Phil Pape 1

1142 Socrates/Glaucon

Moreover, it strikes me, now that it has been mentioned, how sophisti- cated the subject of calculation is and in how many ways it is useful for our purposes, provided that one practices it for the sake of knowing ratherd than trading.

How is it useful? In the very way we were talking about. It leads the soul forcibly upward

and compels it to discuss the numbers themselves, never permitting anyone to propose for discussion numbers attached to visible or tangible bodies. You know what those who are clever in these matters are like: If, in the course of the argument, someone tries to divide the one itself, they laugh and won’t permit it. If you divide it, they multiply it, taking care that onee thing never be found to be many parts rather than one.

That’s very true. Then what do you think would happen, Glaucon, if someone were to

ask them: “What kind of numbers are you talking about, in which the one526 is as you assume it to be, each one equal to every other, without the least difference and containing no internal parts?”

I think they’d answer that they are talking about those numbers that can be grasped only in thought and can’t be dealt with in any other way.

Then do you see that it’s likely that this subject really is compulsory forb us, since it apparently compels the soul to use understanding itself on the truth itself?

Indeed, it most certainly does do that. And what about those who are naturally good at calculation or reason-

ing? Have you already noticed that they’re naturally sharp, so to speak,

Republic VII 1143

in all subjects, and that those who are slow at it, if they’re educated and exercised in it, even if they’re benefited in no other way, nonetheless improve and become generally sharper than they were?

That’s true. Moreover, I don’t think you’ll easily find subjects that are harder to

learn or practice than this. c No, indeed. Then, for all these reasons, this subject isn’t to be neglected, and the

best natures must be educated in it. I agree. Let that, then, be one of our subjects. Second, let’s consider whether the

subject that comes next is also appropriate for our purposes. What subject is that? Do you mean geometry? That’s the very one I had in mind. Insofar as it pertains to war, it’s obviously appropriate, for when it d

comes to setting up camp, occupying a region, concentrating troops, de- ploying them, or with regard to any of the other formations an army adopts in battle or on the march, it makes all the difference whether someone is a geometer or not.