How does the distribution of terms matter in a syllogism?

In logic, the distribution of terms is a fundamental principle used to determine the validity of a syllogism. A term is considered distributed if a proposition refers to all members of the class that the term denotes.12

The distribution of terms matters because of a core rule of formal inference: no term may be distributed in the conclusion unless it was also distributed in the premises. Violating this rule results in a formal fallacy, such as the fallacy of the illicit major or illicit minor, where a term is used more broadly in the conclusion than it was in the premises.12

Additionally, the middle term must be distributed in at least one premise to successfully link the major and minor terms. If the middle term is not distributed in either premise, the argument commits the fallacy of the undistributed middle, rendering the syllogism invalid.3

In summary, distribution ensures that the scope of the terms in the conclusion does not exceed the evidence provided in the premises, maintaining the logical integrity of the argument.12