For the rest, the difficulties that befall those who conceive existentiality in the individual judgment as something sui generis, are illustrated by the theory to which they find themselves led, of a double '.kind of judgment, the existential and the categorical, without their being able to justify this duality. This is at bottom the most apparent manifestation of their more or less un conscious metaphysical dualism, which assumes an object external to the spirit, and makes the spirit apprehend it with an act of faith and after wards reason about it with an act of thought. Why not always continue with an act of faith? Or why not also extend the act of thought to the initial judgment? We have either to continue upon the same path, or to change it altogether — this is the dilemma which imposes itself here.
But in rejecting the double form of the i THE PURE CONCEPT 175 individual judgment, the one existential, the other The predicate of existence as categorical, and in resolving both into the single not sufficing to constitute a constitute a form, which is the categorical by making exist- judgment. ence a predicate among predicates, we must also explain for what reason (in reply to the third of the questions into which we have divided the treatment of existentiality) we now say that the predicate of existence does not suffice to con stitute the judgment. How can it fail to suffice? If I say that " Peter is," or that " The ^Egean is," have I not before me a perfect judgment? and is it not simply a judgment of existence? But here, too, we must repeat: cave; beware of the decep tions of verbalism; think of things, not of words. The judgments adduced as an example are so little judgments of existence that in them we speak of the ^^Egean" and of " Peter," and since we speak of them, it is clear that we know that the ^Egean, for example, is a sea, and what a sea is, and so on; that Peter is a man, and a man made in this or that way, an Italian and not a Bushman, thirty years old' and not a month, and so on. The merely representative element cannot be found in the judgment by fixing it in a word, which, in so far as it forms part of the judgment, is, like all the rest, penetrated with logical character; and when we say that " Peter " 176 LOGIC PART is the subject and is representation, and " exist ing " is the predicate, we speak in a general sort of way and almost symbolically. If we are look ing for the formula of the merely existential judg ment in relation to a representation, that is, of a judgment which leaves the representation free from all other predicate save that of existence, such a formula could only be "Something is." But upon mature consideration this formula would no longer be an individual judgment, since every logical transfiguration of the individual and every individual determination of the universal would not have been excluded: it would corre spond neither more nor less than to a judgment of definition which asserts that "something" (something in general, indeterminate) " is " or that " reality is." The predicate But our theory concerning the indispensability of judgment as...the totality of of other predicates in constituting the judgment the concept.
is not to be understood as an affirmation of the necessity that any other predicate of any sort should be added to the predicate of existence, nor even that all the others possible should be added to it. In the first case, we shall always have an unjustifiable duality of predicates: that of existence and that necessary for essentializing and completing the judgment; in the second, THE PURE CONCEPT 177 duality would certainly be avoided, since to constitute the judgment all the predicates would be necessary, without their distinction into a double order, and all would be qualitative predi cates; but there would remain the idea of a successive addition of predicates. Granted this idea, it is impossible ever to understand what those acts would be, by which the first, or also the second, or also the third predicate, and so on, should be attributed, without yet attaining in such attributions the full totality of truth. They are representations no longer; and not yet judgments: they are then something in sufficient and one-sided, whose existence could not be admitted save arbitrarily (as in Psychology), and which, therefore, would be inadmissible in Philosophy. It therefore only remains to conclude that in the judgment, all possible predicates are given in one act alone; that is, that the subject is predicated as existence, and for this very reason determined in a particular way; de termined in a particular way, and for this very reason, as existence.
In other words, the concept which is predicated in the individual judgment is not and cannot be a foetus or a sketch of a concept; but is the whole concept, in its indivisible unity, as universal, N 178 LOGIC PARTI particular and singular. And if existence seem to be a first predicate, the reason lies perhaps in this, that the concept of existence as actuality and action, and in its distinction from mere possibility, is perhaps the fundamental concept of the real, although on the other hand it is not truly thinkable save as determined in the particular forms of reality; hence that first predi cate is first only in so far as it contains the last, that is to say, is neither last nor first, but the whole. To explain these statements is in any case, as has been said, the task of the whole of Philosophy, not of Logic alone, which here, as elsewhere, must rest satisfied with demonstrating the point that most closely concerns it; that is to say, the impossibility of separating from one another in the judgment, the predicates necessary for the determination of the reality of the fact, the absence of any one of which renders the judgment itself impossible.
VI THE INDIVIDUAL PSEUDOCONCEPTS. CLASSI FICATION AND ENUMERATION As pseudoconcepts imitate pure concepts and individual pseudothe corresponding judgments of definition, so judgments. by means of them are imitated pure individual judgments, and spiritual formations are obtained, which can be conveniently called individual pseudojudgments.
The character of these pseudojudgments, like Their .. practical that of the pseudoconcepts, is not cognitive, but character. 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 Danae is a mythological picture "; or if of ' a literary work we say, " The Promessi Sposi is a historical romance "; — what have we learned as i8o LOGIC PART to the true nature of the Promessi Sposi, of the Transfiguration, of the Danae, 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. Genesis of the This lack of all determination as to value, distinction between judg- which is characteristic of individual pseudoments of fact and judgments concepts, gives support to the distinction beof -value; and tween judgments of fact (as individual pseudo- judgments are sometimes called) and judgments of value; a distinction which makes evident the further need of supplying the spirit with what the THE PURE CONCEPT 181 J 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 arbi trary (that is to say, conceived extrinsically to the determination of fact). True individual judg ments are pure, and in them the universal pene trates the individual and the determination of value coincides with that of fact. In pseudo- judgments 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, com bination or aggregation of subject with predicate.
Having made this clear, it is superfluous to importance of the individual repeat that we do not intend to remove, or even pseudo- judgments. to attenuate, the due importance of individual pseudojudgments, as we did not remove or at tenuate 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 patri mony of his own knowledge? It is easier for a 1 82 LOGIC PART 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 land scapes, and so on; save when I wish to under stand 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 Jive 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 THE PURE CONCEPT 183 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 X 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 i/ cosmos.
But in proceeding further to determine the Empirical individual differential characteristics presented by pseudo- udment and abstract judgments in contrast with individual judgments, V^jjj 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.
In comparing empirical individual judgments LOGIC TART Process of formation of empirical judgments., with pure individual judgments — for example, " The Transfiguration is a sacred picture," an empirical judgment, and " The Transfiguration is an aesthetic work," a pure judgment — the first thing to note is that the empirical individual judgment presupposes the pure individual judg ment. 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 pro nounced, we must first have the empirical con cept 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 " aesthetic work "; and it is only when a certain number, more or less large, of artistic works have been recognized as such, THE PURE CONCEPT 185 that is, when pure individual judgments con cerning them have been formed, that we can abstract the characteristics and pass to the formation of the pseudoconcepts: sacred, his torical, mythological pictures, landscapes, and so on. Having obtained these, then, and only then, when we stand before an aesthetic work, for example, the Transfiguration, and formulate again the pure individual judgment which recognizes it as such (" The Transfiguration is an aesthetic work "), are we enabled finally to apply the pseudoconcept and to pronounce the empirical judgment: " The Transfiguration is a sacred picture."
The consequence of the process here re- its foundation in existence.
cognized 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 exis- tentiality. 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.
LOGIC PART LOGIC PART Dependence of empirical judgments upon pure judgments.
This is the case with hypotheses and with other provisional methods of thought. But the empiri cal judgment is related to the individual or existential judgment, and it also employs pseudo- concepts 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 character istics 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.
Another consequence is that empirical con cepts 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 i 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.
THE PURE CONCEPT 187 New knowledge is expressed in new pure in- I dividual 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 transforma tion 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 judg ments based upon it, now that we no longer admit the existence of that element, which was at one time believed to be separated from com bustible 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 i88 LOGIC PART 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? Empirical The empirical judgment, in so far as it applies judgments as classification, 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.
1 classification Classification is an essential function, for the and intelligence. reasons already given, which it would be use- ( less to repeat; but to classify is not to realize \ intellectually, to understand, to grasp, to com prehend. If therefore, in life, we disapprove of those unmethodical people who detest classifica tion, we do not disapprove any the less of the THE PURE CONCEPT 189 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 re lating 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 estab lishing whether the Promessi Sposi were or were \ not an aesthetic work, and what movement of / the spirit it represents, it was considered to be the duty of criticism to enquire whether that j 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.
The abuse of empirical or classificatory judg- interchange of the two, and ments is not less in relation to perception, which, genesis of perceptive as we know, is nothing but the series of individual ^d judicial illusions.
judgments. It frequently happens that when LOGIC PART entering upon the discussion of real facts, and having in mind ^groups and series of pseudocon- cepts, we hastily form empirical judgments, which take the place of pure individual judgments and are taken in exchange for them. From these ex changes 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 percep tion 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 pre judice 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 THE PURE CONCEPT 191 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.
Passing from the empirical to the abstract Abstract concepts and concepts, if these latter presuppose the pure ^dividual judgments.
concept, they do not on the other hand pre suppose 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.
But if this be so, it is clear that they cannot impossibility...of direct alone be translated into individual pseudoiudo-- application J ' of the first ments. They will certainly give rise to judgments to of definition (though always arbitrary and ab stract), but not to individual judgments. And in truth numerical and geometrical series is not LOGIC LOGIC 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 homo geneous, which amounts to the same thing). Things qualitatively different elude such pro cedure: 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 con stituted; 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. The consequence of this demonstration is then i THE PURE CONCEPT 193 that if abstract concepts can be applied to indi- intervention of empirical vidual judgments (and they are as a fact applied), judgments as intermediaries.
there must be an intermediary which makes the application possible. The Individual empirical ]e0tetrh°egeneous judgments are just such an intermediary. They hom°seneous- 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 homo geneous 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 repre- ' sentative elements contained in a determinate o 194 LOGIC PART 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.
If the procedure proper to individual judg- mentsand ments has been described as classification, that enumeration (measurement, 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 qualitaetc.
THE PURE CONCEPT 195 tive quantity, quantity applied to quality, strictly speaking, to quality rendered homogeneous by the process of classification. The empirico-abstract judgments are in fact qualitative-quantitative.
If classification does not imply understanding Enumeration things and assigning to them their value, neither intelligence. does enumeration imply intelligence and com prehension, 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 100, or 1000, 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.
A mental fact, afterwards called the transition conversion from quantity to quality, or the conversion of of quantity into quality.