Part 13

The abuse of empirical or classificatory judgments is not less in relation to perception, which, as we know, is nothing but the series of individual judgments. It frequently happens that when entering upon the discussion of real facts, and having in mind groups and series of pseudoconcepts, we hastily form empirical judgments, which take the place of pure individual judgments and are taken in exchange for them. From these exchanges have arisen certain famous controversies about the truth of perception, such as that indicated by the instance of the stick immersed in water, which seems to the eye to be broken, whereas it is whole and straight. The usual answer to such a view is that the error lies in the judgment, since perception as perception is never wrong. This answer is not altogether correct, since the perception is a judgment, and if the judgment is wrong, the perception also is wrong. On the contrary, the error is not in the judgment, but in the prejudice that the stick in question is in reality straight, and that when immersed in water the genuine reality is disturbed by a new element; as though the stick outside the water possessed greater or less reality than when immersed in the water. This error arises from the construction of the empirical concept of "stick," taken as a true and proper concept, so that when the stick is immersed in water and seems to be broken it seems not to answer to its true concept. Strictly speaking, the perception of the stick as broken or otherwise altered is not less true than that of the straight stick; the absurdity, occasioned by the empirical concept, arises from seeking the true perception among various perceptions, in order to make of it the basis and foundation of the others declared illusory. This error would seem to be of slight importance, so long at least as it is a matter of a stick; but it entails most serious consequences, since it is owing to similar errors that outside the Spirit there has come to be posited _the Thing in itself._

[Sidenote: _Abstract concepts and individual judgments._]

Passing from the empirical to the abstract concepts, if these latter presuppose the pure concept, they do not on the other hand presuppose individual judgments. For example, in order to form the concepts of numerical series, or of geometrical figures, it is not necessary to know individual things. Those concepts are abstract, just because they are without any representative content, and therefore no representative element is required for their formation.

[Sidenote: _Impossibility of direct application of the first to the second._]

But if this be so, it is clear that they cannot alone be translated into individual pseudojudgments. They will certainly give rise to judgments of definition (though always arbitrary and abstract), but not to individual judgments. And in truth numerical and geometrical series is not applicable to individual facts, as affirmed in individual judgments. These are at the same time different and yet inter-connected, in such a way that the one is somehow in the other. The application of numerical series or geometrical figures implies that we have before us _homogeneous_ objects (or objects which have been made homogeneous, which amounts to the same thing). Things qualitatively different elude such procedure: we cannot add up a cow, an oak, and a poem. It may be urged that all things have this at least in common, that they are _things_ and can therefore be enumerated as such. But things, as such, or things in general are innumerable, being infinite; which amounts to saying that the series of things in general is the same as numerical series. Doubtless numerical series can be constituted; but our enquiry concerns the possibility of making direct applications of numbers to the individual; that is to say, whether or not they give rise to _abstract_ individual judgments. We must reply to this question in the negative. The formula "abstract individual judgments" is itself a contradiction in terms; for the individual taken in itself can never be abstract, nor the abstract ever individual, even through a practical fiction.

[Sidenote: _Intervention of empirical judgments as intermediaries. Reduction of the heterogeneous to the homogeneous._]

The consequence of this demonstration is then that if abstract concepts can be applied to individual judgments (and they are as a fact applied), there must be an intermediary which makes the application possible. The Individual empirical judgments are just such an intermediary. They reduce the heterogeneous to the homogeneous and prepare the ground for the application of the abstract concepts and for the formation of their corresponding pseudojudgments. These are therefore more correctly termed empirico-abstract judgments than individual-abstract judgments. Empirical and empirico-abstract judgments cannot then be presented as two co-ordinate classes of the individual pseudojudgment. They are two forms, of which the second is evolved from the first.

The reduction of the _heterogeneous_ to the _homogeneous_ is effected by means of the procedure already discussed, by the formation of classes and classification with them as basis. Individual varieties, which escape all numerical application, are thus subdued, and we obtain in exchange things belonging to the same class, as for example oaks, cows, men, ploughs, plays, pictures, and so on. These things are finite in number (as we already know from our analysis of the representative elements contained in a determinate empirical concept) and can therefore be numbered. Thus we can finally arrive at pronouncing the empirico-abstract judgments: "These cows number one hundred," "these oaks are three hundred in number," "there are four hundred houses in this village," "it contains two thousand inhabitants," "there are two ploughs in this field," and so on. Or we can say elliptically: "100 cows," "300 oaks," "400 houses," "2000 inhabitants," "2 ploughs," and so on, as is done in statistics and inventories.

[Sidenote: _Empirico-abstract judgments and enumeration (measurement, etc.)._]

If the procedure proper to individual judgments has been described as _classification,_ that of empirico-abstract judgments is rightly called _enumeration._ Enumeration also makes possible another procedure, known as _measurement,_ and what has been said by way of example about abstract concepts of number must be repeated _mutatis mutandis_ of geometrical figures, which are employed as instruments of measurement. The procedure of measurement is somewhat more complicated; enumeration and measurement are related to one another as are arithmetical and geometrical concepts, but substantially they come to the same thing. The definition sometimes given of measurement can be extended to enumeration in general, namely, that it is _qualitative quantity_ applied to quality, strictly speaking, to quality rendered homogeneous by the process of classification. The empirico-abstract judgments are in fact qualitative-quantitative.

[Sidenote: _Enumeration and intelligence._]

If classification does not imply understanding things and assigning to them their value, neither does enumeration imply intelligence and comprehension, because it consists of a manipulation, which is altogether extrinsic and indifferent to the quality of the things enumerated. That given objects are capable of enumeration or measurable as ioo, or iooo, or 10,000 reveals nothing as to their character. It is only as the result of gross illusion that value is sometimes believed to be a function of number, and that value increases or diminishes with the increase or diminution of number. The common saying that number is not quality is a good answer to that illusion.

[Sidenote: _So-called conversion of quantity into quality._]

A mental fact, afterwards called the transition from _quantity_ to _quality,_ or the conversion of quantity into quality, has certainly been known since ancient times. This transition finds a parallel in those logical diversions, in which, granted the admission, apparently as legitimate as it is slight, that by the removal of a single hair from the head of a luxuriantly haired individual, that individual does not become bald, or that by the removal of a single grain from a heap, the heap does not disappear, one hair or one grain after another is removed, and he of the luxuriant locks becomes bald and for the heap is substituted the bare ground. But the error is in reality contained entirely in the first admission. A man with a head of hair or a heap of grain are what they are, so long as nothing in them is changed. The change of quantity is translated into change of quality, not because the first concept is constitutive of the second, but, on the contrary, because the second is constitutive of the first. Quantity has been obtained, measurement has been effected, by starting from quality, determined in the pure individual judgment and made homogeneous in the empirical judgment, which is the basis of the judgment of enumeration and of measurement. Thus quality constitutes the only real content of the abstract quantitative concept. By the taking away of the hair or the grain, _quality_ itself is changed through the _quantitative formula._ That is to say, quantity does not pass into quality, but one quality passes into another quality. Quantity, taken by itself, as an abstract determination, is impotent in presence of the real.

[Sidenote: _Mathematical space and time and their abstraction._]

A final observation, suggested by the difference between pure individual judgments (or judgments of reality and value, if it please you so to call them), and quantitative or empirico-abstract judgments, is that the entire conception of things as occupying various portions of _space_ and following one another in a _discontinuous_ manner, _separated_ from one another in _time,_ is derived from the last type of pseudojudgments, namely the quantitative. It is an _alteration_ effected for practical ends from the ingenuous view offered by pure perception. To show, as we have shown, the genesis of quantitative judgments and so of mathematical space and time, amounts to describing their nature and giving their definition. It amounts to revealing them as thoughts of _abstractions,_ which are not to be confounded with real thought, or with genuine thought of reality. The Kantian concept of the _ideality_ of _time_ and _space_ gives the same result. This doctrine is among the greatest discoveries of history, and should be accepted by every philosophy worthy of the name. In accepting it ourselves, we make but one reservation (justified by the proofs given above), namely, that the character of mathematical space and time should be called not ideality (because ideality is true reality), but rather _unreality_ or _abstract ideality,_ or, as we prefer to call it, _abstractness._

THIRD SECTION

IDENTITY OF THE PURE CONCEPT AND THE INDIVIDUAL JUDGMENT THE LOGICAL _A PRIORI_ SYNTHESIS

I

IDENTITY OF THE JUDGMENT OF DEFINITION (PURE CONCEPT) AND OF THE INDIVIDUAL JUDGMENT

[Sidenote: _Result of preceding enquiry: the judgment of definition and the individual judgment._]

The descent, as we have called it, from the pure concept to the intuition, or the examination of the relations which are established between the concept and the intuitions, when we have attained the first, and of the ensuing transformations, to which the second are subject, might at first sight seem complete. The concept, which was first contemplated in abstraction, has been demonstrated in a more concrete manner, in so far as it takes the form of language and exists as the judgment of definition. Further, we have shown how, when thus concretely possessed, it reacts upon the intuitions from which it was formed, or how it is applied to them, as it is called, giving rise to the individual or perceptive judgment. The transition from the intuitions to the concept, and so to the expression of the concept or the judgment of definition, and from this to the individual judgment, has been followed and demonstrated in its logical necessity. Thus the two distinct forms are also united, the first being the presupposition and base of the second, so that the connection seems at first sight to be perfect. The judgment of definition is not an individual judgment; but the individual judgment implies a previous judgment of definition. To think the concept of man does not mean that the man Peter exists. But if we affirm that the man Peter exists, we must first have affirmed that the concept of man exists, or is thought.

[Sidenote: _Distinction between the two: truth of reason and truth of fact, necessary and contingent, etc., formal and material._]

The distinction between the two forms, the judgment of definition and the individual judgment, is universally recognized. Not only can it be found, as has already been noted, in at least one of the significations which have been attached to the two classes of judgments, analytic and synthetic, but it is even more clearly expressed in the well-known distinction between _truth of reason_ and _truth of fact,_ between _necessary truths_ and _contingent_ truths, between truths _a priori_ and truths _a posteriori,_ between what is _logically_ and what is _historically_ affirmed. Indeed, it is only on the basis of this distinction that it seems possible to give any content to the logical doctrine, which recognizes the possibility of propositions true _in form_ and false _in fact._ This doctrine, as usually stated, is altogether untenable. It is impossible, above all, to maintain that formal truth can be distinguished from effective truth, always assuming that "form" is understood in its philosophical sense and not in that of formalist Logic, where it indicates an arbitrarily fixed externality, which, as such, is neither true nor false. It is therefore impossible to maintain that one and the same proposition can be true in one respect and false in another; for a proposition can be judged only from one point of view, which is that of its unique signification and value. But it is clear that once we admit the distinction between truth of reason and truth of fact, affirmations of both kinds might be found incorporated in the same verbal proposition, one of them false and the other true. For example, that the saying of Cambronne, "The Guard dies and never surrenders," is a "sublime saying" is formally (rationally) true, but it is materially (as fact) false, because Cambronne did not utter those words. On the other hand, that the _Assedio di Fiorenze_ of Guerrazzi is "a very beautiful book, because it inflamed many youthful bosoms with love of country," is materially (as fact) true, but it is formally (rationally) false, because the fact of its having produced such an effect is not proof of the beauty of a book, since beauty does not consist of practical efficacy.

[Sidenote: _Absurdities arising from these distinctions; the individual judgment as ultralogical._]

Yet, notwithstanding the apparently glaring distinction between the judgment of definition and the individual judgment, between truth of reason and truth of fact; notwithstanding its secular celebrity and its confirmation by universal agreement and common usage, this distinction meets with a very grave difficulty. In order to understand it, we must, above all, establish clearly what we have just stated in positing that distinction and in making the individual judgment or truth of fact _follow_ the judgment of definition or truth of reason. We have already posited a distinction of this kind between intuition and concept, and have noted that we have thus distinguished two fundamental forms of the Spirit: the representative or fantastic form, and the logical. Now, in positing as distinct the judgment of definition and the individual judgment, do we mean to do something analogous? Do we mean to distinguish the logical form (concept or definition) from another form, no longer logical, although containing the logical form in itself as overcome and subordinate, in the same way that the concept contains in itself the intuition? In other words, is the individual judgment something _ultralogical_? It can certainly be asserted that it is not mere definition; but can it be asserted that it is not logical? The words used should not lead to misconception. If in the individual judgment the subject be a representation, it is also true that this representation is not found there as it would be found in æsthetic contemplation, but as subject of a judgment, and therefore not as a representation pure and simple, but as a representation thought, or made logical. Hegel has several times remarked that whoever doubts the unity of individual and universal can never have paid attention to the judgments which he utters at every instant. In these, by means of the copula, he resolutely affirms that Peter _is_ a man, or that the individual (the subject) _is_ the universal (predicate); not something different, not a piece or fragment, but just that, the universal. Further, are not truths of fact also truths of reason? Would it not be irrational to think that a fact was not the fact it had been? The existence of Cæsar and of Napoleon is not less _rational_ than that of quality and of becoming. And are not both kinds of facts equally necessary--those called contingent not less than those called necessary? We are right to laugh at those who like to think that things could have happened otherwise than they have happened. Cæsar and Napoleon are as necessary as quality and becoming.

[Sidenote: _or duality of logical forms._]

It follows from these considerations (which could be easily multiplied) that the individual judgment is not less logical than that of definition. Truths of fact, contingent and _a posteriori,_ are not less logical than those of reason, necessary and _a priori._ But if this be so, the distinction between the two forms would not be a distinction between forms of the spirit, but a subdistinction within the logical form of the spirit: a subdistinction of which we have already denied the possibility. For it is not clear how a logical thought, or thought of the universal, can be _two_ thinkings, one in one way, one in another: one universal of the universal, the other universal of the individual. Either the first is void, or the second is improper. Intuition and concept are distinguished as individual from universal; but that universal should be distinguished from universal by the introduction of individuality as element of differentiation is inconceivable.

[Sidenote: _Difficulty of abandoning the distinction._]

The difficulty becomes greater from the equal inconceivability and impossibility of abandoning the result reached above, by which the individual judgment was shown to be possible only by means of a concept or judgment of definition. Every attempt that may be made to cancel that presupposition and to reconceive the individual or perceptive judgment as preceding the concept and being altogether without logical character, a mere assertion of fact, unenlightened by universality, must be considered, for the reasons we have given, to be entirely vain. If we cannot admit a duality of logical forms, still less can we admit that an alogical character, below the level of logic altogether, attaches to the individual judgment.

[Sidenote: _The hypothesis of reciprocal implication and so of the identity of the two forms._]

There seems to be but one way out of such a difficulty: namely, to preserve the result attained, that is to say, the necessity of the judgment of definition as the presupposition of the individual judgment, but to affirm at the same time the necessity of the individual judgment as the presupposition of the judgment of definition. Admitting this supposition by way of hypothesis, let us see what it would mean and what effect it would have in the discussion. Since the one judgment presupposes the other, and this presupposition is reciprocal, we could no longer talk of distinction between the two, but of unity pure and simple, of _identity,_ in which distinction could arise only by abstraction and the arbitrary act of dividing what cannot exist save as indivisible. But, on the other hand, the distinction, although abstract, would always retain its value as a didactic means of making clear the true nature of the logical act. Thus we should justify our first proceeding to develop the concept and the judgment of definition and then the individual judgment, and also the reservation that we have always made as to the provisional nature of such distinction, and thus also the new question as to the unity of the act, put and answered in the way proposed. All the difficulties arising from the appearance of a duality of logical forms would disappear. Definitions and individual judgments, truth of reason and truth of fact, necessity and contingency, _a priori_ and _a posteriori,_ would be revealed as one act and one truth. And we should also be justified in talking of them as distinct acts, for in expressing that single truth and single judgment verbally or in literature, we can attach greater importance now to the definition, and now to the statement of fact; now to the subject, and now to the predicate.

[Sidenote: _Objection: the lack of an historical and representative element in definitions._]

This path, which would offer such advantages and would constitute a true way out of the difficulty, seems, however, to be closed to us by the fact that in definitions there is no trace whatever of individual judgments which, on this hypothesis, would have to be contained within and be one with them. If we say "the will is the practical form of the spirit," or "virtue is the habit of moral actions," where is to be found in such statements the individual judgment and the representative element? We find in them without doubt the verbal form, expressive and representative, which is necessary to the concept for its concrete existence; but we do not find the statement of fact of which we are in search. Thus the proposed hypothesis will prove very ingenious and rich with all the advantages that we have stated; but since it does not appear to be confirmed by facts, we must, it seems, reject it, even at the risk of having to think out a better one, or, if we fail in this, of renouncing as desperate the attempt at a solution.

[Sidenote: _The historical element in definitions, taken in their concreteness._]