LessonsThe Third Figure: Conditions and Six Productive MoodsQuiz

Both premises in figure three tell us something about the same middle class. They establish a relation between the predicates for middle-term instances, but not for all instances of the minor predicate.

Example:
All horses are animals.
All horses are four-legged.

The conclusion is “Some animals are four-legged,” not “All animals are four-legged,” because animals extend beyond horses.

Important qualification: Classical syllogistic inferences from two universals to a particular conclusion presuppose relevant instances. In modern predicate logic, existence must be established separately when an empty subject class is possible.

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Why the conclusion is always particular

The Third Figure: Conditions and Six Productive Moods

Both premises in figure three tell us something about the same middle class. They establish a relation between the predicates for middle-term instances, but not for all instances of the minor predicate.

Example:
All horses are animals.
All horses are four-legged.

The conclusion is “Some animals are four-legged,” not “All animals are four-legged,” because animals extend beyond horses.

Important qualification: Classical syllogistic inferences from two universals to a particular conclusion presuppose relevant instances. In modern predicate logic, existence must be established separately when an empty subject class is possible.