[b] Difference

Essence is mere Identity and reflection in itself only as it is self-relating negativity, and in that way self-repulsion. It contains therefore essentially the characteristic of Difference.

Other-being is here no longer qualitative, taking the shape of the character or limit. It is now in essence, in self-relating essence, and therefore the negation is at the same time a relation – is, in short, Distinction, Relativity, Mediation.

To ask 'How Identity comes to Difference' assumes that Identity as mere abstract Identity is something of itself, and Difference also something else equally independent. This supposition renders an answer to the question impossible. If Identity is viewed as diverse from Difference, all that we have in this way is but Difference; and hence we cannot demonstrate the advance to difference, because the person who asks for the How of the progress thereby implies that for him the starting-point is non-existent. The question then when put to the test has obviously no meaning, and its proposer may be met with the question what he means by Identity; whereupon we should soon see that he attaches no idea to it at all, and that Identity is for him an empty name. As we have seen, besides, Identity is undoubtedly a negative – not however an abstract empty Nought, but the negation of Being and its characteristics. Being so, Identity is at the same time self-relation, and, what is more, negative self-relation; in other words, it draws a distinction between it and itself.

Diversity § 117

Difference is first of all (1) immediate difference, i.e. Diversity or Variety. In Diversity the different things are each individually what they are, and unaffected by the relation in which they stand to each other. This relation is therefore external to them. In consequence of the various things being thus indifferent to the difference between them, it falls outside them into a third thing, the agent of Comparison. This external difference, as an identity of the objects related, is Likeness; as a non-identity of them, is Unlikeness.

The gap which understanding allows to divide these characteristics is so great that although comparison has one and the same substratum for likeness and unlikeness, which are explained to be different aspects and points of view in it, still likeness by itself is the first of the elements alone, viz., identity, and unlikeness by itself is difference.

Diversity has, like Identity, been transformed into a maxim: 'Everything is various or different': or 'There are no two things completely like each other'. Here Everything is put under a predicate, which is the reverse of the identity attributed to it in the first maxim: and therefore under a law contradicting the first. However, there is an explanation. As the diversity is supposed due only to external circumstances, anything taken per se is expected and understood always to be identical with itself, so that the second law need not interfere with the first. But, in that case, variety does not belong to the something or everything in question: it constitutes no intrinsic characteristic of the subject: and the second maxim on this showing does not admit of being stated at all. If, on the other hand, the something itself is, as the maxim says, diverse, it must be in virtue of its own proper character: but in this case the specific difference, and not variety as such, is what is intended. And this is the meaning of the maxim of Leibnitz.

When understanding sets itself to study Identity, it has already passed beyond it, and is looking at Difference in the shape of bare Variety. If we follow the so-called law of Identity, and say, The sea is the sea, The air is the air, The moon is the moon, these objects pass for having no bearing on one another. What we have before us therefore is not Identity, but Difference. We do not stop at this point, however, or regard things merely as different. We compare them one with another, and then discover the features of likeness and unlikeness. The work of the finite sciences lies to a great extent in the application of these categories, and the phrase 'scientific treatment' generally means no more than the method which has for its aim comparison of the objects under examination. This method has undoubtedly led to some important results; we may particularly mention the great advance of modern times in the provinces of comparative anatomy and comparative linguistics. But it is going too far to suppose that the comparative method can be employed with equal success in all branches of knowledge. Nor – and this must be emphasised – can mere comparison ever ultimately satisfy the requirements of science. Its results are indeed indispensable, but they are still labours only preliminary to truly intelligent cognition.

If it be the office of comparison to reduce existing differences to Identity, the science which most perfectly fulfils that end is mathematics. The reason of that is that quantitative difference is only the difference which is quite external. Thus, in geometry, a triangle and a quadrangle, figures qualitatively different, have this qualitative difference discounted by abstraction, and are equalised to one another in magnitude. It follows from what has been said formerly about mere Identity of understanding that, as has also been pointed out (s. 99), neither philosophy nor the empirical sciences need envy this superiority of Mathematics.

The story is told that when Leibnitz propounded the maxim of Variety, the cavaliers and ladies of the court, as they walked round the garden, made efforts to discover two leaves indistinguishable from each other, in order to confute the law stated by the philosopher. Their device was unquestionably a convenient method of dealing with metaphysics – one which has not ceased to be fashionable. All the same, as regards the principle of Leibnitz, difference must be understood to mean not an external and indifferent diversity merely, but difference essential. Hence the very nature of things implies that they must be different.

Likeness and Unlikeness § 118

Likeness is an identity only of those things which are not the same, not identical with each other: and Unlikeness is a relation of things alike. The two therefore do not fall on different aspects or points of view in the thing, without any mutual affinity, but one throws light into the other. Variety thus comes to be reflexive difference or difference (distinction) implicit and essential, determinate or specific difference.

Difference and identity in natural science

While things merely various show themselves unaffected by each other, likeness and unlikeness on the contrary are a pair of characteristics which are in completely reciprocal relation. This advance from simple variety to opposition appears in our common acts of thought when we allow that comparison has a meaning only upon the hypothesis of an existing difference, and that on the other hand we can distinguish only on the hypothesis of existing similarity. Hence, if the problem be the discovery of a difference, we attribute no great cleverness to the man who only distinguishes those objects, of which the difference is palpable, e.g. a pen and a camel: and similarly it implies no very advanced faculty of comparison when the objects compared, e.g. a beech and an oak, a temple and a church, are near akin. In the case of difference, in short, we like to see identity, and in the case of identity, we like to see difference. Within the range of empirical sciences, however, the one of these two categories is often allowed to put the other out of sight and mind.

Thus the scientific problem at one time is to reduce existing differences to identity; on another occasion, with equal one-sidedness, to discover new differences. We see this especially in physical science. There the problem consists, in the first place, in the continual search for new 'elements', new forces, new genera and species. Or, in another direction, it seeks to show that all bodies hitherto thought to be simple are compound: and modern physicists and chemists smile at the ancients, who were satisfied with four elements, and these not simple. Secondly, and on the other hand, mere identity is made the chief question. Thus electricity and chemical affinity are regarded as the same, and even the organic processes of digestion and assimilation are looked upon as a mere chemical operation. Modern philosophy has often been nicknamed the Philosophy of Identity. But, as was already remarked (s. 103, note) it is precisely philosophy, and in particular speculative logic, which lays bare the nothingness of the abstract, undifferentiated identity, known to understanding: though it also undoubtedly urges its disciples not to rest at mere diversity, but to ascertain the inner of all existence.

Difference implicit is essential difference, the Positive and the negative: and that is this way. The Positive is the identical self-relation in such a way as not to be the Negative, and the Negative is the different by itself so as not to be the Positive. Thus either has an existence of its own in proportion as it is not the other. The one is made visible in the other, and is only in so far as that other is. Essential difference is therefore Opposition; according to which the different is not confronted by any other but by its other. That is, either of these two (Positive and Negative) is stamped with a characteristic of its own only in its relation to the other: the one is only reflected into itself as it is reflected into the other. And so with the other. Either in this way is the other's own other.

Difference implicit or essential gives the maxim, Everything is essentially distinct; or, as it has also been expressed, Of two opposite predicates the one only can be assigned to anything, and there is no third possible. This maxim of Contrast or Opposition most expressly controverts the maxim of identity: the one says a thing should be only self-relation, the other says it must be an opposite, a relation to its other. The native unintelligence of abstraction betrays itself by setting in juxtaposition two contrary maxims, like these, as laws, without even so much as comparing them. The Maxim of Excluded Middle is the maxim of the definite understanding, which would fain avoid contradiction, but in so doing falls into it. A must be either +A or -A, it says. It virtually declares in these words a third A which is neither + nor -, and which at the same time is yet invested with + and - characters.

If + W mean 6 miles to the West, and -W mean 6 miles to the East, and if the + and - cancel each other, the 6 miles of way or space remain what they were with and without the contrast. Even the mere plus and minus of number or abstract direction have, if we like, zero, for their third: but it need not be denied that the empty contrast, which understanding institutes between plus and minus, is not without its value in such abstractions as number, direction, &c.

In the doctrine of contradictory concepts, the one notion is, say, blue (for in this doctrine even the sensuous generalised image of a colour is called a notion) and the other not-blue. This other then would not be an affirmative, say, yellow, but would merely be kept at the abstract negative. That the Negative in its own nature is quite as much Positive (see next §), is implied in saying that what is opposite to another is its other. The inanity of the opposition between what are called contradictory notions is fully exhibited in what we may call the grandiose formula of a general law, that Everything has the one and not the other of all predicates which are in such opposition. In this way, mind is either white or not-white, yellow or not-yellow, etc., ad infinitum.

It was forgotten that Identity and Opposition are themselves opposed, and the maxim of Opposition was taken even for that of Identity, in the shape of the principle of Contradiction. A notion, which possesses neither or both of two mutually contradictory marks, e.g. a quadrangular circle, is held to be logically false. Now though a multiangular circle and a rectilinear arc no less contradict this maxim, geometers never hesitate to treat the circle as a polygon with rectilineal sides. But anything like a circle (that is to say its mere character or nominal definition) is still no notion. In the notion of a circle, centre and circumference are equally essential; both marks belong to it; and yet centre and circumference are opposite and contradictory to each other.

The conception of Polarity, which is so dominant in Physics, contains by implication the more correct definition of Opposition. But physics for its theory of the laws of thought adheres to the ordinary logic; it might therefore well be horrified in case it should ever work out the conception of Polarity, and get at the thoughts which are implied in it.

(1) With the positive we return to identity, but in its higher truth as identical self-relation, and at the same time with the note that it is not the negative. The negative per se is the same as difference itself. The identical as such is primarily the yet uncharacterised: the positive on the other hand is what is self-identical, but with the mark of antithesis to an other. And the negative is difference as such, characterised as not identity. This is the difference of difference within its own self.

Positive and negative are supposed to express an absolute difference. The two however are at bottom the same: the name of either might be transferred to the other. Thus, for example, debts and assets are not two particular, self-subsisting species of property. What is negative to the debtor is positive to the creditor. A way to the east is also a way to the west. Positive and negative are therefore intrinsically conditioned by one another, and are only in relation to each other. The north pole of the magnet cannot be without the south pole, and vice versa. If we cut a magnet in two, we have not a north pole in one piece, and a south pole in the other. Similar, in electricity, the positive and the negative are not two diverse and independent fluids. In opposition, the different is not confronted by an other, but by its other.

Usually we regard different things as unaffected by each other. Thus we say: I am a human being, and around me are air, water, animals, and all sorts of things. Everything is thus put outside of every other. But the aim of philosophy is to banish indifference, and to ascertain the necessity of things. By that means the other is seen to stand over against its other. Thus, for example, inorganic nature is not to be considered merely something else than organic nature, but the necessary antithesis of it. Both are in essential relation to one another; and the one of the two is, only in so far as it excludes the other from it, and thus relates itself thereto. Nature in like manner is not without mind, nor mind without nature. An important step has been taken, when we cease in thinking to use phrases like: Of course something else is also possible. While we speak, we are still tainted with contingency: and all true thinking, we have already said, is a thinking of necessity.

In modern physical science the opposition, first observed to exist in magnetism as polarity, has come to be regarded as a universal law pervading the whole of nature. This would be a real scientific advance, if care were at the same time taken not to let mere variety revert without explanation, as a valid category, side by side with opposition. Thus at one time the colours are regarded as in polar opposition to one another, and called complementary colours: at another time they are looked at in their indifferent and merely quantitative difference of red, yellow, green, etc.

(2) Instead of speaking by the maxim of Excluded Middle (which is the maxim of abstract understanding) we should rather say: Everything is opposite. Neither in heaven nor in Earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either-or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself. The finitude of things will then lie in the want of correspondence between their immediate being, and what they essentially are. Thus, in inorganic nature, the acid is implicitly at the same time the base: in other words, its only being consists in its relation to its other. Hence also the acid is not something that persists quietly in the contrast: it is always in effort to realise what it potentially is.

Contradiction is the very moving principle of the world: and it is ridiculous to say that contradiction is unthinkable. The only thing correct in that statement is that contradiction is not the end of the matter, but cancels itself. But contradiction, when cancelled, does not leave abstract identity; for that is itself only one side of the contrariety. The proximate result of opposition (when realised as contradiction) is the Ground, which contains identity as well as difference superseded and deposited to elements in the completer notion.

Contrariety then has two forms. The Positive is the aforesaid various (different) which is understood to be independent, and yet at the same time not to be unaffected by its relation to its other. The Negative is to be, no less independently, negative self-relating, self-subsistent, and yet at the same time as Negative must on every point have this its self-relation, i.e. its Positive, only in the other. Both Positive and Negative are therefore explicit contradiction; both are potentially the same. Both are so actually also; since either is the abrogation of the other and of itself. Thus they fall to the Ground. Or as is plain, the essential difference, as a difference, is only the difference of it from itself, and thus contains the identical: so that to essential and actual difference there belongs itself as well as identity. As self-relating difference it is likewise virtually enunciated as the self-identical. And the opposite is in general that which includes the one and its other, itself and its opposite. The immanence of essence thus defined is the Ground.