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

362 MATHEMATICAL PHILOSOPHY
good. It is the pragmatic meaning of truth that makes
treason a crime, if it fail, and a virtue, if it succeed. It
is a meaning that is especially congenial to practicians
and "politicians," whose "philosophy" never rises above
the question: How can I "get there"? How can I put
this thing "through," "over" or "across"? What is the
means that will "work"? It is a meaning, too, that is
especially congenial to an industrial age,-an experimental age,-an age of laboratories,-an adventurous
age when men act more than they think. In the headlong rush and hurly-burly of such an age, men and women
are not aware of the fact that the world of human affairs
would quickly dash upon utter destruction but for the
guiding and saving influence of a nobler truth-conception
which they do not consciously own,-the conception, I
mean, of truth as having its highest meaning in the unchanging relations and eternal laws of Logical Thought.
I have said that in the pragmatic sense of "true,"
Euclidean geometry may be said to be true of our perceptual space. It may be said because this geometry,
when applied (as we say) to this space, "works"-which
means that temples, aqueducts, tunnels, bridges, railways,
ships and other architectural and engineering structures
whose designing is guided by Euclidean formulas are
successful-they wear out but they do not perish from
any essential defect of structural design.
Does not the fact just stated show that Euclidean
geometry is superior to the other two varieties? It does
not; for, if the designing and the building of the structures alluded to were guided by Lobachevskian or by
Riemannian formulas, the structures, when completed,
would not differ perceptibly from the former ones, and
the railways, ships, and so on, would be equally durable