ind" 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