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rules of the categorical syllogism

Five checks a categorical syllogism must pass to be valid on the Boolean reading.

A standard-form categorical syllogism is valid on the Boolean reading exactly when (1) the middle term is distributed at least once, (2) any term distributed in the conclusion is distributed in its premise, (3) the premises are not both negative, (4) a negative premise goes with a negative conclusion and vice versa, and (5) two universal premises do not yield a particular conclusion.

Examples

  • "All dogs are mammals. All cats are mammals. So all cats are dogs" breaks rule 1.

See also

undistributed middle illicit major exclusive premises existential fallacy
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