In practical life we all expect that 2 × 2 will under all circumstances
make 4, and not 5. We reject Mr. Mill’s idea that there may be even a
possibility of the latter. Is our expectancy really due to _a posteriori_
experience which having been repeated so often in the lives of our
ancestors is now so firmly rooted in our minds that we imagine it to
be necessary and _a priori_? No! certainly not. The experiences of our
race in the struggle for life has produced our ability of thought,
but it has nothing to do with the apriority of the products of formal
thought-operations. A statement of formal thought such as “twice two
makes four,” cannot be compared to statements of sense-experience such
as that sugar has a sweet taste. There may be a moment in which the
taste of sugar will be bitter to our tongue. This is quite possible.
But to say that twice two might in the future or in any other world, as
Mr. Mill maintains, make five is nonsensical, and the possibility of
this assumption cannot be placed in one line with the possibilities of
extraordinary and exceptional sense-experiences.
What does “twice two makes four” mean? Two means 1 + 1, and twice two
means 1 + 1 plus 1 + 1. This sum is called “four”; and what we call
five is 4 + 1. To maintain that the operation 2 × 2 might produce the
result 5, is to admit conditions which have been excluded. Pure forms
are not like animals which multiply; they are and remain such as they
have been posited. When we put two amœbas into a glass and then add two
other amœbas, it is quite possible that in the mean time one of the first
set has divided into two. In that case we would have five amœbas. But
the operation 2 × 2 cannot breed any additional units, so as to produce
a greater number than the sum of 1 + 1 + 1 + 1. Nor can we let any of
these units disappear into naught, so as to produce the result 3, without
committing some inconsistency in our thought-operations, for the products
of our thought-operations are rigid and must remain such as they have
been posited. They are not animals blessed with fertility but pure forms
and nothing but pure forms.
How could Mr. John Stuart Mill overlook so palpable a contrast as
that between formal knowledge and sense-experience? He was apparently
prejudiced against the term “a priori,” which as we freely confess is a
very poor and inadequate expression. Mr. Mill himself states the cause of
his prejudice in his autobiography. He says:
“There is not any idea, feeling, or power, in the human mind,
which, in order to account for it, requires that its origin
should be referred to any other source than experience.”
Mr. Mill was justly exasperated against anything _a priori_, for in his
time, it had become customary among certain philosophers to classify all
pet superstitions which could not be proved by experience as _a priori_.
Mr. Mill continues:
“Whatever may be the practical value of a true philosophy
of these matters, it is hardly possible to exaggerate the
mischiefs of a false one. The notion that truths external
to the mind may be known by intuition or consciousness,
independently of observation and experience, is, I am
persuaded, in these times the great intellectual support of
false doctrines and bad institutions. By the aid of this theory
every inveterate belief and every intense feeling, of which
the origin is not remembered, is enabled to dispense with the
obligation of justifying itself by reason, and is erected into
its own all-sufficient voucher and justification. There never
was such an instrument devised for consecrating all deep-seated
prejudices.”
We appreciate the cause of Mr. Mill’s prejudice, but we cannot agree
with him. And Mr. Mill is mistaken when he imagines that a rejection
of apriority will abolish false doctrines and superstitions. On
the contrary. The recognition of absolute necessity based upon the
universality of formal thought will alone be a safe basis of science
through which we can reject _prima facie_ the wrong pretensions of
superstitions and pseudo-science. If we assume with Mr. Mill that all
formal knowledge partakes of the nature of sense-experience, that there
is no difference between the two, no general judgment would be allowable
and the idea of necessity would be inadmissible. These consequences
are accepted by Mill. In that case science would lose its value and
philosophy would be without foundation. The most absurd superstition
could not be rejected off-hand on the ground of being contrary to that
which through logic and other formal sciences has been found to be
necessary and a condemnation of any superstition on the part of science
would be mere arrogance. Pseudo-science would have the same right with
true science.
It is obvious that without being obliged to consider the apriority of
formal laws as innate, we need not accept the consequence of Mr. Mill’s
philosophy. We can and we do retain the idea of necessity and we consider
it as the corner-stone of all science.