The same could be applied to any assertion, including the statement "Santa Claus does not exist". It has thus been "proven" that Santa Claus exists. However, if "Not all lemons are yellow" (and this is also defined to be true), Santa Claus must exist - otherwise statement 2 would be false.in particular, I guess, the classical rule of ex falso quodlibet which. Therefore the statement that (“All lemons are yellow" OR "Santa Claus exists”) must also be true, since the first part is true. Zach Weber is an expert in philosophical logic, with a focus on paradoxes and.We know that "All lemons are yellow" as it is defined to be true. Johansson in 1936, is intuitionistic logic without the ex falso quodlibet rule A bot vdash A.It may also be defined by starting with Gentzens sequent calculus for classical logic with bot but not ¬ neg, and restricting to sequents Gamma vdash Delta where Delta must contain exactly one formula. "Santa Claus exists", by using the following argument: If that is the case, anything can be proven, e.g. That is, once a contradiction has been asserted, any proposition (or its negation) can be inferred from it.Īs a demonstration of the principle, consider two contradictory statements - “All lemons are yellow” and "Not all lemons are yellow", and suppose (for the sake of argument) that both are simultaneously true. they agree that logic cant guarantee that there are not many more true. The principle of explosion ( Latin: ex falso quodlibet, "from a falsehood, anything follows", or ex contradictione sequitur quodlibet, "from a contradiction, anything follows"), or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction. Dialetheists think that their rejection of ex falso quodlibet means that they. The principle of inference that contradictions entail everything is called explosion (or ex falso quodlibet sequitur ).
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