vided into two unequal parts, and may again
subdivide each part into two lesser segments representative of the
stages of knowledge in either sphere. The lower portion of the lower or
visible sphere will consist of shadows and reflections, and its upper
and smaller portion will contain real objects in the world of nature
or of art. The sphere of the intelligible will also have two
divisions,--one of mathematics, in which there is no ascent but all is
descent; no inquiring into premises, but only drawing of inferences.
In this division the mind works with figures and numbers, the images of
which are taken not from the shadows, but from the objects, although
the truth of them is seen only with the mind's eye; and they are used as
hypotheses without being analysed. Whereas in the other division reason
uses the hypotheses as stages or steps in the ascent to the idea of
good, to which she fastens them, and then again descends, walking firmly
in the region of ideas, and of ideas only, in her ascent as well as
descent, and finally resting in them. 'I partly understand,' he replied;
'you mean that the ideas of science are superior to the hypothetical,
metaphorical conceptions of geometry and the other arts or sciences,
whichever is to be the name of them; and the latter conceptions you
refuse to make subjects of pure intellect, because they have no first
principle, although when resting on a first principle, they pass into
the higher sphere.' You understand me very well, I said. And now to
those four divisions of knowledge you may assign four corresponding
faculties--pure intelligence to the highest sphere; active intelligence
to the second; to the third, faith; to the fourth, the perception of
shadows--and the clearness of the several faculties will be in the same
ratio as the truth of the objects to which they are related...

Like Socrates, we may recapitulate the virtues of the philosopher.
In language which seems to reach beyond the horizon of that age
and country, he is described as 'the spectator of all time and all
existence.' He has the noblest gifts of nature, and makes the highest
use of them. All his desires are absorbed in the love of wisdom, which
is the love of truth. None of the graces of a beautiful soul are wanting
in him; neither can he fear death, or think much of human life. The
ideal of modern times hardly retains the simplicity of the antique;
there is not the same originality either in truth or error which