we have demonstrated by various processes that are usually called
negative, hypothetical, or inductive and based upon observation, is
also confirmed by the process called deductive. For if the thinking
of the concept be a degree superior to pure representation, and if in
the degrees of the spirit the superior contain in itself the inferior,
it is evident that representation as well as conceptual elements must
always be found in the concept. But it is also evident that we can
never find them distinct or distinguishable, but mingled in such a
way that every distinction in them must be introduced solely by a
deliberate act. The logical act is certainly spoken, represented,
individualized. But when it is split up into concept and individual
judgment, one of two things must happen: either we make an empirical
and external distinction, of more or less; or two monstrosities are
asserted: a non-individualized concept, which therefore does not exist,
and a judgment not thought, and therefore non-existent as judgment, and
existing, at the most, as pure intuition.
[Sidenote: _Critique of the false distinction between formal and
material truths._]
As our distinction between definitions and individual judgments was
provisional, so also we must regard the consequence that we showed
to issue from it--the partial justification of the doctrine of
affirmations formally (logically) true and materially (individually)
false. In reality, an error of fact implies a more or less inaccurate
and erroneous definition, and an error of definition implies an error
of fact. Thus this distinction also retains only an empirical meaning
useful for the rough distinction of certain classes of errors from
certain others. And resuming another previous observation, we must
also say that, strictly speaking, it must be held impossible to err as
to facts through the use of pure concepts, since the penetration of
concepts, however great one may think it, is also always penetration
of facts. This formula, too, cannot have anything but an empirical
meaning, to indicate a certain type of errors of concept and of fact,
which is popularly called the use of concepts and the use of facts,
whereas it is the abuse of both.
[Sidenote: _Platonic and Aristotelian men._]
In ordinary life it is customary to distinguish between those who
cultivate ideas and those who cultivate facts, between _Platonic_ and
_Aristotelian_ men. But if the Platonists seriously cultivate ideas,
they cultivate facts and are also Aristotelians, and the Aristotelians
cultivate ideas and are Platonists. Here, too, the difference is
practical and extrinsic, not substantial; so much so that we are often
astonished both at the singular clear-sightedness and penetration of
the actual situation manifested by cultivators of ideas, and at the
profound philosophy which we discover in the pretended cultivators of
facts.
[Sidenote: _Theory of the application of the concepts, true for
abstract concepts and false for pure concepts._]
Hence the further consequence, that we must avoid the formula which
speaks of the _application_ of concepts, as, for instance, that in
the individual judgment the concept is applied to the intuition. To
say this, is, as a saying, innocuous, since like many others, it is
metaphorical; but the doctrine implied in it, or that may be suggested
by it (and that is indeed rarely separated from it), is altogether
erroneous. The concept is not applied to the intuition, because it
does not exist, even for a moment, outside of the intuition, and the
judgment is a _primitive act_ of the spirit, it is the logical spirit
itself. If that formula has been successful, the reason for its success
must usually be sought in the theory of the pseudoconcepts. Even
these, in relation to the question which engages us now, and in so far
as they are empirical concepts, are indistinguishable from individual
pseudojudgments. To construct an empirical concept is equivalent to
pronouncing that the objects _a, b, c, d,_ etc., belong to a definite
class. The two acts of the construction of the class and of effectual
classification are only to be distinguished in an abstract manner. In
conformity with this, we must now correct the theory that we have given
above. But on the other hand, in so far as they are abstract concepts,
they are void of all representative content, and therefore constituted
outside of every individual judgment. They cannot of themselves give
rise to such judgments. Before they can be united to them, we must
_apply them_ to individual judgments, elaborated into pseudojudgments,
or made homogeneous by the process of classification. And in truth,
'not only the doctrine of application, but also the distinctions
between analytic and synthetic judgments, between definitions and
perceptions, between truths of reason and of fact, between necessity
and contingency, find their confirmation in being referred to abstract
concepts, as distinct from empirical. The same may be also said of
the other doctrine, which distinguishes between affirmations that are
formally true and materially false. Two griffins plus three griffins
make five griffins. This is formally true, since it is true that two
plus three equals five; but it is materially false, because griffins
do not exist. Numbers and their laws would, for example, be truths
of reason, necessary, _a priori,_ in analytical judgments and pure
definitions; truths derived from experience would be truths of fact,
contingent, _a posteriori,_ in synthetic and individual judgments. But
though this conception may have currency in a field where, properly
speaking, there is neither thought nor truth, in the field of truth
and of thought the terms of both series are found in the corresponding
terms of the other. Analysis apart from synthesis is as unthinkable
as synthesis apart from analysis. In the same way we can empirically
distinguish intention and action in the practical spirit. But in
reality pure intention outside effectual action, is not even intention,
because it is nothing. And an action beyond and without intention is
nothing, for practical reality is the identity of intention and action.
Here, too, theoretical spirit and practical spirit correspond at every
point.
II
THE LOGICAL, _A PRIORI_ SYNTHESIS
[Sidenote: _The identity of the judgment of definition and of the
individual judgment, as synthesis a priori._]
If analysis apart from synthesis, the _a priori_ apart from the _a
posteriori,_ be inconceivable, and if synthesis apart from analysis,
the _a posteriori_ apart from the _a priori,_ be equally inconceivable,
then the true act of thought will be a synthetic analysis, an analytic
synthesis, an _a posteriori-a priori,_ or, if it be preferred, an _a
priori synthesis._
In this manner, the identity that we have established between the
judgment of definition and the individual judgment comes to assume a
name celebrated in the annals of modern philosophy. And by assuming
it at this point, it is also able to affirm, since it has already
demonstrated, the truth of the _a priori_ synthesis, and to determine
its exact content.
[Sidenote: _Objections raised by abstractionists and empiricists
against the a priori synthesis._]
This is not the place to enter again into the objections which the
Kantian concept elicited (indeed could not fail to elicit): objections
which in Italy too gave rise to very acute attempts at confutation,
and which ended in the partial absorption of that concept into the
mental organism of its opponents. Suffice it to say that all the
objections to the _a priori_ synthesis, when thoroughly examined, seem
to be derived, as was to be expected, from the upholders of the two
one-sided doctrines which were surpassed by the synthesis. Thus the
dogmatists or abstractionists believed the concept to be thinkable
apart from or above the facts (simple analysis); the empiricists
perceived only the representative element and claimed to obtain the
concept from mere facts (simple synthesis). Both failed to explain
perception, or the individual judgment. The former found it to arise
from the external and almost accidental contact between pure concepts
and given facts; the latter sometimes assumed it without explanation,
sometimes confused it with pure intuition, if not altogether with
sensibility and emotion. It can be said that whoever does not accept
the _a priori_ synthesis is outside the path of modern philosophy,
indeed of all philosophy. Strive to find or to rediscover that path,
unless you wish to incur the punishment of trifling with empiricism,
of lying to yourself with mysticism, or of wandering in the void with
scholasticism.
[Sidenote: _False interpretation of the a priori synthesis._]
Instead of noting and of examining all the objections made to the _a
priori_ synthesis (which we have already substantially discussed in
the development of our treatise), it will be of assistance to add some
explanations, which will prevent false interpretations of that concept.
These false interpretations sometimes (as often happens) mingle with
the true even in the philosopher who discovered it, and confer force
and authority upon several of the objections to the very reality of the
_a priori_ synthesis.
[Sidenote: _A priori synthesis in general and logical a priori
synthesis._]
In the first place, in accordance with the formula given in Logic we
must not speak of the _a priori_ synthesis in general, but of the
_logical a priori synthesis._ The _a priori_ synthesis belongs to all
the forms of the Spirit; indeed, the Spirit, considered universally,
is nothing but _a priori_ synthesis. The synthesis is operative in the
æsthetic activity, not less than in the logical. For how could a poet
create a pure intuition, if he did not proceed from a given fact, from
some passionate moment of his own, conditioned and constituted in a
particular way? Without something to intuite and to express could there
ever be a poet? And would he be a poet, if he were to repeat that
something mechanically, without transforming it into pure intuition?
In his pure intuition, there is and there is not matter: not as brute
matter, but as formed matter, or form. Thus it is said with reason
that art is pure form, or that matter and form, content and form, in
art are wholly one (_a priori_ æsthetic synthesis). The _a priori_
synthesis is not less operative in the practical activity than in
the æsthetic and logical (that is, in the theoretic activity). It is
impossible to will without material to will, or to will outside the
given material. The practical man accepts actual conditions, and at the
same time transforms them with his volitional act, creating something
new, in which those conditions are and are not. They are, because
the action achieved is in relation to them; they are not, because
being new, it has transformed them. _A priori_ synthesis, in general,
then, means spiritual activity; not abstract but concrete spiritual
activity, that is to say, the spirit itself, which is _condition_ to
itself and _conditioned_ by itself. Thus the _a priori_ synthesis,
which is constituted by the coincidence or identity of the judgment of
definition with the individual judgment, is not _a priori_ synthesis in
general, but logical _a priori_ synthesis.
[Sidenote: _Non-logical a priori syntheses._]
Having clearly established this point we are enabled to eliminate the
confusion caused by the citation of certain spiritual formations,
which do not correspond with that logical act, as examples of _a
priori_ synthetic judgments. Such for instance is the case of the
famous example: "5 + 7 = 12," concerning which it was long disputed
whether it were an _a priori_ synthetic judgment or simply analytical;
the synthetic element being found or not found in it, according to
the point of view. The same thing has occurred in the case of other
examples of a different nature, as in the judgment: "Snow is white."
Here the dispute has been as to whether it be _a priori_ synthetic,
or simply synthetic. The truth is, on the contrary, that in neither
of these two cases is there _logical a priori_ synthesis, because
the judgment "5 + 7= 12" is the expression of abstract or numerical
concepts, and "snow is white" is the expression of empirical or
classificatory concepts. This amounts to saying that both are products,
not of a logical nature, nor of a theoretic nature, but, as we know,
of an arbitrary or practical nature. For this reason, we have denied
the very possibility of simply analytic or simply synthetic judgments
in pure logic. On the other hand, both these kinds of spiritual
formations are _a priori_ syntheses, precisely because, being spiritual
formations (though of a practical nature), they cannot fail to be
produced by a creative (synthetic) act of the spirit. This explains why
they sometimes appear as _a priori_ syntheses, sometimes as something
altogether different from the _a priori_ synthesis. It suffices to
add to the affirmative solution the adjective "practical" and to the
negative the adjective "logical" to obtain agreement and truth.
[Sidenote: _The a priori synthesis, as synthesis, not of opposites but
of distincts._]
A question of no less importance is whether the logical _a priori_
synthesis (we might say, the _a priori_ synthesis in general) is to be
conceived as a synthesis of opposites; if, in other words, intuition
and concept, matter and form, exist in the _a priori_ synthesis in the
same way as Being and not Being exist in true Being, which is Becoming;
or as good and evil, true and false, and so on, exist in the special
forms of the Spirit. The affirmative reply to this question finds,
as is well known, its chief representative in the doctrine of Hegel.
We do not wish to deny the great truth contained in this doctrine,
in so far as by considering the _a priori_ synthesis as a synthesis
of opposites, it insists upon this essential point: that intuition
and concept matter and form, do not exist in the logical act as two
separable elements, merely externally connected. Outside the synthesis
the subject does not exist as subject, and the predicate does not
exist in any way. We must banish altogether the idea of the _a priori_
synthesis, conceived as the reuniting of two facts existing separately.
But having recognized the true side of the doctrine, we must correct
the inexactness it contains. This arises from the confusion already
criticized, by which the relation of opposition is unduly extended to
distinct concepts, and the unity of effectual distinction is confused
with the dialectic unity, which declares itself synthetic, only in so
far as it makes war against an abstract distinction.[1] The _a priori_
synthesis is a unity of distinct concepts and not of opposites. That
which is the material of the logical synthesis and which outside it
has no logical character (is not subject), yet in another and inferior
grade of the spirit is form and not matter, and is called intuition.
Hence, there is distinction and unity together; form is not without
matter; but the new matter was already form and, therefore, had its
own matter. The logical _a priori_ synthesis presupposes an æsthetic
_a priori_ synthesis. When considered in the logical sphere, this is
certainly no longer a synthesis, but an indispensable element of the
new synthesis. But outside the logical sphere, it possesses its own
proper and peculiar autonomy. In the logical act intuition is _blind_
without the concept, as the concept is _void_ without the intuition.
But pure intuition is not blind, because it has its own proper
intuitive light. The concept contains the intuition, but the intuition
transfigured. It is a synthesis, not of itself and its opposite, but
of itself and its distinct concept which is indistinguishable from
itself, save by an act of abstraction. In this way we satisfy the
demand expressed in the formula of the synthesis as unity of opposites,
and at the same time repress its tendency to usurpation. This tendency
leads to the rejection of the concept of æsthetic synthesis, in favour
of the concept of logical synthesis; it means the negation of art by
philosophy, not only in the philosophical field (which would be just),
but in the whole spiritual field. Extending itself from this to other
usurpations and led on by the mirage of an ill-understood unity, it
claims all the other syntheses for logical synthesis, and produces a
great spiritual desert, in which logical thought itself at length dies
of starvation.
[Sidenote: _The category in the judgment. Difference between category
and innate idea._]
The logical element, the pure concept or judgment of definition
considered in itself, is given the name of _category_ in the logical
_a priori_ synthesis. This term is nothing but the Greek equivalent
for the word "predicate," which we have hitherto employed. It has been
asked if the category is what used to be called an _inniate idea._
The answer must be that it is both that and also something profoundly
different. The innate idea was indeed the category, but the category
taken as possessed and thought _prior_ to experience, according to
the view that we have described as abstract or dogmatic. First the
music, then the words; first definitions, then individual judgments or
perceptions. The category, on the contrary, is neither the mother nor
the first-born. It is born at one birth with the individual judgment,
not as its twin, but as that judgment itself. From this aspect the
category or the _a priori_ is not the innate, but the perpetually
new-born. From this we see the vanity of the question, whether the
judgment or the concept be logically _prior,_ not only in the relation,
which we have already examined, of concept with verbal form (judgment
of definition), but also in the relation of concept with individual
judgment. We can say indifferently that to _think_ is to _conceive,_
or that to _think_ is to _judge,_ because the two formulæ are reduced
to one. Equally vain is the question as to whether the categories
precede the judgment or are obtained from it. They not only do not
precede the judgment, but are not even obtained from it. We never issue
forth from the judgment, as we never issue forth from reality and
history.
[Sidenote: _The a priori synthesis, the destruction of transcendency,
and the objectivity of knowledge._]
A final explanation, not less important than those already given,
concerns the _importance_ of the logical _a priori_ synthesis. This too
has been diminished by the very man who discovered and defined that
mental act, and even more by those who have repeated him, without being
capable of reviving again the moment of discovery, and of understanding
the intimate reasons that brought it about. When the concept was placed
outside and prior to the representative element, and thought prior to
and outside the world, so that the former was applied to the latter,
the world was bound to appear to be something inferior to the concept,
a degradation or an impure contact, which thought had to undergo.
When, on the other hand, the representative element was placed outside
and prior to the concept, the latter seemed to be inferior to it,
almost as though it were an expedient for taking hold of the world,
without truly being able to do so, and thus in its turn a degradation
or defilement of it. Hence the sigh that we hear already in antiquity
and more strongly in modern times: oh, if _words_ (that is to say
_concepts,_ because concepts were called words) were not, how directly
should we apprehend things! Oh, if _thought_ were not, how vigorously
should we embrace genuine reality!
In the first instance, reality is inferior to the concept, in the
second the concept to reality; but in both alike, the two elements
are always thought--as mutually external and truth as undiscoverable.
Thus both these one-sided tendencies end in mystery. According to the
former, the world is created by a God external to it, and will be
disintegrated when it shall seem good to him, while the latter holds
that the truth of things is plunged in impenetrable darkness. But
granted the idea of the _a priori_ synthesis, reality is not inferior
to thought nor thought to reality, nor is the one external to the
other. Representations are docile to thought, and thought conceals
representations even less than the tenuous and scanty veil concealed
the beauty of Alcina. The interpenetration of the two elements is
perfect, and they constitute unity. The false belief in the externality
and heterogeneity of reality and thought can only arise when for the
pure concept and the _a priori_ synthesis there are substitutes, either
abstract concepts with their related analytic judgments, which are
void of all representative content, or empirical concepts with their
related and merely synthetic judgments, which are without logical
form. The value of the _a priori_ synthesis lies in its efficacy in
putting an end to doubts as to the _objectivity_ of thought and the
_cognizability_ of reality, and in making triumphant the power of
thought over the real, which is the power of the real to know itself.
[Sidenote: _Power of the a priori synthesis never known to its
discoverer._]
But this efficacy of the _a priori_ synthesis remained obscure to its
discoverer (and most obscure to his orthodox followers). To such an
extent was this the case, that even to Kant the category did not seem
to be immanent in the real and to be the thinking of its reality,
but an extrinsic, though necessary adjunct, an inevitable alteration
introduced into reality to make it thinkable, an anticipatory
renunciation of the knowledge of genuine reality. Reality itself lay
outside every category and judgment, a _thing in itself._ Even in Kant,
the _a priori_ synthesis was confused with simple analysis and with
simple synthesis. These being manipulations of the real, extrinsic and
not intrinsic, practical and not logical, useful, but without truth, so
the _a priori_ synthesis appeared to him to be an expedient to which
man has recourse and cannot but have recourse, but which constitutes,
not his power, but his weakness. Kant, too, dreamed of an ideal of
knowledge, which was not _a priori_ synthesis, but the _intellectual
intuition,_ the perfect adequacy of thought to reality, unattainable
by the human spirit. He did not perceive that the intellectual
intuition, which he longed for as an impossible ideal, was precisely
the continuous operation of the _a priori_ synthesis, nor did he think
that what is necessary and insuperable cannot be defective. He never
knew that the _a priori_ synthesis, which he had discovered, is alone
the true concept and the true judgment, and, therefore, operates in an
altogether different way from simple analysis and simple synthesis,
which are neither concept nor judgment; nor finally that if these
last postulate a _thing in itself,_ the _a priori_ synthesis cannot
postulate it, because it has _it in itself._
To understand all the richness of the _a priori_ synthesis is to pay
honour to the genius of Emmanuel Kant; but it is also to recognize
that the systematic construction of Kant showed itself altogether
unequal to the great principle he laid down, but whose value he
insufficiently estimated.
[Footnote 1: See above, Sect. I. Chap. VI.]
III
LOGIC AND THE DOCTRINE OF THE CATEGORIES
[Sidenote: _The demand for a complete table of the categories._]
When the definition of the _a priori_ synthesis and of the category has
been attained, it is usual to demand of logical Science (and this will
be demanded also of our exposition) that it should say how many and of
what sort are the categories, how they are connected among themselves,
_i.e._ that it should draw up a _table_ of them.
[Sidenote: _A request extraneous to Logic. Logical and real
categories._]
Logic, in our opinion, should reject this demand, the origin of
which lies in the confusion between thought in general and thought
as the science of thought. The categories are certainly affirmed in
the individual judgment, but Logic, as the science of thought, does
not undertake to formulate judgments which will say what are the
predicable terms, the ultimate or pure concepts, the categories, with
which reality is thought. Logic cannot claim to substitute itself for
the other philosophic sciences and itself to solve all the problems
which offer themselves to thought as to the nature of reality. Its
scope is to define categories and to formulate judgments _only on that
aspect of Reality, which is logical thought._ It is, therefore, under
the obligation to face the question as to whether there be logical
categories, supreme concepts or supreme predicables from the point of
view of logic, and if there be, to indicate and to deduce them. It is
not obliged to indicate and to deduce all the supreme predicables and
categories.