Chapter II: The Concept and the Verbal Form, the Syllogism

[Sidenote: _Identity of definition and syllogism._]

The definition not only is not a formula separable or distinguishable from the thread of the discourse, but it cannot even be separated or distinguished from the ratiocinative forms or forms of demonstration, as is implied in the custom of logicians, who make the doctrine of the definition or of the _systematic_ forms, as they usually call them, follow that of the forms of demonstration. They ingenuously imagine that thought, after having had a rough-and-tumble with its adversaries, and after having proclaimed, shouted, and finally vindicated its own right, mounts the rostrum and henceforth calm and sure of itself begins to define. But, in reality, to think is to combat continuously without any repose; and at every moment of that battle there is always peace and security; and definition is indistinguishable from demonstration, because it is found at every instant of the demonstration and coincides with it. _Definition and Syllogism_ are the same thing.

[Sidenote: _Connection of concepts and thought of the concept._]

The syllogism, indeed, is nothing but a connection of concepts; and although it has been disputed as to whether it must be considered so, or rather as a connection of logical propositions or judgments, the dispute is at once solved, so far as we are concerned, by observing :hat precisely because the syllogism is a connection of concepts, and concepts only exist in verbal forms, that is to say, in propositions or judgments, the syllogism is also a connection of judgments. This serves to reinforce the truth that if the effective presence of the verbal form must always be recognized in the logical fact, it must, on the other hand, be forgotten when Logic is being constructed and the nature of Logic and of the concept is being sought. Now, the connection of the concepts represents nothing new in relation to the thinking of the concept. As has already been seen, to think the concept signifies to think it in its distinctions, to place it in relation with the other concepts and to unify it with them in the unique concept. A concept thought outside its relations is indistinct, that is to say, not thought at all.

Therefore, the connection of the concepts, or syllogizing, cannot be conceived as a new and more complex logical act. To syllogize and to think are synonymous; although, in the ordinary use of language, the term "to syllogize" throws into special relief the verbal aspect of thinking, and, more exactly, the _dynamic_ character of verbal exposition, which is indeed the very character of this exposition, for it is with difficulty, or only empirically, that it can be distinguished into static and dynamic, definition and demonstration.

[Sidenote: _Identity of judgment and of syllogism._]

But if the syllogism be thus identified with the concept itself, it may nevertheless seem that it must be distinguished from the judgment of definition seeing that the syllogism is a form of logical thought, and consequently of verbal expression, quite distinct from and incapable of being confounded with any other: a connection of _three_ judgments, two of which are called _premisses_ and the third _conclusion,_ closely cemented by the syllogistic force, which is placed in the _middle_ term. This character of triplicity seems ineradicable and peculiar to the syllogism in contrast with the judgment.

Some question, however, must be raised concerning this characteristic because of another characteristic universally recognized in the syllogism; namely, that the premisses are conclusions of other syllogisms, just as the conclusion becomes, in its turn, a premiss. This being so, it might be said with greater truth that the syllogism is to syllogize or to think; and since this is infinite, so the propositions of which it consists are also infinite. On the other hand, there is no judgment which is not a syllogism, since it is clear that he who affirms a judgment affirms it by some reasoning or syllogism, present and active in his spirit, though more or less understood in the words. And are not other propositions understood in the syllogisms which are properly so-called, not only in the forms, which are called abbreviated (immediate inferences, enthymemes, etc.), but also in all the other forms; since it is admitted that every syllogism, as has just been observed, presupposes other preceding syllogisms, indeed an infinity of others? It will be replied that at the end of the chain there must yet be found the difference between judgment and syllogism, or two first judgments, which are not produced by syllogism, and form the columns, upon which the structure of the first conclusion rests. But such an answer (if it do not imply simply the strange fancy that thought has a beginning and therefore also an end in time) will mean that judgment and syllogism are distinct in intrinsic character, which makes the one the necessary condition of the other. Now, this intrinsic distinctive character is precisely what cannot be found, because it does not exist; and if it be not in every link, it is vain to seek it at the beginning of the chain.

[Sidenote: _The middle term and the nature of the concept._]

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.

[Sidenote: _Pretended non-definitive logical judgments._]

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.

[Sidenote: _The syllogism as fixed verbal form. Its use and abuse._]

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.[1] _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.

[Sidenote: _Erroneous separation of truth and reason of truth in the pure concepts._]

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.

[Sidenote: _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.

[Footnote 1: Mentioned in Hegel, _Wiss. d. Logik 2,_ iii. 370 _n._]