We know that "All lemons are yellow", as it has been assumed to be true. We know that "Not all lemons are yellow", as it has been assumed to be true.If that is the case, anything can be proven, e.g., the assertion that " unicorns exist", by using the following argument: Mathematicians such as Gottlob Frege, Ernst Zermelo, Abraham Fraenkel, and Thoralf Skolem put much effort into revising set theory to eliminate these contradictions, resulting in the modern Zermelo–Fraenkel set theory.Īs a demonstration of the principle, consider two contradictory statements-"All lemons are yellow" and "Not all lemons are yellow"-and suppose that both are true. Around the turn of the 20th century, the discovery of contradictions such as Russell's paradox at the foundations of mathematics thus threatened the entire structure of mathematics. Due to the principle of explosion, the existence of a contradiction ( inconsistency) in a formal axiomatic system is disastrous since any statement can be proven, it trivializes the concepts of truth and falsity. The proof of this principle was first given by 12th-century French philosopher William of Soissons. That is, once a contradiction has been asserted, any proposition (including their negations) can be inferred from it this is known as deductive explosion. In classical logic, intuitionistic logic and similar logical systems, the principle of explosion ( Latin: ex falso quodlibet, 'from falsehood, anything ' or ex contradictione quodlibet, 'from contradiction, anything '), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a contradiction.
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