Aristotle begins his work on rhetoric by noting that the framers of previous treatises on rhetoric “say nothing about enthymemes, which are the substance of rhetorical persuasion,” but instead deal mostly with with non-essentials, “such as what must be the contents of the ‘introduction’ or the ‘narration’ or any of the other divisions of a speech.” For Aristotle, arrangement is not the essence of persuasion. The big new concept in his rhetoric is the enthymeme.

Aristotle considers rhetoric to be a counterpart of dialectic, which is the art of discovering what is true through syllogisms and inductive arguments.
Rhetoric is a parallel art which deals with the “apparently true” through enthymemes and examples. He defines the enthymeme as “a sort of syllogism,” but perhaps with fewer propositions because

If any of these propositions is a familiar fact, there is no need even to mention it; the hearer adds it himself. Thus, to show that Dorieus has been victor in a contest for which the prize is a crown, it is enough to say ‘For he has been victor in the Olympic games’, without adding ‘And in the Olympic games the prize is a crown’, a fact which everybody knows.

The most famous example of a syllogism is this

• All men are mortal.
• Socrates is a man.
• Therefore, Socrates is mortal.

However, the premise, “All men are mortal” is known by all, and could be omitted, bringing this syllogism closer to the status of an enthymeme.

Enthymemes are based on probable truths, not certain ones, because we are usually deliberating about future actions, the outcome of which is never certain. Thus rhetoric is the art of speaking logically about probabilities and uncertainties.

Aristotle’s observation that in an enthymeme (which he also calls a rhetorical syllogism) we can leave out a premise that everyone knows has lead to some controversy and confusion. Sometimes we leave it out because people will assume it, even if it is unexpressed. However, Aristotle also connects this practice to audience. He says

Before some audiences not even the possession of the exactest knowledge will make it easy for what we say to produce conviction. For argument based on knowledge implies instruction, and there are people whom one cannot instruct.

To summarize:

• Enthymemes are based on probable truths or contingencies.
• Enthymemes may have assumed or omitted premises that everyone already knows.
• Enthymemes may also leave out premises because an audience is either incapable or unwilling to be instructed.

Could a devious rhetor leave out premises that would be uncomfortable or disagreeable to an audience if expressed? Do different audiences make different assumptions and believe different things to be probably true? Do shared but hidden assumptions make an argument more persuasive to the audience? Aristotle does not deal with these possibilities directly, but the answer to all three questions is clearly yes, though one does not have to be devious in order to use enthymemes. That means that an important part of a rhetorical analysis is ferreting out and evaluating hidden assumptions. Let’s look at some examples.

Here is President George W. Bush, in a White House statement delivered on Feb. 24, 2004

THE PRESIDENT: Good morning. Eight years ago, Congress passed, and President Clinton signed, the Defense of Marriage Act, which defined marriage for purposes of federal law as the legal union between one man and one woman as husband and wife.

The Act passed the House of Representatives by a vote of 342 to 67, and the Senate by a vote of 85 to 14. Those congressional votes and the passage of similar defensive marriage laws in 38 states express an overwhelming consensus in our country for protecting the institution of marriage.

In recent months, however, some activist judges and local officials have made an aggressive attempt to redefine marriage. . . . Unless action is taken, we can expect more arbitrary court decisions, more litigation, more defiance of the law by local officials, all of which adds to uncertainty.

Often a single word implies an argument. The word “defense” implies an argument such as this:

• The institution of marriage is in danger.
• Re-defining marriage threatens marriage.
• Therefore, marriage should not be re-defined.

The word “arbitrary” implies something like the following:

• The majority view is that marriage is between a man and a woman.
• Decisions that do not reflect the majority view are arbitrary.
• Therefore, marriage needs to be defended from arbitrary decisions.

Lets look at another example.  Earlier this month (August 4, 2016), President Barack Obama published an essay about feminism in Glamour magazine. He writes

Growing up without a dad, I spent a lot of time trying to figure out who I was, how the world perceived me, and what kind of man I wanted to be. It’s easy to absorb all kinds of messages from society about masculinity and come to believe that there’s a right way and a wrong way to be a man. But as I got older, I realized that my ideas about being a tough guy or cool guy just weren’t me. They were a manifestation of my youth and insecurity. Life became a lot easier when I simply started being myself.

There are lots of assumptions operating here. First

• Dads are role models for young men.
• Without a dad, young men learn how to be men from social messages.
• Society teaches men to be tough and cool.
• Therefore, Obama tried to be tough and cool.

But a more subtle assumption is present too. It’s called “being yourself.”

• Every person has a a true self.
• Society pressures us to be different from our true selves.
• Youth and insecurity cause us to succumb to social pressure.
• Being your true self is better than succumbing to pressure.
• Therefore we should reject society’s norms and be ourselves.

Imagine a world in which everyone simply did their own thing without adapting to any social norms. Would you want to live in it? Most of us would prefer to live in a society that balanced the needs of the individual and the needs of the group. But there I go making assumptions about my audience!

However, as Aristotle notes, it is not wrong to use enthymemes. They are necessary. It is just that it is sometimes instructive, even necessary, to make the assumptions explicit in order to understand the whole argument.

(Quotations from Aristotle’s Rhetoric are all from Book I available online in the the Internet Classics Archive at M.I.T.)