Identify the formal fallacy committed in the following argument. ‘All…

Concept

In modern predicate logic, a universal proposition does not by itself assert that its subject class has any members.

A categorical syllogism commits the existential fallacy when universal premises, which can be true of an empty class, are used to infer a particular conclusion that asserts existence.

Application

The first premise places household pets within domestic animals, and the second excludes unicorns from domestic animals. Both premises can still be true when no unicorn exists. The conclusion, however, says that at least one unicorn exists and is not a household pet, so its existential claim is not licensed by the premises.

Contrast

• Existential fallacy concerns an unsupported move from universal premises to an existence-asserting particular conclusion.

• Denying the antecedent has the conditional form “If P then Q; not P; therefore not Q,” which is not the structure used here.

• Affirming the consequent has the conditional form “If P then Q; Q; therefore P,” which is not the structure used here.

• Inferring an affirmative conclusion from a negative premise requires an affirmative conclusion, whereas “some unicorns are not household pets” is a negative categorical proposition.

Therefore, the formal error is the existential fallacy.