The Cratylus closed with “is a name natural (physis) or conventional (nomos)?” left open (article 041). Aristotle answers it in De Interpretatione chapter 2, inside the definition of the noun.
Ὄνομα μὲν οὖν ἐστὶ φωνὴ σημαντικὴ κατὰ συνθήκην ἄνευ χρόνου.
A noun is a spoken sound significant by convention, without time. (ch. 2, 16a; Greek quotations throughout, Japanese and English are L/LAB working translations.)
“Same” and “different” — where in the chain the arbitrariness lies
In chapter 1 Aristotle had already said plainly that sounds and letters vary from people to people.
Καὶ ὥσπερ οὐδὲ γράμματα πᾶσι τὰ αὐτά, οὐδὲ φωναὶ αἱ αὐταί.
Just as letters are not the same for everyone, neither are spoken sounds. (ch. 1, 16a)
But in the same passage he also says: what sounds and letters “primarily point to” — the affections in the soul (παθήματα τῆς ψυχῆς) — is the same for all, and so are the things (πράγματα) those affections copy. So for Aristotle only the right-hand half of the chain (sound, letters) is arbitrary; the left half (concepts, things) is natural and shared.
This strong premise — “concepts are the same for everyone” — is exactly where later thought about language fights. Humboldt held that each language is a worldview; Whorf argued that a language carves up thought. For them, the very “affections in the soul” that Aristotle took to be natural and common are shaped differently by each language. Whether arbitrariness covers the whole of meaning — the question starts here.
A natural sign, and a sign by convention
Aristotle glosses the phrase “by convention (κατὰ συνθήκην)” himself:
φύσει τῶν ὀνομάτων οὐδέν ἐστιν, ἀλλ᾿ ὅταν γένηται σύμβολον.
No name is by nature; a name arises only when it becomes a symbol. (ch. 2, 16a)
Here a firm line is drawn. An animal’s cry expresses something naturally — but it is not a name. A name is what “becomes a symbol (γένηται σύμβολον)” by a community’s agreement: an artefact. Cratylus’s “every thing has its right name by nature” is set aside. Plato’s sound-symbolism (ρ for motion, λ for smoothness), under this definition, is not the essence of a name but incidental decoration.
The choice of the word “symbolon”
Aristotle calls a spoken sound a symbolon (σύμβολον). The word means a “tally.” In ancient Greece a potsherd or a ring was broken in two as the token of a contract or a guest-friendship, each party keeping half; fitted back together they proved you were a party to the agreement — matching halves that mean something only by prior arrangement. Elsewhere in chapter 1 he also calls the same thing a sēmeion (σημεῖον, sign, indication), but that word is also used for a natural sign, as smoke is a sign of fire. The late-antique commentators Ammonius and Boethius separated the two sharply into “a sign by imposition (signum ad placitum)” and “a natural sign (signum naturale).” Augustine, in On Christian Doctrine, likewise distinguishes signs people give (signa data) from natural signs (signa naturalia). Medieval semiotics stands on this one word-choice.
Aristotle also draws the boundary of “name” strictly. “Not-man (οὐκ ἄνθρωπος)” is not a name but an “indefinite name (ὄνομα ἀόριστον)”; “of Philo / to Philo (genitive, dative)” is not a name but its case (πτῶσις) — not the noun itself.
Two thousand years of the mainstream
This one-line ruling became the standard doctrine through the late-antique commentaries of Ammonius and Boethius, and flowed into both the Arabic tradition (al-Fārābī) and the Latin (Boethius). Through the Middle Ages it was carried in the formula that words signify “by imposition, ad placitum.” Locke, in Book III of the Essay, writes that the tie between words and ideas is “by a perfectly arbitrary imposition.” And in the twentieth century, when Saussure made “the arbitrariness of the sign” the first principle of general linguistics, he was redrawing the very line Aristotle had drawn, at the centre of a system.
But the two also diverge. For Aristotle only the tie between sound and concept is arbitrary; the concept itself is natural and shared. Saussure’s novelty lies past that point — the value (valeur) of a sign arises from differences within a system, and that system carves up the concepts themselves. Aristotle’s sign is “a label on a shared concept”; Saussure’s sign is “the mesh that produces the concepts.”