To build an assertion you need two kinds of part: the noun (ὄνομα) and the verb (ῥῆμα). In chapters 2 and 3 Aristotle defines them apart.
The noun — a sound “no part of which signifies separately”
The definition of the noun has four conditions: it is a sound, it signifies something, it does so by convention, and it is without time. And one more, easy to miss — no part of it signifies separately.
ἧς μηδὲν μέρος ἐστὶ σημαντικὸν κεχωρισμένον· ἐν γὰρ τῷ Κάλλιππος τὸ ἵππος οὐδὲν αὐτὸ καθ᾿ ἑαυτὸ σημαίνει.
No part of it, cut off, has meaning. In “Callippus” the “-ippos (horse)” means nothing on its own. (ch. 2, 16a; Greek quotations throughout, Japanese and English are L/LAB working translations.)
The personal name “Callippus (Κάλλιππος)” happens to contain the sound “horse (ἵππος).” But no one hears the man as “beautiful horse.” A name carries one meaning as a whole block of sound — split it and no fragments of meaning fall out. Here Aristotle is carving out the word as the minimal unit of meaning. Compound words (a compound like “skiff-and-racing-boat”) are a partial exception where a part means something, and even there he adds “not separately.” This point later grows into the question of whether meaning is built up from parts (compositionality).
The verb — time, and being a predicate
Ῥῆμα δέ ἐστι τὸ προσσημαῖνον χρόνον … καὶ ἔστιν ἀεὶ τῶν καθ᾿ ἑτέρου λεγομένων σημεῖον.
A verb is that which additionally signifies time … and it is always a sign of things said of another. (ch. 3, 16b)
Aristotle’s example is plain. “Health (ὑγίεια)” is a noun; “is healthy (ὑγιαίνει)” is a verb. The second co-signifies “being now (τὸ νῦν ὑπάρχειν).” That is what “additionally signifies time (προσσημαίνει χρόνον)” means. Time is not the core of the verb’s meaning but an added layer. “Was healthy” and “will be healthy” are set apart as the case (πτῶσις) of the verb — inflected forms for a time displaced from the present.
Second, a verb is “always a sign of things said of another.” “White,” “walks” — always something is white, something walks. A verb said alone still forms an image in the mind, but it does not yet say whether that thing “is or is not.”
τὰ ῥήματα … σημαίνει τι … ἀλλ᾿ εἰ ἔστιν ἢ μή, οὔπω σημαίνει.
Verbs … signify something … but whether it is or is not, they do not yet signify. (ch. 3, 16b)
The puzzle of “is”
At the end of chapter 3 Aristotle says something strange. The verb “to be (εἶναι),” by itself, means nothing.
Αὐτὸ μὲν γὰρ οὐδέν ἐστι, προσσημαίνει δὲ σύνθεσίν τινα, ἣν ἄνευ τῶν συγκειμένων οὐκ ἔστι νοῆσαι.
In itself it is nothing, but co-signifies some combination, which cannot be thought without the things combined. (ch. 3, 16b)
“A man is white” has three parts: the subject “man,” the predicate “white,” and the “is” that joins them. Medieval logicians called this the “third adjacent (tertium adiacens),” distinguishing it from forms like “a man is,” where “is” comes second (secundum adiacens). The “is” has no content of its own; it is only a sign of the joining — a view that stayed a premise of logic until Mill and Frege argued in the nineteenth century that the copula can be absorbed into the predicate.
Its mark on the history of grammar
The noun/verb division becomes the skeleton of Western grammar. The Latin grammarian Priscian (6th c.) took nomen/verbum from here, and the Port-Royal Grammar (1660) is built on the same distinction. Modern linguistics, by contrast, stresses that the parts of speech can differ from language to language (linguistic typology) and is cautious about treating noun and verb as universal categories present in every language. How far the frame Aristotle drew from Greek is common to humankind — the question is still open.