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Law of Excluded Middle

A law of classical mathematics and logic which states that for any mathematical or logical truth statement, the result or conclusion is either true or false exclusively: there are no values in between or outside of true or false required for establishing the truth of a sentence or proposition. In classical mathematics and logic it is considered that this mechanism is sufficient to appropriate or establish truth. Some anti-realist movements in mathematics, such as intuitionism, however, have rejected the law of excluded middle as an abstract and artificial idea that does not represent the status quo in the real mathematical world. Nevertheless, the law of excluded middle has proven to be powerful and efficacious in many mathematical and logical endeavors, and is incorporated into all systems employing some form of classical logic, including Boolean algebra and binary logic.

Editor(s): Long, B.

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