Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

140 MATHEMATICAL PHILOSOPHY
dazzling of the mind. The disadvantage in question,
though always inferior to the mentioned advantage, is
naturally more serious in cases where the question of
postulate verification is especially difficult to answer with
perfect certitude. Such cases are not merely supposable;
they are in fact of very frequent occurrence in the history
of science. Just at present, we have indeed a living illustration in the world-wide discussion of relativity
theories, wherein the satisfiedness, or verifiedness, of
certain famous postulates (or deductions therefrom)once regarded as established, long so regarded in the
case of some of them-has been called in question and is
now held in doubt or denied. For a presentation of the
great matter of these theories, I have real pleasure in
referring you to C. D. Broad's article, "Euclid, Newton,
and Einstein," in The Hilbert Journal, Vol. XVIII.,
April, 1920; the article, which is easily the best I have
seen on the subject, is quite notable as a sound, intelligible,
semi-popular exposition of an exceedingly recondite scientific development The art of such exposition, let me
say in passing, is difficult and important-quite as difficult and, in its service, quite as important as research
itself; a high degree of skill in it is, I think, not less
rare than a high degree of research ability; once in a
great while, the two things are united in one personality,
as in W. K. Clifford, for example, in Thomas Huxley,
in Helmholz and Ernst Mach, but not in Henri Poincaré
who, though he repeatedly essayed the task of popular
exposition and indeed produced many a lightning flash
1 Since this was written many attempts have been made to explain the
doctrine in popular terms. Among the best attempts may be mentioned
Bolton's Introduction to the Theory of Relativity [E. P. Dutton & Co.]
and W. B. Smith's article, Relativity and Its Philosophic Implications
[Monist, Dec., g921].