We agree with Dr. Potonié that thought-forms grow naturally and that they
grow such as they are, of necessity. In our opinion formal thought, with
its so-called _a priori_ theorems, is derived from the thought-forms by
abstraction. (See “Fundamental Problems” pp. 26-60, the chapter Form and
Formal Thought.) If it had been possible for other thought-forms to have
originated together with those which we possess at present, and it may be
parenthetically remarked that we do not consider it as possible; but _if_
it had been possible, we do not deny that all the other thought-forms
would have gone to the wall, they would have perished in the struggle for
existence and our present thought-forms alone would have survived. In
this we agree with Dr. Potonié, and a naturalist may be satisfied with
this statement, because it suffices for his purposes. The recognition
of the objective validity of the laws of formal thought is all that
the specialist wants for this or that branch of science. But this
recognition is not sufficient for the philosopher. He has to understand
the problem why the subjective laws of purely formal thought possess an
absolute and an objective validity for the world of real existences. He
must understand not only how thought-forms originated, but also why and
on what ground the laws of formal thought are considered as necessary
and universal truths. The question of their origin and growth is of
secondary importance compared with the question of their rigidity and
apriority.
Mr. Herbert Spencer has made the same proposition as Dr. Potonié and
his view briefly expressed is this: “The laws of formal thought are _a
priori_ to the individual, but _a posteriori_ to the race.” In other
words apriority must be explained by heredity. A dog cannot count,
because none of his ancestors have ever counted, but a child has the
faculty to learn counting because innumerable ancestors of his have
counted and his brain possesses a predisposition to learn counting
easily. Concerning our apprehension of space-relations which expressed as
mathematical theorems appear to us necessary and are called _a priori_,
Mr. Spencer says:
“We cannot think otherwise because during that adjustment
between the organism and the environment which evolution has
established, the inner relations have been so moulded upon
the outer relations that they cannot by any effort be made
not to fit them. Just in the same way that an infant’s hand,
constructed so as to grasp by bending the fingers inwards,
implies ancestral hands which have thus grasped, and implies
objects in the environment to be thus grasped by this infantine
hand when it is developed, so the various structures fitting
the infant for apprehension of space-relations, imply such
apprehensions in the past by its ancestors and in the future by
itself.”
Man’s ability to learn counting is inherited, and there may be more or
less of it in different people. Mathematical talent is inherited just as
much as musical talent or other faculties. But the philosophical question
concerning the apriority of mathematical theorems has nothing whatever to
do with the origin of mathematical talent. When Mr. Spencer declares that
apriority is but an inherited aposteriority, this is equivalent and is
intended to be equivalent to an actual denial of all apriority. His very
explanation proves that he does not see the real problem, and in the same
way Dr. Potonié overlooks it entirely. The philosophical problem of the
apriority is not an historical problem, it cannot be solved by tracing
the evolution of thought-forms. The philosopher does not ask how did
thought-forms originate, but why do we attribute to the laws of formal
thought necessity and universality and on what ground can we justify our
assumption?
Mr. Spencer compares our apprehension of space-relations to our inherited
habit to grasp with our hands and to walk with our feet. This comparison
is misleading and inappropriate. That we grasp with our hands and walk
with our feet is incidental. There are animals who have developed other
limbs for the same purposes. There are monkeys who grasp with their
tails and the elephant grasps with his nose. There is no necessity and
no universality in our predisposition of grasping with our hands. Yet
there resides necessity and universality in the laws of formal thought
so that wherever animals develop rational thought we are sure that to
them twice two will always equal four just as much as it does to us.
However they may be different in other respects: they may be winged
creatures or may be somewhat like our ants, they may have developed other
bodily structures than we can dream of, nevertheless their arithmetic,
their logic, and their mathematics will in all essentials be exactly the
same as ours. There are animals whose thought-forms are not as highly
developed as in man, but there are no animals in whom they are developed
differently. We must consider it as impossible even that on other stars
rational creatures can be found whose reason differs from ours. To them
also twice two will be four.