Chapter IX.(21) On Logic In General.
Logic, Dialectic, and Rhetoric go together, because they make up the whole of a _technic of reason_, and under this t.i.tle 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 _a.n.a.lyt. Post._, i. 11), the art of conversation directed to the mutual investigation of truth, especially philosophical truth. But a conversation of this kind necessarily pa.s.ses 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. .h.i.therto 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 pa.s.s 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 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.
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 ident.i.ty 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 a.s.sert 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 ground 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 versa_. 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 princ.i.p.al 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, 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 quant.i.ty, 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 circ.u.mstance 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 quant.i.ty 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 circ.u.mstance that the language has no word to express by itself the part that is here to be separated 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 a.s.sertions as to the relation of two (in the case of the disjunctive judgment even several) categorical judgments to each other. The _hypothetical judgment_ a.s.serts 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, a.s.serts 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 epa????, inductio, is with Aristotle the opposite of the apa????. 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 epa????, 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 apa???? leads to our rejecting it. Therefore the epa????, 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 apa????, 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 a.s.sumed 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.
Chapter X. On The Syllogism.
Although it is very hard to establish a new and correct view of a subject which for more than two thousand years has been handled by innumerable writers, and which, moreover, does not receive additions through the growth of experience, yet this must not deter me from presenting to the thinker for examination the following attempt of this kind.
An inference is that operation of our reason by virtue of which, through the comparison of two judgments a third judgment arises, without the a.s.sistance of any knowledge otherwise obtained. The condition of this is that these two judgments have _one_ conception in common, for otherwise they are foreign to each other and have no community. But under this condition they become the father and mother of a child that contains in itself something of both. Moreover, this operation is no arbitrary act, but an act of the reason, which, when it has considered such judgments, performs it of itself according to its own laws. So far it is objective, not subjective, and therefore subject to the strictest rules.
We may ask in pa.s.sing whether he who draws an inference really learns something new from the new proposition, something previously unknown to him? Not absolutely; but yet to a certain extent he does. What he learns lay in what he knew: thus he knew it also, but he did not know that he knew it; which is as if he had something, but did not know that he had it, and this is just the same as if he had it not. He knew it only _implicite_, now he knows it _explicite_; but this distinction may be so great that the conclusion appears to him a new truth. For example:
All diamonds are stones; All diamonds are combustible: Therefore some stones are combustible.
The nature of inference consequently consists in this, that we bring it to distinct consciousness that we have already thought in the premisses what is a.s.serted in the conclusion. It is therefore a means of becoming more distinctly conscious of one"s own knowledge, of learning more fully, or becoming aware of what one knows. The knowledge which is afforded by the conclusion was _latent_, and therefore had just as little effect as latent heat has on the thermometer. Whoever has salt has also chlorine; but it is as if he had it not, for it can only act as chlorine if it is chemically evolved; thus only, then, does he really possess it. It is the same with the gain which a mere conclusion from already known premisses affords: a previously _bound or latent knowledge_ is thereby set _free_. These comparisons may indeed seem to be somewhat strained, but yet they really are not. For because we draw many of the possible inferences from our knowledge very soon, very rapidly, and without formality, and therefore have no distinct recollection of them, it seems to us as if no premisses for possible conclusions remained long stored up unused, but as if we already had also conclusions prepared for all the premisses within reach of our knowledge. But this is not always the case; on the contrary, two premisses may have for a long time an isolated existence in the same mind, till at last some occasion brings them together, and then the conclusion suddenly appears, as the spark comes from the steel and the stone only when they are struck together. In reality the premisses a.s.sumed from without, both for theoretical insight and for motives, which bring about resolves, often lie for a long time in us, and become, partly through half-conscious, and even inarticulate, processes of thought, compared with the rest of our stock of knowledge, reflected upon, and, as it were, shaken up together, till at last the right major finds the right minor, and these immediately take up their proper places, and at once the conclusion exists as a light that has suddenly arisen for us, without any action on our part, as if it were an inspiration; for we cannot comprehend how we and others have so long been in ignorance of it. It is true that in a happily organised mind this process goes on more quickly and easily than in ordinary minds; and just because it is carried on spontaneously and without distinct consciousness it cannot be learned. Therefore Goethe says: "How easy anything is he knows who has discovered it, he knows who has attained to it." As an ill.u.s.tration of the process of thought here described we may compare it to those padlocks which consist of rings with letters; hanging on the box of a travelling carriage, they are shaken so long that at last the letters of the word come together in their order and the lock opens. For the rest, we must also remember that the syllogism consists in the process of thought itself, and the words and propositions through which it is expressed only indicate the traces it has left behind it-they are related to it as the sound-figures of sand are related to the notes whose vibrations they express. When we reflect upon something, we collect our data, reduce them to judgments, which are all quickly brought together and compared, and thereby the conclusions which it is possible to draw from them are instantly arrived at by means of the use of all the three syllogistic figures. Yet on account of the great rapidity of this operation only a few words are used, and sometimes none at all, and only the conclusion is formally expressed. Thus it sometimes happens that because in this way, or even merely intuitively, _i.e._, by a happy _appercu_, we have brought some new truth to consciousness, we now treat it as a conclusion and seek premisses for it, that is, we desire to prove it, for as a rule knowledge exists earlier than its proofs. We then go through our stock of knowledge in order to see whether we can find some truth in it in which the newly discovered truth was already implicitly contained, or two propositions which would give this as a result if they were brought together according to rule. On the other hand, every judicial proceeding affords a most complete and imposing syllogism, a syllogism in the first figure. The civil or criminal transgression complained of is the minor; it is established by the prosecutor. The law applicable to the case is the major. The judgment is the conclusion, which therefore, as something necessary, is "merely recognised" by the judge.
But now I shall attempt to give the simplest and most correct exposition of the peculiar mechanism of inference.
_Judging_, this elementary and most important process of thought, consists in the comparison of two _conceptions_; _inference_ in the comparison of two _judgments_. Yet ordinarily in text-books inference is also referred to the comparison of conceptions, though of _three_, because from the relation which two of these conceptions have to a third their relation to each other may be known. Truth cannot be denied to this view also; and since it affords opportunity for the perceptible demonstration of syllogistic relations by means of drawn concept-spheres, a method approved of by me in the text, it has the advantage of making the matter easily comprehensible. But it seems to me that here, as in so many cases, comprehensibility is attained at the cost of thoroughness. The real process of thought in inference, with which the three syllogistic figures and their necessity precisely agree, is not thus recognised. In inference we operate _not_ with mere _conceptions_ but with whole _judgments_, to which quality, which lies only in the copula and not in the conceptions, and also quant.i.ty are absolutely essential, and indeed we have further to add modality. That exposition of inference as a relation of _three conceptions_ fails in this, that it at once resolves the judgments into their ultimate elements (the conceptions), and thus the means of combining these is lost, and that which is peculiar to the judgments as such and in their completeness, which is just what const.i.tutes the necessity of the conclusion which follows from them, is lost sight of. It thus falls into an error a.n.a.logous to that which organic chemistry would commit if, for example, in the a.n.a.lysis of plants it were at once to reduce them to their _ultimate_ elements, when it would find in all plants carbon, hydrogen, and oxygen, but would lose the specific differences, to obtain which it is necessary to stop at their more special elements, the so-called alkaloids, and to take care to a.n.a.lyse these in their turn. From three given conceptions no conclusion can as yet be drawn. It may certainly be said: the relation of two of them to the third must be given with them. But it is just the _judgments_ which combine these conceptions, that are the expression of this relation; thus _judgments_, not mere _conceptions_, are the material of the inference. Accordingly inference is essentially a comparison of two _judgments_. The process of thought in our mind is concerned with these and the thoughts expressed by them, not merely with three conceptions. This is the case even when this process is imperfectly or not at all expressed in words; and it is as such, as a bringing together of the complete and una.n.a.lysed judgments, that we must consider it in order properly to understand the technical procedure of inference.
From this there will then also follow the necessity for three really rational syllogistic figures.
As in the exposition of syllogistic reasoning by means of _concept-spheres_ these are presented to the mind under the form of circles, so in the exposition by means of entire judgments we have to think these under the form of rods, which, for the purpose of comparison, are held together now by one end, now by the other. The different ways in which this can take place give the three figures. Since now every premiss contains its subject and its predicate, these two conceptions are to be imagined as situated at the two ends of each rod. The two judgments are now compared with reference to the two _different_ conceptions in them; for, as has already been said, the third conception must be the same in both, and is therefore subject to no comparison, but is that _with which_, that is, in reference to which, the other two are compared; it is the _middle_. The latter is accordingly always only the means and not the chief concern. The two different conceptions, on the other hand, are the subject of reflection, and to find out their relation to each other by means of the judgments in which they are contained is the aim of the syllogism. Therefore the conclusion speaks only of them, not of the middle, which was only a means, a measuring rod, which we let fall as soon as it has served its end. Now if this conception which is _identical_ in both propositions, thus the middle, is the subject of _one_ premiss, the conception to be compared with it must be the predicate, and conversely.
Here at once is established _a priori_ the possibility of three cases; either the subject of one premiss is compared with the predicate of the other, or the subject of the one with the subject of the other, or, finally, the predicate of the one with the predicate of the other. Hence arise the three syllogistic figures of Aristotle; the fourth, which was added somewhat impertinently, is ungenuine and a spurious form. It is attributed to Galenus, but this rests only on Arabian authority. Each of the three figures exhibits a perfectly different, correct, and natural thought-process of the reason in inference.
If in the two judgments to be compared the relation between the _predicate of the one and the subject of the other_ is the object of the comparison, the _first figure_ appears. This figure alone has the advantage that the conceptions which in the conclusion are subject and predicate both appear already in the same character in the premisses; while in the two other figures one of them must always change its roll in the conclusion. But thus in the first figure the result is always less novel and surprising than in the other two. Now this advantage in the first figure is obtained by the fact that the predicate of the major is compared with the subject of the minor, but not conversely, which is therefore here essential, and involves that the middle should a.s.sume both the positions, _i.e._, it is the subject in the major and the predicate in the minor. And from this again arises its subordinate significance, for it appears as a mere weight which we lay at pleasure now in one scale and now in the other. The course of thought in this figure is, that the predicate of the major is attributed to the subject of the minor, because the subject of the major is the predicate of the minor, or, in the negative case, the converse holds for the same reason. Thus here a property is attributed to the things thought through a conception, because it depends upon another property which we already know they possess; or conversely. Therefore here the guiding principle is: _Nota notae est nota rei ipsius, et repugnans notae repugnat rei ipsi_.
If, on the other hand, we compare two judgments with the intention of bringing out the relation which the _subjects of both_ may have to each other, we must take as the common measure their predicate. This will accordingly be here the middle, and must therefore be the same in both judgments. Hence arises the _second figure_. In it the relation of two subjects to each other is determined by that which they have as their common predicate. But this relation can only have significance if the same predicate is attributed to the one subject and denied of the other, for thus it becomes an essential ground of distinction between the two. For if it were attributed to both the subjects this could decide nothing as to their relation to each other, for almost every predicate belongs to innumerable subjects. Still less would it decide this relation if the predicate were denied of both the subjects. From this follows the fundamental characteristic of the second figure, that the premisses must be of _opposite quality_; the one must affirm and the other deny.
Therefore here the princ.i.p.al rule is: _Sit altera negans_; the corollary of which is: _E meris affirmativis nihil sequitur_; a rule which is sometimes transgressed in a loose argument obscured by many parenthetical propositions. The course of thought which this figure exhibits distinctly appears from what has been said. It is the investigation of two kinds of things with the view of distinguishing them, thus of establishing that they are _not_ of the same species; which is here decided by showing that a certain property is essential to the one kind, which the other lacks.
That this course of thought a.s.sumes the second figure of its own accord, and expresses itself clearly only in it, will be shown by an example:
All fishes have cold blood; No whale has cold blood: Thus no whale is a fish.
In the first figure, on the other hand, this thought exhibits itself in a weak, forced, and ultimately patched-up form:
Nothing that has cold blood is a whale; All fishes have cold blood: Thus no fish is a whale, And consequently no whale is a fish.
Take also an example with an affirmative minor:
No Mohamedan is a Jew; Some Turks are Jews: Therefore some Turks are not Mohamedans.
As the guiding principle for this figure I therefore give, for the mood with the negative minor: _Cui repugnat nota, etiam repugnat notatum_; and for the mood with the affirmative minor: _Notato repugnat id cui nota repugnat_. Translated these may be thus combined: Two subjects which stand in opposite relations to one predicate have a negative relation to each other.
The third case is that in which we place two judgments together in order to investigate the relation of their _predicates_. Hence arises the _third figure_, in which accordingly the middle appears in both premisses as the subject. It is also here the _tertium comparationis_, the measure which is applied to both the conceptions which are to be investigated, or, as it were, a chemical reagent, with which we test them both in order to learn from their relation to it what relation exists between themselves. Thus, then, the conclusion declares whether a relation of subject and predicate exists between the two, and to what extent this is the case. Accordingly, what exhibits itself in this figure is reflection concerning two properties which we are inclined to regard either as _incompatible_, or else as _inseparable_, and in order to decide this we attempt to make them the predicates of one subject in two judgments. From this it results either that both properties belong to the same thing, consequently their _compatibility_, or else that a thing has the one but not the other, consequently their _separableness_. The former in all moods with two affirmative premisses, the latter in all moods with one negative; for example:
Some brutes can speak; All brutes are irrational: Therefore some irrational beings can speak.
According to Kant (_Die Falsche Spitzfinigkeit_, -- 4) this inference would only be conclusive if we added in thought: "Therefore some irrational beings are brutes." But this seems to be here quite superfluous and by no means the natural process of thought. But in order to carry out the same process of thought directly by means of the first figure I must say:
"All brutes are irrational; Some beings that can speak are brutes,"
which is clearly not the natural course of thought; indeed the conclusion which would then follow, "Some beings that can speak are irrational,"
would have to be converted in order to preserve the conclusion which the third figure gives of itself, and at which the whole course of thought has aimed. Let us take another example:
All alkalis float in water; All alkalis are metals: Therefore some metals float in water.
[Alkalis and Metals overlapping circles]
Figure 1