The Irrational Intellect

Logic In General.

Logic, Dialectic, and Rhetoric go together, because they make up the whole of a technic of reason, and under this title they ought also to be taught—Logic as the technic of our own thinking, Dialectic of disputing with others, and Rhetoric of speaking to many (concionatio); thus corresponding to the singular, dual, and plural, and to the monologue, the dialogue, and the panegyric. Under Dialectic I understand, in agreement with Aristotle (Metaph., iii. 2, and Analyt. Post., i. 11), the art of conversation directed to the mutual investigation of truth, especially philosophical truth. But a conversation of this kind necessarily passes more or less into controversy; therefore dialectic may also be explained as the art of disputation. We have examples and patterns of dialectic in the Platonic dialogues; but for the special theory of it, thus for the technical rules of disputation, eristics, very little has hitherto been accomplished. I have worked out an attempt of the kind, and given an example of it, in the second volume of the “Parerga,” therefore I shall pass over the exposition of this science altogether here. In Rhetoric the rhetorical figures are very much what the syllogistic figures are in Logic; at all events they are worth considering. In Aristotle’s time they seem to have not yet become the object of theoretical investigation, for he does not treat of them in any of his rhetorics, and in this reference we are referred to Rutilius Lupus, the epitomiser of a later Gorgias. All the three sciences have this in common, that without having learned them we follow their rules, which indeed are themselves first abstracted from this natural employment of them. Therefore, although they are of great theoretical interest, they are of little practical use; partly because, though they certainly give the rule, they do not give the case of its application; partly because in 21 This chapter and the one which follows it are connected with § 9 of the first volume. [286]280 The World As Will And Idea (Vol. 2 of 3) practice there is generally no time to recollect the rules. Thus they teach only what every one already knows and practises of his own accord; but yet the abstract knowledge of this is interesting and important. Logic will not easily have a practical value, at least for our own thinking. For the errors of our own reasoning scarcely ever lie in the inferences nor otherwise in the form, but in the judgments, thus in the matter of thought. In controversy, on the other hand, we can sometimes derive some practical use from logic, by taking the more or less intentionally deceptive argument of our opponent, which he advances under the garb and cover of continuous speech, and referring it to the strict form of regular syllogisms, and thus convicting it of logical errors; for example, simple conversion of universal affirmative judgments, syllogisms with four terms, inferences from the consequent to the reason, syllogisms in the second figure with merely affirmative premisses, and many such. [287] It seems to me that the doctrine of the laws of thought might be simplified if we were only to set up two, the law of excluded middle and that of sufficient reason. The former thus: “Every predicate can either be affirmed or denied of every subject.” Here it is already contained in the “either, or” that both cannot occur at once, and consequently just what is expressed by the laws of identity and contradiction. Thus these would be added as corollaries of that principle which really says that every two concept-spheres must be thought either as united or as separated, but never as both at once; and therefore, even although words are brought together which express the latter, these words assert a process of thought which cannot be carried out. The consciousness of this infeasibility is the feeling of contradiction. The second law of thought, the principle of sufficient reason, would affirm that the above attributing or denying must be determined by something different from the judgment itself, which may be a (pure or empirical) perception, or merely another judgment. This other and different thing is then called the groundChapter IX. On Logic In General. 281 or reason of the judgment. So far as a judgment satisfies the first law of thought, it is thinkable; so far as it satisfies the second, it is true, or at least in the case in which the ground of a judgment is only another judgment it is logically or formally true. But, finally, material or absolute truth is always the relation between a judgment and a perception, thus between the abstract and the concrete or perceptible idea. This is either an immediate relation or it is brought about by means of other judgments, i.e., through other abstract ideas. From this it is easy to see that one truth can never overthrow another, but all must ultimately agree; because in the concrete or perceptible, which is their common foundation, no contradiction is possible. Therefore no truth has anything to fear from other truths. Illusion and error have to fear every truth, because through the logical connection of all truths even the most distant must some time strike its blow at every error. This second law of thought is therefore the connecting link between logic and what is no longer logic, but the matter of thought. Consequently the agreement of the conceptions, thus of the abstract idea with what is given in the perceptible idea, is, on the side of the object truth, and on the side of the subject knowledge. To express the union or separation of two concept-spheres referred to above is the work of the copula, “is—is not.” Through this every verb can be expressed by means of its participle. Therefore all judging consists in the use of a verb, and vice versâ. Accordingly the significance of the copula is that the predicate is to be thought in the subject, nothing more. Now, consider what the content of the infinitive of the copula “to be” amounts to. But this is a principal theme of the professors of philosophy of the present time. However, we must not be too strict with them; most of them wish to express by it nothing but material things, the corporeal world, to which, as perfectly innocent realists at the bottom of their hearts, they attribute the highest reality. To speak, however, of the bodies so directly appears to them too vulgar; and therefore they say “being,” which they think sounds better, [288]282 [289] The World As Will And Idea (Vol. 2 of 3) and think in connection with it the tables and chairs standing before them. “For, because, why, therefore, thus, since, although, indeed, yet, but, if, then, either, or,” and more like these, are properly logical particles, for their only end is to express the form of the thought processes. They are therefore a valuable possession of a language, and do not belong to all in equal numbers. Thus “zwar” (the contracted “es ist wahr”) seems to belong exclusively to the German language. It is always connected with an “aber” which follows or is added in thought, as “if” is connected with “then.” The logical rule that, as regards quantity, singular judgments, that is, judgments which have a singular conception (notio singularis) for their subject, are to be treated as universal judgments, depends upon the circumstance that they are in fact universal judgments, which have merely the peculiarity that their subject is a conception which can only be supported by a single real object, and therefore only contains a single real object under it; as when the conception is denoted by a proper name. This, however, has really only to be considered when we proceed from the abstract idea to the concrete or perceptible, thus seek to realise the conceptions. In thinking itself, in operating with judgments, this makes no difference, simply because between singular and universal conceptions there is no logical difference. “Immanuel Kant” signifies logically, “all Immanuel Kant.” Accordingly the quantity of judgments is really only of two kinds—universal and particular. An individual idea cannot be the subject of a judgment, because it is not an abstraction, it is not something thought, but something perceived. Every conception, on the other hand, is essentially universal, and every judgment must have a conception as its subject. The difference between particular judgments (propositiones particulares) and universal judgments often depends merely on the external and contingent circumstance that the language has no word to express by itself the part that is here to be separatedChapter IX. On Logic In General. 283 from the general conception which forms the subject of such a judgment. If there were such a word many a particular judgment would be universal. For example, the particular judgment, “Some trees bear gall-nuts,” becomes a universal judgment, because for this part of the conception, “tree,” we have a special word, “All oaks bear gall-nuts.” In the same way is the judgment, “Some men are black,” related to the judgment, “All negroes are black.” Or else this difference depends upon the fact that in the mind of him who judges the conception which he makes the subject of the particular judgment has not become clearly separated from the general conception as a part of which he defines it; otherwise he could have expressed a universal instead of a particular judgment. For example, instead of the judgment, “Some ruminants have upper incisors,” this, “All unhorned ruminants have upper incisors.” The hypothetical and disjunctive judgments are assertions as to the relation of two (in the case of the disjunctive judgment even several) categorical judgments to each other. The hypothetical judgment asserts that the truth of the second of the two categorical judgments here linked together depends upon the truth of the first, and the falseness of the first depends upon the falseness of the second; thus that these two propositions stand in direct community as regards truth and falseness. The disjunctive judgment, on the other hand, asserts that upon the truth of one of the categorical judgments here linked together depends the falseness of the others, and conversely; thus that these propositions are in conflict as regards truth and falseness. The question is a judgment, one of whose three parts is left open: thus either the copula, “Is Caius a Roman—or not?” or the predicate, “Is Caius a Roman—or something else?” or the subject, “Is Caius a Roman—or is it some one else who is a Roman?” The place of the conception which is left open may also remain quite empty; for example, “What is Caius?”—“Who is a Roman?” The μÀ±3É3·, inductio, is with Aristotle the opposite of the [290]284 [291] [292] The World As Will And Idea (Vol. 2 of 3) ±À±3É3·. The latter proves a proposition to be false by showing that what would follow from it is not true; thus by the instantia in contrarium. The μÀ±3É3·, on the other hand, proves the truth of a proposition by showing that what would follow from it is true. Thus it leads by means of examples to our accepting something while the ±À±3É3· leads to our rejecting it. Therefore the μÀ±3É3·, or induction, is an inference from the consequents to the reason, and indeed modo ponente; for from many cases it establishes the rule, from which these cases then in their turn follow. On this account it is never perfectly certain, but at the most arrives at very great probability. However, this formal uncertainty may yet leave room for material certainty through the number of the sequences observed; in the same way as in mathematics the irrational relations are brought infinitely near to rationality by means of decimal fractions. The ±À±3É3·, on the contrary, is primarily an inference from the reason to the consequents, though it is afterwards carried out modo tollente, in that it proves the non-existence of a necessary consequent, and thereby destroys the truth of the assumed reason. On this account it is always perfectly certain, and accomplishes more by a single example in contrarium than the induction does by innumerable examples in favour of the proposition propounded. So much easier is it to refute than to prove, to overthrow than to establish.