possibility
of prosecuting scientific researches without having recourse to
reflective thought is true, why should the man of science care whether
the principles and methods of the non-philosophical sciences are
investigated or are merely taken for granted?

I answer: It should be observed that the statements made in the last
section were somewhat guarded. I have used the expressions "as a rule"
and "usually." I have spoken thus because one can work in the way
described, without danger of error, only where a beaten track has been
attained and is followed. In Chapter XVI it was pointed out that even
in the mathematical sciences one may be forced to reflect upon the
significance of one's symbols. As I write this, a pamphlet comes to
hand which is concerned to prove that "every cause is potentially
capable of producing several effects," and proves it by claiming that
the square root of four ([square root symbol]4) is a _cause_ which may
have as _effect_ either two (2) or minus two (-2).

Is this mathematical reasoning? Are mathematical relations ever those
of cause and effect? And may one on the basis of such reasonings claim
that in nature the relation of cause and effect is not a fixed and
invariable one?

Even where there is a beaten track, there is some danger that men may
wander from it. And on the confines of our knowledge there are fields
in which the accepted road is yet to be established. Science makes
constant use of hypotheses as an aid to investigation. What hypotheses
may one frame, and what are inadmissible? How important an
investigation of this question may be to the worker in certain branches
of science will be clear to one who will read with attention Professor
Poincare's brilliant little work on "Science and Hypothesis." [2]

There is no field in art, literature, or science in which the work of
the critic is wholly superfluous. "There are periods in the growth of
science," writes Professor Pearson in his deservedly popular work, "The
Grammar of Science," [3] "when it is well to turn our attention from
its imposing superstructure and to examine carefully its foundations.
The present book is primarily intended as a criticism of the
fundamental concepts of modern science, and as such finds its
justification in the motto placed upon its title-page." The motto in
question is a quotation from the French philosopher Cousin: "Criticism
is the life of science."

We have seen in Chapter XVI that