A mental fact, afterwards called the transition from _quantity_ to
_quality,_ or the conversion of quantity into quality, has certainly
been known since ancient times. This transition finds a parallel in
those logical diversions, in which, granted the admission, apparently
as legitimate as it is slight, that by the removal of a single hair
from the head of a luxuriantly haired individual, that individual does
not become bald, or that by the removal of a single grain from a heap,
the heap does not disappear, one hair or one grain after another is
removed, and he of the luxuriant locks becomes bald and for the heap
is substituted the bare ground. But the error is in reality contained
entirely in the first admission. A man with a head of hair or a heap
of grain are what they are, so long as nothing in them is changed. The
change of quantity is translated into change of quality, not because
the first concept is constitutive of the second, but, on the contrary,
because the second is constitutive of the first. Quantity has been
obtained, measurement has been effected, by starting from quality,
determined in the pure individual judgment and made homogeneous in the
empirical judgment, which is the basis of the judgment of enumeration
and of measurement. Thus quality constitutes the only real content
of the abstract quantitative concept. By the taking away of the hair
or the grain, _quality_ itself is changed through the _quantitative
formula._ That is to say, quantity does not pass into quality, but one
quality passes into another quality. Quantity, taken by itself, as an
abstract determination, is impotent in presence of the real.
[Sidenote: _Mathematical space and time and their abstraction._]
A final observation, suggested by the difference between pure
individual judgments (or judgments of reality and value, if it please
you so to call them), and quantitative or empirico-abstract judgments,
is that the entire conception of things as occupying various portions
of _space_ and following one another in a _discontinuous_ manner,
_separated_ from one another in _time,_ is derived from the last type
of pseudojudgments, namely the quantitative. It is an _alteration_
effected for practical ends from the ingenuous view offered by pure
perception. To show, as we have shown, the genesis of quantitative
judgments and so of mathematical space and time, amounts to describing
their nature and giving their definition. It amounts to revealing them
as thoughts of _abstractions,_ which are not to be confounded with real
thought, or with genuine thought of reality. The Kantian concept of the
_ideality_ of _time_ and _space_ gives the same result. This doctrine
is among the greatest discoveries of history, and should be accepted
by every philosophy worthy of the name. In accepting it ourselves, we
make but one reservation (justified by the proofs given above), namely,
that the character of mathematical space and time should be called not
ideality (because ideality is true reality), but rather _unreality_ or
_abstract ideality,_ or, as we prefer to call it, _abstractness._
THIRD SECTION
IDENTITY OF THE PURE CONCEPT AND THE INDIVIDUAL JUDGMENT THE LOGICAL _A
PRIORI_ SYNTHESIS
I
IDENTITY OF THE JUDGMENT OF DEFINITION (PURE CONCEPT) AND OF THE
INDIVIDUAL JUDGMENT
[Sidenote: _Result of preceding enquiry: the judgment of definition and
the individual judgment._]
The descent, as we have called it, from the pure concept to the
intuition, or the examination of the relations which are established
between the concept and the intuitions, when we have attained the
first, and of the ensuing transformations, to which the second are
subject, might at first sight seem complete. The concept, which was
first contemplated in abstraction, has been demonstrated in a more
concrete manner, in so far as it takes the form of language and exists
as the judgment of definition. Further, we have shown how, when thus
concretely possessed, it reacts upon the intuitions from which it was
formed, or how it is applied to them, as it is called, giving rise
to the individual or perceptive judgment. The transition from the
intuitions to the concept, and so to the expression of the concept or
the judgment of definition, and from this to the individual judgment,
has been followed and demonstrated in its logical necessity. Thus the
two distinct forms are also united, the first being the presupposition
and base of the second, so that the connection seems at first sight to
be perfect. The judgment of definition is not an individual judgment;
but the individual judgment implies a previous judgment of definition.
To think the concept of man does not mean that the man Peter exists.
But if we affirm that the man Peter exists, we must first have affirmed
that the concept of man exists, or is thought.
[Sidenote: _Distinction between the two: truth of reason and truth of
fact, necessary and contingent, etc., formal and material._]
The distinction between the two forms, the judgment of definition and
the individual judgment, is universally recognized. Not only can it be
found, as has already been noted, in at least one of the significations
which have been attached to the two classes of judgments, analytic and
synthetic, but it is even more clearly expressed in the well-known
distinction between _truth of reason_ and _truth of fact,_ between
_necessary truths_ and _contingent_ truths, between truths _a priori_
and truths _a posteriori,_ between what is _logically_ and what is
_historically_ affirmed. Indeed, it is only on the basis of this
distinction that it seems possible to give any content to the logical
doctrine, which recognizes the possibility of propositions true _in
form_ and false _in fact._ This doctrine, as usually stated, is
altogether untenable. It is impossible, above all, to maintain that
formal truth can be distinguished from effective truth, always assuming
that "form" is understood in its philosophical sense and not in that of
formalist Logic, where it indicates an arbitrarily fixed externality,
which, as such, is neither true nor false. It is therefore impossible
to maintain that one and the same proposition can be true in one
respect and false in another; for a proposition can be judged only
from one point of view, which is that of its unique signification and
value. But it is clear that once we admit the distinction between truth
of reason and truth of fact, affirmations of both kinds might be found
incorporated in the same verbal proposition, one of them false and the
other true. For example, that the saying of Cambronne, "The Guard dies
and never surrenders," is a "sublime saying" is formally (rationally)
true, but it is materially (as fact) false, because Cambronne did not
utter those words. On the other hand, that the _Assedio di Fiorenze_ of
Guerrazzi is "a very beautiful book, because it inflamed many youthful
bosoms with love of country," is materially (as fact) true, but it is
formally (rationally) false, because the fact of its having produced
such an effect is not proof of the beauty of a book, since beauty does
not consist of practical efficacy.
[Sidenote: _Absurdities arising from these distinctions; the individual
judgment as ultralogical._]
Yet, notwithstanding the apparently glaring distinction between the
judgment of definition and the individual judgment, between truth
of reason and truth of fact; notwithstanding its secular celebrity
and its confirmation by universal agreement and common usage, this
distinction meets with a very grave difficulty. In order to understand
it, we must, above all, establish clearly what we have just stated
in positing that distinction and in making the individual judgment
or truth of fact _follow_ the judgment of definition or truth of
reason. We have already posited a distinction of this kind between
intuition and concept, and have noted that we have thus distinguished
two fundamental forms of the Spirit: the representative or fantastic
form, and the logical. Now, in positing as distinct the judgment of
definition and the individual judgment, do we mean to do something
analogous? Do we mean to distinguish the logical form (concept or
definition) from another form, no longer logical, although containing
the logical form in itself as overcome and subordinate, in the same way
that the concept contains in itself the intuition? In other words, is
the individual judgment something _ultralogical_? It can certainly be
asserted that it is not mere definition; but can it be asserted that
it is not logical? The words used should not lead to misconception. If
in the individual judgment the subject be a representation, it is also
true that this representation is not found there as it would be found
in æsthetic contemplation, but as subject of a judgment, and therefore
not as a representation pure and simple, but as a representation
thought, or made logical. Hegel has several times remarked that whoever
doubts the unity of individual and universal can never have paid
attention to the judgments which he utters at every instant. In these,
by means of the copula, he resolutely affirms that Peter _is_ a man,
or that the individual (the subject) _is_ the universal (predicate);
not something different, not a piece or fragment, but just that, the
universal. Further, are not truths of fact also truths of reason? Would
it not be irrational to think that a fact was not the fact it had
been? The existence of Cæsar and of Napoleon is not less _rational_
than that of quality and of becoming. And are not both kinds of facts
equally necessary--those called contingent not less than those called
necessary? We are right to laugh at those who like to think that things
could have happened otherwise than they have happened. Cæsar and
Napoleon are as necessary as quality and becoming.
[Sidenote: _or duality of logical forms._]
It follows from these considerations (which could be easily multiplied)
that the individual judgment is not less logical than that of
definition. Truths of fact, contingent and _a posteriori,_ are not
less logical than those of reason, necessary and _a priori._ But if
this be so, the distinction between the two forms would not be a
distinction between forms of the spirit, but a subdistinction within
the logical form of the spirit: a subdistinction of which we have
already denied the possibility. For it is not clear how a logical
thought, or thought of the universal, can be _two_ thinkings, one in
one way, one in another: one universal of the universal, the other
universal of the individual. Either the first is void, or the second is
improper. Intuition and concept are distinguished as individual from
universal; but that universal should be distinguished from universal
by the introduction of individuality as element of differentiation is
inconceivable.
[Sidenote: _Difficulty of abandoning the distinction._]
The difficulty becomes greater from the equal inconceivability and
impossibility of abandoning the result reached above, by which the
individual judgment was shown to be possible only by means of a concept
or judgment of definition. Every attempt that may be made to cancel
that presupposition and to reconceive the individual or perceptive
judgment as preceding the concept and being altogether without logical
character, a mere assertion of fact, unenlightened by universality,
must be considered, for the reasons we have given, to be entirely
vain. If we cannot admit a duality of logical forms, still less can we
admit that an alogical character, below the level of logic altogether,
attaches to the individual judgment.
[Sidenote: _The hypothesis of reciprocal implication and so of the
identity of the two forms._]
There seems to be but one way out of such a difficulty: namely,
to preserve the result attained, that is to say, the necessity of
the judgment of definition as the presupposition of the individual
judgment, but to affirm at the same time the necessity of the
individual judgment as the presupposition of the judgment of
definition. Admitting this supposition by way of hypothesis, let us
see what it would mean and what effect it would have in the discussion.
Since the one judgment presupposes the other, and this presupposition
is reciprocal, we could no longer talk of distinction between the two,
but of unity pure and simple, of _identity,_ in which distinction
could arise only by abstraction and the arbitrary act of dividing
what cannot exist save as indivisible. But, on the other hand, the
distinction, although abstract, would always retain its value as a
didactic means of making clear the true nature of the logical act. Thus
we should justify our first proceeding to develop the concept and the
judgment of definition and then the individual judgment, and also the
reservation that we have always made as to the provisional nature of
such distinction, and thus also the new question as to the unity of the
act, put and answered in the way proposed. All the difficulties arising
from the appearance of a duality of logical forms would disappear.
Definitions and individual judgments, truth of reason and truth of
fact, necessity and contingency, _a priori_ and _a posteriori,_ would
be revealed as one act and one truth. And we should also be justified
in talking of them as distinct acts, for in expressing that single
truth and single judgment verbally or in literature, we can attach
greater importance now to the definition, and now to the statement of
fact; now to the subject, and now to the predicate.
[Sidenote: _Objection: the lack of an historical and representative
element in definitions._]
This path, which would offer such advantages and would constitute a
true way out of the difficulty, seems, however, to be closed to us by
the fact that in definitions there is no trace whatever of individual
judgments which, on this hypothesis, would have to be contained within
and be one with them. If we say "the will is the practical form of the
spirit," or "virtue is the habit of moral actions," where is to be
found in such statements the individual judgment and the representative
element? We find in them without doubt the verbal form, expressive and
representative, which is necessary to the concept for its concrete
existence; but we do not find the statement of fact of which we are
in search. Thus the proposed hypothesis will prove very ingenious and
rich with all the advantages that we have stated; but since it does not
appear to be confirmed by facts, we must, it seems, reject it, even at
the risk of having to think out a better one, or, if we fail in this,
of renouncing as desperate the attempt at a solution.
[Sidenote: _The historical element in definitions, taken in their
concreteness._]
We must not, however, be in a hurry, but rather carefully recall the
observation just made incidentally: that the verbal or literary form
can throw into _relief_ a moment of the judgment, while casting a
shadow over the other and causing it to be forgotten, without thereby
ever being able to suppress it. There seemed, we remember, to be no
trace of concepts in perceptive judgments or judgments of fact, and
especially in those forms of them which are called merely existential
and in those called impersonal. Yet there can be no doubt that none
of those judgments is ever possible without the concept as basis. An
analysis which does not allow itself to be arrested by appearances
and examines verbal forms as regards both what they express and what
they leave to be understood (though this too is expressed in its own
way) has discovered it. Similarly a definition does not exist in the
air, as might appear from the examples given in treatises, in which
the _where_ and the _when_ and the _individual_ and the _actual
circumstances_ in which the definition has been given are omitted. In a
definition thus presented, it would certainly be impossible to discover
a representative element and an individual judgment. But the reason for
this is that it has been mutilated and made abstract and indeterminate,
to such an extent that it can be made determinate only by the meaning
which he to whom it is communicated likes to attach to it. If, on the
contrary, we look at the definition in its concrete reality, we shall
_always_ find in it when we examine it with care the _representative
element_ and the _individual judgment._
[Sidenote: _The definition as answer to a question and solution of a
problem._]
For every definition is the answer to a question, the solution of a
problem. Did we not ask questions and set problems, there would be
no occasion for giving any definition. Why should we give them? What
need could there be? The definition is an act of the spirit and every
act of the spirit is conditioned. Without contradiction, there can
be no agreement; without the shock of multiplicity there can be no
unity; without the travail of doubt that calls for peace, there can be
no affirmation of the true. Not only does the answer presuppose the
question; but every answer implies a certain question. The answer must
be in harmony with the question; otherwise, it would not be an answer,
but the avoiding of an answer. In reply to a question of a certain
kind, we should turn our deaf ear, as the saying is, or reply with a
blow. This means that the nature of the question colours the answer
and that a definition taken in its concreteness is determined by the
problem which gives it rise. The definition varies with the problem.
[Sidenote: _Individual and historical conditionedness of every question
and problem._]
But the question, the problem, the doubt is always individually
conditioned. The doubt of the child is not that of the adult, the
doubt of the uncultured man is not that of the man of culture, or
the doubt of the novice that of the learned. Further, the doubt of
an Italian is not that of a German, and the doubt of a German of the
year 1800 is not that of a German of the year 1900. Indeed, the doubt
formulated by an individual in a given moment, is not that formulated
by the same individual a moment after. It is sometimes said by way
of simplification, that the same question has been put by very many
men, in various countries and at various times. But in the very act of
saying this, we simplify. In reality, every question differs from every
other question. Every definition, though it may seem to be the same and
bounded with certain definite words, which seem to remain unchanged
and constant, differs in reality from every other, because the words,
even when they seem to be materially the same, are in effect different,
according to the spiritual differences of those who pronounce them.
Each of these is an individual, and on that account each finds himself
in circumstances that are individually determined. "Virtue is the habit
of moral actions," is a formula which can be pronounced a hundred
times. But if it be seriously pronounced as a definition of virtue
each of those hundred times, it answers to a hundred psychological
situations, more or less different, and is in reality not _one,_ but _a
hundred_ definitions.
It will be replied that the concept remains the same through all these
definitions, like a man who changes his clothes a hundred times. But
(setting aside the fact that even the man who changes his clothes a
hundred times does not remain the same) the truth is that the relation
between concept and definition is not the same as that between a man
and his clothes. No concept exists save in so far as it is thought and
enclosed in words, or in so far as it is defined. If the definitions
vary, the concept itself varies. There are, certainly, variations
of the concept, of that which is, _par excellence,_ self-identical.
These are the life of the concept, not of the representation. But the
concept does not exist outside its life, and every thinking of it is a
phase of this life, never its overcoming, since however far we go, it
is never possible to swim outside water, or however high we climb, to
fly outside air.
[Sidenote: _The definition as also historical judgment. Unity of truths
of reason and of fact._]
If we posit individual or historical conditions for every thinking of
the concept, or of every definition (conditions which constitute the
doubt, the problem, the question, to which the definition replies),
we must admit that the definition, which contains the answer and
affirms the concept, at the same time illumines by so doing those
individual and historical conditions, that group of facts, from which
it comes. It illumines, that is to say, qualifies it as what it is,
grasps it as subject by giving it a predicate, and judges it. And
since the fact is always individual, it forms an individual judgment.
This means just that every definition is also an individual judgment.
And this agrees with the hypothesis we framed: it is the assumption
that seemed doubtful and now is proved. Truth of reason and truth of
fact, analytic and synthetic judgments, judgments of definition and
individual judgments, do not exist as distinct from one another: they
are abstractions. The logical act is unique: it is the identity of
definition and of individual judgment, the thinking of the pure concept.
[Sidenote: _Considerations confirming this._]
Such a theory as this, although it goes against the ordinary way
of thinking (though this, in its turn, suffers from its own
contradictions), can be made convincing even to ordinary thought,
when it is led to reflect upon what is implicitly understood in any
judgments of definition that are pronounced. For example, definitions
have always in view some particular adversary; they change according to
time and circumstances, and those definitions that we felt constrained
to give, at one stage of our mental development, we abandon at another,
not because we judge them to be erroneous, but because they seem to
us to be inopportune or commonplace. These and other facts, easy to
observe, would not be possible, unless judgment of definite situations
intervened to produce the change. And this judgment, though we may try
to think of it as preceding or as following each one of those acts of
definition, in reality neither precedes nor follows them, but on the
contrary presents itself to the mind as contemporaneous, or rather
coincident and identical with the act of definition. Every one who
attains to a conceptual truth, every one, for instance, who achieves
a definite doctrine of art or of morality, is immediately aware in
himself that henceforth he knows more adequately not only the kingdom
of ideas but also the kingdom of things. He realizes that as soon as
an idea becomes more clear _ipso facto_ it makes clearer the things out
of whose vortex and tumult it comes. The star-gazer who forgets the
earth, will be an astronomer, but certainly not a philosopher. In the
act of thought, in the world of ideas, earth and sky are fused in one.
Whoever looks well at the sky sees in it (miraculously!) the earth.