“So if you [Lysis and Menexenus] are friends to each other, by some nature you belong (oikeioi) to each other… And if one desires (epithumei) or loves (epa) another… he would not desire (epithumei) or love (era) or befriend (ephilei), unless he happened to belong (oikeios) to his beloved (eromeno) in some way according to his soul or according to some habit or character or kind (eidos) of soul.

ὑμεῖς ἄρα εἰ φίλοι ἐστὸν ἀλλήλοις, φύσει πῃ οἰκεῖοί ἐσθ᾽ ὑμῖν αὐτοῖς.

καὶ εἰ ἄρα τις ἕτερος ἑτέρου ἐπιθυμεῖ… ἢ ἐρᾷ, οὐκ ἄν ποτε ἐπεθύμει οὐδὲ ἤρα οὐδὲ ἐφίλει, εἰ μὴ οἰκεῖός πῃ τῷ ἐρωμένῳ ἐτύγχανεν ὢν ἢ κατὰ τὴν ψυχὴν ἢ κατά τι τῆς ψυχῆς ἦθος ἢ τρόπους ἢ εἶδος.

Lysis 222a1-5

The Lysis, of course, is a dialogue about friendship and friends.  By the time the dialogue has moved toward the end, Socrates offers a startling alternative of “what belongs” as a candidate for what is the friend.  What is striking here is not necessarily the concept of “belongingness” but rather the directionality involving who belongs to whom.  It is not that a lover loves someone, and that this relationship involves the lover loving because the particular beloved “belongs” to him.  Rather it is the reverse.  The lover loves the beloved, because he, the lover, belongs to the beloved.  Under examination then, it appears there is a latent reciprocity in this understanding of friendship as well.  Since they are both friends to each other and belong to each other, they both desire and are desired by the other.  However the erotic force compelling them is not the desire of the owner for his possession, but rather of the possession for its owner.   A paradox seems to arise in this understanding of friendship in that the relationship is simultaneously symmetric in that each party is both lover and loved, and, since a possessor is logically anterior to a possession, asymmetric.