John McTaggart A Commentary on Hegel’s Logic 1910
Measure |
Pure Quantity
74. Measure (Das Maass) is divided by Hegel in the following manner:
I. The Specific Quantity. (Die specifische Quantität.)
A. The Specific Quantum. (Das specifische Quantum.)
B. Specifying Measure. (Specifirendes Maass.)
(a) The Rule. (Die Regel.)
(b) The Specifying Measure. (Das specifirende Maass.)
(c) Relation of both Sides as Qualities. (Verhältniss beider Seiten als Qualitäten.)
C. Being for Self in Measure. (Das Fürsichsein im Maasse.)
II. Real Measure. (Das reale Maass.)
A. The Relation of Stable Measures. (Das Verhältniss selbststandigen Maasse.)
(a) Union of two Measures. (Verbindung zweier Maasse.)
(b) Measure as a Series of Measure Relations. (Das Maass als Reihe von MaassVerhältnissen.)
(c) Elective Affinity. (Wahlverwandtschaft.)
B. Nodal Line of Measure Relations. (Knotenlinie von MaassVerhältnissen.)
C. The Measureless. (Das Maasslose.)
III. The Becoming of Essence. (Das Werden des Wesens.)
A. The Absolute Indifference. (Die absolute In differenz.)
B. Indifference as Inverse Relation of its Factors. (Die Indifferenz als umgekehrtes Verhältniss ihrer Factoren.)
C. Transition to Essence. (Uebergang in das Wesen.)
It should be noticed that the title of Specifying Measure is borne both by I. B., and by its second subdivision, I. B. (b).
75. It seems to me that the whole of Hegel’s treatment of Measure is invalid. He has no right to the fundamental conception of Measure — the conception with which he begins, and which, in a modified form, persists till we reach Essence. If this is so, of course, all the categories of Measure must be abandoned, and the transition from Quantity to Essence, if it can be made at all, must be made in some other way. I should depart too largely from the object of a commentary if I attempted, in this book, so large a reconstruction. But it is necessary, before considering Hegel’s treatment in detail, to substantiate my general criticism of the validity of Measure.
The categories of Quantity ended with the result that every Quantitative difference must involve a Qualitative difference. Every Quantum, consequently, must have a common Quality. And since each of the Ones, of which every Quantum is composed, has its own separate and unique Quality, it follows that each One must have at least two Qualities — its unique Quality and another which it shares with other Ones which are united with it in a Quantum.
I maintained in the last chapter that Hegel’s treatment of Quantitative Ratio failed to justify this result, and also that it could be demonstrated another way. But whether Hegel did or not fail to demonstrate the result, I do not think it can be doubted that this is the result which he believed himself to have demonstrated, and that it is, therefore, the only basis which he was justified in taking for the categories of Measure.
His argument all through Quantitative Ratio was directed to show that the Quanta which were thus related had also a Qualitative aspect. His final words are “ The Quantum now m indifferent or external determination (so that it is just as much transcended as such, and is the Quality, and is that, through which anything is what it is) is the truth of the Quantum — to be Measure “ (G. L. i. 392). And again in the Encyclopaedia, “Measure is the Qualitative Quantum, in the first place as immediate — a Quantum to which a Determinate Being or a Quality is attached.” (Enc. 107).
76. This is the last conception of Quantity, and ought to be the first of Measure. At any rate Hegel has no right to go beyond it without justifying the transition by an argument. But directly he begins to deal with Specific Quantum — the first of the categories of Measure, he suddenly assumes that he has reached an entirely different conception. “The Quantum as Measure has ceased to be a limit which is no limit; it is now the determination of the nature of the fact[1] such that this nature is destroyed, if it is increased or diminished beyond this Quantum” (G. L. i. 403). The conception here is that which is involved in the changes, for example, of water into a solid, a liquid, and a gas, according to its varying temperature.
It is clear that this is quite a different conception from that of Qualities common to all the members of a Quantum. It is a more complicated conception. For it involves that each One to which it applies should have at least two Qualities which can be common to it with other Ones. Of these Qualities one — the temperature, in our example — varies in Quantity, but remains the Quality of all the Ones included under this Measure. The second Quality in each case is common to those of the Ones for which the first Quality falls within certain Quantitative limits. Thus all water whose temperature exceeds a certain limit has the second common Quality of being gaseous. Now the conception at the end of Quantitative Ratio only involved the existence, in each One, of one Quality common to it with other Ones.
And, in the second place, the relations of Quality and Quantity to one another. are quite different in the old conception and in the new conception. In the old conception Quantity came in as the number of Ones which had the same Quality. Here it comes in as a Quantity, not of Ones, but in each One. It is a Quantity of a Quality of the One.
The old conception, then at the end of Quantitative Ratio, is quite different from the new one with which Hegel starts in Specific Quantum. And the latter could only be legitimately reached from the former by a fresh step of the dialectic, the necessity of which would have to be demonstrated. But Hegel offers no demonstration of the transition, and, indeed, fails to see that there is any difference between the conceptions. He treats them as if they were identical, and as if he was only using the final result of one section as the starting point of the next — which is what should happen according to the dialectic method, but which is not what has happened here.
77. How he fell into so serious a mistake is a difficult question. The new conception, it is true, resembles the old in so far that they each involve both Quantity and Quality, and that in the new conception also Quantity is limited by Quality[2], though the Quantity limited is not, as the dialectic requires here, a Quantum of Ones. Again, the new conception is compatible with the old, though it is not identical with it or deduced from it. If the Ones A, B, C, have the common Quality x, and the Ones D, E, F, the common Quality y, the old conception would apply to them. And it would be possible that the one group were x because they had a quality z with a certain intensity, and that the other group were y because they had the Quality z with a different intensity. In this case the new conception would apply also.
These circumstances might have led Hegel to confuse the two conceptions. Or, again, it is possible that Hegel started with a presupposition that Measure (In the sense of the new conception) was probably the Synthesis of Quality and Quantity. This would be natural enough, since it does involve them both, and involves them in a form which is frequently present to us in empirical experiences. If he started with such a presupposition he might more easily fail to see that fie had not deduced his new conception of Measure from the previous categories.
Passing to the consideration of the categories of Measure in detail, we have first
78. (G. L. i. 403.) This category is naturally the expression of the new conception of Measure in its simplest form. The Ones have each two Qualities such that if the first varies in Quantity beyond certain limits, the second Quality is changed for another. (The first Quality might be called the permanent Quality, the second and its successors the varying Qualities.)
This category is pronounced inadequate by Hegel because the union of Quality and Quantity is only apparent, and it does not, therefore, really remove the difficulty which called it into being. So long as the Quantitative change keeps within the limits of the Quality — as when fluid water becomes colder without freezing, or hotter without boiling, we get the Quantity changing while the Quality remains the same. The two sides thus remain isolated, and there is nothing which cheeks the inherent instability of Quantity. Now the whole object of our transition to Measure was just to cheek this instability.
At intervals, no doubt, the Quantitative change is accompanied by a Qualitative change. Water passes from a liquid state into the form of ice or steam. But here, also, the changes of Quantity and Quality are not really connected For a Qualitative change is always instantaneous, in the strictest sense of the word.
This may at first sight appear to be inconsistent with our experience. But when we say that a Qualitative change can be gradual, we mean one of two things. We may mean that the different parts of a whole undergo the change successively, as when a kettle full of water is gradually converted into steam. This, of course, is compatible with the change being instantaneous for each part.
Or we may mean that the change from the quality A to the quality B is not instantaneous, because there are intermediate qualitative changes. Ice does not pass instantaneously into steam, for it must first become water. And a process which appeared to go directly from A to B may be found, on closer investigation, to go through the forms X, Y, and Z, before it reaches B.
But however many stages may be intercalated before B, it is certain that, when the quality A changes, it must do so instantaneously. For if A changes, it must change into something which, whatever its positive nature, can be correctly described as not-A. And, by the law of Excluded Middle, the quality must either be A and riot not-A (when the change will not have begun) or else not-A and not A (when the change will be completed). The change, therefore, is instantaneous (G. L. i. 405. Enc. 108).
Quantity, then, can change without Quality changing, and all changes of Quality take place while the Quantitative change is infinitely small. The two terms are thus, in Hegel’s opinion, not really united. It is this defect, he tells us, which is at the root of the old difficulty as to the point at which a head, whose hairs are being pulled out one by one, becomes bald. To say that the absence of one hair can make a head bald, which was not bald before, seems absurd. Yet, if one hair never made the difference, we come to the equally absurd conclusion that a head with no hair on it could not be called bald (G. L. i. 406. Enc. 108).
79. Hegel’s conclusion is that the Measure now becomes double. We have (1) the actually existing Quantity of the permanent Quality, (2) the other Quantity of the permanent Quality which, if reached, would involve the change of one varying Quality into another. The second Quantity forms the limit within which the first can vary, while it is itself fixed. This limitation Hegel expresses by saying that it specifies the first Quantity, and so we reach
(G. L. i. 407.) This transition seems to me erroneous. We have not really got a new category at all. Two Quantities were involved in the idea of Measure from the beginning — the Quantity which exists, and the other which marks the point of transition into a fresh Quality. If a basin of water is fluid, rather than gaseous, because its temperature is 60°, this involves the conception of a further temperature at which it would become gaseous. Thus Specifying Measure takes us no further than Specific Quantum. It is neither a development of the difficulty involved in the transition from Specific Quantum, nor a solution of that difficulty, and it has no right to be the next category to it. Hegel calls its first subdivision
(G. L. i. 408.) This, he tells us, is identical with the general idea of Specifying Measure. The defect of the category is that the Rule — that is, the limiting Quantity, is merely arbitrary. And as this is inconsistent with the nature of Measure, which is not merely arbitrary, the category is inadequate.
But why are we to suppose that the Quantity taken for the Rule is merely arbitrary? Hegel’s example is a linear foot, and this, no doubt, is arbitrary. We might just as well measure length by ells or by metres as by feet. But the example is not fair. Measures of length are used for the measurement of space. And the conception of space makes abstraction of all Qualitative differences. We measure the Quantity of space, and the Quantity only, regardless of the Quality of the matter which fills that space. Any Rule here must be purely arbitrary, for it concerns Quantity only, and all limits of Quantity, taken by itself, are purely arbitrary. But the dialectic has now passed beyond mere Quantity to Measure, where a change of Quantity brings about a change of Quality. And here the Rule is no longer arbitrary. The Rules of the temperature of liquid water are 32° and 212° Fahrenheit, and these are not arbitrary, but grounded in the nature of the subject-matter. (It is arbitrary, no doubt, to call them 32° and 212°, rather than 0° and 100°, or any other numbers. But it is not arbitrary that the limits to the heat of liquid water are these temperatures and not others.)
80. Hegel endeavours to remove the defect of this category by passing on to
(in the narrower sense) (G. L. i. 408). Here the something (Etwas) which is the Measure receives an alteration of the amount of its Quality from outside. It reacts against this, and receives it in a way of its own, so that the resulting Quantum of the Quality, as reproduced in the Something, is not the same Quantum as in the external source of the alteration, but is increased or diminished through the effect of a Qualitative difference in the Something.
The introduction of such a category at this point seems very extraordinary, but Hegel’s language places it, I think, beyond doubt. The description of the category will bear no other meaning, and the nature of the other categories, which immediately follow, supports the same interpretation. And his example is also quite clear. Material objects he tells us (G. L. i. 410) have specific temperatures, which cause the changes of temperature which they receive from outside to be different in them from what they are in the medium from which they are received.
81. This transition appears to me to be quite illegitimate, since it introduces an entirely new conception of Measure without deducing it from the conception previously established.
Hegel does not even say that it is changed. But the change is very great. We. started with a conception of Measure, according to which the continuous change of Quantity involved at certain points a sudden change of Quality. There was only one Quantitative series involved, and there was a Qualitative series. Here, on the other hand, we suddenly find ourselves with a new conception. We have now two Quantities in different Somethings (in the example, the temperature of the medium, and the temperature of the object). The first of these determines the other. We have also two Qualities (in the example, heat, and that Quality in the object which causes its heat to be more or less than that of the medium. But there is no Qualitative series, for neither Quality is conceived as necessarily changing into another Quality.
This category is not in any sense implied in the previous category of Rule. It simply ignores it. The difficulty in Rule, according to Hegel, was to find for the Quantitative changes of any particular Quality, a limit which should not be arbitrary. But in t c new category the Qualities never change into other Qualities at all, and even the imperfect cheek on the Quantitative changes has been swept away.
Again, in this category we have two objects connected with each other — the original object and a second one. (In the example which Hegel ‘gives, the first object is that with a specific temperature, the second object is the medium.) Before this, the Measure of each object was stated without reference to any other object. The introduction of this new element ought to be justified as an inevitable consequence of the preceding category. But, so far as, I can see, Hegel makes no attempt whatever to do this.
Moreover this category, as stated by Hegel, includes the idea of This is not the case with previous categories.
In Quantitative Ratio the Quantities implied one another, but did not cause one another. But here we are told (G. L. i. 408) that the Something experiences an “external alteration” of the amount of its Quality. This is nothing but Causality. It may be doubted, indeed, whether it does not involve more than Hegel’s category of Causality, but it certainly could not be introduced without including that category, and if the dialectic is right in introducing Cause for the first time towards the end of Essence, it cannot be right here.
If what I have said is correct, the dialectic at this point is vitiated by two errors — there was no adequate round for condemning Rule as inadequate, and there has been an unjustified change in the meaning of Measure[3]. I shall now only expound Hegel’s arguments, without further criticism, until we reach the Nodal Series of Measure-Relations, at which point, as will be seen, the effects of the second error are eliminated.
82. So far only one of the two objects has been considered as having a Quality which affects the Quantity of its other Quality. In Hegel’s example, the object which receives heat from the medium is considered as having its specific temperature, while no specific temperature is attributed to the medium. But now Hegel points out that each object must have a similar Quality. In each the Quantity of the quantified Quality will be dependent on the nature of the object (G. L. i. 411). The medium, for example, is either air or something else, which must have a specific nature of its own. We thus reach
(G. L. i. 411.) Here the two sides have each (a) a Quality, which it possesses in a certain (b) Quantity. And each of them has (c) a second Quality, which determines the magnitude of b in it. Xow as the two b’s are each a Quantity, their relation to each other can be expressed by a third Quantity (G. L. i. 412). And, as the nature of the two c’s is just to determine the different amounts of the two b’s, this third Quantity expresses also the relation of the two c’s (G. L. i. 417, 418).
83. This third Quantity is the Measure of the two sides. It is the Quantity which expresses their relation. In Specifying Measure (in the narrower sense) one of the two sides was the Measure of the other, while in. Relation of the two Sides as Qualities each was the other’s Measure. Now that they are united into a whole which has a Measure, we pass out of Specifying Measure (in the wider sense) and reach the third division of Specific Quantity, which Hegel calls
(G. L. i. 417.) The name is apparently due to the fact that we have passed from finding the Measure of anything, outside it to Ending it within itself. For the two Somethings which have may be considered, Hegel tells us the common Measure (G. L. i. 421) as a single Something, which may also be called a Thing. (I shall call them Things, what follows, to distinguish them from their constituent Somethings. But of course Hegel does not mean that we have yet reached the conception of a Thing, properly so called, which does not come till half-way through Essence.)
84. This Measure, he says, must be considered as realised Measure, since both its sides are Measures (G. L. i. 430). Thus we reach the second of the three divisions of Measure
(G. L. i. 421.) This Real Measure relates itself to another Real Measure (G. L. i. 422). This gives us
(G. L. i. 423.) Why it should relate itself to another Real Measure, Hegel does not, so far as I can see, explain.
It should be noted that we have by this time relations of three degrees of complexity. (1) In each Something we have relations of Quality and Quantity. (2) The Somethings are related to one another by a Common Real Measure, which unites the Somethings into a Thing. (3) The Real Measures, or Things, we have just been told, are in relation to one another.
85. This last relation will be, in the first place, immediate (though between terms which are no longer immediate, but stable), thus we get
(G. L. i. 423.) Hegel’s treatment of this is very extraordinary. He starts with considering the union as a relation between the two Things. And this is all that he seems justified in deducing from the previous position — if he is justified in deducing even so much. But suddenly (G. L. i. 425) he tells us that the two Things “in Beziehung stehen und in Verbindung treten.” And from this point he speaks of the actual chemical combination of chemical elements.
Now the fact of chemical combination, which Hegel brings in here, involves, according to his own subsequent statement, the category of Chemism, which occurs in the middle of the categories of the Notion. If Hegel is right in postponing the category of Chemism till the Notion, he cannot be right in introducing here a category under which he professes to explain chemical combination.
And this is not all. Hegel does not merely introduce into this. category the pure idea which is implied in, and specially characteristic of, the facts of chemistry. He also introduces empirical chemical details, which could not form part of the dialectic process of pure thought at any stage, and he introduces them as part of the argument.
86. We read that, while in such combinations the weight of the whole is equal to the weights of the parts (G. L. i. 425), the volume of the whole is not equal to the volume of the parts, but is generally less (G. L. i. 426). This is stated, not illustration only, which might have been legitimate, but as the ground of the transition to the next category. For he says (G. L. i. 426) that the Measure itself of the new combination is thus shown to be variable, and that therefore even so-called Stable Measures have shown themselves not to be stable. We must therefore try to find the determination of the combination in other Measure relations. And this is the way in which he reaches
(G. L. i. 426.) Here each of the Things regains the stability it has lost. It regains it, because it can combine not only with one other, but with any one of many others. Its capability of each of the changes which it could undergo in combining with any of these others is a permanent characteristic of its nature. This gives it stability. When M changes as it combines with _S’, it keeps a permanent nature throughout, for it remains that Thing which would undergo another definite change in combining with 0, another with P, and so on. It has a nature beyond and unaffected by that change which it is actually undergoing, and so remains the same.
87. But in its union with each of the other Things with which it can unite, it does not merge its unity in something which remains unaffected. The other side is also altered, and. they combine to form something new. The union is thus an “exclusive “ unity (ausschliessende Einheit) (G. L. i. 429, 430). By this Hegel appears to mean that neither side is merely passive, awaiting any other Thing that may come to it, but that both sides express their nature in the union, since neither of them would suffer precisely that change, except in combining with the other. Thus we get
(G. L. i. 430.) In connexion with this Hegel introduces a digression on some chemical theories of his time. It does not, however, profess to be part of the main argument.
88. We now come to a very remarkable transition. Each Thing which is formed by Elective Affinity has in it an element of Separability (Trennbarkeit) due to the fact that each of its constituents can enter into other relations (G. L. i. 446). It may be convenient to distinguish these constituents as Elementary Things, and their combinations as Compound Things. It must be remembered that, as was pointed out above (Section 83), even the Elementary Things are compounded of Somethings.
From this we proceed to a passage which I do not venture to paraphrase. “ The exclusive Measure according to this more exact determination is external to itself in its Being for Self. It repels itself from itself, and posits itself both as a merely quantitative other, and also as another relation, such that it is also another Measure; and is determined as a unity which specifies itself, and which produces relations of Measure in itself. These relations are distinguished from the kind of affinities mentioned above, in which one stable object relates itself to stable objects of a different quality, and to a series of such objects. These relations occur in one and the same Substratum, inside the same moments of neutrality The Measure determines itself as repelling itself to other relations which are only quantitatively different, but which form at the same time Affinities and Measures, alternating with such as remain only quantitative differences. They form in this way a Nodal Line of Measures on a scale of more and less” (G. L. i. 446, 447). Thus we get
(G. L. i. 445.) With regard to this category we have to remark three things. In the first place, we have suddenly returned to that conception of Measure which the dialectic suddenly abandoned at Specifying Measure (in the narrower sense, I. B, (b), not I. B). We had started with the conception of Measure as the relation between a Quantity and a Quality, which Quality was such that, when the Quantity altered beyond certain limits, it changed into another Quality. At that point Hegel substituted the entirely different conception of a relation between two Somethings, each with one Quantity and at least two Qualities. And now, when the Somethings have developed into a Thing formed by the union of Somethings, we find in this Thing the old conception of Measure. The Elementary Thing, as its Quantity changes, dissolves the connexion which made it part of one Compound Thing, and forms another connexion, which makes it part of another Compound Thing. And this is a Qualitative change in the Elementary Thing. Once more the Measure of the object is in itself.
That this is the right interpretation seems to follow from the passage quoted above, and also from the next sentences (G. L. i. 447). “Such a Being for Self, since it is at the same time essentially a relation of Quanta, is open to externality and the alteration of Quantum. It has an extent within which it remains indifferent (gleichgültig) to this alteration, and within which it does not alter its Quality. But a point comes in this alteration of the Quantitative, at which the Quality is altered, and the Quantum shows itself as specifying, so that the altered quantitative relation is transformed into a new Quality, a new Something.”
The second point to be noticed is that, in spite of the categories which have intervened, we return to the old conception in a form no higher than that in which we left It, so that, even if the intervening categories had been legitimately deduced, we should have gained nothing by them. It is true that the substratum which undergoes the changes of Quantity and Quality is now a more complex unit,, but this does not make the problem of the relation of the changes a more complex problem, nor does it advance it nearer to a solution. When we consider the treatment in the Encyclopaedia, we shall see that the category of the Nodal Line can be reached directly from the category of Specific Quantum.
89. The third point to be noticed is that the transition from the category of Elective Affinity to that of Nodal Line. is illegitimate. Let us grant that the Elementary Things which are combined by Elective Affinity into Compound Things retain, within these latter, a certain separability, due to the fact that they could combine otherwise than as they do. But what follows from this?
All that can properly be deduced is that the Elements in a Compound can separate, and then combine again, either with one another, in which case the same Compound would be formed again, or with other Elements, thus forming fresh Compounds. But Hegel asserts that the dissolution of the Compound would only take place after there had been certain Quantitative changes in its Elements — changes which did not dissolve the Compound till they had exceeded certain limits. This does not seem justifiable. Elective Affinity caused the Elements to combine in certain proportions. So long as these proportions were observed, the Combinations would not be broken up. But if the proportionate Quantities were altered in the least, it would follow from Hegel’s previous account that the Compound might be instantly destroyed. There is nothing to permit him to treat the nature of the Compound as being variable within limits.
90. Thus both the departure, in Specifying Measure, from the previous conception of Measure, and the return to it at this point are illegitimate. Hegel’s next category is
(G. L. i. 452.) When the Quantitative change has gone beyond its limit, and a Qualitative change has come about, the new Quality is at first to be considered as the Measureless. The Measure of the original Quality is that it cannot go beyond certain Quantitative bounds. Of the new Quality we only know, so far, that it has gone beyond these bounds. It is therefore, so far, the Measureless.
The category, however, contains more than this, so that the name is not very appropriate. The new Quality, Hegel continues, is itself a Measure. It has its Quantitative bounds which it cannot pass. When the Quantity exceeds these fresh bounds, yet a fresh Measureless is created. And so we get an Infinite Series. It is this Infinite Series which seems to be the most characteristic feature of the category.
In this way, we are told, “the first immediate connexion between Quality and Quantity, in which Measure in general consists, is turned back on itself, and is itself posited (G. L. i. 453). The Quantity changes till it brings about a new Quality. The Quality in its turn has a new Quantity of its own, which varies till it once more changes into Quality, and so on indefinitely.
Quantities and Qualities are, then, neither of them stable. Yet something must be stable, for we could not say that Quality A had changed into Quality B, unless something was identical in A and B. Otherwise there would be no reason to suppose that it was A, rather than anything else, which had changed into B.
What is constant then? Hegel answers that it is the substratum. The conception of substratum, he reminds us, has already been introduced. “What is before us is one and the same fact (Sache), which is posited as ground of its difference, and as persisting. This separation of Being from its determination has already begun in Quantum in general; Something has magnitude, in so far as it is indifferent to its determination as Being (seiende Bestimmtheit)” (G. L. i. 453).
It should be noticed that Hegel does not say that this Infinite Series is contradictory. As I said above (Section 33) he never does assert that Infinite Series as such are contradictory, but only that some of them are. His position here is that the Infinite Series would be impossible unless there were something stable underlying it, and that therefore we must conclude that something stable does underlie it.
It must also be noticed that it would have been equally necessary that something stable should underlie the series, if it were not infinite but finite. Any series of Qualitative changes would require the substratum, whatever the length of the series. The transition, therefore, would not be invalidated, if it could be shown that the series here was not, as Hegel holds it to be, infinite.
91. The substratum is stable, then, and the lesson of the ceaseless oscillation — first the change of the Quantity of a Quality, then the change of the Quality, and so on without end — is that the substratum is indifferent to its determinations. Since they change, while it remains unchanged, they can have no effect on it whatever. Thus we reach (G. L. i. 456)
92. But, after all, the Indifference cannot be absolute. That which is indifferent is a substratum. It could not be a substratum, unless there was the series of changes to which it is a substratum, and therefore they have an influence on it. ‘ It is just the externality. and its disappearance which determines the unity of Being to be indifferent and is thus within that unity of Being, which therefore ceases to be merely substratum” (G. L. i. 456). Thus we get
(G. L. i. 457), the characteristic of which is that the Quantities of the different Qualities vary inversely, so that the sum of them is always the same.
This category seems indefensible. The Quantities, we are told, are “variable, indifferent, greater or smaller against one another” (G. L. i. 457). And the substratum is the sum of them and a “fixed Measure” (same page). The increase or decrease of one side must be simultaneous, therefore, with the increase or decrease of the other. But this is impossible, for the sides are the Qualities of the substratum, and the different Qualities of the substratum are alternative and not compatible.
The increase or decrease of Quantity produces one Quality and destroys another. The whole point of that earlier conception of Measure, to which we returned in the category of the Nodal Line, was that a reality had one Quality or another, according to the Quantity. If the Qualities of the series became compatible, we should not only have removed the Absolute Indifference in which Hegel finds a contradiction, but we should have removed all Indifference altogether. For the Indifference arose solely from the permanence of the substratum among the variations of the Quality series, and would cease if the variations were abandoned.
Now it is clear from the title of this category, and from the treatment of the early categories of Essence, that the Indifference of the substratum is not considered to be yet removed.
93. After these considerations Hegel’s transition from this category need not, perhaps, be examined in detail. He argues that the Qualities are not independent of each other, since that would make the Indifference an empty name. Each of them has, therefore, only reality in its quantitative relation to the other, and each, therefore, can only reach as far as the other (G. L. i. 460). It is impossible for either to gain at the expense of the other, and so the Inverse Relation breaks down, and we are driven back to Indifference in the form of a “ contradiction which transcends itself” (G. L. i. 461). In other words, the external is not absolutely unreal, but is not real in its own right. It is the appearance of a reality which is not itself. So we reach (after a digression on Centripetal and Centrifugal Force) the last category of Measure
(G. L. i. 466.) In reaching this category we have already reached the fundamental characteristic of Essence. This consists in the assertion of the duplicity of reality — its possession of an external and an internal nature, capable of distinction from each other, but riot indifferent to each other. And this is the conception which we have now reached.
This conception is rendered necessary by Qualitative change.
All change requires some distinction in the nature of that which changes. For if the nature of reality were all of one piece, then each thine, must be completely the same as something else, or completely different from it. Thus, under the categories of Quality, no change is possible. With the categories of Quantity, it is possible to have Quantitative change. For there each One has its own Quality, and is also part of a Quantum, and so the same One can be part of Quanta of varying sizes, and the Quanta can change. A Quantum, for example, can change into a larger Quantum, and the necessary identity in difference is found in the fact that certain Ones form part of both Quanta.
But now that we have Qualitative change, the duplicity of nature must not be merely between Quality and Quantity, but must be found within Quality. If that which has Quality A is so to change as to have Quality B, there must be a unity in the thing which persists through this change. At the present stage of the dialectic this can only be a permanent Quality X, and so we have the two, strata of Essence.
94. The treatment in the Encyclopaedia is very different from that in the Greater Logic. In the first place, it is much simpler. In the Greater Logic there were thirteen undivided categories. In the Encyclopaedia Hegel gives no divisions at all. This gives indeed an appearance of greater simplicity than really exists, for by observing the course of the argument we can see that it really does form a triad, the three categories of which may be called Specific Quantum, The Measureless, and The Becoming of Essence. Still, there are only three divisions instead of thirteen. The difference is accounted for by the fact that Becoming of Essence forms only one undivided category, instead of three, as in the Greater Logic, and by the omission of the seven categories, from Rule to the Nodal Line inclusive, which only brine, the dialectic back to the point of Specific Quantum again. Also the Encyclopaedia treats under the head of the Measureless what is divided in the Greater Logic into the Nodal Line and the Measureless.
The Encyclopaedia then starts (Enc. 107) with the simple conception of Measure, as it is found in the Greater Logic, to which we may give the name of Specific Quantum, as in the earlier work. Hegel then discusses, as in the Greater Logic, the contrast between the continuous change of Quantity and the instantaneous changes of Quality, and the sophisms which are based on it (Enc. 108)[5]. Then comes the transition to the Measureless, which here, as in the Greater Logic, he seems to connect in some especial manner with the contrast just mentioned between the methods of change in Quantity and Quality.
How it should be connected with this contrast is not very plain, nor does this seem necessary for the transition. The category of Specific Quantum gives us the result that, if anything has the Quality A within certain Quantitative limits, it will also have the Quality M. This inevitably raises the question of the result which will follow if the Quantity of A passes the limits within which it determines the presence of M. “Quantity ... is not only capable of alteration, i.e. of increase or diminution: it is naturally and necessarily a tendency to exceed itself” (Enc. 109). And this is sufficient to take us over to the next category.
In the first place, all that is said is that the object will no longer have the Quality M. It is therefore the Measureless — since Measure consisted in the relation between the permanent Quality A and the variable Quality. But M will be replaced by a fresh Quality N — solidity, e.g., by fluidity, when heat has passed the melting-point. From this Hegel proceeds to the Infinite Series in the same way as in the Greater Logic (Enc. 109).
The transition from the Infinite Series to Becoming of Essence (Enc. 111) is the same as in the Greater Logic, except that the intermediate forms of Absolute Indifference and Indifference as Inverse Relation are omitted, and the transition made direct to the fully developed conception which, in the Greater Logic, forms the third subdivision.
The treatment in the Encyclopaedia is superior to the other in avoiding the unjustified and useless loop which stretches from Rule to Elective Affinity in the Greater Logic. The absence of Indifference as Inverse Relation is also an improvement. On the other hand, the transition from the Infinite Series in the category of the Measureless direct to Essence seems somewhat abrupt, and inferior to the path taken by the Greater Logic through Absolute Indifference.
But the vital defect of the Greater Logic is not removed in the Encyclopaedia. This is the substitution for the conception of Measure, reached at the end of Quantity, of another conception of Measure — undeduced and unjustified. This invalidates the chain of reasoning in both books, and if the broken links are to be replaced it must be by something which is not to be found in Hegel’s own work.
1. The original is “Die Bestimmung der Sache.” On the whole, I think “nature of the fact” fairly represents Sache in this passage.
2. If, e.g., certain water has the Quality of being fluid, the Quantity of its temperature is fixed by that fact.
3. The error in the transition from Specific Quantum to Rule cannot be counted as a third, since the only error there is in supposing that a transition has taken place at all.
4. Since the Measureless and Absolute Indifference are undivided categories, and are respectively Synthesis and new Thesis, the second would naturally be only a repetition of the first, which is not the case. This seems to indicate that the category of the Measureless was really considered by Hegel as subdivided — the Infinite Series forming a separate stage from the Measureless in the stricter sense.
5. In the Encyclopaedia Hegel seems to use Rule to indicate a Measure in which the Quantity does not pass the limits which involve a change of Quality (Enc. 108). This is different from the use of Rule in the Greater Logic (cp. above, Section 79).