Polytropy

Index to this series

In the first part of Book VII of Plato’s Republic, Stephanus 514a–21c, the subject is the Allegory of the Cave and an inference from this:

Education is not the filling of a pail, but the lighting of a fire.

Actually that’s not what Socrates says, although such a saying is attributed to him. He says something close, at least if you think that

• filling a pail is like putting sight into blind eyes, and
• lighting a fire is like turning the soul to the light.

They are not that close.

Perhaps the actual message of Socrates is opposed to the misattributed saying. Here is what he tells Glaucon at 518b–d:

“… education is not what the professions of certain men assert it to be. They presumably assert that they put into the soul knowledge that isn’t in it, as though they were putting sight into blind eyes.”

“Yes,” he said, “they do indeed assert that.”

“But the present argument, on the other hand,” I said, “indicates that this power is in the soul of each, and that the instrument with which each learns – just as an eye is not able to turn toward the light from the dark without the whole body – must be turned around from that which is coming into being together with the whole soul until it is able to endure looking at that which is and the brightest part of that which is. And we affirm that this is the good, don’t we?”

“Yes.”

“There would, therefore,” I said, “be an art of this turning around …”

Lighting a fire is pointless if the student cannot perceive it. The fire of the Good is already burning, like the sun in the sky, and the student has the capacity to see it, as a pail has the capacity to be filled.

One may light a fire not to create something radiant, but to provoke movement. That seems to be the idea of Plutarch in “On Listening to Lectures” (De auditu), which is on Bill Thayer’s amazing site in the translation of F. C. Babbitt, from the first of the 16 volumes in the Loeb edition of the Moralia. That first volume, like others, is available from the Internet Archive, and here is what it says on pages 257–9:

as for those lazy persons whom we have mentioned, let us urge them that, when their intelligence has comprehended the main points, they put the rest together by their own efforts, and use their memory as a guide in thinking for themselves (τῇ μνήμῃ χειραγωγεῖν τὴν εὕρεσιν), and, taking the discourse of another as a germ and seed, develop and expand it. For the mind does not require filling like a bottle, but rather, like wood, it only requires kindling (οὐ γὰρ ὡς ἀγγεῖον ὁ νοῦς ἀποπληρώσεως ἀλλ’ ὑπεκκαύματος μόνον ὥσπερ ὕλη δεῖται) to create in it an impulse to think independently and an ardent desire for the truth (ὁρμὴν ἐμποιοῦντος εὑρετικὴν καὶ ὄρεξιν ἐπὶ τὴν ἀλήθειαν).

According to the Quote Investigator, Waterfield translates that last phrase more freely: “it motivates one towards originality and instills the desire for truth.” I’m not sure independence and originality are really in the Greek: ὁρμὴ εὑρετική seems more like “keenness to discover.”

The adjective εὑρετικός is from the verb εὑρίσκω “to find,” the source of our heuristic. The adjective occurs in the Republic too, in the first part of Book V. There, in the so-called First Wave, women will serve the city as guardians, since no part of the job is peculiar to men as such. The imaginary person who disagrees with this is asked, at 455b,

Did you distinguish between the man who has a good nature for a thing and another who has no nature for it on these grounds: the one learns something connected with that thing easily, the other with difficulty; the one, starting from slight learning, is able to carry discovery far forward in the field he has learned (ὁ μὲν ἀπὸ βραχείας μαθήσεως ἐπὶ πολὺ εὑρετικὸς εἴη οὗ ἔμαθεν), while the other, having chanced on a lot of learning and practice, can’t even preserve what he learned …?

Shorey’s translation of the bold passage is “the one with slight instruction could discover much for himself in the matter studied,” but the “for himself” seems gratuitous. Shorey’s note on the word “discover” reads, “Cf. Polit. 286 E, where this is said to be the object of teaching.” The Politicus is also known as the Statesman, and there, at 286d–e, a younger person called Socrates is told by the Eleatic Stranger,

By far our first and most important object should be to exalt the method itself of ability to divide by classes (τὴν μέθοδον αὐτὴν τιμᾶν τοῦ κατ᾽ εἴδη δυνατὸν εἶναι διαιρεῖν), and therefore, if a discourse, even though it be very long, makes the hearer better able to discover the truth (τὸν ἀκούσαντα εὑρετικώτερον ἀπεργάζηται), we should accept it eagerly and should not be offended by its length …

Evidently the point of education is not to become an original thinker, but to learn what is true. Perhaps one cannot do the latter without the former, and that may be the point of Plutarch, who continues in De auditu where we left off:

Imagine, then, that a man should need to get fire from a neighbour, and, upon finding a big bright fire there, should stay there continually warming himself; just so it is if a man comes to another to share the benefit of a discourse, and does not think it necessary to kindle from it some illumination for himself and some thinking of his own, but, delighting in the discourse, sits enchanted; he gets, as it were, a bright and ruddy glow in the form of opinion imparted to him by what is said, but the mouldiness and darkness of his inner mind he has not dissipated nor banished by the warm glow of philosophy.

These words show why there is a saying in Turkish:

Bakmakla öğrenilse köpekler kasap olurdu.

If one could learn by looking, dogs would be butchers.

There must be people who need that warning. One wants to think that one can learn, just by looking – or hearing. However, just being present in a lecture hall is probably not enough.

Maybe I wouldn’t know. I avoided lectures as an undergraduate by attending a college where there was only one a week. Having delivering that one lecture for the week ending on October 1, 2021, Christopher Frey tweeted tweeted on October 6,

So @stjohnscollege is a pretty remarkable place. They have roughly 500 undergrads, but filled a 100+ capacity lecture room on a Friday evening to hear about de Anima and stayed to ask questions for two (!) hours. I can’t think of many other places where this would happen.

One has to remember that those undergraduates had not heard a lecture since the previous week, if then – as I tweeted. Some students attend the lectures rarely or never. There is no test on them.

The Euclid course in the department in Istanbul where I work now may be an exception, but students in Turkey, and perhaps everywhere, normally get lectured to, at least in mathematics. Some enthusiastic students arrange to hear more lectures, as for example by visiting the Nesin Mathematics Village or just asking people to lecture them. They have asked this of my wife; recently they asked it, even of me, twice, and so the following recordings exist:

• “Introduction to Ordinal Numbers,” October 11, 2021 (Sabancı University IEEE Student Branch, Mathematics Community);
• “Tümevarım ve Özyineleme,” October 16, 2021 (Matematik Türkiye, 2. Cebir Çalıştayı).

The talks are not very smooth, because

• they were more or less extemporaneous;
• I don’t speak smoothly anyway;
• I could not see the audience.

Socrates sees his audience. What he says about education in Book VII on the Republic is directed at Glaucon, to whom the method he describes is not one of inspiring or coaxing or convincing or seducing, but compelling.

The Quran says (2.256),

There is no compulsion in religion. (Marmaduke Pickthall, Maulana Wahiduddin Khan)
There should be no compulsion in religion. (Maulawī SherʿAlī)
There shall be no coercion in matters of faith. (Muhammad Asad)

I say there is no compulsion in education either. This is an extrapolation from the observation that I cannot compel you to know, for example, that the class of ordinal numbers has all of the properties of being an ordinal itself, except for the property of being not just a class, but a set. You have to decide whether you want to know; and if you do, you have to get the knowledge for yourself.

Perhaps you can be forced into a position where you are likely to make the decision in favor of knowledge. An extreme example, albeit fictional, is in Zweig’s novella The Royal Game, where a prisoner held in isolation learns chess, for lack of a book about anything else. But as Ayşe said in her January 2019 defense against a charge of making propaganda for a terrorist organization:

Matematikte yanlış bir cümleyi ya da kanıtı kimse kimseye zorla kabul ettiremez. “Talimatla teoremi kabul etmek” diye bir şey yoktur. Her iddianızı kanıtlamanız gerekir. Aslında kanıtlamak da yetmez, karşınızdakinin de ikna olması gerekir. // In mathematics, nobody can make anybody accept a false statement or proof. There is nothing like “command acceptance of a theorem.” We have to prove our claims. Actually, proving them is not enough, but other persons have to be convinced.

Ayşe’s accusers could not conceive of doing something of one’s own accord, at least if it defied the authorities. If a thousand academics signed a petition against an action of the state, they must be under the orders of some evil mastermind.

Perhaps Socrates is living among people who think that way. In my 2012 article “St John’s College” in the De Morgan Journal, I said,

Having experienced an insistent Turkish hospitality that may not take no for an answer, I feel as if I can finally understand the first page of Plato’s Republic, where Polemarchus compels Socrates and Glaucon to stop by his house in the Piraeus.

I probably should have said that I was beginning to understand that first page. I thought I recognized the kind of host that Polemarchus wanted to be. One may observe further that the initial exchange between Socrates and Polemarchus prefigures what the philosopher has to deal with, when returned to the Cave. This is the kind of thing that my wife had to deal with in the 36th Heavy Penalty Court of Istanbul.

Socrates uses with Glaucon the language of compulsion, force, necessity – ἀνάγκη. The word is of unclear origin, according to Beekes, who says also,

It is not excluded that ἀνάγκη is a substrate word; for the field of meaning, cf. ὕβρις, which has no good etymology either.

In Book X of the Republic, we are going to hear that the Fates are the daughters of Necessity. Meanwhile, Glaucon has already alluded to her, or it, as back in Book II, where he thought everybody who had impunity through a Ring of Gyges would behave the same way, and therefore (360c),

someone could say that this is a great proof
that no one is willingly just but only when compelled to be so.

μέγα τοῦτο τεκμήριον ἂν φαίη τις
ὅτι οὐδεὶς ἑκὼν δίκαιος ἀλλ᾽ ἀναγκαζόμενος.

In the present reading, Socrates describes people tied up in a cave so that they can look only at shadows cast on a wall. They also hear sounds emitted by some of the people who are casting the shadows like puppeteers. When Glaucon calls them strange prisoners, Socrates retorts (515a–b),

They’re like us. For in the first place, do you suppose such men would have seen anything of themselves and one another other than the shadows cast by the fire on the side of the cave facing them?

The question is odd, since there has been no suggestion that shadows of the prisoners themselves are cast on the wall at all. In any case, it is a question, and Glaucon has an answer:

How could they, if they had been compelled to keep their heads motionless throughout life?

πῶς γάρ, ἔφη, εἰ ἀκινήτους γε τὰς κεφαλὰς ἔχειν ἠναγκασμένοι εἶεν διὰ βίου;

Glaucon seems here as quick to surrender to necessity as he was in the beginning, when Polemarchus asked if Socrates could persuade people who refused to listen, and Glaucon jumped in to say no.

Bloom does not try to let us know when ἀνάγκη or a derivative is specifically used. He translates the word into a form of “compulsion” or “necessity,” but none of them is in his Subject Index. When Socrates asks a question whose Greek text is unclear, but suggests that the prisoners would confuse the shadows with the things that cast the shadows, Glaucon replies, Ἀνάγκη; Bloom and Shorey translate this as “Necessarily.” Presently there’s a “Most necessarily,” Πολλὴ ἀνάγκη, which Shorey makes “Quite inevitably” for variety.

Now (515c–e) Socrates talks about a prisoner

who is released and suddenly compelled (ἀναγκάζοιτο) to stand up, to turn his neck around, to walk and look up toward the light; and who, moreover, in doing all this is in pain and, because he is dazzled, is unable to make out those things whose shadows he saw before … What do you suppose he’d say if someone were to tell him that before he saw silly nothings …? … And, if he compelled (ἀναγκάζοι) him to look at the light itself, would his eyes hurt and would he flee …?

Socrates could have told the story another way. A prisoner finding his bonds loosed could have made his own explorations. I think this is what adolescents do, or at least some of them. Does Socrates mean to suggest that nobody grows up willingly? Later he will suggest something else.

As Socrates continues to tell the story, still hypothetically, we get a new word for force:

if someone dragged him away from there by force (ἐντεῦθεν ἕλκοι τις αὐτὸν βίᾳ) along the rough, steep, upward way and didn’t let him go before he had dragged him out into the light of the sun, wouldn’t he be distressed …?

There are three words:

• ἡ βία “strength, force”;
• ὁ βίος “life”;
• ὁ βιός “bow.”

These are unrelated etymologically, though connected phonetically, and the “dragging” or pulling (ἕλκω) in what Socrates says is something done also to a bow.

Heraclitus connected βίος and βιός in a fragment preserved in the Etymologicum Genuinum, which, according to Wikipedia, was

compiled at Constantinople in the mid-ninth century … Modern scholarship discovered the Etymologicum Genuinum only in the nineteenth century. It is preserved in two tenth-century manuscripts …

Under the entry for βίος, the Etymologicum quotes Heraclitus as saying (DK 48, LM D53),

τῷ οὖν τόξῳ ὄνομα βίος, ἔργον δὲ θάνατος.

The name of the bow is life, but its work is death.

Here τὸ τόξον is another word for bow.

If one is going quote Heraclitus, another relevant passage for our reading is DK 60, LM D51:

ὁδος ἄνω κάτω μία καὶ ὡυτή.

The way upward and downward: one and the same.

As for wordplay though, it may be more relevant that Socrates used the word βία in the first part of Book V, now in the Second Wave. Because of the community of women and children, Socrates tells Glaucon (464d–e),

“they will then be free from faction …”

“Yes,” he said, “it’s quite necessary (Πολλὴ ἀνάγκη) that they be rid of factions.”

“And further, there would justly be no suits for assault or insult (οὐδὲ βιαίων γε οὐδ’ αἰκίας δίκαι) among them. For we’ll surely say that it is fine and just for men to take care of their own defense …”

Meanwhile, it can be a game that while, at the beginning of Book III, Socrates banned the disparagement of Hades, as in Odyssey XI.488–92, he now (516d) uses the same passage in support of his contention that the man who gets out of the Cave will not want to go back down, no matter what prizes for clever people are offered there. In Emily Wilson’s translation, the verses are,

Odysseus, you must not comfort me
for death. I would prefer to be a workman,
hired by a poor man on a peasant farm,
than rule as king of all the dead. But come,
tell me about my son. Do you have news?

Bloom notes that Socrates mentions the passage twice; Shorey only notes what the passage is in each case, without connecting the two references.

If those persons who get of the Cave are from another city, they don’t have to go back (520a–b):

it is fitting for them not to participate in the labors of those cities. For they grow up spontaneously (αὐτόματοι γὰρ ἐμφύονται) against the will of the regime in each (ἀκούσης τῆς ἐν ἑκάστῃ πολιτείας) …

I wrote a blog post almost a year ago about what is spontaneous or rather automatic, like the growing up here: it can be self-willed or not willed. As for the form ἀκούσης, it seems to be a case (agreeing with πολιτείας) of a contraction of ἀέκων, the negation of ἐκών “willing.”

If the philosophers are from our city, they are told (520c), “You must go down” (Bloom), “Down you must go” (Shorey): καταβατέον, formed from the verb καταβαίνω “to go down” and the adjective-making necessitative suffix.