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 that 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, &c, _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 multangular circle and a rectilineal 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.