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 prescribe 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, taking care that one
shall continue one and not become lost in fractions.

That is very true.

Now, suppose a person were to say to them: O my friends, what are
these wonderful numbers about which you are reasoning, in which, as you
say, there is a unity such as you demand, and each unit is equal,
invariable, indivisible,--what would they answer?

They would answer, as I should conceive, that they were speaking of
those numbers which can only be realised in thought.

Then you see that this knowledge may be truly called necessary,
necessitating as it clearly does the use of the pure intelligence in
the attainment of pure truth?

Yes; that is a marked characteristic of it.

And have you further observed, that those who have a natural talent for
calculation are gene