We normally do not make explicit mention of all of the premises required to support a given conclusion, expecially when the premises are obvious or noncontroversial. A categorical syllogism with an unstated premise is called an enthymeme.
Suppose someone infers that Jane's new car gets poor gas mileage because it has a V-8 engine. In standard form:
(Any car with a V-8 engine gets poor gas mileage.)
Jane's car is a car with a V-8 engine.
Therefore, Jane's car gets poor gas mileage.
We use parentheses around the major premise to indicate that it is stated implicitly.
We learn to look for a premise that increases the logical strength of the argument. In deductive reasoning, validity is the measure of strength, so we look for a premise that makes the syllogism valid.
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