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 inwords, concepts in propositions. The most considerable attempt of the kind that has been made, which has many zealous followers in our day, ismathematical Logic,also calledcalculatory, algebraical, algorhythmic, symbolic, a new analytic,or aLogical 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 withquantity and quality together; it is a science ofthings in general; it isuniversal mathematics,containing also, subordinated to itself, the mathematical sciences properly so-called, but not coinciding with these. It means to be, not mathematics, buta 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 theproposition 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 byp, 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 logicalsum a + bis the smallest concept, which contains the other twoaandband is what was previously called the "sphere of the concept"; the logicalproduct a x bindicates the greater concept contained inaand inb,and answers to that which was previously called "comprehension." There are also new orrenovated laws, like the law ofidentity,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 ofcommutation,by whichab = ba;—or that of absorption, by whicha(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 thequantification 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 andpredicate. 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 withaand "some mortals" withb,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 thescience 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 theuniversal Language.As a formula ofpractical utilityit 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."
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 perfectlylogical; 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 anewrepresentation, 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 themotherthan they formerly were; from being indiscriminate it makes them discriminate; from fantastic, logical; from clear but indistinct (asused 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 belooked 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 ajudgmentof 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 ordefinitivejudgment, the second may be called anindividualjudgment.
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 therepresentationcan be trulysubject;and only theconceptcan bepredicate.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 arelation 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 theanalyticjudgment, 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; thesyntheticjudgment, 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 meaningand 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 famousintellectual 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 leastperceptive 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 wepossess the world,by means of which aworld exists.
and with the commemorative or historical judgment.
In perceptive judgments also, are comprised those judgments which are called by somecommemorativeorhistorical,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 offactand judgments ofvalue,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 ita 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 anought 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, alyricismof 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 isintuitiveand not perceptive; and that the concepts donot originatefrom the intellectual act of perception, but enter the act itself asconstituents.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, thefirstform of the cognitive spirit, but not because it is the most simple, but precisely because it is thelast; 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 foundanother 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.
[1]See above, Section I.Chap. VI.
[1]See above, Section I.Chap. VI.
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 moreproperly assumes the name ofcoptila,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 liberoPulsanda 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 alwaysexistential,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"; inreply 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. Thereforethe 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 cannotjudge 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 ofgold 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 ahundred dollars, and of a virtuous Pamela." Now the mountain, the dollars, and Pamela are, as such, not the absolutely non-existent, but certain facts,subjectsof 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,differentfrom 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 sometimesarbitrary constructions,made by combining images for amusement or with some other intention; sometimes, on the contrary, thedesires,which accompany every volitional act and are the infinitepossibilitiesof 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 effectivereality and possible reality, into existence and non-existence, or mere representability. Some modern investigators of what is called thetheory 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 tounreal 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 theeffectuality,thereality,or, in short, theexistenceof images, which have theineffectualornon-existentas 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 thatexistencein the individual judgment is apredicate.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 knowledgesui generis,sometimes called a knowledge ofposition,sometimes an act of belief, orfaith;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 thereare 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 calledfaith,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" tobe 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 somethingsui 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 unconsciousmetaphysical dualism,which assumes an object external to the spirit, and makes the spirit apprehend it with anact of faithand afterwards reason about it with an act ofthought.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 theindividual 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."