The argument of the Cratylus opens with Hermogenes’s strong claim: a name is a convention, and there is no “correctness” beyond that.

ὅτι ἄν τίς τῳ θῆται ὄνομα, τοῦτο εἶναι τὸ ὀρθόν

Whatever name anyone sets on a thing, that is the correct one. (Greek quotations throughout; Japanese and English are L/LAB working translations.)

It can be swapped out. Just as one changes a slave’s name, Hermogenes says, a later name is no less correct than the earlier one.

How radical is Hermogenes’s claim?

The “convention view” sounds mild, but Hermogenes puts it strongly. He pushes the correctness of names down to the level of the individual. If I decide “this is a horse,” then for me that is the horse’s right name. If you attach a different name, then for you that one is right.

ἐμοὶ μὲν ἕτερον εἶναι καλεῖν ἑκάστῳ ὄνομα, ὃ ἐγὼ ἐθέμην, σοὶ δὲ ἕτερον, ὃ αὖ σύ

For me it is right to call each thing by the different name I set, and for you by the different name you set. (385d)

This is close to a claim of “private language.” Socrates will grant later that names differ from city to city and people to people (Greeks and non-Greeks, one polis and another). But once you go all the way to “each person may fix names as they please,” language stops being of any use for communication. Can Hermogenes’s position stop short of that? The dialogue tests exactly that point.

Behind it lies a live controversy of the day: “physis (nature) or nomos (custom, convention)?” Are law, justice and social institutions fixed by nature, or merely something people agreed on? The sophists (Protagoras, Antiphon) loved the theme, and the Cratylus applies it to language. Is a name, like justice and law, “merely something people agreed on”?

Socrates’s move — “things have a being”

1. A thing is not "as it appears to me"; it has a being of its own (οὐσία) = Protagoras's "man is the measure of all things" is rejected (385e–386a) 2. Actions (cutting, burning) can't be done any old way; they need the right tool and method = there is a way of cutting that works and a way that fails (386e–387b) 3. "Naming" is also an action (a part of speaking). So it has a right way = Hermogenes's "anything goes" cannot stand (387c–d)
Socrates's inference. Since things have a fixed being, the action that handles them — naming — can be done well or badly. Diagram: L/LAB

Socrates first pulls Hermogenes toward a Protagorean relativism, then cuts it off. “Man is the measure of all things” — if the thing as it appears to me is the thing for me, then the wise and the foolish become indistinguishable. Socrates will not have it. A thing has “a fixity of its own being” (βεβαιότητα τῆς οὐσίας).

If the being of things is fixed, then the action that deals with them has hits and misses. You cannot cut wood however you please. You cut only “not by our opinion but according to the nature (κατὰ τὴν φύσιν)” of the thing. Burning is the same. Unless you use a fit tool in a fit way, the action fails.

Speaking as an action, and its right way

Here Socrates puts “speaking (λέγειν)” in the same frame as cutting and burning. Speaking too is an action (πρᾶξις). So it has a right way and a wrong way.

ἐὰν μὲν ᾗ πέφυκε τὰ πράγματα λέγειν τε καὶ λέγεσθαι καὶ ᾧ, ταύτῃ καὶ τούτῳ λέγῃ, πλέον τέ τι ποιήσει καὶ ἐρεῖ· ἂν δὲ μή, ἐξαμαρτήσεται.

If one speaks of things in the way they are naturally spoken of, and with the fit means, one will achieve something and will have said it; otherwise one fails. (387c)

And “naming (ὀνομάζειν)” is a part (μόριον) of that speaking: “in speaking sentences we name things one by one.” What holds of the whole holds of the part — naming too has hits and misses. So Hermogenes’s “call it whatever you like” is set aside. A name is bound to the being of the thing named, and not left to the speaker’s will.

Note what Socrates has proved so far: only that naming has a correctness. Which naming is the right one — likeness, convention, or both — he has said nothing about yet.

“Convention” has two senses

The argument of the Cratylus keeps talking past itself because the word “convention (συνθήκη)” can point to two different things.

Modern philosophy of language separates the two. David Lewis’s Convention (1969) defined a convention as an “arbitrary but self-perpetuating regularity” — the origin could have been any choice, but once everyone follows it, there is no reason to deviate. Saussure’s “arbitrariness of the sign” likewise does not mean “changeable at will”: the individual sign lacks motivation, but toward the community it is compulsory, he insists. The Cratylus, lacking this distinction, moves back and forth between the two senses.

But this is not a win for the nature view

Physis (nature) or nomos (convention) — Socrates never simply picks a side. He leans toward the nature view in the “name as tool” argument (article 038), pushes further in the etymologies and the sound of letters (article 039, article 040), and then turns on its strong form near the end (article 041).

The “nature or convention” dispute about language did not stop here. In the Hellenistic period the Epicureans held that names arose naturally (from the outpouring of human feeling), while the Stoics split the difference. When modern linguistics declares the sign to be arbitrary, it is ruling for Hermogenes 2,300 years on. But the Cratylus itself leaves the verdict open and moves to the harder question — whether truth can be learned from names.