Universal affirmative

A universal affirmative is a categorical statement taking the form: “Every A is B.” where A and B are predicates. In the language of predicate logic, this can be expressed as: ∀x:A(x)⟹B(x).

Universal affirmatives can only be partially converted. “All of Alma Cogan is dead, but only some of the class of dead people are Alma Cogan.”

As Monty Python had it, given the premise, "all fish live underwater" and "all mackerel are fish", one cannot conclude that "all mackerel live underwater", or that "if she buys kippers it will not rain", or that "trout live in trees", much less that "I do not love you any more."

See also

• Correlation and causation