y subjective theories is inconceivable. For evidence in
favour of this view we must take a rapid survey of the whole domain of
human science, and test the chief departments of it to see how far
they contain, on the one hand, objective knowledge and facts, and on
the other, subjective knowledge and hypotheses. We may begin directly
with Kant's assertion that in every science only so much true--that is
objective--knowledge is to be found as it contains of mathematics.
Unquestionably mathematics stand at the head of all the sciences as
regards the certainty of its teaching. But how as to those deepest and
simplest fundamental axioms which constitute the firm basis on which
the proud edifice of mathematical teaching rests? Are these certain
and proved? Certainly not. The bases of its teaching are simply
"axioms" which are incapable of proof. To give only one example of how
the very first principles of mathematics might be attacked by
scepticism and shaken by philosophical speculation, we may remember
the recent discussions as to the three dimensions of space and the
possibility of a fourth dimension; disputes which are carried on even
at the present day by the most eminent mathematicians, physicists, and
philosophers. So much as this is certain, that mathematics as little
constitute an absolutely objective science as any other, but by the
very nature of man are subjectively conditioned. A man's subjective
power of knowing can only discern the objective facts of the outer
world in general so far as his organs of sense and his brain admit in
his own individual degree of cultivation.

However, granting that mathematics practically constitute an
absolutely certain and objective science, how is it with the rest of
the sciences? Undoubtedly the most certain among them are those "exact
sciences" whose principles are to be directly proved by mathematics;
thus, in the first place, a great part of physics. We say, "a great
part," for another large part--to speak accurately, by far the
greatest--is incapable of any exact mathematical proof. For what do we
know for certain of the essential nature of matter, or the essential
nature of force? What do we know for certain of gravitation, of the
attraction of mass, of its effects at great distances, and so on?
Newton's theory of gravitation is regarded as the most important and
certain theory of physics, and yet gravitation itself is a hypothesis.
Then, as to the other branches of physics--