Chapter VI: The Individual Pseudoconcepts. Classification and Enumeration

[Sidenote: _Individual pseudojudgments._]

As pseudoconcepts imitate pure concepts and the corresponding judgments of definition, so by means of them are imitated pure individual judgments, and spiritual formations are obtained, which can be conveniently called _individual pseudojudgments._

[Sidenote: _Their practical character._]

The character of these pseudojudgments, like that of the pseudoconcepts, is not cognitive, but practical and more properly mnemonic. Fixing our attention upon certain examples of such judgments, if we say of an animal: "It is a squirrel," or "It is a platyrrhine monkey"; if we say of a house: "This house is thirty metres high and forty wide"; if of a painting we say: "The _Transfiguration_ is a sacred picture," or "The _Danaë_ is a mythological picture"; or if of a literary work we say, "The _Promessi Sposi_ is a historical romance";--what have we learned as to the true nature of the _Promessi Sposi,_ of the _Transfiguration,_ of the _Danaë,_ of that house and of those animals? Upon close consideration, nothing at all. The animals have been put into one or another compartment or glass case, decorated with a name which might also be different from what it is, as the compartment and the glass case might also be different; the house has been compared in respect of its dimensions to other houses or to an object arbitrarily assumed as the unit of measurement, which is the metre, but which might be the foot, the palm, and so on; the two pictures and the literary work have been looked at from the visual angle of an arbitrary character, such as the mythological, religious or historical subject. As to what they truly are, as to how all these things came to be and to live, and as to their relation with other things and with the Whole, we have been silent. Their _value,_ as it is called, remains unknown.

[Sidenote: _Genesis of the distinction between judgments of fact and judgments of value; and criticism of them._]

This lack of all determination as to value, which is characteristic of individual pseudoconcepts, gives support to the distinction between judgments of _fact_ (as individual pseudojudgments are sometimes called) and judgments of _value;_ a distinction which makes evident the further need of supplying the spirit with what the first judgments do not give, that is to say, with the meaning or value of things. But since the individual pseudojudgments are not for us what they boast themselves to be, judgments of fact, we have no need to complete them with judgments of value; which would thus be themselves arbitrary (that is to say, conceived extrinsically to the determination of fact). True individual judgments are pure, and in them the universal penetrates the individual and the determination of value coincides with that of fact. In pseudojudgments there takes place no such penetration, but only the mechanical _application_ of a predicate to a subject; so much so, that here is a true occasion for employing words which signify an extrinsic placing side by side, a reunion, combination or aggregation of subject with predicate.

[Sidenote: _Importance of the individual pseudojudgments._]

Having made this clear, it is superfluous to repeat that we do not intend to remove, or even to attenuate, the due importance of individual pseudojudgments, as we did not remove or attenuate that of pseudoconcepts, when we defined them for what they are. And how can we deny their importance, if each one of us create and employ them at every instant, if each one of us strive to keep in order as best he can the patrimony of his own knowledge? It is easier for a student to work without notes and memoranda than for any one not to make use of individual pseudojudgments. If I pass mentally in review the material that must go to form the history of Italian painting or literature, I must of necessity arrange it in works of greater or less importance, in plays and novels, in sacred pictures and landscapes, and so on; save when I wish to understand those facts historically, and then I must abandon those divisions. I must abandon them during that act of comprehension; but I must immediately resume them, if I wish to give the result of my historical research; and in this exposition it will be impossible for me to avoid saying that Manzoni, after having composed _five sacred hymns_ and _two tragedies,_ set to work upon a historical _romance_; or that _landscape painting_ was developed in the seventeenth century. These words are necessary instruments for swift understanding, and only a philosophical pedant could propose to expel them. In like manner, if I wish to buy a house, I shall visit several houses and arrange them in memory, according to the situation, their arrangement, their size and other characteristics, all formulated in pseudojudgments. I shall have to abandon all of these in the act of choice, for then the house that I shall choose will possess one only characteristic: that of being the one that suits my wants, that is to say, the one _that pleases me._ But I shall again have to employ those abstract characteristics, in my conversation with the person who sells it to me and in the contract that I make; there I shall speak, not only of my will and pleasure, but also of a house thirty metres high and forty wide, and so on. The same must be said of the squirrels and platyrrhine monkeys, which I cannot contrive to see in a museum or zoological garden, unless I describe them in that way; and I shall continue so to describe them, although those abstract characteristics have no definite value, either in permitting me to describe those animals with accuracy, or in making me understand their meaning in the universe, or in the history of the cosmos.

[Sidenote: _Empirical individual judgments and abstract individual judgments._]

But in proceeding further to determine the differential characteristics presented by pseudojudgments in contrast with individual judgments, it is necessary to consider them according to the double form, empirical and abstract, assumed by pseudoconcepts, thus distinguishing them as empirical individual judgments and abstract individual judgments.

[Sidenote: _Process of formation of empirical judgments._]

In comparing empirical individual judgments with pure individual judgments--for example, "The _Transfiguration_ is a sacred picture," an empirical judgment, and "The _Transfiguration_ is an æsthetic work," a pure judgment--the first thing to note is that the empirical individual judgment presupposes the pure individual judgment. We already know that pseudoconcepts, empirical or abstract, presuppose the idea of the pure concept; but that idea does not suffice for the formation of determinate empirical concepts, which can be employed as predicates of empirical judgments. We must not only think effectively these or those pure concepts, but they must be translated into individual judgments. Were this not so, where would empirical concepts obtain their material? Before the judgment: "The _Transfiguration_ is a sacred picture," can be pronounced, we must first have the empirical concept of "sacred picture." Now this empirical concept (setting aside the fact that it presupposes other empirical concepts which we do not here take into account, because they would complicate the problem without aiding the solution that we wish to give) presupposes in its turn the pure concept of "æsthetic work"; and it is only when a certain number, more or less large, of artistic works have been recognized as such, that is, when pure individual judgments concerning them have been formed, that we can abstract the characteristics and pass to the formation of the pseudoconcepts: sacred, historical, mythological pictures, landscapes, and so on. Having obtained these, then, and only then when we stand before an æsthetic work, for example, the _Transfiguration,_ and formulate again the pure individual judgment which recognizes it as such ("The _Transfiguration_ is an æsthetic work"), are we enabled finally to apply the pseudoconcept and to pronounce the empirical judgment: "The _Transfiguration_ is a sacred picture."

[Sidenote: _Its foundation in existence._]

The consequence of the process here recognized as to the manner in which individual empirical judgments are formed, and in virtue of which they have pure judgments as their base, is that empirical judgments also in the last analysis are based upon the concept of existentiality. Pseudoconcepts of possibility are not formed, because possibilities are infinite, and it would be vain, or of no mnemonic use, to fix types of them. When, as sometimes occurs, such types seem to be formed outside of all existence, their appearance serves, not a mnemonic purpose, but a purpose of research. This is the case with hypotheses and with other provisional methods of thought. But the empirical judgment is related to the individual or existential judgment, and it also employs pseudoconcepts of existential origin. For this reason, when giving examples of judgments of existence in the preceding chapter, we availed ourselves without scruple of empirical judgments also; for these obey the same law in relation to existentiality. "This animal is a monkey" implies, not only the existence of the animal taken as subject of the judgment; but also of that class of animals, of which the character has been abstracted, and the complex of characteristics which under the name of a monkey fulfil the function of predicate. An animal that does not exist and a class of animals that does not exist are not reducible to subject and predicate, and do not give rise to judgment of any sort.

[Sidenote: _Dependence of empirical judgments upon pure judgments._]

Another consequence is that empirical concepts and judgments are continually originated and modified by pure individual judgments. The object of empirical concepts and judgments is to maintain the possession and the easy use of our knowledge; and this with no other end than that of serving as base for our actions, and thus also as a means of attaining new knowledge. New knowledge is expressed in new pure individual judgments, which in their turn supply material for the elaboration of new empirical concepts and judgments. In this way empirical concepts and judgments must be and continually are renewed, by being dipped in the waters of pure individual judgments, true judgments of reality. From these waters they issue forth with youth renewed. If they do not do this, the worse for them: they fall ill, waste away and die. Given a rapid and profound revolution of thought, or, as it is also called, a transvaluation of all the values of life and reality, we should also have at once a no less rapid and profound transformation of all the empirical concepts and judgments previously possessed and employed. But this is continually occurring in the life of the spirit, if not in cataclysmic form, then in a more modest way. For example, who now employs the empirical concept of phlogiston, or forms judgments based upon it, now that we no longer admit the existence of that element, which was at one time believed to be separated from combustible bodies in the act of combustion? Who now says (save in jest) that such and such a syllogism is in _bramantip_ or in _fresison,_ or that a certain part of a speech is an _ornatum_ or a _hypotyposis,_ now that we no longer believe the facts upon which such concepts of the old Logic and Rhetoric were based? Who still distinguishes human destinies according to the _conjunctions_ of the stars that presided at birth, as was done when astrology was believed?

[Sidenote: _Empirical judgments as classification._]

The empirical judgment, in so far as it applies a predicate to a subject supplied by the pure individual judgment, makes that subject _enter_ that predicate, which is a _type_ or _class_; and therefore it _classifies_ the subjects of individual judgments. Thus we may also call empirical judgments, judgments of _classification._ This explains why the judgment has sometimes been considered to be nothing but a relation of subordination: for the empirical judgment does indeed subordinate a representation (which has first been logically determined by the individual judgment) to an empirical concept; that is, it places it in a class.

[Sidenote: _Classification and intelligence._]

_Classification_ is an essential function, for the reasons already given, which it would be useless to repeat; but to classify is not to _realize intellectually,_ to understand, to grasp, to comprehend. If therefore, in life, we disapprove of those unmethodical people who detest classification, we do not disapprove any the less of the perpetual classifiers, who content themselves with arranging things in classes, when on the contrary the needful thing is to penetrate their nature and peculiar value. It is a very common error to believe that something has been thoroughly understood and every problem relating to it completely solved, when it has simply been put into a drawer, that is, into a class. Thus in the not distant past, instead of establishing whether the _Promessi Sposi_ were or were not an æsthetic work, and what movement of the spirit it represents, it was considered to be the duty of criticism to enquire whether that book were a romance or a novel, a historical or didactic romance, a historical representation of persons or of environment, and so on. The zoologist too, instead of studying the history and transformations of animals, their life and habits, limited himself to adding a rare specimen to a variety, or a variety to a subspecies, or a subspecies to a species, and believed that by so doing he had completely fulfilled the function of science.

[Sidenote: _Interchange of the two, and genesis of perceptive and judicial illusions._]

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