What is the significance of the subtitles in Fahrenheit 451?For example The Hearth and the Salamander

Each of the titles reflects Montag's
development as a character. They symbolize the various stages of his
rejection of society's values, and the ways in which he goes about declaring his
independence, if you will.

Hearth is another
word for fireplace, and the salamander is the official symbol of the firemen, as well as
what they call their fire trucks. Both of these symbols have to do with
fire, which dominates Montag's life at this point. As a fireman, Montag lives with fire
and loves it, taking pride in his work (as the opening line points out). As far as how
these images connect to this idea: one would light a fire in a hearth, and the
salamander of myth lives in fire and is unaffected by flames. Thus, this section is an
introduction to Montag's home and his job.

The title of
the next section, “The Sieve and the Sand”, describes Montag's attempt to read and
memorize the entire Bible. He connects it to a childhood memory of trying
to fill a sieve with sand on the beach, which ends with him crying at the futility of
the task. The sand becomes the words of the books, and the truths within them, while the
sieve is the human mind. Truth is elusive and, the metaphor suggests, impossible to
grasp in any permanent
way.

The final
section, entitled "Burning Bright", is the section where Montag fully breaks away from
his former life, and chooses to live instead on the margins. He is
"burning" in that his revolt is in full force, and he is stripping away the remnants of
his old identity. He burns his house, he burns Captain Beatty and his co-workers, and he
runs. It may also be a reference to the nuclear bomb which destroys the city at the end
of the novel.