identicals, disparates, primitives, and derivatives, etc._]
This is not the place to dwell upon the other forms of concepts met
with in Logic, known as _identical_ concepts, which cannot be anything
but synonyms, or words;--or upon _disparate_ concepts, which are simply
distinct concepts, in so far as they are taken in a relation, which
is not that given in the distinction, and is therefore arbitrary, so
that the concepts, thus presented without the necessary intermediaries,
appear disparate;--or _primitive and derived concepts, or simple and
compound concepts_; a distinction which does not exist for the pure
concepts, since they are always simple and primitive, never compound or
derived.
[Sidenote: _Universals, particulars, and singulars. Intension and
extension._]
But the distinction of concepts into _universal, particular,_ and
_singular_ deserves elucidation, for the reason that we are now
giving. Concepts, which are only universal, or only particular, or
only singular, or to which any one of these determinations is wanting,
are not conceivable. Indeed, universality only means that the distinct
concept is also the unique concept, of which it is a distinction and
which is composed of such distinctions; particularity means that the
distinct concept is in a determinate! relation with another distinct
concept; and singularity that in this particularity and in that
universality it is also itself. Thus the distinct concept is always
singular, and therefore universal and particular; and the universal
concept would be abstract were it not also particular and singular. In
every concept there is the whole concept, and all other concepts; but
there is also one determinate concept. For example, beauty is spirit
(universality), theoretic spirit (particularity), and intuitive spirit
(singularity); that is to say, the whole spirit, in so far as it is
intuition. Owing to this distinction into universal, particular, and
singular, it is self-evident that intension and extension are, as the
phrase is, in inverse ratio, since this amounts to repeating that the
universal is universal, the particular particular, and the singular
singular.
[Sidenote: _Logical definition._]
The interest of this distinction of universality, particularity, and
singularity lies in this, that upon it is founded the doctrine of
_definition,_ since it is not possible to define, that is, to think
a concept, save by thinking its _singularity_ (peculiarity), nor to
think this, save by determining it as _particularity_ (relation with
the other distinct concepts) and _universality_ (relation with the
whole). Conversely, it is not possible to think universality without
determining its particularity and singularity; otherwise that universal
would be empty. The distinct concepts are defined by means of the one,
and the one by means of the distinct. This doctrine, thus made clear,
is also in harmony with that of the nature of the concepts.
[Sidenote: _Unity, distinction as circle._]
But the theory of the distinct concepts and that of their unity still
present something irrational and give rise to a new difficulty.
Because, if it be true that the distinct concepts constitute an ideal
history or series of grades, it is also true that in such a history
and series there is a _first_ and _last,_ the concept _a,_ which opens
the series, and, let us say, the concept _d,_ which concludes it.
Commencement and end thus remain both without motive. But in order
that the concept be unity in distinction and that it may be compared
to an organism, it is necessary that it have no other commencement
save itself, and that none of its single distinct terms be an absolute
commencement. For, in fact, in the organism no member has priority over
the others; but each is reciprocally first and last. Now this means
that the symbol of _linear series_ is inadequate to the concept; and
that its true symbol is the _circle,_ in which _a_ and _d_ function, in
turn, as first and last. And indeed the distinct concepts, as eternal
ideal history, are an eternal going and returning, in which _a, b, c,
d_ arise from _d,_ without possibility of pause or stay, and in which
each one, whether _a_ or _b_ or _c_ or _d,_ being unable to change its
place, is to be designated, in turn, as first or as last. For example,
in the Philosophy of Spirit it can be said with equal truth or error
that the end or final goal of the spirit is to know or to act, art or
philosophy; in truth, neither in particular, but only their totality
is the end; or only the Spirit is the end of the Spirit. Thus is
eliminated the rational difficulty, which might be urged in relation to
this part.
[Sidenote: _Distinction in the pseudoconcepts._]
It is still better eliminated, and the whole doctrine of the pure
concepts which we have been expounding is thereby illumined and thrown
into clearer outline when we observe the transformation (which we will
not call either inversion or perversion), to which it is submitted in
the doctrine of the pseudoconcepts. It is therefore expedient to refer
rapidly to this for the sake of contrast and emphasis.
Above all, certain distinctions, which in the doctrine of the pure
concepts have been seen to be without significance or importance,
find their significance in the doctrine of the pseudoconcepts. We
understand, for instance, how and why _identical_ concepts can be
discussed; since, in the field of caprice, one and the same thing,
or one and the same not-thing, can be defined in different ways
and give rise to two or more concepts which, owing to the identity
of their matter, are thus identical. The concept of a figure having
three angles, or that of a figure having three sides, are identical
concepts, alike applicable to the triangle; the concept of 3 x 4 and
that of 6 x 2 are identical, since both are definitions of the number
12; the concept of a feline domestic animal and that of a domestic
animal that eats mice are identical, both being definitions of the cat.
It is likewise clear how and why _primary_ and _derived, simple_ and
_compound_ concepts are discussed; for our arbitrary choice, by forming
certain concepts and making use of these to form others, comes to posit
the first as simple and primitive in relation to the second, which are,
in their turn, to be considered as compound or secondary.
[Sidenote: _The subordination and co-ordination of the empirical
concepts._]
We have already seen that the arbitrary concept differs from the pure
concept in that, of necessity, it produces two forms by the two acts of
empiricism and emptiness and thereby gives rise to two different types
of formations, empirical and abstract concepts. Empirical concepts
have this property, that in them unity is outside distinction and
distinction outside unity. And it is natural: for if it were the case
that these two determinations penetrated one another, the concepts
would be, as we have already noted, not arbitrary, but necessary and
true. If the distinction is placed outside the unity, every division
that is given of it is, like the concepts themselves, arbitrary;
and every enumeration is also arbitrary, because those concepts can
be infinitely multiplied. In exchange for the rationally determined
and completely unified distinctions of the pure concepts, the
pseudoconcepts offer multiple groups, arbitrarily formed, and sometimes
also unified in a single group, which embraces the entire field of the
knowable, but in such a way as not to exclude an infinite number of
other ways of apprehending it.
In these groups the empirical concepts simulate the arrangement of
the pure concepts, reducing the particular to the universal, that is
to say, a certain number of concepts beneath another concept. But
it is impossible in any way to think these subordinate concepts, as
actualizations of the fundamental concept, which are developed from
one another and return into themselves; hence we are compelled to
leave them external to one another, simply co-ordinated. The scheme
of _subordination_ and _co-ordination,_ and its relative spatial
symbol (the symbol of _classification_), which is a right line, on
the upper side of which falls perpendicularly another right line,
and from whose lower side descend other perpendicular and therefore
parallel right lines, is opposed to the circle and is the most evident
ocular demonstration of the profound diversity of the two procedures.
It will always be impossible to dispose a nexus of pure concepts in
that classificatory scheme without falsifying them; it will always be
impossible to transform empirical concepts into a series of grades
without destroying them.
[Sidenote: _The definition in the empirical concepts, and the notes of
the concept._]
In consequence of the scheme of classification, the definition which,
in the case of pure concepts, has the three moments of universality,
particularity, and singularity, in the case of empirical concepts
has only two, which are called _genus_ and _species_; and is applied
according to the rule, by means of the _proximate genus_ and the
_specific difference._ Its object indeed is simply to record, not to
understand and to think, a given empirical formation; and this is fully
attained when its position is determined by means of the indication of
what is above and what is beside it. In order to determine it yet more
accurately, the doctrine of the definition has been gradually enriched
with other _marks_ or _predicables,_ which, in traditional Logic,
are five: _genus, species, differentia, property, accident._ But it
is a question of caprice upon caprice, of which it is not advisable
to take too much account. And as it would be barbaric to apply the
classificatory scheme to the pure concepts, so it would be equally
barbaric to define the pure concepts by means of _marks,_ that is, by
means of characteristics mechanically arranged.
[Sidenote: _Series in the abstract concepts._]
Where the thinker forgets the true function of the empirical concepts
and is seized with the desire to develop them rationally, and thus
to overcome the atomism of the scheme of classification and of
extrinsic definition, he is led to refine them into abstract concepts,
in which that scheme and that method of definition are overcome:
the classification becomes a _series_ (numerical series, series of
geometrical forms, etc.), and the definition becomes _genetic._ But
this improvement not only makes the empirical concepts disappear,
and is therefore not improvement but death (like the death which the
empirical concepts find in true knowledge when they return or mount up
again to pure thought); but such improvement substitutes for empiricism
emptiness. Series and genetic definitions answer without doubt to
demands of the practical spirit; but, as we know, they do not yield
truth, not even the truth which lies at the bottom of an empirical
concept or of a falsified and mutilated representation. Hence, here as
elsewhere, empirical concepts and abstract concepts reveal their double
one-sidedness, and exhibit more significantly the value of the unity
which they break up; the distinction, which is not classification,
but circle and unity; the definition, which is not an aggregate of
intuitive data; the series, which is a complete series; the genesis,
which is not abstract but ideal.
VI
OPPOSITION AND LOGICAL PRINCIPLES
[Sidenote: _Opposite or contrary concepts._]
By what has been said, we have made sufficiently clear the nature of
distinct concepts, that is to say, unity in distinction and distinction
in unity, and we have left no doubt as to the kind of unity which
the concept affirms, that it is not _in spite of_ but _by means of_
distinction. But another difficulty seems to arise, due to another
order of concepts, which are called _opposites_ or _contraries._
[Sidenote: _Their difference from distincts._]
It is indubitable that opposite concepts neither are nor can be reduced
to distincts; and this becomes evident so soon as instances of both
are recalled to mind. In the system of the spirit, for instance, the
practical activity will be distinct from the theoretic, and within
the practical activity the utilitarian and ethical activities will
be distinct. But the contrary of the practical activity is practical
inactivity, the contrary of utility, harmfulness, the contrary of
morality, immorality. Beauty, truth, utility, moral good are distinct
concepts; but it is easy to see that ugliness, falsehood, uselessness,
evil cannot be added to or inserted among them. Nor is this all: upon
closer inspection we perceive that the second series cannot be added
to or mingled with the first, because each of the contrary terms
is already inherent in its contrary, or accompanies it, as shadow
accompanies light. Beauty is such, because it denies ugliness; good,
because it denies evil, and so on. The opposite is not positive, but
negative, and as such is accompanied by the positive.
[Sidenote: _Confirmation of this given by the Logic of empiria._]
This difference of nature between opposite concepts and distinct
concepts is also reflected in empirical Logic, that is, in the theory
of pseudoconcepts; because this Logic, while it reduces the distinct
concepts to _species,_ refuses to treat the opposites in like manner.
Hence one does not say that the genus _dog_ is divided into the species
_live_ dogs and _dead_ dogs; or that the genus _moral man_ is divided
into the species _moral_ and _immoral_ man; and if such has sometimes
been affirmed, an impropriety--even for this kind of Logic--has been
committed, since the _species_ can never be the _negation_ of the
_genus._ So this empirical Logic confirms in its own way that opposite
concepts are different from distinct.
[Sidenote: _Difficulty arising from the double type of concepts,
opposites, and distincts._]
It is, however, equally evident that we cannot content ourselves with
enumerating the opposite, side by side with the distinct concepts;
because we should thus be adopting non-philosophical methods in place
of philosophical, and in the philosophical theory of Logic should be
lapsing into illogicality or empiricism. If the unity of the concept
be at the same time its _self-distinction,_ how can that same unity
have another parallel sort of division or self-distinction, which is
_self-opposition!_ If it is inconceivable to resolve the one into
the other, and to make of the opposites distinct concepts, or of the
distincts opposite concepts, then it is not less inconceivable to leave
both distincts and opposites within the unity of the concept unmediated
and unexplained.
[Sidenote: _Nature of the opposites; and their identity with the
distincts when distinguished from them._]
It will possibly serve towards a solution of this
difficulty--undoubtedly a very grave one--to go deeply into the
nature of the difference between opposite and distinct concepts.
These latter are distinguishable in unity; reality is their unity and
also their distinction. Man is thought and action; indivisible but
distinguishable forms; so much so that in so far as we think we deny
action, and in so far as we act we deny thought. But the opposites are
not distinguishable in this way: the man who commits an evil action,
_if he really does something,_ does not commit an evil action, but an
action which is useful to him; the man who thinks a false thought, _if
he does something real,_ does not think the false thought, indeed does
not think at all, but, on the contrary, lives and provides for his own
convenience and in general for a good which at that instant he desires.
Hence we see that the opposites, when taken as distinct moments, are no
longer opposites, but distincts; and in that case they retain negative
denominations only metaphorically, whereas, strictly speaking, they
would merit positive. In order, therefore, that the consideration of
opposition be not changed when superficially regarded into that of
distinction, it is desirable not to make of it a distinction in the
bosom of the concept, that is to say, to combat every distinction by
opposition, by declaring it to be _merely abstract._
[Sidenote: _Impossibility of distinguishing one opposite from another,
as concept from concept._]
So true is this, that no sooner are opposite terms taken as distincts
than the one becomes the other, that is to say, both evaporate into
emptiness. The disputes caused by the opposition of _being_ to
_not-being_ and the unity of both in _becoming_ are celebrated in this
connection. And we know that being, thought as pure being, is the same
as not-being or nothing; and nothing, thought as pure nothingness,
is the same as pure being. Thus, the truth is neither the one nor
the other, but is becoming, in which both are, but as opposites, and,
therefore, indistinguishable: becoming is being itself, which has in
it not-being, and so is also not-being. We cannot think the relation
of being to not-being as the relation of one form of the spirit, or
of reality, to another form. In the latter case we have unity in
distinction: in the former, rectified or _restored_ unity, that is to
say, reaffirmed against _emptiness;_ against the empty unity of mere
being, or of mere not-being; or against the mere sum of being and of
not-being.
[Sidenote: _The dialectic._]
The two moments should certainly be synthesized, when we attack the
abstract thought, which divides them: taken in themselves, they
are, not two moments united in a third, but one only, the third
(in this case also the number is a symbol), that is to say, the
indistinguishability of the moments. It thus happens (be it said in
passing) that Hegel, to whom we owe the polemic against empty being,
was content for this purpose neither with the words _unity_ and
_identity,_ nor with _synthesis,_ nor with _triad,_ and preferred
to call this indistinguishable opposition in unity the objective
_dialectic_ of the real. But whatever be the words that we chose to
employ, the thing is what has been said. The opposite is not the
distinct of its opposite, but the abstraction of the true reality.
[Sidenote: _The opposites are not concepts, but the unique concept
itself._]
If this be the fact, the duality and parallelism of distinct and
opposite concepts no longer exist. The opposites are the concept
itself, and therefore the concepts themselves, each one in itself,
in so far as it is determination of the concept, and in so far as it
is conceived in its true reality. Reality, of which logical thought
elaborates the concept, means, not motionless being or pure being,
but opposition: the forms of reality, which the concept thinks in
order to think reality in its fullness, are opposed in themselves;
otherwise, they would not be forms of reality, or would not be at
all. _Fair is foul and foul is fair_: beauty is such, because it has
within it ugliness, the true is such because it has in it the false,
the good is such because it has within it evil. If the negative term
be removed, as is usually done in abstract thought, the positive also
disappears; but precisely because, with the negative, the positive
itself has been removed. When we talk of negative terms, or of
non-values and so of not-beings as existing, existence really means
that to the _establishment_ of the fact we add the _expression of the
desire_ that another existence should arise upon that existence. "You
are dishonest" means "You are a man that seeks your own pleasure" (a
theoretic judgment); "but you _ought to be_" (no longer a judgment, but
the expression of a desire) "something else, and so serve the universal
ends of Reality." "You have written an ugly verse" will mean, for
example, "You have provided for your own convenience and repose, and
so have accomplished an economic act" (a theoretic judgment); "but you
_ought to_ accomplish an æsthetic act" (no longer judgment, but the
expression of a wish). Examples can be multiplied. But every one has in
him evil, because he has good: Satan is not a creature extraneous to
God, nor the Minister of God, called Satan, but God himself. If God had
not Satan in himself, he would be like food without salt, an abstract
ideal, a simple _ought to be_ which is not, and therefore impotent
and useless. The Italian poet who had sung of Satan, as "rebellion"
and "the avenging force of reason," had a profound meaning when he
concluded by exalting God: as "the most lofty vision to which peoples
attain in the force of their youth," "the Sun of sublime minds and of
ardent hearts." He corrected and integrated the one abstraction with
the other, and thus unconsciously attained to the fullness of truth.
[Sidenote: _Affirmation and negation._]
Thought, in so far as it is itself life (that is to say, the life
which is thought, and therefore life of life), and in so far as it is
reality (that is to say, the reality which is thought, and therefore
reality of reality) has in itself opposition; and for this reason it
is also _affirmation and negation_; it does not affirm save by denying,
and does not deny save by affirming. But it does not affirm and deny
save by distinguishing, because thought is distinction, and we cannot
distinguish (truly distinguish _i.e.,_ which is a different thing from
the rough and ready separations made by the pseudoconcepts) save by
unifying. He who meditates upon the connections of affirmation-negation
and unity-distinction has before him the problem of the nature of
thought, and so of the nature of reality; and he ends by seeing that
those two connections are not parallel nor disparate, but are in their
turn unified in unity-distinction understood as effective reality, and
not as simple abstract possibility, or desire, or mere ought to be.
[Sidenote: _The principle of identity and contradiction; its true
meaning and false interpretation._]
If we now wish to state the nature of thought as reality in the form of
_law_ (a form which we know to be one with that of the concept, though
the first term be adopted by preference for the pseudoconcepts), we can
only say that the law of thought is the law of unity and distinction,
and therefore that it is expressed in the two formulæ A is A (unity)
and A is not B (distinction), which are precisely what is called
the law or _principle of identity and contradiction._ It is a very
improper, or, rather, a very equivocal formula, chiefly because it
allows it to be supposed that the law or principle is outside or above
thought, like a bridle and guide, whereas it is thought itself; and it
has the further inconvenience of not placing in clear relief the unity
of identity and distinction. But these are not too great evils, because
misunderstandings can be made clear, and because--what we will not tire
of repeating--all, all words indeed, are exposed to misunderstandings.
[Sidenote: _Another false interpretation; struggle with the principle
of opposition. False application of this principle._]