This rhetorical trick — suddenly breaking off in speech — is perhaps best illustrated by examples. One is from Zuleika Dobson, by Max Beerbohm: “‘If you are acquainted with Miss Dobson, a direct invitation should be sent to her,’ said the Duke. ‘If you are not ...’ The aposiopesis was icy.” Another is from P G Wodehouse, in The Adventures of Sally: “‘So ...’ said Mr. Carmyle, becoming articulate, and allowed an impressive aposiopesis to take the place of the rest of the speech.”
It’s a way to imply something without spelling it out, while at the same time suggesting unwillingness or inability to continue, as a result of being overcome by a passion such as modesty, fear or anger.
The word is from Latin, one of that vast stock of rhetorical terms that was the backbone of political training in ancient Rome. When speech was the only way to persuade an audience, mastery of the tricks of oratory was vital. Its origins, however, lie further back, in the Greek aposiopan, be silent.
Many terms of rhetoric are hardly known today and leave us as bemused and uncomprehending as a character in Robert Silverberg’s SF novel Born With the Dead:
They spoke in fragments and ellipses, in periphrastics and aposiopesis, in a style abundant in chiasmus, metonymy, meiosis, oxymoron, and zeugma; their dazzling rhetorical techniques left him baffled and uncomfortable, which beyond much doubt was their intention.
The nineteenth-century historian Lord Macaulay dismissed the need to learn such tricks and the names for them, here quoted in Trevelyan’s Life: “Who ever reasoned better for having been taught the difference between a syllogism and an enthymeme? Who ever composed with greater spirit and elegance because he could define an oxymoron or an aposiopesis?”