Exposition of Constructivism: Why Some Like it
Scientific Reasoning Research Institute
University of Massachusetts
Man, having within
himself an imagined World of lines and
numbers, operates in it with abstractions, just
as God, in the universe, did with
When the Neapolitan philosopher
Giambattista Vico published his treatise
on the construction of knowledge, it triggered quite a
controversy in the Giornale
de' Letterati d'Italia, one of the most
journals at the time. This was in the years 1710-12. The
first reviewer, who remained anonymous,
had carefully read the treatise and was obviously
shocked by the implications it had for traditional
epistemology-- all the more so
because, as he conceded, the arguments showed great learning and
were presented with elegance. He was therefore impelled
to question Vico's position, and he very
politely suggested that one thing was
lacking in the treatise: the proof that
what it asserted was true.
Today, those constructivists who are "radical" because they take their
theory of knowing seriously, frequently meet the same objection--except that it
is sometimes expressed less politely than at the beginning of the 18th
century. Now, no less than then, it is difficult to show the critics that what
they demand is the very thing constructivism must do without. To claim that
one's theory of knowing is true, in the traditional sense of representing a
state or feature of an experiencer-independent world, would be perjury for a
One of the central points of the theory is
precisely that this kind of "truth", can never be claimed for the knowledge
(or any piece of it) that human reason produces. To mark this radical
departure, I have in the last few years taken to calling my orientation a
theory of knowing rather than a "theory of knowledge". I agree
Noddings when she says, at the beginning of her contribution
to this volume, that radical constructivism should be "offered as a
post-epistemological perspective". One of the consequences of
such an appraisal, however, must be that one does not persist in
arguing against it as though it were or purported to be a traditional theory of
Another consequence--for me the more important one--is that constructivism
needs to be radical and must explain that one can, indeed,
manage without the traditional notion of Truth. That this task is possible,
may become more plausible if I trace the sources of some of the ideas that
made the enterprise seem desirable.
In retrospect, the path along which I picked up relevant ideas
(somewhat abbreviated and idealized) led from the early doubts of the
Pre-Socratics, via Montaigne, Berkeley, Vico, and Kant, to thinkers who
developed instrumentalism and pragmatism at the turn of this century,
and eventually to the Italian Operational School and Piaget's genetic epistemology.
The Way of the Sceptics
To Xenophanes (6th century B.C.) we may credit the insight
that even if someone succeeded in describing exactly how the world really
is, he or she would have no way of
knowing that it was the "true"
This is the major argument the sceptics have repeated for two thousand
five hundred years. It is based on the assumption that whatever ideas or
knowledge we have must have been derived in some way from our experience,
which includes sensing, acting, and thinking. If this is the case, we have no
way of checking the truth of our knowledge with the world presumed to
be lying beyond our experiential interface, because to do this, we
would need an access to such a world that does not involve our experiencing
Plato tried to get around this by claiming that some god had
placed the pure ideas inside us and that experience with the fuzzy,
imperfect world of the senses could only serve to make us "remember" what was
Thus, there would be no need (and no way) to check our
knowledge against an
independent external reality. Consequently, in Plato's famous
metaphor, the man who is led out of the cave of his commonplace experience
is blinded by a splendid vision. But his vision is the pure realm of an
interpersonal soul and not the fuzzy world perceived by the
point of view, Plato created an ingenious poetic or "metaphysical" myth, but
not a rational theory of knowing.
The sceptics position, developed into a school under Pyrrho at
the end of the next century, was diligently compiled and documented by
Sextus Empiricus about 200 A.D. It smoldered under the theological debates of
the middle ages and burst into full flame in the 16th century when the works
of Sextus Empiricus were rediscovered. Descartes set out to put an end
to it, but succeeded only in strengthening the side he was opposing (cf.
The British Empiricists then helped to harden the sceptical
doctrine by their detailed analyses. First, Locke discarded the secondary
(sensory) properties of things as sources of "true" information about
the real world.
Then, Berkeley showed that Locke's arguments applied equally
to the primary properties (spatial extension, motion, number,etc.), and
finally Hume delivered an even more serious blow by attributing the notion
of causality (and other relations that serve to organize experience) to
the conceptual habits of the human knower. The final demolition of realism
was brought about when Kant suggested that the concepts of space and time
were the necessary forms of human experience, rather than
characteristics of the universe. This meant that we cannot even imagine what the
structure of the real world might be like, because whatever we call structure
is necessarily an arrangement in space, time, or both.
These are extremely uncomfortable arguments. Philosophers
have forever tried to dismantle them, but they have had little success. The
arguments are uncomfortable because they threaten a concept which we feel we
cannot do without. "Knowledge" is something of which we are quite sure
that we have a certain amount, and we are not prepared to relinquish it. The
trouble is that throughout the occidental history of ideas and right down
to our own days, two requisites have been considered fundamental in any
epistemological discussion of knowledge. The first of these requisites demands
we would like to call "true knowledge" has to be independent
of the knowing subject. The second requisite is that knowledge is to be taken
seriously only if it claims to represent a world of
"things-in-themselves" in a more
or less veridical fashion. In other words, it is tacitly taken
for granted that a fully structured and knowable world "exists" and that
it is the business of the cognizing human subject to discover what that
The weakness of the sceptics' position lies in its polemical
It always sounds as though the traditional epistemologists'
definition of knowledge were the only possible one. Hence, when Montaigne
says "la peste de
l'homme c'est l'opinion de savoir" (mankind's plague is the
conceit of knowing), it sounds as though we ought to give up all
knowing. But he was
referring to absolutistic claims of experiential knowledge and
was discussing them in the context of the traditional dogmatic belief that
religious revelation is unquestionable. He had in mind absolute truth,
and he was castigating those who claimed that a rational interpretation
of experience (of which "scientific observation" is, after all, a
sophisticated form) would lead to such truth. He certainly did not intend to
discredit the kind of know-how that enabled his peasants to make a good
In short, what the sceptics failed to stress was that, though
no truths about a "real" world could be derived from experience,
experience nevertheless supplied a great deal of useful knowledge.
The Changed Concept of Knowledge
Unbeknownst to Kant, who in the 1780s hammered this limitation in
with his Critiques of pure and practical reason, Giambattista Vico
had come to a very similar conclusion in 1710. The human mind can know only
what the human mind has made, was his slogan and, more like Piaget than Kant,
he did not assume that space and time were necessarily a priori
categories, but suggested that they, too, were human
constructs (Vico, 1858).
Pursuing this way of thinking, one is led to what I have
called "a reconstruction of the concept of knowledge" (von Glasersfeld,
1985). Some reconstruction is needed because, on the one hand, one can no
longer maintain that the cognizing activity should or could produce a
true representation of an objective world, and on the other, one
does not want to end up with a solipsistic form of idealism. The only way
out, then, would seem to be a drastic modification of the relation between the
cognitive structures we build up and that "real" world which we are
inclined to assume as "existing" beyond our perceptual
interface. Instead of the
illusory relation of "representation", one has to find a way of
relating knowledge to
reality that does not imply anything like match or
Neither Vico nor Kant explicitly mentioned such a conceptual
It was supplied, however, in Darwin's theory of evolution by
the concept of fit. Once this relational concept has been stripped of its
erroneous formulation in the slogan "survival of the fittest" (cf.
Pittendrigh, 1958; von Glasersfeld, 1980), it offers a way around the paradox of
the traditional theory of knowledge. As far as I know, this was
first suggested by Willam
James (1880). Georg Simmel (1885) elaborated it,
and Aleksandr Bogdanov (1909) developed it into a comprehensive
instrumentalist epistemology. Hans Vaihinger (1913), who had been working at
of As If" since the 1870s and who probably was quite unaware
of Vico, reintroduced the idea of conceptual construction.
Today, in retrospect, these and other authors can be cited as
"sources" of constructivism. However, the great pioneer of the
constructivist theory of
knowing today, Jean Piaget started from Kant and arrived at
his view of cognition as a biologist who looked at intelligence and
knowledge as biological functions whose development had to be explained and
mapped in the ontogeny of organisms.
In interpreting Piaget, it is important to remember that his
publications range over an astounding variety of topics and are spread over
more than half a century. As with any versatile and original thinker,
his ideas did not cease to develop and change (Vuik, 1981). It is,
therefore, not surprising that one can spot contradictions in his work. An
obvious instance is his theory of stages, which was gradually superseded by his
theory of equilibration (cf. Rowell, in press). Thus it is not too
difficult to dismiss Piaget on the strength of one or two quotations; or,
what is even more frequent, on the strength of what superficial summarizers
have said about him. It is also likely that arguments about what Piaget
actually believed will continue and that different scholars will
provide different interpretations. In my view, the following basic principles of
radical constructivism emerge quite clearly if one tries to comprise
as much as possible of Piaget's writings in one coherent theory
− but I
would argue for these principles even if they could be shown to diverge from
||Knowledge is not passively received either through the
senses or by
way of communication;
||knowledge is actively built up by the cognizing subject.
||The function of cognition is adaptive, in the biological
the term, tending towards fit or viability;
||cognition serves the subject's organization of the
world, not the discovery of an objective ontological reality.
One cannot adopt these principles casually. If taken
seriously, they are
incompatible with the traditional notions of knowledge, truth,
and objectivity, and they require a radical reconstruction of
one's concept of reality. Instead of an inaccessible realm beyond perception
and cognition, it now becomes the experiential world we actually live in.
This world is not an unchanging independent structure, but the result of
distinctions that generate a physical and a social environment to which, in
turn, we adapt as best we can.
Consequently, one cannot adopt the constructivist principles
as an absolute truth, but only as a working hypothesis that may or
may not turn out to be viable. This is the main reason why the constructivist
orientation is unequivocally post-epistemological (Noddings, this volume).
The Concept of Viability
To relinquish the inveterate belief that knowledge must
eventually represent something that lies beyond our experience is,
indeed, a frightening step to take. It constitutes a feat of decentering
that is even more demanding than the one accomplished by a few outstanding
thinkers in the 16th century who realized that the earth was not the center of
the universe. Because it goes against an age-old habit, it is
immensely difficult to accept that, no matter how well we can predict
the results of certain actions we take or the "effects" of certain "causes"
we observe, this must never be interpreted as a proof that we have
discovered how the "real"
The key to this insight lies in what Piaget formulated in the
phrase "l'objet se laisse faire" ("the object allows itself to be
treated"; 1970; p.35) At the symposium on the occasion of his 80th birthday he
repeated the phrase and explained it further: "When one comes to have a
true theory, this is because the object permitted it; which amounts to saying
that it contained something analogous to my actions." (Inhelder et al.
In this context − as in so many in Piaget's works
− it is
important to remember that an "object" is never a thing-in-itself for
Piaget, but something that the cognizing subject has constructed by making
distinctions and coordinations in his or her perceptual field
That is all very well, one might say, but how does it come
about that the reality we construct is in many ways remarkably stable?
And, one might also ask why, if we ourselves construct our experiential
reality, can we not
construct any reality we might like? The first question was
answered in a categorical way by George Kelly: "To the living creature,
then, the universe
is real, but it is not inexorable unless he chooses to
construe it that way" (1955; p.8). The living creature, be it fish, fowl, or
human, thrives by abstracting regularities and rules from experience that
enable it to avoid disagreeable situations and, to some extent, to generate
agreeable ones. This "abstracting of regularities" is always the result
of assimilation. No experience is ever the same as another in the
absolute sense. Repetition and, consequently, regularity can be
obtained only by disregarding certain differences. This notion of assimilation
is at the core of Piaget's scheme theory. No schemes could be developed if
the organism could not isolate situations in which a certain action leads
to a desirable result. It is the focus on the result that distinguishes a
scheme from a reflex and makes possible the form of learning that Piaget
called accommodation. It takes place when a scheme does not lead to
the expected result. This produces a perturbation, and the perturbation may
to a modification of the pattern that was abstracted as the
"triggering situation" or to a modification of the action. All this, I
want to emphasize, concerns the experiential world of the acting
organism, not any "external" reality. And the patterns a cognizing organism can
and does abstract from experience depend on the operations of
distinction and coordination the organism can and does
brilliantly demonstrated for a variety of organisms more than fifty years
ago by Jakob von Uexküll (1933/1970).
The second question − why we cannot construct any
reality we like − can be raised only if the concept of viability is misunderstood or
ignored. The absurdity of solipsism stems from the denial of any relation
between knowledge and an experiencer-independent world.
Constructivism has been careful to stress that all action, be it physical or
conceptual, is subject to constraints. I can no more walk through the desk in
front of me than I can argue that black is white at one and the same time.
What constrains me, however, is not quite the same in the two
cases. That the desk
constitutes an obstacle to my physical movement is due to the
particular distinctions my sensory system enables me to make and to the
particular way in which I have come to coordinate them. Indeed, if I now
could walk through the desk, it would no longer fit the abstraction I have made
in prior experience. This, I think, is simple enough. What is not so
simple is the realization that the fact that I am able to make the
and coordinations and establish their permanence in my
does not tell me anything other than the fact that it is one
of the things my experiential reality allows me to do. Using a spatial
metaphor, I have at
times expressed this by saying that the viability of an action
shows no more than that the "real" world leaves us room to act in that way.
Conversely, when my actions fail and I am compelled to make a physical or
conceptual accommodation, this does not warrant the assumption that my
failure reveals something that "exists" beyond my experience. Whatever
obstacle I might conjecture, can be described only in terms of my own
actions. (In this context, it is important to remember that the constructivist
theory holds that perception is not passive, but under all circumstances
the result of action; cf. Piaget, 1969.)
The constraints that preclude my saying that black is white
are, of course, not physical but conceptual. The way we use symbols to
handle abstractions we have made from experience, requires among
other things that we exclude contradiction (cf. von Glasersfeld, in press).
Consistency, in maintaining semantic links and in avoiding contradictions, is
an indispensable condition of what I would call our "rational
The Question of Certainty
The domain of mathematics is in some sense the epitome of the
rational game. The certainty of mathematical results has often been
brought up as an argument against constructivism.
To indicate that the theoretical infallibility of mathematical
operations (in practice, mistakes may, of course, occur) cannot be
claimed as proof that
these operations give access to an ontological reality, I have
compared this generation of certainty to the game of chess. At the painful
moment when you discover that your opponent can put you into a "checkmate"
position, you have no way of doubting it and your shock is as real as any
shock can be.
Yet, it is obvious that the certainty you are experiencing
springs from nothing but the conceptual relations that constitute the rules
of the game; and it is equally obvious that these conceptual relations
are absolute in the sense that if I broke them and thus destroyed the
certainty they generate, I would no longer be playing that particular game.
The comparison with chess has caused remonstrations, and I
would like to clarify my position. I still believe that the certainty in
mathematics springs from the same conceptual source, but this does not
mean that I hold mathematics to be like chess in other ways. The biggest
difference is that the elements to which the rules of chess apply are all
specific to the game. Flesh and blood kings cannot be put into
"mate" positions, equestrian knights move unlike their chess
namesakes, and living
queens show their power in ways that are inconceivable on the
In contrast, the elements to which the rules of mathematics
are applied, are not free inventions. In counting, for example, the elements
start out as ordinary things that have been abstracted from ordinary
experience, and the
basic abstract concepts, such as "oneness" and "plurality",
have a life of their own before they are incorporated in the realm of
mathematics. It is precisely this connection with everyday experience and
that leads to the contention that mathematics "reflects" the
The "imagined world of lines and numbers" of which Vico speaks
in the quotation I have put at the beginning of this essay, is in no
sense an arbitrary world. At the roots of the vast network of
mathematical abstractions are the simple operations that allow us to
perceive discrete items in the field of our experience, and simple relational
concepts that allow us to unite them as "units of units". On subsequent
levels of abstraction, the representations of sensory-motor material of
everyday experience (Piaget's "figurative" elements) drop out, and
what remains is the purely "operative", i.e., abstractions from operations.
None of this is developed in a free, wholly arbitrary fashion.
Every individual's abstraction of experiential items is constrained
(and thus guided) by social interaction and the need of collaboration
and communication with other members of the group in which he or
she grows up.
No individual can afford not to establish a relative fit with
the consensual domain of the social
An analogous development takes place with regard to
mathematics, but here
the social interaction specifically involves those who are
active in that field. The consensual domain into which the individual must
learn to fit is that of mathematicians, teachers, and other adults insofar as
they practice mathematics. The process of adaptation is the same as in other
social domains, but there is an important difference in the way the
degree of adaptation can be assessed. In the domain of everyday
living, fit can be demonstrated by sensory-motor evidence of successful
interaction (e.g. when
an individual asked to buy apples, returns with items that the
other recognizes as apples). The only observable manifestation of
the demand as well as of the response, in the abstract reaches of the domain
of mathematics, are symbols of operations. The operations
themselves remain unobservable. Understanding can therefore never be demonstrated by the
presentation of results that may have been acquired by rote
This is one of the reasons why mathematics teachers often
insist (to the immense boredom of the students) on the exact documentation of
the algorithm by means of which the result was obtained. The flaw in this
procedure is that any documentation of an algorithm is again a sequence of
symbols which in themselves do not demonstrate the speaker's or writer's
understanding of the symbolized operations. Hence, the production of such a
sequence, too, may be the result of rote learning.
Other contributions to this volume will illustrate how a
constructivist approach to instruction deals with this problem. They will
also show that the constructivist teacher does not give up his or her role as a
guide − but this leadership takes the form of encouraging and orienting
the students' constructive effort rather than curtailing their autonomy by
presenting ready-made results as the only permitted path.
Here, I would merely stress the sharp distinction which, in my
view, has to be made between teaching and training. The first aims
at the students' conceptual fit with the consensual domain of the
particular field, a fit which, from the teacher's perspective, constitutes
understanding. The second aims at the students' behavioral fit which, from the
teacher's perspective, constitutes acceptable performance. This is not
to say, that rote learning and the focus on adequate performance should
have no place in
constructively oriented instruction. But it does mean that, where the domain of mathematics is concerned, instruction that focuses on
performance alone can be no better than trivial.
If one seriously wants to adopt the radical constructivist
orientation, the changes of thinking and of attitudes one has to make are
formidable. It is also far from easy to maintain them consequentially. Much
like physical habits, old ways of thinking are slow to die out and tend to
In everyday living we don't risk much if we continue to speak
of lovely sunsets and say that tomorrow the sun will rise at such and
such a time − even though we now hold that it is the earth that
moves and not the sun. Similarly, there is no harm in speaking of knowledge,
mathematical and other, as though it had ontological status and could be
"objective" in that
sense; as a way of speaking this is virtually inevitable in
the social interactions of everyday life. But when we let scientific
knowledge turn into belief and begin to think of it as unquestionable dogma,
we are on a dangerous slope.
The critics of Copernicus who argued that his system must be
"wrong" because it denied that the earth is the center of the
universe, could not claim to be "scientific"
− they argued in that way for
political and religious reasons. Science, as Bellarmino pointed out,
and as such, they may or may not be useful. Their use may also
be temporary. The science we have today, holds that neither the
earth nor the sun has a privileged position in the universe. Like the
contemporary philosophers of science, constructivists have tried to learn
from that development and to give up the traditional conception of
knowledge as a "true" representation of an experiencer-independent state of
That is why radical constructivism does not claim to have found an
ontological truth but merely proposes a hypothetical model that may turn
out to be a useful one.
Let me conclude with a remark that is not particularly
relevant to the teaching of mathematics but might be considered by educators
Throughout the two thousand five hundred years of Western
epistemology, the accepted view has been a realist view. According to it, the
human knower can attain some knowledge of a really existing world and can
use this knowledge to modify it. People tended to think of the world as
governed by a God who would not let it go under. Then faith shifted from God
to science and the world that science was mapping was called "Nature" and
believed to be ultimately understandable and controllable. Yet, it was
also believed to be so immense that mankind could do no significant harm to it.
Today, one does not have to look far to see that this attitude has
endangered the world we are actually experiencing.
If the view is adopted that "knowledge" is the conceptual
means to make sense of experience, rather than a "representation" of
something that is supposed to lie beyond it, this shift of perspective brings
with it an important corollary: the concepts and relations in terms of
which we perceive and conceive the experiential world we live in are
necessarily generated by ourselves. In this sense it is we who are responsible for
the world we are experiencing. As I have reiterated many times,
radical constructivism does not suggest that we can construct anything
we like, but it does claim that within the constraints that limit our
construction there is room for an infinity of alternatives. It therefore does not
seem untimely to suggest a theory of knowing that draws attention to the
knower's responsibility for what the knower constructs.
Anonymous (1711), Osservazioni, Giornale de'Letterati
d'Italia, 5(6). (reprinted in Vico, 1858; p. 137-140 ).
Bogdanov, A. (1909) Science and philosophy. In (anonymous
editor), Essays on the philosophy of collectivism, Vol.1. St. Petersburg.
Diels, H. (1957) Die Vorsokratiker. Hamburg: Rowohlt.
Feyerabend, P. (1987) Farewell to reason. London/New York:
Inhelder, B., Garcia, R., & Voneche, J. (1977) Epistemologie
genetique et equilibration. Neuchatel/Paris: Delachauz et Niestle.
James, W. (1880), Great men, great thoughts, and the
Monthly, 46, 441-459.
Kelly, G.A. (1955) A theory of personality - The psychology of
personal constructs. New York: Norton.
Kitchener, R. (1989), Genetic epistemology and the prospects
for a cognitive sociology of science: A critical synthesis, Social
Epistemology, 3(2), 153-169.
Maturana, H. (1980) Biology and cognition. In H.Maturana & F.
Varela, Autopoiesis: The organization of the living. Dordrecht:
Montaigne, Michel de (1972) Essais, Vol.2. Paris: Librairie
Piaget, J. (1937 La construction du reel chez l'enfant.
Neuchatel: Delachaux et Niestle.
Piaget, J. (1969) Mechanisms of perception. (Translation by
G.N.Seagrim) New York: Basic Books.
Piaget, J. (1970) Le structuralisme. Paris: Presses
Universitaires de France.
Pittendrigh, C.S. (1958), Adaptation, natural selection, and
behavior. In A.Roe & G.G.Simpson (Eds.), Behavior and evolution. New
Haven, CT: Yale University Press.
Plato, Great dialogues of Plato (1956). New York: New American
Popkin, R. (1979) The history of scepticism from Erasmus to
Spinoza. Berkeley/Los Angeles: University of California Press.
Rowell, J.A. (1989), Equilibration and the teaching of
science, Synthese, 1989; in press.
Simmel, G. (1895) Ueber eine Beziehung der Selectionslehre zur
Erkenntnistheorie, Archiv für systematische Philosophie, 1,
Vaihinger, H. (1913) Die Philosophie des Als Ob. Berlin:
Reuther & Reichard.
Vico, G.-B. (1858) De antiquissima Italorum sapientia (1710)
Naples: Stamperia de'
von Glasersfeld, E. (1980), Adaptation and viability, American
Psychologist, 35(11), 970-974.
von Glasersfeld, E. (1985), Reconstructing the concept of
knowledge, Archives de Psychologie, 53, 91-101.
von Glasersfeld, E. (1989) Abstraction, representation, and
reflection. In L.P.Steffe (Ed.) Epistemological foundations of
mathematical experience. New York: Springer, in press.
von Uexküll, J. 1970 Streifzüge durch die Umwelten von Tieren
und Menschen (with Georg Kriszat). Frankfurt am Main: Fischer. (Originally
published in 1933).
Vuyk, R. (1981) Overview and critique of Piaget's genetic
epistemology, Vols. 1 & 2. New York: Academic Press.
1. Vico's reply to his critics, included in the 2nd edition of
De Antiquissima Italorum Sapientia, 1711; reprinted in Vico (1858)
2. De Antiquissima Italorum Sapientia, Naples, 1710; reprinted
with Italian translation, 1858.
3. Giornale de'Letterati d'Italia, 1711, vol.V, article VI;
reprinted in Vico (1858), p. 137.
4. cf. Hermann Diels (1957), Xenophanes, fragment 34.
5. cf. Plato's "The Republic" in Great Dialogues of Plato
(1956), p. 312ff.
6. Montaigne wrote this in his Apologie de Raymond Sebond
(1575-76); cf. Essais, 1972, vol.2,, p.139.
7. Though most philosophers, today, would agree that the
ontological realm is perceptually inaccessible, they balk at Kant's suggestion
that it is also conceptually inaccessible to us. They are therefore still
stuck with the paradox that they have no way of showing the truth of
the ontological claims they make.
8. This reference was brought to my attention by a personal
communication from Jacques Voneche (Geneva, 1985).
9. See, for instance, Kitchener's recent article (1989) on
Piaget's early work on the role of social interaction and exchange.
10. Paul Feyerabend's recent comment (1987) on the famous
letter Cardinal Bellarmino wrote in the context of Galileo's trial,
makes this point in exemplary fashion: "To use modern terms: astronomers
are entirely safe when saying that a model has predictive advantages over
another model, but they get into trouble when asserting that it is
therefore a faithful image of reality. Or, more generally: the fact that a
model works does not by itself show that reality is structured like the
11. The focus on "operations of distinction" is a major
contribution of Humberto Maturana's biological approach to cognition (1980);
the notion as such, however, is implicit in much of Piaget's work, e.g,, his
Mechanisms of perception (1969).
12. Lest this be interpreted as a concession to realism, let
me point out that, in the constructivist view, the term "environment"
always refers to the environment as experientially constructed by the
particular subject, not to an "objective" external world.
13. Thinking, conceptual development, understanding, and
meaning are located in someone's head and are never directly observable. A
formidable confusion was generated by the behaviorist program
that tried to equate meaning with observable response.