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 196 LOGIC PART 196 LOGIC PART 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 con stitutive 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 homo geneous 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. Mathematical A final observation, suggested by the difference space and time space and time between pure individual judgments (or judgments THE PURE CONCEPT 197 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 follow ing 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 un reality or abstract ideality, or, as we prefer to call it, abstractness.
THIRD SECTION THIRD SECTION IDENTITY OF THE PURE CONCEPT AND THE INDIVIDUAL JUDGMENT THE LOGICAL A PRIORI SYNTHESIS I Result of preceding enquiry: the judgment of definition and the individual judgment.
IDENTITY OF THE JUDGMENT OF DEFINITION (PURE CONCEPT) AND OF 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 demon strated 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 PARTI THE PURE CONCEPT 199 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 con cept of man exists, or is thought.
The distinction between the two forms, the Distinction between the judgment of definition and the individual judg- two.-truth of reason and ment, is universally recognized. Not only can truth of fact, necessary and it be found, as has already been noted, in at contingent,etc., J formal and least one of the significations which have been material- attached to the two classes of judgments, analytic and synthetic, but it is even more clearly expressed in the well - known distinc - tion between truth of reason and truth of fact, 200 LOGIC PART between necessary truths and contingent truths, between truths a prori 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 pro position, 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 i THE PURE CONCEPT 201 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 (ration ally) 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.
Yet, notwithstanding the apparently glaring Absurdities arising distinction between the judgment of definition from these distinctions; and the individual judgment, between truth of the J ° judgment as 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 distinc tion 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 dis tinguished two fundamental forms of the Spirit: the representative or fantastic form, and the logical. Now, in positing as distinct the judg ment of definition and the individual judgment, 202 LOGIC PART 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 some thing ultralogicaP. 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 representa tion, it is also true that this representation is not found there as it would be found in aesthetic con templation, 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 i THE PURE CONCEPT 203 think that a fact was not the fact it had been? The existence of Caesar 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. Caesar and Napoleon are as necessary as quality and becoming.
It follows from these considerations (which or duality of logical could be easily multiplied) that the individual forms. 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 dis tinction between forms of the spirit, but a sub- distinction 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 • 204 LOGIC PART that universal should be distinguished from universal by the introduction of individuality as element of differentiation is inconceivable. Difficulty of The difficulty becomes greater from the equal abandoning the distinction, inconceivability and impossibility of abandoning the result reached above, by which the individual J 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 uni versality, 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. The hypothesis There seems to be but one way out of such a of reciprocal implication difficulty i namely, to preserve the result attained, and so of the J identity of the 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, THE PURE CONCEPT 205 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 pre supposition 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 206 LOGIC PART can attach greater importance now to the defini tion, and now to the statement of fact; now to the subject, and now to the predicate. objection; the This path, which would offer such advantages lack of an historical and and would constitute a true way out of the representative element in difficulty, seems, however, to be closed to us by definitions.
the fact that in definitions there is no trace what ever 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.
We must not, however, be in a hurry, but rather carefully recall the observation just made THE PURE CONCEPT 207 incidentally: that the verbal or literary form can The historical element in throw into relief a moment of the judgment, definitions, taken in their 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 per ceptive 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 pre sented, it would certainly be impossible to dis cover a representative element and an individual judgment. But the reason for this is that it has been mutilated and made abstract and indeter minate, to such an extent that it can be made 208 LOGIC PART 208 LOGIC PART 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. The definition For every definition is the answer to a as answer to a question and question, the solution of a problem. Did we solution of a problem. 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; with out 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 VJ question colours the answer and that a definition taken in its concreteness is determined by the THE PURE CONCEPT 209 problem which gives it rise. The definition varies with the problem.
But the question, the problem, the doubt, historical conis always individually conditioned. The doubt ditionednessof J J every question of the child is not that of the adult, the doubt of ^d problem. 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 1 800 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 p 2IO LOGIC PART 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 defini tions.
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 t 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 THE PURE CONCEPT 211 outside water, or however high we climb, to fly outside air.
If we posit individual or historical conditions The definition as also for every thinking of the concept, or of every historical judgment.
definition (conditions which constitute the doubt, x of reason and the problem, the question, to which the definition °ffact- 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.
Such a theory as this, although it goes against considerations .. confirming this.
the ordinary way of thinking (though this, in its 2i2 LOGIC PART turn, suffers from its own contradictions), can be made convincing even to ordinary thought, when it is led to reflect upon what is implicitly under stood 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 coin- • cident 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 THE PURE CONCEPT 213 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.