Material implication

The implication $p\Rightarrow q$ is the connective that surprises the most at first, because its behaviour in the cases where the hypothesis is false does not match the intuition of everyday language.

Remark — The implication is strange only at first

The curious row of the truth table is the third: if the hypothesis is false, the implication is true. “If it rains then I take my umbrella” remains true even on the days when it does not rain: on those days the promise is not put to the test.

The implication is false only when $p$ is true but $q$ is false: it is the only case in which I can be “caught out”.

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Topics: Set theory
Concepts: Implication