Paradoxes of material implication

The paradoxes of material implication are a group of formulae that are truths of classical logic but are intuitively problematic.

The root of the paradoxes lies in a mismatch between the interpretation of the validity of logical implication in natural language, and its formal interpretation in classical logic, dating back to George Boole's algebraic logic. In classical logic, implication describes conditional if-then statements using a truth-functional interpretation, i.e. "p implies q" is defined to be "it is not the case that p is true and q false".

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