An enthymeme is a syllogism with one premise left unstated, for the audience to supply. “Socrates is mortal, because he is a man” omits the major premise that all men are mortal — and omits it because stating it would be tedious, not because it is doubtful.
Aristotle called it the body of persuasion. Almost all real argument is enthymematic.
“She'll be a good manager — she's run a team before.” The unstated premise is that people who have run teams before make good managers. Said aloud it invites immediate objection. Left out, it passes.
This is the device where rhetoric and formal logic meet most directly: an enthymeme is a logical form, examined for what it leaves out rather than for how it sounds.
Enthymemes are not a flaw in reasoning; they are how reasoning is actually conducted. Spelling out every premise would make argument unreadable, and the suppressed premise is usually something both parties already accept. The device is cooperative by default.
It becomes the single most useful thing to look for the moment an argument is contested. The suppressed premise is where disagreement lives, because it is the part nobody has had to defend. Two people arguing from the same evidence to opposite conclusions are almost always differing about something neither has said aloud.
This makes reconstructing the missing premise the most valuable habit in argument analysis. Write out what would have to be true for the conclusion to follow, then ask whether the author would have asserted it in those words. When the answer is no — when the premise is something they relied on but would not defend — the argument has a hole that no amount of style will close.
A surprising number of entries in the fallacy library are, at bottom, enthymemes with an indefensible premise suppressed.
