My dear Glaucon, what study could draw the soul from the world of becoming to the world of being? . . . this, which they all have in common, which is used in addition by all arts and all sciences and ways of thinking, which is one of the first things every man must learn of necessity.”
“What’s that?” he asked again.
“Just this trifle, I said—to distinguish between one and two and three: I mean, in short, number and calculation . . .”
“Number, then, appears to lead towards the truth?”
“That is abundantly clear.”
“Then, as it seems, this would be one of the studies we seek; for this is necessary for the soldier to learn because of arranging his troops, and for the philosopher, because he must rise up out of the world of becoming and lay hold of real being or he will never become a reckoner.”
“That is true,” said he.
“Again, our guardian is really both soldier and philosopher.”
“Certainly.”
“Then, my dear Glaucon, it is proper to lay down that study by law, and to persuade those who are to share in the highest things in the city to go for and tackle the art of calculation, and not as amateurs; they must keep hold of it until they are led to contemplate the very nature of numbers by thought alone, practicing it not for the purpose of buying and selling like merchants or hucksters, but for war, and for the soul itself, to make easier the change from the world of becoming to real being and truth.”
“Excellently said,” he answered.
“And besides,” I said, “it comes into my mind, now the study of calculations has been mentioned, how refined that is and useful to us in many ways for what we want, if it is followed for the sake of knowledge and not for chaffering.”
“How so?” he asked.
“In this way, as we said just now; how it leads the soul forcibly into some upper region and compels it to debate about numbers in themselves; it nowhere accepts any account of numbers as having tacked onto them bodies which can be seen or touched. . . . I think they are speaking of what can only be conceived in the mind, which it is impossible to deal with in any other way.”
“You see then, my friend, said I, that really this seems to be the study we need, since it clearly compels the soul to use pure reason in order to find out the truth.”
“So it most certainly does. . . .
“For all these reasons, the best natures must be trained in it.”
After arithmetic, Glaucon and Socrates consider geometry.
Says Socrates, “The knowledge the geometricians seek is not knowledge of something which comes into being and passes, but knowledge of what always is.”
“Agreed with all my heart, said he, for geometrical knowledge is of that which always is.”
“A generous admission! Then it would attract the soul toward truth, and work out the philosopher’s mind so as to direct upwards what we now improperly keep downwards.”
After arithmetic and plane geometry, Glaucon proposes astronomy as the third subject in the curriculum of the Guardians. Socrates objects; solid geometry is more appropriate, he says.
“Quite so,” says Glaucon, “but it seems that those problems have not yet been solved.”
“For two reasons,” I said, “because no city holds them in honour, they are weakly pursued, being difficult. Again, the seekers lack a guide, without whom they could not discover; it is hard to find one in the first place, and if they could, as things now are, the seekers in these matters would be too conceited to obey him. But if any whole city should hold these things honourable and take a united lead and supervise, they would obey, and solutions sought constantly and earnestly would become clear. Indeed even now, although dishonoured by the multitude, and held back by the seekers themselves having no conception of the objects for which they are useful, these things do nevertheless force on and grow against all this by their own charm, and I should not be too surprised if they should really come to light. . . .
“Let us put astronomy as the fourth study, assuming that solid geometry, which we leave aside now, is there for us if only the city would support it.”
[The Republic (“Great Dialogues of Plato,” pp. 315–16, 323–31). Plato gave Socrates the first person, “I.”]
