It is easy to demonstrate the extreme inadequacy of such a view of the
+concept+, which Hegel ridicules, with facts relating to the psychology of
development of the mental capacities of the child.
[89] These facts show that such an understanding does not bear comparison
even with elementary mental activity, even with mental activity based on
the simplest mathematical concepts.
Contemporary soviet psychology (we have in mind the series of experimental
studies carried out by colleagues of MGU over recent years) has reliably
demonstrated that the process of mastery by the child of the capacity to
operate with concepts, the capacity to reflect sensuously given facts in
concepts, can in no way be reduced to the process of mastering the capacity
to operate with words and the abstractions contained in them.
The child, for example, learns quite early on to count objecs which are
given to him in sensation, to produce the most simple sum.
He will name three matches or three sweets identically with the word
+three+. Furthermore, he very quickly learns the operation of +addition+:
taking three matches and three buttons and putting them together in a heap
he may count them and, having counted them, name the heap of different
kinds of objects lying in in view in front of him by the word +six+.
This means that he has already learnt to carry out a quite complex
operation of abstraction, the produce an abstraction which abstracts from
the objects given to him in sensation only their quantitative
determination, has learnt to carry out a socially significant abstraction
and to fix it in the word.
According to the logic of empiricism, he is already in possession of the
+concept+: in fact one may see in his mental actions the whole structure of
the nominalistic conception of the concept. He abstracts the +general+,
calls it by a word, and moreover this is the very kind of +general+ feature
which is uniquely important and +essential+ from the point of view of the
tasks which are given to him to solve.
But at this stage he has still not mastered mathematical concepts. The
simplest experiment demonstrates this. A sign of the absence at this stage
of the ability to operate with the concept of number contained and
expressed in the words +three+, +six+, etc, is the complete inability of
the child to effect the simplest operation of addition +in the head+.
Initially he is obliged to produce the sensuous-practical counting of
objects added together in a heap, begining again from the +unit+ even
though he knows very well that in this heap he himself added together
+three+ and +three+.
[90] At this stage the words +one, two, three,...six+ for him in themselves
are unconnected [something or other] to what is sensuouly given, have
absolutely no meaning or sense. The only meaning of these words is the
meaning of externally attached signs, nothing more. The child counts the
objects in a sensuous-practical way, and the words only accompany, in
parallel, his sensuous-practical actions. He still has not mastered to any
degree the simplest mathematical concept of +three+. But he has perfectly
well mastered the word +three+ and the ability to abstract the abstraction
which corresponds to this word. He will very easily use the word +three+ to
designate three sweets, or three pencils, or three toys. He is already
able, when somebody says the word +three+ to him, to evoke in his own
sensuous imagination the image of three objects, irrespective of which
objects they are, and is already able to count these objects again on plan
of sensuously represented reality. That is, he is already able, using the
word which brings forth in his consciousness a sensuously represented
image, to count objects represented in sensation. With the word he actively
evokes in his imagination a sensuous picture of three objects and counts
them one after the other on the plane of sensuous representation.
But here precisely is contained the fatal point for the teacher proceeding
on the basis of the Lockean conception of the concept. The child ...??? has
learnt to count +in his head+ - he raises his eyes to the ceiling and
whispering to himself, +puts together+ three and three and gets six. Does
this mean that he has mastered the concept of +three+? Is he operating with
the concept as the highest form of mental processing of sensuously given
facts? For teaching and the teacher this is not an idle question, not just
and not so much a theoretical +nicety+. On the answer to this question
depends the plan for the whole further pedagogical influence on
consciouness in the process of formation.
Experimental tests reliably show that the child does not have the concept
at this stage. Those operations which appear to the teacher who bases
himself on the Lockean conception of thinking, to be actions with the
concept, in fact are only actions on the plane of sensuous representation
based on the word. The word functions here as a sign, as a signal, evoking
in living imagination the sensuous-concrete image of the [91] thing. With
this form of imagination, evoked by the word, and certainly not with the
concept, the child carries out a counting operation.
This fact can be shown by the simplest test. It is enough to ask the child
to +add together+ not three and three - this is a comparatively easy thing
to +represent+ to oneself in living imagination - but larger numbers, let
us say one hundred and eight, for action on the plane of representation to
fail. The child starts by trying to represent sensuously and then to count
a heap of objects, starting from units... But this is a task for which it
is not only the child+s head which fails in the attempt. This means that
the word, designating a sensuously given totality, +heap+ of objects
(sensuously contemplated or sensuously represented) still does not play
the role of a concept for the child. It still does not carry within itself
that special, higher spiritual reality with the help of which sense data
are processed by man on the plane of logical activity. It does not contain
in compressed instantaneous form, cognitive actions, does not serve the
child as a really generalized image of reality with which he could act in
place of the immediately tangible reality. It, the word (and the
abstraction contained within it) here simply designates the sensuously
given image or evokes it in the imagination. The child is not acting with a
concept but initially with a sensuous representation. The words which the
child whispers to himself in this way, finding in them support for sensuous
images, only passively and in parallel accompany his actions on the plane
of imagination, designate these actions and that sensuous reality with
which he acts. But this is still not the whole story. Later on the child
learns to forget altogether about the sensuously imagined objects. He
counts not matches, not sweets, even imaginary ones, but effects a purely
verbal count. But here, the word, its phonetic sound, functions as a purely
mechanical replacement for the sensuously represented object. The sounds
+one+, +two+, +three+ for him play the same role which sensuously tangible
objects played heretofore. And he uses these word-objects in exactly the
same way as he used sweets or matches. To start with he cannot immediatly
add +in his head+ two and three. He whispers to himself the whole quantity
given to him, starting each time again from the unit. He is incapable of
being immediately aware of three as three. He must again, before +adding+
them up -
[92] sensuously reproduce this +three+ in his imagination. He whispers once
more: +one+, +two+, +three+ and only when he has arrived again at this
point adds +...four, five!+.
The last word he pronounces out loud, as the word coinciding with the place
in the counting operation. The words +four+ and +five+ for him are here
sensuously perceived word-objects. Having carried out, after the word
+three+, another two steps in the count, two steps which he whispers to
himself, he stops and pronounces the word +five+ out loud.
The mechanics of this counting operation are very complex, and demand a
large effort from the child, a lot of strain, the more the quantity to be
counted is higher. After the word +three+ he has to carry out the
following: he knows that he still has to carry out two more steps, the
first of which is called +four+ and the second +five+. Whispering the word
+four+ to himself, he has to make a note to himself that this is not only
+four+ but also step number +one+ after the first three. Each step in the
counting operation suddenly acquires two different numerical designations:
+four (ie one after three)+, and +five (ie two after three+, and +six (ie
three after three)+, etc.
+Addition+ carried out in such an unwieldy fashion demands considerable
work and effort from even the adult. Each of the sensuously counted +units+
acquires two different names which have to be borne in mind simultaneously;
it is not easy to connect them, to +add+ in such a way when the numbers are
bigger.
+Seventeen, that is twenty three; eighteen that is twenty four; nineteen,
that is twenty five+ - this is the kind of complex and {>>} artificialy
operation which is carried out in his head. In the course of this operation
he must constantly remember at which step in the sequence +after three+ he
must stop, and must remember that he must pronounce out loud not the number
which corresponds to the first set of units being counted, but another
number, another word which is connected to the first only accidentally, in
a way that is different each time. In one case he may have to remember that
+two+ is in fact (in the second series) not +two+ but seventeen, and in
another case when adding different numbers he may have to whisper +two,
that is seven+ or +two, that is forty four+ and so on.
[93] This use of two different names for one and the same mental action
constitutes at this stage the mechanics of counting in addition. Two
entirely unconnected, apart from the unique conditions of the task, series
which are counted in parallel are made manifest, each of which begins from
the +unit+. It+s not difficult to understand why the child often goes wrong
when adding. A so-called +conflictual situation+ arises in consciousness,
demanding the maximum amount of attention, memory, will, concentration. All
the usual canons of +mental actions+ for the child collapse - he must call
one and the same thing by two different names and must understand the
+meaning+ precisely in this.
And all these collisions are the result of the fact that he does not really
have the concept but only the word which abstractly generalizes the
sensuously perceived or sensuously imagined reality. He is obliged to
resolve a logical task with the help of illogical means - with the help of
the word which designates the abstractly general sensuous
representation...
In this case, at this stage of mental development, he has to do with the
purest quantitative abstraction, fixed by the corresponding verbal
designation or term. From the word +three+ (+five+, +eight+ etc) have
already evaporated all traces of the sensuously perceived properties of
things. But then this very word, its phonetic sound envelope, has
transformed itself for him into a special sensuously perceived object, with
which he acts exactly in the same way that he acted earlier with the match
or with the sweet. He acts with an abstraction of the purest water,
expressed in the word. The word itself becomes for him a special reality
with which he may act in the same way as with the real sweets. The more so
that the adults reward his successful actions precisely with sweets...
But if he is in possession of the word and the abstraction which it
contains, is he in possession of the concept?
Not at all. Rather the concept is +in possession+ of him. It is the adult,
who really is in possession of the concept, who puts the child into
artificially created conditions within which the child must act,
correcting him all the time and guiding each of his mental steps.
Here often the adult is not properly aware himself of how complex the
processes happening in the child+s head are, of by what stages
[94] the process of mastering concepts is being realized in the child+s
head.
It is clear that the process of aquiring the concept is really being
effected only in the course of resolving tasks, the conditions of which are
created by the adult and are given to the child in the form of
sensuously-practical conditions within which he is obliged to act.
In the course of solving these tasks the child acquires the modes of ideal
action, which correspond to the complex nature of the concept. In this way
he ultimately acquires the concept.
But it is clear that he is not in a position to carry out any logical (in
the full meaning of the word) actions until a certain time. Until a certain
time he acts only on the plane of representation, basing himself on the
word and not more. He is still not in possession of the concept as a
special +object+ which allows him to carry out logical actions.
And consequently he is not in a position to carry out even the most
elementary logical actions with the abstraction which is expressed in the
word.
He has acquired the word +three+ very well and very confidently; he no
longer makes mistakes with the word, does not call eight matches or five
sweets with the word. With such confidence he will take just three objects
(of whatever kind) if he is offered them. This abstraction he carries out
completely exactly and also the reverse operation - preparing the sensuouly
given abstraction which corresponds to that abstraction (takes and places
before himself exactly the given quantity).
But he may not act with it as with the concept, may not solve +in his head+
the simplest task in addition or subtraction. He must initially evoke in
the imagination, basing himself on the word, the whole sensuously tangible
collection of +units+ embraced by the name +three+ and act with just this
collection.
But this collection does not serve him as a really generalized, really
compressed expression of reality with which he could act instead of with
the sensuousy given reality. It does not serve him as a tool with the help
of which he could actively process sense data in a compressed fashion,
without repeating over and over again the fruitless methodical counting
operation, without beginning right from the beginning again each time from
units.
[95] He is not aware of the fact that in the number +three+ the counting
operation has alreadly been done, that the number three is the expression
of an already accomplished counting operation, is the result in which this
counting operation is contained.
All this shows that the concept is something more than an
abstractly-general, many times repeated sensuously perceived sameness,
expressed in a word (or term or name).