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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.