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Illicit Major
-------------------------------------------------------------------------------- Definition:
The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.
Examples:
(i) All Texans are Americans, and no Californians are Texans, therefore, no Californians are Americans.
The predicate term in the conclusion is 'Americans'. The conclusion refers to all Americans (every American is not a Californian, according to the conclusion). But the premises refer only to some Americans (those that are Texans).
Proof:
Show that there may be other members of the predicate category not mentioned in the premises which are contrary to the conclusion.
For example, from (i) above, one might argue, "While it's true that all Texans are Americans, it is also true that Ronald Regan is American, but Ronald Regan is Californian, so it is not true that No Californians are Americans."
References: Copi and Cohen: 207