The true formula of the judgment then is not 'A is A,' nor 'A is B,' nor 'A has B,' nor anything of a cognate character which treats the terms as simple entities. The formula is A(x) is B, or, perhaps more suggestively, Xa is Xb - X being conceived as a mutually implicatory system such that in expressing itself as A it necessarily expresses itself as B. 'A as such is B' gives us, on the contrary, the very essence of contradiction. In asserting differences to be one per se, it merely annuls what it posits. They can be 'one' only as differentiations of a system which prescribes their mutual implication. This, if I am right, is what Bradley means when he urges that to bring differences together in 'bare conjunction' is the very type of contradiction.1 Brought together thus they collide, and must collide. To avoid collision, they must be brought together at a point in which 'internal diversity' is posited; brought together, that is, within a system X. Conjoined simply, at a point which has no internal diversity, the differences are denied the sole condition which can save their identification from being a flat self-contradiction.
Let us now notice the kind of objection which will be felt against what I have said from the side of 'common sense.' A brief discussion of it will, I think, assist in elucidating further the particular point I am anxious to make.
'What you are saying,' it may be protested, 'implies that a self-contradictory character attaches to by far the greater part of the affirmations made in ordinary life. Ordinary cognitive experience consists of numberless assertions which connect greenness with grass, a cylindrical shape with this pipe, surliness with such and such a person, and so on, and it is the exception rather than the rule that in cases of the sort we think of the connection as "mediated." As a rule it never occurs to us when we attribute a character to an object that there is any difficulty in the immediate connecting of the differents, or any necessity for this internal diversity in the subject which you claim to be logically demanded. Yet we certainly are not aware of uttering anything that is abhorrent to the nature of the intellect. And if ordinary experience suggests so strongly that the intellect does not shrink from a "bare conjunction," does this not throw some doubt upon the result of your logical analysis?'
1 Appearance and Reality (2nd ed.), p. 566.
The answer to this is, I think, not very difficult if it is borne in mind that on the whole man thinks to live, not lives to think. A purely intellectual interest is rare, and is certainly not present in the normal commerce of man with his world. Hence it is seldom indeed that the intellect 'functions pure.' The rational interest is controlled by the practical, and it is enough for us if the connections we affirm are such as to 'work' satisfactorily for the ordinary purposes of our contacts with our natural and social environment. Such satisfactory 'working' is notoriously compatible with gross intellectual falsity.1 It is, with the ordinary man at ordinary times, only when 'Situation' gives the lie to 'expectation,' when, accordingly, established beliefs do not 'work,' that misgivings are aroused and, possibly, an intellectual interest stimulated. We may say, in short, that in respect of the connections asserted in everyday experience, mere pragmatical considerations play a very large part indeed, and that therefore no just inferences can be drawn from the nature of these assertions as to what the intellect does or does not demand.2 And we must go on to insist upon this. If, as we must in philosophy, we abandon the standard of practical utility and examine these everyday assertions from the point of view of rational tenability - preferably through the medium of some simple symbolism which will ensure that our judgment be not warped by the illusions and prejudices instilled by habitual experience - there can be but one verdict on the matter. So long as mediation, not necessarily explicit but at least implicit, is lacking, these affirmations are reducible to the form 'A as such is not-A,' and their self-contradiction is starkly manifest.
1 E.g. the belief that the sun moves round the earth works perfectly satisfactorily for all the ordinary purposes of life.
2 At the same time I should agree that common-sense's case for the everyday assertion of unmediated connections, as put on the previous page, involves an overstatement. There are traces of an implicit demand for a rationale in, for example, the universal insistence upon 'relevance' of predicate to subject (vide Bosanquet, Implication and Linear Inference, p. 87 et seq.). But my present point is that the plain man's pre-occupation with practice ensures that the demand for a rationale is not 'pushed' as it must be where an intellectual interest dominates.
Furthermore if, desiring to observe intellectual process in its integrity, we turn from that sphere in which intellect is a relatively unpredominant feature - the sphere of everyday life - to the experiences which are professedly theoretical in character, such as philosophy and scientific inquiry, it seems clear enough that here the intellect does decline to accept a bare or unmediated conjunction. Whether such a conjunction does or does not happen to accord with a strongly entrenched belief is, for science, immaterial. It is of the nature of philosophy and the sciences to look upon the unmediated conjunction, however widely subscribed to, as an implicit problem. These disciplines differ from 'common sense' perhaps most radically just in their habitual disrespect for the merely de facto connection. They insist upon the thoroughgoing mediation of whatever lays claim to be believed - science, it is true, only within the ambit of its presuppositions, but philosophy absolutely.
And that is why, in the last resort, it is commonly regarded as the failure of any metaphysical system that it should be forced to accept a dualism. For a metaphysical dualism is a dualism of two ultimate principles, i.e. it consists in the presentation to the intellect of differences which not only do not, but in virtue of their professed ultimacy cannot, find any ground of union in a system beyond themselves. This is the root cause of the mind's dissatisfaction with all dualism. We are offered, perhaps, God on the one hand, matter on the other, neither being reducible to the other nor resoluble into any higher unity. And we are asked to accept the interaction of these two 'ultimates' as the final truth about things. But so long as these concepts are really 'two' for thought, we are aware of failure. We realise that our 'system' bids us to predicate of a subject 'God' something that we do not see to issue from His nature, something that is genuinely different from God, while at the same time we are forbidden to look to any superior principle beyond the differences which might explain and justify the connection. From such de facto connections the intellect recoils. It is the very type of the irrational, and the history of philosophy shows that sooner or later the irrationality of it is appreciated. It is, of course, open to the critic to urge that unless, even in the end, there remain real differences for thought, we could not judge or predicate at all. This I believe to be true, and to be of the utmost importance. But what it points to, I shall later argue, is not some irrational necessity of resting in a dualism as ultimate truth, but rather the need of recognising an insuperable barrier which lies in the path of the intellect's search for ultimate truth.