Now the ideal of the whole is a plan or scheme in which the constructive principles of the mind are conceived as having untrammeled course and unhindered application, and the task of world-building, or rather universe-building, is in idea carried out to completion.
The attempt to present an ideal forecast, or outline of the whole of reality, as it would satisfy a mind constituted like ours, an ideal landscape of this sort, is not at all to be confounded with the arrogation of a priori knowledge. A priori knowledge is supposed to be a kind of knowledge, and knowledge of the whole is utterly and confessedly beyond our reach. The phrase a priori, too, is objectionable and unfortunate for two reasons. First, as just said, because it has been supposed to be a kind of knowledge. By some theologians men were supposed to possess a priori knowledge of God.[28] Secondly, because the word a priori suggests precedence in time, and our knowledge of the human mind and of its irreducible capacities comes out only in the course of experience. Much that has been called a priori, that is implicit in experience, did not become explicit until after prolonged experience. The Greek thinkers before Aristotle doubtless thought in terms of syllogism, but it was not until Greek science had attained a certain ripeness that Aristotle was able to dissect out the logic which had previously been employed more or less unconsciously.
Instead, therefore, of using the term a priori, which gives rise to the two-fold misapprehension of an a priori knowledge and of temporal precedence, and instead of throwing out the child with the bath, that is, of ignoring the independent part played by our mental constitution in building up experience, and in affording us the conviction of certainty, and of reality, it is highly desirable that a new term be found to take the place of a priori. The term “functional finality” suggests itself to me for this purpose.[29]
My field is ethics. I am entirely desirous of sticking to my own last, that is, dealing with such concepts as the data of my subject force upon me. I do not wish to trespass, or to seem to trespass, on the domain of my neighbors. Hence in dealing with functional finalities I must deal with them primarily as they appear in the field of ethics, that is, in the domain of the actions and reactions of human beings upon one another. Irreducible principia of ethics are the functional finalities, which prescribe rules for such intercourse, or better which create a scheme of ideal intercourse whereby the conduct of men shall be measured and determined.
I must, however, glance for a moment at fields outside my own, for the purpose not of controversy but of elucidation; not to deal with the subject matter of my neighbors, but to mark off my own more definitely. What then, I ask, is the most general expression by which to designate the singularities of the human mind, the principles on which it acts, its immutable modes of behavior, the invariants that recur amid all the complex varieties of its processes? The principal invariants are the positing of a manifold of some kind, and the apprehending of that manifold as coherent. The manifold is not given, but is posited by the mind. The positing is a mental function, just as much as the apprehending of the plurality as coherent is a mental function. The particular manifolds of space and time experience are said to be given, but they would not be received by the mind were not the function of manifold-positing prepared to apprehend them.
In recent physical science the notion of the manifold plays a conspicuous rôle. Subtle speculations are employed to define the kinds of manifold which the physicist finds opportune, and the kind of unity of which these manifolds are respectively capable. The two terms mentioned are themselves the most abstract conceivable, and naturally, that which is here taken to underlie all the constructive, world-building activity of the mind in every possible direction can only be expressed in the most sublimated language. But the notions themselves, or rather the acts of the mind, the functions designated, are rich and replete with concrete utility when applied to subject matter in the different fields.
Wherever we turn we find that the assurance of reality depends on the joint use of the two principles mentioned, the joint operation of the two kinds of mental action; that is to say—on the positing of a manifold and on the simultaneous apprehension of the subject matter to which it relates as coherent, as unified.
The simultaneity, the inseparableness of the two mental acts or functions in regard to the same subject-matter is the essential point on which hangs the web of the argument here submitted. Thus in geometry space must be regarded as a continuum, unbroken, uninterrupted at any point, and at the same time the same space must be treated as capable of puncture, of linear and superficial delimitations; that is to say, of division. That which is one must yet be apprehended as divided; that which is divided, or delimitated, must yet be apprehended as one. The difficulties that arise spring from the vain endeavor to separate the two inseparable acts—the act of apprehending the manifold of space sub specie pluralitatis, and the act of apprehending it sub specie unitatis. Hence arises the puzzling question: How can that which is continuous be divided, how can chasms between the parts of space, however infinitesimal, be bridged? Witness the problem of Zeno, and the pragmatist solution of it by a demonstration that satisfies us indeed as to the fact (which no one doubts), but leaves the mental puzzle as before; and also Bergson’s Method of accounting for division by a comparison of the inner and the outer flux, wherein he seems to overlook the difficulty that for the purpose of comparison two points must be fixed, one in each flux, that is to say, the division in the flux must be regarded as already existing.
In the physical sciences we are compelled to assume on the one hand the atomic or granular constitution of matter, in other words, manifoldness. On the other hand, if “action at a distance” is to be escaped, we are bound to assume a continuum of some sort like the ether. Again, in the organic world there is the manifold of structures and functions, and the unity of organism. To whatever object of inquiry we give our attention, we find ourselves not only restricted fundamentally to the two functions described, but we discover that to their insunderable co-operation we owe whatever of truth we possess.
Now the business of ethics is to define its own subject-matter, that is to say the particular kind of manifold with which it deals, and the kind of unity of which that manifold is susceptible. But as I approach this first goal of my enterprise, there is one obstacle which I must try to remove out of the way of the reader, before I can hope to win him to a hospitable consideration of my conclusions. The jointness or inseparableness of the two acts out of which certainty or reality issues has created all the difficulties. The fact that the manifold must be regarded as remaining a manifold, unaltered in its character as such, not derivative from the One (there is no such One), and that the unity does not contrariwise result from the manifold in the sense of springing from or being derived from it;—in other words that we must see the same landscape of things and events both sub specie pluralitatis and sub specie unitatis—has been the stumbling-block. The history of philosophy might be written under the two headings: 1, monistic systems that undertake, collapsing in their futile effort, to derive the world and its plurality from the One, as if there were such an One, out of whose bosom philosophy might evoke the many (creational systems, pantheistic systems, emanation systems, evolution systems); 2, pluralistic systems that essay, with equal lack of success, to explain the unity as somehow the offspring of the plurality.