From all this it follows that the soul, while an inhabitant of earth, is
in a fallen condition, an apostate from deity, an exile from the orb of
light. Hence Plato, in the 7th book of his Republic, considering our life
with reference to erudition and the want of it, assimilates us to men in
a subterranean cavern, who have been there confined from their childhood,
and so fettered by chains as to be only able to look before them to the
entrance of the cave which expands to the light, but incapable through
the chain of turning themselves round. He supposes too, that they have
the light of a fire burning far above and behind them; and that between
the fire and the fettered men, there is a road above, along which a low
wall is built. On this wall are seen men bearing utensils of every kind,
and statues in wood and stone of men and other animals. And of these men
some are speaking and others silent. With respect to the fettered men in
this cave, they see nothing of themselves or another, or of what is
carrying along, but the shadows formed by the fire falling on the
opposite part of tho cave. He supposes too, that the opposite part of
this prison has an echo; and that in consequence of this the fettered
men, when they hear any one speak, will imagine that it is nothing else
than the passing shadow.

Here, in the first place, as we have observed in the notes on that book,
the road above between the fire and the fettered men, indicates that
there is a certain ascent in the cave itself from a more abject to a more
elevated life. By this ascent, therefore Plato signifies the contemplation
of dianoetic objects in the mathematical disciplines. For as the shadows
in the cave correspond to the shadows of visible objects, and visible
objects are the immediate images of dianoetic forms, or those ideas which
the soul essentially participates, it is evident that the objects from
which these shadows are formed must correspond to such as are dianoetic.