Why does Joyce not mention the object of the narrator's affection in the middle of the third paragraph?"Araby" by James Joyce
As Joyce's title "Araby" suggests, there is a sense of the exotic in the infatuation of the boy for Morgan's sister. For against the the "blind" (dead-end) of the street upon which he lives, and the "brown imperturbable faces" of the houses, the narrator fashions a romantic world in which Mangan's sister's figure is "defined by the light" and dress
swung as she moved her body and the soft rope of her hair tossed from side to side.
Actually, he narrator is a bit of a voyeur as he lies on the floor watching her door with the blind arranged so she cannot see him. But, he romanticizes his actions:
When she came out on the doorstep my heart leaped...and yet her name was like a summons to all my foolish blood.
As Joyce's narrative continues, Mangan's sister becomes more and more the romantic ideal for the boy, like the maidens of Arthurian legend. As she helps his mother with her purchases on Saturdays, all the noises of the market become "a single sensation of life for me," and he imagines that he bears
[his] chalice safely through a throng of foes. Her name sprang to my lips at moments in strange prayers and praises which I myself did not understand.
This exotic and romantic ideal that the boy makes of his infatuation for Mangan's sister is in great contrast to the setting described in the first two paragraphs. And it is in the realization of the boy at the mundane bazaar in which the girl makes small talk--his epiphany--that the reader understands why Joyce has created this contrast. For, the boy of the brown streets understands that he has allowed his imagination to create a Arthurian love for the girl that is completely unrealistic against the harsh realities in which he lives, realities described in the first two paragraphs.
Concerning Joyce's "Araby," you should first realize that no one can really speak for a writer. We can only deal with effects and functions, results. We cannot speak with any kind of certainty about what went on in a writer's mind.
Secondly, the object of the speaker's affection, Mangan's sister, is mentioned in the third paragraph of the story. She is affectionately described by the narrator.
I can only assume, then, that what you're really interested in knowing, is why she isn't identified as the object of the speaker's affection in paragraph three. And to that, I answer that she is, although indirectly. Here are the lines:
Her brother always teased her before he obeyed and I stood by the railings looking at her. Her dress swung as she moved her body and the soft rope of her hair tossed from side to side.
I've supplied the italics. These lines demonstrate the speaker's interest, fascination, and infatuation. Those are words from a young boy infatuated with an older girl. Thus, she is identified as the object of his affection, even though the identification is made indirectly. The speaker shows the reader, instead of telling the reader. In this case, the showing is very effective.