And a property is that which does not make evident the essence of a thing, but it belongs to the thing alone and can be predicated reciprocally of the thing, for example a property of a human is a natural capacity toward grammar. For if he is a human, he has the capacity of grammar, and conversely, if he has the capacity of grammar, he is a human. For no one says that a property is that which is able to belong to another thing, such as sleeping belongs to the human. Not even if the thing happened to belong to it alone for a certain time. And if one of these things would be called a property, it will not be called a property purely, but a temporary property or a property in relation to something else. For, “Being on the right,” is a temporary property, and “Being two-footed,” happens to be a property in relation to something else, such as man is two-footed with respect to a horse or a dog. And it is obvious that of the things able to belong to another thing, none of them are able to be predicated reciprocally. For it is not necessary, if something sleeps, that it is a human. 1
Topica 102a18-30

After the introduction of “definition,” which is the essence of something, Aristotle transitions to the idea of what a “property” is. Possibly one of the motivations leading Aristotle to discuss property secondly is that there is a common misconception that the property of something simply is its essence. But Aristotle has told us that the essence of something is its definition, not a property. Man, he informs us, has as one of his properties, the ability to understand grammar. But this is only a property insofar as it can be uniquely said of an individual human being as well, and in addition can be mutually said in reverse: i.e. A man is grammar-capable, the one who is grammar-capable is a man.

As one “proof” of his conception, Aristotle, as he often does, seems to appeal to the common opinion and sense of his listeners: “No one says ‘sleeping’ is a property of the human.” In the background of this comment lies the latent idea that people implicitly only attribute properties if they appear to belong uniquely to some one thing. Not only must a property belong to that thing alone, but it must always belong to it. If not, in Aristotle’s eyes, it is merely a temporary or quasi-property. He gives as examples the relative property “being on the right,” relative because it depends on a temporary relation of space and can change. Similarly, “bipedal,” as a biological categorization, is a term created to distinguish it from other animals which have 4 feet.

Near the end of his discussion Aristotle returns to the idea that properties must apply reciprocally to the things they are properties of, and shows the absurdity of disagreeing. “If something sleeps, it is a man,” is absurd. Although one could understandably (and mistakenly) think that sleep is a property of man, the possibility can be tested by “flipping” the subject and predicate and deciding if what ensues is nonsense.

1
Ἴδιον δ’ ἐστὶν ὃ μὴ δηλοῖ μὲν τὸ τί ἦν εἶναι, μόνῳ δ’
ὑπάρχει καὶ ἀντικατηγορεῖται τοῦ πράγματος. οἷον ἴδιον
ἀνθρώπου τὸ γραμματικῆς εἶναι δεκτικόν· εἰ γὰρ ἄνθρωπός (20)
ἐστι, γραμματικῆς δεκτικός ἐστι, καὶ εἰ γραμματικῆς δε-
κτικός ἐστιν, ἄνθρωπός ἐστιν. οὐθεὶς γὰρ ἴδιον λέγει τὸ ἐν-
δεχόμενον ἄλλῳ ὑπάρχειν, οἷον τὸ καθεύδειν ἀνθρώπῳ, οὐδ’
ἂν τύχῃ κατά τινα χρόνον μόνῳ ὑπάρχον. εἰ δ’ ἄρα τι
καὶ λέγοιτο τῶν τοιούτων ἴδιον, οὐχ ἁπλῶς ἀλλὰ ποτὲ ἢ (25)
πρός τι ἴδιον ῥηθήσεται· τὸ μὲν γὰρ ἐκ δεξιῶν εἶναι ποτὲ
ἴδιόν ἐστι, τὸ δὲ δίπουν πρός τι ἴδιον τυγχάνει λεγόμενον,
οἷον τῷ ἀνθρώπῳ πρὸς ἵππον καὶ κύνα. ὅτι δὲ τῶν ἐνδεχο-
μένων ἄλλῳ ὑπάρχειν οὐθὲν ἀντικατηγορεῖται, δῆλον· οὐ γὰρ
ἀναγκαῖον, εἴ τι καθεύδει, ἄνθρωπον εἶναι. (30)