republic (books 6 - 10)
tion of plurality, then thought begins to be aroused within us,
and the soul perplexed and wanting to arrive at a decision asks,
"What is absolute unity?" This is the way in which the study
of the one has a power of drawing and converting the mind
to the contemplation of true being.
And surely, he said, this occurs notably in the case of one;
for we see the same thing to be both one and infinite in multi-
Yes, I said; and this being true of one must be equally true
of all number?
And all arithmetic and calculation have to do with number?
And they appear to lead the mind toward truth?
Yes, in a very remarkable manner.
Then this is knowledge of the kind for which we are seeking,
having a double use, military and philosophical; for the man of
war must learn the art of number or he will not know how to
array his troops, and the philosopher also, because he has to
rise out of the sea of change and lay hold of true being, and
therefore he must be an arithmetician.
That is true.
And our guardian is both warrior and philosopher?
Then this is a kind of knowledge which legislation may fitly
prescribe; and we must endeavor to persuade those who are to
be the principal men of our State to go and learn arithmetic,
not as amateurs, but they must carry on the study until they see
the nature of numbers with the mind only; nor again, like mer-
chants or retail-traders, with a view to buying or selling, but
for the sake of their military use, and of the soul herself; and
because this will be the easiest way for her to pass from becom-
ing to truth and being.
That is excellent, he said.
Yes, I said, and now having spoken of it, I must add how
charming the science is! and in how many ways it conduces to
our desired end, if pursued in the spirit of a philosopher, and
not of a shopkeeper!
How do you mean?
I mean, as I was saying, that arithmetic has a very great and
elevating effect, compelling the soul to reason about abstract
number, and rebelling against the introduction of visible or
tangible objects into the argument. You know how steadily
the masters of the art repel and ridicule anyone who attempts
to divide absolute unity when he is calculating, and if you
divide, they multiply, taking care that one shall continue one
and not become lost in fractions.