ality, 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 multitude?

Yes, I said; and this being true of one must be equally true of all
number?

Certainly.

And all arithmetic and calculation have to do with number?

Yes.

And they appear to lead the mind towards 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?

Certainly.

Then this is a kind of knowledge which legislation may fitly prescribe;
and we must endeavour 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 merchants 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
becoming 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 any one who attempts to divide absolute unity when he is
calculating, and if you divide, they multiply (Meaning either (1)
that they integrate the number because they deny the possibility of
fractions; or (2) that division is regarded by them as a process of
multiplication, for the fractions of one continue