BENEDETTO CROCE (continued 3)

Difference between truth and reason of truth in the pseudoconcepts.

Naturally, all that has been said as to the definition and the syllogism has reference to the true and proper concept, or the pure concept. In the case of pseudoconcepts, where practical motives enter, definition is a simple command (a nominalist definition), and demonstration has no place, save for those of its elements that are derived from the pure concept: given the definitions, the reasoning must logically proceed in a determinate manner. In pseudoconcepts, then, definitions are separate from demonstrations: the first do not spring from the second and are not all one with them; the second presuppose the first and do not produce them. Of these definitions infinite demonstrations are possible, precisely because in reality none is possible, for the definitions themselves are infinite; and when a demonstration is given, this is done only pro forma; it is a deception, to conceal a practical convenience, or rather a logical reasoning employed to make it clear. It is for this reason also that the definitions employed in those demonstrations seem to be obtained by means of an act of faith in the irrational; and here faith signifies, not the confidence of thought in itself, but the making a virtue of necessity, accepting as true what is not known as such.—For the rest, pseudoconcepts and concepts have the same relation with the verbal form; that is to say, all are expressed in the most various ways, and there is no obligatory form of language, which can be called the literary form of logical character. The style of the Civil Code, which aroused the admiration of Stendhal, is not the eternal style of laws, for laws were once even put into verse; as in like barbaric times the sciences used to be put into verse. In the life of the word, concepts and pseudoconcepts rush forward in such a way that it is vain to seek there for distinction among them.

III

CRITIQUE OF FORMALIST LOGIC

Intrinsic impossibility of formal Logic.

From the fact that in the verbal form all distinctions (pure concepts, and empirical and abstract concepts, distinct concepts and opposite concepts) are indistinguishable, and on the other hand all identities, such as that of concept, definition and demonstration, appear differentiated or capable of differentiation, we can deduce the impossibility of constructing logical Science by means of an analysis of the verbal form. The condemnation of all formal Logic is thus pronounced.

Its nature.

This Logic has been variously called Aristotelian, peripatetic, scholastic, after its authors and historical representatives; syllogistic, from the doctrine that forms its principal content; formal, from its pretensions to philosophic purity; empirical, by those who tried to drive it back to its place; and although this last name is correct, it would be better to call it formal, and still better, verbal, to indicate of what the empiricism to which it is desired to allude, chiefly consists. Indeed, if empiricism be marked by its limiting itself to single representations, regrouping them in types and arranging them in classes, there is no doubt that that method of treatment is empirical, which takes the logical function, not in the eternal peculiarity of its character as thought of the universal, but only in its various particular translations or manifestations, in which it acquires contingent characteristics. Since these contingent characteristics come to it, in the first place, from the verbal form, it can well be called verbalism. Owing to its verbalism, too, it has happened, that over and above the grammars of individual languages, there has been conceived as existing a general, rational and logical Grammar; and this hybrid science, which is no longer grammar and arose from logical assumptions, has developed in such a way as to be indistinguishable from empirical or verbal Logic.

Its partial justification.

Certainly, as mere empiricism, this so-called Logic could not be condemned. And Hegel was not wrong in remarking that if people are interested in establishing that there are sixty species of parrots and one hundred and thirty-seven of veronica, it is not clear why it should be of less interest to establish the various forms of the judgment and of the syllogism. That discipline has its utility as mere empiricism, and it may be useful to any one to employ in certain cases the terminology in which an affirmation is characterized as positive or as merely negative, as particular or as universal, as a judgment that awaits reasoning and demonstration, as an immediate inference, enthymeme or sorites, as a conclusive or an inconclusive, or as a correct or an incorrect syllogism, and so on. It is also comprehensible how, as mere empiricism, it assumed a normative character, and was translated into rules; rules, which are valid within their own sphere, neither more nor less than are all empirical rules.

Its error.

But it does not limit itself to acting simply as an empirical description, nor even as a simple technique; it usurps a much more lofty office. Just as Rhetoric and Grammar, innocent and useful so long as they limit themselves to the functions of convenient grouping and convenient terminology, become false and harmful when they assume the attitude of sciences of absolute values, and must then be resolved into, and replaced by Æsthetic; so empirical or verbal Logic becomes transformed into error when it claims to give the laws of thought, or the thought of thought, which cannot be other than the concept of the concept. It is not, then, formal, as it boasts itself to be, because the only logical form is the universal, and this alone is the object of logical investigation; but it is falsely formal, since it relies upon contingencies, and must, therefore, be called formalist. We reject it here exclusively in its formalist aspect; that is to say, in so far as it is a complex of empirical distinctions that wish to pass as rational and usurp the place of true rationality.

Its traditional constitution.

Several of such empirical distinctions, such as the distinction between thought and principle of thought, truth and reason of truth, judgments and syllogisms, and such-like, have been recorded and criticized; we shall proceed to mention others, when suitable opportunities occur. Here it will be well to refer to the general physiognomy and structure of that Logic, as it was embodied for centuries in the schools and still persists in treatises.

The three logical forms.

Its point of departure is the external distinction between words and connections of words, which belongs properly to Grammar. But words are then treated by it as concepts, and connections of words, as judgments. Thus it obtains the identification of the concept with the abstract and mutilated grammatical word and arrives at the monstrous determination of the concepts as things which are not in themselves either true or false. Thus, again, by constantly calling upon the connections of the concepts for succour, it succeeds in distinguishing the judgment from the mere proposition. A double criterion is constantly adopted in establishing these and other fundamental forms: the verbal and the logical; and formalist Logic oscillates equivocally between the two different determinations; whence the alternating appearance of truth and of falsehood, with which its distinctions present themselves. The syllogism, which should be the third fundamental form, is conceived as the connection of three distinct judgments; but if it yet retains its importance and preponderance over two-membered forms or over serial forms of more than three propositions and judgments, this is really because to the distinction and enumeration of the three propositions there is added the criterion of the concept as a nexus, or as a triunity of universal, particular and singular.

The theories of the concept and of the judgment.

The three fundamental forms have been reduced by some logicians to two, by others; amplified to four or to five, by adding to them the perceptive form or the definitive and systematic form. These restrictions and amplifications have always encountered resistance, because it was justly felt that in this way one form of empiricism was being mingled with another: the verbal form with empirical distinctions drawn from other presuppositions. But in determining in particular the three fundamental forms, formalist Logic has not been able to restrict itself to the mere distinction of words and propositions, artificially placed in relation with the pure concept; but has been obliged to draw from other sources. The concepts are variously classified, sometimes from the verbal point of view, as identical, equivalent, equivocal, anonymous and synonymous; sometimes from the logical point of view, as distinct, disparate, contrary or contradictory; sometimes from the psychological point of view, as incomplete and complete, obscure and clear, the concepts further always being understood as names, so that, for example, distinct concepts are indifferently philosophically distinct concepts, and empirically distinct concepts; and the contraries are both the philosophical contraries and those empirically so-called. The same has occurred in the classification of judgments where sometimes the determinations of the concept are taken as foundation and the judgments distinguished as universal particular and individual; sometimes the intrinsic dialectic nature of the concept, and they are distinguished as affirmative, negative and indeterminate or infinite; sometimes the stages passed through in the search for truth, and they are distinguished into categorical, hypothetical and disjunctive, or apodeictic, assertory and problematic. And these forms have further always been understood verbally. "Universality" is the "totality" empirically designated by the word, and not true universality; and "individuality," on the contrary, is not only the individuality of the representation, but also the single particularity of the distinct concept; "affirmative" is differentiated from "negative" by accidental grammatical form, and not because that unique act which is thought, at once affirmation and negation (as the will is both love and hatred) can be truly divided.

The theory of the syllogism.

The classification of syllogisms, founded exactly upon the empirical conception of the judgment as the copulation of a subject and a predicate affords a suitable parallel to this method of treatment of the judgment; subject and predicate being understood in an empirical and grammatical manner, whence they are also discovered in those verbal affirmations, in which they are not distinct, because they are identical, as in the case of the judgment of definition. For empirical Logic, in the judgment: "The will is the practical form of the spirit," "will" is subject and "practical form" predicate in the same way as in "Peter is a man," "Peter" is subject, and "man" predicate. From the distinction between subject and predicate, arise the four figures of the syllogism; the criterion being the position of the middle term in the two premisses of the three propositions of which the syllogism is formed. If the middle term be subject in the first premiss and predicate in the second, we have the first figure; if it be predicate in both, the second; if it be subject in both, the third; if it be predicate in the first and subject in the second, the fourth figure ("sub-prae, turn prae-prae, turn sub-sub, turn prae-sub"). But in order to deduce the moods of each figure recourse is then had to another criterion, indeed to two other criteria; that is, to the empirical distinctions of judgments into universal and particular, and into affirmative and negative, with the four consequent determinations into universal-affirmative judgments (A), universal-negative (E), particular-affirmative (I), and particular-negative (O). Thus, in the first figure, two universal affirmative premisses constitute the first mood, and the conclusion is universal affirmative (Barbara); two premisses, both universal, but one affirmative and the other negative, constitute the second, and the conclusion is universal negative (celarent); two premisses, one universal affirmative and the other particular affirmative, constitute the third mood, and the conclusion is particular affirmative (darii); two premisses, one universal negative and one particular affirmative, constitute the fourth mood, and the conclusion is particular negative (ferio). And so on.

Spontaneous reductions to the absurd of formal Logic.

This is not the occasion to go on expounding in its other particulars this construction, of which we have given an example, for it is very well known: nor to attach importance to criticizing it, since' its foundations themselves have already been shown to be false and its hybrid genesis explained. Verbal Logic, which vaunts itself as rational, carries its own caricature in itself, namely the creation of Sophisms; because, since it seeks the force of thought in words, it cannot prevent sophistical ability from making use, in its turn, of words, in order capriciously to create thoughts and forms of thought. Thus verbal Logic, in order to combat sophisms, is constrained hastily and eagerly to abandon simple verbal connections, and to take refuge in concepts and connections of concepts thought in words; that is to say, neither more nor less than to negate the formalist point of view. And with analogous self-irony it renounces that point of view and dissolves itself, when it tries to refute the fourth figure of the syllogism, or to reduce the second, third and fourth to the first, as the only real figure, and then the first to a connection of three concepts; not to mention the permanent self-irony and patent demonstration of falsity involved in the logical deduction of the figures of the syllogism which it makes from a series of moods, recognized as not conclusive.

Mathematical Logic or Logistic.

Formalist Logic has been the object of many violent attacks from the Renaissance onwards; but it cannot be said that it has been struck in its essential part, because up to the present, the principle itself, or the incoherence from which it springs, has not been attacked. Several attempts at reform have followed and still follow; they have all of them the same defect, which is the wish to reform formal Logic without issuing from its circle, and without refuting its tacit presumption— the pretension of obtaining thought in words, concepts in propositions. The most considerable attempt of the kind that has been made, which has many zealous followers in our day, is mathematical Logic, also called calculatory, algebraical, algorhythmic, symbolic, a new analytic, or a Logical calculus or Logistic.

Its non-mathematical character.

It is admitted by those who profess it and is for the rest evident from the definitions of Logistic that have been given, that it has nothing in common with mathematics, for although the majority of its cultivators are mathematicians and use is made of the phraseology usual in Mathematics, and it is directed toward Mathematics, in certain of its practical intentions, there is nothing intrinsically mathematical in it. Logistic is a science which deals, not with quantity alone, but with quantity and quality together; it is a science of things in general; it is universal mathematics, containing also, subordinated to itself, the mathematical sciences properly so-called, but not coinciding with these. It means to be, not mathematics, but a general science of thought.

Example of its mode of treatment.

But the "thought" of Logistic is nothing but the "verbal proposition," which, in fact, supplies its starting-point. What the proposition is; whether it be possible truly to distinguish the proposition we call "verbal" from all the others, poetical, musical, pictorial; whether the verbal proposition does not bear indistinctly in itself, a series of very diverse spiritual formations, from poetry to mathematics, from history and philosophy to the natural sciences; what language is and what the concept is—these and all other questions concerning the forms of the spirit and the nature of thought, remain altogether extraneous to Logistic and do not disturb it in its work. The propositions (the concept of the proposition remaining an unexplained presupposition) can be indicated by p, q, etc.; the relation of implication of one proposition in another can be indicated by the sign ⊃, hence an isolated proposition is "that which implies itself" (p.⊃.q.). By following a method such as this, many distinctions of the traditional formalist Logic are eliminated, and in compensation for this, new ones are added and old and new are dressed in a new phraseology. The logical sum a + b is the smallest concept, which contains the other two a and b and is what was previously called the "sphere of the concept"; the logical product a x b indicates the greater concept contained in a and in b, and answers to that which was previously called "comprehension." There are also new or renovated laws, like the law of identity, by force of which, in Logic (differently from Algebra), a + a + a ... = a; by which it is desired to signify this profound truth, that the repetition of one and the same concept as many times as one wishes, always gives the same concept;—the law of commutation, by which ab = ba;—or that of absorption, by which a(a + b) = a; or—(the convention being that the negation of a concept is indicated by placing against it a vertical line) the other beautiful laws and formulæ: a + a | = a| (a | )a = a; aa | = o. This is a charming amusement for those who have a taste for it.

Identity of nature of Logistic with formalist Logic.

Thus it is seen that if the words and the formulæ be somewhat different, the nature of mathematical Logic in no respect differs from that of formalist Logic. Where the new Logic contradicts the old, it is not possible to say which of the two is right; as of two people walking side by side over insecure ground, it is impossible to say which of the two walks securely. The very doctrine of the quantification of the predicate (which has been the leaven of the reform) in no wise alters the traditional manner of conceiving the judgment, with the corresponding arbitrary manner of distinguishing subject and predicate. It simply establishes a convention with the object of being able to symbolize, with the sign of equality, the subject and the predicate:—the subject being included in the predicate, is part of it: "men are mortal" equals: "men are some mortals"; and so, "men" being indicated with a and "some mortals" with b, the judgment can be symbolized: a = b. For us, it is indifferent whether the modes of the syllogism be the 64 and the 19 recognized as valid by traditional Logic, or the 12 affirmative and the 24 negative of Hamilton's Logic, which distinguishes four classes of affirmative and four of negative propositions. It is indifferent whether the methods of conversion be three or two or one. It is indifferent whether logical laws or principles be enumerated as two, three, five or ten. Since we do not accept the point of departure, it is impossible for us, far from admitting the development, even to discuss it; save to demonstrate that from capricious choice comes capricious choice, as we have made sufficiently clear in our treatment of formalist Logic. Mathematical Logic is a new manifestation of this formalist Logic, involving a great change in traditional formulæ, but none in the intimate substance of that pretended science of thought.

Practical aspect of Logistic.

As the science of thought, Logistic is a laughable thing; worthy, for that matter, of the brains that conceive and advocate it, which are the same that are promulgating a new Philosophy of language, indeed a new Æsthetic, with their insipid theories of the universal Language. As a formula of practical utility it is not incumbent upon us to examine it here; all the more since we have already had occasion to give our opinion upon this subject. In the time of Leibnitz, fifty years later in the last days of Wolffianism; a century ago in Hamilton's time; forty years ago in the time of Jevons and of others; and finally now, when Peano, Boole, and Couturat are flourishing, these new arrangements are offered on the market. But every one has always found them too costly and complicated, so that they have not hitherto been generally used. Will they be so in the future? The practical work of persuasion, proper to the commercial traveller seeking purchasers of a new product, and the foresight of the merchant or manufacturer as to the fortune that may await that product, are not pertinent to Philosophy; which, being disinterested, could here, at the most, reply with words of benevolent patience: "If they be roses, they will bloom."

IV

THE INDIVIDUAL JUDGMENT AND PERCEPTION

Reaction of the concept upon the representation.

Problems of a widely different nature from these formalist playthings await exploration in the depths of the Science of Logic. And resuming what we have called the descent of the universal into the individual, it is of importance, after having established the relation between concept and form of expression, to examine in what way the concept reacts upon the representation, from which it appears to be at a stroke and altogether separated.

In more precise terms: Beyond doubt the concept is thought only in so far as it becomes concrete in an expressive form and itself also becomes, from this point of view, representative. Thus, a logical affirmation, or one that presents itself as logical, can be viewed under a twofold aspect, as logical and as æsthetic. It can be regarded as well thought-out, and so also very well expressed, perfectly æsthetic because perfectly logical; or as very well expressed but ill thought, or not truly thought, and so not logical, and yet sentimental, passionate and imaginative. But this expression-representation, in which the concept lives (and which is, for example, the tone, the accent, the personal form, the style, which I am employing in this book to expound Logic), is a new representation, conditioned by the concept. We now ask, not indeed the character of this representation (which is sufficiently clear), but of what kind are those representations, about and upon which, the thought of the concept has been kindled. Do they remain apart, excluded from the light of the concept, obscure as before, that is, logically obscure? Does the concept illuminate only itself in a sort of egoistic satisfaction, without irradiating with its light the representations upon which it has arisen?

Logicization of the representations.

That would be inconceivable and contrary to the unity of the spirit; and indeed, such separation and indifference do not exist. The appearance of the concept transfigures the representations upon which it arises, making them other than they formerly were; from being indiscriminate it makes them discriminate; from fantastic, logical; from clear but indistinct (as used to be said), clear and distinct. I am, for example, in such a condition of soul as prompts me to sing or to versify, and thus to make myself objective and known to myself; but I am objective and known only to fancy, so much so, that at the moment of poetical or musical expression I should not be able to say what was really happening in me: whether I wake or dream, whether I see clearly, or catch glimpses, or see wrongly. When from the variety of the multitude of representations, which have preceded and which follow it, I pass on to enquire as to the truth of them all (that is to say, the reality, which does not pass), and rise to the concept, those representations themselves must be revised in the light of the concept that has been attained, but no longer with the same eyes as formerly,—they must not be looked at, but henceforth, thought. My state of soul then becomes determinate; and I shall say, for example: "What I have experienced (and sung and made poetry of), was an absurd desire; it was a clash of different tendencies that needed to be overcome and arranged; it was a remorse, a pious desire," and so on. Thus by means of the concept is formed a judgment of that representation.

The individual judgment and its difference from the definitive judgment.

We have already studied the judgment, which is proper to the concept, and called it definitive judgment or judgment of definition. We have shown how in it there is no distinction of subject and predicate, so much so that it may be said, with regard to it, that there is neither subject nor predicate, but the complete identity of the two: a predicate or universal, which is subject to itself. However, the judgment which is now being discussed is not a simple definition and does not coincide with the first. It certainly has as its base a concept and therefore a definition; but it contains something more, a representative or individual element, which is transformed into logical fact, but does not lose individuality on that account; indeed it reaffirms its individuality with more precise distinction. This judgment is connected with the first, but it represents a further stage of thought. If the first form be a conceptual or definitive judgment, the second may be called an individual judgment.

Distinction of subject and predicate in the individual judgment

Owing to this new element, which the individual judgment contains, and the judgment of definition does not contain, we eventually find fully justified in the former that distinction between subject and predicate which verbal Logic in vain claims to discover in all judgments, including those of universal character (and even in simple propositions); so that it ends by attributing to that distinction, of which later we shall perceive the capital philosophical importance, a purely grammatical or verbal significance. Subject and predicate can be distinguished only in so far as the one is not and the other is universal, in so far as the one is not and the other is concept, that is to say, only in so far as the one is representation and the other concept. A particular or singular concept (for example, the will) is always also a universal concept; and therefore not adapted to function as a subject to which a predicate is applied; because that predicate, that universal, is already explicitly in the pretended subject itself which is net thinkable, save by means of that predicate. Only the representation can be truly subject; and only the concept can be predicate. This takes place plainly in the individual judgment, where the two elements are connected. "Peter is good," an individual judgment, implies the subject "Peter" and the predicate "good," the one not to be confounded with the other; whereas, in the definition "the will is the practical form of the spirit," "practical form" and "will" are identical.

Reasons for the variety of definitions of the judgment and of certain of its divisions.

When the attempt was made to define the judgment as differing both from the concept and from the definition, what was aimed at was the individual judgment. But, if this be so, then the definitions which conceive the judgment either as relation of representations or as relation of concepts (the subsumption of one concept under another, etc.), must be termed false, since it is henceforth clear that, as individual judgment, it must be conceived as a relation of representation and concept. On the other hand, some celebrated divisions of the judgment find their origin in the distinction made by us (which, we again repeat, is given at this point provisionally with the intention of seeking the definite formula further on), between the judgment of the concept and the judgment of the representation, between definition and individual judgment. In this way the analytic judgment, defined as that in which the concept of predicate was obtained from the subject, reveals itself as nothing but the definition, the identity of subject and predicate; the synthetic judgment, which adds to the subject something which was not there previously, is the individual judgment, logical thinking of the intuition, at first only intuited and not thought. We shall examine further on the true meaning and the definite formula of this distinction also.

The individual judgment and intellectual intuition.

To ignore the form of the individual judgment, and to recognize only that of the concept and of the definition, is an impossible position, though occasionally there appears a tendency in that direction. We perceive it, for instance, in those who seek for definitions of everything, and limit themselves to syllogizing, when there is certainly a case for thinking, but also one for looking, or for thinking while we look, and for looking while we think. This may be said truly to represent knowledge, that complete knowledge in which all anterior forms unite, and which is the result of all of them. To know is to know reality; and knowledge of reality is translated into representations, penetrated with thought. That famous intellectual intuition, which has sometimes been described as the faculty to which man aspires, but does not possess, and sometimes as a prodigious faculty, superior to knowledge itself, should be declared, with the full rigour of letter and concept, to be nothing but the individual judgment; which is, in truth, intellectual intuition or intuited intellection.

Identity of the individual judgment with perception or perceptive judgment.

But the individual judgment can take another name, much better known and more familiar: perception; and perception, in its turn, should be called, synonymously, individual judgment, or at least perceptive judgment. Perception does not consist of opening the eyes, of offering the ear, and of unlocking any of the other senses, which are wont to be enumerated, nor, in general, of abandoning oneself to sensation. The world does not enter our spirit by these wide gates; but has itself announced, in order to be received with due honours. That good folk (and among the best of folk are to be counted many philosophers) think otherwise is in truth to be explained by their wonted neglect or lack of analysis and reflection.

And further, perception is not intuition, i.e., an impression theoretically fashioned, or that stage or moment of the spirit which is represented in an eminent degree by the poet, who intuites and does not know what he intuites, indeed does not know that he does not know (because the pertinent question has not arisen, and cannot arise, in him, as poet). To perceive means to apprehend a given fact as having this or that nature; and so means to think and to judge it. Not even the lightest impression, the smallest fact, the most insignificant object, is perceived by us, save in so far as it is thought.

Hence the supreme importance of the individual judgment, which is that which embraces all knowledge produced by us at every moment, by means of which we possess the world, by means of which a world exists.

and with the commemorative or historical judgment.

In perceptive judgments also, are comprised those judgments which are called by some commemorative or historical, that is to say, those by which it is recognized that a given fact has occurred in the past. This recognition can never be founded upon anything other than present intuitions, intuitions, that is to say, of our present life, which contains the past in it, and persuades us of the veracity of a given piece of evidence, as now apprehended by us. And conversely, all perceptive judgments are, in some way, commemorative and historical, because the present, in the very act by which we hold it before our spirit, becomes a past, that is to say an object of memory and of history.

Erroneous distinction of individual judgments as of fact and of value.

On the other hand, it would be erroneous to divide individual judgments, as has often been attempted, into judgments of fact and judgments of value, claiming that the judgment, "Peter is a man," is of a different nature from: "Peter is good." Every judgment of fact, in so far as it attributes a predicate to a subject, gives to it a value, declaring it to participate in the universal or in a determination of the universal. And conversely, every judgment of value, in so far as it attributes a value, cannot attribute other than the universal or a determination of the universal, since outside the universal there is no value. Even judgments of negative form, such as: "Peter is not good," or "is not-good," or: "Peter is bad," are attributes of universality and of value; because, as we know, theoretically they do not affirm anything other than that Peter has a spiritual determination different from goodness (for example, that he is utilitarian, not yet moral). Certainly, in judgments such as these which we have selected as examples, there is mingled (this too has been noted; and at this point it suffices to recall it) the expression of an ought to be, which, in this case, is revealed in the negative formula adopted; but the expression of an ought to be or of a desire is not a judgment either of fact or of value; indeed, it is not a judgment at all; it is a mere proposition, a logos semanticos, not apophanticos, an optative or desiderative formula, a lyricism of the spirit directed to the future.[1]

The individual judgment as ultimate and perfect form of knowledge.

There is no other cognitive fact to know, beyond perception or individual judgment. In this, the ultimate and the most perfect of cognitive facts, the circle of knowledge is completed. Obscure sensibility, having become clear intuition, and then having made itself thought of the universal, in the individual judgment is logically thought, and is, henceforward, knowledge of fact or of event, that is, of effectual reality. The individual judgment, or perception, is fully adequate to reality.

Error of treating it as the first fact of knowledge.

But precisely because perception is the completion of knowledge, it must be placed not at the beginning, but at the end of cognitive life. To place it at the beginning, as mere sensibility, and to derive from it the concepts, either as the effect of psychological mechanism, or by an arbitrary act of will, is the error of sensationalists and empiricists. To conceive it as judgment, and nevertheless to place it at the beginning, and to deduce from it the concepts by further elaboration, is the error of rationalists and intellectualists. Against these, it must be firmly maintained that the first moment of knowledge is intuitive and not perceptive; and that the concepts do not originate from the intellectual act of perception, but enter the act itself as constituents. To begin with perception, understood as perceptive judgment, is to begin at the end, that is to say, with the most highly complex. Perception is thus the sole problem of gnoseology; but only because it is the whole problem, which contains in itself all the others. And it also is, if you like, the first form of the cognitive spirit, but not because it is the most simple, but precisely because it is the last; and the last, being also the whole, can also in an absolute sense be called first.

Origin of this error.

Certainly, the misunderstanding of the sensationalists and the opposing error of the rationalists contain an element of truth, since both are really concepts, which are developed from perception and presuppose it. But, on the other hand, they are not true and proper concepts, but pseudoconcepts, as we have already defined them, and these, being developed from perception, give rise, in their turn, to pseudojudgments. We shall treat of this further on; and thereby explain the genesis of the misunderstanding, that is to say, the erroneous theory will be overcome as misunderstanding and determined as truth. In this difference between individual judgments and individual pseudojudgments, between perceptions and pseudoperceptions, will also clearly be found another of the motives (and perhaps the most profound), which have divided judgments into judgments of fact and judgments of value.

Individual syllogisms.

It is also easy to understand that, as there are individual judgments, so there are also individual syllogisms; or rather, that since it is not possible to distinguish between judgments and syllogisms in philosophical Logic, for they constitute one indivisible whole, so it is not possible to distinguish individual syllogisms from individual judgments, or it is only possible to do so verbally. "Caius is dead," is indeed the conclusion of a syllogism; since it is not possible to affirm that he is mortal without some reason: for example, because he is a man, an animal, or a finite being. Thus, the syllogism: "Men are mortal, Caius is a man; therefore, Caius is mortal," is only verbally different from "Caius is mortal." We do not say that the difference of words is nothing; there is always a spiritual difference, even when, instead of saying, "Caius is mortal," we say, "He, whom I call Caius, is mortal," or when the same thought is expressed in Latin or German. But being here occupied with Logic, we declare that there is none, because, indeed, there is none, in point of difference of logical act, both forms being the realization of logical reasoning alone.

V

THE INDIVIDUAL JUDGMENT AND THE PREDICATE OF EXISTENCE

The copula: its verbal and logical significance.

Subject and predicate are indistinguishable in the judgment of definition, and distinguishable and distinct in the individual judgment; but the act of distinction (which is also union) between subject and predicate, representation and concept, is again, in the individual judgment, the same as the act of distinction and union, by means of which, in the judgment of definition, the concept is defined. In both cases thought makes essential what it thinks. In this respect there is no difference between the two forms of judgment, which we have analysed and have hitherto kept distinct for reasons of analysis. One identical act of thought distinguishes both from mere representation, in which there is wanting the "is" (logical and not verbal)—that "is," which belongs to the judgment of definition and to the individual judgment, and which in the second of these more properly assumes the name of coptila, because it unites two distinct elements, the one representative, the other logical. Here, too, of course, we must not allow ourselves to be deceived by verbalism. The essentialization, the copula, thought, cannot be made to consist of a word, which, abstracted from the whole, becomes a simple sound, and as sound can assume any other signification. In mere representation there can also be found the "is," or what, verbally and grammatically, is called copula, but there it has no value whatever as act of thought.

Nunc est bibendum, nunc pede libero Pulsanda tellus

is a proposition which possesses the "is," but in this case it has merely the value of a sign, not of an act of thought, for that phrase of old Horace is nothing but the expression of a hortatory motion. The word, too, can be suppressed, but we do not thereby suppress the act of thought. The exclamation "beautiful!" uttered before a picture may be an individual judgment, having as subject the representation of the picture, and as predicate the æsthetic universal, which is called beautiful, in which the copula (and here, also, the subject) is verbally understood, but logically existent, and therefore always also capable of verbal reintegration. On the other hand, this reintegration cannot be effected when it is a case of a mere representation or an expression of a state of the soul; because, in that case, there would be, not a reintegration, but an integration, that is to say, it would carry out that act of thought, and produce that individual judgment which was not present before.

Questions concerning propositions without subject. Verbalism.

Thus, in asking a last question concerning the individual judgment, that is to say, whether it be always existential, we must, as always, transfer the enquiry from verbal to logical analysis, and not waste time with speculations as to words or fragments of propositions, arbitrarily torn from their context, and therefore insignificant and equivocal. The dispute has been most keen in relation to what are called propositions without a subject, such as "It rains" and the like. But, although we do not intend to negate the results, obtained or obtainable from these disputes, we cannot accept the position which they imply and which renders it possible to agitate and to discuss the problem to infinity and therefore makes it insoluble. "It is raining" said with a smile of satisfaction means: "Thank heaven, it is raining"; with a feeling of disappointment: "Bother the rain for preventing my taking a walk"; in reply to some one asking what is the noise audible on the window-panes: "The audible sound is the sound of rain"; to contradict some one who says the weather is fine: "You are stating a falsehood and have not given yourself the trouble of observing; it is raining"; or it is the correction of an historical error. And so on. It is therefore waste of breath to dispute as to the logical nature of that proposition if its precise signification be not determined; and when it is truly determined (for the propositions we have substituted, taken abstractly, can also appear to have many senses and give rise to misunderstandings), we have quite abandoned the materiality of verbalism and passed to the thinking of spiritual acts, taken in themselves.

Confusion between different forms of judgments with relation to existentiality.

The question of existentiality in the act of judgment has been strangely confused, owing both to this verbalism and to the failure to keep distinct the judgment of definition and the individual judgment, and even the concept and the pseudoconcept. The question as to existence has been asked, as if it were the same in the case of a judgment of definition, like: "The Idea is," and in the case of an individual judgment like "Peter is." But in the first case, as we already know, existence coincides with essence, and that judgment only says that the Idea is thought, and therefore is; whereas the second not only says that Peter is representable, and therefore is, but that he exists; Peter might be representable and not exist; the griffin is representable and does not exist. Pseudoconcepts have also been incorrectly adduced as examples of judgment of definition in such statements as: "The triangle is thinkable, but does not possess existence," or: "The genus mammifer is thinkable, but does not exist as single animals"; for in this case it should have been said that "triangle" and "mammifer" are not thought at all, but are constructed, and therefore have neither essence nor existence. For us, then, the question of existentiality cannot arise, either for the pure judgment of definition, which is a concept and has existence as a concept, that is to say, essence; nor for the definitive judgment of the pseudoconcepts, which is not even thought; but arises only for the individual judgment, into which there enters as a constituent a representative element, that is to say, something individual and finite. Essence does not coincide with existence in the individual and finite; indeed its definition is just this: the inadequacy of existence to essence. Therefore the individual changes at every instant, and although being at every instant the universal, yet it is adequate to it only at infinity.

Determination and subdivision of the question of existence in individual judgments.

Having limited the question to the individual judgment, for which alone it has meaning, we can opportunely divide it into three particular questions: (i.) Does the individual judgment always imply that the subject of the judgment is existent? (ii.) What is the character of existentiality? (iii.) Does this character suffice to construct that judgment?

Necessity of the existential character in these judgments.

Beginning with the first, we believe that without doubt the answer is affirmative and that adherence should be given to those who have discovered and persistently defended the necessity of the existential character, thus contributing in no small degree to the progress of logical science. Whether what is represented exist or not, is doubtless indifferent to the intuitive man, to the poet or artist, simply because he does not leave the circle of representation. But it is not indifferent to the logical man, since he forms an individual judgment. He cannot judge of what does not exist.

It has been incorrectly objected that the logical judgment always remains the same, whether I have a hundred dollars in my pocket or only in my imagination; that a mountain of gold is a subject of judgment, although hitherto at least no one has found one in any part of the earth; that Pamela is a virtuous woman (whatever Barretti may have written to the contrary), although she has never lived elsewhere than in the imagination of Richardson and of Goldoni. No predicate whatsoever can be attributed to a hundred dollars, to a mountain of gold, and to a Pamela which do not exist; and if it be said that those hundred dollars are exactly divisible by two or by five; or that that mountain of gold, imagined as of a certain base and height, is measurable in terms of cubic metres, and has a value of so many millions or milliards on the market; or that Pamela is worthy of esteem and of reward; it must be noted that neither the hundred imagined dollars, nor the imagined mountain, nor the imagined Pamela are judged with these judgments, but that the judgments define simply the arithmetical concepts of number, prime number and divisibility, or the geometrical concepts of the cube, and the economic concepts of gold as merchandise, or the moral concepts of virtue, esteem and reward. No judgment whatever has been given as to those non-existent facts, because where there is nothing the king (in this case, thought) loses his rights.

The absolute and the relative non-existent.

It will be replied that we talk at every moment about these non-existent things, and consequently judge them. But here care must be taken not to confuse absolute with relative non-existence, which latter is non-existent only in name. The absolutely non-existent is what is excluded from the judgment, implicitly in the affirmative formula, explicitly in the negative formula. To him who speaks of the mountain of gold, of the possession of a hundred dollars, and of Pamela as existing realities, we reply by denying these existences, that is to say, by denying them in an absolute manner; and of those negated existences it is not possible to judge, or even to talk, precisely because they are altogether negated. Here, in fact, we are speaking of the individual judgment, which excludes its contradictory from itself, as, for that matter, is also the case with the judgment of definition. But in that absolute affirmation and negation there is also made, explicitly or implicitly, a relative affirmation or negation; as when we say, in the examples given: "The mountain of gold, the hundred dollars, Pamela, do not exist," we say at the same time: "There do exist phantasms, products of the fancy or of the imagination, of a mountain of gold, of a hundred dollars, and of a virtuous Pamela." Now the mountain, the dollars, and Pamela are, as such, not the absolutely non-existent, but certain facts, subjects of judgment, of which the predicate is expressed by the word "non-existent," which in this case is equivalent to "existing as phantasms." The absolutely non-existent is the contradictory, true and proper nothingness; the relatively non-existent (which is precisely that of the individual judgment) is an existence, different from that which the same individual judgment affirms.

Certainly relative non-existence, and the whole content of the concept of existence in general, would require more minute analysis; from which it would perhaps be seen that the so-called non-existent resolves itself into certain categories of practical facts; and thus designates sometimes arbitrary constructions, made by combining images for amusement or with some other intention; sometimes, on the contrary, the desires, which accompany every volitional act and are the infinite possibilities of the real. And it would also be seen that non-existence in the second sense, or the desires, which have been represented by art, are not in its circle in any way distinguished from effective volitions and actions; since, in order to distinguish them, it would be necessary that art should possess a philosophy of the will, however summary, whereas art is without any philosophy. This examination would lead us, however, not only outside the problem now before us, but also outside Logic, to another part of Philosophy,[1] which, although closely related to Logic (as Logic to it), must be the object of special treatment if we do not wish to produce mental confusion by offering everything at once. This was the defect, for example, of G. B. Vico, who put all books into one book, the whole book into a chapter, and frequently his whole philosophy and history into a page or a period. The present writer, though proud to call himself a Vichian, does not propose to imitate the didactic obtuseness of that man of genius.

Suffice it to have made clear, as concerns the problem which now occupies us, that every individual judgment implies the existence of what is spoken of, or of the fact given in the representation, even when this fact consists of an act of imagination, that this act may be recognized as such and as such existentialized. It assumes a concept of reality, which divides into effective reality and possible reality, into existence and non-existence, or mere representability. Some modern investigators of what is called the theory of values (students who fluctuate between psychology and philosophy, and between an antiquated philosophy and one that has the future before it) have maintained that a judgment of value cannot be pronounced when we are not dealing with an existing thing. Since for us a judgment of value is equivalent to any individual judgment, we must accept their thesis; freeing it from the embarrassment in which it finds itself in regard to unreal images (which yet give rise, as they themselves confess, to such judgments of value as the æsthetic) by observing that in that case there is the effectuality, the reality, or, in short, the existence of images, which have the ineffectual or non-existent as their content.

The character of existence as predicate.

We have in this way opened a path for the solution of the second question enunciated, which concerns the character to be assigned to the existentializing act of the judgment. Does this consist of an act of thought, that is to say, of the application of a predicate to a subject; or is it an original act of an altogether peculiar nature, which does not find its parallel in the other acts of thought? In short, is existence a predicate, or is it not? The answer, already implicitly contained in the foregoing explanations, affirms that existence in the individual judgment is a predicate. And we say "in the individual judgment" because in the judgment of definition it is not predicate, for the reason already expounded, that in that judgment there is no distinction between subject and predicate, and that in it existence coincides with essence.

Critique of existentiality as position and faith.

The traditional reply is, on the other hand, that existence, in the judgment of existence, is not a predicate, but a knowledge sui generis, sometimes called a knowledge of position, sometimes an act of belief, or faith; two determinations, which are reducible to a single one. Because, if being is conceived as external to the human spirit, and knowledge as separable from its object, so much so that the object could be without being known, it is evident that the existence of the object becomes a position, or something placed before the spirit, given to the spirit, extraneous to it, which the spirit would never appropriate to itself unless it were courageously to swallow the bitter mouthful with an irrational act of faith. But all the philosophy which we are now developing demonstrates that there is nothing external to the spirit, and therefore there are no positions opposed to it. These very conceptions of something external, mechanical, natural, have shown themselves to be conceptions, not of external positions, but of positions of the spirit itself, which creates the so-called external, because it suits it to do so, as it suits it to annul this creation, when it is no longer of use. On the other hand, it has never been possible to discover in the circle of the spirit that mysterious and unqualifiable faculty called faith, which is said to be an intuition that intuites the universal, or a thinking of the universal, without the logical process of thought. All that has been called faith has revealed itself step by step as an act of knowledge or of will, as a theoretic or as a practical form of the spirit.

There is therefore no doubt that existence, if it be something that is affirmed or denied, cannot be anything but a predicate; it can only be asked what sort of predicate it is, that is to say, what is the precise content or concept of existence, and this has already been indicated or at least sketched in the preceding explications. Objections have been made to the conceptual and predicative character of existence, such as that which maintains that if it were a predicate it would be necessary in the judgment "A is" to be able to think the two terms—A and existence—separately, whereas in the thought of A, A is already existentialized. But these objections show themselves to be sophistical; because outside the judgment A is not thinkable, but only representable, and therefore without existentiality, which predicate it only acquires in the act of judgment.

Absurd consequences of those doctrines.

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 unconscious metaphysical dualism, which assumes an object external to the spirit, and makes the spirit apprehend it with an act of faith and afterwards 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.

The predicate of existence as not sufficing to constitute a judgment.

But in rejecting the double form of the individual judgment, the one existential, the other categorical, and in resolving both into the single form, which is the categorical by making existence 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 constitute the judgment. How can it fail to suffice? If I say that "Peter is," or that "The Ægean 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 deceptions 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 "Ægean" and of "Peter," and since we speak of them, it is clear that we know that the Ægean, 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" is the subject and is representation, and "existing" is the predicate, we speak in a general sort of way and almost symbolically. If we are looking for the formula of the merely existential judgment 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 correspond 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 of judgment as the totality of the concept.

But our theory concerning the indispensability of other predicates in constituting the judgment 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, 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 predicates; 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 insufficient 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; determined 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 fœtus or a sketch of a concept; but is the whole concept, in its indivisible unity, as universal, 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 predicate 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. CLASSIFICATION AND ENUMERATION

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.

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.

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.

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.

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.

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."

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.

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

The historical element in definitions, taken in their concreteness.

We must not, however, be in a hurry, but rather carefully recall the observation just made incidentally: that the verbal or literary form can throw into relief a moment of the judgment, while casting a shadow over the other and causing it to be forgotten, without thereby ever being able to suppress it. There seemed, we remember, to be no trace of concepts in perceptive judgments or judgments of fact, and especially in those forms of them which are called merely existential and in those called impersonal. Yet there can be no doubt that none of those judgments is ever possible without the concept as basis. An analysis which does not allow itself to be arrested by appearances and examines verbal forms as regards both what they express and what they leave to be understood (though this too is expressed in its own way) has discovered it. Similarly a definition does not exist in the air, as might appear from the examples given in treatises, in which the where and the when and the individual and the actual circumstances in which the definition has been given are omitted. In a definition thus presented, it would certainly be impossible to discover a representative element and an individual judgment. But the reason for this is that it has been mutilated and made abstract and indeterminate, to such an extent that it can be made determinate only by the meaning which he to whom it is communicated likes to attach to it. If, on the contrary, we look at the definition in its concrete reality, we shall always find in it when we examine it with care the representative element and the individual judgment.