Definitions
Prior to Aristotle: A "thought" or "piece of logic". Translated "conclusion" in Aeschines 2.110
Aristotle: "I call a rhetorical syllogism an enthymeme" (Rhetoric I.8, 1356b)
Aristotle is commonly acknowledged as the originator of the enthymeme, though he recognized that earlier Greek rhetoricians had also employed it. In Rhetoric, Aristotle provides a definition of an enthymeme. Summarized, this is a logical argument composed of a major premise, minor premise and conclusion in which one premise remains unstated. He contends that this technique proves to be especially powerful because it allows speakers to tap into their audience's existing knowledge and beliefs instead of attempting to persuade them with new information.
Despite its effectiveness in persuasion, some view the enthymeme unfavorably due to its potential for manipulation and deceitfulness towards audiences. By omitting premises or conclusions, speakers can avoid addressing opposing arguments or presenting evidence against their own position. Therefore, utilizing an enthymeme necessitates exercising caution and ethical judgement carefully.
Examples
1. There is a good example of an unstated premise in Eleanor Roosevelt's address on the Universal Declaration of Human Rights:
We in the United States admire those who fight for their convictions, and the Soviet delegation has fought for their convictions. But in the older democracies we have learned that sometimes we bow to the will of the majority. In doing that, we do not give up our convictions. We continue sometimes to persuade, and eventually we may be successful. But we know that we have to work together and we have to progress. So, we believe that when we have made a good fight, and the majority is against us, it is perhaps better tactics to try to cooperate.
In this example, there is an implied syllogism: "Americans admire those who fight for their convictions. The Soviet delegation has fought for their convictions. Therefore we Americans admire the Soviets." The next argument then follows: "Older democracies have learned to bow to the majority. The Soviets have not bowed to the majority. Therefore, they have not learned what the older democracies have learned." In the first argument the unexpressed element is actually the conclusion. In the second argument, both the minor premise and the conclusion are left to the audience to infer. Stating it outright would of course have been an open criticism of the Soviets' ability to do diplomacy in a democratic frame.
2. A famous enthymeme used in rebuttal was spoken by Sen. Lloyd Bentsen to Sen. Dan Quayle during their 1988 Vice Presidential debate. When Quayle compared his qualifications to those of J. F. Kennedy, who was Quayles' age when he was elected President, Bentsen responded with:
Senator, I served with Jack Kennedy. I knew Jack Kennedy. Jack Kennedy was a friend of mine. Senator, you're no Jack Kennedy.