CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article includes a list of references , related reading or external links , but its sources remain unclear because it lacks inline citations . Please improve this article by introducing more precise citations. (February 2012) The paradoxes of material implication are a group of formulae which are truths of classical logic , but which are intuitively problematic. One of these paradoxes is the paradox of entailment . 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 de...