Logic as the Science of the Pure Concept

by Benedetto Croce

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.

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.

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.

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.

Erroneous separation of truth and reason of truth in the pure concepts.