The Carriage held but just Ourselves –
The “Carriage” seems to be a hearse, which the dead speaker shares with allegorized Death, but also with Immortality. Dickinson intimates that death is a necessary part of the passage to immortality. (The Carriage may also simply be a fantasy, the vehicle of an imagined journey that the speaker is taking into the realm of death.)
Dickinson may be hinting here at poetic immortality; i.e. she will remain “immortal” despite death because her words live on and are read centuries later. (An old trope that’s alive and well today: see Jay Z’s “Threat.”)
The speaker and Death are about to travel to the grave — depicted in stanza 5 as a “house”. This might be a funeral procession or a dramatization of the “life flashing before your eyes” scenario.
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