For the rest, the identity of definition and individual judgment, which 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 repre sentation, 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, indi vidualized. But when it is split up into concept and individual judgment, one of two things must happen: either we make an empirical and PART Critique of the false distinc tion between formal and material truths.
2i4 LOGIC external distinction, of more or less; or two mon strosities are asserted: a non-individualized concept, which therefore does not exist, and a judgment not thought, and therefore non-existent as judg ment, and existing, at the most, as pure intuition. 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.
, THE PURE CONCEPT 215 In ordinary life it is customary to distinguish Platonic and Aristotelian between those who cultivate ideas and those who men. cultivate facts, between Platonic and Aristotelian men. But if the Platonists seriously cultivate ideas, they cultivate facts and are also Aristo telians, 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.
Hence the further consequence, that we must Theory of the application of avoid the formula which speaks of the application the concepts, true for of concepts, as, for instance, that in the individual abstract 1 concepts and judgment the concept is applied to the intuition. f^ecef°rs pure 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 216 LOGIC PART 216 LOGIC PART 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, by 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 dis tinguished 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 homo geneous 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 THE PURE CONCEPT 217 may be also said of the other doctrine, which dis tinguishes between affirmations that are form ally 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 de finitions; 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 II THE LOGICAL, A PRIORI SYNTHESIS The identity IF analysis apart from synthesis, the a priori of the judgment of definition apart from the a posteriori, be inconceivable, and of the individual and if synthesis apart from analysis, the a judgment, as 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.
This is not the place to enter again into the objections which the Kantian concept elicited (indeed could not fail to elicit): objections which PART I THE PURE CONCEPT 219 in Italy too gave rise to very acute attempts objecti at confutation, and which ended in the partial abstractionists and empiriabsorption of that concept into the mental asts against the a priori 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 think able 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 in dividual 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 ex planation, sometimes confused it with pure in tuition, 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 22O LOGIC PART 22O LOGIC PART mysticism, or of wandering in the void with scholasticism.
Instead of noting and of examining all the interpretation of the a priori objections made to the a priori synthesis (which synthesis.
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. A priori In the first place, in accordance with the synthesis in general and formula given in Logic we must not speak of the logical a priori synthesis. 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 aesthetic 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 THE PURE CONCEPT 221 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 aesthetic synthesis). The a priori synthesis is not less operative in the practical activity than in the aesthetic 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 defini tion with the individual judgment, is not a priori synthesis in general, but logical a priori synthesis. / 222 LOGIC PART Non-logical Having clearly established this point we are a priori a priori syntheses. 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 = 1 2," 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 4- 7 = 1 2 " 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 possi bility of simply analytic or simply synthetic judgments in pure logic. On the other hand, i THE PURE CONCEPT 223 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.
A question of no less importance is whether The a priori .. synthesis, as the logical a priori synthesis (we might say, the synthesis, not of opposites but of 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 224 LOGIC PART 224 LOGIC PART 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 I 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 pre supposes an aesthetic a priori synthesis. When 1 See above, Sect. I. Chap. VI.
THE PURE CONCEPT 225 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 awn 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 aesthetic 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.
Q The category in the judgment. Difference between category and innate idea.
LOGIC PART LOGIC PART 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 innate 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 in- THE PURE CONCEPT 227 differently that to think is to conceive, or that to think is to judge, because the two formulae 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.
A final explanation, not less important than The a priori synthesis, the those already given, concerns the importance of destruction of transcendency, the logical a priori synthesis. This too has "??'**.
•* J objectivity been diminished by the very man who discovered °fknowledse- and defined that mental act, and even more by those who have repeated him, without being capable of reviving again the moment of dis covery, 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 re presentative element was placed outside and prior to the concept, the latter seemed to be 228 LOGIC PART 228 LOGIC PART inferior to it, almost as though it were an ex pedient 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 appre hend 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 THE PURE CONCEPT 229 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 J 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 cogniza- bility of reality, and in making triumphant the power of thought over the real, which is the power of the real to know itself.
But this efficacy of the a priori synthesis re- Power of mained obscure to its discoverer (and most .. never known to obscure to his orthodox followers). To such its discoverer.
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 PART 230 LOGIC synthesis was confused with simple analysis and with simple synthesis. These being manipula tions 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 con stitutes, 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; no/ 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 i THE PURE CONCEPT 231 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.
Ill LOGIC AND THE DOCTRINE OF THE CATEGORIES The demand WHEN the definition of the a priori synthesis for a complete table of the and of the category has been attained, it is usual categories.
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. A request Logic, in our opinion, should reject this extraneous to Logic. demand, the origin of which lies in the confusion Logical and \j real categories, 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 PARTI THE PURE CONCEPT 233 as to the nature of reality. Its scope is to define categories and to formulate judgments only on t that aspect of Reality, which is logical tho^lght. 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 indi cate and to deduce them. It is not obliged to indicate and to deduce all the supreme predicables and categories.
Now we have already treated of the question The uniqueness of the logical as to the categories of Logic and have solved it, category: the concept.
partly affirmatively, partly in the negative. That is to say, we have denied to Logic a multiplicity of categories, since the three fundamental cate gories, usually given as concept, judgment, and ^ syllogism, have been revealed to be identical. The others, derived from formalist Logic and relating to classes of concepts, to forms of judg ments and to figures of the syllogism (and even these three preceding, if they are taken as separ able or distinguishable), have been shown to be empirical and arbitrary. Finally, those that were based upon the gnoseology of the pseudoconcepts have shown themselves to be extraneous to pure Logic. On the other hand, we have affirmed the category proper to Logic, — the unique category PART The other categories. No longer logical, but real. $ Systems of categories.
234 LOGIC to which it gives rise. It has been defined as the pure concept, at once judgment of definition and i ^individual judgment, the logical a priori synthesis. Thus the enquiry can be looked upon as exhaust ive as regards this part of the subject.