I should have been a pair of ragged claws
Scuttling across the floors of silent seas.
Ragged claws, floors of silent seas: the speaker is likening himself to a bottom-dwelling crab. Crabs scuttle horizontally and never forward, much as the speaker moves horizontally in thought but never forward in his actions. The image also conveys the speaker’s feeling of pathetic aloneness and apartness, as well as his immersion in the deep seas of fantasy (compare the final lines of the poem).
This may also be an allusion to Hamlet’s quip to Polonius (Hamlet Act 2, Scene 2): “Yourself, sir, should be old as I am, if like a crab you could go backward.”
The line may also suggest that Prufrock wishes he were free from the burdens of consciousness and volition (see the end of Marianne Moore’s “A Grave”). Note that he wishes not to be the creature, but its claws.
These lines also appear in the movie Apocalypse Now.
Optionally, it might express his desire, subjacent to all his doubts, of being heard and outspoken- a sound in an otherwise silent sea, the unpleasant grinding of claws on the floor… if you will, a loud, discordant sound in the miasma of topics, conventional, pseudo-intellectual conversation of the women that “Come and go talking of Michaelangelo”.
To help improve the meaning of these lyrics, visit “The Love Song of J. Alfred Prufrock” by T.S. Eliot and leave a comment on the lyrics box