In mythology and symbolism, salamanders and phoenixes are both associated with fire, salamanders being composed of fire and having the ability to live within it and phoenixes having the ability to incinerate themselves and emerge anew from the ashes. The tattoo and the disk, as worn by Montag and the other firemen, are emblems of their work, essentially propaganda proclaiming to the citizenry the good of the work they do. Conversely, the emblems proclaim to the reader the thematically central irony associated with that work - specifically, that no matter how much they burn, the words and ideas they are attempting to destroy will, like the salamander and the phoenix, survive the flames.
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