Part 10

Certainly, that venatio medii, that ergo, that unification of triplicity, are things of much importance. But whence comes their importance if not from being the expression of the synthetic force of thought, of thought which unifies and distinguishes, and distinguishes because it unifies and unifies because it distinguishes? And is triplicity truly triplicity, one, two, three, arithmetically enumerable? But if this be so, how is it that we never succeed in counting those three, resolving each one of them into a series of similar terms, or of other propositions and concepts? Upon attentive consideration we perceive that here, too, the number three is symbolical, and that it does no more than designate the distinction, which unifies or thinks the singular concept in the universal through the particular, or determines the universal through the particular, by making it a singular concept, whence it remains perfectly certain that the relation of these three determinations is not numerical. Such a logical operation, not being anything special, but simply logical reasoning itself, is of necessity found also in the judgment.

A possible objection at this point is that even if the unity of judgment and syllogism can be held to be demonstrated as regards definitions and syllogisms which are the basis of definitions, yet it has not been demonstrated for the other forms of syllogisms and logical judgments, which are not definitive. But if these judgments and syllogisms be logical, they cannot fail to be definitive, or to have for their content affirmations of concepts. "All men are mortal" is a definition of the concept of man, whose mortality is verbally emphasized or his immortality denied. It is without doubt an incomplete definition, because it is torn from the web of thoughts and of speech of which it formed part; and this web will also always be incomplete or capable of infinite completion by means of new affirmations and new negations. But in its incompleteness it is at the same time also complete, because it affirms a concept of reality, of life and death, of finite and infinite, of spirituality and of its forms, and so on; these are all presupposed determinations, and therefore existing and operating in the concepts of man and mortality. "Caius is a man" (which is the second premiss of the syllogism traditionally adduced as an example) is certainly not a definition (though it presupposes and contains many definitions) precisely for the reason that it is not a pure logical judgment. Hence it happens that the conclusion itself: "therefore Caius is mortal," is more than a pure logical conclusion, since it also contains a historical element, the person of Caius. But we shall speak further on of these individual or historical judgments; and then we shall also see in what relation they stand to the universal or pure logical judgments, and if it be truly possible to distinguish between them, otherwise than for the sake of convenience. The distinction is in any case convenient and does no harm at this point; and therefore for didactic reasons we allow it to stand; indeed we make use of it.

Just as in the case of definitions, so also in the case of the syllogism, it is to be noted that the verbal expression does not consist of an obligatory formula, but assumes the most varied forms, apparently very remote from syllogizing as commonly understood. The abuse of the syllogism as a formula continued for centuries, notably in mediæval Scholasticism, and notwithstanding the rebellion of the Renaissance, it has persisted among many philosophical schools, its last conspicuous manifestation being the didactic elaboration of the Leibnitzian philosophy, or Wolffianism. Certain of Wolff's demonstrations have remained famous, such as that concerning the construction of windows, contained in his Manual of Architecture. "A window must be large enough for two persons to lean against it, side by side," he developed it in this way: "Demonstration. It is customary to lean against a window with another person in order to look out. But the architect must serve the interests of his employer in everything. Therefore he must make the window large enough for two persons to be able to be there side by side. Q.E.D."

No more such syllogistic pedantries have been seen in our times, but (as has been already remarked in reference to pedantry of definition) contempt for the formula has too often resulted in contempt even for the correctness of the reasoning. So that it has sometimes been necessary to advise a bracing bath of scholasticism, and it has been observed and lamented of certain new civilizations (for example, of Russian culture, or of the Japanese people, who are so little addicted to mathematics), that they have not had a scholastic period, like that of the West, so general with them is the habit of incorrect, loose, and passionately impulsive and fantastic reasoning. Certainly the formula, the exercise of disputation in forma, the logica scholastica utens has its merits; and we must know how to have recourse to it when it is advantageous to do so, and to express thought in the brief and perspicuous formulæ of the syllogism, of the sorites, or of the dilemma. From this point of view the new methods of mathematical Logic or Logistic, upon which some are now working, and even the logical machines which have been constructed, would help; they would help--if they helped. For the point is just this: when formulæ, methods of demonstration, machines and the like, are recommended, expedients and instruments of practical or economic use are thereby proposed; and these cannot make good their existence otherwise than by getting themselves accepted for the utility--the saving of time and space, and so of fatigue, which they effect. Like all technical inventions, those products must be brought to the market; and the market alone decides upon their value and assigns to them their price. At the present time, it seems that logistic methods have no value and price, save for certain narrow circles of people, who amuse themselves with them in their own way and so pass the time.

Certain erroneous doctrines take their origin from the undue separation of demonstration and definition, conspicuously that particular error which places a difference of degree between truth and reason of truth, and consequently admits that a truth can be known without its reason being known. But a truth, of which the reason is not known, is not even truth; or it is truth only in preparation and in hypothesis. We hear much about the intuition with which men of genius are equipped, and which enables them to go straight to the truth, even when they are not capable of demonstrating it. But this intuition, when it is not that truth in preparation, or that orientation towards a truth still quite hypothetical, must of necessity be thought and thus also be demonstration of truth; it must be truth and also reason of truth; thought and reasoning performed no doubt with lightning rapidity, which is expressed in brief propositions and needs going over again and rethinking, in order that it may afford a more ample and, from the didactic point of view, a more persuasive, exposition; but it is always thought and reasoning.

Things are still worse, when not only is a diversity of degree admitted, but the complete indifference of demonstration to truth is proclaimed, so that many or infinite possible demonstrations of one identical truth would be possible. If by this it were meant merely that one identical truth, or one identical concept, can assume infinite verbal or expressive forms, and if demonstration were understood as "exposition" or "expression," there would be nothing to object. But if by demonstration be meant something truly logical, that which is properly called by that name in Logic, this thesis leads directly to the negation of truth, making the demonstration of truth, or truth itself, an illusion, a sophistical appearance created simply to persuade. Those acquainted with courts of law know that very often when a magistrate has made his decision and pronounced sentence he deputes to a younger colleague the task of "reasoning" it, or of providing an appearance of reasoning to what is indeed not a logical product, but simply the voluntas of a certain provision. But though this procedure be intelligible and useful when it occurs in the field of practice and of law, it cannot be admitted in the theoretical field, where it would be the ruin of thought and indirectly of the will itself.

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

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.

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.

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.

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.

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.

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 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 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.

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.

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.

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.

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.

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.

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."

THE INDIVIDUAL JUDGMENT AND PERCEPTION

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?

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.

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.