earth as well as the
heavens,--not forgetting to notice the intimation to which allusion has
been already made, that besides astronomy and harmonics the science
of solids in motion may have other applications. Still more will he be
struck with the comprehensiveness of view which led Plato, at a time
when these sciences hardly existed, to say that they must be studied in
relation to one another, and to the idea of good, or common principle
of truth and being. But he will also see (and perhaps without surprise)
that in that stage of physical and mathematical knowledge, Plato has
fallen into the error of supposing that he can construct the heavens a
priori by mathematical problems, and determine the principles of harmony
irrespective of the adaptation of sounds to the human ear. The illusion
was a natural one in that age and country. The simplicity and certainty
of astronomy and harmonics seemed to contrast with the variation and
complexity of the world of sense; hence the circumstance that there was
some elementary basis of fact, some measurement of distance or time or
vibrations on which they must ultimately rest, was overlooked by him.
The modern predecessors of Newton fell into errors equally great; and
Plato can hardly be said to have been very far wrong, or may even claim
a sort of prophetic insight into the subject, when we consider that
the greater part of astronomy at the present day consists of abstract
dynamics, by the help of which most astronomical discoveries have been
made.

The metaphysical philosopher from his point of view recognizes
mathematics as an instrument of education,--which strengthens the
power of attention, developes the sense of order and the faculty of
construction, and enables the mind to grasp under simple formulae the
quantitative differences of physical phenomena. But while acknowledging
their value in education, he sees also that they have no connexion with
our higher moral and intellectual ideas. In the attempt which Plato
makes to connect them, we easily trace the influences of ancient
Pythagorean notions. There is no reason to suppose that he is speaking
of the ideal numbers; but he is describing numbers which are pure
abstractions, to which he assigns a real and separate existence, which,
as 'the teachers of the art' (meaning probably the Pythagoreans) would
have affirmed, repel all attempts at subdivision, and in which unity and
every other number are conceived of as absolute. The