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Prolegomena to the study of Hegel's philosophy and especially of his logic online

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keeps out of sight his other qualities. Our notions in
this way are more abstract or more concrete, according
as our grasp of thought extends to less or more of the
relations which are necessarily pre-supposed by them.
On the other hand, when a term of thought owns and
emphasises its solidarity with others, when it is not
circumscribed to a single relation, but becomes a focus
in which a variety of relations converge, when it is
placed in its right post in the organism of thought, its
limits and qualifications as it were recognised and its
degree ascertained, — then that thought is rendered 'con-
crete.' A concrete notion is a notion in its totality,
looking before and after, connected indissolubly with
others : a unity of elements, a meeting-point of opposites.
An abstract notion is one withdrawn from everything
that naturally goes along with it, and enters into its
constitution. All this is no disparagement of abstrac-
tion. To abstract is a necessary stage in the process
of knowledge. But it is equally necessary to insist on
the danger of clinging, as to an ultimate truth, to the
pseudo-simplicity of abstraction, which forgets alto-
gether what it is in certain situations desirable for a
time to overlook.

In a short essay, with much grim humour and quaint
illustrations, Hegel tried to show what was meant by
the name ' abstract,' which in his use of it denotes the
cardinal vice of the ' practical ' habit of mind. From
this essay, entitled ' Who is the Abstract Thinker ' ? '
it may be interesting to quote a few lines. 'A murderer
is, we may suppose, led to the scaffold. In the eyes
of the multitude he is a murderer and nothing more.
The ladies perhaps may make the remark that he is

' ' Wer denkt abstrakt \ ' {Vermischte Schrifien, vol. ii. p, 40a.)


a Strong, handsome, and interesting man. At such
a remark the populace is horrified. " What ! a murderer
handsome ? Can anybody's mind be so low as to call
a murderer handsome? You must be little better your-
selves." And perhaps a priest who sees into the heart,
and knows the reasons of things, will point to this
remark, as evidence of the corruption of morals pre-
vailing among the upper classes. A student of character,
again, inquires into the antecedents of the criminal's
up-bringing : he finds that he owes his existence to ill-
assorted parents ; or he discovers that this man has
suffered severely for some trifling offence, and that
under the bitter feelings thus produced he has spurned
the rules of society, and cannot support himself other-
wise than by crime. No doubt there will be people
who when they hear this explanation will say " Does
this person then mean to excuse the murderer ? " In
my youth I remember hearing a city magistrate com-
plain that book-writers were going too far, and trying
to root out Christianity and good morals altogether.
Some one, it appeared, had written a defence of suicide.
It was horrible ! too horrible ! On further inquiry it
turned out that the book in question was the Sorrows of

' By abstract thinking, then, is meant that in the
murderer we see nothing but the simple fact that he is
a murderer, and by this single quality annihilate all the
human nature which is in him. The polished and
sentimental world of Leipsic thought otherwise. They
threw their bouquets, and twined their flowers round
the wheel and the criminal who was fastened to it. —
But this also is the opposite pole of abstraction. — It
was in a different strain that I once heard a poor old
woman, an inmate of the workhouse, rise above the
abstraction of the murderer. The sun shone, as the



severed head was laid upon the scaffold. "How
finely," said the woman, " does God's gracious sun
lighten up Binder's head ! " We often say of a poor
creature who excites our anger that he is not worth
the sun shining on him. That woman saw that the
murderer's head was in the sunlight, and that it had
not become quite worthless. She raised him from the
punishment of the scaffold into the sunlit grace of God.
It was not by wreaths of violets or by sentimental
fancies that she brought about the reconciliation : she
saw him in the sun above received into grace.'



Induction and Experience are names to which is
often assigned the honour of being the source of all our
knowledge. But what induction and experience consist
in, is what we are supposed to be already aware of; and
that is — it may be briefly said — the concentration of the
felt and sense-given fragments into an intimate unity.
The accidents and fortunes that have befallen us in
lapses of time, the scenes that have been set before and
around us in breadths of space, are condensed into
a mood of mind, a habitual shading of judgment,
or frame of thought. The details of fact re-arrange
themselves into a general concept ; their essence gets
distilled into a concentrated form. Their meaning
disengages itself from its embodiment, and floats as
a self sustaining form in an ideal world. Thus if we
look at the larger process of history, we see every
period trying to translate the sensuous fact of its life
into a formula of thought, and to fix it in definite
characters. The various parts of existence, and exist-
ence as a whole, are stripped of their sensible or factual
nature, in which we originally feel and come into
contact with them, and are reduced to their simple
equivalents in terms of thought. From sense and
immediate feeling there is, in the first place, generated
an image or idea which at least represents and stands
for reality ; and from that, in the second place, comes

X 2

3o8 PROLEGOMENA. [xxil.

a thought or notion proper, which holds the facts in

The phenomenon may, perhaps, be illustrated by the
case of numbers. To the adult European, numbers and
numbering are an obvious and essential part of our
scheme of things that seems to need no special ex-
planation. But the experience of children suggests
its artificiality, and the evidence from the history of
language corroborates that surmise. If number be in
a way describable as part of the sense-experience, or
total impression, it certainly does not come upon us
with the same passivity on our part as the perception of
taste or colour, or even of shape. It postulates a higher
grade of activity. As Plato says, it ' awakes the intelli-
gence ' : it implies a question and looks forward to an
answer : it is thus the first appearance of what in its
later fullness will be called ' Dialectic' To put it
otherwise : Numbering can only proceed where there is
a unit, and an identity : it implies a one, and it implies
an infinite repetibility of that one '. It thus postulates
the double mental act, first of reducing the various to its
basis of identity, and, secondly, of performing a synthesis
of the identical units thus created. In the highly artificial
world in which we live all this seems simple enough.
The products of machinery, articles of furniture, dress,
&c., &c., are already uniform items : and the strokes
of a clock seem almost to invite summation. But in
free nature this similarity is much less obviously
stamped on things : and the products of primitive art —
of literal manu-facture — display an individuality, an
element of personal taste, even, which is necessarily
lacking in things turned out by machinery. Thus it
was necessary, before we could number, to reduce the
qualitatively different to a quantitative equality or com-

' See vol. ii. p. igo, (^Logic, § 102).


parability. There are indeed some instances, in that
nearest of things to us, the human body, which might
help. There is the obvious similarity of organs and
limbs which go in pairs, and which might easily suggest
a dual, as, so to speak, a sensuous fact amongst other
facts. Again, there is the hand and its five fingers, or
the two hands and the ten fingers. The five or ten, as
a whole naturally given, suggest a grouping of numbers
in natural aggregates. The fingers, again, (and here
we may keep at first to the fingers proper, minus the
thumb,) may be without much ingenuity said to give us
a set of four, naturally distinct, yet naturally alike, and
needing, so to speak, the minimum of intelligence to
create the numerical scale from one to four. It is by
them, indeed, that Plato, it may be unconsciously,
illustrates the genesis of number. Here in short you
have the natural abacus of the nations, but one re-
stricted, first, perhaps to the group 1-4, secondly to the
group I -10.

We have seen how the dual was, in certain instances,
almost a natural perceptive fact. But when it is so
envisaged, it is hardly recognised as number strictly so
called. It is only a fresh and peculiar sensuous at-
tribute of things : a thing which has the quality of
duplication, not a thought which is the synthesis of
two identical units. It is a sort of accident, not part
of a regular system or series. So again with the plural,
which may appear in several shapes before it is as-
signed to its proper place as a systematic function of
the singular. If the Malay, in order to say 'the king
of all apes ' has to enumerate one after another the
several sub-species of ape, or if to express ' houses ' he
has to reduplicate the singular, to insert a word mean-
ing ' all ' or ' many,' we can see that the conception of
number is for him still in the bonds of sense. It is not

310 PROLEGOMENA. [xxil.

a synthetic category, but only a material multitude.
But in other cases the plural proper is almost con-
founded with the so-called 'collective.' It is not an
unfamiliar fact in Greek and Latin that the plural has
acquired a meaning of its own, — not the mere multiple
of its singular; as also that the collective term is
occasionally used as an abstract, occasionally as the
more or less indeterminate collection of the individuals.
Such plurals and such collectives represent a stage of
language and conception when the aggregate of singu-
lars form a uniquely-qualified case of the object. And
the peculiarity of them is seen in the way the plurality
is immersed in and restricted to the special class of
objects : as e. g. when in English the plurality of
a number of ships is verbally stereotyped as against the
plurality of a number of sheep, or of partridges (fleet,
flock, covey). In such instances the category of
number is completely pervaded and modified by the
quality of the objects it is applied to. So, in the
Semitic languages, the so-called ' broken plural ' is
a quasi-collective, which grammatically counts as a
feminine singular (like so many Latin and Greek
collectives) : and whereas the more regular plural is
generally shown by separable affix, this quasi-collective
plural enters the very body of the word by vowel-
change, indicating as it were by this absorption the
constitution of a specifically new view of things. On the
other hand, it may be said, there is in this collective
a trace of the emergence of the universal and identical
element through the generalisation due to the con-
junction of several similars all acting as one'.

In a true plural, on the contrary, it is required that the
sign of number be clearly eliminated from any peculiari-
ties of its special object, and be distinctly separated

' See Max Muller in Mind, vol. i. 345.


from the collective. And similarly the true numeral
has to be realised in its abstractness, as a category
per se. And to do this requires some amount of
abstraction. In Greek, for example, we meet the dis-
tinction between numbers in the abstract, pure numbers
(such as four and six), and bodily or physical numbers
(such as four men, six trees) '. The geometrical aspect
under which numbers were regarded by the Greeks,
e. g. as oblong or square numbers, bears in the same
direction. But another phenomenon in language tells
the tale more distinctly ^ Abundantly in Sanscrit and
Greek, more rarely in Zend and Teutonic, and here
and there in the Semitic languages, we meet with what
is known as the dual number, a special grammatical
form intended to express a pair of objects. The witty
remark of Du Ponceau ' concerning the Greek dual,
that it had apparently been invented only for lovers
and married people, may illustrate its uses, but hardly
suffices to explain its existence in language. But
a comparison of barbarian dialects serves to show that
the dual is, as it were, a prelude to the plural, — a first
attempt to grasp the notion of plurality in a definite
way, which served its turn in primitive society, but
afterwards disappeared, when the plural had been
developed, and the numerals had attained a form of

' Pure number is apiS/id! fiovaSmos : applied number is dpiSfios
tpvaiKis or aai/uiTiKoi. Aristotle, Metaph. N. 5, speaks of afiBjxiri
vipivos ^ ■yrj'ivos. But this is only Greek idiom : as we say ' Greek
history' instead of 'History of Greece,' or vice versa, when we
translate Populus Romanus by ' people of Rome.' Aristotle is
speaking of 'proportions' or 'amounts' of fire or earth in the
compounds of these elements.

^ See L. Geiger, Ursprung und Entwkkelung der menschlichen
Sprache und Vernunft (vol. i. p. 380). And Gabelenz (' Die me-
lanesischen Sprachen ') in the Abhand'.ungen der Sdchsischen Gesell-
schaft der Wissenschaften (VIII), 1861, pp. 89-91.

^ Memoire sur le systeme grammatical, &c. p. 155.



their own. If this be so, the dual is what physiologists
call a rudimentary organ, and tells the same story as
these organs do of the processes of nature.

The language of the Melanesian island of Annatom,
one of the New Hebrides, may be taken as an instance
of a state of speech in which the dual is natural. That
language possesses a fourfold distinction of number in
its personal pronouns, a different form to mark the
singular, dual, trial, and plural : and the pronoun of the
first person plural distinguishes in addition whether the
person addressed is or is not included in the ' we-two,'
'we-three,' or ' we-many ' of the speaker'. The same
language however possesses onlythefirst three numerals,
and in the translation of the Bible into this dialect it
was necessary to introduce the English words, four,
five, &c. The two facts must be taken together : the
luxuriance of the personal pronouns and the scanty
development of numerals in such languages are two
phenomena of the same law. The numeral ' four ' to
these tribes is said to bear the meaning of ' many ' or
' several.' Another fact points in the same direction.
In many languages, such as those of China, Further
India and Mexico, it is customary in numbering to use
what W. von Humboldt has called class-words. Here
it is felt that an artificial unity has to be created,
a common denominator found, and all reduced to it,
before any summation can be carried out. Scholars
and officials, in Chinese, can only be classed under the
rubric of 'jewel' or dignity: and animals or fish by
'tails,' as if thereby only could one get a handle to hold

' Cf. nous and nous autres. The same distinction is found in some
American languages. There is a dual in the language of the Green-
landers ; but it is not, however, used when a natural duality seems to
call for it, but in cases when, though there might have been several
things, only two are actually found.


them and count them. (The idiom still lingers in
western languages : as in English, heads of cabbage, or of
cattle : or German, sechs Mann Soldaten.) So in Mala}',
instead of 'five boys' the phrase used is 'boy five-man':
in other words, the numerals are supposed to inhere as
yet in objects of a special kind or common occurrence'.
And among the South Sea Islanders the consciousness
of number is decidedly personal : that is to say, the
distinction between one and two is first conceived as
a distinction between ' I ' and ' we two.' Even this
amount of simplification surpasses what is found
amongst som.e Australian tribes. There we find four
duals : one for brothers and sisters : one for parents
and children : one for husbands and wives : and one
between brothers-in-law •'. Each pair has a different
form. We thus seem to see to what early language is
applied : not to designate the objects of nature, but the
members of the primitive family and their interests.
The consciousness of numbers was first awakened by
the need of distinguishing and combining the things
that belonged to and specially interested men and
women in the narrow circle of barbarian life ^ It is
not altogether imaginative in principle, though it may
be occasionally surmise in details, to connect the rise
of grammatical forms with the temperament and char-
acter of the people, and therefore with its social
organisation. If the Bantoo or Caffir languages of
Southern Africa instead of a single third personal

' W. von Humboldt, Verschiedenheit des nienschlichen Sprachbaues,
p. 423 (ed. 1841); Misteli, Typen des Sprachbaues (1893).

^ Capt. Grey, Vocabulary of the dialects of S. IV. Australia, pp. xxi
and 104 (1840).

' The sharp distinction between the first and second personal
pronouns and the third : the want of any apparent connexion in
the Indo-Germanic languages between the first and second persons
singular and the plural form seems to point in the same direction.


pronoun and third personal termination to the verb
use the separate forms corresponding to the ten class-
prefixes of the nouns, it must be in accordance with the
general spirit and system of these tribes. The various
plural forms, if they persist, will reflect contemporary
modes of life.

Numbers were at first immersed in the persons, and
then, as things came to be considered also, in the
things numbered. The mind seems to have proceeded
slowly from the vague one to definite numbers. And
the first decided step was taken towards an appre-
hension of numbers when two was distinguished from
one, and the distinction was made part of the personal
terminations. The plural was a further step in the
same direction : the real value of which, however, did
not become apparent until the numerals had been sepa-
rately established in forms of their own. When that
was accomplished, the special form of the dual became
useless : it had outlived its purpose, and henceforth it
ceased to have any but that poetical beauty of old asso-
ciation which often adorns the once natural, but now
obsolete growths of the past. When the numerals were
thus emancipated from their material and sensuous
environment, quantity was translated from outward
being in its embodiments into a form of thought. At
first, indeed, it was placed in an ethereal or imagi-
native space, the counterpart as it were of the sensuous
space in which it had been previously immersed. It
became a denizen of the mental region, as it had been
before a habitant of the sense-world.

The mind was informed with quantity in the shape of
number : but it does not follow from this, that the new
product was comprehended, or the process of its pro-
duction kept in view. Like all new inventions (and
numeration may fairly be classed under that head), it


was laid hold of, and all its consequences, results, and
uses estimated and realised by the practical and defining
intellect. In one direction, it became, like many new
inventions in the early days of society, a magic charm,
and was invested with mystery, sacredness, and mar-
vellous powers. But the intelligent mind,— the under-
standing,— resolved to make better use of the new
instrument : and that in two ways, in practical work
and in theory. On the one hand it was applied prac-
tically in the dealings of life, — in commerce, contracts,
legislation, and religion. On the other hand, the new
conception of number, which common sense and the
instinctive action of men had evolved, was carried out
in all its theory : it was analysed in all directions, and
its elements combined in all possible ways. The result
was the science of arithmetic, and mathematics in
general. Such consequences did the reflective under-
standing derive from the analysis of its datum, — the
fact of quantity freed from its sensuous envelope.

The general action of understanding, and of practical
thought, is of this kind. It accepts the representative
images which have emerged from sensation, as they
occur : and tries to appreciate them, to give them
precision, to carry them into details, and to analyse
them until their utmost limits of meaning are explored.
Where they have come from, and where they lead to, —
the process out of which they spring, and which fixes
the extent of their validity, — are questions of no interest
to the understanding '. It takes its objects, as given in
popular conception, as fixed and ultimate entities to be
expounded in detail.

We have taken number as one example of the trans-
ference of a sensible or sense-immersed fact into a form
of thought : but a form which is still placed in a supe-

' Cf. vol. ii. Notes and Illustrations, p. 400.

3l6 , PROLEGOMENA. [xxil.

rior or mental space. One advantage of taking number
as illustration, is that numbered things are distinguished
from numbers in an emphatic and recognised way.
Nobody will dispute that the abstraction, as it is called,
has an existence of its own, and can be made a legiti-
mate object of independent investigation. But if the
process be more obvious in the case of the numerals,
there must have been a similar course of development
leading to the pronouns, the prepositions, and the
auxiliary verbs — to what has been called the ' formal '
or ' pronominal ' or ' demonstrative ' element, the con-
nective and constructive tissue of language. Whether
these pronominal ' roots ' form a special and originally-
distinct class of their own, or are derived from a trans-
mutation of more material or substantial elements, is
a question on which linguistic research casts as yet no ■
very certain light. It is true that on the one hand
etymology is mainly silent on the origin of pronouns,
numerals, and the more fundamental prepositions (i. e. can-
not refer them to roots significant of qualitative being) :
and one need not lay much stress on remarks, like that
of Gabelenz ', that in the Indo-Chinese languages the
words for /, five, fish have a like sound, as do those for
thou, two, ear, or that / am, originally means / breathe.
In all languages — though with immense diversities of
degree, this formal element has attained a certain inde-
pendence. And in many instances we can more or less
trace the process by which there grew up in language
an independent world of thought : we can see the
natural existence passing out of the range of the senses
into spiritual relations. Before our eyes a world of
reason is slowly constituting itself in the history of
culture : and we, who live now, enter upon the inherit-
ance which past ages have laid up for us.

' Die Sprachwissensthaft, p. i68.


There is, however, a difference between the way in
which these results look to us now, and the way in
which they originally organised themselves. The child
who begins to learn a language in the lesson-books and
the grammars finds the members of it all, as it were,
upon one level : adjectives, adverbs, prepositions, and
verbs confront him with the same authority and rank.
This appearance is deceptive : it may easily suggest
that the words are not members in an organism, in and
out of which they have developed. And this organism
of thought has its individual tjrpes, expressed in the
great families of human speech. Its generic form (as
drawn out in a logical system) appears in different
grades, with different degrees of fullness, in Altaic and
Dravidian from what it does in Malay, or in Chinese,
and these again have their own predominant categories
as compared with those used in the American or
African languages, or in Indo-Germanic and Semitic.
If the Altaic languages e. g. are wanting in the verb
proper, and manage with possessive suffixes and nouns ;
if the Semitic tenses display a poverty which contrasts
with their wealth in Greek ; and yet each group per-
forms its function, we may infer that each speech has
a complete organism, though it does not bring all its
parts to adequate expression. All this distinction of
'parts of speech,' of forms, prefixes and suffixes, &c., is

Online LibraryWilliam WallaceProlegomena to the study of Hegel's philosophy and especially of his logic → online text (page 24 of 36)