In logic, a relation that holds between two propositions when
they are linked as antecedent and consequent of a true
conditional proposition. Logicians distinguish two main types of
implication, material and strict. Proposition p materially
implies proposition q if and only if the material conditional p
⊃ q (read “if p then q”) is true. A proposition of the form p ⊃
q is false whenever p is true and q is false; it is true in the
other three possible cases (i.e., p true and q true; p false and
q true; p false and q false). It follows that whenever p is
false, p ⊃ q is automatically true: this is a peculiarity that
makes the material conditional inadequate as an interpretation
of the meaning of conditional sentences in ordinary English. On
the other hand, proposition p strictly implies proposition q if
and only if it is impossible for p to be true without q also
being true (i.e., if the conjunction of p and not-q is
impossible). Learn more about implication with a free trial on
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