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All number has also an elevating effect; it raises the mind out

of the foam and flux of generation to the contemplation of being,

having lesser military and retail uses also. The retail use is

not required by us; but as our guardian is to be a soldier as

well as a philosopher, the military one may be retained. And to

our higher purpose no science can be better adapted; but it must

be pursued in the spirit of a philosopher, not of a shopkeeper.

It is concerned, not with visible objects, but with abstract

truth; for numbers are pure abstractions-the true arithmetician

indignantly denies that his unit is capable of division. When you

divide, he insists that you are only multiplying; his 'one' is

not material or resolvable into fractions, but an unvarying and

absolute equality; and this proves the purely intellectual

character of his study.