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 Poincaré'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