ut by the imagination, with various attributes of immediate experience,
but just in so far as this concept is employed in verified descriptions
of radiation, magnetism, or electricity. Strictly speaking science
asserts nothing about the existence of ether, but only about the
behavior, _e. g._, of light. If true descriptions of this and other
phenomena are reached by employing units of wave propagation in an
elastic medium, then ether is proved to exist in precisely the same
sense that linear feet are proved to exist, if it be admitted that there
are 90,000,000 x 5,280 of them between the earth and the sun. And to
imagine in the one case a jelly with all the qualities of texture,
color, and the like, that an individual object of sense would possess,
is much the same as in the other to imagine the heavens filled with
foot-rules and tape-measures. There is but one safe procedure in dealing
with scientific concepts: to regard them as true so far as they
describe, and no whit further. To supplement the strict meaning which
has been verified and is contained in the formularies of science, with
such vague predicates as will suffice to make entities of them, is mere
ineptness and confusion of thought. And it is only such a
supplementation that obscures their abstractness. For a mechanical
description of things, true as it doubtless is, is even more indubitably
incomplete.

[Sidenote: The Meaning of Abstractness in Truth.]

Sect. 52. But though the abstractness involved in scientific description
is open and deliberate, we must come to a more precise understanding of
it, if we are to draw any conclusion as to what it involves. In his
"Principles of Human Knowledge," the English philosopher Bishop Berkeley
raises the question as to the universal validity of mathematical
demonstrations. If we prove from the image or figure of an isosceles
right triangle that the sum of its angles is equal to two right angles,
how can we know that this proposition holds of all triangles?

"To which I answer, that, though the idea I have in view
whilst I make the demonstration be, for instance, that of an
isosceles rectangular triangle whose sides are of a
determinate length, I may nevertheless be certain it extends
to all other rectilinear triangles, of what sort or bigness
soever. And that because neither the right angle, nor the
equality, nor determinate length of the sides are at all
concerned in the dem