In both stories, "A Clean Well-Lighted Place" (Hemingway) and "This Is What It Means to Say Phoenix, Arizona" (Alexie), the use of the word nothing is minimal, not scattered throughout. In Hemingway's story, nothing is used liberally along with its Spanish language counterpart nada in one of Hemingway's more famous passages about "nada y pues nada y naday pues nada."
In Alexie's story, the first use of nothing occurs in a flashback during which the boyhood relationship between Victor and Thomas Builds-the-Fire is described and during which Thomas tells a story--which isn't in a traditional Western civilization form:
"Late at night he sits in the dark. Watches the television until there's nothing but that white noise. ..."
Alexie uses nothing here as a symbolic representation of Victor's father's desire to run and hide. Presumably, this desire, compelled by fear of his family and Victor, is the product of his knowledge of his weak heart.
In Hemingway's story, the first use of nothing occurs at the very beginning when the younger waiter tell the older waiter that "Last week" the deaf, old man customer "tried to commit suicide." When asked by the older waiter what the old man was in "despair" about, the younger waiter replies, "Nothing," to which the other responds with the query, "How do you know it was nothing?" Hemingway uses nothing here (1) as an introduction to his theme asking what constitutes and how to attain meaning and (2) to set up a juxtaposed antithesis to his understanding about meaning via the younger waiter's unreasoned response: "He has plenty of money," whereby the reader knows what does not constitute meaning and what is therefore the first true instance of something being nothing.
The meaning of nothing in Alexie's story and in Hemingway's story takes on differing aspects. In Alexie's story, the meaning is revealed in the last instance of usage of the word. Victor and Thomas both wish to throw the ashes into the waterfall at Spokane. Victor expects it will be like "letting things go after they've stopped having any use." Thomas knows though that disposing of the ashes at the falls will be like creating a salmon to jump over him and swim back home. Thomas therefore replies to Victor by saying, "Nothing stops, cousin ... Nothing stops." Therefore, the "white noise" that the father thought was nothing, a place to run to and hide in, was really the something of his fears and escape. "Nothing stops" can signify the perpetuity of the bad in us and the good in us. Thomas closes the sad saga of Victor's anger and loss by promising the perpetuity of the good in Victor's father and therefore the perpetuity of good for Victor because his father will "find his way home."
In Hemingway's story, the meaning of nothing is revealed in the old waiter's soliloquy, his "nada y pues nada" speech. He makes Hemingway's thematic point that personal dignity and human meaning in life is hard to attain because everything that is purported as contributing to meaning is in fact nothing after all. The shocking Great War had proved to many tattered hearts and minds that all, even man, had become as nothing. Light and a clean and pleasant place, as the old waiter points out, helps to foster some feeling of dignity despite the "nothingness." In the shadow of the vast scope of nothing as described in the nada speech, Hemingway asks what constitutes and how is a man (humanity) to attain meaning.