking. 8

The fact that the relations of Classical Logic appear to underlie the 9

behavior of each and every human being, since not even a single case 10

among children living in a society has disproved such observation, 11

leads Piaget to hypothesize that the very functioning of the brain occurs 12

according to Classical Logic. In his own words, Piaget says: 13

14

“In conclusion, the mental activities whose progressive structuring 15

prepares the logical structures thus cover the entire development field (or 16

ontogenetic evolution), which means that logic has its roots situated in a 17

much deeper level than commonly imagined. In pursuing them, we are 18

forced to go back so far that we may ask ourselves whether the integrations 19

proper to the nervous mechanisms are not already an outline of logical 20

fittings.” (…) This leads us to assume that the evolutionary process, which 21

we have referred to, is isomorphic to an organic evolution (1954, p. 22

144/145; Synthèse). 23

24

The originality of Piaget’s hypothesis (1952) is to assume the 25

organic brain functioning as an expression of Classical Logic, for since 26

Aristotle who created logic by observing the arguments of those who 27

discussed in the public Square, up to George Boole it was understood as 28

a set of laws of thought. Subsequently, it will be understood, in general, 29

just as a language. 30

Piaget adds that when looking at contemporary cybernetic models, 31

related to brain activity, appeal to equilibrium processes using the 32

mathematical structures of network and groups, there are indications (or 33

would it be an illusion?) that the evolutionary process of Reason or 34

logical mathematical intelligence in ontogenesis is concomitant with the 35

organic evolution of specific mental structures for the act of knowing. 36

In fact, in the 21st century, we have had important articles on this 37

subject that justly address the Piagetian theory, such as: Aksoy, E. E.; 38

Schoeler, M.; Wörgötter, F. Testing Piaget’s ideas on robots: 39

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Assimilation and accommodation using the semantics of actions. In: 1

Development and Learning and Epigenetic Robotics (ICDL-Epirob), 2014 2

Joint IEEE International Conferences on. IEEE, p. 107-108, 2014. 3

In Piaget’s article Biologie et Connaissance, (1966, p. 4), a summary 4

of the book with the same title he was writing and later published in 5

1967, Piaget says a great many interesting things about his fundamental 6

concern that, for example, when aiming to compare knowledge 7

mechanisms to those of life, he finds that the former ones prolong and 8

use the organic self-regulations from which they derive. Piaget shows 9

us that if his multiple analyses lead him to highlight the continuity that 10

links organic life and cognitive mechanisms, they must also show that 11

they are differentiated and specialized organs of physiological 12

regulations in their interactions with the environment, that is, when 13

prolonging organic structures have special functions, even if they are 14

still biological, until reaching the level of logical and mathematical 15

production, the result of brain functioning, which is organic, but 16

capable of generating purely abstract knowledge; for Piaget physiology 17

ends where logical and mathematical need begins. 18

In this 1966 article, exactly between the end of his research with the 19

Lymnaea Stagnalis and the preparation of his theory of knowledge 20

exposed in Biologie et Connaissance, Piaget seeks to fill a certain gap 21

that could exist between the study of “phenocopy” in phylogenesis and 22

ontogenesis. Actually, what is the link that would link his research with 23

the Lymnaea Stagnalis and children, the human offspring? Right, he 24

reveals to us the isomorphisms between phylogenesis and ontogenesis, 25

but how can we explain the emergence of the conscious logical and 26

mathematical functioning in humans? 27

The text that prepares us for the book Biologie et Connaisance 28

shows us this link. 29

Piaget says that starting from Ethology’s elementary data, animal 30

knowledge is of the “savoir faire” order, or of the useful and practical 31

know-how; instinct essentially consists of: nourishment, protection 32

against the enemy and reproduction, added to the different modes of 33

social organization in the sense of survival of the species and the 34

individual. Perceptual or sensorimotor types of learning do not emerge 35

from a functional framework and the same is true of a large part of 36

practical or sensorimotor intelligence. As we know, mammals sidestep 37

this norm a little and they have their environment expanded by 38

playing. 39

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Human beings expand their environment much more rapidly, but 1

their cognitive processes therein involved go through the expansion of 2

their universe, such as discoveries of other lands, maritime discovery, 3

other continents, and exploration of the universe. What do Physics and 4

Chemistry do other than build knowledge that always goes in this 5

direction of expanding our environment, our universe? It can be said 6

that knowing is expanding the world of the subject who acts, always on 7

the basis of their possibilities, programmed at first but then undergoes 8

changes in function of exchanges with the environment and 9

transmission of new knowledge to their descendants. 10

Wonderful interpretation proposed by Piaget for the mobile 11

structure of knowledge, suitable for both phylogenesis and ontogenesis, 12

and this is the link between both of them: knowing the world around us 13

and thus expand it more and more. 14

Where does the difference between knowledge in other animals and 15

humans, whose achievements are unmatched, begin? Piaget replies: in 16

“éclatement de l’instinct”, (1966, p. 23 and 1967, p. 410), that is, at the 17

outbreak of instinct; in the almost complete disappearance, among 18

anthropoids and human beings, of a totally organic form of knowing 19

that now extends into new forms of regulation that, when overcoming 20

the previous one, do not take their place, but instead preserve it by 21

dividing its components in two complementary directions. With the 22

outbreak of the instinct, the hereditary programming of the form of 23

knowing disappears for the benefit of cognitive, mobile and constructed 24

self-regulations. Knowledge built in ontogenesis starts from the very 25

beginning, but we must not forget that this is a possibility for the 26

human being who is born with certain inherited build, thanks to which 27

they live and want to know the world. This start from the very 28

beginning made theoreticians of logical-mathematical knowledge not 29

even dream of seeking its origin in the functioning of the living 30

organization, “at least before the relationship between the logic of cybernetic 31

models and that of brain functioning, and before McCulloch spoke of neuronal 32

logic,” says Piaget. (1966, p. 25-1967; p. 256/257). 33

Piaget states: There is no exaggeration or metaphor in saying that 34

the nervous reaction ensures the continuous transition between 35

physiological assimilation in its broad sense and cognitive assimilation 36

in the sensorimotor form already. “At all levels, inference is thus at the 37

center of cognitive processes long before the development of general and stable 38

operating structures.” (p. 241). 39

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How did Piaget himself try to demonstrate his biological Theory of 1

Knowledge? 2

Jean Piaget and Jean-Blaise Grize (1972) thought that if it was 3

possible to formally prove that there is an intermediate form of 4

thinking to reason between alogical thinking and human logical 5

thinking; this would be the demonstration of Epigenetic Ontogenesis. It 6

would not be “proving” with actions (with observational facts), but 7

formally. 8

They then demonstrated the existence of an intermediate moment 9

between those sufficiently known moments in the ontogenesis of 10

logical-mathematical thinking: 1st) that of a total absence of logic in the 11

individual’s consciousness, (from birth and continuing in the first years 12

of life, in which a logic underlying the actions is gradually being 13

outlined, but not at the level of consciousness); 2nd) that of the ability to 14

understand abstract relationships that correspond to the structure of the 15

classic Group in mathematics. Many researchers were already aware of 16

that. 17

The great merit of Piaget’s Theory of Knowledge was to detect an 18

intermediate moment between the ones above mentioned, previously 19

unknown to both mathematicians and epistemologists in general, and 20

those dedicated to biological knowledge, including neurologists. This 21

abstract, formal model, named grouping of the intermediate moment 22

between the alogical one of the first years of life and the possibility of 23

thinking according to the properties inherent to the Abelian Group, 24

demonstrates the ontogenesis of logical-mathematical thinking. Until 25

then scholars had not perceived the capacity of children being aware of 26

a logic performed with objects in a concrete world and that corresponds 27

to that of an imperfect Group, underlying their actions and discourse, 28

it is necessarily a precursor to the Abelian Group, the logical relations 29

made aware by the human child are, as shown by Piaget, in this stage of 30

their evolution, still always connected to the concrete level, that is, to 31

their actions. Hence the name given to that intermediate moment Piaget 32

discovered, and that would constitute the very possibilities of the 33

human brain, as the Period of Concrete Logic, expressed in the model he 34

named Groupement, almost a Group, (“Groupe”), but not yet, it lacks 35

some abstract relations in the process of being acquired in the next 36

moment, and not by all human beings. 37

Grouping is then an incomplete mathematical structure that reveals 38

and formalizes the reasoning of the average 7/10 year old children. The 39

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laws expressed in the model designated as Grouping are: composition, 1

reversibility, associativity, and identical operation (which includes 2

tautologies). Epigenetic ontogenesis will lead human beings to the 3

possibilities of reasoning expressed in the model named the INRC 4

Group. Identity relations, iNversion, Reciprocity, and Correlative 5

operations. These would be the essential possibilities of propositional 6

operations, thus allowing the subject to think through hypotheses, 7

verifying or falsifying them. That moment when human beings become 8

capable of thinking according to all the possibilities of the Abelian Group 9

would signal the end of the physiological construction of the human 10

brain. This construction would be ready and the reasoning thereof 11

would no longer be only a result of an organic functioning, but an 12

abstract result of this very functioning. Thus, henceforth, human beings 13

would be able to create new things and understand complex systems in 14

the different areas of Mathematical Logic, Philosophy etc. 15

Here Piaget finds a cognitive phenocopy equivalent to a purely 16

organic phenocopy, in which the operations determined by the 17

functioning of mental structures imitate, copy initially phenotypic 18

behaviors demanded by the pressure of the environment. 19

Piaget explains that in phenocopy, whose real meaning might be 20

pheno-endogenous requirements, actions with objects or facts in the 21

environment affect endogenous processes with repercussions on those 22

that are under construction causing them to evolve. 23

Cognitive phenocopy begins with the construction of mental 24

structures while there is a direct relationship between the cognoscente 25

and the physical environment. However, at some point in the dialectical 26

process, by virtue of which the construction of Reason takes place, the 27

exchange of the organism and the environment is no longer restricted to 28

object as such, but involves concepts. These concepts already 29

correspond to the abstract product of brain functioning; they derive 30

from reasoning, from the ability to develop relationships, products of 31

organic functioning, that is, generated by it. Whether it is about 32

biological or cognitive phenocopies, or reflective abstraction, as 33

previously explained, says Piaget, we find the same mechanism again; a 34

rebalancing by endogenous reconstruction and then overcoming with 35

conservation, (an aufhebung) thanks to a reorganization with new 36

combinations, but whose elements are removed from the previous 37

system. 38

39

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Conclusion 1

2

It is possible for human beings to achieve the necessary and 3

Universal Knowledge, thanks to the exchanges that their organism 4

develops with the environment that give rise to the epigenetic 5

ontogenesis of their specific organic mental structures for the act of 6

knowing. 7

8

9

References 10

11

Adam, C. & Tannery, P. Oeuvres de Descartes, [Descarte’s Works] 12

VRIN, Paris, 1969/1996. XI vols. 13

Cassirer, E. El Problema del Conocimiento, v. IV, De la muerte de Hegel a 14

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problem of Knowledge, From Hegel to present days). 16

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the path to epigenetic innovation. Journal Paradigm. ISSN 1120-18

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Paris, PUF, 1950. 29

Mc Culloch, W.; Pitts, W. A logical calculus of the ideas immanent in 30

neurons activity. Bulletin of Mathematical Biophysics, New York, v. 31

7, p. 115-133, 1943 32

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Structure in the Piaget´s work] Genève, Archives Jean Piaget: S.I.V. 36

2, 64 p., 1972. 37

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Ramozzi-Chiarottino, Z. Et allii, Jean Piaget’s Unrecogized Epigenetic 1

Ontogenesis of the Logical-Mathematical Thought, Athiner’s 2

Conference Paper Series. Athens, LEI, 2017. 3

Trindade dos Santos, J. Fragmentos do poema de Parmênides. 4

[Parmenides Poem Fragments] Gulbekian, Lisboa, 1997. 5

Waddington, C. H. The strategy of the genes. London: George Allen & 6

Unwin Ltd., 1957. 7

Waddington, C.H. The evolution of an Evolutionist. (p. 92) Edinburgh 8

University Press, 1975. 9

10

Piaget’s Works: 11

12

Piaget, J. Recherche, [Research] Lausanne, La Concorde,1918. 13

Piaget, J. Les Races Lacustres de la "Limnaea Stagnalis" - Recherches 14

sur les rapports de l’adaptation héréditaire avec le milieu. [The 15

lake Species of the ‘limnaea Stagnalis’- Reseach on the relationship 16

between heredity adaptation and the enviroment] In: Bulletin 17

biologique de la France et de la Belgique. Vol. 63, n. 3, p. 424-455 – 18

Université de Paris.1929. 19

Piaget, J. La logistique axiomatique ou “pure”, la logistique opératoire 20

ou psychologique et les réalités auxquelles elles correspondent. 21

[The axiomatic logistics or «pure», operational logistics or 22

psychology and the realities to which they correspond] In: 23

Methodos: rivista trimestrali di metodologia e di analisi del linguaggio. 24

Vol. 4, n. 13, p. 72-84, 1952. 25

Piaget, J. Les activités mentales en rapport avec les expressions 26

symboliques logiques et mathématiques. [Mental activities in 27

relation to symbolic, logical and mathematical expressions] In: 28

Synthese, v. 9, issue 2, n. 2, p.144-CLA II, 1954. 29

Piaget, J. Les modèles abstraits sont-il opposés aux interprétations 30

Psycho-physiologiques dans l’explication en psychologie? [Are the 31

abstract models opposed to the psycho-physiological 32

interpretations in psychological interpretation] Revue Suisse de 33

Psychologie pure et appliquée, vol. XIX - Nº 1- Édition Hans Huber, 34

Berne et Stutgart. 1960. 35

Piaget, J. Notes sur des Limnea stagnalis L. var. lacustris Stud: élevées 36

dans une mare du plateau vaudois. [Notes on the Limnaea 37

Stagnallis L. Var. Lacustris stud raised in a pond of Vaudois 38

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Plateau] In: Revue Suisse de Zoologie, v. 72, n. 38- Décembre, p. 1

769/787, 1965. 2

Piaget, J. Sagesse et illusions de la philosophie. [Wisdom and Illusions of 3

philosophy] Paris, PUF, 1965. 4

Piaget, J. Biologie et connaissance. [Biology and Knowledge] In: 5

Diogène. n. 54, p. 3-26, 1966a. 6

Piaget, J. Biologie et connaissance. Essai sur les relations entre les 7

régulations organiques et les processus cognitifs. [Biology and 8

Knowledge: an essay sur les relations between organic relations 9

and cognitive processes.] Paris, Gallimard, 1967a. 10

Piaget, J. et Grize, J.B. Essai de logique opératoire. [Essay by the operative 11

logic] 2e éd. Paris, Dunod, 1972. 12

Piaget, J. Adaptation vitale et psychologie de l’intelligence. Sélection 13

organique et phénocopie. [Vital Adaptation ad psychology of 14

intelligence. Organic selection and phenocopy] Paris, Hermann, 15

1974. 16

Piaget, J. Essai sur la nécessité. [An Essay on the necessary knowledge] 17

Archives de Psychologie, Université de Genève, CH. XLV, 175, p. 18

235/245, 1977. 19


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