The second part of our task—which is the reader’s task as much as mine—is not so easy; and the reason is evident. It is this: The false creeds in question—the fatal misconceptions they involve—are so _familiar_ to us—they have been so long and so deeply imbedded in our thought and speech and ways of life—we have been so thoroughly _bred_ in them by home and school and church and state—that we _habitually_ and _unconsciously_ take them for granted and have to be virtually _stung_ into an awareness of the fact that we do actually hold them and that they do actually reign to-day throughout the world and have so reigned from time immemorial. We have, therefore, to shake ourselves awake, to _prick_ ourselves into a realization of the truth.
I assume that the reader is at once hard-headed, rational, I mean, and interested in the welfare of mankind. If he is not, he will not be a “reader” of this book. He, therefore, knows that the third task—the task of detecting and exposing the fundamental error of the misconceptions in question—is a task of the utmost importance. What is that error? It is, I have said, an error in logic. But logical errors are not all alike—they are of many kinds. What is the “kind” of _this_ one? It is the kind that consists in what mathematicians call “confusion of types,” or “mixing of dimensions.” The answer can not be made too clear nor too emphatic, for its importance in the criticism of _all_ our thinking is great beyond measure. There are millions of examples that help to make the matter clear. I will again employ the simplest of them—one so simple that a child can understand it. It is a mathematical example, as it ought to be, for the whole question of logical types, or dimensions, is a mathematical one. I beg the reader not to shy at, or run away from, the mere word mathematical, for, although most of us have but little mathematical _knowledge_, we all of us have the mathematical _spirit_, for else we should not be human—we are all of us mathematicians _at heart_. Let us, then, proceed confidently and at once to our simple example. Here is a _surface_, say a _plane_ surface. It has length and breadth—and so it has, we say, _two_ dimensions; next consider a _solid_, say a _cube_. It has length, breadth and thickness—and so _it_ has, we say, _three_ dimensions. Now we notice that the cube _has_ surfaces and so _has certain surface properties_. Do we, therefore, say that a solid _is_ a surface? That the cube is a member of the class of surfaces? If we did, we should be fools—type-confusing fools—dimension-mixing fools. That is evident. Or suppose we notice that solids have certain _surface_ properties and certain properties that surfaces do _not_ have; and suppose we say the _surface_ properties of solids are _natural_ but the other properties are so mysterious that they must be “_super_natural” or somehow “divine”; and suppose we then say that solids are unions, mixtures, compounds or hybrids of surfaces and something divine or _super_natural; is it not evident that, if we did that, we should be again blundering like fools? Type-confusing fools? Dimension-mixing fools? That such would be the case any one can see. Let us now consider animals and human beings, and let us look squarely and candidly at the facts. To get a start, think for a moment of plants. Plants are living things; they take, transform and appropriate the energies of sun, soil, and air, but they have _not_ the _autonomous_ power to move about in space; we may say that plants constitute the lowest order or class or type or dimension of life—the dimension _one_; plants, we see are binders of the _basic_ energies of the world. What of animals? Like the plants, animals, too, take in, transform and appropriate the energies of sun, soil and air, though in large part they take them in forms already prepared by the plants themselves; but, _unlike_ the plants, animals possess the _autonomous_ power to move about in space—to creep or crawl or run or swim or fly—it is thus evident that, compared with plants, animals belong to a higher order, or higher class, or higher type, or higher dimension of life; we may therefore say that the type of animal life is a type of _two_ dimensions—a two-dimensional type; I have called them space-binders because they are distinguished, or marked, by their autonomous power to move about in space, to abandon one place and occupy another and so to appropriate the natural fruits of many localities; the life of animals is thus a life-in-space in a sense evidently not applicable to plants.