Tolstoy’s Childhood—in which he enters into that departed condition with the sureness he alone possesses—includes a description of the narrator’s father (Chapter 10). Among his characteristics is one reminiscent of a definition of “virtue,” i.e., human excellence (ἀρετή, aretê), offered by Plato’s Meno. The son writes,

Он был знаток всех вещей, доставляющих удобства и наслаждения, и умел пользоваться ими.

“He was a connoisseur of all things that afford comfort and enjoyment, and knew how to take advantage of them.” Or: “He was knowledgeable in all… and was able to take…”

Compare Meno on virtue (Meno 77b):

δοκεῖ τοίνυν μοι, ὦ Σώκρατες, ἀρετὴ εἶναι, καθάπερ ὁ ποιητὴς λέγει, ‘χαίρειν τε καλοῖσι καὶ δύνασθαι:’ καὶ ἐγὼ τοῦτο λέγω ἀρετήν, ἐπιθυμοῦντα τῶν καλῶν δυνατὸν εἶναι πορίζεσθαι.

“Well, in my opinion, Socrates, virtue is, as the poet says, ‘to rejoice in fine [beautiful, noble, honorable] things and be able.’ I too say this is virtue, that one who desires the things that are fine is capable of procuring them.”

Here the sense of the (unknown) poet’s last word is uncertain: it may mean “be able for them,” i.e., have the power of attaining them; but possibly it means “be capable,” or “powerful” absolutely. Meno understands it in the former sense.

Although the things in which Tolstoy’s character rejoices may have less of nobility than what Meno’s man desires, still I think that his description accords quite well with the proposed definition of virtue. —Observe, by the way, that virtue as here considered has two aspects, or steps: one is interested in certain things, and takes action to gain them. This is an instance of a universal pairing: attend and act, choose and take, diagnose and treat, aim and shoot. It is found very simply in the computer mouse: point and click.

Having noticed the resemblance reported here, I wondered whether Tolstoy alludes to the Meno elsewhere. A brief search produced a paper by Alexandr Draganov[1] in which the author ingeniously interprets the dialogue between Levin and a carpenter in Anna Karenina (Part 6, Chapter 8) as an echo of the famous slave-boy passage in the Meno (82b ff). I feel sure that he is right—and I wish I had made the connection myself. Draganov goes on to argue that “according to Levin, and contrary to Kant [Critique of Practical Reason], notions of the good and of moral law cannot be derived by reason.” Rather, Levin looks within himself, finding the source of moral judgments in what he already knows; that is, he behaves in accordance with the doctrine of recollection presented in Meno.

Although Draganov does not mention it, the invocation of the slave episode not only provides evidence for Levin’s application of that doctrine, but also indicates the limitations of reason. For the diagonal of a square is incommensurable with its side: their ratio, Greek logos, is not a ratio of whole numbers. We call it irrational. Draganov writes,

Approximately at the time of writing Anna Karenina, Tolstoy came to a differentiation between reason (разум) and understanding (разумение), with the latter being similar to the ancient concept of logos.[2] One interpretation of reason’s inability to grasp the notion of good is that this notion pertains to understanding, and not reason.

Now Jacob Klein points out that

as we know from the very beginning and as Meno presumably has heard before,[3] the given side and the side sought are “incommensurable magnitudes,”[4] and an answer in terms of the length of the given side is “impossible.”[5] At best, this side can only be drawn or “shown.” And Socrates will hint at this situation at every decisive turn of the search.[6]

Thus it is better not to say, as Draganov does, that Socrates is “giving the slave hints for calculating the length of the hypotenuse of a right triangle.” Calculation is precisely what cannot be done in this case: the ratio (logos) is to be grasped not by the kind of reason (logos) that can be set out in speech (logos), but in another way. Perhaps Tolstoy would call the boy’s grasping what can only be “shown” the work of разумение, “understanding,” even though he doesn’t use that word of the carpenter.[7] Just how the latter means to proceed is not explained. If he does “apply the Pythagorean theorem,” as Draganov suggests, he will do so approximately, unless the appropriate right triangle should chance to be one with commensurable sides (such as 3, 4, 5). Whatever he does, all of his measurements will be commensurable.

From the fact that Meno was in Tolstoy’s mind at the time he was composing Anna Karenina we cannot conclude anything about his acquaintance with it twenty years before, when Childhood was written. As a young man he did read Platonic dialogues, in French translation; was Meno among them? At any rate, we can add to the comparison above a couple of other similarities between our narrator’s father and the ancient Greek interlocutor. Klein observes that in quoting the poet, Meno is exhibiting again the reliance on others that he has already shown in the preceding discussion, where his words were derived from his teacher Gorgias. In fact, says Klein,

his thinking is always “colored” by what other people say and by what has some standing in the eyes of the world. If this condition is to a large degree the general condition of men, it seems to characterize Meno in his very being.[8]

As for the father,

His nature was one of those which, for a good deed, need a public. And that only he considered good, which the public called good.

Further, neither he nor Meno is remarkable for virtue in its moral aspect. I would not be surprised if Tolstoy, as a military man, read Xenophon’s story of the march of the Ten Thousand (Anabasis), which “depicts [Meno]… as greedy, self-seeking and treacherous” (W. R. M. Lamb). The father is nothing like that; but his son goes on to observe that his life of enjoyment left no time to form moral convictions, while his good fortune made them seem unnecessary. Finally, Meno in our dialogue appears to make no real progress, while as the father ages his way of life only becomes more what it was.

Does it matter very much whether or when Tolstoy read Meno? Suppose that he did recollect a notion of virtue, or an explanation of the diagonal—was it drawn from the text, or from the common well out of which that text suggests we all drink? Did the writer himself know? But suppose that he was fully aware of his literary source. Then where a lesser artist would have introduced an allusion, he simply left us to our own understanding; that is, to our own experience of recollection.

 

Postscript.  If the side of a square has length 1, the length of its diagonal, we now say, is √2. Here is an elegant proof that √2 is irrational.[9]

If not, there is a smallest positive integer n such that n√2 is an integer. But that is impossible, since if n is such an integer, then n√2 − n is a smaller one.

Can you generalize this proof to other square roots?

 

[1] “Socratic and Kantian Ideas of Virtue in Anna Karenina,” Tolstoy Studies Journal, vol. XXV (2013), 52–56; freely available at https://www.tolstoy-studies-journal.com/volume-xxv .

[2] Here Draganov provides a reference.

[3] Here Klein refers to earlier passages in his book.

[4] Cf. Euclid, Elements X, Def. 1. [Klein’s note]

[5] If post-Cartesian notations and notions are barred. [Klein’s note]

[6] A Commentary on Plato’s Meno, The University of North Carolina Press (1965), 99.

[7] He does use the verb “to understand” (понять). In view of Draganov’s comment on разумение, it is noteworthy that, if a search of an online text can be trusted, the word never appears in Anna Karenina. What does appear, a number of times, is недоразумение, “misunderstanding.”

[8] Klein 72.

[9] Notices of the American Mathematical Society, vol. 68 (2021), 1185; possibly due to Ivan Niven.