Part 14

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.

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 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._]