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.