nd trying to get rid of the illusions of sense, nearly
the whole of education is contained in them. They seemed to have an
inexhaustible application, partly because their true limits were not yet
understood. These Plato himself is beginning to investigate; though
not aware that number and figure are mere abstractions of sense,
he recognizes that the forms used by geometry are borrowed from the
sensible world. He seeks to find the ultimate ground of mathematical
ideas in the idea of good, though he does not satisfactorily explain the
connexion between them; and in his conception of the relation of ideas
to numbers, he falls very far short of the definiteness attributed to
him by Aristotle (Met.). But if he fails to recognize the true limits of
mathematics, he also reaches a point beyond them; in his view, ideas
of number become secondary to a higher conception of knowledge. The
dialectician is as much above the mathematician as the mathematician is
above the ordinary man. The one, the self-proving, the good which is
the higher sphere of dialectic, is the perfect truth to which all things
ascend, and in which they finally repose.

This self-proving unity or idea of good is a mere vision of which no
distinct explanation can be given, relative only to a particular stage
in Greek philosophy. It is an abstraction under which no individuals
are comprehended, a whole which has no parts (Arist., Nic. Eth.). The
vacancy of such a form was perceived by Aristotle, but not by Plato.
Nor did he recognize that in the dialectical process are included two or
more methods of investigation which are at variance with each other.
He did not see that whether he took the longer or the shorter road, no
advance could be made in this way. And yet such visions often have an
immense effect; for although the method of science cannot anticipate
science, the idea of science, not as it is, but as it will be in the
future, is a great and inspiring principle. In the pursuit of knowledge
we are always pressing forward to something beyond us; and as a false
conception of knowledge, for example the scholastic philosophy, may lead
men astray during many ages, so the true ideal, though vacant, may draw
all their thoughts in a right direction. It makes a great difference
whether the general expectation of knowledge, as this indefinite feeling
may be termed, is based upon a sound judgment. For mankind may often
entertain a true conception of what knowledge ough