An Enthymeme is:

• A short, pithy rebuttal (ancient definition)
• A rhetorical syllogism (Aristotle’s definition)
• A syllogism in which one or more premises are supplied by the audience (and therefore, sometimes, unexpressed) (Lloyd Bitzer)

Examples:

"Senator Quayle, I knew Jack Kennedy. I worked with Jack Kennedy. And I can tell you, you’re no Jack Kennedy." Lloyd Bentsen, 1988.

"There is no law against composing music when one has no ideas whatsoever. The music of Wagner, therefore, is perfectly legal." - Mark Twain

"Your Honor, years ago I recognized my kinship with all living beings, and I made up my mind that I was not one bit better than the meanest on earth. I said then, and I say now, that while there is a lower class, I am in it, and while there is a criminal element I am of it, and while there is a soul in prison, I am not free." Eugene Debs, 1918, upon being convicted for violating the WWI Espionage Act.