An enthymeme, first described by Aristotle in Rhetoric is an incomplete logical construct. It's based on an unspoken premise shared between a speaker and her audience.
Here's a familiar enthymeme:
"Make America Great Again."
The unspoken shared premise:
"America used to be great."
An enthymeme's power comes not from what's spoken, but what's unspoken, Aristotle says. When a premise is left unspoken, the audience supplies it, completing the circle.
So, instead of the speaker persuading us, we persuade ourselves.
For Aristotle, self-persuasion is especially effective because we take pleasure in participating in the exchange. We're tickled with our ability to connect the dots—to "get it" without handholding.
But self-persuasion is also self-absorption, Aristotle warns.
An enthymeme helps us see a resemblance—a likeness—and we like most what is like ourselves. "All are more or less lovers of themselves," Aristotle says.
The effective speaker exploits this self-love.
She knows that—when the audience completes the circle—it chooses to hear what it wants to hear.