John McTaggart A Commentary on Hegel’s Logic 1910
Being | The Division of Being
14. The Logic is divided into Being (Sein), Essence (Wesen), and Notion (Begriff). Being is divided into Quality (Qualität), Quantity (Quantität), and Measure (Maass). The divisions of Quality are as follows:
I. Being. (Sein.)
A. Being. (Sein.)
B. Nothing. (Nichts.)
C. Becoming. (Werden.)
II. Being Determinate. (Dasein.)
A. Being Determinate as Such. (Dasein als solches.)
(a) Being Determinate in General. (Dasein überhaupt.)
(b) Quality. (Qualität.)
(c) Something. (Etwas.)
B. Finitude. (Die Endlichkeit.)
(a) Something and an Other. (Etwas und ein Anderes.)
(b) Determination, Modification and Limit. (Bestimmung, Beschaffenheit und Grenze.)
(c) Finitude. (Die Endlichkeit.)
C. Infinity. (Die Unendlichkeit.)
(a) Infinity in General. (Die Unendlichkeit überhaupt)
(b) Reciprocal Determination of the Finite and Infinite. (Wechselbestimmung des Endlichen und Unendlichen.)
(c) Affirmative Infinity. (Die affirmative Unendlichkeit.)
III. Being for Self. (Das Fursichsein.)
A. Being for Self as Such. (Das Fursichsein als solches.)
(a) Being Determinate and Being. for Self, (Dasein und Fürsichsein.)
(b) Being for One. (Sein für Eines.)
(c) One. (Eins.)
B. The One and the Many. (Eines und Vieles.)
(a) The One in Itself. (Das Eins an ihm selbst.)
(b) The One and the Void. (Das Eins und das Leere.)
(c) Many Ones. Repulsion. (Viele Eins. Repulsion.)
C. Repulsion and Attraction. (Repulsion und Attraktion.)
(a) Exclusion of the One. (Ausschliessen des Eins.)
(b) The one One of Attraction. (Das Eine Eins der Attraktion.)
(c) The Relation of Repulsion and Attraction. (Die Beziehung der Repulsion und Attraktion.)
We must notice the ambiguity with which Hegel uses the word Being. It is used (i) for one of the three primary divisions into which the whole Logic is divided; (ii) for one of the three tertiary divisions into which Quality is divided; and (iii) for one of the three divisions of the fourth order into which Being, as a tertiary division, is divided. In the same way Quality, besides being the general name for the secondary division which forms the subject of this Chapter, is also the name for a division of the fifth order, which fails within Being, Determinate as Such. And Finitude, again, is the name of a division ,of the fourth order, and also of a division of the fifth order.
15. (G. L. i. 77. Enc. 86.) I do not propose to discuss here the :validity of the category of Being. Since the dialectic process starts with this. category, its validity is rather a question affecting the whole nature of the process than a detail of the earliest stage, and I have treated it elsewhere. If, then, we begin with the category of Being, what follows?
It must be remembered that the position is not merely that we are affirming Being, but that, so far, we are affirming nothing else. It is to indicate this absence of anything else that Hegel speaks of Being in this division as Pure Being (reines Sein), though the adjective does not appear in the headings.
Pure Being, says Hegel (G. L. i. 78. Enc., 87) has no determination of any sort. Any determination would give some particular nature, as against some other particular nature — would make it X rather than not-X. It has therefore no determination whatever. But to be completely free of any determination is just what we mean by Nothing. Accordingly, when we predicate Being as an adequate expression of existence, we find that in doing so we are also predicating Nothing as an adequate expression of existence. And thus we pass over to the second category.
16. (G. L. i. 78. Enc. 87.) This transition, which has been the object of so much wit, and of so many indignant denials, is really a very plain and simple matter. Wit and indignation both depend, as Hegel remarks (G. L. i. 82. Enc. 88), on the mistaken view that the Logic asserts the identity of a concrete object which has a certain definite quality with another concrete object which has not that quality — of a white table with a black table , or of a table with courage. This is a mere parody of Hegel’s meaning. Whiteness is not Pure Being. When we speak of a thing as white, we apply to it many categories besides Pure Being — Being Determinate, for example. Thus the fact that the presence of whiteness is not equivalent to its absence is quite consistent with the identity of Pure Being and Nothing.
When the dialectic process moves from an idea to its Antithesis, that Antithesis is never the mere logical contradictory of the first, but is some new idea which stands to the first in the relation of a contrary. No reconciling Synthesis could possibly spring from two contradictory ideas — that is, from the simple affirmation and denial of the same idea.) In most parts of the dialectic, the relation is too clear to be doubted. But at first sight it might be supposed that Nothing was the contradictory of Being. This, however, is not the case. If we affirmed not-Being, in the sense in which it is the mere contradictory of being, we should only affirm that, whatever reality might be, it had not the attribute of Being. And this is clearly not the same as to say that it has the attribute of Nothing. It may be the case that wherever the predicate Being can be denied, the predicate Nothing can be asserted, but still the denial of the one is not the affirmation of the other.
Hegel says, indeed (G. L. i. 79) that we could as well say Not-being (Nichtsein) as Nothing (Nichts). But it is clear that he means by Not-Being, as he meant by Nothing, not the mere denial of Being, but the assertion of the absence of all determination.
If the identity of Being and Nothing were all that could be said about them, the dialectic process would stop with its second term. There would be no contradiction, and therefore no ground for a further advance. But this is not the whole truth (G. L. i. 89. Enc. 88). For the two terms originally meant different things. By Being was intended a pure positive reality without unreality. By Nothing was intended a pure negative — unreality without reality. If each of these is now found to be equivalent to the other, a contradiction has arisen. Two terms, defined so as to be incompatible, have turned out to be equivalent, Nor have we got rid of the original meaning. For it is that same characteristic which made the completeness of their opposition which determines their equivalence. A reconciliation must be found for this contradiction, and Hegel finds it in
17. The reconciliation which this category affords appears to consist in t he recognition of the intrinsic connexion of Being and Nothing (G. L. i. 78. Enc. 88). When we had these two as separate categories, each of these asserted itself to be an independent. and stable expression of the nature of reality. By the affirmation of either its identity with the other was denied, and when it was found, nevertheless, to be the same as the other, there was a contradiction. But Becoming according to Hegel, while it recognises Being and Nothing, recognises them only as united, and not as claiming to be independent of one another. It recognises them, for Becoming is always the passage of Being into Nothing, or of Nothing into Being. But, since they only exist in Becoming in so far as they pass away into their contraries, they are only affirmed as connected, not as separate, and therefore there is no longer any opposition between their connexion and their separation.
But, Hegel continues, this is not the end of the matter. Being and Nothing only exist in Becoming as disappearing moments. But Becoming only exists in so far as they are separate, for, if they are not separate, how can they pass into one another ? As they vanish, therefore, Becoming ceases to be Becoming, and collapses into a state of rest, which Hegel calls Being Determinate (G. L. i. 109. Enc. 89).
18. I confess that I regret the choice of Becoming as a name for this category. What Hegel meant seems to me to be quite valid. But the name of the category suggests something else which seems to me not to be valid at all.
All that Hegel means is, as I have maintained above, that Being is dependent on Nothing in order that it should be Being and that Nothing is dependent on Being in order that it should be Nothing. In other words, a category of Being Without Nothing, or of Nothing without Being, is inadequate and leads to contradictions which prove its falsity. The only truth of the two is a category which expresses the relation of the two. And this removes the contradiction. For there is no contradiction in the union of Being and Nothing. The previous contradiction was between their identity and their difference.
Hegel seems to have thought it desirable to name the new category after a concrete fact. But, as I have said above (Section 9), the use of the names of concrete facts to designate abstract categories is always dangerous. In the present case, the concrete state of becoming contains, no doubt, the union of Being and Nothing, as everything must, except abstract Being and Nothing. But the concrete state of becoming contains a great deal more — a great deal which Hegel had not deduced, and would have had no right to include in this category. I do not believe that he meant to include it, but his language almost inevitably gives a false impression.
When we speak of Becoming we naturally think of a process of change. For the most striking characteristic of the concrete state of becoming is that it is a change from something to something else. Now Hegel’s category of Becoming cannot be intended to include the idea of change.
Change involves the existence of some permanent element in what changes — an element which itself does not change. For, if there were nothing common to the two states, there would be no reason to say that the one had changed into the other. Thus, in order that an thing should be capable of change, it must be analysable into two elements, one of which does not change. This is impossible under the categories of Quality. Under them each thing — if the word thing could properly be used of what is so elementary — is just one simple undifferentiated quality. Either it is itself — and then it is completely the same — or its complete sameness vanishes, and then the thing also vanishes, since its undifferentiated nature admits no partial identity of content. Its absolute shallowness leaves no room for distinction between a changing and an unchanging layer of reality.
This was recognised by Hegel, who says that it is the characteristic of Quantity that in it, for the first time, a thing can change, and yet remain the same (G. L. i. 211. Enc. 99). He not therefore have considered his category of Becoming, which comes before Quantity, as including change.
But, it may be objected, although Hegel’s category of Becoming is incompatible with fully developed change, may it not be compatible with change in a more rudimentary form ? Is it not possible that, even among the categories of Quality, a place may be found for a category which involves, not the change of A into B, but the disappearance of A and the appearance of B instead of it? To this I should reply, in the first place, that if such replacement of A by B was carefully analysed, it would be found to involve the presence of some element which persisted unchanged in connexion first with A and then with B. The case would then resolve itself into an example of change proper. To defend this view would however, be an unnecessary digression here. For it is clear that, if such a replacement could exist without being a change of A into B, then A would be quite disconnected with B. But in Hegel’s category of Becoming the whole point lies in the intrinsic and essential connexion of Being and Nothing. The category could not, therefore, be an example of such replacement.
19. Thus Becoming, as a category of the cannot consistently involve change. And when we look at the transition by which Hegel reaches it, we see, as I said above, that the essence of the new category lies in the necessary implication of Being and Nothing, and not in any change taking place between them.
But the name of Becoming is deceptive in itself, and so is Hegel’s remark that the category can be analysed into the moments of Beginning (Entstehen) and Ceasing (Vergehen) (G. L. i. 109). e implication of the two terms is to be called Becoming, there is, indeed, no reason why these names should not be given to the implication of Being in Nothing, and of Nothing in Being. It all tends, however, to strengthen the belief that we have here a category of change. The same result is produced by the mention of the philosophy of Heraclitus in connexion with the category of Becoming. Of course a philosophy which reduced everything to a perpetual flow of changes would involve the principle of the implication of Being and Nothing. But it would also involve a great deal more, and once again, therefore, we meet the misleading suggestion that this great deal more is to be found in the category of Becoming.
20. For these reasons I believe that the course of the dialectic would become clearer if the name of Becoming were given up, and the Synthesis of Being and Nothing were called Transition to Being Determinate (Uebergang in das Dasein).
This follows the precedent set by Hegel in the case of the last category of Measure, which he calls Transition to Essence (Uebergang in das Wesen) (G. L. i. 466).
When we have taken this view of the category, the transition to the next triad becomes easy. So long’ as the third category was regarded as involving change, it might well be doubted whether Hegel had succeeded in eliminating, in Being Determinate, the change he had introduced in Becoming. And to do this was necessary, since Being Determinate is certainly not a category of change. But on the new interpretation change has never been introduced, and does not require to be eliminated.
The assertion that Being Determinate contains Being as an element is simple enough. But to say that it contains Nothing as an element seems strange. The difficulty is, however, merely verbal. The Antithesis to Being should rather have been called Negation than Nothing. The word Being involves a positive element, but does not exclude a negative element — unless we expressly say Pure Being. But Nothing is commonly used to designate a negative element combined with the absence of any positive element. It corresponds to Pure Being while Being corresponds to Negation.
Now Being Determinate contains Being as a moment, but not Pure Being, since Pure Being means “Being and nothing else.” In the same way, then, we must say that Being Determinate contains as an element, not Nothing, but Negation. Hegel recognises this, for he says (G. L. i. 81) that in Being Determinate we have as moments Positive and Negative, rather than Being and Nothing. But he fails to see that Being and Nothing are not in ordinary usage correlative terms, and that, while, when he came to the Synthesis, he had to substitute Negative for Nothing, he could just as well have kept Being instead of Positive. It seems to me that it would have been better if he had spoken of the Thesis and Antithesis as Being and Negation. He could then have said in this triad, as he does in other cases, that it was the Thesis and Antithesis themselves which are the moments of the Synthesis.
21. It is easy to see that in Being Determinate Being and Negation are synthesised. If anything has a definite quality, this involves that it has not other definite qualities, inconsistent with the first. A thing cannot be green unless it is not red, and thus its greenness has a negative aspect, as well as a positive one.
(G. L. i. 112. Enc. 89.) This, as the first subdivision of the first division of Being Determinate, has, as its name implies, no other meanin except the general meaning of Being Determinate, namely, that in all existence Being and Nothing are united.
And now, for the first time, we get the possibility of differentiation and plurality. Being and Nothing did not admit of this. Whatever simply Is is exactly the same. And this is also true of whatever simply Is Not. But under the category of (Being Determinate, it is possible to have an a which is not b, and is thus distinguished from b, which is not a.) And not only the possibility of such differentiation, but also its necessity is now established. For whatever is anything must also not be something, and cannot be what it is not. It must therefore not be something else than what it is. And thus the reality of anything implies the reality of something else. (The validity of this will be discussed in Section 25.) Hegel calls the various differentiations by the name of Qualities, and so we reach the second subdivision of Being Determinate as such, namely
22. (G. L. i. 114.) We must not be misled by the ordinary use of the phrase “a Quality.” As a rule, when we speak of a Quality or of Qualities, we mean characteristics which inhere in a Thing, and of which one Thing may possess m any. Hegel calls these, when he comes to treat of, Essence, by the name of Eigenschaften. We have not yet got any idea so advanced as this. It is not until Essence has been reached that we shall be able to make a distinction between a Thing and its characteristics. And although we have now attained a plurality, we have not yet acquired the idea of plurality in unity, which would be necessary before we could conceive one Thing as having many characteristics.
The Qualities of which Hegel speaks here are simply the immediate differentiations of Being Determinate. They do not inhere -in anything more substantial than themselves; they, in their immediacy, are the reality. Consequently they are not anything separate from the Being Determinate. Each Quality has Determinate Being, and the universe is nothing but the aggregate of the Qualities. There is not one Being Determinate with many Qualities, but there are many Determinate Beings. These may be called, not inappropriately, Somethings. And this is the transition to the third division of Being Determinate m Such, namely,
23. (G. L. i. 119.) At this point, says Hegel, we first get the Real (G. L. i. 120. Enc. 91). The reason for this is not very obvious. Reality seems to be taken as a matter of degree -a thing is more or less Real in proportion as it is regarded under a more or less true category. Something is, no doubt, a truer category than those which preceded it, but it is less true than those that follow it, and I cannot see why Reality comes in here, if it did not come in before. Something is not even the first Synthesis.
24. Looking back on the two last transitions-from Being Determinate in General to Quality, and from Quality to Something-they must, I think, be pronounced to be valid. A doubt might perhaps arise as to the necessity of passing through them. Is it not clear, it might be asked, that the differentiations cannot lie on the surface of Being Determinate (since that would involve a distinction between Essence and Appearance) but must be in it? And in that case could we not have simplified the process by taking Something as the immediate form of Being Determinate, and so forming the undivided first moment of it?
But between simple Being Determinate and Something there is a difference-namely the explicit introduction of plurality. The fact that the name Something is in the singular number (inevitable with the German word Etwas) may obscure this if we confine ourselves to the titles, but in reading the demonstrations it soon becomes evident that, between Being Determinate in General and Something, plurality has been introduced. In the idea of Something, therefore, we have more than is in the simple idea of Being Determinate, and a transition between them is required.
We can also see why there should be two steps between Being Determinate in General and Something, and why the road from the one to the other should lie through the category of Quality. The transition to plurality takes place in the transition to Quality, since Hegel speaks of one Being Determinate in General, but of many Qualities. Now we can see, I think, that it is natural that, in passing from what is singular to a plurality, we should first think that what is plural is something different from that which had previously been before us (and in Quality the suggestion is that they are different) and that we should require a fresh step of the process to show us that the plurality is the true form of what we had previously taken not to be plural (and this is what is gained by the transition to Something).
We have, then, a plurality, and a plurality which does not inhere in anything else. It must therefore be regarded as a rudimentary form of plurality of substance, rather than of plurality of attributes. Now the categories are assertions about the nature of existence. So, when we have got a plurality of Somethings, we have got a plurality of existence. Is this justified?
25. It may be objected that we are not entitled to argue in this way from the existence of one Something to the existence of others. No doubt, it may be said, if this Something is x, there must, by the results we have already reached, be some y, which x is not, but it does not follow that y exists. If (to take an example from a more complex sphere than that of Something) an existent object is red, it must be not-green, but it does not follow that any green object exists. Thus, it is urged, there might, for anything we have proved to the contrary, be only one existent Something, whose definite nature consisted in the fact that it was x, and was not y, z, etc.
I do not, however, think that this is valid. For if we get the definiteness of the Something out of the fact that it is x and not y, not z, etc., then it will have a plurality of qualities, x, not-y, not-z, etc. This requires the conception of a thing as a unity which holds together a plurality of attributes, and is not identical with any one of them. And this is a conception which we have not yet reached, and have no right to use. Thus the negative element in each Something cannot fall within it, and must fall outside it, and so we are compelled to follow Hegel in asserting the plurality of existent Somethings.
It may be replied that what belongs to the nature of anything cannot be wholly outside it, and that if two existent Somethings are distinguished from each other by being respectively x and y, then after all it must be true of x that it is not-y, and of y that it is not-x, and so that there will be the plurality of attributes in, each Something, in which case the possibility that there is only one Something has not been effectively refuted.
It is quite true, no doubt, that the existence of a plurality of substantial beings does involve a plurality of attributes in each of them. But the recognition of this forms a further stage of the dialectic, in which we shall have passed beyond the category of Something. We have not yet reached this stage, and at present, since there is no plurality of attributes in a Something, each Something can only find its determinateness in another existent Something.
When we do reach to the conception of a thing with a plurality of attributes, we shall no longer have our present reason to believe in a substantial plurality. For that reason, as we have seen, is that plurality is necessary, and that no other plurality is possible, and this becomes invalid when a plurality of attributes in one thing has been established. If the conception of a substantial plurality is finally retained, it must rest on considerations not yet before us.
Thus we have a plurality of Somethings. Each of these is dependent for its nature on not being the others. It may thus be said, in a general sense, to be limited by them. (Limit, as a technical term in the dialectic, denotes a particular species of limitation in the more general sense.) With this we pass to the second division of Being Determinate, which is
26. (G. L. i. 122.) This category should be a restatement, in a more immediate form, of the category of Something. This is exactly what it is. For the category of Something, as I have said, included the idea of a plurality of such Somethings. And, from the point of view of any one of these, the other Somethings will be primarily not itself So we get the idea of Something and an Other.
Since each Something is dependent for its own nature on an Other, its nature may be called a Being-for-Other. (Sein für Anderes.) But this is not the only aspect of its nature. The relation to an Other is what makes it what it is. And thus this relation is also what it is By Itself or implicitly (An Sich). And thus this relation is also a quality of the Something itself, (G. L. i. 129. Cp. also Enc. 91, though the explanation is here so condensed as scarcely to be recognisable.) This takes us to the next subdivision, Determination. Modification and Limit. (1 admit that Modification is not a very happy translation of Beschaffenheit, but it is impossible to get really good names for so many meanings which differ so slightly.)
27. (G. L. i. 129.) Not content with the analysis of his subject-matter by five successive trichotomies, Hegel further analyses this category into a triad of the sixth order, the terms of which are Determination, Modification, and Limit. The subtlety of the distinctions at this point is so great that I must, confess to having only a very vague idea of what is meant. So far as I can see, Determination is the character of the Something viewed as its inner nature, and Modification is that character viewed as something received by it from outsider-is, in fact, the Being for Other come back again. It follows then, naturally enough, that Determination and Modification are identical. And from this again it follows that, as the Something was conceived as having a nature which was both a characteristic of itself and or its Other, that nature should be conceived as a Limit. In such a sense a meadow is limited by the fact that it is not a wood, nor a pond. (Enc. 92.) Now it is clear that we only get such a Limit when the nature of the Something is seen to be both in itself and in its relation to an Other. The conception of a Limit implies that it makes the Something what it is-no more and no less. That it should be no less than itself requires that its nature should be in itself, so that it should maintain itself against the Other. That it should be no more than itself requires, at the present stage of the dialectic, that its nature should also be outside itself, that the Other should maintain itself against it.
The correctness of this interpretation is, no doubt, very problematic. But whatever Hegel’s meaning may have been in this obscure passage, we can see for ourselves that the category of Limit would necessarily have come in at this point. For, in the category of Something and an Other, the nature of each Something lay in the Other. But it is also true, as Hegel points out without any. obscurity, that the nature of Something must also lie in itself, And, since the nature of Something lies both in itself and in its Other, we have the idea of a Limit-of a characteristic which, while it belongs both to Something and to its Other, keeps them apart.
Here, as Hegel remarks (G. L. i. 133), we get for the first time the conception of Not-being for Other. In the category of Something and an Other we had the conception of Being for Other, but now in Limit the Something has its nature in itself as well as in the Other, and so it has a certain stability and exclusiveness.
At this point, therefore, we may be said to get the first glimpse of the conception of Being for Self. But it is not yet seen to be the truth of Being for Other. On the contrary it appears to be in opposition to it, and this opposition produces fresh contradictions, which cannot be solved until the true nature of Being for Self is discovered in the category which bears that name.
We now come to Finitude in the narrower sense. That this conception should only be reached at this point will not seem strange if we realise the meaning which Hegel always gives to this term. (For him the Finite is not simply that which has something outside it, and the Infinite is not simply that which has nothing outside it. the Infinite for him is that whose nature and, consequently, whose limits, are self-determined. The Finite, on the other hand, is that whose nature is limited by something outside itself.) The essential feature of the Infinite is free self-determination. The essential feature of the Finite is subjection to an Other.
This explains why Finitude only becomes explicit at this Point. Two things are necessary for subjection to an Other — the Other, and a definite nature in the Something to be subjected to it. The conception of plurality was only reached at the end of Being Determinate as Such, and till then there could be no question of Finitude. When this point was reached, Finitude began to appear, and accordingly the second division of Being Determinate, which we are now considering, is, as we have seen, called Finitude. But Finitude does not become fully explicit till the Something’s nature is seen to be also in itself, and not only in the Other. For till then there can scarcely be said to be anything to be subjected to the Other. Only with the conception of Limit does Finitude become fully explicit. And therefore the next category-the last subdivision of Finitude in the wider sense is called in a special sense
28. (G. L. i. 137.) This category is merely a restatement of the last moment of the previous subdivision-that is to say, of Limit. The idea of a Limit is, as has already been said, the idea of Finitude, since they both mean that the limited thing has a nature of its own, and that its nature is’ in subjection to an Other. This conception takes the form of Limit when we view it as overcoming the difficulties which arise from the opposition between the nature as in an Other and the nature as in the object itself, When the conception is taken as a more immediate statement of the truth, it takes the form of Finitude.
Finitude is the Synthesis of a triad of which Something and an Other is Thesis, and Determination Modification and Limit is the Antithesis. The Thesis asserted that the nature of the Something lay in its Other, the Antithesis asserted that the nature of the Something lay in itself These assertions are reconciled in Finitude.
29. On looking back we can see, I think, that the subdivisions found within the category of Determination Modification and Limit are useless. Modification is only a repetition of Something and an Other, while Limit is identical with Finitude. The only idea remaining is Determination. (It would have been better, therefore if Determination by itself had been the Antithesis of Something and an Other. The name of Limit, not being wanted for a subdivision of the Antithesis, would be set free, and could be used, instead of Finitude, as the name of the Synthesis, and this would avoid the inconvenience of using Finitude here, for a division of the fifth order, when it is also used for a division of the fourth order.
30. In Finitude. as was said above, there are two sides — the internal nature of the finite Something and the relation in which it stands to the Other. These Hegel calls respectively the Ought and the Barrier. (Das Sollen und die Schranke.) (G. L. i. 140.) The Barrier seems an appropriate name. But why the internal nature of the Something should be called the Ought is not so clear. It may be said that a conscious being, when he feels himself limited by something, says that the limit ought to be removed, and that he ought to have room to develop freely. But the resemblance between such a conscious being and a limited Something is very slight, and far less important than the difference. When a man says that he ought to be able to do what, in point of fact, external circumstances do not allow him to do, he has an ideal of some course of action different from the one which he is forced to take, and he judges that his ideal course would fulfil his true nature more completely than the other. The position here is entirely different. The content of the two opposed sides is here the same, for the Something has only one nature, which may be looked at either as in itself or in the Other, and the opposition is only between the two ways of loo king at it.
Why then did Hegel use the word Ought? I believe he did so because it gave him a chance of introducing an attack on the ethics of Kant and Fichte (G. L. i. 142; Enc. 94). This was a temptation which he was never able to resist.
31. But the inner nature of the Something now bursts its Barrier. The Other which limits it has no nature which is not expressed in the limitation itself, And the limitation belongs to the nature of the Something. So that it now finds its own nature beyond the Barrier, which it has, therefore, passed. (G. L. i. 147. The line -of the argument in the Encyclopaedia is different, and will be considered later on.) To go back to Hegel’s own example, a meadow is limited by the fact that it is not a wood. Not to be a wood is a part, and an essential part, of the nature of the meadow. Thus the nature of the meadow is to be found in the nature of the wood, and is thus no longer something bounded and confined by the wood’s nature-for what is left to be bound?
We thus pass to
the third division of Being Determinate (G. L. i. 147). For, the Barrier being abolished, the Something is no longer determined by anything outside itself. Thus we have got rid of Finitude, and so attained Infinity, though only, so far, in a very rudimentary form.
The transition here, it will be noticed, is a distinct advance. Infinity is a fresh conception from Finitude. This is not what might have been expected, for Finitude (in the narrower sense of the word) is a division of the fifth order and stands to the next division of the fifth order (Infinity in general) as the Synthesis of one triad to the Thesis of the next. According to the general scheme of the dialectic, therefore, their content should have been the same.
And the transition seems to me to be invalid. I cannot see that anything which Hegel has said entitles him to conclude, as apparently he does, that in this category we have got rid of Limit and Barrier. The nature of the meadow is determined by that of the wood-but it is determined negatively. It is its nature not to be the wood. And this determination, while it relates the two, does not in any way destroy the difference between them, so that there is no justification for concluding that the second of them has ceased to limit the first, or to act as its Barrier.) For the proper transition at this point, we must, I believe, adopt the view of the Encyclopaedia, rather than that of the Greater Logic.
Continuing the treatment of the subject in the Greater Logic, we find that when, in the first place, the Something passes over its Barrier, it finds itself outside the Barrier, and so unlimited. Thus the first stage is
32. (G. L. i. 148.) And now Hegel proceeds to restore the limitations which, if I am right, he ought never to have discarded. What, he asks (G. L. i. 153), is this Infinity? It has been gained by negating Finitude, and passing beyond it. Now nothing can negate anything definite, except by being definite itself. But we have seen that a thing can only be definite if it has a limit and is finite. And thus the Infinite which we seemed to have reached turns out to be another Finite. A meadow, for example, cannot be negated by pure Being, or by Nothing. It must be by some other Being Determinate. And this must be finite.
The Infinity, which had been reached, thus turns out to be finite. But, being, finite, it will have its nature outside itself, and so again passes the Barrier, and becomes infinite — only once more to become finite. This process goes on without end, and thus we have the second subdivision (G. L. i. 149)
33. which may be called more briefly Negative Infinity (cp. Enc. 94). It must be noted that this is not a category of change. A category of change would assert that the reality, when viewed under that category, is viewed as changing its nature. This is not the case here. The reality-the nature of the Something is not conceived as changing All that changes is the way in which we judge it. We conceive its nature, first as being generally outside itself, then as being in another Something, then as generally outside that other Something again. We oscillate endlessly between these two views. But this does not involve any judgment that the reality changes. It is only a change of judgment about the reality.
This involves a contradiction. The nature of the Something is first seen not to be Finite, but Infinite. But it is then seen to be, not Infinite, but Finite again. And the second step does not transcend the first, for the second leads back again to the first. Therefore a part of the nature of the Something-that part which lies outside the Something-cannot be pronounced either Finite or Infinite. Thus it can be found nowhere-for the category recognises no third alternative. And since this part of the nature of the Something has been shown to be essential to the Something, there can be no Something, and so (so far as can be seen under this category) no Determinate Being at all. And so there is a contradiction.
It is sometimes said that Hegel holds that an Infinite Series is as such contradictory. But this is a mistake. He denies that there is anything sublime in endless repetition, and asserts that its only important feature is its tediousness (Enc. 94), but he does not assert it to be intrinsically impossible. It is only Infinite Series of particular kinds which are contradictory, and then only for some reason other than their infinity. In the case of the present series, as we have seen, there is such a reason.
34. How do we get rid of this contradiction? Hegel points out (G. L. i. 155) that the same fact which produced the contradiction has only to be looked at in a rather different light to give the solution. That fact is the unity of the Finite and Infinite-or, in other words, of what is within any finite Something and of what is outside it. It was this which produced the contradictory infinite series, for it was this which made the content of the Something first overstep its Barrier. But if we put it in another way-that the content of the Something is in part its relation to what is outside it, then the Something has an internal nature which is stable through its relation to what is outside it, and the contradictory infinite series never begins.) Instead of saying that the nature of the Something must be found in what is outside it, we must now say that it has its nature through what is outside it. The conception of relatively self-centred reality thus ached is called by Hegel (G. L. i. 155)
35. The treatment of the subject in the Encyclopaedia is different. After establishing the category of Limit, Hegel continues (Enc. 93) “Something becomes an Other: this Other is itself Something: therefore it likewise becomes an Other, and so on ad infinitum.” The transition here is not alternately from Finite to Finite. The only Infinite is the infinite number of such Finites.
This seems to me to be better than the argument in the Greater Logic. In the first place, the categories are so arranged in the Encyclopaedia as to avoid the difference of content between a Synthesis and the succeeding Thesis which, as we saw above, occurs in the Greater Logic.
In the second place, the Encyclopaedia avoids the transition from the limited to the unlimited, which I have maintained above to be invalid. And the transition which it substitutes is, I think, valid. Part of the nature of A is found in its Other, B, since it is part of its nature not to be B. But this can only be a definite characteristic of A, if B is definite. Nosy part of B’s nature, on the same principle, must be found in its Other C. Thus the nature of A will be partly found in C, since it is part of its nature to be not-B, while B’s nature includes being not-C. A similar argument will prove that the nature of A is partly in C’s Other, D, and so on without end.
Here, again, we get an infinite series which is a contradiction. A, as a Something, must have a definite nature. But part of this nature is not to be found in itself It must, according to the category, be found in one of the series of Others. But it cannot be found in any one of them, for whichever we take proves to have part of its own nature, and therefore of A’s nature, in yet another. Thus this indispensable part of A’s nature is to be found in none of the series of Others, and therefore, according to this category, can be found nowhere. Thus A has no definite nature, though -1t is a Something. And this is a contradiction.
Nor can we escape from this contradiction by saying that the part of A’s nature which is external to itself is found in the whole series, though it is not found in any one term of it. For nothing which we have yet reached entitles us to regard the series as a unity, with which A can enter into relations. Its relations can only be to some particular Something which forms part of the series.
It will be seen that the contradiction does not rest on the impossibility that a mind working in time should ever reach the end of an infinite series. This impossibility might prove that the full nature of any Something could never be known to any mind working in this way, but in this there would be no contradiction.
36. From this contradiction we are freed by passing to the category of True Infinity. Hegel says that the Something stands in the same Position to its Other, as the Other stands to the Something. The Something is the Other of its own Other, and, therefore, “Something in its passage into Other only joins with itself” (Enc. 95). This means that, while the nature of A is partly to be found in B, and the nature of B is partly to be found in something other than B, this need not be a third Something, C, but can be A, which is after all other than B. So the infinite series, with its contradiction, is avoided. A and B are each determinate through the fact of not being the other. Thus we reach Being for Self. A’s nature is now wholly in itself. It no longer has part of its nature in its Other, but its nature within itself is what it is because of its relation to its Other. (The Encyclopaedia is very condensed here, but it seems to be certain that this is the meaning.)
This position, Hegel says, is that of True Infinity, and it is identical with what was called, in the Greater Logic, Affirmative Infinity. The name of Infinity may appear inappropriate. For here all assertion of Infinity, in the ordinary sense of the word, has disappeared, since the necessity for an Infinite Series of Somethings has disappeared. According to the category we have just reached there must be at least two Somethings, and there may be any number, but, so far as 1 can see, there may be only two.
It is very characteristic of Hegel’s thought that he should call this concept True or Affirmative Infinity. According to him the essence of Infinity lies in the fact that it is what is unconstrained, unthwarted, free. And freedom, according to him, can only be found, not in being unbounded, but in being self-bounded. That is truly infinite whose boundaries are determined by the fact that it is itself, and not by mere limitation from outside.) It is through applications of this principle that Hegel holds that a conscious spirit has more true infinity than endless space or endless time. Now in this category we have reached self-determination, though only as yet in a very rudimentary form. And therefore, in comparison with what has gone before, Hegel calls it True Infinity.
37. From this point the Greater Logic and the Encyclopaedia again coincide in their treatment. It is here, says Hegel, that we first get Ideality (G. L. i. 164. Enc. 95) and that Idealism becomes possible (G. L. i. 171). Idealism, he says, consists in maintaining that the Ideal (das Ideelle, not das Ideal), and this, again, means that the Finite is recognised “not truly to be.” For this it is necessary that the Finite should have been reached, and should have been transcended, and that we should recognise that wh at, is merely Finite is impossible. (Finite is, of course, used in Hegel’s own sense, and means, not that which is bounded, but that which is not self-bounded.) This is the first category in which such a recognition is involved.
Affirmative Infinity gives us, as we saw when dealing with the Encyclopaedia, Being for Self. In the Greater Logic they form two separate categories, but the content of Affirmative Infinity-the final Synthesis of Being Determinate-is identical with the content with which the new division of Being for Self begins. The Something has now its whole nature inside itself.
(G. L. i. 173. Enc. 96) is the last of the three tertiary divisions to be found in Quality. Its first subdivision is called by Hegel
(G. L. i. 174), while the first subdivision of this again is named
(G. L. i. 175.) The position here is that a thing has both Being Determinate and Being for Self. (This seems to me to be invalid, but the discussion of its validity had better be postponed until we reach the end of Being for Self as Such.) Since it has both, it is qualitatively differentiated from its Other, while the Being for Self gives it stability and saves it from the infinite series of Others, in which Being Determinate, taken by itself, is compelled to seek the nature of each differentiation.
But the position, Hegel continues (G. L. i. 176), cannot be maintained. For Being Determinate has, by the previous transition, been transcended in Being for Self, and is a moment of Being for Self In so far as it is valid at all, its validity is summed up in Being for Self. In so far as it claims to be anything distinct from, and supplementary to, Being for Self, it is not valid. Therefore all Being for Other has now disappeared, and Being, for Self is not for an Other. Being. for Self has not negation “an ihm” as a determinateness or limit, and therefore not as a relation to a Being Determinate other than itself.
We have no longer a Something, since Hegel confines that term to the sphere of Being Determinate. At the same time we are not yet entitled to speak of a One. Let us for the present call the reality, which was previously called the Something, by the neutral name of X. The point of the present argument is that the relation of the X to the not-X has become more negative than before.
We must not exaggerate the change. The relation of the Something to the Other was already, in a sense, negative, for the Something was limited by its Other, and was what the Other was not. And, again, X is still related to the not-X. For it is only by distinguishing itself from the not-X that it got Being for Self at all, and this distinction is itself a relation, as will appear more explicitly when we come to the categories of the Many and of Attraction. (When Hegel says that Being for Self. does not contain negation “,is a relation to a Being Determinate other than itself” (G. L. i. 176), the emphasis is, I believe, on the last five words. There is a relation, but it is not a relation to a Being Determinate, nor to anything which is, in the technical sense, the “Other” of the Being for Self.)
But the change is there, and is important. When the Something was determined by its Other, the positive nature of the Other was essential to the determination. The Something was this quality, and not any other, and it was determined in this way because the Other was what it was, and nothing else. Now it is different. In Being for Self all that is essential is that there should be something else which is not X. Whatever this other thing may be, X can determine itself by means of a relation to it. It has no longer its own peculiar Other. This increased independence of X is the natural consequence of X being more individual and self-centred than before.
The new category to which we now pass is called by Hegel
38. (G. L. i. 176.) We ought, I think, to consider the significance of this category as mainly negative, in spite of its positive name. Its essence is that Being for Self is not also Being Determinate, and it might not unfairly have received the name of Not-Being for Other.
Hegel has then no difficulty in proving that the One, for which the X is, can only be itself, If it were anything else the Being for One would be Being for Other. And this is impossible, since Being for Other has already been transcended. The Being for One of X, then, is Being for Self.
This takes us to a new category which consists in the restatement of Being for Self, but this time by itself without Bein ‘g Determinate. To this Hegel (G. L. i. 181) gives the name of
39. which emphasises the negative and exclusive character of Being, for Self.
It seems to me that Hegel was wrong in subdividing Being for Self as Such. The category of Being Determinate and Being for Self is unjustified, for he only reached Being, for Self by transcending Being Determinate. Being Determinate, therefore, in so far as it is true at all, is contained in Being for Self and cannot properly be put side by side with it. The Thesis of the triad must thus be rejected, and the Antithesis must go with it, since the only thing done in Being, for One is to remove the Being Determinate which had been improperly introduced in the Thesis. There only remains the Synthesis of e triad-namely, One. (Now Hegel’s conception of One is just the same as his conception of Being for Self. So the Thesis and Antithesis are removed, and the Synthesis is the same as the undivided category. Thus all the sub-divisions are removed. It would be convenient to call this undivided category One, rather than Being for Self as Such, as this distinguishes it more clearly from the wider tertiary category of Being for Self of which it is a subdivision. This is the course actually taken by Hegel in the Encyclopaedia (Enc. 96), where an undivided category of One is the Thesis in the triad of Being for Self,
We now pass to the second division of Being for Self,
40. (G. L. i. 182. Enc. 97) of which the first subdivision is
(G. L. i. 183.) The first subdivision here is, as is to be expected, a restatement of the last subdivision of the previous division. The two bear, in this instance, almost the same name. Now the One, since it is Being for Self, has its nature by relating itself to, and distinguishing itself from, something other than itself. But this other is at first only determined negatively in regard to the One. The relation of the other term to the One is simply that the other term is not the One. This other term has therefore, to begin with, a merely negative nature. The One is limited by the not-One, by which is meant, so far, not the Many, but only something which is not the One. Thus we get
41. (G. L. i. 184.) The name of this category is appropriate enough as a metaphor, but we must remember that it is nothing but a metaphor. If it were a Void, in the literal sense of the term, which was thus related to the One, the One could only be an atom in space, which is not the case.
But the One can only be negated by something like itself
(G. L. i. 187). The One is definite, and its definiteness depends on a definite relation with the other term. And the relation between them cannot be a definite relation to a definite One, unless the other term is itself definite. Now it has been shown that nothing can be definite, unless it is for itself, and so is a One. Thus the One can only be negated by another One, which bring us to the category of
42. (G. L. i. 186), to which Hegel gives the additional name of Repulsion, since the relation of the Ones to each other is mainly negative.
Since the conception of the Many has been reached, the natural question to ask is How Many? Hegel does not regard this, I think, as a question which can be answered by pure thought. Pure thought has proved the necessity for a plurality has proved, that is, there must he at least two Ones, but not that there must be more than two. The proof of that would rest on the empirical fact that we are presented with more than two differentiations of our experience. So far as the dialectic can tell us, the number of Ones may be any number not less than two. There is no reason, that I can see, why the number should not be infinite, since the contradiction in the infinite series in Being Determinate did not depend on the infinity of the series but on the way in which its members were connected. This, of course, leaves the question undetermined whether, as we advance in the dialectic, we shall discover objections to an infinite number of differentiations.
Hegel says that the deduction of the Many Ones from the One must not be considered a Becoming “for Becoming is a transition from Being to Nothing; One, on the other hand only becomes One “ (G. L. i. 187). And he also warns us (G. L. i. 188) that the plurality is not to be regarded as Other-being, for each One is only externally related to all the other Ones-while in Other-being the whole nature of the Something,, was found in its Other.
The divisions of the One and the Many may perhaps be condemned as superfluous. If we start with the conception of a One determined by its relation to something else, it might be possible to conclude directly that this must be another One, and so reach the Many without the intervening stage of the One and the Void. At the worst, however, the subdivisions here only are superfluous, and not, as in Being for Self as Such, positively erroneous.
We now pass to the last division of Being for Self which is
43. (G. L. i. 190. Enc. 98) of which the first subdivision is
(G. L. i. 190.) This is a restatement of the category of Many Ones, which, as was said above, involves the Repulsion by each One of the rest of the Many. But what is the nature of this Many which the One repels? They are other Ones, and thus the One in Repulsion only relates itself to itself (G. L. i. 191). The Repulsion thereupon becomes Attraction, and the Many Ones come together in a single One.
The new category thus obtained is called by Hegel (G. L. i. 194)
44. It shows itself to be as untenable as its opposite. If .there were only one One there could be no Attraction. For what would there be to attract it, or to be attracted by it? And, again, that there should be only one One is impossible, because as has been shown already, One implies many Ones.
The truth is, m we now see, that Attraction is only possible on condition of Repulsion, and Repulsion is only possible on condition of Attraction. They must be united, and so we reach
45. (G. L. i. 195) which concludes the categories of Quality.
It seems to me that the subdivisions of Repulsion and Attraction, like those of Being for Self as Such, are positively erroneous. No doubt that which each One repels is other Ones, but this does not make them identical with it. Each One has Being for Self, each has its own nature, and the fact that they are all Ones does not destroy their plurality. If this is correct, we must reject the transition to the Antithesis, and therefore Hegel’s deduction of the Synthesis must be invalid.
The Relation of Repulsion and Attraction, which Hegel makes the Synthesis of the triad of Repulsion and Attraction, ought really, I think, to be the whole content of the undivided category of Repulsion and Attraction. And, if so, it may be very easily deduced. The previous category-the last in One and Many — was Repulsion. But Repulsion is impossible by itself. Two things cannot have merely negative relations to one ,another. If A is itself only on condition of not being B, then the existence of B is essential to A, and the relation is positive as well as negative. To take an example from a more concrete field, the relation of a combatant to his antagonist is negative. But it is also positive, for, if he had no one to fight, he could not be a combatant. Thus the relation of each One to the other One which it repels is positive as well as negative, and we have arrived at Hegel’s conclusion, though in a simpler and more valid manner.
We must, of course, here, as else where, be on our guard against confusing Hegel’s categories of Repulsion and Attraction with the far more concrete ideas of Physics after which he has named them. The Repulsion and Attraction of Physics may exemplify these categories, but they also contain empirical elements which Hegel has not deduced, and which he does not think that he has deduced.
46. The dialectic has now reached Quantity. Quantity involves that the units should be so far indifferent to one another, as to be capable of combination or separation without any change in their nature. This is rendered possible by the equipoise between Repulsion and Attraction which has now been established. The Ones are sufficiently under the influence of Attraction to be brought together in aggregates. They are sufficiently under the influence of Repulsion to retain their separate existence in their aggregates, so that the quantity of the aggregate varies according to the number of its units.
The dialectic thus regards it as an advance to pass from Quality to Quantity. This may seem to conflict with the ordinary view that quantitative determinations are more abstract and less profound than qualitative. But it must be remembered that this is said with reference to those qualitative relations which have transcended and absorbed Quantity, while Hegel, as we have seen, means by Quality only the simplest and most rudimentary form of what usually goes by the name. The Most abstract Quantity may be an advance on this, although such Quantity may be very inadequate as compared with more complex qualitative determinations.
1. By the Greater Logic I mean the work published in 1812-1816. Hegel himself calls this simply the Logic, but I use the adjective to distinguish it from the Logic which forms part of the Encyclopaedia. My references to the Greater Logic are to the pages of the complete edition of Hegel’s works, in which the Greater Logic occupies Vols. 3, 4 and 5 (quoted as G. L. i., G. L. ii., G. L. iii.) published in 1833-1834. My references to the Encyclopaedia are to Sections, and in quoting from it I have generally, though not always, availed myself of Professor Wallace’s valuable translation. When, in expounding” the Greater Logic, I give references both to the Greater Logic and to the Encyclopaedia, the latter merely indicates that it is in this Section of the Encyclopaedia that the Corresponding point is treated, and not that the treatment is the same as in the ,Greater Logic.
2. Cp. the editor’s Preface to the Logic of the Encyclopaedia in Vol. 6 of the Collected Works.
3. Studies in the Hegelian Dialectic, Chapters 1. to IV, but cp. below, Sections 10-13.
4. op. cit. Chapter VII.
5. I had not realised this distinction with sufficient clearness when I wrote my Studies in the Hegelian Dialectic, but what is said there is not inconsistent with my present view. Cp. Sections 17, 18, and 79 of that work.
6. It has lately been objected to Hegel’s treatment of Quantity that it does not include the conception of Series, which is of such great importance in mathematics. If the dialectic process can go from Being to the Absolute Idea without passing through the conception of Series, then the omission of that conception is no defect in the dialectic. But this truth is obscured by Hegel’s anxiety to bring all important scientific conceptions into the dialectic process.
7. The use of logical terms as names for the categories of Subjectivity is an example of the same practice, though in this case the conceptions are not borrowed from empirical knowledge. But, relatively to the dialectic process, they are concrete, for the logical processes, which give the names, have characteristics not to be found in the categories which they exemplify. Cp. Chapter VIII.
8. Such a perception would, of course, be held by Hegel to be more or less erroneous. Nothing really exists, according to his system, but Spirits. Bodies only appear to exist.
9. Studies in the Hegelian Dialectic, Sections 41-43.
10. Cp. Section 6. Also Studies in the Hegelian Dialectic, Sections 17, 18, 79.
11. This objection may be made clearer by a table.
I. Hegel’s division of Being Determinate.
II. Division proposed by Objection.
A. Being Determinate as Such.
(a) Being Determinate in General.
(without any sub-divisions).
12. Cp. Sections 101-102.
13. It is, so far as I know, impossible to find any one English phrase which will adequately render An Sich. I have followed Prof. Wallace’s example in using either By Itself or Implicitly, according to the context.
14. Hegel denies this, but I cannot see that he has shown any difference between them.
15. It might be said that any question of the number of Ones is improper, since Hegel does not introduce Number till he comes to Quantum. But it seems to me that what he introduces in Quantum is only the conception of a number of units less than the whole, and that therefore even before Quantum it is legitimate to enquire about the total number of Ones. (See below, Section 54.)