Артур Шопенгауэр
The World as Will and Idea (Vol. 2 of 3)
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 assistance 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 passing 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 asserted 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 assumed 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 illustration 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 apperçu, 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 quantity 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 constitutes the necessity of the conclusion which follows from them, is lost sight of. It thus falls into an error analogous to that which organic chemistry would commit if, for example, in the analysis 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 analyse 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 unanalysed 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 assume 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 notæ est nota rei ipsius, et repugnans notæ 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 principal 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 assumes 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.
When this is transposed into the first figure the minor must be converted, and thus runs: “Some metals are alkalis.” It therefore merely asserts that some metals lie in the sphere “alkalis,” thus [Figure 1], while our actual knowledge is that all alkalis lie in the sphere “metals,” thus [Figure 2]: It follows that if the first figure is to be regarded as the only normal one, in order to think naturally we would have to think less than we know, and to think indefinitely while we know definitely. This assumption has too much against it. Thus in general it must be denied that when we draw inferences in the second and third figures we tacitly convert a proposition. On the contrary, the third, and also the second, figure exhibits just as rational a process of thought as the first. Let us now consider another example of the other class of the third figure, in which the separableness of two predicates is the result; on account of which one premiss must here be negative:
No Buddhist believes in a God;
Some Buddhists are rational:
Therefore some rational beings do not believe in a God.
As in the examples given above the compatibility of two properties is the problem of reflection, now their separableness is its problem, which here also must be decided by comparing them with one subject and showing that one of them is present in it without the other. Thus the end is directly attained, while by means of the first figure it could only be attained indirectly. For in order to reduce the syllogism to the first figure we must convert the minor, and therefore say: “Some rational beings are Buddhists,” which would be only a faulty expression of its meaning, which really is: “Some Buddhists are yet certainly rational.”
As the guiding principle of this figure I therefore give: for the affirmative moods: Ejusdem rei notœ, modo sit altera universalis, sibi invicem sunt notœ particulares; and for the negative moods: Nota rei competens, notœ eidem repugnanti, particulariter repugnat, modo sit altera universalis. Translated: If two predicates are affirmed of one subject, and at least one of them universally, they are also affirmed of each other particularly; and, on the contrary, they are denied of each other particularly whenever one of them contradicts the subject of which the other is affirmed; provided always that either the contradiction or the affirmation be universal.
In the fourth figure the subject of the major has to be compared with the predicate of the minor; but in the conclusion they must both exchange their value and position, so that what was the subject of the major appears as the predicate of the conclusion, and what was the predicate of the minor appears as the subject of the conclusion. By this it becomes apparent that this figure is merely the first, wilfully turned upside down, and by no means the expression of a real process of thought natural to the reason.
On the other hand, the first three figures are the ectypes of three real and essentially different operations of thought. They have this in common, that they consist in the comparison of two judgments; but such a comparison only becomes fruitful when these judgments have one conception in common. If we present the premisses to our imagination under the sensible form of two rods, we can think of this conception as a clasp that links them to each other; indeed in lecturing one might provide oneself with such rods. On the other hand, the three figures are distinguished by this, that those judgments are compared either with reference to the subjects of both, or to the predicates of both, or lastly, with reference to the subject of the one and the predicate of the other. Since now every conception has the property of being subject or predicate only because it is already part of a judgment, this confirms my view that in the syllogism only judgments are primarily compared, and conceptions only because they are parts of judgments. In the comparison of two judgments, however, the essential question is, in respect of what are they compared? not by what means are they compared? The former consists of the concepts which are different in the two judgments; the latter consists of the middle, that is, the conception which is identical in both. It is therefore not the right point of view which Lambert, and indeed really Aristotle, and almost all the moderns have taken in starting from the middle in the analysis of syllogisms, and making it the principal matter and its position the essential characteristic of the syllogisms. On the contrary, its role is only secondary, and its position a consequence of the logical value of the conceptions which are really to be compared in the syllogism. These may be compared to two substances which are to be chemically tested, and the middle to the reagent by which they are tested. It therefore always takes the place which the conceptions to be compared leave vacant, and does not appear again in the conclusion. It is selected according to our knowledge of its relation to both the conceptions and its suitableness for the place it has to take up. Therefore in many cases we can change it at pleasure for another without affecting the syllogism. For example, in the syllogism:
All men are mortal;
Caius is a man:
I can exchange the middle “man” for “animal existence.” In the syllogism:
All diamonds are stones;
All diamonds are combustible:
I can exchange the middle “diamond” for “anthracite.” As an external mark by which we can recognise at once the figure of a syllogism the middle is certainly very useful. But as the fundamental characteristic of a thing which is to be explained, we must take what is essential to it; and what is essential here is, whether we place two propositions together in order to compare their predicates or their subjects, or the predicate of the one and the subject of the other.
Therefore, in order as premisses to yield a conclusion, two judgments must have a conception in common; further, they must not both be negative, nor both particular; and lastly, in the case in which the conceptions to be compared are the subjects of both, they must not both be affirmative.
The voltaic pile may be regarded as a sensible image of the syllogism. Its point of indifference, at the centre, represents the middle, which holds together the two premisses, and by virtue of which they have the power of yielding a conclusion. The two different conceptions, on the other hand, which are really what is to be compared, are represented by the two opposite poles of the pile. Only because these are brought together by means of their two conducting wires, which represent the copulas of the two judgments, is the spark emitted upon their contact – the new light of the conclusion.
