But, it may be said, no one really supposes that thinking, in uniting differences A and B, pronounces them to be identical. This is to misread the significance of the 'is' of the copula. 'A is B' (this rose is red) really means 'A has B' (this rose has red). And with this (as it may be said) we escape the easy reduction to self-contradiction. But do we? On the contrary this new formula but disguises, and in no way removes, the contradiction evident in the rejected formula. Let us suppose that what thought means to assert is that 'A has B.' Surely to assert that 'A has B' is just to assert that 'A is such-as-to-have-B'? We are asserting now the identity of A with 'such-as-to-have-B.' But since 'such-as-to-have-B' cannot be taken to be merely the same as A (for if it were, we should be back to the tautological 'A is A'), it must be something different, must be, let us say, C. Thus what we are doing in our new formula is to replace 'A is B' by 'A is C' - which seems no great advance. We are still saying that 'A is not-A.' Our new formula is still the formula of contradiction.
At a first glance, then, the uniting of differents appears to give us contradiction at once. Yet it is obvious that it must be capable of being understood in a way in which it does not give us contradiction. For to unite differences is the very life of thought. It must, then, be only some particular way of uniting differences which is contradictory, and there must also be some way to which thought can give its assent. There must be some way in which A and B may be united without 'asserting and annulling in the same act.' What is this way? How does thought endeavour to effect the union of differents? The answer to this question should throw into sharper outline the precise nature of that union of differents which is self-contradictory, at the same time as it indicates the conditions which must be observed by any union of differents which the intellect can accept as expressing the real.
How then (for this is what we are asking) are differences to be conceived so as to be compatible with their unity? There is, I think, but one answer possible - that found in the idea of 'system.' So long as the diversities in question are thought of as self-contained units, thought recoils, and must recoil, from the declaration of their identity. But it is otherwise if the differences are conceived not as self-contained units but as diverse expressions of a system which is a whole of mutually implicatory elements. If the differences are so conceived, what we are doing when we connect A and B in predication is not to assert that A as such is B as such, but that a system X which expresses itself as A docs also and thereby necessarily express itself as B. And there is no contradiction in this if X is indeed a system of mutually implicatory elements. For it is the very mark of such a system that it expresses itself as A only in so far as it is also B (C, D, etc.), in B only in so far as it is also A (C, D, etc.), and so on. In such a whole, diversity, although a fact, is not a fact opposed to identity. For there is nothing in the diversities which is external to the system, nothing in them, therefore, which is not derivable from the identity. Once admit into the diversities any element of being not internal to the system, and you find that, in sundering the differences from the identity, you have also destroyed the idea of a mutually implicatory system. If, however, we hold fast to the idea of such a system, we find that therein identity and diversity are but obverse sides of the same fact. The variety of the elements has no particle of being apart from their oneness. A and B are, though different, at the same time one, for their whole nature derives from the identity of which they are expressions.
It is under the controlling idea of such a system, accordingly, that the uniting of differences characteristic of thought must proceed throughout. We need make only the simplest 'ideal experiment' to discover that to unite differences per se, or simply, is abhorrent to thought. On the other hand, their union as connected expressions of a systematic identity seems not only abstractly intelligible, but also to represent plainly the goal of the intellect in actual practice. For it is clear enough that the constant aim of intellect is to mediate connections. It is not content with the conjunction of B with A. It endeavours to offer a ground for the conjunction. And this is just to say that thought endeavours to treat the differences of experience not as entities per se, but as members of a system which prescribes their mutual relations. Refusal to do this is tantamount to giving up the business of thinking.
Bringing together the points of our discussion so far, we can now suggest an answer to our question, 'How may differences be united for thought without self-contradiction?' The answer is, only in so far as the differences are conceived as mutually implicatory elements of a system. The whole effort of thought is directed to the establishment of such a system - or, not to prejudge an important issue, of such systems. And it is only in proportion to the perfection of the established system that the differences are with logical assurance pronounced to be one.