But there is a still more fatal objection to the theory of mental units 'compounding with themselves' or 'integrating.' It is logically unintelligible; it leaves out the essential feature of all the 'combinations' we actually know.
All the 'combinations' which we actually know are effects, wrought by the units said to be 'combined,' upon some entity other than themselves. Without this feature of a medium or vehicle, the notion of combination has no sense.
"A multitude of contractile units, by joint action, and by being all connected, for instance, with a single tendon, will pull at the same, and will bring about a dynamical effect which is undoubtedly the resultant of their combined individual energies.... On the whole, tendons are to muscular fibres, and bones are to tendons, combining recipients of mechanical energies. A medium of composition is indispensable to the summation of energies. To realize the complete dependence of mechanical resultants on a combining substratum, one may fancy for a moment all the individually contracting muscular elements severed from their attachments. They might then still be capable of contracting with the same energy as before, yet no co-operative result would be accomplished. The medium of dynamical combination would be wanting. The multiple energies, singly exerted on no common recipient, would lose themselves on entirely isolated and disconnected efforts."[173]
In other words, no possible number of entities (call them as you like, whether forces, material particles, or mental elements) can sum themselves together. Each remains, in the sum, what it always was; and the sum itself exists only for a bystander who happens to overlook the units and to apprehend the sum as such; or else it exists in the shape of some other effect on an entity external to the sum itself. Let it not be objected that H2 and O combine of themselves into 'water,' and thenceforward exhibit new properties. They do not. The 'water' is just the old atoms in the new position, H-O-H; the 'new properties' are just their combined effects, when in this position, upon external media, such as our sense-organs and the various reagents on which water may exert its properties and be known.
"Aggregations are organized wholes only when they behave as such in the presence of other things. A statue is an aggregation of particles of marble, but as such it has no unity. For the spectator it is one; in itself it is an aggregate; just as, to the consciousness of an ant crawling over it, it may again appear a mere aggregate. No summing up of parts can make an unity of a mass of discrete constituents, unless this unity exist for some other subject, not for the mass itself."[174]
Just so, in the parallelogram of forces, the 'forces' themselves do not combine into the diagonal resultant; a body is needed on which they may impinge, to exhibit their resultant effect. No more do musical sounds combine per se into concords or discords. Concord and discord are names for their combined effects on that external medium, the ear.
Where the elemental units are supposed to be feelings, the case is in no wise altered. Take a hundred of them, shuffle them and pack them as close together as you can (whatever that may mean); still each remains the same feeling it always was, shut in its own skin, windowless, ignorant of what the other feelings are and mean. There would be a hundred-and-first feeling there, if, when a group or series of such feelings were set up, a consciousness belonging to the group as such should emerge. And this 101st feeling would be a totally new fact; the 100 original feelings might, by a curious physical law, be a signal for its creation, when they came together; but they would have no substantial identity with it, nor it with them, and one could never deduce the one from the others, or (in any intelligible sense) say that they evolved it.
Take a sentence of a dozen words, and take twelve men and tell to each one word. Then stand the men in a row or jam them in a bunch, and let each think of his word as intently as he will; nowhere will there be a consciousness of the whole sentence.[175] We talk of the 'spirit of the age,' and the 'sentiment of the people,' and in various ways we hypostatize 'public opinion.' But we know this to be symbolic speech, and never dream that the spirit, opinion, sentiment, etc., constitute a consciousness other than, and additional to, that of the several individuals whom the words 'age,' 'people,' or 'public' denote. The private minds do not agglomerate into a higher compound mind. This has always been the invincible contention of the spiritualists against the associationists in Psychology,—a contention which we shall take up at greater length in [Chapter X]. The associationists say the mind is constituted by a multiplicity of distinct 'ideas' associated into a unity. There is, they say, an idea of a, and also an idea of b. Therefore, they say, there is an idea of a + b, or of a and b together. Which is like saying that the mathematical square of a plus that of b is equal to the square of a + b, a palpable untruth. Idea of a + idea of b is not identical with idea of (a + b). It is one, they are two; in it, what knows a also knows b; in them, what knows a is expressly posited as not knowing b; etc. In short, the two separate ideas can never by any logic be made to figure as one and the same thing as the 'associated' idea.
This is what the spiritualists keep saying; and since we do, as a matter of fact, have the 'compounded' idea, and do know a and b together, they adopt a farther hypothesis to explain that fact. The separate ideas exist, they say, but affect a third entity, the soul. This has the 'compounded' idea, if you please so to call it; and the compounded idea is an altogether new psychic fact to which the separate ideas stand in the relation, not of constituents, but of occasions of production.