productive, and yet may be poor critics. We are often wofully
disappointed when we attend a lecture on poetry by a poet, or one on
painting by an artist.

It may be said: If what is maintained above regarding the 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