John McTaggart A Commentary on Hegel’s Logic 1910
Subjectivity | The Doctrine of the Notion
182. The last of the three main divisions of the dialectic is called the Doctrine of the Notion (Begriff). Notion is not, perhaps, a very satisfactory translation of Begriff, but it would be difficult to find a better, and it is the translation usually adopted. The Doctrine of the Notion is divided into three divisions — Subjectivity, Objectivity, and The Idea. (In the Encyclopaedia the two first are called the Subjective Notion and the Objective Notion.)
Subjectivity is divided as follows:
I. The Notion. (Der Begriff.)
A. The Universal Notion. (Der allgemeine Begriff.)
B. The Particular Notion. (Der besondere Begriff.)
C. The Individual. (Das Einzelne.)
II. The Judgment. (Das Urtheil.)
A. The Judgment of Inherence. (Das Urtheil des Daseins.)
(a) The Positive Judgment. (Das positive Urtheil.)
(b) The Negative Judgment. (Das negative Urtheil.)
(c) The Infinite Judgment. (Das unendliche Urtheil.)
B. The Judgment of Subsumption. (Das Urtheil der Reflexion.)
(a) The Singular Judgment. (Das singulare Urtheil.)
(b) The Particular Judgment. (Das partikulare Urtheil.)
(c) The Universal Judgment. (Das universelle Urtheil.)
C. The Judgment of Necessity. (Das Urtheil der Nothwendigkeit.)
(a) The Categorical Judgment. (Das kategorische Urtheil.)
(b) The Hypothetical Judgment. (Das hypothetische Urtheil.)
(c) The Disjunctive Judgment. (Das disjunktive Urtheil.)
D. The Judgment of the Notion. (Das Urtheil des Begriffs.)
(a) The Assertoric Judgment. (Das assertorische Urtheil.)
(b) The Problematic Judgment. (Das problematische Urtheil.)
(c) The Apodictic Judgment. (Das Urtheil.)
III. The Syllogism. (Der Schluss.)
A. The Qualitative Syllogism. (Der Schluss des Daseins.)
(a) First Figure. (Erste Figur.)
(b) Second Figure. (Zweite Figur.)
(c) Third Figure. (Dritte Figur.)
(d) Fourth Figure. (Vierte Figur.)
B. The Syllogism of Reflection. (Der Schluss der Reflexion.)
(a) The Syllogism of Allness. (Der Schluss der Allheit.)
(b) The Syllogism of Induction. (Der Schluss der Induktion.)
(c) The Syllogism of Analog . (Der Schluss der Analogie.)
C. The Syllogism of Necessity. (Der Schluss der Nothwendigkeit.)
(a) The Categorical Syllogism. (Der kategorische Schluss.)
(b) The Hypothetical Syllogism. (Der hypothetische Schluss.)
(c) The Disjunctive Syllogism. (Der disjunktive Schluss.)
The only ambiguity in the nomenclature here is that Notion is used both for the primary division of which Subjectivity is a secondary division, and also for the first tertiary division of Subjectivity. Judgment of Inherence and Judgment of Subsumption. are not, it will be seen, translations of the titles given by, Hegel. But he suggests Urtheil der Inharenz and Urtheil der Subsumption as alternative names (G. L. iii. 94) and, as these seem more expressive than the original titles, I have thought it better to adopt them. In the same way I have called the Schluss des Daseins by the simpler name of Qualitative Syllogism, which is also given by Hegel (G. L. 133).
It will be noticed that Judgment and the Qualitative Syllogism have each four divisions instead of three, though the irregularity in the latter case will prove to be more apparent than real.
183. The names of the categories of Subjectivity suggest at first that this part of the dialectic deals only with the workings of our minds and not with all reality. This might account, it would appear, for the name of Subjectivity, and for such names as Judgment and Syllogism among the subdivisions.
But such a use of Subjectivity would not be Hegelian. For Hegel Subjective does not mean mental. It means rather the particular, contingent, and capricious, as opposed to the universal, necessary, and reasonable.
And when we examine the categories which have the titles of Notion, Judgment, and Syllogism, it is evident that, in spite of their names, they do not apply only to the states of our minds, but to all reality. They follow, by the dialectic process, from the categories of Essence, and the categories of Objectivity and then the categories of the Idea, in like manner, follow from them. They must therefore, if there is to be any validity in the process, apply to the same subject as the categories of Essence and the Idea, which admittedly apply to all reality.
Hegel’s own language, too, renders it clear that these categories are meant to apply to all reality. He says, for example, all things are a categorical (Enc. 177), and again, everything is a syllogism” (Enc. 181).
184. We must look, then, for another explanation of the terminology. We can find it, I think, in the relation of this part of the dialectic to formal logic. Formal logic owes its existence to abstraction. When we take its standpoint we make abstraction of all but certain qualities of reality. Now these qualities, we shall find, are those which are demonstrated to be valid in the categories of Subjectivity.
We find that formal logic assumes that we have the power of ascribing general notions as predicates to subjects, and in this way arriving at complete truth with regard to these subjects. And it also assumes that we are in possession, in some way or another, of various general truths of the type All A is B, No A is C, Some A is D.
On the other hand we find that there are other characteristics of reality of which formal logic takes no account. It makes no distinction between trivial and important propositions. “No man is wholly evil” and “No man has green hair” are, for formal logic, assertions of exactly the same sort. And, in the second place, it only concerns itself with the deduction of one proposition from others. It does not enquire into the validity of the ultimate propositions from which all deduction must start.
Now we shall see that Hegel’s Subjectivity begins with the conception of universal notions, and that it soon proceeds to the further conception of valid general propositions — the two assumptions of formal logic. And we shall also see that among the defects which Hegel finds in the course of Subjectivity are, in the first place, the inability to distinguish between the importance of propositions equally true, and, in the second place, the failure to take account of ultimate general propositions, while the further failure to take account of ultimate particular propositions, though not mentioned by Hegel, must be taken into account if we are to justify his transition to Objectivity.
This will enable us to explain why the divisions of Subjectivity drew their names from formal logic. The reason is not that these categories apply only to the subject-matter of formal logic, but that the procedure of formal logic involves the validity of these categories in a way in which it does not involve those which come later in the chain. This is, of course, the same principle of nomenclature which we have already found in so many categories, from Repulsion onwards.
We can now understand, also, why the whole division is called Subjectivity. The reason is that it is contingent, and its contingency is the same which we find in formal logic — that the principle of classifying which adopted entirely indifferent. For formal logic all universals are of the same and it sees no difference between a classification which arranges pictures by their painters, and one which arranges them by the size of their frames.
185. At the end of Essence we had attained to the idea of necessary determination. The category of Reciprocity asserts that everything is so connected with other things that the existence and nature of the one is completely dependent on the existence and nature of the other, and vice versa. And the connexions of this nature, direct or indirect, which belong to each thing, extend to everything else in the universe, so that the universe forms a connected whole.
Hegel tells us that in this complete necessity we find freedom. “ Freedom shows itself as the truth of necessity (G. L. iii. 6. Enc. 158). In examining this apparent paradox, we must remember that for Hegel freedom never means the power to act without motives, or with an unmotived choice of motives. For him freedom always means of restraint, That is free which is what its own nature prompts it to be, however inevitable may be its possession of that, and its action in accordance with it.
If we say, then, that a thing is deficient ill freedom, we must mean that, while its inner nature if unthwarted, would lead it to be ABC, it is compelled by external influences to be ABD instead. Now this appeared possible m the categories of Essence. For there we conceived everything as having an inner nature, which was connected, indeed, with its external relations, but a, not identical with them, which could be either in or out of harmony with them, and, in the latter case, would be constrained. But when we reach we have transcended this view. The thing has no nature t all, except in so far a, it is (Intertwined by other and in its turn determines them. What is thus determined is its inner nature. And thus it reaches freedom. Since it has no inner nature except the results of this external determination, it is clear that its external determinations can never make it do anything against its inner nature. This is, indeed, only a negative freedom. But any more positive freedom requires higher categories. In necessity we have gained all the freedom which is possible at this stage.
This point is so important that, to prevent it may be well to anticipate some considerations which belong more properly to the Idea. In self-conscious beings we can distinguish between free, and constrained states, even when we recognise that both states are determined in the same way — as an inner state determined from outside. A man feels himself free if he can do what he wants, and feels himself constrained if he cannot. And yet his desire and its gratification are as completely determined in the one case as his desire and its disappointment are in the other.
This, however, does not contradict our previous result. For an act of volition in a conscious being is not only an occurrence, but an occurrence with a meaning — a characteristic which belongs to no occurrence except mental acts. And while the occurrence of the volition, like any other act, must be in complete harmony with the rest of the universe, its meaning may not be in such a harmony. If a man in the Arctic Circle desires to see a palm-tree, the occurrence of that desire in him will be in perfect harmony with the rest of the universe, for it will be connected with it by reciprocal causation. But the meaning of the act will not be in harmony with the universe. The same nature of the universe, which determines his desire for a palm-tree will determine the absence of palm-trees, and so there will, in this sense, be want of harmony between the desire and the universe. Hence there will constraint and absence of freedom.
This conflict ill require a deeper reconciliation than that which proved in Reciprocity. For here there is something inner which, however it has arisen, deals with the world around it as an independent power. The reconciliation could only lake place by a demonstration that the two independent powers do in fact harmonize with one another.
The freedom which is attained by the establishment of complete is only a negative and imperfect freedom, but it is all that can be attained at the point of the dialectic where it is introduced. It is also all that is requited, since it removes all the constraint which is, at this point, possible.
186. The first (G. L. iii. 3.5. Enc. A 163) is
(G. L. iii. 36. Enc. The deduction of this category from the last is found at the end of Essence (G. L. ii. 242) and is as follows: “The absolute Substance as absolute Form separates itself from itself, and consequently no longer repels itself from itself as Necessity; nor falls as Contingency into Substances indifferent and external to each other, but separates itself. On the one hand it separates itself into the totality, previously the passive Substance, which is original as the reflection into self out of determinateness (Bestimmtheit), as the simple whole which contains its positing m itself, and is posited as therein identical with itself — the Universal. On the other hand it separates itself into the totality, previously the causal Substance, which in its reflection out of it, determinateness in itself is negatively determined, and so, as the determinateness which is identical with itself, is likewise the whole, but is posited as the negativity which is identical with itself — the Individual.”
I must confess myself unable to follow this. Why is Determinateness more negative in the Cause than in the Effect? The one is as definite as the other, and would therefore, it should seem, have the same element of negativity. And why is the Effect more a simple whole than the Cause ? And how could it be so, if the relations of Cause and Effect are reciprocal?
And, again how does this deduction give us the Universal and the Individual which Hegel proceeds to use? The Universal has to be common to many Individuals while the Individual has to be determined by many Universals. I cannot see how a aspect of Substance can be common to several active aspects, or how one active aspect can be determined by several passive aspects.
187. But, even if we cannot accept Hegel’s own deduction, it is not, I think, difficult to see why Subjectivity, and the Universal Notion in particular, should succeed Reciprocity.
The Universal Notion is, as we shall see, a common quality to be found in two or more which are united by their participation in it. Things, again, are united by the reciprocal determinations which have been established by the category of Reciprocity. But these are clearly not the Universal Notions for which we seek. The relation of things which are connected by the same Notion is not a relation of reciprocal causation, but a relation of similarity.
Nevertheless, we know that these things, whose nature is determined by reciprocal causation, are determined by that causation to similarity with one another. For it was shown in the category of Variety that everything is both like and unlike every other thing. From Variety to Reciprocity there are many categories, but in none of them is this particular conclusion transcended. And at the present stage in the dialectic we have the result that the various qualities in the reciprocally determined things must be such that no thing is entirely like or entirely unlike any other thing.
Things, then, ,ire doubly connected — by similarity and by reciprocal causation. And it is that a thing may be, and generally is, connected by the one tie to things very different from those to which it is. connected by the other. A sparrow in England resembles very closely a sparrow in New Zealand, though the influence exerted by one on the other may be as slight as can possibly exist between any two beings on the same planet. On the other hand, the English sparrow’s state is largely determined by his relations — positive and negative — to worms and to cats, ,although their resemblance to him is not great.
Both these connexions have to be worked out further. And this the dialectic proceeds to do. It first takes tip the relation of similarity, and works it out through the course of Subjectivity. Then in Objectivity it proceeds to work out the relation of determination — not going back arbitrarily to pick it up, but led on to it again by dialectical necessity, since Subjectivity, when fully worked out, shows itself to have a defect which can only be remedied — by the further development of the relation of determination. Finally, the two are united in the Idea as a Synthesis.
188. This, as we have is riot the way in which Hegel makes the transition. But it seems to me that in this way it is valid, and I can See no valid alternative, It might be objected that such a transition would destroy the continuity of the dialectic. The for is unquestionably continuous. Each result must come from the one before it. And here, it might be thought we have dropped the result gained in Reciprocity, put aside till we shall have come to Objectivity, and, in order to get started in Subjectivity, gone back to a result which had been gained toward the beginning of the Doctrine of Essence.
This, however, would be a mistake. For if, in one sense, we nosy start with the conception gained in Variety, that idea has been transformed, or we could not use it here. And it can only be transformed by the application of the conception of complete determination, which came fur the first time with the category of Reciprocity. Thus both accusations of want of continuity are answered. We have not one back to take up a long past result, but are taking it the moment it has been transformed to suit our present purpose. We have not dropped the result, last attained, since it is only through this that the transformation has come about.
Before this point we could not have taken the like and unlike qualities as Notions, because those qualities did not — as the Notions do — express the whole nature of the thing. The thing had these qualities, and they might be said to form part of its nature, but there was also an inner core of Nature, affected by these connexions with the outside, but not completely expressed by them. This is the characteristic position of Essence.
But when, at the end of Essence, we come to Reciprocity, this is changed. We saw there that a thing has no inner nature distinct from its outer nature, but that the two are identical. Thus the whole nature of the thing consists of the qualities in which consist its likeness and unlikeness to every thing else. And thus the transition from Reciprocity is the natural and proper transition to the Universal since it is Reciprocity which first enables its to regard the like and unlike qualities as Notions.
The transition may then be summed tip as follows — the whole nature of everything consists in its qualities, which are determined by the relations of reciprocal causality which exist between it and every thing else. And, as every thing has some qualities in common with every other thing, the nature of any thing may always be expressed in part by pointing out seine, common quality which it shares with something else. These common qualities are Universal Notions.
189. It is, however, evident that this is only one side of the truth. If we found that every thing, must have some quality in common with every other thin,,,, we also found that no two things could have exactly the same qualities. And so, if we express in part the nature of A and B by pointing out that they have the common quality X, we are able to assert that it must also be the case that A possesses some quality F, not shared by B, and that B possesses some quality Z, not, shared by A. These qualities which distinguish the two things, united in their possession of X, are what Hegel calls Particular Notions.
(G. L. iii. 42. Enc. 163.) We see from this that a Notion can be used both as Universal and as Particular. The quality Y may be shared by A with other things, and could then be made a Universal, with X as a Particular tinder it. For example, if we decide to classify a gallery of pictures by their painters, we may bring two pictures together as both painted by Raphael. They may be distinguished from one another by having, one a good frame and the other a bad frame. Here “painted by Raphael” is the Universal, while “having a good frame” and “having a bad frame” are the Particulars. But it would be possible, from caprice or when deciding on repairs of frames, to make the condition of the frames the primary principle of classification. The first Raphael might then be separated from its companion and classed with a Velasquez. Here the Universal would be “having a good frame,” and the Particulars would be painted by Raphael “ and “painted by Velasquez.”
This brings out the contingency which earns for this part of the dialectic the name of Subjectivity. According to this category, all of the innumerable classifications possible are equally good. Any two things can be brought into the same class, for no two things are destitute of some common quality. Any two things can be separate(], for no two things are without some difference in their qualities. There is no distinction made here between a classification based on deep and fundamental similarities, and one based on similarities merely trivial. One similarity is as good as another.
190. At the same time it must be noticed that, while many Notions can be used either as Universals or as Particulars, yet some can be used only as Universals and some, perhaps, only as Particulars. A Universal is a Notion which unites existent things, a Particular is a Notion which divides existent things. Any Notion therefore which is true of all existent things can be used as a Universal, and not as a Particular, since all things are united by their possession of it, and nothing is discriminated, by its possession of it, from anything else. And it is clear that there is at least one Notion which is true of all existent things, namely the Notion of Existence.
Again, while all Notions, being general, are applicable, so far as their own meaning goes, to more things than one, yet it might be the case that some Notion applied only to one existent thing in the universe. Suppose, for example, the universe were such that one being in it, and only one in its whole duration, were yellow. Then the quality of being yellow would be a Particular Notion, but not a Universal. It could be used to discriminate that thing from other existent beings, but not to unite it with any other existent being Hegel does not mention — perhaps he did not realise — this three-fold division of Notions which could only be Universal, Notions which could only be Particular, and Notions which could be either. But there is nothing in his language inconsistent with it, nor is the point essential to the dialectic process.
191. For there is no Notion which is neither Universal nor Particular, and so, by a combination of Universal and Particular Notions, we can get all the Notions which are applicable to any thing, and so express its whole nature. And thus we reach
(G. L. iii. 60. Enc. 164.) It must be noted that, while the last two categories are the Universal and Particular Notions, this is not the Individual Notion, but the Individual. In the Thesis the conception was that the nature of each thing was partially expressed by the Notions which joined it to others. In the Antithesis the conception was that the nature of each thing, was partially expressed by the Notions which separated it from others. Here in the Synthesis the conception is that by combining both classes of Notions the nature of the thing is completely determined. From this point onward the thing is called an Individual.
192. We now pass to
(G. L. iii. 65. Enc. 166), and, in the first place (G. L. iii. 75. Enc. 172) to
(G. L. iii. 76. Enc. 172.) The reality of an Individual, we have seen, was expressible only by a combination of Notions. It must therefore be possible to assert some relation between the Individual and each of these Notions. And this is what is asserted in Judgment. The question which was implicit in the categories of the Notion — how an Individual and a Notion can be connected with each other — becomes explicit in the categories of Judgment.
This problem, to begin with, takes the form that, starting from the Individual, we endeavour to adjust a Notion to it. This is the Judgment of Inherence, as distinguished from the ,Judgment of Subsumption, in which we start with the Notion and endeavour to connect the Individual with it. The Judgment of Inherence comes first, because, in the preceding categories, the problem was to determine the Individual. And so we start here with the Individual as the datum, to which the Notion has to be related. The only relation hitherto considered between an Individual and a Notion has been an affirmative one, and so we start with a Positive Judgment of Inherence.
Hegel expresses this Judgment as ‘I the Individual is the Universal” (G. L. iii. 77). If Universal were used here in the same sense as in the categories of the Notion, this would be an inadequate way of expressing the category. For a Notion which can only be Particular is true of an Individual as much as any other Notion. And with respect to one of those Notions which can be either Universal or Particular, there is no reason to call it one rather than the other unless we know whether it is being used to unite or disunite this particular Individual from others. And to determine this, we should have to determine what other Individuals are being considered. Now in the Judgment which we have at present reached, only one Individual is under consideration.
But the fact is that in the course of the Doctrine of the Notion the term Universal is used in very different senses. This is a defect in nomenclature, but one which need not lead to any error on the part of a careful student, as the changes made and the points at which Hegel makes them, are quite definite. Throughout the categories of the Judgment, Universal means an general idea which is true of an existent Individual.
Hegel takes as an example of this category “the rose is red,” and not merely “this is red.” This is quite legitimate, if we use the example to remind ourselves that the Individual, which is the subject of the Universal which we are considering, is also the subject of many other Universals — in this case organic, vegetable, and so forth. For we have seen that each Individual must have more than one Universal (in the new sense of Universal introduced in Judgment). But we must not, when enquiring how the Universal can be connected with the Individual, assume that the Individual is already determined by other Universals, since that would beg the question at issue — the nature and possibility of the connexion between a Universal and an Individual.
193. How does this category break down, and compel us to continue the dialectic process ? Hegel says (Cr. L. iii. 81. Enc. 172) that all statements of the form I is LT are necessarily false. If, for example, we say of a rose “ this is red “ there is a double falsity. Red is not identical with the rose at which we point, for, in the first place, there are many red things in the world besides this rose. And, in the second place, it is not identical with it, because every Individual has more than one quality. The rose will be organic, vegetable, etc., as well as red.
It seems at first sight as if this was a mere quibble. “Of course,” it might be answered, “no one supposed that the is here was to be taken in the sense of absolute equivalence, as when we say the sum of three and two is five. A change of language will remove the difficulty. Say that the subject, has the quality of being red, and the criticism ceases to have any force.” But Hegel’s objection, though I cannot regard it as valid, goes deeper than this.
Hegel’s reply would, I conceive, have been as follows. We cannot say that the Individual has the Universal. In the Doctrine of Essence, indeed, we were able to say that the Thing had its Properties. But a difficulty has arisen since then. Before anything can be said to have something else, it must itself be real. If it is not real, it cannot possess anything. And so, if we are to say that the Individual has the Universal, we must previously assign to the Individual some nature other than that Universal. Now in the case of a Thing and its Properties, this was possible. For the Thin,, was conceived as a Substratum, of which the Properties were the Surface, but which had a nature in some way distinguished from them. But this distinction has disappeared in the Notion. Our Individual is completely expressed by its Universals. It has nothing. else in it. Where, then, can we find a nature for the Individual which has the Universal?
Each Individual, of course, has many Universals. But it is not possible to determine the nature of the Individual which is asserted to have one Universal, by means of the others which are true of it. For the difficulty would recur. The Individual is not identical with these Universals any more than with the first. We should be compelled to say that it had them. And so the difficulty would arise once more.
194. I do not think, however, that Hegel’s argument can be finally sustained. It is true, no doubt, that the Individual has no nature except what can be expressed by Universals. And this would be fatal if it were necessary that a thing, which was related to its qualities as possessing them, should have a nature logically prior to those qualities. But I do not see that this is so. It was doubtless the position in the Doctrine of Essence, but by this time Hegel regards it as transcended. The nature of a thing is to be sought in its connexions with other things — by Universals or by causal relations — and not in some inner core of reality distinguished from them. This is certainly Hegel’s general position with regard to the difference between Essence and the Notion, and he has therefore no right to fall back, in a category of the Notion, on the transcended conceptions of Essence, in order to demonstrate a contradiction.
Thus I see no contradiction in “ the rose is red.” We can state it, to avoid the ambiguity of “is,” in the form “the rose has redness.” If we ask what it is which has this redness, no contradiction arises. Let us take redness, sweetness, and value as standing for the whole infinite number of Universals which are true of any particular rose. Then, if it is asked, “what is the nature of this which has redness, sweetness, and value?” the answer is “ its nature is to have redness, sweetness, and value.” This involves no vicious circle. It does involve the rejection of the principle that a thing must be logically prior to its qualities. But this principle is not true, and is recognised by Hegel not to be true. He has therefore no ground, that I can see, for rejecting this solution.
195. He does, however, reject it, and passes on. The Positive Judgment, he holds, has broken down because the Individual and the Universal could not be made to coincide. Now a Negative Judgment the assertion is precisely that they do not coincide. We thus reach
(G. L. iii. 82. Enc. 172.) Since the Negative Judgment is introduced in order to avoid the contradiction which Hegel finds in the Positive Judgment, it is clear that the Negative Judgment will have to replace the Positive Judgment altogether. We must have Negative Judgments, then, which do not involve any Positive Judgments.
Hegel now points out, (G. L. iii. 87. Enc. 173) that if we take a rose which is not red, it will nevertheless have some colour, and so will fall within the wider class of coloured objects. And thus we get the Positive Judgment that it is coloured. Can we ever get a Negative Judgment without such a Positive Judgment? Only, he says, if we can deny of the Individual A a Universal Z, such that no common Universal would be true both of A and of all those Individuals of whom Z would be true. If we could find a predicate so far removed from A as this, the negative relation between it and A would form what Hegel calls an Infinite Judgment, to which we now pass.
196. (G. L. iii. 89. Enc. 173) He now tells us that, besides this Infinite Judgment, which he also calls the Negative Infinite Judgment, there is also a Positive-Infinite Judgment the Judgment of Identity. This takes either the form “the Individual is the Individual” or else the form “the Universal is the Universal “ (G. L. iii. 90).
It is quite true, of course, that if all Universals are denied of Individuals, we shall still be able to assert these barren tautologies, anti they will be the only positive assertions which we shall be able to make. But Hegel’s treatment of these identities as if they were a subdivision of the Infinite Judgment is misleading. The true Infinite Judgment — the Negative-Infinite — denies the Universal of the Individual, and is in its proper place in the chain of attempts to determine the relation of the Individual to the Universal which runs right through the Judgments of Inherence and Subsumption. The affirmations that the Individual is the Individual, and the Universal is the Universal, have no place in this chain. They are true here, as they .ire true at every point after Individual and Universal have been once introduced. But they do not form, a category at this point. The attempt to explain the nature of existent reality by the affirmation that anything is itself belongs to the category of Identity at the beginning of Essence.
Hegel appears to have intended to express the same view in the Encyclopaedia on this point as he had already expressed in the Greater Logic (Enc. 173). But he makes the whole argument un intelligible by making the Positive-Infinite Judgment (there called simply Identical) precede the Negative-Infinite Judgment (there called simply Infinite). By doing this he throws the transition from Negative Judgment into obscurity which can only be cleared up by comparison with the Greater Logic. This obscurity is increased by the extreme condensation which prevails in the whole treatment of Subjectivity in the Encyclopaedia.
197. Hegel’s transition from Infinite Judgment is as follows. He takes as examples of Infinite Judgments, “ the rose is not an elephant,” “ the understanding is not a table,” and he says that, although correct or true (richtig oder wahr) they are nonsensical and trivial (widersinnig und abgeschmackt) (G. L. iii. 90. Enc. 173). And it certainly is true that such Judgments are seldom, if ever, worth the trouble of asserting A Negative Judgment is interesting in proportion as the Individual of whom the Universal is denied, resembles those Individuals of whom it could be affirmed. Thus “the elephant is not carnivorous “ is a more interesting and important proposition than “ the oak is not carnivorous,” while this, again, is better worth asserting than the equally correct proposition “the binomial theorem is not carnivorous.”
But this would riot be sufficient for Hegel’s purpose. For to pass from Infinite Judgment to the Judgment of Subsumption it would be necessary to show that there is some contradiction in Infinite Judgment. And this is not done by showing that the propositions which, from the point of view of Infinite Judgment, would describe the universe, are trivial and unimportant. It would be necessary to show that they would be, taken by themselves, contradictory, whereas Hegel admits them to be correct and true.
The fact is that Hegel does not do Justice to his own position. The examples he gives are not contradictory, but then they are not Infinite Judgments. “The understanding is not a table” is not an Infinite Judgment. For an understanding has certain Universals in common with tables. Tables and understandings, for example, are both substances and both existent. A real Infinite Judgment is impossible. In an Infinite Judgment the Subject, of which the Predicate is denied, must have no Universal in common with the Individuals of whom the Predicate could be affirmed. This is clearly impossible, if all Individuals have any Universal common to all of them. And all Individuals have, at any rate, the common Universal of Individuality. There cannot, therefore, be any Judgment which is really Infinite.
It seems to me that Hegel was mistaken in making Infinite Judgment a separate category, and in making it the Synthesis in the triad of Judgment of Inherence. For an Infinite Judgment is only a Negative Judgment which can be true without any Positive Judgment being true. If “A is not Z” is not Infinite, then A has some Universal Y in common with the Individuals which are Z, and this would be the basis of a Positive Judgment. Now the transition from Positive to Negative Judgments involved that no Positive Judgments are true, and t
we had already
198. It would be easy, no
as to avoid this defect, without departing from
Hegel’s argument. The category of Negative Judgment
down because it requires that only Negative Judgments should be true of Individuals, which is impossible, since at any rate the Positive Judgment, “this is an Individual,” is true of every Individual. Then the argument by which Hegel passes to Judgment of Subsumption from Infinite Judgment would take us from Negative Judgment to a Synthesis which contains the principle of Subsumption, and which, by the usual “collapse, into immediacy” will take us to the Singular Judgment, the first division of Subsumption.
That argument is as follows (G. L. iii. 93). In the Judgment of Inherence “its movement itself in the predicate'’ while the subject was what was regarded as fundamental. But in the Judgment of Subsumption the fundamental element is the predicate “by which the subject is to be measured and in correspondence to which the subject is to be determined.”
Both Positive and Negative Judgments of Inherence — this appears to be the line of Hegel’s thought — have broken down. The difficulty has arisen from the inevitable incompatibility of the subject and the predicate in the Judgment of’ Inherence. How can this be changed? So far ‘we have started with the subject and endeavoured to fit the predicate to it. And we have failed There remains the alternative of starting with the predicate, and endeavouring to fit the subject to it. Instead, that is, of asking what Universal is true of a given Individual, we shall ask of what Individuals a given Universal is true. The last triad was called Judgment of Inherence because the question was what Universals belonged to, or inhered in, an
possess a second Universal, or all of those who possess it
Judgment may be “this is Z,” or “ some Y are Z,” or “ all Y are Z.” It can be either Singular, Particular, or Universal,
199. Hegel gives another characteristic of this triad, which apparently forms the ground for its other title of Judgment of Reflection. “If examples are to be given of the predicates of Judgments of Reflection, they must be of a different kind than those of the Judgments of Determinate Being1. In the Judgment of Reflection is given for the first time a really determined content, that is, a content at all....In the Judgment of Determinate Being the content is only something immediate, abstract, undetermined. Thus the following can serve as examples of Judgments of Reflection: man is mortal, things are perishable, this thing is useful or hurtful. Hardness and elasticity of bodies, happiness, etc., are characteristic predicates of this sort. They express an essentiality, which however is a determination by means of Relations, or a unifying (zusammenfassende) Universality” (G. L. iii. 92. Enc. 174).
The point apparently is that a predicate must now assert some relation of the subject with another subject. But all the examples are not happily chosen. Useful and elastic, indeed, assert a relation, but perishable and happy do not seem to assert a relation any more than red does, which is taken by Hegel as an example of a Judgment of Determined Being.
I do not think Hegel is justified in ascribing this second characteristic to the new triad. He has now made it differ from the former in two respects, (a) the predicates must express relations, (b) the predicate, and not the subject, is the datum from which we start. If the new category to have both these characteristics, he is bound to show that they are some how connected, so that we are forced, if we modify our previous conception in one respect, to modify it also in the other. So far as I can see, he does not make any attempt to do this. And it seems difficult to conceive how it could be done. What is there in the fact that a predicate expresses a relation, that should involve. the fact that the predicate, rather than the subject, should be taken as the datum? Or what is there in the fact that the predicate, rather than the subject, should be taken as the datum, which should involve the fact that the predicate taken should be one which expresses a relation?
If the changes, then, are separate and unconnected, which of them is really the characteristic idea of the new triad? It seems clear that it is Subsumption, and not Relational Predicates which must be taken as the meaning of the new the to be considered valid. For we saw above that the change to Subsumption was a real attempt to remove the difficulty which Hegel found in Judgments of Inherence — the impossibility of finding a predicate which should coincide with the subject. Now a change to Relational Predicates does nothing to remove this difficulty. If there really were, as believed, a contradiction in “ this rose is red,” owing to the want of coincidence between the subject and the predicate, there would be just the same contradiction in “this rose is useful.”
Again, it is clearly essential to the new triad that the distinction of Quantity should be introduced. The subdivisions of the triad turn entirely on Quantity, and without it we should not reach the Universal Judgment, which is vital for the rest of the argument of the dialectic. Now, as we have seen, the change to Subsumption does involve the introduction of Quantity into Judgments. But the change to Relational Predicates would not. If we continued to take the subject as the datum for starting, there would be no more reason to make distinctions of Quantity in predicating utility than in predicating redness.
For these reasons I think that we must regard Hegel as having, illegitimately added the change to Relational Predicates, when he ought to have confined himself to the change to, Subsumption.
200. (G. L. iii. 94. Enc. 175.) All Judgments of Inherence are, as we have said, Singular in form. The Judgment of Subsumption, which is derived from the Judgment of Inherence, will consequently start as a Singular Judgment. Its outer form, therefore, will be exactly the same as in a Positive Judgment of Inherence — for example, “ this is red “ or , this is useful.” But the difference is that, in the former triad, the singularity of the Judgment was an essential part of its nature as a Judgment of Inherence. (Here, on the other hand, it is merely the form with which we start, which can be modified if it is found not to be suitable.
201. This Hegel considers he has already shown, in his criticism of the Positive Judgment. We must pass on to
(G. L. iii. 94. Enc. 175.) The example Hegel gives of this is “ some men are happy.” It will be noticed that the change is mo re than a mere increase in the number of Individuals. Our Singular Judgment had only one Universal — the Universal in the predicate. For, as we saw above (Section 192), although, even in Judgments of Inherence, we may speak of “ this rose and not simply “ this,” it is only to remind us that the Individual is, in point of fact, a concrete Individual with many qualities. We did not make our assertion of redness in any way dependent on the Individual being a rose. It would have been as good an example of the category if we had only said “ this is red.” Here, however, it is the nature of our Judgment to have a, Universal in the subject as well as in the predicate. The subject is defined in relation to this Universal. It is “some men.”
It is necessary that the Particular Judgment should take this form, if it is to remove the difficulty which Hegel finds in the Singular Judgment. For if we merely took a plurality of separate Individuals, instead of a single Individual, we should leave the difficulty untouched. It would. occur about each Individual separately, and the only chancre would be that it would be repeated many times over. It is not transcended till we have grouped the Individuals under another Universal, and so made the Judgment the expression of the relation between two Universals.
The statement “some X is Y” is, however, ambiguous. It may mean “some, but not all, X is Y,” or it may leave it doubtful whether there is any X which is not Y. Hegel takes it here in the former sense. “In the judgment ‘some men are happy’ is implied the immediate consequence ‘some men are not happy"’ (G. L. iii. 95). In this, however, he seems to me to be wrong. He has no right to put any more into this new category than is required to avoid the inadequacy of the previous category. Now all that is required for that purpose is that the Individuals in the subject should be united by all being X. It would not be at all helped by the existence of other X’s which were not Y.
If we take the Particular Judgment in the second sense is leaving doubtful if any X not Y — then, apart from the necessity of transcending the inadequacy of Singular Judgments, we can see that, if Individuals have Universals at all, Particular Judgments must be true. For the relation of any number of Individuals, A, B, C, etc., to the Universal Z, which they all possess, call be expressed in a Particular Judgment, “some Y is Z,” if any other Universal Y can be found which also belongs to A, B, and C. And, whatever A, B, C, etc., are, this is the case. If there are at least two Universals which are common to all Individuals, any two Individuals which have one common Universal must also have another common Universal. And the Universals of existence and individuality — not to mention any others — are common to all Individuals. So, when we have predicated a Universal of two or more Individuals, however dissimilar in other respects those Individuals may be, we know that some other Universal may always be found, which they have in common, and can express the fact in the form of a Particular Judgment.
Of course, the higher we have to go for the Universal in the subject, the less information we get. “ Some judges are corrupt” gives us more information than “some functionaries are corrupt,” and the latter again gives us more information than “ some men are corrupt.” But though the importance of the proposition which we can obtain will vary, some proposition of this form will always be true.
202. But while Particular Judgments are true, the category of Particular Judgments develops a contradiction. By taking it as a category we undertake to express the nature of the existent by it. And this cannot be (lone. For if a Particular Judgment is true, then something else must be true which is not expressed in the Particular Judgment. The Particular Judgment says of a certain class that some of its members have a certain Universal. This leaves it possible that some have not got it. Thus of every member of the class we assert that it may or may not have it. But this is not the whole truth. For the truth about certain members of the class is that they do have it. And the truth about certain members of the class may be that they do not have it. Thus assertions of actual possession or non-possession must be true about each member, while all that the Particular Judgment gives us about each member is an assertion of possible possession.
Now we cannot take them one by one, and, pointing to each in turn, say that A has it, B has it not, and so on. For then we should have got back to predicating Universals directly of Individuals, and this has already been decided to be inadmissible. Since the Individuals of the subject, then, are not to be taken individually, they must be united by a Universal — there is no other way. And it will riot be sufficient to unite them, by a Universal which covers other Individuals besides them, since this will give only a Particular Judgment. There is only one course left. We must group our Individuals by means of a Subject-Universal which just covers them, so that we can say that wherever the Subject-Universal is found the Predicate-Universal will be found too. In other words, we must be able to make general propositions, and say “all X are Z.” It is not necessary, indeed, that all Z should also be X. The position may be that all Z are either X or W, and that all X, and likewise all W, are Z. But every individual which is Z must have some other Universal, which Universal is never found in any case without Z.
203. (G. L. iii. 96. Enc. 175.) The advance which is made in this category is evident and striking. Here, for the first time, we become entitled to assert general propositions, other than the general propositions which make tip the Logic itself. That is to say, for the first time science becomes possible. However certain it might be that nothing happened without a cause, and that everything was in relations of reciprocal causality with everything else, this would not be sufficient for science. Unless the results of that determination could be expressed in general propositions, so that we could say that some Universals are always or never found in conjunction with others, it would be impossible to classify, to predict, or to explain.
This is the point at which scepticism of a certain type stops. It will admit that there really are Universals shared by more than one Individual, but it denies that there really are any general laws connecting one Universal with another. It doe not merely assert that many general laws which we at present accept may possibly be erroneous, which no one could, in the present imperfect state of our reasonably deny. It asserts that there are no trite laws at all, known or unknown, and that all inferences are erroneous which conclude the presence or absence of one Universal in an Individual from the presence or absence of another Universal.
Hegel’s answer would be that there must be true general propositions, as this is the only way in which the contradiction which appears in the Particular Judgment can be removed. Let us recapitulate. The Individuals of which a certain Universal is predicated must be either isolated or connected. If they are connected, it can only be by a second Universal introduced into the subject. And this Subject-Universal may either include other Individuals, of which the Predicate Universal is not true, or it may include only those of which the Predicate-Universal is true. We have thus three casts. The first gives the Singular Judgment. The second gives the Particular Judgment. We have seen that both of these, when taken as categories, involve contradictions, and must therefore be transcended. There remains only the third alternative, and this gives us Universal Judgments.
In thus transcending the categories of Singular and Particular Judgments we do not assert that no Singular or Particular Judgments tire true. It may be quite true to say this is red,” or “ some roses are red.” What we have gained in this triad is the knowledge that “this” (whatever it may be) could not be red unless it possessed some other Universal, which is never found except where redness — found also. And the same will be true of each individual rose which is, in fact, red.
The whole force of the argument for this category rests, of course, on Hegel’s view that there is a contradiction in the category of Positive Judgment. Without that we could never have proceeded to — Negative Judgment, or passed over to Subsumption. I have endeavoured to show that Hegel was not justified in r ejecting Positive Judgment for the reasons given by him. In that case. we must pronounce the transition to Universal Judgment unsound, without raising the question whether, if the contradiction in Positive Judgment could have been justified, Hegel could finally have transcended it by the course which he has taken.
It is possible that the gap which this leaves in the dialectic process could be supplied. For example it might be the ease that a consideration of what is involved in the complete reciprocal determination established at the end of Essence might lead us by a shorter path to the validity of the category of Universal Judgment. But an attempt to consider this question would take us too far from Hegel to permit its introduction here.
We nosy leave the direct consideration of the Individual for the present, since our Judgment has become a relation between Universals. This will develop a certain one-sidedness which will be counterbalanced in Objectivity.
204. (G. L. iii. 101. Enc. 177.) It is to be noticed that the Necessity is not in the connexion of Universals, but in the determination of Individuals under them. The truth about the universe is now taken as expressed in Judgments of the type “all X are Z” This Judgment is not held as necessary, for there is nothing given as yet to necessitate it. But what is now necessary is the determination of the Individual. Of any Individual which is X it can be said, not only that it is Z, but that, since it is X, it must be Z. And here we get the conception of Necessity.
205. (G. L. iii. 101. Enc. 177.) This, as is to be expected, is a restatement of the Universal Judgment. When, in the Universal Judgment, we found that all X were Z, that could not mean only that, in point of fact, each Individual which was X was also Z. For then the Universal Judgment would only be the abbreviated expression of a series of Singular Judgments could not, therefore, transcend the defects of Judgments. The Universal Judgment must mean that the presence of the one Universal the presence of the other. And the only difference which we find when we pass to the Categorical Judgment is that the assertion of the connexion between the Universals is rather more explicit. This is marked by discarding the form of Subsumption which was still left in the Universal Judgment. Instead of saying “all lions are mammals,'’ we now say “the lion is a mammal.'’
Hegel tells us here, as he did before with Judgments of Subsumption, that this form is only appropriate to certain Universals. “The rose is a plant” is a legitimate Categorical Judgment, but not “the rose is red” (G. L. iii. 102). Presumably the Universals appropriate to Judgments of Reflection, such as transitory or useful, would also be inappropriate here. He does not in any way define the class of Universals appropriate to Judgments of Necessity. The examples he gives are “ the rose is a plant,” “ this ring is gold,'’ and (in the Encyclopaedia) “gold is a metal.”
It seems to me that this view, like the corresponding view in Judgments of Subsumption, is unjustifiable. If Hegel regards the change as first introduced in the passage from Universal to Categorical Judgments, which his words seem to suggest, this is inconsistent with the fact that he does not treat this passage as involving any advance in the dialectic, but merely as a restatement. If, on the other hand, he regards it as first introduced in the transition from Particular to Universal Judgments, he does not give any reason why this change should accompany the change from Particularity to Universality. He does show why we cannot be satisfied with a category of Particularity, and why we must proceed to Universality, but he gives no indication of any necessity for changing, at the same time, the class of predicates employed.
And, again, when we come to the Syllogism of Determinate Being, we find that any restriction on the character of Universals has disappeared, though it 1.3 difficult to imagine — and we find nothing in Hegel to help us — how such a restriction, when once made, could again be removed. On all these grounds I think that the limitation to a special class of Universals must be rejected.
206. Hegel now proceeds to
(G .L. iii. 103. Enc. 177.) If by this category had been meant, as would naturally have been supposed, a view of existence which could be expressed in the form “if anything is X, then it is Z,” there would have been no difficulty. It is clear that if the lion is a mammal, then, if anything is a lion, it is a mammal. The Categorical Judgment involves the Hypothetical. The only possible criticism would be that the Hypothetical Judgment is a mere restatement of the Categorical, and that this relation, though appropriate between a Synthesis and a new Thesis, is out of place between a Thesis and an Antithesis in the same triad.
But this is not the Hypothetical Judgment which Hegel has in view. His example, both in the Greater Logic and in the Encyclopaedia, is, “ if A is, B is.” He expands this in the Greater Logic, “the Being of A is not its own Being, but the Being of another, of B.”
Here, again, Hegel seems to me quite unjustified in his procedure. The whole of Subjectivity is devoted to determining the nature of Individuals by means of Universals. This is what was being done in Categorical Judgment. It is what is done again, in the next category, in Disjunctive Judgment. Is it possible that between these there should be inserted a category which determines, not the nature, but the existence, of an Individual, and which determines it, not by Universals, but by another Individual? It would at any rate require a very clear deduction of the necessity of such a category before we could accept it. Now all that Hegel says is “ the Categorical Judgment corresponds for the first time to its objective universality by this necessity of its immediate being, and in this way passes over to the Hypothetical Judgment “ (G. L. iii. 103). This might serve to explain the transition from “the X is Y” to if anything is X, it is Y,” where X and Y are both Universals. It entirely fails to justify the transition from “the X is Y” to , if A is, B is,” where A and B are Individuals. Nor would the return from Individuals to Universals at the transition into the Disjunctive Judgment be any more intelligible (cp. G. L. iii. 105). The category must then, in my opinion, be rejected.
207. (G. L. iii. 105. Enc. 177.) Although Hegel’s transition from Categorical to Disjunctive Judgments thus breaks down, we can see that a transition from Categorical to Disjunctive Judgments is necessary.
We know that there are cases in which it is true that all X are Z, while it is false that all Z are X. The proof of this is as follows. Any two Individuals, as we have seen, will have some Universals in common, and each of them will have some Universals which the other has not. Let its take Z as standing for a Universal common to some two Individuals, and Q and R as two Universals each of which belongs to one of them only. The first Individual will be ZQ, and the second ZR. Now as any predication of Universals of any Individual can only be made by means of a Universal Judgment, there must be some X such that all X will be ZQ. Then all X will be Z, but all Z will not be X. For all X are Q, and all Z are not Q, since there is the class ZR, of which our second Individual was an example.
We know, therefore, that in some of our Universal (or Categorical) Judgments the predicate will be wider than the subject. All X will be Z, but there are some Z which are not X. Now these Individuals, which are not X, cannot be Z as simply isolated Individuals. This, according to He gel was proved when we transcended Positive Judgments. Each of these Individuals must have some Universal, with which Z is connected by means of another Categorical Judgment. How many of them there may be we do not know, but we do know that every Individual which has Z, must have one of them. Thus we arrive at the conclusion that all Z is either X, or W, or Y, where W and V represent an unknown number of Universals.
Of course this does not exclude the possibility that in some cases the connexion of the Universals is reciprocal, so that not only all X is Z, but all Z is X. This cannot, for the reasons just given, be true in all cases, but it can in some. Thus we may say that the category before us asserts that for every Universal Z there may be found a group of Universals, X, W, V, such that whatever is X, W, or V is Z, and that whatever is Z is either X, W, or V, and asserts further that in some cases the group X, W, V, may contain only a single Universal, but that it is impossible that this should be so in all cases.
The necessity of passing from Categorical Judgment to Disjunctive Judgment applies, of course, to the nature of existence and not to our knowledge about it. If Categorical Judgments are true of existence, then Disjunctive Judgments are true of existence. But if our knowledge enables us to make a Categorical Judgment on any subject, it by no means follows that it will enable us to make the corresponding Disjunctive. I may know that the lion is a mammal, without knowing the complete list of species, to one of which every mammal must belong. In the same way a Positive Judgment can be known without knowing the corresponding Universal. I may know that this Individual is red, without being able to determine what Universal it possesses, the possession of which involves redness, though, if Hegel is right, such a Universal must exist.
208. The two sides of the Judgment are now, according to Hegel, “identical” (G. L. iii. 110). By this he means that they have the same denotation. Every Z is either X or W or V, while all X, all TV, and all V are Z. Thus the denotation of Z is the same as the denotations of X, TV, and V added together. “This Unity,” he continues, “ the Copula of this Judgment, in which the extremes have come together through their identity, is thereby the Notion itself, and, moreover, the Notion as posited; the mere Judgment of Necessity has thus raised itself to the Judgment of the Notion.”
209. (G. L. iii. 110. Enc. 178.) This transition appears to relate exclusively to the relation of the Subject with the Predicate. But here, as with Judgments of Subsumption and Judgments of Necessity, Hegel introduces, along with this distinction, the further distinction that only a special sort of Predicates are appropriate for Judgments of this form. The examples he gives are good, bad, true, beautiful and correct. All these, as he remarks, have reference to some ideal (ein Sollen). BLit he establishes no connexion between these Predicates on the one hand, and, on the other, the closer relation between Subject and Predicate which formed the transition to Judgments of the ‘Notion. Nor is there any connexion between the use of such Predicates, and the three subdivisions of Judgments of the Notion, of which the first is
(G. L. iii. 112. Enc. 178.) The example given of this is “this deed is good.” This does not appear to differ from a Categorical Judgment, except in the sort of Predicate used. But the Assertoric Judgment does differ from the Categorical Judgment in another characteristic, though this characteristic does not seem to have any relation to the closer connexion of Subject and Predicate which was given in the passage quoted above as the characteristic of Judgments of the Notion.
The new difference concerns, not what is asserted, but the justification which he who asserts it possesses for his assertion. Its proof is a subjective assurance” ( G. L. iii. 113).
210. And this gives the transition to the next category, for, as Hegel goes on to remark, “over against the assurance of the Assertoric Judgment there stands with equal right the assurance of its opposite.” If the only ground for believing this deed to be Yood is that the assertion is made, then we are plunged in doubt. For it is equally possible to make the assertion that this deed is not good, and one assertion is as good as another. This doubt takes us to (G. L. iii. 114.Enc. 178)
211. Hegel does not give any reason why we must pass from this category to the next. He merely gives the transition without justifying it. of simply saving “the deed is good,” we must say “the deed of such and such a nature is good.” Here the nature of the deed is, in effect, given as a reason why we should accept the Judgment that it is good rather than the Judgment that it is not good. This is
(G. L. iii. 116. Enc. 178.) The characteristic of the Subject, thus given as the reason why the Subject should have the Predicate, is said by Hegel to be the Copula of the Judgment become “completed or full of content (erfüllte oder inhaltsvolle); the unity of the Notion again restored out of the Judgment, in the extremes of which it was lost.” From this Hegel makes his transition to Syllogism.
212. Is this triad of the Judgment of the Notion valid? I believe that it is not, and that the transition ought to go direct from Disjunctive Judgment to Syllogism. In support of this I would urge four considerations.
In the first place, grave suspicion is thrown upon the triad by the fact that, if it is accepted, it gives Judgment as a whole four subdivisions instead of the three which are essential to Hegel’s method. The excuse which he gives for this is that of the “three chief kinds of Judgment parallel to the stages of Being, Essence, and Notion,” the second “ as required by the character of Essence, which is the stage of differentiation, must be doubled” (Enc. 171). This however cannot be accepted as a justification for Judgment having four subdivisions, when other stages have only three. For, throughout the whole dialectic, the second subdivision of the three in each stage always corresponds to Essence, arid, if this involved dividing into two, four subdivisions would be the invariable rule, and not the exception.
The second difficulty is still more serious. The Assertoric, Problematic, and Apodictic Judgments are distinguished from one another, and from those which precede them, not by any distinction in the propositions asserted, but by distinctions as to the characteristics of mental states of those who assert the propositions. An Assertoric Judgment is one believed firmly, but without a reason. A Problematic Judgment is one which is regarded as possibly, but not certainly, true. An Apodictic Judgment is one which is believed firmly, with a reason for believing it.
Hegel, indeed, denies (G. L. iii. 111) that these categories are thus subjective. But he does not explain what other meaning they can have, and when he conies to treat them, in detail, as we have already seen, h is treatment is inexplicable except on the hypothesis that they have this meaning
For the Assertoric Judgment clearly differs from those which go before it in something else besides the sort of Predicates applicable. This is evident both from the transition to it, and from its name. And if this new feature is not “our subjective assurance” of it, why does Hegel, on p. 113, give that account of it? And what else could that new feature be? And how, if it were not a question of beliefs rather than propositions, could two be opposed to one another with equal right, as Hegel in the transition to Problematic Judgments asserts that. they are?
So, too, with the Problematic Judgment. This arises because two incompatible Assertoric Judgments about the same Subject are held with equal right. Now this cannot possibly produce any new Judgment about the Subject, but may very well produce a doubt and uncertainty about each of them. It seems impossible to deduce anything else here, and this makes the distinction relate entirely to the way in which we believe the truth. And the name clearly indicates the same fact. Problematic means doubtful, and no proposition is doubtful except in relation to the knowledge of some particular knower. I may be doubtful whether A is B, but A cannot be doubtfully B. It is B or it is not.
The same is, I think, the case with the Apodictic Judgment. The examples Hegel gives are not decisive. The nature of the deed might be given either as the reason why it was good, or as the reason why I believed it to be good. But it seems clear to me that Hegel regarded the Apodictic Judgment as differing from the Assertoric and Problematic in the same manner in which the Assertoric and Problematic differ from one another. In that case the Apodictic Judgment is also a category which applies to beliefs only, and not to all realities, and the reason given iii it is not the reason of the fact believed, but the reason of the belief.
If Hegel has introduced either two or three categories of this sort here, his treatment is clearly invalid The whole argument of the dialectic rests on the supposition that all the categories are applicable to the same subject-matter — namely all existent reality. Again, the Disjunctive Judgment clearly applied to all existence, and not merely to belief. How could we deduce from it a new category which applies merely to beliefs? It seems impossible to conceive how such a deduction could be justified, and certainly Hegel does not attempt to justify it. And, in the same way, how could he be justified in passing back, from categories which deal merely with beliefs, to categories which deal with all existence? And, by the time he reaches Syllogism he has certainly done this.
213. In the third place, the transition to the Judgment of the Notion seems to me erroneous. It is no doubt the case, as was said above, that Judgments made according. to Hegel’s category of Disjunctive Judgment have the same denotation for their Subjects and their Predicates. But I cannot see how this would enable us to pass to the Judgment of the Notion, where the denotations are not identical, though the connotations are said to be more closely connected. Nor can I see why Assertoric, Problematic, and Apodictic Judgments should be the subdivisions of Judgment of the Notion, defined as Hegel has defined it.
In the fourth place the Judgment of the Notion can be removed without destroying the continuity of the dialectic. For it is not difficult to see that Syllogism necessarily follows from Disjunctive Judgment. Syllogism starts, as we shall see, with the position that it is necessary to give some reason why the two Universals in a general proposition are connected with one another. Now this necessity will be seen so soon as we find that two Universals are connected in such a way — that is, in the Categorical Judgment. In the Disjunctive Judgment the question becomes more pressing, since the alternative nature of the connexion renders it more obvious that we must face the problem. Z is in some cases X, in some cases W, and in some cases V. Why, in each case, is it the one and not the other? Thus Syllogism could follow directly from Disjunctive Judgment. For these four reasons I think that the Judgment of the Notion must be rejected.
214. We now pass to
(G. L. iii. 118. Enc. 181.) The essential characteristic here is the mediation of the connexion between two Universals. The connexion, in the first place, is made by what was, in Apodictic Judgment, the reason (cp. above, Section 211). This is based on another Universal. The reason that the deed was good was that its nature had a certain characteristic, and such a characteristic is expressed by a Universal. Thus mediation is by a third Universal, which gives us
(G. L. iii. 121. Enc. 183.) This is again divided by Hegel, the subdivisions being named after the Figures of formal logic. We shall have to consider later whether this is valid, but there is at any rate no doubt that, if we are to have these divisions, we must begin with the First Figure. For the linking. of Universals gives Universal Propositions, some of which are Affirmative. And Universal Affirmative Propositions can only be proved by the First Figure.
(G. L. iii. 122. Enc. 183.) Hegel says that this category can be expressed as I P U. The Subject of the conclusion, that is, is an Individual, the Predicate of the conclusion is a Universal, and the Middle Term is a Particular.
This seems unjustifiable. The distinction between Particular and Universal Notions at the beginning of Subjectivity (cp. above, Section 190) does not apply to the ‘Middle and Major terms of a Syllogism of the First Figure, and if Hegel means anything else here by Universal and Particular, he does not tell us what it is.
Nor has he, I think, any right to bring in the Individual here. In the Categorical Judgment the result reached was a connexion of two Universals. In several places between that and the present stage Hegel speaks a., if the Subject of the Judgment might or must be an Individual, but lie never expressly acknowledges this transition, or attempts to justify it. We have no right here to deal with any connexion. except that between Universals.
Nor does the formal logic, or’ whose Figures he has availed himself to provide names for his categories, offer any excuse for the introduction of the Individual. For the Individual is not recognised by formal logic, which treats “ Caesar is mortal” as a proposition of exactly the same type as “all Bishops are mortal.”
215. How is the inadequacy of the First Figure proved? Hegel makes two objections to its validity. The first is as follows. The Subject has many characteristics which may be used as Middle Terms, and each Middle Term, again, can connect it with many Major Terms. Thus it is “ contingent and capricious” (zufällig und willkurlich) with what Major Term the Subject will be connected, and also what Predicate will be given it in the conclusion (G. L. iii. 127. Enc. 184).
This is quite true. All Cambridge Doctors of Divinity are Anglican clergymen, and are graduates of the University. From the first of these, as a Middle Term, we can conclude either that they have been ordained, or that they are incapable of sitting in Parliament. From the second we can conclude, either that the Graces for their degrees passed the Senate, or that they were presented for their degrees by a member of the University. All four conclusions are true, but it is quite contingent and capricious which we shall take. There is nothing in the idea of the Subject “all Cambridge Doctors of Divinity” to decide which we shall prefer to the others.
But how does this produce a contradiction? The Subject is united, by two Middle Terms, to four Predicates. But why should this not be the case? If, indeed, we had to choose one in preference to others, a difficulty would arise, for no ground of preference is given. But there is no necessity to choose. For all these Judgments can be true of the Subject together.
The defect which Hegel thinks that he has found here is like the defect which he says constitutes the inadequacy of the category of Variety (cp. above, Section 116). But while it was a defect there, it is not one here. There the whole point of the category was to range things by their Likeness or Unlikeness to one another. And no such arrangement was possible, if everything was connected with everything else both by Likeness and Unlikeness.
Here it is different. No doubt it is the case that Individuals, or classes of Individuals, are Like or Unlike one another, by reason of the Universals which can be predicated of them. But the point here is not arrangement simply as Like or Unlike, but arrangement as sharing or not sharing certain Universals. Thus arrangement is possible though each Individual or class should be Like or Unlike every other, because it would be in virtue of different Universals.
There is thus no necessity to take one grouping rather than another, because the different groupings are now compatible, which was not the case in the category of Variety. And thus the fact that the preference of one grouping to another would be “ contingent and capricious” while it is a valid objection to the category of Variety, is not a valid objection here.
Hegel asserts (G. L. iii. 127) that this contingency involves that contradictory Predicates must be held true of the same Subject. He bases this on the statement that , Difference, which is in the first place indifferent Variety, is just as essentially Opposition (Entgegensetzung).” But he makes no attempt to prove that the two different Predicates must necessarily be incompatible Predicates:, which is what his sentence must mean if it is to bear out his assertion. And his examples (G. L. iii. 128) do not help him. The first which lie gives — the rest are substantially similar — is “ If from the Middle Term that a stick was painted blue, it is concluded that it therefore is blue, this is concluded correctly ; but the stick, in spite of this conclusion, can be green, if it has also been covered over with yellow paint, from which last circumstance, taken by itself, would result that it was yellow.”
It is true that a stick cannot at once be blue and green. But the first conclusion — that it is blue — could only be reached from the Minor Premise which Hegel. gives, “ this stick has been painted blue,” by the help of the Major Premise “ whatever has ever been painted blue is now blue.” And this Major Premise is notoriously false, so that one of the contradictory conclusions has not been proved. In each of the other examples he gives the saint. fallacy is present. The contradictory conclusions do not follow legitimately from the diverse premises, but only follow by the aid of other premises which are false.
216. But Hegel also gives another objection to this category, and this, I think, must be accepted as valid. We reached the category by taking the position that two Universals which are connected with one another must have their connexion mediated by a third. But the third Universal, being connected with the first and the second, will, on the same principle, require a fourth and a fifth Universal to mediate these connexions. The four connexions so established will require ‘four fresh Universals, and so on infinitely (G. L. iii. 130. Enc. 185).
The Infinite Series thus established will involve a contradiction, for the earlier members are logically dependent on the later, as no Universal can mediate till it is connected with the Universals it mediates, and, to be connected, it must itself be mediated by Universals given in later members. Thus Hegel rejects the category, on this second ground also, as invalid.
217. Hegel considers that these defects require the alteration of the Middle Term. The Individual is now become the Middle Term, and the Syllogism will no longer be represented by I P U, but by P I U. And in this he finds a transition to what he calls
(G. L. iii. 139. Enc. 186.) By this, however, he means, as he explains in the Greater Logic iii. 135), what is generally called the Third Figure. (In the Encyclopaedia he also uses the name in this unusual sense, without any warning that he has departed from the common custom.)
The defect here, according to Hegel (G. L. iii. 134), is that the new form “ought to correspond to the Species, that is, the Universal Schema, I P U. But to this it does not correspond... the Middle Term is on both occasions Subject, in which therefore the other two terms inhere.” The fault is thus in the position of the Middle Term — the same characteristic which, as we see in formal logic, prevents a Syllogism in this Figure from having any but a Particular conclusion.
218. Hegel then tells us that “the Individuality connects the Particular and the Universal in so far as it transcends the determination of the Particular; ... the extremes are not connected through their determined relation which they had as Middle Term; it is therefore not their determined unity, and the positive unity, which it still has, is only abstract Universality” (G. L. iii. 136). The Middle Term is thus U, and the new form of the Syllogism is I U P. This, according to Hegel, gives us
(G. L. iii. 137. Enc. 187.) This is what is usually called the Second Figure. This leads only to negative conclusions. Hegel mentions this (G. L. ill. 138), but does not regard it as the ground of the inadequacy of the category. The inadequacy lies in the fact that the Universal, which is the Middle Term, has no inherent connexion with either of the extremes, and would have to be connected with them by a fresh process, independent of the original Syllogism. All this, he says, is just as contingent as in the preceding forms of the Syllogism.
219. (G. L. iii. 139. Enc. 188.) This is not the Fourth Figure of formal logic, which he rejects as useless (G. L. iii. 138. Enc. 187). What he substitutes for it is what he calls the Mathematical Syllogism, of which, he tells us, the formula is U U U. Its principle, he also tells us, is “if two things are equal to a third, they are equal to one another.” The three equal things are apparently taken as the three terms.
The relation between the three things in question, however, is by no means the relation between the terms of a Syllogism. The third thing, whose equality to each of the others is the basis of the argument, may be said to mediate between them, but not in the same way as the _Middle Term of a Syllogism. does. And if we were to take this Fourth Figure seriously, there would be the additional difficulty that it would disregard the triadic movement of the dialectic.
Hegel, however, does not take it seriously. The Fourth Figure is not a legitimate and necessary stage in the dialectic process. It is only the result which would be reached if we took the wrong track. This seems clear from the following passage. “The merely negative result is the disappearance of qualitative determinations of form in mere quantitative and mathematical Syllogisms. But what we really get (was wahrhaft vorhanden ist) is the positive result, that the mediation does not take place through an individual qualitative determination of form, but through the concrete identity” of the extremes. “The defect and the formalism of the three Figures of the Syllogism. consists just in this that such an individual determination had ,to serve as their Middle Term. The mediation has thus determined itself as the indifference of immediate or abstract determinations of form, and as positive Reflection of the one into the other. The immediate Qualitative Syllogism is thus transferred into the Syllogism of Reflection (G. L. iii. 141). Thus the real movement of the dialectic is from the Third Figure to the Syllogism of Reflection. Under these circumstances it seems curious that Hegel should have given the Fourth Figure as a separate heading, as if it were a real category.
220. I have given the transitions from each Figure to the next without criticising the validity of each transition taken by itself, because I believe that the argument is invalid as a whole. The Second and Third Figures appear to me to be unjustified.
What Hegel calls the First Figure should, in my opinion, be the whole of an undivided category of Qualitative Syllogism, and from this the transition should be made directly to Syllogism of Reflection.
Hegel gave, as we saw above, two objections to the validity of the First Figure. The first was the contingency of the Middle Term relatively to the Subject, and of the Predicate relatively to the Middle Term. The second was the infinite series of mediations which would be required. The first objection, as I endeavoured to show, was unfounded. If this is really the case, then any valid transition to the Second Figure must be determined by the second objection.
Now this is not what happens. The Second and Third Figures do not even profess to remove this defect, or to alter it in any way. The infinite series of mediations would arise in them just as inevitably, and exactly in the same way, as in the First Figure. The transition, therefore, is invalid.
And not only do the Second and Third Figures fail to remove the defects of the First, but they reintroduce defects which had been long ago transcend ed. For the (Hegelian) Second Figure can only prove Particular conclusions, and the (Hegelian) Third Figure can only prove Negative conclusions, and we saw, when we treated of Judgments of Inherence and Subsumption, that no category could be possible according to which only Negative, or only Particular, propositions were true. These categories therefore, so far from being more adequate than the First Figure, are less adequate.
Hegel seems more or less to realise this when he condemns the Second Figure on the ground that it does not, as it should do, correspond to the Species, that is, the universal Schema, I P W’ (G. L. iii. 131; cp. above, Section 217). For I P U is, according to Hegel, the Schema of the First Figure. But the Second Figure is wrong because it is not the First, how can it take its place in the dialectic series as the successor of the First?
I have not thought it necessary to consider whether Hegel was right in appropriating the Schema P I U to his Second Figure, and I U P to his Third Figure. The enquiry is superfluous if, as I have tried to show, the Second and Third Figures have no rightful place in the dialectic at all. And again any enquiry as to the particular appropriation is superfluous, if, as I have also tried to show (cp. above, Section 214) Hegel was wrong, in introducing the conceptions of Individual and Particular terms into any of the Figures of Qualitative Syllogism.
221. The omission of the Second and Third Figures will not leave any gap in the dialectic process. For we can pass quite legitimately from the First Figure to the Syllogism of Reflection. If every connexion of Universals must be mediated by a Universal, we are involved in a contradictory infinite series. But this might be averted if Universals were mediated by something else, for perhaps the connexions of this something else with a Universal might not again require mediation. What else could mediate the connexion of Universals, except Universals? There is nothing left but Individuals, We have seen above (Section 202) that it is impossible that the Universal Judgment should be equivalent to a series of Judgments about mete Individuals. We have now to consider whether the Universal Judgment can be based on such a series of Judgments. This would take us direct to Hegel’s Syllogism of Reflection from his First Figure.
222. On all these grounds, therefore, I think the Second and Third Figures should be rejected. We nosy arrive, whether by the argument just given, or by Hegel’s argument quoted above, at
(G. L. iii. 149. Enc. 190.) In this category the fact that all Z are X is held to be dependent on the facts that this, that, and the other things which are Z are also in point of fact X. “This, that, and the other” here include all the things which are Z. Since each of them individually is X, it is certain that all Z are X. If the House of Lords has a gallery for strangers, and the House of Commons has a gallery for strangers, then all houses of the British Parliament have galleries for strangers.
This category corresponds to the logical process called Perfect Induction, and not to any form of Syllogism. Hegel, however, speaks of a Syllogism of Allness. His example is if all men are mortal, Caius is a man, therefore Caius is mortal.” This differs, according to him, from the ordinary Syllogism of the First Figure, because the Major Premise is reached by a complete enumeration of Individuals — though, of course, in the example lie has taken, this could not be the case.
It seems to me, however, that Hegel is wrong here. No doubt we can use the result of the Perfect Induction as the Premise of a Syllogism. But what corresponds to the Syllogism of previous categories is not the Syllogism which Hegel gives here, but the proposition he takes as Major Premise. In Qualitative Syllogism two Universals were mediated by a third Universal, and this mediation made the Syllogism. Here two Universals are mediated by an enumeration of Individuals, and it is the proposition thus reached which corresponds to the Syllogism in Qualitative Syllogism. The change is that while in Qualitative Syllogism we reach the conclusion “allmen are mortal” by some such argument as “ all men are animals, and all animals are mortal,” here we should reach it by an enumeration of Individuals. What was done before by Syllogism is not now done by Syllogism but by enumeration, and thus the name of Syllogism here is incorrect.
223. Hegel’s objection to this Syllogism (G. L. iii. 1.51. Enc. 190) is that the conclusion presupposes the Major Premise. We could not know, in this way, that all men were mortal, unless, among others, we knew that Caius was mortal. Thus we cannot prove the mortality of Caius from the mortality of all men. This is, no doubt, correct, but, as was said above, the category is exemplified in the assertion that all men are mortal, not in the assertion that Caius is mortal, and the objection is therefore irrelevant.
Hegel now proceeds to
(G. L. iii. 152. Enc. 190.) Here we have a category which corresponds to ordinary Induction. The connexion between the two Universals is mediated by the fact that they do occur together in some of the Individuals included in the denotation of the Subject. We conclude that all men are mortal, because it is so as a matter of fact in those cases which we have examined.
The transition to this category is not brought out very clearly, by Hegel, but we can see that it will remove the defect which he found in the last. When we have established by induction that all men are. mortal, we may conclude that Caius is mortal without necessarily arguing in a circle. For Caius may not have been one of the men on whose mortality we founded the general statement. He may, for example, be still alive.
The defect which Hegel finds in this category is that our enumeration of the Individuals can never he complete. (G. L. iii. 154. Enc. 190.) It is not at first evident why we should wish to have it complete, since then we should et back to the previous category, which has already been abandoned as inadequate. But as he ends his criticism with the words “the conclusion of Induction remains problematic” he appears to have in his mind the fact that no general conclusion arrived at by Induction can be more than probable, and that therefore we can never, by means of such a conclusion, arrive at absolute certainty as to any Individual. The only Individuals “ to whom we can be certain are those whose natures formed the basis of our Induction. And these are not the whole number.
224. The defect of Induction compels [is, according to Hegel, to pass to
1.5.5. Enc. 190.) The example which he gives of this is “ the earth has inhabitants, the moon is an earth, therefore the moon has inhabitants.’ If we remove the ambiguity in the use of earth, it might be put as follows the planet. on which we live is an earth, and is inhabited; the moon is an earth, therefore it is inhabited.” This is an Induction, based on a single instance. It does not seem, however, that the fact that there is only a single instance, is essential to the category. Hegel says (G. L. iii. 1.57) that earth is taken here “as something concrete, which in its truth is just as much a universal
nature or species, as it is an individual”; and he continues that the category breaks down because we cannot tell whether the first Individual has the second quality because it has the first quality, or for some other reason. We cannot, e.g., be sure whether it is because it is an earth, or for some other reason, that this planet is inhabited. If it were for some other reason, we could not be sure that the moon shared the quality of being inhabited.
It seems, therefore, that Analogy is Induction made explicit.
When, in Induction, we conclude that, since A, B, C, etc. are all both X and Y, therefore all things which are X are Y, we also, implicitly conclude that there is some intrinsic connexion, direct or indirect, between X and Y If there is no such intrinsic connexion, our conclusion would be illegitimate. And this connexion between the qualities X and Y is made explicit ill Analogy. It is the impossibility of being certain of that connexion, as has just been pointed out, which wrecks Analogy. And it is this impossibility, also, which prevented us from ever reaching an absolutely certain Induction.
225. From this Hegel to the Syllogism of Necessity as follows The of Reflection, taken as a whole, comes under the Schema P I U : in it the Individual as such still forms the essential determination of the Middle Term., but in so far as its immediacy has transcended itself, and the Middle Term is determined as Universality in and for itself, in so far the Syllolgism has come under the formal Schema I U P, and the Syllogism of Reflection has passed over into the Syllogism of Necessity'’ (G. L. iii. 1.59).
This transition seems to me unconvincing. It is true that there is a certain appropriateness iii calling the Middle Term of the explicit Induction of Analogy by the name of Universal. And the nature of the Middle Term of the new category is also such as to give some appropriateness to the description of it as Universal. But in the two cases Universal is used in different senses. It means much more in the Categorical Syllogism, which is the first form of Syllogism of Necessity, than it did in the Syllogism of Analogy.
It is natural that it should do this. For the Categorical Syllogism is not, as we should expect from its position, a mere restatement of the Syllogism of Analogy after a collapse into Immediacy. The Syllogism of Analogy has, according to Hegel, broken down, and the transition to the Syllogism of Necessity removes a contradiction. The new category must be an advance, then, and not a mere restatement, and it is an advance, for it contains, as we shall see, an entirely new conception.
If this is the case, Hegel’s account of the transition must be wrong, for he speaks as if the Universality of the Middle Term in Analogy had already brought us to the Syllogism of Necessity, and as if, therefore, there was no real advance.
226. The criticism which I venture to suggest on the triad of Syllogism of Reflection is that, here as in the Qualitative Syllogism the subdivisions are unjustified. The conception which Hegel treats, under the Syllogism of Allness should have been the sole content of an undivided Syllogism of Reflection.
No doubt Induction and Analogy, as processes of acquiring knowledge, are quite different from so-called Perfect Induction. But categories are descriptions of reality and not processes of acquiring knowledge, and I cannot see that any separate description of reality corresponds to these processes.
The category which we reached in the Syllogism of Allness asserted that the validity of Universal Judgments depends on the fact that every Individual, which possesses the Subject-Universal, possesses, as a matter of fact, the Predicate-Universal also. We have seen that this category corresponds to the logical process of Perfect Induction. But how shall we find a second category to correspond to the logical process of Induction in the ordinary sense of the word?
The difference between the processes of acquiring knowledge is that in Perfect Induction the conclusion is based on an examination of all the Individuals who possess the Subject-Universal, while in ordinary Induction we examine only some of them. Hegel’s category of Induction would thus have to mean that the validity of Universal Judgments depends on the fact that some of the Individuals, which possess the Subject-Universal, do, as a matter of fact, possess the Predicate-Universal also.
What could be meant by this dependence on some of the Individuals? In the case of the Judgment all X are Y, it is clear that it cannot mean that the rest of X (those which are not included in the “ some “) are not-Y, since the conclusion is that they are all Y. It could only mean that, while every X was Y, yet some of them were Y in their own right, and exercised some power which caused the other X’s to be Y, and so made the general proposition true.
This conception would riot be in any way an advance on the Syllogism of Allness, nor would it remove any of the difficulties to which that category was exposed. On the contrary, it would add to them by introducing a new complexity — the difference between the “ some “ X’s and the other X’s — which had not been deduced from the previous category, and could riot be justified.
The logical process of Induction can give a natural and reasonable meaning to the “ some “ — namely that though, if the law is true, every X is Y, yet there are only some cases in which ‘his has been ascertained when the Induction is made. But the distinction between known and unknown cases is irrelevant to the metaphysical category.
Thus we must reject the category of And, if Analogy is only explicit Induction, Analogy must go too. This leaves Allness, as the sole form of the of Reflection.
Here, as with the Qualitative Syllogism, the error seems to have arisen from Hegel’s attempt to push a parallel too far. There is one category which has a, real resemblance to the Syllogism of deductive logic, and another which has a real resemblance to induction as a whole. But the attempt to find categories corresponding to the different figures and the different varieties of induction has led to errors.
And here, as with Qualitative Syllogism, the dialectic process goes all the better for the simplification. The undivided Syllogism of Reflection is the Antithesis of which Qualitative Syllogism was the Thesis. The transition from the one to the other was shown above (Section 221), And this new Antithesis, we can see, will break down. For we saw, in dealing with Judgments of Inherence and Subsumption, that a Judgment about an Individual could only be valid when it was dependent upon a Universal Judgment. Since all Individual Judgments must be based upon Universal Judgments, it is obviously impossible that all Universal Judgments should be based upon Individual Judgments.
It thus becomes evident that it is impossible that all Universal Judgments should be mediated. Whether we attempt to mediate them by Universals or by Individuals we have found that insuperable difficulties presented themselves. Only one alternative remains — to assert that some, at any rate, among Universal Judgments, do not require mediation. And this takes us on to Hegel’s next category
227. (G. L. iii. 161. Enc. 191.) The first feature of the Categorical Syllogism is that the Middle Term is the essential nature of the Subject of the conclusion, and, in the same way, the Predicate of the is the essential nature of the Middle Term. And thus the contingency disappears, which. arose the fact that the Subject, might be taken as connected with any one of several Middle Terms, and each Middle Term as connected with any one of several Predicates (G. L. iii. 162). This contingency, it will be remembered, was treated by Hegel as a defect of the First Figure. He regards it as finally removed here, making the assumption that a Term can only have one “ essential nature,” so that there is here no alternative Middle Term for a Subject, and no alternative Predicate for a Middle Term.
“Since,” he continues, “the connections of the extremes with the Middle Terms have not that external immediacy which they have in the Qualitative Syllogism, the demand for a proof does not come in here in the same way as in the Qualitative Syllogism, where it led to an Infinite Series” iii. 162). In this way the second defect of the First Figure is removed. It is clear, therefore, that Hegel regards the essential connections of the Categorical Syllogism as being ultimate connections. They may be used to mediate, but they do not themselves require mediation.
Here, then, for the first time, Hegel regards the defects of the First Figure as transcended. And this confirms my view that the subdivisions of Qualitative Syllogism and Syllogism of Reflection are mistaken. For the special defect of each category should be cured when we reach the next Synthesis. And, by the simplification I propose, Syllogism of Necessity is the next Synthesis after these defects have manifested themselves.
The connexions in the new category are, according, to Hegel, essential,” so as to remove the first defect of the First Figure, and ultimate, so as to remove its second defect. If I was right in my previous contention that the first defect — the contingency — has not been shown to involve the inadequacy of the First Figure, and that the only real necessity for a transition lay in the second defect, we shall have to take a somewhat different view, since the “essentiality” of the connexions will not have been deduced. We shall only be able to say that the connexions are ultimate — that certain propositions of the form “all X is Y” are true, without any mediation of the being either possible or necessary.
Whatever other characteristic the connexions may have, they are certainly ultimate. Awl, therefore, I think Hegel is wrong in calling this category by the name of Syllogism, for reasons analogous to those which made me regard the name of Syllogism as improper when applied to Allness, Induction, and Analogy (cp. above, Section 222). The categories of Qualitative Syllogism were called by the name of Syllogism because, from the point of view of those categories, every proposition had to be mediated by two others, which were the premises, while it was the conclusion. Now we have reached a point where we see that all propositions need not be mediated in this way, but that some do not require mediation. Thus the characteristic which made the name appropriate is gone. That characteristic was the fact that the truth of every proposition depended on the truth of two others from which it followed logically.
The Syllogism which Hegel gets here is one in which a derivative and mediated conclusion follows from two ultimate premises. And it is, of course, true that many propositions have a derivative truth of this kind, dependent on the truth of two’ ultimate propositions. But the essential characteristic of this category — the characteristic which enables it to remove the defects of the First Figure — is not that the ultimate Judgments can mediate, but that they do not themselves require mediation. In other words, the essential characteristic is not that they can be the premises of Syllogisms, but that the need not be the conclusions of Syllogisms. And this logical priority of the ultimate Judgments to Syllogisms, makes the name of Syllogism inappropriate here. A better name for the category, I suggest, would have been Ultimate Laws.
228. (G. L. iii. 161. Enc. 191.) Hegel’ s example of this is “ if A is, B is. but A is, therefore B is. “It seems to me that Hegel has erred here in the same way as in the Hypothetical Judgment cp, above, Section 206). From the ultimate Categorical Judgment “all A is B,” it certainly follows that the ultimate Hypothetical Judgment, “if anything is A, it is B,” is also true, and that this can be made, if we wish to do so, a premise in a Syllogism.
But, as we just seen, Hegel’s Hypothetical Syllogism is not this, but something quite different. And how are we to pass from “all A are B,” where the same Individuals are A and B, and “are” is only a copula, to “ if A is, B is,” where A and B are different Individuals, and “ is “ seems to be an assertion of existence? Hegel does not tell us how this can be done — he does not seem indeed to realise the greatness of the difference — and I fail to see how such’ a transition is to be demonstrated. ‘Nor do I see how we could make the further transition from it to “A is either B, C, or D” of the Disjunctive Syllogism, since that takes us back again to the same type of proposition as we found in Categorical Syllogism.
229. The transition to the Disjunctive Syllogism from the Categorical Syllogism is, I think, valid, although it appears to violate the triadic movement by moving directly without an Antithesis. (The valid Hypothetical “ if anything is A, it is B” will scarcely serve as an Antithesis, since it is only a restatement of the Categorical)
The transition is as follows. We have seen that the nature of Individuals must be based on Universal Judgments. And we also saw (Section 207) that from the fact that every Individual is Like and Unlike every other Individual it follows that some of these Universal Judgments must be such that it is true that all X is Z, when it is false that all Z is X.
If this is the case, it will follow that there are not only true Judgments of this type, but true ultimate Judgments. For we have now reached the conclusion that the whole content of all Judgments must be found in ultimate Judgments. The derivative Judgments only combine what is found in their ultimate premises, and give no new truth. The nature of ,Individuals is therefore based on ultimate Universal Judgments. And as that nature requires for its expression Judgments that all X is Z, while all Z is not X, there must be true ultimate Judgments of this type.
Those Individuals which are Z without being X must be connected with Z by one or more other Universals, whose connexion with Z is ultimate. And thus we reach the conclusion that the nature of the universe is expressed by Universal Judgments of the type that all Z is X, W, or Y, where all X, all W, and all V are Z, and where V and W represent a number of Universals which may vary indefinitely from zero upwards, though we know that in some cases it is greater than zero. Thus we reach
(G. L. iii. 167. Enc. 191.), for this, as given by Hegel, is a Syllogism of which the Major Premise is one of these Judgments.
230. The position at which we have arrived is that the nature of the universe is expressed by ultimate Universal Judgments which are such that by their means is expressed both the Likeness and the Unlikeness which every Individual bears to every other Individual.
Hegel would regard all these ultimate Judgments m forming a single hierarchy, without cross-classifications. For he says that, in the Syllogism of Necessity, ever Subject has only one possible Middle Term, and every Middle only one possible Predicate. Thus everything has only one higher class to which it can immediately be referred, and cross-classifications would be impossible.
Whether this single system of classification could possibly explain the whole complex nature of existence is a difficult problem which Hegel does not discuss. In the absence of any treatment of the subject by him, it is sufficient to say here that the conclusion that each Subject could only have one possible Middle Term, and each Middle Term only one possible Predicate, arose from the asserted necessity of removing the “contingency” in the First Figure. If, as I have tried to show, that contingency is not a defect, and need not be remove( the conclusion will not be justified. In that case, the connexion of Universals, expressed by the ultimate Judgments can be more complex, and can admit of cross-classifications.
231. In the ultimate Disjunctive Judgments found in Disjunctive Syllogisms we have the conception of the Self-Differentiating Notion. (So far as I know, the phrase is not Hegel’s own. At any rate he does not use it frequently. But it is often used by commentators, and it expresses a conception which has great importance for Hegel.) This conception is simpler than the name would suggest. It means nothing but a Notion, which is always accompanied by one of a certain number of subordinate Notions, the connexion between the first Notion and its subordinates being intrinsic — not due to any outside circumstance, but to the nature of the terms — and also being ultimate and not derivative. (In the ease of the Notions contemplated by the present category the subordinate Notions are of less extent than the self-differentiating Notion, and they are peculiar to it, so that no cross-classification is possible.)
Let us, for example, assume that it is true that all finite spirits must be either angels, men, or brutes. Then if the connexion between the terms is not external, but intrinsic, and not derivative but ultimate, the Notion of a finite spirit would be one which was said to differentiate itself into angels, men, and brutes.
The conception of a self-differentiating Notion has. often been misunderstood. It has been supposed that by such a Notion Hegel meant one from whose nature the nature of the subordinate Notions could be deduced by pure thought. We should only have to take the conception of the class, and examine it with sufficient, care, and it would proceed to develop the conceptions of its sub-classes. The mythical German who conducted his zoological studies by endeavouring to evolve the idea of a camel from his inner consciousness was acting very much in this manner.
Such a theory is obviously incorrect, nor do I believe that there is the slightest evidence to support the view that Hegel held it. The only case in which Hegel professes to evolve anything by pure thought is in the dialectic. He there evolves only categories, which are themselves forms of pure thought. But most of the Notions which Hegel held to be self-differentiating contain an empirical element. And there is nothing to suggest that Hegel believed that a new empirical idea could ever be produced by pure thought.
Nor, even in the dialectic, does Hegel give us a Notion differentiating itself by pure thought.’ The lower (in the sense of the less adequate) passes into the higher, but the higher (in the sense of the more extensive) never splits itself up into the lower. (This very important distinction has, I think, sometimes escaped the notice both of disciples and of critics of Hegel, and this has sometimes led to considerable confusion.)
The self-differentiation. of a Notion, then, does not imply any inherent dialectic. It only means that it is an ultimate and intrinsic characteristic of that Notion, that it is always united with one of several others. What those others are must be discovered by us through observation and experiment, and, when they are found, the conjunction must be accepted by us as an ultimate fact.
Some of the mistakes about the self-differentiating Notion may be due to the name, which is rather misleading. The active participle suggests a logical, if not a temporal process, and so leads us to suppose that the unity is the agent which produces the plurality, and is therefore prior to it. This might to some extent be remedied if we were also to use the correlative phrase of a self-unifying multiplicity, which would be as true a description of the same fact.
With the Disjunctive Syllogism we reach the end of Subjectivity. The treatment of Subjectivity in the Encyclopaedia does not differ from that in the Greater Logic, though its extreme condensation renders it more obscure.
1. The only case, so far as I know, in which Hegel uses Subjective in any other way occurs in the Greater Logic, when he calls the Doctrines of Being and Essence by the name of Objective Logic, and the Doctrine of the Notion (including Objectivity and the Idea as well as Subjectivity) by the name of Subjective Logic. But lie says (G. L. i. 51) that this use of Subjective and Objective, though usual, is tin satisfactory.
2. Cp. his attempt to demonstrate that particular sorts of predicates are appropriate to Particular forms of Judgment.
3. If the Universal was one of those predicates which belong only to a single existent Individual, this would not apply. But even then the Universal would not be identical with the Individual, though it would denote nothing else.
4. If the Universal was one of those predicates which belong only to a single existent Individual, this would not apply. But even then the Universal would not be identical with the Individual, though it would denote nothing else.
5. This point is partially obscured by Hegel’s treatment of Identical Judgment, which suggests that it is a subdivision of Infinite Judgment.
6. It will be remembered that Judgments of Inherence are also called Judgments of Determinate Being.
7. If we take the Particular Judgment as Hegel does himself (G. L. iii. 95, loc. cit.) this is not only possible, but necessary. The rest of the argument would be unchanged.
8. It will be remembered that both the Universal Notion and the Particular Notion of the beginning of Subjectivity have, since the beginning of Judgment, been classed together as Universals (cp. above, Section 192).
9. It can he zero in some cases, because these are cases where it is true both that all X are Z, and that all Z are X (cp. Section 207).